GroupNames

GroupNames [Beta]

Finite groups of order ≤500, group names, extensions, presentations, properties and character tables.

Orders with >300 groups of order n
n = 128, 192, 256, 288, 320, 384, 432, 448, 480.

[non]abelian, [non]soluble, supersoluble, [non]monomial, Z-groups, A-groups, metacyclic, metabelian, p-groups, elementary, hyperelementary, linear, perfect, simple, almost simple, quasisimple, rational groups.

Groups of order 1

		d	ρ	Label	ID
C₁	Trivial group	1	1+	C1	1,1

Groups of order 2

		d	ρ	Label	ID
C₂	Cyclic group	2	1+	C2	2,1

Groups of order 3

		d	ρ	Label	ID
C₃	Cyclic group; = A₃ = triangle rotations	3	1	C3	3,1

Groups of order 4

		d	ρ	Label	ID
C₄	Cyclic group; = square rotations	4	1	C4	4,1
C₂²	Klein 4-group V₄ = elementary abelian group of type [2,2]; = rectangle symmetries	4		C2^2	4,2

Groups of order 5

		d	ρ	Label	ID
C₅	Cyclic group; = pentagon rotations	5	1	C5	5,1

Groups of order 6

		d	ρ	Label	ID
C₆	Cyclic group; = hexagon rotations	6	1	C6	6,2
S₃	Symmetric group on 3 letters; = D₃ = GL₂(𝔽₂) = triangle symmetries = 1^st non-abelian group	3	2+	S3	6,1

Groups of order 7

		d	ρ	Label	ID
C₇	Cyclic group	7	1	C7	7,1

Groups of order 8

		d	ρ	Label	ID
C₈	Cyclic group	8	1	C8	8,1
D₄	Dihedral group; = He₂ = AΣL₁(𝔽₄) = 2₊¹⁺² = square symmetries	4	2+	D4	8,3
Q₈	Quaternion group; = C₄ .C₂ = Dic₂ = 2_-¹⁺²	8	2-	Q8	8,4
C₂³	Elementary abelian group of type [2,2,2]	8		C2^3	8,5
C₂×C₄	Abelian group of type [2,4]	8		C2xC4	8,2

Groups of order 9

		d	ρ	Label	ID
C₉	Cyclic group	9	1	C9	9,1
C₃²	Elementary abelian group of type [3,3]	9		C3^2	9,2

Groups of order 10

		d	ρ	Label	ID
C₁₀	Cyclic group	10	1	C10	10,2
D₅	Dihedral group; = pentagon symmetries	5	2+	D5	10,1

Groups of order 11

		d	ρ	Label	ID
C₁₁	Cyclic group	11	1	C11	11,1

Groups of order 12

		d	ρ	Label	ID
C₁₂	Cyclic group	12	1	C12	12,2
A₄	Alternating group on 4 letters; = PSL₂(𝔽₃) = L₂(3) = tetrahedron rotations	4	3+	A4	12,3
D₆	Dihedral group; = C₂×S₃ = hexagon symmetries	6	2+	D6	12,4
Dic₃	Dicyclic group; = C₃ ⋊C₄	12	2-	Dic3	12,1
C₂×C₆	Abelian group of type [2,6]	12		C2xC6	12,5

Groups of order 13

		d	ρ	Label	ID
C₁₃	Cyclic group	13	1	C13	13,1

Groups of order 14

		d	ρ	Label	ID
C₁₄	Cyclic group	14	1	C14	14,2
D₇	Dihedral group	7	2+	D7	14,1

Groups of order 15

		d	ρ	Label	ID
C₁₅	Cyclic group	15	1	C15	15,1

Groups of order 16

		d	ρ	Label	ID
C₁₆	Cyclic group	16	1	C16	16,1
D₈	Dihedral group	8	2+	D8	16,7
Q₁₆	Generalised quaternion group; = C₈ .C₂ = Dic₄	16	2-	Q16	16,9
SD₁₆	Semidihedral group; = Q₈ ⋊C₂ = QD₁₆	8	2	SD16	16,8
M₄(2)	Modular maximal-cyclic group; = C₈ ⋊₃ C₂	8	2	M4(2)	16,6
C₄○D₄	Pauli group = central product of C₄ and D₄	8	2	C4oD4	16,13
C₂²⋊C₄	The semidirect product of C₂² and C₄ acting via C₄/C₂=C₂	8		C2^2:C4	16,3
C₄⋊C₄	The semidirect product of C₄ and C₄ acting via C₄/C₂=C₂	16		C4:C4	16,4
C₄²	Abelian group of type [4,4]	16		C4^2	16,2
C₂⁴	Elementary abelian group of type [2,2,2,2]	16		C2^4	16,14
C₂×C₈	Abelian group of type [2,8]	16		C2xC8	16,5
C₂²×C₄	Abelian group of type [2,2,4]	16		C2^2xC4	16,10
C₂×D₄	Direct product of C₂ and D₄	8		C2xD4	16,11
C₂×Q₈	Direct product of C₂ and Q₈	16		C2xQ8	16,12

Groups of order 17

		d	ρ	Label	ID
C₁₇	Cyclic group	17	1	C17	17,1

Groups of order 18

		d	ρ	Label	ID
C₁₈	Cyclic group	18	1	C18	18,2
D₉	Dihedral group	9	2+	D9	18,1
C₃⋊S₃	The semidirect product of C₃ and S₃ acting via S₃/C₃=C₂	9		C3:S3	18,4
C₃×C₆	Abelian group of type [3,6]	18		C3xC6	18,5
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	6	2	C3xS3	18,3

Groups of order 19

		d	ρ	Label	ID
C₁₉	Cyclic group	19	1	C19	19,1

Groups of order 20

		d	ρ	Label	ID
C₂₀	Cyclic group	20	1	C20	20,2
D₁₀	Dihedral group; = C₂×D₅	10	2+	D10	20,4
F₅	Frobenius group; = C₅ ⋊C₄ = AGL₁(𝔽₅) = Aut(D₅) = Hol(C₅) = Sz(2)	5	4+	F5	20,3
Dic₅	Dicyclic group; = C₅ ⋊₂ C₄	20	2-	Dic5	20,1
C₂×C₁₀	Abelian group of type [2,10]	20		C2xC10	20,5

Groups of order 21

		d	ρ	Label	ID
C₂₁	Cyclic group	21	1	C21	21,2
C₇⋊C₃	The semidirect product of C₇ and C₃ acting faithfully	7	3	C7:C3	21,1

Groups of order 22

		d	ρ	Label	ID
C₂₂	Cyclic group	22	1	C22	22,2
D₁₁	Dihedral group	11	2+	D11	22,1

Groups of order 23

		d	ρ	Label	ID
C₂₃	Cyclic group	23	1	C23	23,1

Groups of order 24

		d	ρ	Label	ID
C₂₄	Cyclic group	24	1	C24	24,2
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	4	3+	S4	24,12
D₁₂	Dihedral group	12	2+	D12	24,6
Dic₆	Dicyclic group; = C₃ ⋊Q₈	24	2-	Dic6	24,4
SL₂(𝔽₃)	Special linear group on 𝔽₃²; = Q₈ ⋊C₃ = 2T = <2,3,3> = 1^st non-monomial group	8	2-	SL(2,3)	24,3
C₃⋊D₄	The semidirect product of C₃ and D₄ acting via D₄/C₂²=C₂	12	2	C3:D4	24,8
C₃⋊C₈	The semidirect product of C₃ and C₈ acting via C₈/C₄=C₂	24	2	C3:C8	24,1
C₂×C₁₂	Abelian group of type [2,12]	24		C2xC12	24,9
C₂²×C₆	Abelian group of type [2,2,6]	24		C2^2xC6	24,15
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	6	3+	C2xA4	24,13
C₄×S₃	Direct product of C₄ and S₃	12	2	C4xS3	24,5
C₃×D₄	Direct product of C₃ and D₄	12	2	C3xD4	24,10
C₂²×S₃	Direct product of C₂² and S₃	12		C2^2xS3	24,14
C₃×Q₈	Direct product of C₃ and Q₈	24	2	C3xQ8	24,11
C₂×Dic₃	Direct product of C₂ and Dic₃	24		C2xDic3	24,7

Groups of order 25

		d	ρ	Label	ID
C₂₅	Cyclic group	25	1	C25	25,1
C₅²	Elementary abelian group of type [5,5]	25		C5^2	25,2

Groups of order 26

		d	ρ	Label	ID
C₂₆	Cyclic group	26	1	C26	26,2
D₁₃	Dihedral group	13	2+	D13	26,1

Groups of order 27

		d	ρ	Label	ID
C₂₇	Cyclic group	27	1	C27	27,1
He₃	Heisenberg group; = C₃² ⋊C₃ = 3₊¹⁺²	9	3	He3	27,3
3_-¹⁺²	Extraspecial group	9	3	ES-(3,1)	27,4
C₃³	Elementary abelian group of type [3,3,3]	27		C3^3	27,5
C₃×C₉	Abelian group of type [3,9]	27		C3xC9	27,2

Groups of order 28

		d	ρ	Label	ID
C₂₈	Cyclic group	28	1	C28	28,2
D₁₄	Dihedral group; = C₂×D₇	14	2+	D14	28,3
Dic₇	Dicyclic group; = C₇ ⋊C₄	28	2-	Dic7	28,1
C₂×C₁₄	Abelian group of type [2,14]	28		C2xC14	28,4

Groups of order 29

		d	ρ	Label	ID
C₂₉	Cyclic group	29	1	C29	29,1

Groups of order 30

		d	ρ	Label	ID
C₃₀	Cyclic group	30	1	C30	30,4
D₁₅	Dihedral group	15	2+	D15	30,3
C₅×S₃	Direct product of C₅ and S₃	15	2	C5xS3	30,1
C₃×D₅	Direct product of C₃ and D₅	15	2	C3xD5	30,2

Groups of order 31

		d	ρ	Label	ID
C₃₁	Cyclic group	31	1	C31	31,1

Groups of order 32

		d	ρ	Label	ID
C₃₂	Cyclic group	32	1	C32	32,1
D₁₆	Dihedral group	16	2+	D16	32,18
Q₃₂	Generalised quaternion group; = C₁₆ .C₂ = Dic₈	32	2-	Q32	32,20
2₊¹⁺⁴	Extraspecial group; = D₄ ○D₄	8	4+	ES+(2,2)	32,49
SD₃₂	Semidihedral group; = C₁₆ ⋊₂ C₂ = QD₃₂	16	2	SD32	32,19
2_-¹⁺⁴	Gamma matrices = Extraspecial group; = D₄ ○Q₈	16	4-	ES-(2,2)	32,50
M₅(2)	Modular maximal-cyclic group; = C₁₆ ⋊₃ C₂	16	2	M5(2)	32,17
C₄≀C₂	Wreath product of C₄ by C₂	8	2	C4wrC2	32,11
C₂²≀C₂	Wreath product of C₂² by C₂	8		C2^2wrC2	32,27
C₈○D₄	Central product of C₈ and D₄	16	2	C8oD4	32,38
C₄○D₈	Central product of C₄ and D₈	16	2	C4oD8	32,42
C₂³⋊C₄	The semidirect product of C₂³ and C₄ acting faithfully	8	4+	C2^3:C4	32,6
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	8	4+	C8:C2^2	32,43
C₄⋊D₄	The semidirect product of C₄ and D₄ acting via D₄/C₂²=C₂	16		C4:D4	32,28
C₄⋊₁D₄	The semidirect product of C₄ and D₄ acting via D₄/C₄=C₂	16		C4:1D4	32,34
C₂²⋊C₈	The semidirect product of C₂² and C₈ acting via C₈/C₄=C₂	16		C2^2:C8	32,5
C₂²⋊Q₈	The semidirect product of C₂² and Q₈ acting via Q₈/C₄=C₂	16		C2^2:Q8	32,29
D₄⋊C₄	1^st semidirect product of D₄ and C₄ acting via C₄/C₂=C₂	16		D4:C4	32,9
C₄²⋊C₂	1^st semidirect product of C₄² and C₂ acting faithfully	16		C4^2:C2	32,24
C₄²⋊₂C₂	2^nd semidirect product of C₄² and C₂ acting faithfully	16		C4^2:2C2	32,33
C₄⋊C₈	The semidirect product of C₄ and C₈ acting via C₈/C₄=C₂	32		C4:C8	32,12
C₄⋊Q₈	The semidirect product of C₄ and Q₈ acting via Q₈/C₄=C₂	32		C4:Q8	32,35
C₈⋊C₄	3^rd semidirect product of C₈ and C₄ acting via C₄/C₂=C₂	32		C8:C4	32,4
Q₈⋊C₄	1^st semidirect product of Q₈ and C₄ acting via C₄/C₂=C₂	32		Q8:C4	32,10
C₄.D₄	1^st non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	8	4+	C4.D4	32,7
C₈.C₄	1^st non-split extension by C₈ of C₄ acting via C₄/C₂=C₂	16	2	C8.C4	32,15
C₄.₄D₄	4^th non-split extension by C₄ of D₄ acting via D₄/C₄=C₂	16		C4.4D4	32,31
C₈.C₂²	The non-split extension by C₈ of C₂² acting faithfully	16	4-	C8.C2^2	32,44
C₄.₁₀D₄	2^nd non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	16	4-	C4.10D4	32,8
C₂².D₄	3^rd non-split extension by C₂² of D₄ acting via D₄/C₂²=C₂	16		C2^2.D4	32,30
C₂.D₈	2^nd central extension by C₂ of D₈	32		C2.D8	32,14
C₄.Q₈	1^st non-split extension by C₄ of Q₈ acting via Q₈/C₄=C₂	32		C4.Q8	32,13
C₂.C₄²	1^st central stem extension by C₂ of C₄²	32		C2.C4^2	32,2
C₄².C₂	4^th non-split extension by C₄² of C₂ acting faithfully	32		C4^2.C2	32,32
C₂⁵	Elementary abelian group of type [2,2,2,2,2]	32		C2^5	32,51
C₄×C₈	Abelian group of type [4,8]	32		C4xC8	32,3
C₂×C₁₆	Abelian group of type [2,16]	32		C2xC16	32,16
C₂×C₄²	Abelian group of type [2,4,4]	32		C2xC4^2	32,21
C₂²×C₈	Abelian group of type [2,2,8]	32		C2^2xC8	32,36
C₂³×C₄	Abelian group of type [2,2,2,4]	32		C2^3xC4	32,45
C₄×D₄	Direct product of C₄ and D₄	16		C4xD4	32,25
C₂×D₈	Direct product of C₂ and D₈	16		C2xD8	32,39
C₂×SD₁₆	Direct product of C₂ and SD₁₆	16		C2xSD16	32,40
C₂²×D₄	Direct product of C₂² and D₄	16		C2^2xD4	32,46
C₂×M₄(2)	Direct product of C₂ and M₄(2)	16		C2xM4(2)	32,37
C₄×Q₈	Direct product of C₄ and Q₈	32		C4xQ8	32,26
C₂×Q₁₆	Direct product of C₂ and Q₁₆	32		C2xQ16	32,41
C₂²×Q₈	Direct product of C₂² and Q₈	32		C2^2xQ8	32,47
C₂×C₄○D₄	Direct product of C₂ and C₄○D₄	16		C2xC4oD4	32,48
C₂×C₂²⋊C₄	Direct product of C₂ and C₂²⋊C₄	16		C2xC2^2:C4	32,22
C₂×C₄⋊C₄	Direct product of C₂ and C₄⋊C₄	32		C2xC4:C4	32,23

Groups of order 33

		d	ρ	Label	ID
C₃₃	Cyclic group	33	1	C33	33,1

Groups of order 34

		d	ρ	Label	ID
C₃₄	Cyclic group	34	1	C34	34,2
D₁₇	Dihedral group	17	2+	D17	34,1

Groups of order 35

		d	ρ	Label	ID
C₃₅	Cyclic group	35	1	C35	35,1

Groups of order 36

		d	ρ	Label	ID
C₃₆	Cyclic group	36	1	C36	36,2
D₁₈	Dihedral group; = C₂×D₉	18	2+	D18	36,4
Dic₉	Dicyclic group; = C₉ ⋊C₄	36	2-	Dic9	36,1
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	6	4+	C3^2:C4	36,9
C₃⋊Dic₃	The semidirect product of C₃ and Dic₃ acting via Dic₃/C₆=C₂	36		C3:Dic3	36,7
C₃.A₄	The central extension by C₃ of A₄	18	3	C3.A4	36,3
C₆²	Abelian group of type [6,6]	36		C6^2	36,14
C₂×C₁₈	Abelian group of type [2,18]	36		C2xC18	36,5
C₃×C₁₂	Abelian group of type [3,12]	36		C3xC12	36,8
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	6	4+	S3^2	36,10
S₃×C₆	Direct product of C₆ and S₃	12	2	S3xC6	36,12
C₃×A₄	Direct product of C₃ and A₄	12	3	C3xA4	36,11
C₃×Dic₃	Direct product of C₃ and Dic₃	12	2	C3xDic3	36,6
C₂×C₃⋊S₃	Direct product of C₂ and C₃⋊S₃	18		C2xC3:S3	36,13

Groups of order 37

		d	ρ	Label	ID
C₃₇	Cyclic group	37	1	C37	37,1

Groups of order 38

		d	ρ	Label	ID
C₃₈	Cyclic group	38	1	C38	38,2
D₁₉	Dihedral group	19	2+	D19	38,1

Groups of order 39

		d	ρ	Label	ID
C₃₉	Cyclic group	39	1	C39	39,2
C₁₃⋊C₃	The semidirect product of C₁₃ and C₃ acting faithfully	13	3	C13:C3	39,1

Groups of order 40

		d	ρ	Label	ID
C₄₀	Cyclic group	40	1	C40	40,2
D₂₀	Dihedral group	20	2+	D20	40,6
Dic₁₀	Dicyclic group; = C₅ ⋊Q₈	40	2-	Dic10	40,4
C₅⋊D₄	The semidirect product of C₅ and D₄ acting via D₄/C₂²=C₂	20	2	C5:D4	40,8
C₅⋊C₈	The semidirect product of C₅ and C₈ acting via C₈/C₂=C₄	40	4-	C5:C8	40,3
C₅⋊₂C₈	The semidirect product of C₅ and C₈ acting via C₈/C₄=C₂	40	2	C5:2C8	40,1
C₂×C₂₀	Abelian group of type [2,20]	40		C2xC20	40,9
C₂²×C₁₀	Abelian group of type [2,2,10]	40		C2^2xC10	40,14
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	10	4+	C2xF5	40,12
C₄×D₅	Direct product of C₄ and D₅	20	2	C4xD5	40,5
C₅×D₄	Direct product of C₅ and D₄	20	2	C5xD4	40,10
C₂²×D₅	Direct product of C₂² and D₅	20		C2^2xD5	40,13
C₅×Q₈	Direct product of C₅ and Q₈	40	2	C5xQ8	40,11
C₂×Dic₅	Direct product of C₂ and Dic₅	40		C2xDic5	40,7

Groups of order 41

		d	ρ	Label	ID
C₄₁	Cyclic group	41	1	C41	41,1

Groups of order 42

		d	ρ	Label	ID
C₄₂	Cyclic group	42	1	C42	42,6
D₂₁	Dihedral group	21	2+	D21	42,5
F₇	Frobenius group; = C₇ ⋊C₆ = AGL₁(𝔽₇) = Aut(D₇) = Hol(C₇)	7	6+	F7	42,1
S₃×C₇	Direct product of C₇ and S₃	21	2	S3xC7	42,3
C₃×D₇	Direct product of C₃ and D₇	21	2	C3xD7	42,4
C₂×C₇⋊C₃	Direct product of C₂ and C₇⋊C₃	14	3	C2xC7:C3	42,2

Groups of order 43

		d	ρ	Label	ID
C₄₃	Cyclic group	43	1	C43	43,1

Groups of order 44

		d	ρ	Label	ID
C₄₄	Cyclic group	44	1	C44	44,2
D₂₂	Dihedral group; = C₂×D₁₁	22	2+	D22	44,3
Dic₁₁	Dicyclic group; = C₁₁ ⋊C₄	44	2-	Dic11	44,1
C₂×C₂₂	Abelian group of type [2,22]	44		C2xC22	44,4

Groups of order 45

		d	ρ	Label	ID
C₄₅	Cyclic group	45	1	C45	45,1
C₃×C₁₅	Abelian group of type [3,15]	45		C3xC15	45,2

Groups of order 46

		d	ρ	Label	ID
C₄₆	Cyclic group	46	1	C46	46,2
D₂₃	Dihedral group	23	2+	D23	46,1

Groups of order 47

		d	ρ	Label	ID
C₄₇	Cyclic group	47	1	C47	47,1

Groups of order 48

		d	ρ	Label	ID
C₄₈	Cyclic group	48	1	C48	48,2
D₂₄	Dihedral group	24	2+	D24	48,7
Dic₁₂	Dicyclic group; = C₃ ⋊₁ Q₁₆	48	2-	Dic12	48,8
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	8	2	GL(2,3)	48,29
CSU₂(𝔽₃)	Conformal special unitary group on 𝔽₃²; = Q₈ .S₃ = 2O = <2,3,4>	16	2-	CSU(2,3)	48,28
C₄○D₁₂	Central product of C₄ and D₁₂	24	2	C4oD12	48,37
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	12	3	A4:C4	48,30
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	12	3	C4^2:C3	48,3
C₂²⋊A₄	The semidirect product of C₂² and A₄ acting via A₄/C₂²=C₃	12		C2^2:A4	48,50
D₆⋊C₄	The semidirect product of D₆ and C₄ acting via C₄/C₂=C₂	24		D6:C4	48,14
D₄⋊S₃	The semidirect product of D₄ and S₃ acting via S₃/C₃=C₂	24	4+	D4:S3	48,15
C₈⋊S₃	3^rd semidirect product of C₈ and S₃ acting via S₃/C₃=C₂	24	2	C8:S3	48,5
C₂₄⋊C₂	2^nd semidirect product of C₂₄ and C₂ acting faithfully	24	2	C24:C2	48,6
D₄⋊₂S₃	The semidirect product of D₄ and S₃ acting through Inn(D₄)	24	4-	D4:2S3	48,39
Q₈⋊₂S₃	The semidirect product of Q₈ and S₃ acting via S₃/C₃=C₂	24	4+	Q8:2S3	48,17
Q₈⋊₃S₃	The semidirect product of Q₈ and S₃ acting through Inn(Q₈)	24	4+	Q8:3S3	48,41
C₃⋊C₁₆	The semidirect product of C₃ and C₁₆ acting via C₁₆/C₈=C₂	48	2	C3:C16	48,1
C₄⋊Dic₃	The semidirect product of C₄ and Dic₃ acting via Dic₃/C₆=C₂	48		C4:Dic3	48,13
C₃⋊Q₁₆	The semidirect product of C₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	48	4-	C3:Q16	48,18
Dic₃⋊C₄	The semidirect product of Dic₃ and C₄ acting via C₄/C₂=C₂	48		Dic3:C4	48,12
C₄.A₄	The central extension by C₄ of A₄	16	2	C4.A4	48,33
D₄.S₃	The non-split extension by D₄ of S₃ acting via S₃/C₃=C₂	24	4-	D4.S3	48,16
C₄.Dic₃	The non-split extension by C₄ of Dic₃ acting via Dic₃/C₆=C₂	24	2	C4.Dic3	48,10
C₆.D₄	7^th non-split extension by C₆ of D₄ acting via D₄/C₂²=C₂	24		C6.D4	48,19
C₄×C₁₂	Abelian group of type [4,12]	48		C4xC12	48,20
C₂×C₂₄	Abelian group of type [2,24]	48		C2xC24	48,23
C₂³×C₆	Abelian group of type [2,2,2,6]	48		C2^3xC6	48,52
C₂²×C₁₂	Abelian group of type [2,2,12]	48		C2^2xC12	48,44
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	6	3+	C2xS4	48,48
C₄×A₄	Direct product of C₄ and A₄	12	3	C4xA4	48,31
S₃×D₄	Direct product of S₃ and D₄; = Aut(D₁₂) = Hol(C₁₂)	12	4+	S3xD4	48,38
C₂²×A₄	Direct product of C₂² and A₄	12		C2^2xA4	48,49
C₂×SL₂(𝔽₃)	Direct product of C₂ and SL₂(𝔽₃)	16		C2xSL(2,3)	48,32
S₃×C₈	Direct product of C₈ and S₃	24	2	S3xC8	48,4
C₃×D₈	Direct product of C₃ and D₈	24	2	C3xD8	48,25
C₆×D₄	Direct product of C₆ and D₄	24		C6xD4	48,45
S₃×Q₈	Direct product of S₃ and Q₈	24	4-	S3xQ8	48,40
C₂×D₁₂	Direct product of C₂ and D₁₂	24		C2xD12	48,36
S₃×C₂³	Direct product of C₂³ and S₃	24		S3xC2^3	48,51
C₃×SD₁₆	Direct product of C₃ and SD₁₆	24	2	C3xSD16	48,26
C₃×M₄(2)	Direct product of C₃ and M₄(2)	24	2	C3xM4(2)	48,24
C₆×Q₈	Direct product of C₆ and Q₈	48		C6xQ8	48,46
C₃×Q₁₆	Direct product of C₃ and Q₁₆	48	2	C3xQ16	48,27
C₄×Dic₃	Direct product of C₄ and Dic₃	48		C4xDic3	48,11
C₂×Dic₆	Direct product of C₂ and Dic₆	48		C2xDic6	48,34
C₂²×Dic₃	Direct product of C₂² and Dic₃	48		C2^2xDic3	48,42
S₃×C₂×C₄	Direct product of C₂×C₄ and S₃	24		S3xC2xC4	48,35
C₂×C₃⋊D₄	Direct product of C₂ and C₃⋊D₄	24		C2xC3:D4	48,43
C₃×C₄○D₄	Direct product of C₃ and C₄○D₄	24	2	C3xC4oD4	48,47
C₃×C₂²⋊C₄	Direct product of C₃ and C₂²⋊C₄	24		C3xC2^2:C4	48,21
C₂×C₃⋊C₈	Direct product of C₂ and C₃⋊C₈	48		C2xC3:C8	48,9
C₃×C₄⋊C₄	Direct product of C₃ and C₄⋊C₄	48		C3xC4:C4	48,22

Groups of order 49

		d	ρ	Label	ID
C₄₉	Cyclic group	49	1	C49	49,1
C₇²	Elementary abelian group of type [7,7]	49		C7^2	49,2

Groups of order 50

		d	ρ	Label	ID
C₅₀	Cyclic group	50	1	C50	50,2
D₂₅	Dihedral group	25	2+	D25	50,1
C₅⋊D₅	The semidirect product of C₅ and D₅ acting via D₅/C₅=C₂	25		C5:D5	50,4
C₅×C₁₀	Abelian group of type [5,10]	50		C5xC10	50,5
C₅×D₅	Direct product of C₅ and D₅; = AΣL₁(𝔽₂₅)	10	2	C5xD5	50,3

Groups of order 51

		d	ρ	Label	ID
C₅₁	Cyclic group	51	1	C51	51,1

Groups of order 52

		d	ρ	Label	ID
C₅₂	Cyclic group	52	1	C52	52,2
D₂₆	Dihedral group; = C₂×D₁₃	26	2+	D26	52,4
Dic₁₃	Dicyclic group; = C₁₃ ⋊₂ C₄	52	2-	Dic13	52,1
C₁₃⋊C₄	The semidirect product of C₁₃ and C₄ acting faithfully	13	4+	C13:C4	52,3
C₂×C₂₆	Abelian group of type [2,26]	52		C2xC26	52,5

Groups of order 53

		d	ρ	Label	ID
C₅₃	Cyclic group	53	1	C53	53,1

Groups of order 54

		d	ρ	Label	ID
C₅₄	Cyclic group	54	1	C54	54,2
D₂₇	Dihedral group	27	2+	D27	54,1
C₉⋊C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	9	6+	C9:C6	54,6
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	9	6+	C3^2:C6	54,5
He₃⋊C₂	2^nd semidirect product of He₃ and C₂ acting faithfully; = Aut(3_-¹⁺²)	9	3	He3:C2	54,8
C₉⋊S₃	The semidirect product of C₉ and S₃ acting via S₃/C₃=C₂	27		C9:S3	54,7
C₃³⋊C₂	3^rd semidirect product of C₃³ and C₂ acting faithfully	27		C3^3:C2	54,14
C₃×C₁₈	Abelian group of type [3,18]	54		C3xC18	54,9
C₃²×C₆	Abelian group of type [3,3,6]	54		C3^2xC6	54,15
S₃×C₉	Direct product of C₉ and S₃	18	2	S3xC9	54,4
C₃×D₉	Direct product of C₃ and D₉	18	2	C3xD9	54,3
C₂×He₃	Direct product of C₂ and He₃	18	3	C2xHe3	54,10
S₃×C₃²	Direct product of C₃² and S₃	18		S3xC3^2	54,12
C₂×3_-¹⁺²	Direct product of C₂ and 3_-¹⁺²	18	3	C2xES-(3,1)	54,11
C₃×C₃⋊S₃	Direct product of C₃ and C₃⋊S₃	18		C3xC3:S3	54,13

Groups of order 55

		d	ρ	Label	ID
C₅₅	Cyclic group	55	1	C55	55,2
C₁₁⋊C₅	The semidirect product of C₁₁ and C₅ acting faithfully	11	5	C11:C5	55,1

Groups of order 56

		d	ρ	Label	ID
C₅₆	Cyclic group	56	1	C56	56,2
D₂₈	Dihedral group	28	2+	D28	56,5
F₈	Frobenius group; = C₂³ ⋊C₇ = AGL₁(𝔽₈)	8	7+	F8	56,11
Dic₁₄	Dicyclic group; = C₇ ⋊Q₈	56	2-	Dic14	56,3
C₇⋊D₄	The semidirect product of C₇ and D₄ acting via D₄/C₂²=C₂	28	2	C7:D4	56,7
C₇⋊C₈	The semidirect product of C₇ and C₈ acting via C₈/C₄=C₂	56	2	C7:C8	56,1
C₂×C₂₈	Abelian group of type [2,28]	56		C2xC28	56,8
C₂²×C₁₄	Abelian group of type [2,2,14]	56		C2^2xC14	56,13
C₄×D₇	Direct product of C₄ and D₇	28	2	C4xD7	56,4
C₇×D₄	Direct product of C₇ and D₄	28	2	C7xD4	56,9
C₂²×D₇	Direct product of C₂² and D₇	28		C2^2xD7	56,12
C₇×Q₈	Direct product of C₇ and Q₈	56	2	C7xQ8	56,10
C₂×Dic₇	Direct product of C₂ and Dic₇	56		C2xDic7	56,6

Groups of order 57

		d	ρ	Label	ID
C₅₇	Cyclic group	57	1	C57	57,2
C₁₉⋊C₃	The semidirect product of C₁₉ and C₃ acting faithfully	19	3	C19:C3	57,1

Groups of order 58

		d	ρ	Label	ID
C₅₈	Cyclic group	58	1	C58	58,2
D₂₉	Dihedral group	29	2+	D29	58,1

Groups of order 59

		d	ρ	Label	ID
C₅₉	Cyclic group	59	1	C59	59,1

Groups of order 60

		d	ρ	Label	ID
C₆₀	Cyclic group	60	1	C60	60,4
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	5	3+	A5	60,5
D₃₀	Dihedral group; = C₂×D₁₅	30	2+	D30	60,12
Dic₁₅	Dicyclic group; = C₃ ⋊Dic₅	60	2-	Dic15	60,3
C₃⋊F₅	The semidirect product of C₃ and F₅ acting via F₅/D₅=C₂	15	4	C3:F5	60,7
C₂×C₃₀	Abelian group of type [2,30]	60		C2xC30	60,13
S₃×D₅	Direct product of S₃ and D₅	15	4+	S3xD5	60,8
C₃×F₅	Direct product of C₃ and F₅	15	4	C3xF5	60,6
C₅×A₄	Direct product of C₅ and A₄	20	3	C5xA4	60,9
C₆×D₅	Direct product of C₆ and D₅	30	2	C6xD5	60,10
S₃×C₁₀	Direct product of C₁₀ and S₃	30	2	S3xC10	60,11
C₅×Dic₃	Direct product of C₅ and Dic₃	60	2	C5xDic3	60,1
C₃×Dic₅	Direct product of C₃ and Dic₅	60	2	C3xDic5	60,2

Groups of order 61

		d	ρ	Label	ID
C₆₁	Cyclic group	61	1	C61	61,1

Groups of order 62

		d	ρ	Label	ID
C₆₂	Cyclic group	62	1	C62	62,2
D₃₁	Dihedral group	31	2+	D31	62,1

Groups of order 63

		d	ρ	Label	ID
C₆₃	Cyclic group	63	1	C63	63,2
C₇⋊C₉	The semidirect product of C₇ and C₉ acting via C₉/C₃=C₃	63	3	C7:C9	63,1
C₃×C₂₁	Abelian group of type [3,21]	63		C3xC21	63,4
C₃×C₇⋊C₃	Direct product of C₃ and C₇⋊C₃	21	3	C3xC7:C3	63,3

Groups of order 64

		d	ρ	Label	ID
C₆₄	Cyclic group	64	1	C64	64,1
D₃₂	Dihedral group	32	2+	D32	64,52
Q₆₄	Generalised quaternion group; = C₃₂ .C₂ = Dic₁₆	64	2-	Q64	64,54
SD₆₄	Semidihedral group; = C₃₂ ⋊₂ C₂ = QD₆₄	32	2	SD64	64,53
M₆(2)	Modular maximal-cyclic group; = C₃₂ ⋊₃ C₂	32	2	M6(2)	64,51
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	8	4+	C2wrC4	64,32
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	8	4+	C2wrC2^2	64,138
C₈○D₈	Central product of C₈ and D₈	16	2	C8oD8	64,124
D₄○D₈	Central product of D₄ and D₈	16	4+	D4oD8	64,257
D₄○SD₁₆	Central product of D₄ and SD₁₆	16	4	D4oSD16	64,258
Q₈○M₄(2)	Central product of Q₈ and M₄(2)	16	4	Q8oM4(2)	64,249
Q₈○D₈	Central product of Q₈ and D₈	32	4-	Q8oD8	64,259
D₄○C₁₆	Central product of D₄ and C₁₆	32	2	D4oC16	64,185
C₄○D₁₆	Central product of C₄ and D₁₆	32	2	C4oD16	64,189
C₈○₂M₄(2)	Central product of C₈ and M₄(2)	32		C8o2M4(2)	64,86
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	8	4+	D4:4D4	64,134
C₄²⋊C₄	2^nd semidirect product of C₄² and C₄ acting faithfully	8	4+	C4^2:C4	64,34
C₂³⋊C₈	The semidirect product of C₂³ and C₈ acting via C₈/C₂=C₄	16		C2^3:C8	64,4
C₁₆⋊C₄	2^nd semidirect product of C₁₆ and C₄ acting faithfully	16	4	C16:C4	64,28
D₈⋊₂C₄	2^nd semidirect product of D₈ and C₄ acting via C₄/C₂=C₂	16	4	D8:2C4	64,41
D₄⋊₅D₄	1^st semidirect product of D₄ and D₄ acting through Inn(D₄)	16		D4:5D4	64,227
C₁₆⋊C₂²	The semidirect product of C₁₆ and C₂² acting faithfully	16	4+	C16:C2^2	64,190
C₄²⋊₆C₄	3^rd semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	16		C4^2:6C4	64,20
C₄²⋊₃C₄	3^rd semidirect product of C₄² and C₄ acting faithfully	16	4	C4^2:3C4	64,35
C₂⁴⋊₃C₄	1^st semidirect product of C₂⁴ and C₄ acting via C₄/C₂=C₂	16		C2^4:3C4	64,60
C₂²⋊D₈	The semidirect product of C₂² and D₈ acting via D₈/D₄=C₂	16		C2^2:D8	64,128
C₂³⋊₃D₄	2^nd semidirect product of C₂³ and D₄ acting via D₄/C₂=C₂²	16		C2^3:3D4	64,215
C₂³⋊₂Q₈	2^nd semidirect product of C₂³ and Q₈ acting via Q₈/C₂=C₂²	16		C2^3:2Q8	64,224
D₈⋊C₂²	4^th semidirect product of D₈ and C₂² acting via C₂²/C₂=C₂	16	4	D8:C2^2	64,256
M₄(2)⋊₄C₄	4^th semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	16	4	M4(2):4C4	64,25
M₅(2)⋊C₂	6^th semidirect product of M₅(2) and C₂ acting faithfully	16	4+	M5(2):C2	64,42
C₄²⋊C₂²	1^st semidirect product of C₄² and C₂² acting faithfully	16	4	C4^2:C2^2	64,102
C₂⁴⋊C₂²	4^th semidirect product of C₂⁴ and C₂² acting faithfully	16		C2^4:C2^2	64,242
C₂²⋊SD₁₆	The semidirect product of C₂² and SD₁₆ acting via SD₁₆/D₄=C₂	16		C2^2:SD16	64,131
D₄⋊C₈	The semidirect product of D₄ and C₈ acting via C₈/C₄=C₂	32		D4:C8	64,6
C₈⋊₉D₄	3^rd semidirect product of C₈ and D₄ acting via D₄/C₂²=C₂	32		C8:9D4	64,116
C₈⋊₆D₄	3^rd semidirect product of C₈ and D₄ acting via D₄/C₄=C₂	32		C8:6D4	64,117
C₄⋊D₈	The semidirect product of C₄ and D₈ acting via D₈/D₄=C₂	32		C4:D8	64,140
C₈⋊₈D₄	2^nd semidirect product of C₈ and D₄ acting via D₄/C₂²=C₂	32		C8:8D4	64,146
C₈⋊₇D₄	1^st semidirect product of C₈ and D₄ acting via D₄/C₂²=C₂	32		C8:7D4	64,147
C₈⋊D₄	1^st semidirect product of C₈ and D₄ acting via D₄/C₂=C₂²	32		C8:D4	64,149
C₈⋊₂D₄	2^nd semidirect product of C₈ and D₄ acting via D₄/C₂=C₂²	32		C8:2D4	64,150
C₈⋊₅D₄	2^nd semidirect product of C₈ and D₄ acting via D₄/C₄=C₂	32		C8:5D4	64,173
C₈⋊₄D₄	1^st semidirect product of C₈ and D₄ acting via D₄/C₄=C₂	32		C8:4D4	64,174
C₈⋊₃D₄	3^rd semidirect product of C₈ and D₄ acting via D₄/C₂=C₂²	32		C8:3D4	64,177
D₈⋊C₄	3^rd semidirect product of D₈ and C₄ acting via C₄/C₂=C₂; = Aut(SD₃₂)	32		D8:C4	64,123
D₄⋊D₄	2^nd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂	32		D4:D4	64,130
D₄⋊₆D₄	2^nd semidirect product of D₄ and D₄ acting through Inn(D₄)	32		D4:6D4	64,228
C₂²⋊C₁₆	The semidirect product of C₂² and C₁₆ acting via C₁₆/C₈=C₂	32		C2^2:C16	64,29
Q₈⋊D₄	1^st semidirect product of Q₈ and D₄ acting via D₄/C₂²=C₂	32		Q8:D4	64,129
D₄⋊Q₈	1^st semidirect product of D₄ and Q₈ acting via Q₈/C₄=C₂	32		D4:Q8	64,155
D₄⋊₂Q₈	2^nd semidirect product of D₄ and Q₈ acting via Q₈/C₄=C₂	32		D4:2Q8	64,157
Q₈⋊₅D₄	1^st semidirect product of Q₈ and D₄ acting through Inn(Q₈)	32		Q8:5D4	64,229
Q₈⋊₆D₄	2^nd semidirect product of Q₈ and D₄ acting through Inn(Q₈)	32		Q8:6D4	64,231
D₄⋊₃Q₈	The semidirect product of D₄ and Q₈ acting through Inn(D₄)	32		D4:3Q8	64,235
Q₃₂⋊C₂	2^nd semidirect product of Q₃₂ and C₂ acting faithfully	32	4-	Q32:C2	64,191
C₄⋊SD₁₆	The semidirect product of C₄ and SD₁₆ acting via SD₁₆/Q₈=C₂	32		C4:SD16	64,141
C₂³⋊₂D₄	1^st semidirect product of C₂³ and D₄ acting via D₄/C₂=C₂²	32		C2^3:2D4	64,73
C₂³⋊Q₈	1^st semidirect product of C₂³ and Q₈ acting via Q₈/C₂=C₂²	32		C2^3:Q8	64,74
SD₁₆⋊C₄	1^st semidirect product of SD₁₆ and C₄ acting via C₄/C₂=C₂	32		SD16:C4	64,121
C₄⋊M₄(2)	The semidirect product of C₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	32		C4:M4(2)	64,104
C₂²⋊Q₁₆	The semidirect product of C₂² and Q₁₆ acting via Q₁₆/Q₈=C₂	32		C2^2:Q16	64,132
M₄(2)⋊C₄	1^st semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	32		M4(2):C4	64,109
C₈⋊Q₈	The semidirect product of C₈ and Q₈ acting via Q₈/C₂=C₂²	64		C8:Q8	64,182
C₄⋊C₁₆	The semidirect product of C₄ and C₁₆ acting via C₁₆/C₈=C₂	64		C4:C16	64,44
Q₈⋊C₈	The semidirect product of Q₈ and C₈ acting via C₈/C₄=C₂	64		Q8:C8	64,7
C₈⋊C₈	3^rd semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:C8	64,3
C₈⋊₂C₈	2^nd semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:2C8	64,15
C₈⋊₁C₈	1^st semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:1C8	64,16
C₈⋊₄Q₈	3^rd semidirect product of C₈ and Q₈ acting via Q₈/C₄=C₂	64		C8:4Q8	64,127
C₈⋊₃Q₈	2^nd semidirect product of C₈ and Q₈ acting via Q₈/C₄=C₂	64		C8:3Q8	64,179
C₈⋊₂Q₈	1^st semidirect product of C₈ and Q₈ acting via Q₈/C₄=C₂	64		C8:2Q8	64,181
C₁₆⋊₅C₄	3^rd semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:5C4	64,27
C₁₆⋊₃C₄	1^st semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:3C4	64,47
C₁₆⋊₄C₄	2^nd semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:4C4	64,48
Q₈⋊Q₈	1^st semidirect product of Q₈ and Q₈ acting via Q₈/C₄=C₂	64		Q8:Q8	64,156
Q₈⋊₃Q₈	The semidirect product of Q₈ and Q₈ acting through Inn(Q₈)	64		Q8:3Q8	64,238
C₄⋊₂Q₁₆	The semidirect product of C₄ and Q₁₆ acting via Q₁₆/Q₈=C₂	64		C4:2Q16	64,143
C₄⋊Q₁₆	The semidirect product of C₄ and Q₁₆ acting via Q₁₆/C₈=C₂	64		C4:Q16	64,175
C₄²⋊₄C₄	1^st semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:4C4	64,57
C₄²⋊₈C₄	5^th semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:8C4	64,63
C₄²⋊₅C₄	2^nd semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:5C4	64,64
C₄²⋊₉C₄	6^th semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	64		C4^2:9C4	64,65
Q₁₆⋊C₄	3^rd semidirect product of Q₁₆ and C₄ acting via C₄/C₂=C₂	64		Q16:C4	64,122
(C₂²×C₈)⋊C₂	2^nd semidirect product of C₂²×C₈ and C₂ acting faithfully	32		(C2^2xC8):C2	64,89
C₈.Q₈	The non-split extension by C₈ of Q₈ acting via Q₈/C₂=C₂²	16	4	C8.Q8	64,46
C₈.C₈	1^st non-split extension by C₈ of C₈ acting via C₈/C₄=C₂	16	2	C8.C8	64,45
C₂³.C₈	The non-split extension by C₂³ of C₈ acting via C₈/C₂=C₄	16	4	C2^3.C8	64,30
D₄.₈D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4	D4.8D4	64,135
D₄.₉D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4	D4.9D4	64,136
D₄.₃D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	16	4	D4.3D4	64,152
D₄.₄D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	16	4+	D4.4D4	64,153
C₈.₂₆D₄	13^rd non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	16	4	C8.26D4	64,125
D₄.₁₀D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4-	D4.10D4	64,137
C₄.₉C₄²	1^st central stem extension by C₄ of C₄²	16	4	C4.9C4^2	64,18
C₄².C₄	2^nd non-split extension by C₄² of C₄ acting faithfully	16	4	C4^2.C4	64,36
C₄².₃C₄	3^rd non-split extension by C₄² of C₄ acting faithfully	16	4-	C4^2.3C4	64,37
C₂⁴.₄C₄	2^nd non-split extension by C₂⁴ of C₄ acting via C₄/C₂=C₂	16		C2^4.4C4	64,88
C₂.C₂⁵	6^th central stem extension by C₂ of C₂⁵	16	4	C2.C2^5	64,266
C₂³.₉D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	16		C2^3.9D4	64,23
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	16	4	C2^3.D4	64,33
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	16	4	C2^3.7D4	64,139
C₄.₁₀C₄²	2^nd central stem extension by C₄ of C₄²	16	4	C4.10C4^2	64,19
C₂³.₃₁D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	16		C2^3.31D4	64,9
C₂³.₃₇D₄	8^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	16		C2^3.37D4	64,99
M₄(2).C₄	1^st non-split extension by M₄(2) of C₄ acting via C₄/C₂=C₂	16	4	M4(2).C4	64,111
C₂³.C₂³	2^nd non-split extension by C₂³ of C₂³ acting via C₂³/C₂=C₂²	16	4	C2^3.C2^3	64,91
C₂².SD₁₆	1^st non-split extension by C₂² of SD₁₆ acting via SD₁₆/Q₈=C₂	16		C2^2.SD16	64,8
C₂².₁₁C₂⁴	7^th central extension by C₂² of C₂⁴	16		C2^2.11C2^4	64,199
C₂².₁₉C₂⁴	5^th central stem extension by C₂² of C₂⁴	16		C2^2.19C2^4	64,206
C₂².₂₉C₂⁴	15^th central stem extension by C₂² of C₂⁴	16		C2^2.29C2^4	64,216
C₂².₃₂C₂⁴	18^th central stem extension by C₂² of C₂⁴	16		C2^2.32C2^4	64,219
C₂².₄₅C₂⁴	31^st central stem extension by C₂² of C₂⁴	16		C2^2.45C2^4	64,232
C₂².₅₄C₂⁴	40^th central stem extension by C₂² of C₂⁴	16		C2^2.54C2^4	64,241
M₄(2).₈C₂²	3^rd non-split extension by M₄(2) of C₂² acting via C₂²/C₂=C₂	16	4	M4(2).8C2^2	64,94
D₄.C₈	The non-split extension by D₄ of C₈ acting via C₈/C₄=C₂	32	2	D4.C8	64,31
D₄.Q₈	The non-split extension by D₄ of Q₈ acting via Q₈/C₄=C₂	32		D4.Q8	64,159
C₄.D₈	1^st non-split extension by C₄ of D₈ acting via D₈/D₄=C₂	32		C4.D8	64,12
C₈.D₄	1^st non-split extension by C₈ of D₄ acting via D₄/C₂=C₂²	32		C8.D4	64,151
C₄.₄D₈	4^th non-split extension by C₄ of D₈ acting via D₈/C₈=C₂	32		C4.4D8	64,167
C₈.₂D₄	2^nd non-split extension by C₈ of D₄ acting via D₄/C₂=C₂²	32		C8.2D4	64,178
C₈.₄Q₈	3^rd non-split extension by C₈ of Q₈ acting via Q₈/C₄=C₂	32	2	C8.4Q8	64,49
D₈.C₄	1^st non-split extension by D₈ of C₄ acting via C₄/C₂=C₂	32	2	D8.C4	64,40
D₄.₇D₄	2^nd non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	32		D4.7D4	64,133
D₄.D₄	1^st non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32		D4.D4	64,142
D₄.₂D₄	2^nd non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32		D4.2D4	64,144
D₄.₅D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32	4-	D4.5D4	64,154
C₂.D₁₆	1^st central extension by C₂ of D₁₆	32		C2.D16	64,38
C₈.₁₇D₄	4^th non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	32	4-	C8.17D4	64,43
C₈.₁₈D₄	5^th non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	32		C8.18D4	64,148
C₈.₁₂D₄	8^th non-split extension by C₈ of D₄ acting via D₄/C₄=C₂	32		C8.12D4	64,176
Q₈.D₄	2^nd non-split extension by Q₈ of D₄ acting via D₄/C₄=C₂	32		Q8.D4	64,145
C₄.C₄²	3^rd non-split extension by C₄ of C₄² acting via C₄²/C₂×C₄=C₂	32		C4.C4^2	64,22
C₄².₆C₄	3^rd non-split extension by C₄² of C₄ acting via C₄/C₂=C₂	32		C4^2.6C4	64,113
C₂².D₈	3^rd non-split extension by C₂² of D₈ acting via D₈/D₄=C₂	32		C2^2.D8	64,161
C₂³.₇Q₈	2^nd non-split extension by C₂³ of Q₈ acting via Q₈/C₄=C₂	32		C2^3.7Q8	64,61
C₂³.₈Q₈	3^rd non-split extension by C₂³ of Q₈ acting via Q₈/C₄=C₂	32		C2^3.8Q8	64,66
C₂³.Q₈	3^rd non-split extension by C₂³ of Q₈ acting via Q₈/C₂=C₂²	32		C2^3.Q8	64,77
C₂³.₄Q₈	4^th non-split extension by C₂³ of Q₈ acting via Q₈/C₂=C₂²	32		C2^3.4Q8	64,80
C₄².₁₂C₄	9^th non-split extension by C₄² of C₄ acting via C₄/C₂=C₂	32		C4^2.12C4	64,112
C₂³.₃₄D₄	5^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.34D4	64,62
C₂³.₂₃D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₄=C₂	32		C2^3.23D4	64,67
C₂³.₁₀D₄	3^rd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.10D4	64,75
C₂³.₁₁D₄	4^th non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.11D4	64,78
C₂³.₂₄D₄	3^rd non-split extension by C₂³ of D₄ acting via D₄/C₄=C₂	32		C2^3.24D4	64,97
C₂³.₃₆D₄	7^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.36D4	64,98
C₂³.₃₈D₄	9^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.38D4	64,100
C₂³.₂₅D₄	4^th non-split extension by C₂³ of D₄ acting via D₄/C₄=C₂	32		C2^3.25D4	64,108
C₂³.₄₆D₄	17^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.46D4	64,162
C₂³.₁₉D₄	12^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.19D4	64,163
C₂³.₄₇D₄	18^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.47D4	64,164
C₂³.₄₈D₄	19^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	32		C2^3.48D4	64,165
C₂³.₂₀D₄	13^rd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	32		C2^3.20D4	64,166
C₄².C₂²	1^st non-split extension by C₄² of C₂² acting faithfully	32		C4^2.C2^2	64,10
C₂².C₄²	2^nd non-split extension by C₂² of C₄² acting via C₄²/C₂×C₄=C₂	32		C2^2.C4^2	64,24
C₂⁴.C₂²	2^nd non-split extension by C₂⁴ of C₂² acting faithfully	32		C2^4.C2^2	64,69
C₂⁴.₃C₂²	3^rd non-split extension by C₂⁴ of C₂² acting faithfully	32		C2^4.3C2^2	64,71
C₄².₆C₂²	6^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.6C2^2	64,105
C₄².₇C₂²	7^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.7C2^2	64,114
C₄².₇₈C₂²	21^st non-split extension by C₄² of C₂² acting via C₂²/C₂=C₂	32		C4^2.78C2^2	64,169
C₄².₂₈C₂²	28^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.28C2^2	64,170
C₄².₂₉C₂²	29^th non-split extension by C₄² of C₂² acting faithfully	32		C4^2.29C2^2	64,171
C₂³.₃₂C₂³	5^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.32C2^3	64,200
C₂³.₃₃C₂³	6^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.33C2^3	64,201
C₂³.₃₆C₂³	9^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.36C2^3	64,210
C₂².₂₆C₂⁴	12^nd central stem extension by C₂² of C₂⁴	32		C2^2.26C2^4	64,213
C₂³.₃₇C₂³	10^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.37C2^3	64,214
C₂³.₃₈C₂³	11^st non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.38C2^3	64,217
C₂².₃₁C₂⁴	17^th central stem extension by C₂² of C₂⁴	32		C2^2.31C2^4	64,218
C₂².₃₃C₂⁴	19^th central stem extension by C₂² of C₂⁴	32		C2^2.33C2^4	64,220
C₂².₃₄C₂⁴	20^th central stem extension by C₂² of C₂⁴	32		C2^2.34C2^4	64,221
C₂².₃₅C₂⁴	21^st central stem extension by C₂² of C₂⁴	32		C2^2.35C2^4	64,222
C₂².₃₆C₂⁴	22^nd central stem extension by C₂² of C₂⁴	32		C2^2.36C2^4	64,223
C₂³.₄₁C₂³	14^th non-split extension by C₂³ of C₂³ acting via C₂³/C₂²=C₂	32		C2^3.41C2^3	64,225
C₂².₄₆C₂⁴	32^nd central stem extension by C₂² of C₂⁴	32		C2^2.46C2^4	64,233
C₂².₄₇C₂⁴	33^rd central stem extension by C₂² of C₂⁴	32		C2^2.47C2^4	64,234
C₂².₄₉C₂⁴	35^th central stem extension by C₂² of C₂⁴	32		C2^2.49C2^4	64,236
C₂².₅₀C₂⁴	36^th central stem extension by C₂² of C₂⁴	32		C2^2.50C2^4	64,237
C₂².₅₃C₂⁴	39^th central stem extension by C₂² of C₂⁴	32		C2^2.53C2^4	64,240
C₂².₅₆C₂⁴	42^nd central stem extension by C₂² of C₂⁴	32		C2^2.56C2^4	64,243
C₂².₅₇C₂⁴	43^rd central stem extension by C₂² of C₂⁴	32		C2^2.57C2^4	64,244
C₂².M₄(2)	2^nd non-split extension by C₂² of M₄(2) acting via M₄(2)/C₂×C₄=C₂	32		C2^2.M4(2)	64,5
Q₈.Q₈	The non-split extension by Q₈ of Q₈ acting via Q₈/C₄=C₂	64		Q8.Q8	64,160
C₈.₅Q₈	4^th non-split extension by C₈ of Q₈ acting via Q₈/C₄=C₂	64		C8.5Q8	64,180
C₄.₁₀D₈	2^nd non-split extension by C₄ of D₈ acting via D₈/D₄=C₂	64		C4.10D8	64,13
C₄.₆Q₁₆	2^nd non-split extension by C₄ of Q₁₆ acting via Q₁₆/Q₈=C₂	64		C4.6Q16	64,14
C₂.Q₃₂	1^st central extension by C₂ of Q₃₂	64		C2.Q32	64,39
C₄.Q₁₆	3^rd non-split extension by C₄ of Q₁₆ acting via Q₁₆/Q₈=C₂	64		C4.Q16	64,158
C₄.SD₁₆	4^th non-split extension by C₄ of SD₁₆ acting via SD₁₆/C₈=C₂	64		C4.SD16	64,168
C₂².₄Q₁₆	1^st central extension by C₂² of Q₁₆	64		C2^2.4Q16	64,21
C₄².₂C₂²	2^nd non-split extension by C₄² of C₂² acting faithfully	64		C4^2.2C2^2	64,11
C₂².₇C₄²	2^nd central extension by C₂² of C₄²	64		C2^2.7C4^2	64,17
C₂³.₆₃C₂³	13^rd central extension by C₂³ of C₂³	64		C2^3.63C2^3	64,68
C₂³.₆₅C₂³	15^th central extension by C₂³ of C₂³	64		C2^3.65C2^3	64,70
C₂³.₆₇C₂³	17^th central extension by C₂³ of C₂³	64		C2^3.67C2^3	64,72
C₂³.₇₈C₂³	4^th central stem extension by C₂³ of C₂³	64		C2^3.78C2^3	64,76
C₂³.₈₁C₂³	7^th central stem extension by C₂³ of C₂³	64		C2^3.81C2^3	64,79
C₂³.₈₃C₂³	9^th central stem extension by C₂³ of C₂³	64		C2^3.83C2^3	64,81
C₂³.₈₄C₂³	10^th central stem extension by C₂³ of C₂³	64		C2^3.84C2^3	64,82
C₄².₃₀C₂²	30^th non-split extension by C₄² of C₂² acting faithfully	64		C4^2.30C2^2	64,172
C₂².₅₈C₂⁴	44^th central stem extension by C₂² of C₂⁴	64		C2^2.58C2^4	64,245
C₈²	Abelian group of type [8,8]	64		C8^2	64,2
C₄³	Abelian group of type [4,4,4]	64		C4^3	64,55
C₂⁶	Elementary abelian group of type [2,2,2,2,2,2]	64		C2^6	64,267
C₄×C₁₆	Abelian group of type [4,16]	64		C4xC16	64,26
C₂×C₃₂	Abelian group of type [2,32]	64		C2xC32	64,50
C₂³×C₈	Abelian group of type [2,2,2,8]	64		C2^3xC8	64,246
C₂⁴×C₄	Abelian group of type [2,2,2,2,4]	64		C2^4xC4	64,260
C₂²×C₁₆	Abelian group of type [2,2,16]	64		C2^2xC16	64,183
C₂²×C₄²	Abelian group of type [2,2,4,4]	64		C2^2xC4^2	64,192
C₂×C₄×C₈	Abelian group of type [2,4,8]	64		C2xC4xC8	64,83
D₄²	Direct product of D₄ and D₄	16		D4^2	64,226
C₂×2₊¹⁺⁴	Direct product of C₂ and 2₊¹⁺⁴	16		C2xES+(2,2)	64,264
C₈×D₄	Direct product of C₈ and D₄	32		C8xD4	64,115
C₄×D₈	Direct product of C₄ and D₈	32		C4xD8	64,118
D₄×Q₈	Direct product of D₄ and Q₈	32		D4xQ8	64,230
C₂×D₁₆	Direct product of C₂ and D₁₆	32		C2xD16	64,186
C₄×SD₁₆	Direct product of C₄ and SD₁₆	32		C4xSD16	64,119
C₂×SD₃₂	Direct product of C₂ and SD₃₂	32		C2xSD32	64,187
C₂²×D₈	Direct product of C₂² and D₈	32		C2^2xD8	64,250
D₄×C₂³	Direct product of C₂³ and D₄	32		D4xC2^3	64,261
C₄×M₄(2)	Direct product of C₄ and M₄(2)	32		C4xM4(2)	64,85
C₂×M₅(2)	Direct product of C₂ and M₅(2)	32		C2xM5(2)	64,184
C₂²×SD₁₆	Direct product of C₂² and SD₁₆	32		C2^2xSD16	64,251
C₂²×M₄(2)	Direct product of C₂² and M₄(2)	32		C2^2xM4(2)	64,247
C₂×2_-¹⁺⁴	Direct product of C₂ and 2_-¹⁺⁴	32		C2xES-(2,2)	64,265
Q₈²	Direct product of Q₈ and Q₈	64		Q8^2	64,239
C₈×Q₈	Direct product of C₈ and Q₈	64		C8xQ8	64,126
C₄×Q₁₆	Direct product of C₄ and Q₁₆	64		C4xQ16	64,120
C₂×Q₃₂	Direct product of C₂ and Q₃₂	64		C2xQ32	64,188
Q₈×C₂³	Direct product of C₂³ and Q₈	64		Q8xC2^3	64,262
C₂²×Q₁₆	Direct product of C₂² and Q₁₆	64		C2^2xQ16	64,252
C₂×C₄≀C₂	Direct product of C₂ and C₄≀C₂	16		C2xC4wrC2	64,101
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	16		C2xC2^3:C4	64,90
C₂×C₈⋊C₂²	Direct product of C₂ and C₈⋊C₂²	16		C2xC8:C2^2	64,254
C₂×C₄.D₄	Direct product of C₂ and C₄.D₄	16		C2xC4.D4	64,92
C₂×C₂²≀C₂	Direct product of C₂ and C₂²≀C₂	16		C2xC2^2wrC2	64,202
C₂×C₄×D₄	Direct product of C₂×C₄ and D₄	32		C2xC4xD4	64,196
C₄×C₄○D₄	Direct product of C₄ and C₄○D₄	32		C4xC4oD4	64,198
C₂×C₈○D₄	Direct product of C₂ and C₈○D₄	32		C2xC8oD4	64,248
C₂×C₄○D₈	Direct product of C₂ and C₄○D₈	32		C2xC4oD8	64,253
C₂×C₄⋊D₄	Direct product of C₂ and C₄⋊D₄	32		C2xC4:D4	64,203
C₂×D₄⋊C₄	Direct product of C₂ and D₄⋊C₄	32		C2xD4:C4	64,95
C₂×C₈.C₄	Direct product of C₂ and C₈.C₄	32		C2xC8.C4	64,110
C₂×C₄⋊₁D₄	Direct product of C₂ and C₄⋊₁D₄	32		C2xC4:1D4	64,211
C₄×C₂²⋊C₄	Direct product of C₄ and C₂²⋊C₄	32		C4xC2^2:C4	64,58
C₂×C₂²⋊C₈	Direct product of C₂ and C₂²⋊C₈	32		C2xC2^2:C8	64,87
C₂×C₂²⋊Q₈	Direct product of C₂ and C₂²⋊Q₈	32		C2xC2^2:Q8	64,204
C₂×C₄²⋊C₂	Direct product of C₂ and C₄²⋊C₂	32		C2xC4^2:C2	64,195
C₂×C₄.₄D₄	Direct product of C₂ and C₄.₄D₄	32		C2xC4.4D4	64,207
C₂²×C₄○D₄	Direct product of C₂² and C₄○D₄	32		C2^2xC4oD4	64,263
C₂×C₈.C₂²	Direct product of C₂ and C₈.C₂²	32		C2xC8.C2^2	64,255
C₂×C₄²⋊₂C₂	Direct product of C₂ and C₄²⋊₂C₂	32		C2xC4^2:2C2	64,209
C₂×C₄.₁₀D₄	Direct product of C₂ and C₄.₁₀D₄	32		C2xC4.10D4	64,93
C₂²×C₂²⋊C₄	Direct product of C₂² and C₂²⋊C₄	32		C2^2xC2^2:C4	64,193
C₂×C₂².D₄	Direct product of C₂ and C₂².D₄	32		C2xC2^2.D4	64,205
C₄×C₄⋊C₄	Direct product of C₄ and C₄⋊C₄	64		C4xC4:C4	64,59
C₂×C₄⋊C₈	Direct product of C₂ and C₄⋊C₈	64		C2xC4:C8	64,103
C₂×C₄×Q₈	Direct product of C₂×C₄ and Q₈	64		C2xC4xQ8	64,197
C₂×C₄⋊Q₈	Direct product of C₂ and C₄⋊Q₈	64		C2xC4:Q8	64,212
C₂×C₈⋊C₄	Direct product of C₂ and C₈⋊C₄	64		C2xC8:C4	64,84
C₂²×C₄⋊C₄	Direct product of C₂² and C₄⋊C₄	64		C2^2xC4:C4	64,194
C₂×Q₈⋊C₄	Direct product of C₂ and Q₈⋊C₄	64		C2xQ8:C4	64,96
C₂×C₂.D₈	Direct product of C₂ and C₂.D₈	64		C2xC2.D8	64,107
C₂×C₄.Q₈	Direct product of C₂ and C₄.Q₈	64		C2xC4.Q8	64,106
C₂×C₂.C₄²	Direct product of C₂ and C₂.C₄²	64		C2xC2.C4^2	64,56
C₂×C₄².C₂	Direct product of C₂ and C₄².C₂	64		C2xC4^2.C2	64,208

Groups of order 65

		d	ρ	Label	ID
C₆₅	Cyclic group	65	1	C65	65,1

Groups of order 66

		d	ρ	Label	ID
C₆₆	Cyclic group	66	1	C66	66,4
D₃₃	Dihedral group	33	2+	D33	66,3
S₃×C₁₁	Direct product of C₁₁ and S₃	33	2	S3xC11	66,1
C₃×D₁₁	Direct product of C₃ and D₁₁	33	2	C3xD11	66,2

Groups of order 67

		d	ρ	Label	ID
C₆₇	Cyclic group	67	1	C67	67,1

Groups of order 68

		d	ρ	Label	ID
C₆₈	Cyclic group	68	1	C68	68,2
D₃₄	Dihedral group; = C₂×D₁₇	34	2+	D34	68,4
Dic₁₇	Dicyclic group; = C₁₇ ⋊₂ C₄	68	2-	Dic17	68,1
C₁₇⋊C₄	The semidirect product of C₁₇ and C₄ acting faithfully	17	4+	C17:C4	68,3
C₂×C₃₄	Abelian group of type [2,34]	68		C2xC34	68,5

Groups of order 69

		d	ρ	Label	ID
C₆₉	Cyclic group	69	1	C69	69,1

Groups of order 70

		d	ρ	Label	ID
C₇₀	Cyclic group	70	1	C70	70,4
D₃₅	Dihedral group	35	2+	D35	70,3
C₇×D₅	Direct product of C₇ and D₅	35	2	C7xD5	70,1
C₅×D₇	Direct product of C₅ and D₇	35	2	C5xD7	70,2

Groups of order 71

		d	ρ	Label	ID
C₇₁	Cyclic group	71	1	C71	71,1

Groups of order 72

		d	ρ	Label	ID
C₇₂	Cyclic group	72	1	C72	72,2
D₃₆	Dihedral group	36	2+	D36	72,6
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	9	8+	F9	72,39
Dic₁₈	Dicyclic group; = C₉ ⋊Q₈	72	2-	Dic18	72,4
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	9	8+	PSU(3,2)	72,41
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	6	4+	S3wrC2	72,40
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	12	6+	C3:S4	72,43
C₃⋊D₁₂	The semidirect product of C₃ and D₁₂ acting via D₁₂/D₆=C₂	12	4+	C3:D12	72,23
D₆⋊S₃	1^st semidirect product of D₆ and S₃ acting via S₃/C₃=C₂	24	4-	D6:S3	72,22
C₃²⋊₂C₈	The semidirect product of C₃² and C₈ acting via C₈/C₂=C₄	24	4-	C3^2:2C8	72,19
C₃²⋊₂Q₈	The semidirect product of C₃² and Q₈ acting via Q₈/C₂=C₂²	24	4-	C3^2:2Q8	72,24
C₉⋊D₄	The semidirect product of C₉ and D₄ acting via D₄/C₂²=C₂	36	2	C9:D4	72,8
C₁₂⋊S₃	1^st semidirect product of C₁₂ and S₃ acting via S₃/C₃=C₂	36		C12:S3	72,33
C₃²⋊₇D₄	2^nd semidirect product of C₃² and D₄ acting via D₄/C₂²=C₂	36		C3^2:7D4	72,35
C₉⋊C₈	The semidirect product of C₉ and C₈ acting via C₈/C₄=C₂	72	2	C9:C8	72,1
Q₈⋊C₉	The semidirect product of Q₈ and C₉ acting via C₉/C₃=C₃	72	2	Q8:C9	72,3
C₃²⋊₄C₈	2^nd semidirect product of C₃² and C₈ acting via C₈/C₄=C₂	72		C3^2:4C8	72,13
C₃²⋊₄Q₈	2^nd semidirect product of C₃² and Q₈ acting via Q₈/C₄=C₂	72		C3^2:4Q8	72,31
C₆.D₆	2^nd non-split extension by C₆ of D₆ acting via D₆/S₃=C₂	12	4+	C6.D6	72,21
C₃.S₄	The non-split extension by C₃ of S₄ acting via S₄/A₄=C₂	18	6+	C3.S4	72,15
C₂×C₃₆	Abelian group of type [2,36]	72		C2xC36	72,9
C₃×C₂₄	Abelian group of type [3,24]	72		C3xC24	72,14
C₆×C₁₂	Abelian group of type [6,12]	72		C6xC12	72,36
C₂×C₆²	Abelian group of type [2,6,6]	72		C2xC6^2	72,50
C₂²×C₁₈	Abelian group of type [2,2,18]	72		C2^2xC18	72,18
C₃×S₄	Direct product of C₃ and S₄	12	3	C3xS4	72,42
S₃×A₄	Direct product of S₃ and A₄	12	6+	S3xA4	72,44
C₆×A₄	Direct product of C₆ and A₄	18	3	C6xA4	72,47
S₃×C₁₂	Direct product of C₁₂ and S₃	24	2	S3xC12	72,27
C₃×D₁₂	Direct product of C₃ and D₁₂	24	2	C3xD12	72,28
S₃×Dic₃	Direct product of S₃ and Dic₃	24	4-	S3xDic3	72,20
C₃×Dic₆	Direct product of C₃ and Dic₆	24	2	C3xDic6	72,26
C₆×Dic₃	Direct product of C₆ and Dic₃	24		C6xDic3	72,29
C₃×SL₂(𝔽₃)	Direct product of C₃ and SL₂(𝔽₃)	24	2	C3xSL(2,3)	72,25
C₄×D₉	Direct product of C₄ and D₉	36	2	C4xD9	72,5
D₄×C₉	Direct product of C₉ and D₄	36	2	D4xC9	72,10
C₂²×D₉	Direct product of C₂² and D₉	36		C2^2xD9	72,17
D₄×C₃²	Direct product of C₃² and D₄	36		D4xC3^2	72,37
Q₈×C₉	Direct product of C₉ and Q₈	72	2	Q8xC9	72,11
C₂×Dic₉	Direct product of C₂ and Dic₉	72		C2xDic9	72,7
Q₈×C₃²	Direct product of C₃² and Q₈	72		Q8xC3^2	72,38
C₂×S₃²	Direct product of C₂, S₃ and S₃	12	4+	C2xS3^2	72,46
C₃×C₃⋊D₄	Direct product of C₃ and C₃⋊D₄	12	2	C3xC3:D4	72,30
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	12	4+	C2xC3^2:C4	72,45
C₂×C₃.A₄	Direct product of C₂ and C₃.A₄	18	3	C2xC3.A4	72,16
C₃×C₃⋊C₈	Direct product of C₃ and C₃⋊C₈	24	2	C3xC3:C8	72,12
S₃×C₂×C₆	Direct product of C₂×C₆ and S₃	24		S3xC2xC6	72,48
C₄×C₃⋊S₃	Direct product of C₄ and C₃⋊S₃	36		C4xC3:S3	72,32
C₂²×C₃⋊S₃	Direct product of C₂² and C₃⋊S₃	36		C2^2xC3:S3	72,49
C₂×C₃⋊Dic₃	Direct product of C₂ and C₃⋊Dic₃	72		C2xC3:Dic3	72,34

Groups of order 73

		d	ρ	Label	ID
C₇₃	Cyclic group	73	1	C73	73,1

Groups of order 74

		d	ρ	Label	ID
C₇₄	Cyclic group	74	1	C74	74,2
D₃₇	Dihedral group	37	2+	D37	74,1

Groups of order 75

		d	ρ	Label	ID
C₇₅	Cyclic group	75	1	C75	75,1
C₅²⋊C₃	The semidirect product of C₅² and C₃ acting faithfully	15	3	C5^2:C3	75,2
C₅×C₁₅	Abelian group of type [5,15]	75		C5xC15	75,3

Groups of order 76

		d	ρ	Label	ID
C₇₆	Cyclic group	76	1	C76	76,2
D₃₈	Dihedral group; = C₂×D₁₉	38	2+	D38	76,3
Dic₁₉	Dicyclic group; = C₁₉ ⋊C₄	76	2-	Dic19	76,1
C₂×C₃₈	Abelian group of type [2,38]	76		C2xC38	76,4

Groups of order 77

		d	ρ	Label	ID
C₇₇	Cyclic group	77	1	C77	77,1

Groups of order 78

		d	ρ	Label	ID
C₇₈	Cyclic group	78	1	C78	78,6
D₃₉	Dihedral group	39	2+	D39	78,5
C₁₃⋊C₆	The semidirect product of C₁₃ and C₆ acting faithfully	13	6+	C13:C6	78,1
S₃×C₁₃	Direct product of C₁₃ and S₃	39	2	S3xC13	78,3
C₃×D₁₃	Direct product of C₃ and D₁₃	39	2	C3xD13	78,4
C₂×C₁₃⋊C₃	Direct product of C₂ and C₁₃⋊C₃	26	3	C2xC13:C3	78,2

Groups of order 79

		d	ρ	Label	ID
C₇₉	Cyclic group	79	1	C79	79,1

Groups of order 80

		d	ρ	Label	ID
C₈₀	Cyclic group	80	1	C80	80,2
D₄₀	Dihedral group	40	2+	D40	80,7
Dic₂₀	Dicyclic group; = C₅ ⋊₁ Q₁₆	80	2-	Dic20	80,8
C₄○D₂₀	Central product of C₄ and D₂₀	40	2	C4oD20	80,38
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	10	5+	C2^4:C5	80,49
C₄⋊F₅	The semidirect product of C₄ and F₅ acting via F₅/D₅=C₂	20	4	C4:F5	80,31
C₂²⋊F₅	The semidirect product of C₂² and F₅ acting via F₅/D₅=C₂	20	4+	C2^2:F5	80,34
D₄⋊D₅	The semidirect product of D₄ and D₅ acting via D₅/C₅=C₂	40	4+	D4:D5	80,15
D₅⋊C₈	The semidirect product of D₅ and C₈ acting via C₈/C₄=C₂	40	4	D5:C8	80,28
Q₈⋊D₅	The semidirect product of Q₈ and D₅ acting via D₅/C₅=C₂	40	4+	Q8:D5	80,17
C₈⋊D₅	3^rd semidirect product of C₈ and D₅ acting via D₅/C₅=C₂	40	2	C8:D5	80,5
C₄₀⋊C₂	2^nd semidirect product of C₄₀ and C₂ acting faithfully	40	2	C40:C2	80,6
D₄⋊₂D₅	The semidirect product of D₄ and D₅ acting through Inn(D₄)	40	4-	D4:2D5	80,40
Q₈⋊₂D₅	The semidirect product of Q₈ and D₅ acting through Inn(Q₈)	40	4+	Q8:2D5	80,42
D₁₀⋊C₄	1^st semidirect product of D₁₀ and C₄ acting via C₄/C₂=C₂	40		D10:C4	80,14
C₅⋊C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5:C16	80,3
C₅⋊₂C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₈=C₂	80	2	C5:2C16	80,1
C₄⋊Dic₅	The semidirect product of C₄ and Dic₅ acting via Dic₅/C₁₀=C₂	80		C4:Dic5	80,13
C₅⋊Q₁₆	The semidirect product of C₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	80	4-	C5:Q16	80,18
C₄.F₅	The non-split extension by C₄ of F₅ acting via F₅/D₅=C₂	40	4	C4.F5	80,29
D₄.D₅	The non-split extension by D₄ of D₅ acting via D₅/C₅=C₂	40	4-	D4.D5	80,16
C₄.Dic₅	The non-split extension by C₄ of Dic₅ acting via Dic₅/C₁₀=C₂	40	2	C4.Dic5	80,10
C₂³.D₅	The non-split extension by C₂³ of D₅ acting via D₅/C₅=C₂	40		C2^3.D5	80,19
C₂².F₅	The non-split extension by C₂² of F₅ acting via F₅/D₅=C₂	40	4-	C2^2.F5	80,33
C₁₀.D₄	1^st non-split extension by C₁₀ of D₄ acting via D₄/C₂²=C₂	80		C10.D4	80,12
C₄×C₂₀	Abelian group of type [4,20]	80		C4xC20	80,20
C₂×C₄₀	Abelian group of type [2,40]	80		C2xC40	80,23
C₂²×C₂₀	Abelian group of type [2,2,20]	80		C2^2xC20	80,45
C₂³×C₁₀	Abelian group of type [2,2,2,10]	80		C2^3xC10	80,52
D₄×D₅	Direct product of D₄ and D₅	20	4+	D4xD5	80,39
C₄×F₅	Direct product of C₄ and F₅	20	4	C4xF5	80,30
C₂²×F₅	Direct product of C₂² and F₅	20		C2^2xF5	80,50
C₈×D₅	Direct product of C₈ and D₅	40	2	C8xD5	80,4
C₅×D₈	Direct product of C₅ and D₈	40	2	C5xD8	80,25
Q₈×D₅	Direct product of Q₈ and D₅	40	4-	Q8xD5	80,41
C₂×D₂₀	Direct product of C₂ and D₂₀	40		C2xD20	80,37
D₄×C₁₀	Direct product of C₁₀ and D₄	40		D4xC10	80,46
C₅×SD₁₆	Direct product of C₅ and SD₁₆	40	2	C5xSD16	80,26
C₂³×D₅	Direct product of C₂³ and D₅	40		C2^3xD5	80,51
C₅×M₄(2)	Direct product of C₅ and M₄(2)	40	2	C5xM4(2)	80,24
C₅×Q₁₆	Direct product of C₅ and Q₁₆	80	2	C5xQ16	80,27
Q₈×C₁₀	Direct product of C₁₀ and Q₈	80		Q8xC10	80,47
C₄×Dic₅	Direct product of C₄ and Dic₅	80		C4xDic5	80,11
C₂×Dic₁₀	Direct product of C₂ and Dic₁₀	80		C2xDic10	80,35
C₂²×Dic₅	Direct product of C₂² and Dic₅	80		C2^2xDic5	80,43
C₂×C₄×D₅	Direct product of C₂×C₄ and D₅	40		C2xC4xD5	80,36
C₂×C₅⋊D₄	Direct product of C₂ and C₅⋊D₄	40		C2xC5:D4	80,44
C₅×C₄○D₄	Direct product of C₅ and C₄○D₄	40	2	C5xC4oD4	80,48
C₅×C₂²⋊C₄	Direct product of C₅ and C₂²⋊C₄	40		C5xC2^2:C4	80,21
C₂×C₅⋊C₈	Direct product of C₂ and C₅⋊C₈	80		C2xC5:C8	80,32
C₅×C₄⋊C₄	Direct product of C₅ and C₄⋊C₄	80		C5xC4:C4	80,22
C₂×C₅⋊₂C₈	Direct product of C₂ and C₅⋊₂C₈	80		C2xC5:2C8	80,9

Groups of order 81

		d	ρ	Label	ID
C₈₁	Cyclic group	81	1	C81	81,1
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	9	3	C3wrC3	81,7
C₉○He₃	Central product of C₉ and He₃	27	3	C9oHe3	81,14
C₂₇⋊C₃	The semidirect product of C₂₇ and C₃ acting faithfully	27	3	C27:C3	81,6
C₃²⋊C₉	The semidirect product of C₃² and C₉ acting via C₉/C₃=C₃	27		C3^2:C9	81,3
He₃⋊C₃	2^nd semidirect product of He₃ and C₃ acting faithfully	27	3	He3:C3	81,9
C₉⋊C₉	The semidirect product of C₉ and C₉ acting via C₉/C₃=C₃	81		C9:C9	81,4
He₃.C₃	The non-split extension by He₃ of C₃ acting faithfully	27	3	He3.C3	81,8
C₃.He₃	4^th central stem extension by C₃ of He₃	27	3	C3.He3	81,10
C₉²	Abelian group of type [9,9]	81		C9^2	81,2
C₃⁴	Elementary abelian group of type [3,3,3,3]	81		C3^4	81,15
C₃×C₂₇	Abelian group of type [3,27]	81		C3xC27	81,5
C₃²×C₉	Abelian group of type [3,3,9]	81		C3^2xC9	81,11
C₃×He₃	Direct product of C₃ and He₃	27		C3xHe3	81,12
C₃×3_-¹⁺²	Direct product of C₃ and 3_-¹⁺²	27		C3xES-(3,1)	81,13

Groups of order 82

		d	ρ	Label	ID
C₈₂	Cyclic group	82	1	C82	82,2
D₄₁	Dihedral group	41	2+	D41	82,1

Groups of order 83

		d	ρ	Label	ID
C₈₃	Cyclic group	83	1	C83	83,1

Groups of order 84

		d	ρ	Label	ID
C₈₄	Cyclic group	84	1	C84	84,6
D₄₂	Dihedral group; = C₂×D₂₁	42	2+	D42	84,14
Dic₂₁	Dicyclic group; = C₃ ⋊Dic₇	84	2-	Dic21	84,5
C₇⋊A₄	The semidirect product of C₇ and A₄ acting via A₄/C₂²=C₃	28	3	C7:A4	84,11
C₇⋊C₁₂	The semidirect product of C₇ and C₁₂ acting via C₁₂/C₂=C₆	28	6-	C7:C12	84,1
C₂×C₄₂	Abelian group of type [2,42]	84		C2xC42	84,15
C₂×F₇	Direct product of C₂ and F₇; = Aut(D₁₄) = Hol(C₁₄)	14	6+	C2xF7	84,7
S₃×D₇	Direct product of S₃ and D₇	21	4+	S3xD7	84,8
C₇×A₄	Direct product of C₇ and A₄	28	3	C7xA4	84,10
C₆×D₇	Direct product of C₆ and D₇	42	2	C6xD7	84,12
S₃×C₁₄	Direct product of C₁₄ and S₃	42	2	S3xC14	84,13
C₇×Dic₃	Direct product of C₇ and Dic₃	84	2	C7xDic3	84,3
C₃×Dic₇	Direct product of C₃ and Dic₇	84	2	C3xDic7	84,4
C₄×C₇⋊C₃	Direct product of C₄ and C₇⋊C₃	28	3	C4xC7:C3	84,2
C₂²×C₇⋊C₃	Direct product of C₂² and C₇⋊C₃	28		C2^2xC7:C3	84,9

Groups of order 85

		d	ρ	Label	ID
C₈₅	Cyclic group	85	1	C85	85,1

Groups of order 86

		d	ρ	Label	ID
C₈₆	Cyclic group	86	1	C86	86,2
D₄₃	Dihedral group	43	2+	D43	86,1

Groups of order 87

		d	ρ	Label	ID
C₈₇	Cyclic group	87	1	C87	87,1

Groups of order 88

		d	ρ	Label	ID
C₈₈	Cyclic group	88	1	C88	88,2
D₄₄	Dihedral group	44	2+	D44	88,5
Dic₂₂	Dicyclic group; = C₁₁ ⋊Q₈	88	2-	Dic22	88,3
C₁₁⋊D₄	The semidirect product of C₁₁ and D₄ acting via D₄/C₂²=C₂	44	2	C11:D4	88,7
C₁₁⋊C₈	The semidirect product of C₁₁ and C₈ acting via C₈/C₄=C₂	88	2	C11:C8	88,1
C₂×C₄₄	Abelian group of type [2,44]	88		C2xC44	88,8
C₂²×C₂₂	Abelian group of type [2,2,22]	88		C2^2xC22	88,12
C₄×D₁₁	Direct product of C₄ and D₁₁	44	2	C4xD11	88,4
D₄×C₁₁	Direct product of C₁₁ and D₄	44	2	D4xC11	88,9
C₂²×D₁₁	Direct product of C₂² and D₁₁	44		C2^2xD11	88,11
Q₈×C₁₁	Direct product of C₁₁ and Q₈	88	2	Q8xC11	88,10
C₂×Dic₁₁	Direct product of C₂ and Dic₁₁	88		C2xDic11	88,6

Groups of order 89

		d	ρ	Label	ID
C₈₉	Cyclic group	89	1	C89	89,1

Groups of order 90

		d	ρ	Label	ID
C₉₀	Cyclic group	90	1	C90	90,4
D₄₅	Dihedral group	45	2+	D45	90,3
C₃⋊D₁₅	The semidirect product of C₃ and D₁₅ acting via D₁₅/C₁₅=C₂	45		C3:D15	90,9
C₃×C₃₀	Abelian group of type [3,30]	90		C3xC30	90,10
S₃×C₁₅	Direct product of C₁₅ and S₃	30	2	S3xC15	90,6
C₃×D₁₅	Direct product of C₃ and D₁₅	30	2	C3xD15	90,7
C₅×D₉	Direct product of C₅ and D₉	45	2	C5xD9	90,1
C₉×D₅	Direct product of C₉ and D₅	45	2	C9xD5	90,2
C₃²×D₅	Direct product of C₃² and D₅	45		C3^2xD5	90,5
C₅×C₃⋊S₃	Direct product of C₅ and C₃⋊S₃	45		C5xC3:S3	90,8

Groups of order 91

		d	ρ	Label	ID
C₉₁	Cyclic group	91	1	C91	91,1

Groups of order 92

		d	ρ	Label	ID
C₉₂	Cyclic group	92	1	C92	92,2
D₄₆	Dihedral group; = C₂×D₂₃	46	2+	D46	92,3
Dic₂₃	Dicyclic group; = C₂₃ ⋊C₄	92	2-	Dic23	92,1
C₂×C₄₆	Abelian group of type [2,46]	92		C2xC46	92,4

Groups of order 93

		d	ρ	Label	ID
C₉₃	Cyclic group	93	1	C93	93,2
C₃₁⋊C₃	The semidirect product of C₃₁ and C₃ acting faithfully	31	3	C31:C3	93,1

Groups of order 94

		d	ρ	Label	ID
C₉₄	Cyclic group	94	1	C94	94,2
D₄₇	Dihedral group	47	2+	D47	94,1

Groups of order 95

		d	ρ	Label	ID
C₉₅	Cyclic group	95	1	C95	95,1

Groups of order 96

		d	ρ	Label	ID
C₉₆	Cyclic group	96	1	C96	96,2
D₄₈	Dihedral group	48	2+	D48	96,6
Dic₂₄	Dicyclic group; = C₃ ⋊₁ Q₃₂	96	2-	Dic24	96,8
U₂(𝔽₃)	Unitary group on 𝔽₃²; = SL₂(𝔽₃)⋊₂ C₄	24	2	U(2,3)	96,67
D₄○D₁₂	Central product of D₄ and D₁₂	24	4+	D4oD12	96,216
C₈○D₁₂	Central product of C₈ and D₁₂	48	2	C8oD12	96,108
C₄○D₂₄	Central product of C₄ and D₂₄	48	2	C4oD24	96,111
Q₈○D₁₂	Central product of Q₈ and D₁₂	48	4-	Q8oD12	96,217
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	8	6+	C2^2:S4	96,227
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	8	6+	C2^4:C6	96,70
C₂³⋊A₄	2^nd semidirect product of C₂³ and A₄ acting faithfully	8	4+	C2^3:A4	96,204
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	12	6+	C4:S4	96,187
C₄²⋊S₃	The semidirect product of C₄² and S₃ acting faithfully	12	3	C4^2:S3	96,64
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	12	6+	A4:D4	96,195
C₄²⋊C₆	1^st semidirect product of C₄² and C₆ acting faithfully	16	6	C4^2:C6	96,71
A₄⋊C₈	The semidirect product of A₄ and C₈ acting via C₈/C₄=C₂	24	3	A4:C8	96,65
A₄⋊Q₈	The semidirect product of A₄ and Q₈ acting via Q₈/C₄=C₂	24	6-	A4:Q8	96,185
C₈⋊D₆	1^st semidirect product of C₈ and D₆ acting via D₆/C₃=C₂²	24	4+	C8:D6	96,115
D₆⋊D₄	1^st semidirect product of D₆ and D₄ acting via D₄/C₂²=C₂	24		D6:D4	96,89
D₈⋊S₃	2^nd semidirect product of D₈ and S₃ acting via S₃/C₃=C₂	24	4	D8:S3	96,118
D₄⋊D₆	2^nd semidirect product of D₄ and D₆ acting via D₆/C₆=C₂	24	4+	D4:D6	96,156
D₄⋊₆D₆	2^nd semidirect product of D₄ and D₆ acting through Inn(D₄)	24	4	D4:6D6	96,211
Q₈⋊₃D₆	2^nd semidirect product of Q₈ and D₆ acting via D₆/S₃=C₂	24	4+	Q8:3D6	96,121
Q₈⋊A₄	1^st semidirect product of Q₈ and A₄ acting via A₄/C₂²=C₃	24	6-	Q8:A4	96,203
D₁₂⋊C₄	4^th semidirect product of D₁₂ and C₄ acting via C₄/C₂=C₂	24	4	D12:C4	96,32
C₄²⋊₄S₃	3^rd semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	24	2	C4^2:4S3	96,12
C₂⁴⋊₄S₃	1^st semidirect product of C₂⁴ and S₃ acting via S₃/C₃=C₂	24		C2^4:4S3	96,160
C₂³⋊₂D₆	1^st semidirect product of C₂³ and D₆ acting via D₆/C₃=C₂²	24		C2^3:2D6	96,144
Q₈⋊₃Dic₃	2^nd semidirect product of Q₈ and Dic₃ acting via Dic₃/C₆=C₂	24	4	Q8:3Dic3	96,44
D₁₂⋊₆C₂²	4^th semidirect product of D₁₂ and C₂² acting via C₂²/C₂=C₂	24	4	D12:6C2^2	96,139
Q₈⋊Dic₃	The semidirect product of Q₈ and Dic₃ acting via Dic₃/C₂=S₃	32		Q8:Dic3	96,66
D₆⋊C₈	The semidirect product of D₆ and C₈ acting via C₈/C₄=C₂	48		D6:C8	96,27
C₃⋊D₁₆	The semidirect product of C₃ and D₁₆ acting via D₁₆/D₈=C₂	48	4+	C3:D16	96,33
C₄₈⋊C₂	2^nd semidirect product of C₄₈ and C₂ acting faithfully	48	2	C48:C2	96,7
D₈⋊₃S₃	The semidirect product of D₈ and S₃ acting through Inn(D₈)	48	4-	D8:3S3	96,119
D₆⋊₃D₄	3^rd semidirect product of D₆ and D₄ acting via D₄/C₄=C₂	48		D6:3D4	96,145
C₄⋊D₁₂	The semidirect product of C₄ and D₁₂ acting via D₁₂/C₁₂=C₂	48		C4:D12	96,81
C₁₂⋊D₄	1^st semidirect product of C₁₂ and D₄ acting via D₄/C₂=C₂²	48		C12:D4	96,102
C₁₂⋊₇D₄	1^st semidirect product of C₁₂ and D₄ acting via D₄/C₂²=C₂	48		C12:7D4	96,137
C₁₂⋊₃D₄	3^rd semidirect product of C₁₂ and D₄ acting via D₄/C₂=C₂²	48		C12:3D4	96,147
D₆⋊Q₈	1^st semidirect product of D₆ and Q₈ acting via Q₈/C₄=C₂	48		D6:Q8	96,103
D₆⋊₃Q₈	3^rd semidirect product of D₆ and Q₈ acting via Q₈/C₄=C₂	48		D6:3Q8	96,153
D₂₄⋊C₂	5^th semidirect product of D₂₄ and C₂ acting faithfully	48	4+	D24:C2	96,126
C₄²⋊₂S₃	1^st semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	48		C4^2:2S3	96,79
C₄²⋊₇S₃	6^th semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	48		C4^2:7S3	96,82
C₄²⋊₃S₃	2^nd semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	48		C4^2:3S3	96,83
Q₁₆⋊S₃	2^nd semidirect product of Q₁₆ and S₃ acting via S₃/C₃=C₂	48	4	Q16:S3	96,125
D₄⋊Dic₃	1^st semidirect product of D₄ and Dic₃ acting via Dic₃/C₆=C₂	48		D4:Dic3	96,39
Dic₃⋊₄D₄	1^st semidirect product of Dic₃ and D₄ acting through Inn(Dic₃)	48		Dic3:4D4	96,88
Dic₃⋊D₄	1^st semidirect product of Dic₃ and D₄ acting via D₄/C₂²=C₂	48		Dic3:D4	96,91
Dic₃⋊₅D₄	2^nd semidirect product of Dic₃ and D₄ acting through Inn(Dic₃)	48		Dic3:5D4	96,100
C₃⋊C₃₂	The semidirect product of C₃ and C₃₂ acting via C₃₂/C₁₆=C₂	96	2	C3:C32	96,1
C₁₂⋊Q₈	The semidirect product of C₁₂ and Q₈ acting via Q₈/C₂=C₂²	96		C12:Q8	96,95
C₁₂⋊C₈	1^st semidirect product of C₁₂ and C₈ acting via C₈/C₄=C₂	96		C12:C8	96,11
C₂₄⋊C₄	5^th semidirect product of C₂₄ and C₄ acting via C₄/C₂=C₂	96		C24:C4	96,22
C₂₄⋊₁C₄	1^st semidirect product of C₂₄ and C₄ acting via C₄/C₂=C₂	96		C24:1C4	96,25
C₃⋊Q₃₂	The semidirect product of C₃ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	96	4-	C3:Q32	96,36
Dic₃⋊C₈	The semidirect product of Dic₃ and C₈ acting via C₈/C₄=C₂	96		Dic3:C8	96,21
C₁₂⋊₂Q₈	1^st semidirect product of C₁₂ and Q₈ acting via Q₈/C₄=C₂	96		C12:2Q8	96,76
C₈⋊Dic₃	2^nd semidirect product of C₈ and Dic₃ acting via Dic₃/C₆=C₂	96		C8:Dic3	96,24
Q₈⋊₂Dic₃	1^st semidirect product of Q₈ and Dic₃ acting via Dic₃/C₆=C₂	96		Q8:2Dic3	96,42
Dic₆⋊C₄	5^th semidirect product of Dic₆ and C₄ acting via C₄/C₂=C₂	96		Dic6:C4	96,94
Dic₃⋊Q₈	2^nd semidirect product of Dic₃ and Q₈ acting via Q₈/C₄=C₂	96		Dic3:Q8	96,151
C₄⋊C₄⋊₇S₃	1^st semidirect product of C₄⋊C₄ and S₃ acting through Inn(C₄⋊C₄)	48		C4:C4:7S3	96,99
C₄⋊C₄⋊S₃	6^th semidirect product of C₄⋊C₄ and S₃ acting via S₃/C₃=C₂	48		C4:C4:S3	96,105
C₂³.₃A₄	1^st non-split extension by C₂³ of A₄ acting via A₄/C₂²=C₃	12	6+	C2^3.3A4	96,3
C₂³.A₄	2^nd non-split extension by C₂³ of A₄ acting faithfully	12	6+	C2^3.A4	96,72
D₄.A₄	The non-split extension by D₄ of A₄ acting through Inn(D₄)	16	4-	D4.A4	96,202
C₄.₆S₄	3^rd central extension by C₄ of S₄	16	2	C4.6S4	96,192
C₄.₃S₄	3^rd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	16	4+	C4.3S4	96,193
Q₈.D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/C₂=S₃	16	4-	Q8.D6	96,190
Q₈.A₄	The non-split extension by Q₈ of A₄ acting through Inn(Q₈)	24	4+	Q8.A4	96,201
C₁₂.D₄	8^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	24	4	C12.D4	96,40
C₁₂.₄₆D₄	3^rd non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	24	4+	C12.46D4	96,30
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	24	4	C2^3.6D6	96,13
C₂³.₇D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	24	4	C2^3.7D6	96,41
C₈.A₄	The central extension by C₈ of A₄	32	2	C8.A4	96,74
C₄.S₄	2^nd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	32	4-	C4.S4	96,191
D₆.C₈	The non-split extension by D₆ of C₈ acting via C₈/C₄=C₂	48	2	D6.C8	96,5
D₈.S₃	The non-split extension by D₈ of S₃ acting via S₃/C₃=C₂	48	4-	D8.S3	96,34
D₁₂.C₄	The non-split extension by D₁₂ of C₄ acting via C₄/C₂=C₂	48	4	D12.C4	96,114
C₆.D₈	2^nd non-split extension by C₆ of D₈ acting via D₈/D₄=C₂	48		C6.D8	96,16
C₈.₆D₆	3^rd non-split extension by C₈ of D₆ acting via D₆/S₃=C₂	48	4+	C8.6D6	96,35
C₈.D₆	1^st non-split extension by C₈ of D₆ acting via D₆/C₃=C₂²	48	4-	C8.D6	96,116
C₁₂.C₈	1^st non-split extension by C₁₂ of C₈ acting via C₈/C₄=C₂	48	2	C12.C8	96,19
C₂₄.C₄	1^st non-split extension by C₂₄ of C₄ acting via C₄/C₂=C₂	48	2	C24.C4	96,26
D₆.D₄	2^nd non-split extension by D₆ of D₄ acting via D₄/C₂²=C₂	48		D6.D4	96,101
D₄.D₆	4^th non-split extension by D₄ of D₆ acting via D₆/S₃=C₂	48	4-	D4.D6	96,122
C₂.D₂₄	2^nd central extension by C₂ of D₂₄	48		C2.D24	96,28
D₄.Dic₃	The non-split extension by D₄ of Dic₃ acting through Inn(D₄)	48	4	D4.Dic3	96,155
Q₈.₇D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/S₃=C₂	48	4	Q8.7D6	96,123
C₁₂.₅₃D₄	10^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48	4	C12.53D4	96,29
C₁₂.₄₇D₄	4^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48	4-	C12.47D4	96,31
C₁₂.₅₅D₄	12^nd non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48		C12.55D4	96,37
C₁₂.₁₀D₄	10^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	C12.10D4	96,43
C₄.D₁₂	5^th non-split extension by C₄ of D₁₂ acting via D₁₂/D₆=C₂	48		C4.D12	96,104
C₁₂.₄₈D₄	5^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48		C12.48D4	96,131
C₁₂.₂₃D₄	23^rd non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	48		C12.23D4	96,154
Q₈.₁₁D₆	1^st non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4	Q8.11D6	96,149
Q₈.₁₃D₆	3^rd non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4	Q8.13D6	96,157
Q₈.₁₄D₆	4^th non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4-	Q8.14D6	96,158
Q₈.₁₅D₆	1^st non-split extension by Q₈ of D₆ acting through Inn(Q₈)	48	4	Q8.15D6	96,214
C₂³.₈D₆	3^rd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.8D6	96,86
C₂³.₉D₆	4^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.9D6	96,90
Dic₃.D₄	1^st non-split extension by Dic₃ of D₄ acting via D₄/C₂²=C₂	48		Dic3.D4	96,85
C₂³.₁₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/S₃=C₂	48		C2^3.16D6	96,84
C₂³.₁₁D₆	6^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.11D6	96,92
C₂³.₂₁D₆	6^th non-split extension by C₂³ of D₆ acting via D₆/S₃=C₂	48		C2^3.21D6	96,93
C₂³.₂₆D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₆=C₂	48		C2^3.26D6	96,133
C₂³.₂₈D₆	4^th non-split extension by C₂³ of D₆ acting via D₆/C₆=C₂	48		C2^3.28D6	96,136
C₂³.₂₃D₆	8^th non-split extension by C₂³ of D₆ acting via D₆/S₃=C₂	48		C2^3.23D6	96,142
C₂³.₁₂D₆	7^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.12D6	96,143
C₂³.₁₄D₆	9^th non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	48		C2^3.14D6	96,146
Dic₃.Q₈	The non-split extension by Dic₃ of Q₈ acting via Q₈/C₄=C₂	96		Dic3.Q8	96,96
C₆.Q₁₆	1^st non-split extension by C₆ of Q₁₆ acting via Q₁₆/Q₈=C₂	96		C6.Q16	96,14
C₁₂.Q₈	2^nd non-split extension by C₁₂ of Q₈ acting via Q₈/C₂=C₂²	96		C12.Q8	96,15
C₁₂.₆Q₈	3^rd non-split extension by C₁₂ of Q₈ acting via Q₈/C₄=C₂	96		C12.6Q8	96,77
C₄².S₃	1^st non-split extension by C₄² of S₃ acting via S₃/C₃=C₂	96		C4^2.S3	96,10
C₆.C₄²	5^th non-split extension by C₆ of C₄² acting via C₄²/C₂×C₄=C₂	96		C6.C4^2	96,38
C₆.SD₁₆	2^nd non-split extension by C₆ of SD₁₆ acting via SD₁₆/D₄=C₂	96		C6.SD16	96,17
C₄.Dic₆	3^rd non-split extension by C₄ of Dic₆ acting via Dic₆/Dic₃=C₂	96		C4.Dic6	96,97
C₂.Dic₁₂	1^st central extension by C₂ of Dic₁₂	96		C2.Dic12	96,23
C₄×C₂₄	Abelian group of type [4,24]	96		C4xC24	96,46
C₂×C₄₈	Abelian group of type [2,48]	96		C2xC48	96,59
C₂⁴×C₆	Abelian group of type [2,2,2,2,6]	96		C2^4xC6	96,231
C₂²×C₂₄	Abelian group of type [2,2,24]	96		C2^2xC24	96,176
C₂³×C₁₂	Abelian group of type [2,2,2,12]	96		C2^3xC12	96,220
C₂×C₄×C₁₂	Abelian group of type [2,4,12]	96		C2xC4xC12	96,161
C₄×S₄	Direct product of C₄ and S₄	12	3	C4xS4	96,186
D₄×A₄	Direct product of D₄ and A₄	12	6+	D4xA4	96,197
C₂²×S₄	Direct product of C₂² and S₄	12		C2^2xS4	96,226
C₂×GL₂(𝔽₃)	Direct product of C₂ and GL₂(𝔽₃)	16		C2xGL(2,3)	96,189
C₈×A₄	Direct product of C₈ and A₄	24	3	C8xA4	96,73
S₃×D₈	Direct product of S₃ and D₈	24	4+	S3xD8	96,117
Q₈×A₄	Direct product of Q₈ and A₄	24	6-	Q8xA4	96,199
C₂³×A₄	Direct product of C₂³ and A₄	24		C2^3xA4	96,228
S₃×SD₁₆	Direct product of S₃ and SD₁₆	24	4	S3xSD16	96,120
S₃×M₄(2)	Direct product of S₃ and M₄(2)	24	4	S3xM4(2)	96,113
C₃×2₊¹⁺⁴	Direct product of C₃ and 2₊¹⁺⁴	24	4	C3xES+(2,2)	96,224
C₄×SL₂(𝔽₃)	Direct product of C₄ and SL₂(𝔽₃)	32		C4xSL(2,3)	96,69
C₂×CSU₂(𝔽₃)	Direct product of C₂ and CSU₂(𝔽₃)	32		C2xCSU(2,3)	96,188
C₂²×SL₂(𝔽₃)	Direct product of C₂² and SL₂(𝔽₃)	32		C2^2xSL(2,3)	96,198
C₆×D₈	Direct product of C₆ and D₈	48		C6xD8	96,179
S₃×C₁₆	Direct product of C₁₆ and S₃	48	2	S3xC16	96,4
C₃×D₁₆	Direct product of C₃ and D₁₆	48	2	C3xD16	96,61
C₄×D₁₂	Direct product of C₄ and D₁₂	48		C4xD12	96,80
C₂×D₂₄	Direct product of C₂ and D₂₄	48		C2xD24	96,110
D₄×C₁₂	Direct product of C₁₂ and D₄	48		D4xC12	96,165
S₃×Q₁₆	Direct product of S₃ and Q₁₆	48	4-	S3xQ16	96,124
S₃×C₄²	Direct product of C₄² and S₃	48		S3xC4^2	96,78
S₃×C₂⁴	Direct product of C₂⁴ and S₃	48		S3xC2^4	96,230
C₃×SD₃₂	Direct product of C₃ and SD₃₂	48	2	C3xSD32	96,62
D₄×Dic₃	Direct product of D₄ and Dic₃	48		D4xDic3	96,141
C₆×SD₁₆	Direct product of C₆ and SD₁₆	48		C6xSD16	96,180
C₂²×D₁₂	Direct product of C₂² and D₁₂	48		C2^2xD12	96,207
C₃×M₅(2)	Direct product of C₃ and M₅(2)	48	2	C3xM5(2)	96,60
C₆×M₄(2)	Direct product of C₆ and M₄(2)	48		C6xM4(2)	96,177
C₃×2_-¹⁺⁴	Direct product of C₃ and 2_-¹⁺⁴	48	4	C3xES-(2,2)	96,225
C₃×Q₃₂	Direct product of C₃ and Q₃₂	96	2	C3xQ32	96,63
Q₈×C₁₂	Direct product of C₁₂ and Q₈	96		Q8xC12	96,166
C₆×Q₁₆	Direct product of C₆ and Q₁₆	96		C6xQ16	96,181
C₈×Dic₃	Direct product of C₈ and Dic₃	96		C8xDic3	96,20
C₄×Dic₆	Direct product of C₄ and Dic₆	96		C4xDic6	96,75
Q₈×Dic₃	Direct product of Q₈ and Dic₃	96		Q8xDic3	96,152
C₂×Dic₁₂	Direct product of C₂ and Dic₁₂	96		C2xDic12	96,112
C₂²×Dic₆	Direct product of C₂² and Dic₆	96		C2^2xDic6	96,205
C₂³×Dic₃	Direct product of C₂³ and Dic₃	96		C2^3xDic3	96,218
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	12	3	C2xC4^2:C3	96,68
C₂×C₂²⋊A₄	Direct product of C₂ and C₂²⋊A₄	12		C2xC2^2:A4	96,229
C₂×C₄×A₄	Direct product of C₂×C₄ and A₄	24		C2xC4xA4	96,196
C₂×S₃×D₄	Direct product of C₂, S₃ and D₄	24		C2xS3xD4	96,209
C₃×C₄≀C₂	Direct product of C₃ and C₄≀C₂	24	2	C3xC4wrC2	96,54
C₂×A₄⋊C₄	Direct product of C₂ and A₄⋊C₄	24		C2xA4:C4	96,194
S₃×C₄○D₄	Direct product of S₃ and C₄○D₄	24	4	S3xC4oD4	96,215
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	24	4	C3xC2^3:C4	96,49
S₃×C₂²⋊C₄	Direct product of S₃ and C₂²⋊C₄	24		S3xC2^2:C4	96,87
C₃×C₈⋊C₂²	Direct product of C₃ and C₈⋊C₂²	24	4	C3xC8:C2^2	96,183
C₃×C₄.D₄	Direct product of C₃ and C₄.D₄	24	4	C3xC4.D4	96,50
C₃×C₂²≀C₂	Direct product of C₃ and C₂²≀C₂	24		C3xC2^2wrC2	96,167
C₂×C₄.A₄	Direct product of C₂ and C₄.A₄	32		C2xC4.A4	96,200
S₃×C₂×C₈	Direct product of C₂×C₈ and S₃	48		S3xC2xC8	96,106
D₄×C₂×C₆	Direct product of C₂×C₆ and D₄	48		D4xC2xC6	96,221
S₃×C₄⋊C₄	Direct product of S₃ and C₄⋊C₄	48		S3xC4:C4	96,98
C₂×S₃×Q₈	Direct product of C₂, S₃ and Q₈	48		C2xS3xQ8	96,212
C₄×C₃⋊D₄	Direct product of C₄ and C₃⋊D₄	48		C4xC3:D4	96,135
C₂×C₈⋊S₃	Direct product of C₂ and C₈⋊S₃	48		C2xC8:S3	96,107
C₂×D₆⋊C₄	Direct product of C₂ and D₆⋊C₄	48		C2xD6:C4	96,134
C₂×D₄⋊S₃	Direct product of C₂ and D₄⋊S₃	48		C2xD4:S3	96,138
C₃×C₈○D₄	Direct product of C₃ and C₈○D₄	48	2	C3xC8oD4	96,178
C₃×C₄○D₈	Direct product of C₃ and C₄○D₈	48	2	C3xC4oD8	96,182
C₆×C₄○D₄	Direct product of C₆ and C₄○D₄	48		C6xC4oD4	96,223
C₃×C₄⋊D₄	Direct product of C₃ and C₄⋊D₄	48		C3xC4:D4	96,168
S₃×C₂²×C₄	Direct product of C₂²×C₄ and S₃	48		S3xC2^2xC4	96,206
C₂×C₂₄⋊C₂	Direct product of C₂ and C₂₄⋊C₂	48		C2xC24:C2	96,109
C₂×C₄○D₁₂	Direct product of C₂ and C₄○D₁₂	48		C2xC4oD12	96,208
C₃×D₄⋊C₄	Direct product of C₃ and D₄⋊C₄	48		C3xD4:C4	96,52
C₃×C₈.C₄	Direct product of C₃ and C₈.C₄	48	2	C3xC8.C4	96,58
C₃×C₄⋊₁D₄	Direct product of C₃ and C₄⋊₁D₄	48		C3xC4:1D4	96,174
C₃×C₂²⋊C₈	Direct product of C₃ and C₂²⋊C₈	48		C3xC2^2:C8	96,48
C₆×C₂²⋊C₄	Direct product of C₆ and C₂²⋊C₄	48		C6xC2^2:C4	96,162
C₂×D₄.S₃	Direct product of C₂ and D₄.S₃	48		C2xD4.S3	96,140
C₂×C₆.D₄	Direct product of C₂ and C₆.D₄	48		C2xC6.D4	96,159
C₂²×C₃⋊D₄	Direct product of C₂² and C₃⋊D₄	48		C2^2xC3:D4	96,219
C₃×C₂²⋊Q₈	Direct product of C₃ and C₂²⋊Q₈	48		C3xC2^2:Q8	96,169
C₂×D₄⋊₂S₃	Direct product of C₂ and D₄⋊₂S₃	48		C2xD4:2S3	96,210
C₃×C₄²⋊C₂	Direct product of C₃ and C₄²⋊C₂	48		C3xC4^2:C2	96,164
C₂×Q₈⋊₂S₃	Direct product of C₂ and Q₈⋊₂S₃	48		C2xQ8:2S3	96,148
C₂×Q₈⋊₃S₃	Direct product of C₂ and Q₈⋊₃S₃	48		C2xQ8:3S3	96,213
C₃×C₄.₄D₄	Direct product of C₃ and C₄.₄D₄	48		C3xC4.4D4	96,171
C₃×C₈.C₂²	Direct product of C₃ and C₈.C₂²	48	4	C3xC8.C2^2	96,184
C₂×C₄.Dic₃	Direct product of C₂ and C₄.Dic₃	48		C2xC4.Dic3	96,128
C₃×C₄²⋊₂C₂	Direct product of C₃ and C₄²⋊₂C₂	48		C3xC4^2:2C2	96,173
C₃×C₄.₁₀D₄	Direct product of C₃ and C₄.₁₀D₄	48	4	C3xC4.10D4	96,51
C₃×C₂².D₄	Direct product of C₃ and C₂².D₄	48		C3xC2^2.D4	96,170
C₄×C₃⋊C₈	Direct product of C₄ and C₃⋊C₈	96		C4xC3:C8	96,9
C₃×C₄⋊C₈	Direct product of C₃ and C₄⋊C₈	96		C3xC4:C8	96,55
C₆×C₄⋊C₄	Direct product of C₆ and C₄⋊C₄	96		C6xC4:C4	96,163
C₂×C₃⋊C₁₆	Direct product of C₂ and C₃⋊C₁₆	96		C2xC3:C16	96,18
Q₈×C₂×C₆	Direct product of C₂×C₆ and Q₈	96		Q8xC2xC6	96,222
C₃×C₄⋊Q₈	Direct product of C₃ and C₄⋊Q₈	96		C3xC4:Q8	96,175
C₃×C₈⋊C₄	Direct product of C₃ and C₈⋊C₄	96		C3xC8:C4	96,47
C₂²×C₃⋊C₈	Direct product of C₂² and C₃⋊C₈	96		C2^2xC3:C8	96,127
C₂×C₄×Dic₃	Direct product of C₂×C₄ and Dic₃	96		C2xC4xDic3	96,129
C₂×C₃⋊Q₁₆	Direct product of C₂ and C₃⋊Q₁₆	96		C2xC3:Q16	96,150
C₂×C₄⋊Dic₃	Direct product of C₂ and C₄⋊Dic₃	96		C2xC4:Dic3	96,132
C₃×Q₈⋊C₄	Direct product of C₃ and Q₈⋊C₄	96		C3xQ8:C4	96,53
C₃×C₂.D₈	Direct product of C₃ and C₂.D₈	96		C3xC2.D8	96,57
C₃×C₄.Q₈	Direct product of C₃ and C₄.Q₈	96		C3xC4.Q8	96,56
C₂×Dic₃⋊C₄	Direct product of C₂ and Dic₃⋊C₄	96		C2xDic3:C4	96,130
C₃×C₂.C₄²	Direct product of C₃ and C₂.C₄²	96		C3xC2.C4^2	96,45
C₃×C₄².C₂	Direct product of C₃ and C₄².C₂	96		C3xC4^2.C2	96,172

Groups of order 97

		d	ρ	Label	ID
C₉₇	Cyclic group	97	1	C97	97,1

Groups of order 98

		d	ρ	Label	ID
C₉₈	Cyclic group	98	1	C98	98,2
D₄₉	Dihedral group	49	2+	D49	98,1
C₇⋊D₇	The semidirect product of C₇ and D₇ acting via D₇/C₇=C₂	49		C7:D7	98,4
C₇×C₁₄	Abelian group of type [7,14]	98		C7xC14	98,5
C₇×D₇	Direct product of C₇ and D₇; = AΣL₁(𝔽₄₉)	14	2	C7xD7	98,3

Groups of order 99

		d	ρ	Label	ID
C₉₉	Cyclic group	99	1	C99	99,1
C₃×C₃₃	Abelian group of type [3,33]	99		C3xC33	99,2

Groups of order 100

		d	ρ	Label	ID
C₁₀₀	Cyclic group	100	1	C100	100,2
D₅₀	Dihedral group; = C₂×D₂₅	50	2+	D50	100,4
Dic₂₅	Dicyclic group; = C₂₅ ⋊₂ C₄	100	2-	Dic25	100,1
C₅²⋊C₄	4^th semidirect product of C₅² and C₄ acting faithfully	10	4+	C5^2:C4	100,12
C₂₅⋊C₄	The semidirect product of C₂₅ and C₄ acting faithfully	25	4+	C25:C4	100,3
C₅⋊F₅	1^st semidirect product of C₅ and F₅ acting via F₅/C₅=C₄	25		C5:F5	100,11
C₅²⋊₆C₄	2^nd semidirect product of C₅² and C₄ acting via C₄/C₂=C₂	100		C5^2:6C4	100,7
D₅.D₅	The non-split extension by D₅ of D₅ acting via D₅/C₅=C₂	20	4	D5.D5	100,10
C₁₀²	Abelian group of type [10,10]	100		C10^2	100,16
C₂×C₅₀	Abelian group of type [2,50]	100		C2xC50	100,5
C₅×C₂₀	Abelian group of type [5,20]	100		C5xC20	100,8
D₅²	Direct product of D₅ and D₅	10	4+	D5^2	100,13
C₅×F₅	Direct product of C₅ and F₅	20	4	C5xF5	100,9
D₅×C₁₀	Direct product of C₁₀ and D₅	20	2	D5xC10	100,14
C₅×Dic₅	Direct product of C₅ and Dic₅	20	2	C5xDic5	100,6
C₂×C₅⋊D₅	Direct product of C₂ and C₅⋊D₅	50		C2xC5:D5	100,15

Groups of order 101

		d	ρ	Label	ID
C₁₀₁	Cyclic group	101	1	C101	101,1

Groups of order 102

		d	ρ	Label	ID
C₁₀₂	Cyclic group	102	1	C102	102,4
D₅₁	Dihedral group	51	2+	D51	102,3
S₃×C₁₇	Direct product of C₁₇ and S₃	51	2	S3xC17	102,1
C₃×D₁₇	Direct product of C₃ and D₁₇	51	2	C3xD17	102,2

Groups of order 103

		d	ρ	Label	ID
C₁₀₃	Cyclic group	103	1	C103	103,1

Groups of order 104

		d	ρ	Label	ID
C₁₀₄	Cyclic group	104	1	C104	104,2
D₅₂	Dihedral group	52	2+	D52	104,6
Dic₂₆	Dicyclic group; = C₁₃ ⋊Q₈	104	2-	Dic26	104,4
C₁₃⋊D₄	The semidirect product of C₁₃ and D₄ acting via D₄/C₂²=C₂	52	2	C13:D4	104,8
C₁₃⋊C₈	The semidirect product of C₁₃ and C₈ acting via C₈/C₂=C₄	104	4-	C13:C8	104,3
C₁₃⋊₂C₈	The semidirect product of C₁₃ and C₈ acting via C₈/C₄=C₂	104	2	C13:2C8	104,1
C₂×C₅₂	Abelian group of type [2,52]	104		C2xC52	104,9
C₂²×C₂₆	Abelian group of type [2,2,26]	104		C2^2xC26	104,14
C₄×D₁₃	Direct product of C₄ and D₁₃	52	2	C4xD13	104,5
D₄×C₁₃	Direct product of C₁₃ and D₄	52	2	D4xC13	104,10
C₂²×D₁₃	Direct product of C₂² and D₁₃	52		C2^2xD13	104,13
Q₈×C₁₃	Direct product of C₁₃ and Q₈	104	2	Q8xC13	104,11
C₂×Dic₁₃	Direct product of C₂ and Dic₁₃	104		C2xDic13	104,7
C₂×C₁₃⋊C₄	Direct product of C₂ and C₁₃⋊C₄	26	4+	C2xC13:C4	104,12

Groups of order 105

		d	ρ	Label	ID
C₁₀₅	Cyclic group	105	1	C105	105,2
C₅×C₇⋊C₃	Direct product of C₅ and C₇⋊C₃	35	3	C5xC7:C3	105,1

Groups of order 106

		d	ρ	Label	ID
C₁₀₆	Cyclic group	106	1	C106	106,2
D₅₃	Dihedral group	53	2+	D53	106,1

Groups of order 107

		d	ρ	Label	ID
C₁₀₇	Cyclic group	107	1	C107	107,1

Groups of order 108

		d	ρ	Label	ID
C₁₀₈	Cyclic group	108	1	C108	108,2
D₅₄	Dihedral group; = C₂×D₂₇	54	2+	D54	108,4
Dic₂₇	Dicyclic group; = C₂₇ ⋊C₄	108	2-	Dic27	108,1
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	9	6+	C3^2:D6	108,17
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	12	4	C3^3:C4	108,37
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	12	4	C3^2:4D6	108,40
He₃⋊C₄	The semidirect product of He₃ and C₄ acting faithfully	18	3	He3:C4	108,15
C₃²⋊A₄	The semidirect product of C₃² and A₄ acting via A₄/C₂²=C₃	18	3	C3^2:A4	108,22
C₉⋊A₄	The semidirect product of C₉ and A₄ acting via A₄/C₂²=C₃	36	3	C9:A4	108,19
C₉⋊C₁₂	The semidirect product of C₉ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C9:C12	108,9
C₃²⋊C₁₂	The semidirect product of C₃² and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C3^2:C12	108,8
He₃⋊₃C₄	2^nd semidirect product of He₃ and C₄ acting via C₄/C₂=C₂	36	3	He3:3C4	108,11
C₉⋊Dic₃	The semidirect product of C₉ and Dic₃ acting via Dic₃/C₆=C₂	108		C9:Dic3	108,10
C₃³⋊₅C₄	3^rd semidirect product of C₃³ and C₄ acting via C₄/C₂=C₂	108		C3^3:5C4	108,34
C₃².A₄	The non-split extension by C₃² of A₄ acting via A₄/C₂²=C₃	18	3	C3^2.A4	108,21
C₉.A₄	The central extension by C₉ of A₄	54	3	C9.A4	108,3
C₂×C₅₄	Abelian group of type [2,54]	108		C2xC54	108,5
C₃×C₃₆	Abelian group of type [3,36]	108		C3xC36	108,12
C₆×C₁₈	Abelian group of type [6,18]	108		C6xC18	108,29
C₃×C₆²	Abelian group of type [3,6,6]	108		C3xC6^2	108,45
C₃²×C₁₂	Abelian group of type [3,3,12]	108		C3^2xC12	108,35
S₃×D₉	Direct product of S₃ and D₉	18	4+	S3xD9	108,16
C₉×A₄	Direct product of C₉ and A₄	36	3	C9xA4	108,18
C₆×D₉	Direct product of C₆ and D₉	36	2	C6xD9	108,23
S₃×C₁₈	Direct product of C₁₈ and S₃	36	2	S3xC18	108,24
C₄×He₃	Direct product of C₄ and He₃	36	3	C4xHe3	108,13
C₃²×A₄	Direct product of C₃² and A₄	36		C3^2xA4	108,41
C₃×Dic₉	Direct product of C₃ and Dic₉	36	2	C3xDic9	108,6
C₉×Dic₃	Direct product of C₉ and Dic₃	36	2	C9xDic3	108,7
C₂²×He₃	Direct product of C₂² and He₃	36		C2^2xHe3	108,30
C₃²×Dic₃	Direct product of C₃² and Dic₃	36		C3^2xDic3	108,32
C₄×3_-¹⁺²	Direct product of C₄ and 3_-¹⁺²	36	3	C4xES-(3,1)	108,14
C₂²×3_-¹⁺²	Direct product of C₂² and 3_-¹⁺²	36		C2^2xES-(3,1)	108,31
C₃×S₃²	Direct product of C₃, S₃ and S₃	12	4	C3xS3^2	108,38
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	12	4	C3xC3^2:C4	108,36
C₂×C₉⋊C₆	Direct product of C₂ and C₉⋊C₆; = Aut(D₁₈) = Hol(C₁₈)	18	6+	C2xC9:C6	108,26
S₃×C₃⋊S₃	Direct product of S₃ and C₃⋊S₃	18		S3xC3:S3	108,39
C₂×C₃²⋊C₆	Direct product of C₂ and C₃²⋊C₆	18	6+	C2xC3^2:C6	108,25
C₂×He₃⋊C₂	Direct product of C₂ and He₃⋊C₂	18	3	C2xHe3:C2	108,28
S₃×C₃×C₆	Direct product of C₃×C₆ and S₃	36		S3xC3xC6	108,42
C₆×C₃⋊S₃	Direct product of C₆ and C₃⋊S₃	36		C6xC3:S3	108,43
C₃×C₃⋊Dic₃	Direct product of C₃ and C₃⋊Dic₃	36		C3xC3:Dic3	108,33
C₂×C₉⋊S₃	Direct product of C₂ and C₉⋊S₃	54		C2xC9:S3	108,27
C₃×C₃.A₄	Direct product of C₃ and C₃.A₄	54		C3xC3.A4	108,20
C₂×C₃³⋊C₂	Direct product of C₂ and C₃³⋊C₂	54		C2xC3^3:C2	108,44

Groups of order 109

		d	ρ	Label	ID
C₁₀₉	Cyclic group	109	1	C109	109,1

Groups of order 110

		d	ρ	Label	ID
C₁₁₀	Cyclic group	110	1	C110	110,6
D₅₅	Dihedral group	55	2+	D55	110,5
F₁₁	Frobenius group; = C₁₁ ⋊C₁₀ = AGL₁(𝔽₁₁) = Aut(D₁₁) = Hol(C₁₁)	11	10+	F11	110,1
D₅×C₁₁	Direct product of C₁₁ and D₅	55	2	D5xC11	110,3
C₅×D₁₁	Direct product of C₅ and D₁₁	55	2	C5xD11	110,4
C₂×C₁₁⋊C₅	Direct product of C₂ and C₁₁⋊C₅	22	5	C2xC11:C5	110,2

Groups of order 111

		d	ρ	Label	ID
C₁₁₁	Cyclic group	111	1	C111	111,2
C₃₇⋊C₃	The semidirect product of C₃₇ and C₃ acting faithfully	37	3	C37:C3	111,1

Groups of order 112

		d	ρ	Label	ID
C₁₁₂	Cyclic group	112	1	C112	112,2
D₅₆	Dihedral group	56	2+	D56	112,6
Dic₂₈	Dicyclic group; = C₇ ⋊₁ Q₁₆	112	2-	Dic28	112,7
C₄○D₂₈	Central product of C₄ and D₂₈	56	2	C4oD28	112,30
D₄⋊D₇	The semidirect product of D₄ and D₇ acting via D₇/C₇=C₂	56	4+	D4:D7	112,14
Q₈⋊D₇	The semidirect product of Q₈ and D₇ acting via D₇/C₇=C₂	56	4+	Q8:D7	112,16
D₁₄⋊C₄	The semidirect product of D₁₄ and C₄ acting via C₄/C₂=C₂	56		D14:C4	112,13
C₈⋊D₇	3^rd semidirect product of C₈ and D₇ acting via D₇/C₇=C₂	56	2	C8:D7	112,4
C₅₆⋊C₂	2^nd semidirect product of C₅₆ and C₂ acting faithfully	56	2	C56:C2	112,5
D₄⋊₂D₇	The semidirect product of D₄ and D₇ acting through Inn(D₄)	56	4-	D4:2D7	112,32
Q₈⋊₂D₇	The semidirect product of Q₈ and D₇ acting through Inn(Q₈)	56	4+	Q8:2D7	112,34
C₇⋊C₁₆	The semidirect product of C₇ and C₁₆ acting via C₁₆/C₈=C₂	112	2	C7:C16	112,1
C₄⋊Dic₇	The semidirect product of C₄ and Dic₇ acting via Dic₇/C₁₄=C₂	112		C4:Dic7	112,12
C₇⋊Q₁₆	The semidirect product of C₇ and Q₁₆ acting via Q₁₆/Q₈=C₂	112	4-	C7:Q16	112,17
Dic₇⋊C₄	The semidirect product of Dic₇ and C₄ acting via C₄/C₂=C₂	112		Dic7:C4	112,11
D₄.D₇	The non-split extension by D₄ of D₇ acting via D₇/C₇=C₂	56	4-	D4.D7	112,15
C₄.Dic₇	The non-split extension by C₄ of Dic₇ acting via Dic₇/C₁₄=C₂	56	2	C4.Dic7	112,9
C₂³.D₇	The non-split extension by C₂³ of D₇ acting via D₇/C₇=C₂	56		C2^3.D7	112,18
C₄×C₂₈	Abelian group of type [4,28]	112		C4xC28	112,19
C₂×C₅₆	Abelian group of type [2,56]	112		C2xC56	112,22
C₂²×C₂₈	Abelian group of type [2,2,28]	112		C2^2xC28	112,37
C₂³×C₁₄	Abelian group of type [2,2,2,14]	112		C2^3xC14	112,43
C₂×F₈	Direct product of C₂ and F₈	14	7+	C2xF8	112,41
D₄×D₇	Direct product of D₄ and D₇	28	4+	D4xD7	112,31
C₈×D₇	Direct product of C₈ and D₇	56	2	C8xD7	112,3
C₇×D₈	Direct product of C₇ and D₈	56	2	C7xD8	112,24
Q₈×D₇	Direct product of Q₈ and D₇	56	4-	Q8xD7	112,33
C₂×D₂₈	Direct product of C₂ and D₂₈	56		C2xD28	112,29
D₄×C₁₄	Direct product of C₁₄ and D₄	56		D4xC14	112,38
C₇×SD₁₆	Direct product of C₇ and SD₁₆	56	2	C7xSD16	112,25
C₂³×D₇	Direct product of C₂³ and D₇	56		C2^3xD7	112,42
C₇×M₄(2)	Direct product of C₇ and M₄(2)	56	2	C7xM4(2)	112,23
C₇×Q₁₆	Direct product of C₇ and Q₁₆	112	2	C7xQ16	112,26
Q₈×C₁₄	Direct product of C₁₄ and Q₈	112		Q8xC14	112,39
C₄×Dic₇	Direct product of C₄ and Dic₇	112		C4xDic7	112,10
C₂×Dic₁₄	Direct product of C₂ and Dic₁₄	112		C2xDic14	112,27
C₂²×Dic₇	Direct product of C₂² and Dic₇	112		C2^2xDic7	112,35
C₂×C₄×D₇	Direct product of C₂×C₄ and D₇	56		C2xC4xD7	112,28
C₂×C₇⋊D₄	Direct product of C₂ and C₇⋊D₄	56		C2xC7:D4	112,36
C₇×C₄○D₄	Direct product of C₇ and C₄○D₄	56	2	C7xC4oD4	112,40
C₇×C₂²⋊C₄	Direct product of C₇ and C₂²⋊C₄	56		C7xC2^2:C4	112,20
C₂×C₇⋊C₈	Direct product of C₂ and C₇⋊C₈	112		C2xC7:C8	112,8
C₇×C₄⋊C₄	Direct product of C₇ and C₄⋊C₄	112		C7xC4:C4	112,21

Groups of order 113

		d	ρ	Label	ID
C₁₁₃	Cyclic group	113	1	C113	113,1

Groups of order 114

		d	ρ	Label	ID
C₁₁₄	Cyclic group	114	1	C114	114,6
D₅₇	Dihedral group	57	2+	D57	114,5
C₁₉⋊C₆	The semidirect product of C₁₉ and C₆ acting faithfully	19	6+	C19:C6	114,1
S₃×C₁₉	Direct product of C₁₉ and S₃	57	2	S3xC19	114,3
C₃×D₁₉	Direct product of C₃ and D₁₉	57	2	C3xD19	114,4
C₂×C₁₉⋊C₃	Direct product of C₂ and C₁₉⋊C₃	38	3	C2xC19:C3	114,2

Groups of order 115

		d	ρ	Label	ID
C₁₁₅	Cyclic group	115	1	C115	115,1

Groups of order 116

		d	ρ	Label	ID
C₁₁₆	Cyclic group	116	1	C116	116,2
D₅₈	Dihedral group; = C₂×D₂₉	58	2+	D58	116,4
Dic₂₉	Dicyclic group; = C₂₉ ⋊₂ C₄	116	2-	Dic29	116,1
C₂₉⋊C₄	The semidirect product of C₂₉ and C₄ acting faithfully	29	4+	C29:C4	116,3
C₂×C₅₈	Abelian group of type [2,58]	116		C2xC58	116,5

Groups of order 117

		d	ρ	Label	ID
C₁₁₇	Cyclic group	117	1	C117	117,2
C₁₃⋊C₉	The semidirect product of C₁₃ and C₉ acting via C₉/C₃=C₃	117	3	C13:C9	117,1
C₃×C₃₉	Abelian group of type [3,39]	117		C3xC39	117,4
C₃×C₁₃⋊C₃	Direct product of C₃ and C₁₃⋊C₃	39	3	C3xC13:C3	117,3

Groups of order 118

		d	ρ	Label	ID
C₁₁₈	Cyclic group	118	1	C118	118,2
D₅₉	Dihedral group	59	2+	D59	118,1

Groups of order 119

		d	ρ	Label	ID
C₁₁₉	Cyclic group	119	1	C119	119,1

Groups of order 120

		d	ρ	Label	ID
C₁₂₀	Cyclic group	120	1	C120	120,4
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	5	4+	S5	120,34
D₆₀	Dihedral group	60	2+	D60	120,28
Dic₃₀	Dicyclic group; = C₁₅ ⋊₂ Q₈	120	2-	Dic30	120,26
SL₂(𝔽₅)	Special linear group on 𝔽₅²; = C₂ .A₅ = 2I = <2,3,5>	24	2-	SL(2,5)	120,5
C₅⋊S₄	The semidirect product of C₅ and S₄ acting via S₄/A₄=C₂	20	6+	C5:S4	120,38
C₁₅⋊D₄	1^st semidirect product of C₁₅ and D₄ acting via D₄/C₂=C₂²	60	4-	C15:D4	120,11
C₃⋊D₂₀	The semidirect product of C₃ and D₂₀ acting via D₂₀/D₁₀=C₂	60	4+	C3:D20	120,12
C₅⋊D₁₂	The semidirect product of C₅ and D₁₂ acting via D₁₂/D₆=C₂	60	4+	C5:D12	120,13
C₁₅⋊₇D₄	1^st semidirect product of C₁₅ and D₄ acting via D₄/C₂²=C₂	60	2	C15:7D4	120,30
C₁₅⋊Q₈	The semidirect product of C₁₅ and Q₈ acting via Q₈/C₂=C₂²	120	4-	C15:Q8	120,14
C₁₅⋊₃C₈	1^st semidirect product of C₁₅ and C₈ acting via C₈/C₄=C₂	120	2	C15:3C8	120,3
C₁₅⋊C₈	1^st semidirect product of C₁₅ and C₈ acting via C₈/C₂=C₄	120	4	C15:C8	120,7
D₃₀.C₂	The non-split extension by D₃₀ of C₂ acting faithfully	60	4+	D30.C2	120,10
C₂×C₆₀	Abelian group of type [2,60]	120		C2xC60	120,31
C₂²×C₃₀	Abelian group of type [2,2,30]	120		C2^2xC30	120,47
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	15	8+	S3xF5	120,36
C₅×S₄	Direct product of C₅ and S₄	20	3	C5xS4	120,37
D₅×A₄	Direct product of D₅ and A₄	20	6+	D5xA4	120,39
C₆×F₅	Direct product of C₆ and F₅	30	4	C6xF5	120,40
C₁₀×A₄	Direct product of C₁₀ and A₄	30	3	C10xA4	120,43
C₅×SL₂(𝔽₃)	Direct product of C₅ and SL₂(𝔽₃)	40	2	C5xSL(2,3)	120,15
S₃×C₂₀	Direct product of C₂₀ and S₃	60	2	S3xC20	120,22
D₅×C₁₂	Direct product of C₁₂ and D₅	60	2	D5xC12	120,17
C₃×D₂₀	Direct product of C₃ and D₂₀	60	2	C3xD20	120,18
C₅×D₁₂	Direct product of C₅ and D₁₂	60	2	C5xD12	120,23
C₄×D₁₅	Direct product of C₄ and D₁₅	60	2	C4xD15	120,27
D₄×C₁₅	Direct product of C₁₅ and D₄	60	2	D4xC15	120,32
D₅×Dic₃	Direct product of D₅ and Dic₃	60	4-	D5xDic3	120,8
S₃×Dic₅	Direct product of S₃ and Dic₅	60	4-	S3xDic5	120,9
C₂²×D₁₅	Direct product of C₂² and D₁₅	60		C2^2xD15	120,46
Q₈×C₁₅	Direct product of C₁₅ and Q₈	120	2	Q8xC15	120,33
C₆×Dic₅	Direct product of C₆ and Dic₅	120		C6xDic5	120,19
C₅×Dic₆	Direct product of C₅ and Dic₆	120	2	C5xDic6	120,21
C₃×Dic₁₀	Direct product of C₃ and Dic₁₀	120	2	C3xDic10	120,16
C₁₀×Dic₃	Direct product of C₁₀ and Dic₃	120		C10xDic3	120,24
C₂×Dic₁₅	Direct product of C₂ and Dic₁₅	120		C2xDic15	120,29
C₂×S₃×D₅	Direct product of C₂, S₃ and D₅	30	4+	C2xS3xD5	120,42
C₂×C₃⋊F₅	Direct product of C₂ and C₃⋊F₅	30	4	C2xC3:F5	120,41
D₅×C₂×C₆	Direct product of C₂×C₆ and D₅	60		D5xC2xC6	120,44
S₃×C₂×C₁₀	Direct product of C₂×C₁₀ and S₃	60		S3xC2xC10	120,45
C₃×C₅⋊D₄	Direct product of C₃ and C₅⋊D₄	60	2	C3xC5:D4	120,20
C₅×C₃⋊D₄	Direct product of C₅ and C₃⋊D₄	60	2	C5xC3:D4	120,25
C₅×C₃⋊C₈	Direct product of C₅ and C₃⋊C₈	120	2	C5xC3:C8	120,1
C₃×C₅⋊C₈	Direct product of C₃ and C₅⋊C₈	120	4	C3xC5:C8	120,6
C₃×C₅⋊₂C₈	Direct product of C₃ and C₅⋊₂C₈	120	2	C3xC5:2C8	120,2

Groups of order 121

		d	ρ	Label	ID
C₁₂₁	Cyclic group	121	1	C121	121,1
C₁₁²	Elementary abelian group of type [11,11]	121		C11^2	121,2

Groups of order 122

		d	ρ	Label	ID
C₁₂₂	Cyclic group	122	1	C122	122,2
D₆₁	Dihedral group	61	2+	D61	122,1

Groups of order 123

		d	ρ	Label	ID
C₁₂₃	Cyclic group	123	1	C123	123,1

Groups of order 124

		d	ρ	Label	ID
C₁₂₄	Cyclic group	124	1	C124	124,2
D₆₂	Dihedral group; = C₂×D₃₁	62	2+	D62	124,3
Dic₃₁	Dicyclic group; = C₃₁ ⋊C₄	124	2-	Dic31	124,1
C₂×C₆₂	Abelian group of type [2,62]	124		C2xC62	124,4

Groups of order 125

		d	ρ	Label	ID
C₁₂₅	Cyclic group	125	1	C125	125,1
He₅	Heisenberg group; = C₅² ⋊C₅ = 5₊¹⁺²	25	5	He5	125,3
5_-¹⁺²	Extraspecial group	25	5	ES-(5,1)	125,4
C₅³	Elementary abelian group of type [5,5,5]	125		C5^3	125,5
C₅×C₂₅	Abelian group of type [5,25]	125		C5xC25	125,2

Groups of order 126

		d	ρ	Label	ID
C₁₂₆	Cyclic group	126	1	C126	126,6
D₆₃	Dihedral group	63	2+	D63	126,5
C₃⋊F₇	The semidirect product of C₃ and F₇ acting via F₇/C₇⋊C₃=C₂	21	6+	C3:F7	126,9
C₇⋊C₁₈	The semidirect product of C₇ and C₁₈ acting via C₁₈/C₃=C₆	63	6	C7:C18	126,1
C₃⋊D₂₁	The semidirect product of C₃ and D₂₁ acting via D₂₁/C₂₁=C₂	63		C3:D21	126,15
C₃×C₄₂	Abelian group of type [3,42]	126		C3xC42	126,16
C₃×F₇	Direct product of C₃ and F₇	21	6	C3xF7	126,7
S₃×C₂₁	Direct product of C₂₁ and S₃	42	2	S3xC21	126,12
C₃×D₂₁	Direct product of C₃ and D₂₁	42	2	C3xD21	126,13
C₇×D₉	Direct product of C₇ and D₉	63	2	C7xD9	126,3
C₉×D₇	Direct product of C₉ and D₇	63	2	C9xD7	126,4
C₃²×D₇	Direct product of C₃² and D₇	63		C3^2xD7	126,11
S₃×C₇⋊C₃	Direct product of S₃ and C₇⋊C₃	21	6	S3xC7:C3	126,8
C₆×C₇⋊C₃	Direct product of C₆ and C₇⋊C₃	42	3	C6xC7:C3	126,10
C₇×C₃⋊S₃	Direct product of C₇ and C₃⋊S₃	63		C7xC3:S3	126,14
C₂×C₇⋊C₉	Direct product of C₂ and C₇⋊C₉	126	3	C2xC7:C9	126,2

Groups of order 127

		d	ρ	Label	ID
C₁₂₇	Cyclic group	127	1	C127	127,1

Groups of order 128

		d	ρ	Label	ID
C₁₂₈	Cyclic group	128	1	C128	128,1
D₆₄	Dihedral group	64	2+	D64	128,161
Q₁₂₈	Generalised quaternion group; = C₆₄ .C₂ = Dic₃₂	128	2-	Q128	128,163
2₊¹⁺⁶	Extraspecial group; = D₄ ○2₊¹⁺⁴	16	8+	ES+(2,3)	128,2326
2_-¹⁺⁶	Extraspecial group; = D₄ ○2_-¹⁺⁴	32	8-	ES-(2,3)	128,2327
SD₁₂₈	Semidihedral group; = C₆₄ ⋊₂ C₂ = QD₁₂₈	64	2	SD128	128,162
M₇(2)	Modular maximal-cyclic group; = C₆₄ ⋊₃ C₂	64	2	M7(2)	128,160
D₄≀C₂	Wreath product of D₄ by C₂	8	4+	D4wrC2	128,928
C₈≀C₂	Wreath product of C₈ by C₂	16	2	C8wrC2	128,67
Q₈≀C₂	Wreath product of Q₈ by C₂	16	4-	Q8wrC2	128,937
C₂³≀C₂	Wreath product of C₂³ by C₂	16		C2^3wrC2	128,1578
(C₂×C₄)≀C₂	Wreath product of C₂×C₄ by C₂	16		(C2xC4)wrC2	128,628
D₈○D₈	Central product of D₈ and D₈	16	4+	D8oD8	128,2024
C₁₆○D₈	Central product of C₁₆ and D₈	32	2	C16oD8	128,902
C₈○D₁₆	Central product of C₈ and D₁₆	32	2	C8oD16	128,910
D₄○D₁₆	Central product of D₄ and D₁₆	32	4+	D4oD16	128,2147
D₈○Q₁₆	Central product of D₈ and Q₁₆	32	4-	D8oQ16	128,2025
D₈○SD₁₆	Central product of D₈ and SD₁₆	32	4	D8oSD16	128,2022
D₄○SD₃₂	Central product of D₄ and SD₃₂	32	4	D4oSD32	128,2148
M₄(2)○D₈	Central product of M₄(2) and D₈	32	4	M4(2)oD8	128,1689
Q₈○M₅(2)	Central product of Q₈ and M₅(2)	32	4	Q8oM5(2)	128,2139
M₄(2)○₂M₄(2)	Central product of M₄(2) and M₄(2)	32		M4(2)o2M4(2)	128,1605
D₄○C₃₂	Central product of D₄ and C₃₂	64	2	D4oC32	128,990
C₄○D₃₂	Central product of C₄ and D₃₂	64	2	C4oD32	128,994
Q₈○D₁₆	Central product of Q₈ and D₁₆	64	4-	Q8oD16	128,2149
C₁₆○₂M₅(2)	Central product of C₁₆ and M₅(2)	64		C16o2M5(2)	128,840
C₄○C₂≀C₄	Central product of C₄ and C₂≀C₄	16	4	C4oC2wrC4	128,852
D₄○(C₂²⋊C₈)	Central product of D₄ and C₂²⋊C₈	32		D4o(C2^2:C8)	128,1612
D₈⋊D₄	The semidirect product of D₈ and D₄ acting via D₄/C₂=C₂²	16	8+	D8:D4	128,922
D₁₆⋊C₄	The semidirect product of D₁₆ and C₄ acting faithfully; = Aut(D₁₆) = Hol(C₁₆)	16	8+	D16:C4	128,913
C₂³⋊D₈	The semidirect product of C₂³ and D₈ acting via D₈/C₂=D₄	16		C2^3:D8	128,327
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	16	8+	C2^4:Q8	128,764
D₈⋊₃D₄	2^nd semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	16	4+	D8:3D4	128,945
D₈⋊₆D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	16	4	D8:6D4	128,2023
D₈⋊₃Q₈	3^rd semidirect product of D₈ and Q₈ acting via Q₈/C₄=C₂	16	4	D8:3Q8	128,962
D₈⋊₁₁D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	16	8+	D8:11D4	128,2020
C₂⁴⋊C₈	1^st semidirect product of C₂⁴ and C₈ acting via C₈/C₂=C₄	16		C2^4:C8	128,48
C₂⁵⋊C₄	1^st semidirect product of C₂⁵ and C₄ acting faithfully	16		C2^5:C4	128,513
C₄²⋊D₄	1^st semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:D4	128,643
C₄²⋊₉D₄	3^rd semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	16		C4^2:9D4	128,734
C₄²⋊₂D₄	2^nd semidirect product of C₄² and D₄ acting faithfully	16	4	C4^2:2D4	128,742
C₂⁴⋊D₄	1^st semidirect product of C₂⁴ and D₄ acting faithfully	16		C2^4:D4	128,753
C₄²⋊₄D₄	4^th semidirect product of C₄² and D₄ acting faithfully	16	4	C4^2:4D4	128,929
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:5D4	128,931
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:6D4	128,932
C₂⁴⋊₂Q₈	1^st semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	16		C2^4:2Q8	128,761
D₈⋊C₂³	6^th semidirect product of D₈ and C₂³ acting via C₂³/C₂²=C₂	16	8+	D8:C2^3	128,2317
M₄(2)⋊₅D₄	5^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	16	8+	M4(2):5D4	128,740
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	16	8+	C2^4:C2^3	128,1758
C₄²⋊C₂³	4^th semidirect product of C₄² and C₂³ acting faithfully	16		C4^2:C2^3	128,2264

Full list: Groups of order 128 (2328 groups)

Groups of order 129

		d	ρ	Label	ID
C₁₂₉	Cyclic group	129	1	C129	129,2
C₄₃⋊C₃	The semidirect product of C₄₃ and C₃ acting faithfully	43	3	C43:C3	129,1

Groups of order 130

		d	ρ	Label	ID
C₁₃₀	Cyclic group	130	1	C130	130,4
D₆₅	Dihedral group	65	2+	D65	130,3
D₅×C₁₃	Direct product of C₁₃ and D₅	65	2	D5xC13	130,1
C₅×D₁₃	Direct product of C₅ and D₁₃	65	2	C5xD13	130,2

Groups of order 131

		d	ρ	Label	ID
C₁₃₁	Cyclic group	131	1	C131	131,1

Groups of order 132

		d	ρ	Label	ID
C₁₃₂	Cyclic group	132	1	C132	132,4
D₆₆	Dihedral group; = C₂×D₃₃	66	2+	D66	132,9
Dic₃₃	Dicyclic group; = C₃₃ ⋊₁ C₄	132	2-	Dic33	132,3
C₂×C₆₆	Abelian group of type [2,66]	132		C2xC66	132,10
S₃×D₁₁	Direct product of S₃ and D₁₁	33	4+	S3xD11	132,5
C₁₁×A₄	Direct product of C₁₁ and A₄	44	3	C11xA4	132,6
S₃×C₂₂	Direct product of C₂₂ and S₃	66	2	S3xC22	132,8
C₆×D₁₁	Direct product of C₆ and D₁₁	66	2	C6xD11	132,7
C₁₁×Dic₃	Direct product of C₁₁ and Dic₃	132	2	C11xDic3	132,1
C₃×Dic₁₁	Direct product of C₃ and Dic₁₁	132	2	C3xDic11	132,2

Groups of order 133

		d	ρ	Label	ID
C₁₃₃	Cyclic group	133	1	C133	133,1

Groups of order 134

		d	ρ	Label	ID
C₁₃₄	Cyclic group	134	1	C134	134,2
D₆₇	Dihedral group	67	2+	D67	134,1

Groups of order 135

		d	ρ	Label	ID
C₁₃₅	Cyclic group	135	1	C135	135,1
C₃×C₄₅	Abelian group of type [3,45]	135		C3xC45	135,2
C₃²×C₁₅	Abelian group of type [3,3,15]	135		C3^2xC15	135,5
C₅×He₃	Direct product of C₅ and He₃	45	3	C5xHe3	135,3
C₅×3_-¹⁺²	Direct product of C₅ and 3_-¹⁺²	45	3	C5xES-(3,1)	135,4

Groups of order 136

		d	ρ	Label	ID
C₁₃₆	Cyclic group	136	1	C136	136,2
D₆₈	Dihedral group	68	2+	D68	136,6
Dic₃₄	Dicyclic group; = C₁₇ ⋊Q₈	136	2-	Dic34	136,4
C₁₇⋊C₈	The semidirect product of C₁₇ and C₈ acting faithfully	17	8+	C17:C8	136,12
C₁₇⋊D₄	The semidirect product of C₁₇ and D₄ acting via D₄/C₂²=C₂	68	2	C17:D4	136,8
C₁₇⋊₃C₈	The semidirect product of C₁₇ and C₈ acting via C₈/C₄=C₂	136	2	C17:3C8	136,1
C₁₇⋊₂C₈	The semidirect product of C₁₇ and C₈ acting via C₈/C₂=C₄	136	4-	C17:2C8	136,3
C₂×C₆₈	Abelian group of type [2,68]	136		C2xC68	136,9
C₂²×C₃₄	Abelian group of type [2,2,34]	136		C2^2xC34	136,15
C₄×D₁₇	Direct product of C₄ and D₁₇	68	2	C4xD17	136,5
D₄×C₁₇	Direct product of C₁₇ and D₄	68	2	D4xC17	136,10
C₂²×D₁₇	Direct product of C₂² and D₁₇	68		C2^2xD17	136,14
Q₈×C₁₇	Direct product of C₁₇ and Q₈	136	2	Q8xC17	136,11
C₂×Dic₁₇	Direct product of C₂ and Dic₁₇	136		C2xDic17	136,7
C₂×C₁₇⋊C₄	Direct product of C₂ and C₁₇⋊C₄	34	4+	C2xC17:C4	136,13

Groups of order 137

		d	ρ	Label	ID
C₁₃₇	Cyclic group	137	1	C137	137,1

Groups of order 138

		d	ρ	Label	ID
C₁₃₈	Cyclic group	138	1	C138	138,4
D₆₉	Dihedral group	69	2+	D69	138,3
S₃×C₂₃	Direct product of C₂₃ and S₃	69	2	S3xC23	138,1
C₃×D₂₃	Direct product of C₃ and D₂₃	69	2	C3xD23	138,2

Groups of order 139

		d	ρ	Label	ID
C₁₃₉	Cyclic group	139	1	C139	139,1

Groups of order 140

		d	ρ	Label	ID
C₁₄₀	Cyclic group	140	1	C140	140,4
D₇₀	Dihedral group; = C₂×D₃₅	70	2+	D70	140,10
Dic₃₅	Dicyclic group; = C₇ ⋊Dic₅	140	2-	Dic35	140,3
C₇⋊F₅	The semidirect product of C₇ and F₅ acting via F₅/D₅=C₂	35	4	C7:F5	140,6
C₂×C₇₀	Abelian group of type [2,70]	140		C2xC70	140,11
D₅×D₇	Direct product of D₅ and D₇	35	4+	D5xD7	140,7
C₇×F₅	Direct product of C₇ and F₅	35	4	C7xF5	140,5
C₁₀×D₇	Direct product of C₁₀ and D₇	70	2	C10xD7	140,8
D₅×C₁₄	Direct product of C₁₄ and D₅	70	2	D5xC14	140,9
C₇×Dic₅	Direct product of C₇ and Dic₅	140	2	C7xDic5	140,1
C₅×Dic₇	Direct product of C₅ and Dic₇	140	2	C5xDic7	140,2

Groups of order 141

		d	ρ	Label	ID
C₁₄₁	Cyclic group	141	1	C141	141,1

Groups of order 142

		d	ρ	Label	ID
C₁₄₂	Cyclic group	142	1	C142	142,2
D₇₁	Dihedral group	71	2+	D71	142,1

Groups of order 143

		d	ρ	Label	ID
C₁₄₃	Cyclic group	143	1	C143	143,1

Groups of order 144

		d	ρ	Label	ID
C₁₄₄	Cyclic group	144	1	C144	144,2
D₇₂	Dihedral group	72	2+	D72	144,8
Dic₃₆	Dicyclic group; = C₉ ⋊₁ Q₁₆	144	2-	Dic36	144,4
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	9	8+	AGammaL(1,9)	144,182
C₆²⋊C₄	1^st semidirect product of C₆² and C₄ acting faithfully	12	4+	C6^2:C4	144,136
Dic₃⋊D₆	2^nd semidirect product of Dic₃ and D₆ acting via D₆/S₃=C₂; = Hol(Dic₃)	12	4+	Dic3:D6	144,154
C₃²⋊D₈	The semidirect product of C₃² and D₈ acting via D₈/C₂=D₄	24	4	C3^2:D8	144,117
D₆⋊D₆	2^nd semidirect product of D₆ and D₆ acting via D₆/S₃=C₂	24	4	D6:D6	144,145
C₃⋊D₂₄	The semidirect product of C₃ and D₂₄ acting via D₂₄/D₁₂=C₂	24	4+	C3:D24	144,57
D₁₂⋊S₃	3^rd semidirect product of D₁₂ and S₃ acting via S₃/C₃=C₂	24	4	D12:S3	144,139
C₃²⋊₅SD₁₆	3^rd semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₄=C₂²	24	4+	C3^2:5SD16	144,60
C₃²⋊₂SD₁₆	The semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₂=D₄	24	4-	C3^2:2SD16	144,118
C₃²⋊M₄(2)	The semidirect product of C₃² and M₄(2) acting via M₄(2)/C₄=C₄	24	4	C3^2:M4(2)	144,131
C₄²⋊C₉	The semidirect product of C₄² and C₉ acting via C₉/C₃=C₃	36	3	C4^2:C9	144,3
C₂⁴⋊C₉	2^nd semidirect product of C₂⁴ and C₉ acting via C₉/C₃=C₃	36		C2^4:C9	144,111
C₃²⋊Q₁₆	The semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₂=D₄	48	4-	C3^2:Q16	144,119
D₆⋊Dic₃	The semidirect product of D₆ and Dic₃ acting via Dic₃/C₆=C₂	48		D6:Dic3	144,64
C₃²⋊₂D₈	1^st semidirect product of C₃² and D₈ acting via D₈/C₄=C₂²	48	4	C3^2:2D8	144,56
D₁₂⋊₅S₃	The semidirect product of D₁₂ and S₃ acting through Inn(D₁₂)	48	4-	D12:5S3	144,138
C₃²⋊₂C₁₆	The semidirect product of C₃² and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^2:2C16	144,51
C₃²⋊₂Q₁₆	1^st semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3^2:2Q16	144,61
C₃²⋊₃Q₁₆	2^nd semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4-	C3^2:3Q16	144,62
Dic₃⋊Dic₃	The semidirect product of Dic₃ and Dic₃ acting via Dic₃/C₆=C₂	48		Dic3:Dic3	144,66
Dic₆⋊S₃	2^nd semidirect product of Dic₆ and S₃ acting via S₃/C₃=C₂	48	4	Dic6:S3	144,58
D₄⋊D₉	The semidirect product of D₄ and D₉ acting via D₉/C₉=C₂	72	4+	D4:D9	144,16
Q₈⋊D₉	The semidirect product of Q₈ and D₉ acting via D₉/C₃=S₃	72	4+	Q8:D9	144,32
D₁₈⋊C₄	The semidirect product of D₁₈ and C₄ acting via C₄/C₂=C₂	72		D18:C4	144,14
C₈⋊D₉	3^rd semidirect product of C₈ and D₉ acting via D₉/C₉=C₂	72	2	C8:D9	144,6
C₇₂⋊C₂	2^nd semidirect product of C₇₂ and C₂ acting faithfully	72	2	C72:C2	144,7
C₂₄⋊S₃	5^th semidirect product of C₂₄ and S₃ acting via S₃/C₃=C₂	72		C24:S3	144,86
C₂₄⋊₂S₃	2^nd semidirect product of C₂₄ and S₃ acting via S₃/C₃=C₂	72		C24:2S3	144,87
D₄⋊₂D₉	The semidirect product of D₄ and D₉ acting through Inn(D₄)	72	4-	D4:2D9	144,42
Q₈⋊₂D₉	The semidirect product of Q₈ and D₉ acting via D₉/C₉=C₂	72	4+	Q8:2D9	144,18
Q₈⋊₃D₉	The semidirect product of Q₈ and D₉ acting through Inn(Q₈)	72	4+	Q8:3D9	144,44
C₃²⋊₅D₈	2^nd semidirect product of C₃² and D₈ acting via D₈/C₈=C₂	72		C3^2:5D8	144,88
C₃²⋊₇D₈	2^nd semidirect product of C₃² and D₈ acting via D₈/D₄=C₂	72		C3^2:7D8	144,96
D₃₆⋊₅C₂	The semidirect product of D₃₆ and C₂ acting through Inn(D₃₆)	72	2	D36:5C2	144,40
C₆²⋊₅C₄	3^rd semidirect product of C₆² and C₄ acting via C₄/C₂=C₂	72		C6^2:5C4	144,100
C₃²⋊₉SD₁₆	2^nd semidirect product of C₃² and SD₁₆ acting via SD₁₆/D₄=C₂	72		C3^2:9SD16	144,97
C₃²⋊₁₁SD₁₆	2^nd semidirect product of C₃² and SD₁₆ acting via SD₁₆/Q₈=C₂	72		C3^2:11SD16	144,98
C₉⋊C₁₆	The semidirect product of C₉ and C₁₆ acting via C₁₆/C₈=C₂	144	2	C9:C16	144,1
C₄⋊Dic₉	The semidirect product of C₄ and Dic₉ acting via Dic₉/C₁₈=C₂	144		C4:Dic9	144,13
C₉⋊Q₁₆	The semidirect product of C₉ and Q₁₆ acting via Q₁₆/Q₈=C₂	144	4-	C9:Q16	144,17
Dic₉⋊C₄	The semidirect product of Dic₉ and C₄ acting via C₄/C₂=C₂	144		Dic9:C4	144,12
C₃²⋊₅Q₁₆	2^nd semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₈=C₂	144		C3^2:5Q16	144,89
C₃²⋊₇Q₁₆	2^nd semidirect product of C₃² and Q₁₆ acting via Q₁₆/Q₈=C₂	144		C3^2:7Q16	144,99
C₁₂⋊Dic₃	1^st semidirect product of C₁₂ and Dic₃ acting via Dic₃/C₆=C₂	144		C12:Dic3	144,94
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	12	4+	S3^2:C4	144,115
C₃⋊S₃⋊₃C₈	2^nd semidirect product of C₃⋊S₃ and C₈ acting via C₈/C₄=C₂	24	4	C3:S3:3C8	144,130
C₄⋊(C₃²⋊C₄)	The semidirect product of C₄ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	24	4	C4:(C3^2:C4)	144,133
C₆.₆S₄	6^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	24	4+	C6.6S4	144,125
D₆.D₆	1^st non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	24	4	D6.D6	144,141
D₆.₆D₆	2^nd non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	24	4+	D6.6D6	144,142
D₆.₃D₆	3^rd non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	24	4	D6.3D6	144,147
D₆.₄D₆	4^th non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	24	4-	D6.4D6	144,148
C₁₂.₂₉D₆	3^rd non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.29D6	144,53
C₁₂.₃₁D₆	5^th non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.31D6	144,55
C₆.D₁₂	6^th non-split extension by C₆ of D₁₂ acting via D₁₂/D₆=C₂	24		C6.D12	144,65
C₆².C₄	2^nd non-split extension by C₆² of C₄ acting faithfully	24	4-	C6^2.C4	144,135
Dic₃.D₆	2^nd non-split extension by Dic₃ of D₆ acting via D₆/S₃=C₂	24	4	Dic3.D6	144,140
C₂.PSU₃(𝔽₂)	The central extension by C₂ of PSU₃(𝔽₂)	24	8+	C2.PSU(3,2)	144,120
C₆.S₄	3^rd non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	36	6-	C6.S4	144,33
C₆.₇S₄	7^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	36	6-	C6.7S4	144,126
C₂.F₉	The central extension by C₂ of F₉	48	8-	C2.F9	144,114
C₆.₅S₄	5^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	48	4-	C6.5S4	144,124
D₆.Dic₃	The non-split extension by D₆ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D6.Dic3	144,54
Dic₃.A₄	The non-split extension by Dic₃ of A₄ acting through Inn(Dic₃)	48	4+	Dic3.A4	144,127
D₁₂.S₃	1^st non-split extension by D₁₂ of S₃ acting via S₃/C₃=C₂	48	4-	D12.S3	144,59
C₆².C₂²	5^th non-split extension by C₆² of C₂² acting faithfully	48		C6^2.C2^2	144,67
D₄.D₉	The non-split extension by D₄ of D₉ acting via D₉/C₉=C₂	72	4-	D4.D9	144,15
Q₈.C₁₈	The non-split extension by Q₈ of C₁₈ acting via C₁₈/C₆=C₃	72	2	Q8.C18	144,36
C₄.Dic₉	The non-split extension by C₄ of Dic₉ acting via Dic₉/C₁₈=C₂	72	2	C4.Dic9	144,10
C₁₈.D₄	7^th non-split extension by C₁₈ of D₄ acting via D₄/C₂²=C₂	72		C18.D4	144,19
C₁₂.₅₈D₆	19^th non-split extension by C₁₂ of D₆ acting via D₆/C₆=C₂	72		C12.58D6	144,91
C₆.₁₁D₁₂	11^st non-split extension by C₆ of D₁₂ acting via D₁₂/C₁₂=C₂	72		C6.11D12	144,95
C₁₂.₅₉D₆	20^th non-split extension by C₁₂ of D₆ acting via D₆/C₆=C₂	72		C12.59D6	144,171
C₁₂.D₆	24^th non-split extension by C₁₂ of D₆ acting via D₆/C₃=C₂²	72		C12.D6	144,173
C₁₂.₂₆D₆	26^th non-split extension by C₁₂ of D₆ acting via D₆/C₃=C₂²	72		C12.26D6	144,175
Q₈.D₉	The non-split extension by Q₈ of D₉ acting via D₉/C₃=S₃	144	4-	Q8.D9	144,31
C₂₄.S₃	9^th non-split extension by C₂₄ of S₃ acting via S₃/C₃=C₂	144		C24.S3	144,29
C₆.Dic₆	4^th non-split extension by C₆ of Dic₆ acting via Dic₆/C₁₂=C₂	144		C6.Dic6	144,93
C₃⋊S₃.Q₈	The non-split extension by C₃⋊S₃ of Q₈ acting via Q₈/C₂=C₂²	24	4	C3:S3.Q8	144,116
C₁₂²	Abelian group of type [12,12]	144		C12^2	144,101
C₄×C₃₆	Abelian group of type [4,36]	144		C4xC36	144,20
C₂×C₇₂	Abelian group of type [2,72]	144		C2xC72	144,23
C₃×C₄₈	Abelian group of type [3,48]	144		C3xC48	144,30
C₆×C₂₄	Abelian group of type [6,24]	144		C6xC24	144,104
C₂²×C₃₆	Abelian group of type [2,2,36]	144		C2^2xC36	144,47
C₂³×C₁₈	Abelian group of type [2,2,2,18]	144		C2^3xC18	144,113
C₂²×C₆²	Abelian group of type [2,2,6,6]	144		C2^2xC6^2	144,197
C₂×C₆×C₁₂	Abelian group of type [2,6,12]	144		C2xC6xC12	144,178
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	12	9+	A4^2	144,184
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	12	6+	S3xS4	144,183
C₆×S₄	Direct product of C₆ and S₄	18	3	C6xS4	144,188
C₂×F₉	Direct product of C₂ and F₉	18	8+	C2xF9	144,185
C₂×PSU₃(𝔽₂)	Direct product of C₂ and PSU₃(𝔽₂)	18	8+	C2xPSU(3,2)	144,187
S₃×D₁₂	Direct product of S₃ and D₁₂	24	4+	S3xD12	144,144
C₃×GL₂(𝔽₃)	Direct product of C₃ and GL₂(𝔽₃)	24	2	C3xGL(2,3)	144,122
S₃×SL₂(𝔽₃)	Direct product of S₃ and SL₂(𝔽₃); = SL₂(ℤ/6ℤ)	24	4-	S3xSL(2,3)	144,128
D₄×D₉	Direct product of D₄ and D₉	36	4+	D4xD9	144,41
C₁₂×A₄	Direct product of C₁₂ and A₄	36	3	C12xA4	144,155
Dic₃×A₄	Direct product of Dic₃ and A₄	36	6-	Dic3xA4	144,129
S₃×C₂₄	Direct product of C₂₄ and S₃	48	2	S3xC24	144,69
C₃×D₂₄	Direct product of C₃ and D₂₄	48	2	C3xD24	144,72
C₆×D₁₂	Direct product of C₆ and D₁₂	48		C6xD12	144,160
Dic₃²	Direct product of Dic₃ and Dic₃	48		Dic3^2	144,63
S₃×Dic₆	Direct product of S₃ and Dic₆	48	4-	S3xDic6	144,137
C₆×Dic₆	Direct product of C₆ and Dic₆	48		C6xDic6	144,158
C₃×Dic₁₂	Direct product of C₃ and Dic₁₂	48	2	C3xDic12	144,73
Dic₃×C₁₂	Direct product of C₁₂ and Dic₃	48		Dic3xC12	144,76
C₆×SL₂(𝔽₃)	Direct product of C₆ and SL₂(𝔽₃)	48		C6xSL(2,3)	144,156
C₃×CSU₂(𝔽₃)	Direct product of C₃ and CSU₂(𝔽₃)	48	2	C3xCSU(2,3)	144,121
C₈×D₉	Direct product of C₈ and D₉	72	2	C8xD9	144,5
C₉×D₈	Direct product of C₉ and D₈	72	2	C9xD8	144,25
Q₈×D₉	Direct product of Q₈ and D₉	72	4-	Q8xD9	144,43
C₂×D₃₆	Direct product of C₂ and D₃₆	72		C2xD36	144,39
D₄×C₁₈	Direct product of C₁₈ and D₄	72		D4xC18	144,48
C₉×SD₁₆	Direct product of C₉ and SD₁₆	72	2	C9xSD16	144,26
C₃²×D₈	Direct product of C₃² and D₈	72		C3^2xD8	144,106
C₂³×D₉	Direct product of C₂³ and D₉	72		C2^3xD9	144,112
C₉×M₄(2)	Direct product of C₉ and M₄(2)	72	2	C9xM4(2)	144,24
C₃²×SD₁₆	Direct product of C₃² and SD₁₆	72		C3^2xSD16	144,107
C₃²×M₄(2)	Direct product of C₃² and M₄(2)	72		C3^2xM4(2)	144,105
C₉×Q₁₆	Direct product of C₉ and Q₁₆	144	2	C9xQ16	144,27
Q₈×C₁₈	Direct product of C₁₈ and Q₈	144		Q8xC18	144,49
C₄×Dic₉	Direct product of C₄ and Dic₉	144		C4xDic9	144,11
C₂×Dic₁₈	Direct product of C₂ and Dic₁₈	144		C2xDic18	144,37
C₃²×Q₁₆	Direct product of C₃² and Q₁₆	144		C3^2xQ16	144,108
C₂²×Dic₉	Direct product of C₂² and Dic₉	144		C2^2xDic9	144,45
C₂×S₃≀C₂	Direct product of C₂ and S₃≀C₂	12	4+	C2xS3wrC2	144,186
C₂×S₃×A₄	Direct product of C₂, S₃ and A₄	18	6+	C2xS3xA4	144,190
C₂×C₃⋊S₄	Direct product of C₂ and C₃⋊S₄	18	6+	C2xC3:S4	144,189
C₂×C₃.S₄	Direct product of C₂ and C₃.S₄	18	6+	C2xC3.S4	144,109
C₄×S₃²	Direct product of C₄, S₃ and S₃	24	4	C4xS3^2	144,143
C₃×S₃×D₄	Direct product of C₃, S₃ and D₄	24	4	C3xS3xD4	144,162
S₃×C₃⋊D₄	Direct product of S₃ and C₃⋊D₄	24	4	S3xC3:D4	144,153
C₆×C₃⋊D₄	Direct product of C₆ and C₃⋊D₄	24		C6xC3:D4	144,167
C₃×D₄⋊S₃	Direct product of C₃ and D₄⋊S₃	24	4	C3xD4:S3	144,80
C₂²×S₃²	Direct product of C₂², S₃ and S₃	24		C2^2xS3^2	144,192
C₄×C₃²⋊C₄	Direct product of C₄ and C₃²⋊C₄	24	4	C4xC3^2:C4	144,132
C₃×C₄○D₁₂	Direct product of C₃ and C₄○D₁₂	24	2	C3xC4oD12	144,161
C₂×C₃⋊D₁₂	Direct product of C₂ and C₃⋊D₁₂	24		C2xC3:D12	144,151
C₃×D₄.S₃	Direct product of C₃ and D₄.S₃	24	4	C3xD4.S3	144,81
C₃×C₆.D₄	Direct product of C₃ and C₆.D₄	24		C3xC6.D4	144,84
C₂×C₆.D₆	Direct product of C₂ and C₆.D₆	24		C2xC6.D6	144,149
C₃×D₄⋊₂S₃	Direct product of C₃ and D₄⋊₂S₃	24	4	C3xD4:2S3	144,163
C₂²×C₃²⋊C₄	Direct product of C₂² and C₃²⋊C₄	24		C2^2xC3^2:C4	144,191
C₃×C₄.Dic₃	Direct product of C₃ and C₄.Dic₃	24	2	C3xC4.Dic3	144,75
A₄×C₂×C₆	Direct product of C₂×C₆ and A₄	36		A4xC2xC6	144,193
D₄×C₃⋊S₃	Direct product of D₄ and C₃⋊S₃	36		D4xC3:S3	144,172
C₃×A₄⋊C₄	Direct product of C₃ and A₄⋊C₄	36	3	C3xA4:C4	144,123
C₄×C₃.A₄	Direct product of C₄ and C₃.A₄	36	3	C4xC3.A4	144,34
C₃×C₄²⋊C₃	Direct product of C₃ and C₄²⋊C₃	36	3	C3xC4^2:C3	144,68
C₃×C₂²⋊A₄	Direct product of C₃ and C₂²⋊A₄	36		C3xC2^2:A4	144,194
C₂²×C₃.A₄	Direct product of C₂² and C₃.A₄	36		C2^2xC3.A4	144,110
C₆×C₃⋊C₈	Direct product of C₆ and C₃⋊C₈	48		C6xC3:C8	144,74
S₃×C₃⋊C₈	Direct product of S₃ and C₃⋊C₈	48	4	S3xC3:C8	144,52
C₃×C₃⋊C₁₆	Direct product of C₃ and C₃⋊C₁₆	48	2	C3xC3:C16	144,28
C₃×S₃×Q₈	Direct product of C₃, S₃ and Q₈	48	4	C3xS3xQ8	144,164
S₃×C₂×C₁₂	Direct product of C₂×C₁₂ and S₃	48		S3xC2xC12	144,159
C₃×C₈⋊S₃	Direct product of C₃ and C₈⋊S₃	48	2	C3xC8:S3	144,70
C₃×D₆⋊C₄	Direct product of C₃ and D₆⋊C₄	48		C3xD6:C4	144,79
C₃×C₄.A₄	Direct product of C₃ and C₄.A₄	48	2	C3xC4.A4	144,157
S₃×C₂²×C₆	Direct product of C₂²×C₆ and S₃	48		S3xC2^2xC6	144,195
C₂×S₃×Dic₃	Direct product of C₂, S₃ and Dic₃	48		C2xS3xDic3	144,146
Dic₃×C₂×C₆	Direct product of C₂×C₆ and Dic₃	48		Dic3xC2xC6	144,166
C₃×C₂₄⋊C₂	Direct product of C₃ and C₂₄⋊C₂	48	2	C3xC24:C2	144,71
C₃×C₃⋊Q₁₆	Direct product of C₃ and C₃⋊Q₁₆	48	4	C3xC3:Q16	144,83
C₂×D₆⋊S₃	Direct product of C₂ and D₆⋊S₃	48		C2xD6:S3	144,150
C₃×C₄⋊Dic₃	Direct product of C₃ and C₄⋊Dic₃	48		C3xC4:Dic3	144,78
C₃×Dic₃⋊C₄	Direct product of C₃ and Dic₃⋊C₄	48		C3xDic3:C4	144,77
C₂×C₃²⋊₂C₈	Direct product of C₂ and C₃²⋊₂C₈	48		C2xC3^2:2C8	144,134
C₃×Q₈⋊₂S₃	Direct product of C₃ and Q₈⋊₂S₃	48	4	C3xQ8:2S3	144,82
C₃×Q₈⋊₃S₃	Direct product of C₃ and Q₈⋊₃S₃	48	4	C3xQ8:3S3	144,165
C₂×C₃²⋊₂Q₈	Direct product of C₂ and C₃²⋊₂Q₈	48		C2xC3^2:2Q8	144,152
C₂×C₄×D₉	Direct product of C₂×C₄ and D₉	72		C2xC4xD9	144,38
D₄×C₃×C₆	Direct product of C₃×C₆ and D₄	72		D4xC3xC6	144,179
C₈×C₃⋊S₃	Direct product of C₈ and C₃⋊S₃	72		C8xC3:S3	144,85
C₂×C₉⋊D₄	Direct product of C₂ and C₉⋊D₄	72		C2xC9:D4	144,46
Q₈×C₃⋊S₃	Direct product of Q₈ and C₃⋊S₃	72		Q8xC3:S3	144,174
C₉×C₄○D₄	Direct product of C₉ and C₄○D₄	72	2	C9xC4oD4	144,50
C₂×C₁₂⋊S₃	Direct product of C₂ and C₁₂⋊S₃	72		C2xC12:S3	144,170
C₉×C₂²⋊C₄	Direct product of C₉ and C₂²⋊C₄	72		C9xC2^2:C4	144,21
C₂³×C₃⋊S₃	Direct product of C₂³ and C₃⋊S₃	72		C2^3xC3:S3	144,196
C₃²×C₄○D₄	Direct product of C₃² and C₄○D₄	72		C3^2xC4oD4	144,181
C₂×C₃²⋊₇D₄	Direct product of C₂ and C₃²⋊₇D₄	72		C2xC3^2:7D4	144,177
C₃²×C₂²⋊C₄	Direct product of C₃² and C₂²⋊C₄	72		C3^2xC2^2:C4	144,102
C₂×C₉⋊C₈	Direct product of C₂ and C₉⋊C₈	144		C2xC9:C8	144,9
C₉×C₄⋊C₄	Direct product of C₉ and C₄⋊C₄	144		C9xC4:C4	144,22
Q₈×C₃×C₆	Direct product of C₃×C₆ and Q₈	144		Q8xC3xC6	144,180
C₂×Q₈⋊C₉	Direct product of C₂ and Q₈⋊C₉	144		C2xQ8:C9	144,35
C₃²×C₄⋊C₄	Direct product of C₃² and C₄⋊C₄	144		C3^2xC4:C4	144,103
C₄×C₃⋊Dic₃	Direct product of C₄ and C₃⋊Dic₃	144		C4xC3:Dic3	144,92
C₂×C₃²⋊₄C₈	Direct product of C₂ and C₃²⋊₄C₈	144		C2xC3^2:4C8	144,90
C₂×C₃²⋊₄Q₈	Direct product of C₂ and C₃²⋊₄Q₈	144		C2xC3^2:4Q8	144,168
C₂²×C₃⋊Dic₃	Direct product of C₂² and C₃⋊Dic₃	144		C2^2xC3:Dic3	144,176
C₂×C₄×C₃⋊S₃	Direct product of C₂×C₄ and C₃⋊S₃	72		C2xC4xC3:S3	144,169

Groups of order 145

		d	ρ	Label	ID
C₁₄₅	Cyclic group	145	1	C145	145,1

Groups of order 146

		d	ρ	Label	ID
C₁₄₆	Cyclic group	146	1	C146	146,2
D₇₃	Dihedral group	73	2+	D73	146,1

Groups of order 147

		d	ρ	Label	ID
C₁₄₇	Cyclic group	147	1	C147	147,2
C₇²⋊₃C₃	3^rd semidirect product of C₇² and C₃ acting faithfully	21	3	C7^2:3C3	147,5
C₄₉⋊C₃	The semidirect product of C₄₉ and C₃ acting faithfully	49	3	C49:C3	147,1
C₇²⋊C₃	2^nd semidirect product of C₇² and C₃ acting faithfully	49		C7^2:C3	147,4
C₇×C₂₁	Abelian group of type [7,21]	147		C7xC21	147,6
C₇×C₇⋊C₃	Direct product of C₇ and C₇⋊C₃	21	3	C7xC7:C3	147,3

Groups of order 148

		d	ρ	Label	ID
C₁₄₈	Cyclic group	148	1	C148	148,2
D₇₄	Dihedral group; = C₂×D₃₇	74	2+	D74	148,4
Dic₃₇	Dicyclic group; = C₃₇ ⋊₂ C₄	148	2-	Dic37	148,1
C₃₇⋊C₄	The semidirect product of C₃₇ and C₄ acting faithfully	37	4+	C37:C4	148,3
C₂×C₇₄	Abelian group of type [2,74]	148		C2xC74	148,5

Groups of order 149

		d	ρ	Label	ID
C₁₄₉	Cyclic group	149	1	C149	149,1

Groups of order 150

		d	ρ	Label	ID
C₁₅₀	Cyclic group	150	1	C150	150,4
D₇₅	Dihedral group	75	2+	D75	150,3
C₅²⋊S₃	The semidirect product of C₅² and S₃ acting faithfully	15	3	C5^2:S3	150,5
C₅²⋊C₆	The semidirect product of C₅² and C₆ acting faithfully	15	6+	C5^2:C6	150,6
C₅⋊D₁₅	The semidirect product of C₅ and D₁₅ acting via D₁₅/C₁₅=C₂	75		C5:D15	150,12
C₅×C₃₀	Abelian group of type [5,30]	150		C5xC30	150,13
D₅×C₁₅	Direct product of C₁₅ and D₅	30	2	D5xC15	150,8
C₅×D₁₅	Direct product of C₅ and D₁₅	30	2	C5xD15	150,11
S₃×C₂₅	Direct product of C₂₅ and S₃	75	2	S3xC25	150,1
C₃×D₂₅	Direct product of C₃ and D₂₅	75	2	C3xD25	150,2
S₃×C₅²	Direct product of C₅² and S₃	75		S3xC5^2	150,10
C₂×C₅²⋊C₃	Direct product of C₂ and C₅²⋊C₃	30	3	C2xC5^2:C3	150,7
C₃×C₅⋊D₅	Direct product of C₃ and C₅⋊D₅	75		C3xC5:D5	150,9

Groups of order 151

		d	ρ	Label	ID
C₁₅₁	Cyclic group	151	1	C151	151,1

Groups of order 152

		d	ρ	Label	ID
C₁₅₂	Cyclic group	152	1	C152	152,2
D₇₆	Dihedral group	76	2+	D76	152,5
Dic₃₈	Dicyclic group; = C₁₉ ⋊Q₈	152	2-	Dic38	152,3
C₁₉⋊D₄	The semidirect product of C₁₉ and D₄ acting via D₄/C₂²=C₂	76	2	C19:D4	152,7
C₁₉⋊C₈	The semidirect product of C₁₉ and C₈ acting via C₈/C₄=C₂	152	2	C19:C8	152,1
C₂×C₇₆	Abelian group of type [2,76]	152		C2xC76	152,8
C₂²×C₃₈	Abelian group of type [2,2,38]	152		C2^2xC38	152,12
C₄×D₁₉	Direct product of C₄ and D₁₉	76	2	C4xD19	152,4
D₄×C₁₉	Direct product of C₁₉ and D₄	76	2	D4xC19	152,9
C₂²×D₁₉	Direct product of C₂² and D₁₉	76		C2^2xD19	152,11
Q₈×C₁₉	Direct product of C₁₉ and Q₈	152	2	Q8xC19	152,10
C₂×Dic₁₉	Direct product of C₂ and Dic₁₉	152		C2xDic19	152,6

Groups of order 153

		d	ρ	Label	ID
C₁₅₃	Cyclic group	153	1	C153	153,1
C₃×C₅₁	Abelian group of type [3,51]	153		C3xC51	153,2

Groups of order 154

		d	ρ	Label	ID
C₁₅₄	Cyclic group	154	1	C154	154,4
D₇₇	Dihedral group	77	2+	D77	154,3
C₁₁×D₇	Direct product of C₁₁ and D₇	77	2	C11xD7	154,1
C₇×D₁₁	Direct product of C₇ and D₁₁	77	2	C7xD11	154,2

Groups of order 155

		d	ρ	Label	ID
C₁₅₅	Cyclic group	155	1	C155	155,2
C₃₁⋊C₅	The semidirect product of C₃₁ and C₅ acting faithfully	31	5	C31:C5	155,1

Groups of order 156

		d	ρ	Label	ID
C₁₅₆	Cyclic group	156	1	C156	156,6
D₇₈	Dihedral group; = C₂×D₃₉	78	2+	D78	156,17
F₁₃	Frobenius group; = C₁₃ ⋊C₁₂ = AGL₁(𝔽₁₃) = Aut(D₁₃) = Hol(C₁₃)	13	12+	F13	156,7
Dic₃₉	Dicyclic group; = C₃₉ ⋊₃ C₄	156	2-	Dic39	156,5
C₃₉⋊C₄	1^st semidirect product of C₃₉ and C₄ acting faithfully	39	4	C39:C4	156,10
C₁₃⋊A₄	The semidirect product of C₁₃ and A₄ acting via A₄/C₂²=C₃	52	3	C13:A4	156,14
C₂₆.C₆	The non-split extension by C₂₆ of C₆ acting faithfully	52	6-	C26.C6	156,1
C₂×C₇₈	Abelian group of type [2,78]	156		C2xC78	156,18
S₃×D₁₃	Direct product of S₃ and D₁₃	39	4+	S3xD13	156,11
A₄×C₁₃	Direct product of C₁₃ and A₄	52	3	A4xC13	156,13
S₃×C₂₆	Direct product of C₂₆ and S₃	78	2	S3xC26	156,16
C₆×D₁₃	Direct product of C₆ and D₁₃	78	2	C6xD13	156,15
Dic₃×C₁₃	Direct product of C₁₃ and Dic₃	156	2	Dic3xC13	156,3
C₃×Dic₁₃	Direct product of C₃ and Dic₁₃	156	2	C3xDic13	156,4
C₂×C₁₃⋊C₆	Direct product of C₂ and C₁₃⋊C₆	26	6+	C2xC13:C6	156,8
C₃×C₁₃⋊C₄	Direct product of C₃ and C₁₃⋊C₄	39	4	C3xC13:C4	156,9
C₄×C₁₃⋊C₃	Direct product of C₄ and C₁₃⋊C₃	52	3	C4xC13:C3	156,2
C₂²×C₁₃⋊C₃	Direct product of C₂² and C₁₃⋊C₃	52		C2^2xC13:C3	156,12

Groups of order 157

		d	ρ	Label	ID
C₁₅₇	Cyclic group	157	1	C157	157,1

Groups of order 158

		d	ρ	Label	ID
C₁₅₈	Cyclic group	158	1	C158	158,2
D₇₉	Dihedral group	79	2+	D79	158,1

Groups of order 159

		d	ρ	Label	ID
C₁₅₉	Cyclic group	159	1	C159	159,1

Groups of order 160

		d	ρ	Label	ID
C₁₆₀	Cyclic group	160	1	C160	160,2
D₈₀	Dihedral group	80	2+	D80	160,6
Dic₄₀	Dicyclic group; = C₅ ⋊₁ Q₃₂	160	2-	Dic40	160,8
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	10	5+	C2^4:D5	160,234
2_-¹⁺⁴⋊C₅	The semidirect product of 2_-¹⁺⁴ and C₅ acting faithfully	32	4-	ES-(2,2):C5	160,199
C₈⋊F₅	3^rd semidirect product of C₈ and F₅ acting via F₅/D₅=C₂	40	4	C8:F5	160,67
C₄₀⋊C₄	2^nd semidirect product of C₄₀ and C₄ acting faithfully	40	4	C40:C4	160,68
C₂³⋊F₅	The semidirect product of C₂³ and F₅ acting via F₅/C₅=C₄	40	4	C2^3:F5	160,86
D₈⋊D₅	2^nd semidirect product of D₈ and D₅ acting via D₅/C₅=C₂	40	4	D8:D5	160,132
C₈⋊D₁₀	1^st semidirect product of C₈ and D₁₀ acting via D₁₀/C₅=C₂²	40	4+	C8:D10	160,129
D₄⋊F₅	2^nd semidirect product of D₄ and F₅ acting via F₅/D₅=C₂	40	8-	D4:F5	160,83
Q₈⋊F₅	1^st semidirect product of Q₈ and F₅ acting via F₅/D₅=C₂	40	8-	Q8:F5	160,84
Q₈⋊₂F₅	2^nd semidirect product of Q₈ and F₅ acting via F₅/D₅=C₂	40	8+	Q8:2F5	160,85
D₂₀⋊₄C₄	1^st semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	40	2	D20:4C4	160,12
D₂₀⋊₇C₄	4^th semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	40	4	D20:7C4	160,32
D₂₀⋊C₄	1^st semidirect product of D₂₀ and C₄ acting faithfully	40	8+	D20:C4	160,82
D₄₀⋊C₂	6^th semidirect product of D₄₀ and C₂ acting faithfully	40	4+	D40:C2	160,135
D₄⋊D₁₀	2^nd semidirect product of D₄ and D₁₀ acting via D₁₀/C₁₀=C₂	40	4+	D4:D10	160,170
D₄⋊₆D₁₀	2^nd semidirect product of D₄ and D₁₀ acting through Inn(D₄)	40	4	D4:6D10	160,219
D₄⋊₈D₁₀	4^th semidirect product of D₄ and D₁₀ acting through Inn(D₄)	40	4+	D4:8D10	160,224
D₅⋊M₄(2)	The semidirect product of D₅ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	40	4	D5:M4(2)	160,202
C₂⁴⋊₂D₅	1^st semidirect product of C₂⁴ and D₅ acting via D₅/C₅=C₂	40		C2^4:2D5	160,174
C₂³⋊Dic₅	The semidirect product of C₂³ and Dic₅ acting via Dic₅/C₅=C₄	40	4	C2^3:Dic5	160,41
D₄⋊₂Dic₅	2^nd semidirect product of D₄ and Dic₅ acting via Dic₅/C₁₀=C₂	40	4	D4:2Dic5	160,44
C₂²⋊D₂₀	The semidirect product of C₂² and D₂₀ acting via D₂₀/D₁₀=C₂	40		C2^2:D20	160,103
C₂³⋊D₁₀	1^st semidirect product of C₂³ and D₁₀ acting via D₁₀/C₅=C₂²	40		C2^3:D10	160,158
D₅⋊C₁₆	The semidirect product of D₅ and C₁₆ acting via C₁₆/C₈=C₂	80	4	D5:C16	160,64
C₅⋊D₁₆	The semidirect product of C₅ and D₁₆ acting via D₁₆/D₈=C₂	80	4+	C5:D16	160,33
C₈₀⋊C₂	5^th semidirect product of C₈₀ and C₂ acting faithfully	80	2	C80:C2	160,5
D₈⋊₃D₅	The semidirect product of D₈ and D₅ acting through Inn(D₈)	80	4-	D8:3D5	160,133
C₁₆⋊D₅	2^nd semidirect product of C₁₆ and D₅ acting via D₅/C₅=C₂	80	2	C16:D5	160,7
C₂₀⋊₄D₄	1^st semidirect product of C₂₀ and D₄ acting via D₄/C₄=C₂	80		C20:4D4	160,95
C₄⋊D₂₀	The semidirect product of C₄ and D₂₀ acting via D₂₀/D₁₀=C₂	80		C4:D20	160,116
C₂₀⋊₇D₄	1^st semidirect product of C₂₀ and D₄ acting via D₄/C₂²=C₂	80		C20:7D4	160,151
C₂₀⋊₂D₄	2^nd semidirect product of C₂₀ and D₄ acting via D₄/C₂=C₂²	80		C20:2D4	160,159
C₂₀⋊D₄	3^rd semidirect product of C₂₀ and D₄ acting via D₄/C₂=C₂²	80		C20:D4	160,161
C₅⋊SD₃₂	The semidirect product of C₅ and SD₃₂ acting via SD₃₂/Q₁₆=C₂	80	4+	C5:SD32	160,35
D₂₀⋊₆C₄	3^rd semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	80		D20:6C4	160,16
D₁₀⋊₁C₈	1^st semidirect product of D₁₀ and C₈ acting via C₈/C₄=C₂	80		D10:1C8	160,27
D₂₀⋊₅C₄	2^nd semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	80		D20:5C4	160,28
D₁₀⋊C₈	2^nd semidirect product of D₁₀ and C₈ acting via C₈/C₄=C₂	80		D10:C8	160,78
D₁₀⋊D₄	1^st semidirect product of D₁₀ and D₄ acting via D₄/C₄=C₂	80		D10:D4	160,105
D₂₀⋊₈C₄	5^th semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	80		D20:8C4	160,114
D₄₀⋊₇C₂	The semidirect product of D₄₀ and C₂ acting through Inn(D₄₀)	80	2	D40:7C2	160,125
D₁₀⋊Q₈	1^st semidirect product of D₁₀ and Q₈ acting via Q₈/C₄=C₂	80		D10:Q8	160,117
D₁₀⋊₂Q₈	2^nd semidirect product of D₁₀ and Q₈ acting via Q₈/C₄=C₂	80		D10:2Q8	160,118
Q₁₆⋊D₅	2^nd semidirect product of Q₁₆ and D₅ acting via D₅/C₅=C₂	80	4	Q16:D5	160,139
D₁₀⋊₃Q₈	3^rd semidirect product of D₁₀ and Q₈ acting via Q₈/C₄=C₂	80		D10:3Q8	160,167
C₄²⋊D₅	1^st semidirect product of C₄² and D₅ acting via D₅/C₅=C₂	80		C4^2:D5	160,93
C₄²⋊₂D₅	2^nd semidirect product of C₄² and D₅ acting via D₅/C₅=C₂	80		C4^2:2D5	160,97
D₄⋊Dic₅	1^st semidirect product of D₄ and Dic₅ acting via Dic₅/C₁₀=C₂	80		D4:Dic5	160,39
Dic₅⋊₄D₄	1^st semidirect product of Dic₅ and D₄ acting through Inn(Dic₅)	80		Dic5:4D4	160,102
SD₁₆⋊D₅	2^nd semidirect product of SD₁₆ and D₅ acting via D₅/C₅=C₂	80	4-	SD16:D5	160,136
SD₁₆⋊₃D₅	The semidirect product of SD₁₆ and D₅ acting through Inn(SD₁₆)	80	4	SD16:3D5	160,137
Dic₅⋊D₄	2^nd semidirect product of Dic₅ and D₄ acting via D₄/C₂²=C₂	80		Dic5:D4	160,160
C₅⋊C₃₂	The semidirect product of C₅ and C₃₂ acting via C₃₂/C₈=C₄	160	4	C5:C32	160,3
C₂₀⋊Q₈	The semidirect product of C₂₀ and Q₈ acting via Q₈/C₂=C₂²	160		C20:Q8	160,109
C₅⋊₂C₃₂	The semidirect product of C₅ and C₃₂ acting via C₃₂/C₁₆=C₂	160	2	C5:2C32	160,1
C₂₀⋊₃C₈	1^st semidirect product of C₂₀ and C₈ acting via C₈/C₄=C₂	160		C20:3C8	160,11
C₄₀⋊₈C₄	4^th semidirect product of C₄₀ and C₄ acting via C₄/C₂=C₂	160		C40:8C4	160,22
C₄₀⋊₆C₄	2^nd semidirect product of C₄₀ and C₄ acting via C₄/C₂=C₂	160		C40:6C4	160,24
C₄₀⋊₅C₄	1^st semidirect product of C₄₀ and C₄ acting via C₄/C₂=C₂	160		C40:5C4	160,25
C₅⋊Q₃₂	The semidirect product of C₅ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	160	4-	C5:Q32	160,36
C₂₀⋊C₈	1^st semidirect product of C₂₀ and C₈ acting via C₈/C₂=C₄	160		C20:C8	160,76
C₂₀⋊₂Q₈	1^st semidirect product of C₂₀ and Q₈ acting via Q₈/C₄=C₂	160		C20:2Q8	160,90
Q₈⋊Dic₅	1^st semidirect product of Q₈ and Dic₅ acting via Dic₅/C₁₀=C₂	160		Q8:Dic5	160,42
Dic₅⋊C₈	3^rd semidirect product of Dic₅ and C₈ acting via C₈/C₄=C₂	160		Dic5:C8	160,79
Dic₅⋊₃Q₈	The semidirect product of Dic₅ and Q₈ acting through Inn(Dic₅)	160		Dic5:3Q8	160,108
Dic₅⋊Q₈	2^nd semidirect product of Dic₅ and Q₈ acting via Q₈/C₄=C₂	160		Dic5:Q8	160,165
C₄⋊C₄⋊₇D₅	1^st semidirect product of C₄⋊C₄ and D₅ acting through Inn(C₄⋊C₄)	80		C4:C4:7D5	160,113
C₄⋊C₄⋊D₅	6^th semidirect product of C₄⋊C₄ and D₅ acting via D₅/C₅=C₂	80		C4:C4:D5	160,119
C₂³.F₅	The non-split extension by C₂³ of F₅ acting via F₅/C₅=C₄	40	4	C2^3.F5	160,88
D₅.D₈	The non-split extension by D₅ of D₈ acting via D₈/C₈=C₂	40	4	D5.D8	160,69
C₂₀.D₄	8^th non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	40	4	C20.D4	160,40
D₁₀.D₄	1^st non-split extension by D₁₀ of D₄ acting via D₄/C₂=C₂²	40	4+	D10.D4	160,74
D₄.D₁₀	1^st non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D4.D10	160,153
C₂₀.₄₆D₄	3^rd non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	40	4+	C20.46D4	160,30
D₁₀.₃Q₈	3^rd non-split extension by D₁₀ of Q₈ acting via Q₈/C₄=C₂	40		D10.3Q8	160,81
C₂³.₁D₁₀	1^st non-split extension by C₂³ of D₁₀ acting via D₁₀/C₅=C₂²	40	4	C2^3.1D10	160,13
D₁₀.C₂³	11^st non-split extension by D₁₀ of C₂³ acting via C₂³/C₂²=C₂	40	4	D10.C2^3	160,205
D₈.D₅	The non-split extension by D₈ of D₅ acting via D₅/C₅=C₂	80	4-	D8.D5	160,34
D₄.F₅	The non-split extension by D₄ of F₅ acting through Inn(D₄)	80	8-	D4.F5	160,206
Q₈.F₅	The non-split extension by Q₈ of F₅ acting through Inn(Q₈)	80	8+	Q8.F5	160,208
C₈.F₅	3^rd non-split extension by C₈ of F₅ acting via F₅/D₅=C₂	80	4	C8.F5	160,65
C₂₀.₄C₈	1^st non-split extension by C₂₀ of C₈ acting via C₈/C₄=C₂	80	2	C20.4C8	160,19
C₄₀.₆C₄	1^st non-split extension by C₄₀ of C₄ acting via C₄/C₂=C₂	80	2	C40.6C4	160,26
C₄₀.C₄	2^nd non-split extension by C₄₀ of C₄ acting faithfully	80	4	C40.C4	160,70
C₂₀.C₈	1^st non-split extension by C₂₀ of C₈ acting via C₈/C₂=C₄	80	4	C20.C8	160,73
C₄.D₂₀	5^th non-split extension by C₄ of D₂₀ acting via D₂₀/C₂₀=C₂	80		C4.D20	160,96
C₈.D₁₀	1^st non-split extension by C₈ of D₁₀ acting via D₁₀/C₅=C₂²	80	4-	C8.D10	160,130
D₄.Dic₅	The non-split extension by D₄ of Dic₅ acting through Inn(D₄)	80	4	D4.Dic5	160,169
D₂₀.₃C₄	The non-split extension by D₂₀ of C₄ acting through Inn(D₂₀)	80	2	D20.3C4	160,122
D₂₀.₂C₄	The non-split extension by D₂₀ of C₄ acting via C₄/C₂=C₂	80	4	D20.2C4	160,128
D₄.₈D₁₀	3^rd non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	80	4	D4.8D10	160,171
D₄.₉D₁₀	4^th non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	80	4-	D4.9D10	160,172
C₂₀.₅₃D₄	10^th non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	80	4	C20.53D4	160,29
C₄.₁₂D₂₀	4^th non-split extension by C₄ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4-	C4.12D20	160,31
C₂₀.₅₅D₄	12^nd non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	80		C20.55D4	160,37
C₂₀.₁₀D₄	10^th non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	80	4	C20.10D4	160,43
C₂₀.₄₈D₄	5^th non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	80		C20.48D4	160,145
C₂₀.₁₇D₄	17^th non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	80		C20.17D4	160,157
C₂₀.₂₃D₄	23^rd non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	80		C20.23D4	160,168
D₁₀.Q₈	2^nd non-split extension by D₁₀ of Q₈ acting via Q₈/C₄=C₂	80	4	D10.Q8	160,71
Q₈.D₁₀	5^th non-split extension by Q₈ of D₁₀ acting via D₁₀/D₅=C₂	80	4+	Q8.D10	160,140
C₂³.₂F₅	1^st non-split extension by C₂³ of F₅ acting via F₅/D₅=C₂	80		C2^3.2F5	160,87
D₁₀.₁₂D₄	1^st non-split extension by D₁₀ of D₄ acting via D₄/C₂²=C₂	80		D10.12D4	160,104
D₁₀.₁₃D₄	2^nd non-split extension by D₁₀ of D₄ acting via D₄/C₂²=C₂	80		D10.13D4	160,115
D₄.₁₀D₁₀	The non-split extension by D₄ of D₁₀ acting through Inn(D₄)	80	4-	D4.10D10	160,225
Q₈.₁₀D₁₀	1^st non-split extension by Q₈ of D₁₀ acting through Inn(Q₈)	80	4	Q8.10D10	160,222
Dic₅.D₄	1^st non-split extension by Dic₅ of D₄ acting via D₄/C₂=C₂²	80	4-	Dic5.D4	160,80
Dic₅.₅D₄	1^st non-split extension by Dic₅ of D₄ acting via D₄/C₄=C₂	80		Dic5.5D4	160,106
C₂³.D₁₀	3^rd non-split extension by C₂³ of D₁₀ acting via D₁₀/C₅=C₂²	80		C2^3.D10	160,100
C₂².D₂₀	3^rd non-split extension by C₂² of D₂₀ acting via D₂₀/D₁₀=C₂	80		C2^2.D20	160,107
C₂₀.C₂³	15^th non-split extension by C₂₀ of C₂³ acting via C₂³/C₂=C₂²	80	4	C20.C2^3	160,163
Dic₅.₁₄D₄	1^st non-split extension by Dic₅ of D₄ acting via D₄/C₂²=C₂	80		Dic5.14D4	160,99
C₂³.₁₁D₁₀	1^st non-split extension by C₂³ of D₁₀ acting via D₁₀/D₅=C₂	80		C2^3.11D10	160,98
C₂³.₂₁D₁₀	2^nd non-split extension by C₂³ of D₁₀ acting via D₁₀/C₁₀=C₂	80		C2^3.21D10	160,147
C₂³.₂₃D₁₀	4^th non-split extension by C₂³ of D₁₀ acting via D₁₀/C₁₀=C₂	80		C2^3.23D10	160,150
C₂³.₁₈D₁₀	8^th non-split extension by C₂³ of D₁₀ acting via D₁₀/D₅=C₂	80		C2^3.18D10	160,156
C₁₀.D₈	1^st non-split extension by C₁₀ of D₈ acting via D₈/D₄=C₂	160		C10.D8	160,14
C₂₀.Q₈	2^nd non-split extension by C₂₀ of Q₈ acting via Q₈/C₂=C₂²	160		C20.Q8	160,15
C₂₀.₈Q₈	5^th non-split extension by C₂₀ of Q₈ acting via Q₈/C₄=C₂	160		C20.8Q8	160,21
C₂₀.₆Q₈	3^rd non-split extension by C₂₀ of Q₈ acting via Q₈/C₄=C₂	160		C20.6Q8	160,91
C₂₀.₄₄D₄	1^st non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	160		C20.44D4	160,23
C₁₀.Q₁₆	2^nd non-split extension by C₁₀ of Q₁₆ acting via Q₁₆/Q₈=C₂	160		C10.Q16	160,17
C₄².D₅	1^st non-split extension by C₄² of D₅ acting via D₅/C₅=C₂	160		C4^2.D5	160,10
C₁₀.C₄²	4^th non-split extension by C₁₀ of C₄² acting via C₄²/C₄=C₄	160		C10.C4^2	160,77
Dic₅.Q₈	1^st non-split extension by Dic₅ of Q₈ acting via Q₈/C₄=C₂	160		Dic5.Q8	160,110
C₄.Dic₁₀	3^rd non-split extension by C₄ of Dic₁₀ acting via Dic₁₀/Dic₅=C₂	160		C4.Dic10	160,111
C₁₀.₁₀C₄²	5^th non-split extension by C₁₀ of C₄² acting via C₄²/C₂×C₄=C₂	160		C10.10C4^2	160,38
C₄×C₄₀	Abelian group of type [4,40]	160		C4xC40	160,46
C₂×C₈₀	Abelian group of type [2,80]	160		C2xC80	160,59
C₂²×C₄₀	Abelian group of type [2,2,40]	160		C2^2xC40	160,190
C₂³×C₂₀	Abelian group of type [2,2,2,20]	160		C2^3xC20	160,228
C₂⁴×C₁₀	Abelian group of type [2,2,2,2,10]	160		C2^4xC10	160,238
C₂×C₄×C₂₀	Abelian group of type [2,4,20]	160		C2xC4xC20	160,175
D₄×F₅	Direct product of D₄ and F₅; = Aut(D₂₀) = Hol(C₂₀)	20	8+	D4xF5	160,207
D₅×D₈	Direct product of D₅ and D₈	40	4+	D5xD8	160,131
C₈×F₅	Direct product of C₈ and F₅	40	4	C8xF5	160,66
Q₈×F₅	Direct product of Q₈ and F₅	40	8-	Q8xF5	160,209
D₅×SD₁₆	Direct product of D₅ and SD₁₆	40	4	D5xSD16	160,134
C₂³×F₅	Direct product of C₂³ and F₅	40		C2^3xF5	160,236
D₅×M₄(2)	Direct product of D₅ and M₄(2)	40	4	D5xM4(2)	160,127
C₅×2₊¹⁺⁴	Direct product of C₅ and 2₊¹⁺⁴	40	4	C5xES+(2,2)	160,232
D₅×C₁₆	Direct product of C₁₆ and D₅	80	2	D5xC16	160,4
C₅×D₁₆	Direct product of C₅ and D₁₆	80	2	C5xD16	160,61
C₄×D₂₀	Direct product of C₄ and D₂₀	80		C4xD20	160,94
C₂×D₄₀	Direct product of C₂ and D₄₀	80		C2xD40	160,124
D₄×C₂₀	Direct product of C₂₀ and D₄	80		D4xC20	160,179
C₁₀×D₈	Direct product of C₁₀ and D₈	80		C10xD8	160,193
D₅×Q₁₆	Direct product of D₅ and Q₁₆	80	4-	D5xQ16	160,138
C₅×SD₃₂	Direct product of C₅ and SD₃₂	80	2	C5xSD32	160,62
D₄×Dic₅	Direct product of D₄ and Dic₅	80		D4xDic5	160,155
D₅×C₄²	Direct product of C₄² and D₅	80		D5xC4^2	160,92
D₅×C₂⁴	Direct product of C₂⁴ and D₅	80		D5xC2^4	160,237
C₁₀×SD₁₆	Direct product of C₁₀ and SD₁₆	80		C10xSD16	160,194
C₂²×D₂₀	Direct product of C₂² and D₂₀	80		C2^2xD20	160,215
C₅×M₅(2)	Direct product of C₅ and M₅(2)	80	2	C5xM5(2)	160,60
C₁₀×M₄(2)	Direct product of C₁₀ and M₄(2)	80		C10xM4(2)	160,191
C₅×2_-¹⁺⁴	Direct product of C₅ and 2_-¹⁺⁴	80	4	C5xES-(2,2)	160,233
C₅×Q₃₂	Direct product of C₅ and Q₃₂	160	2	C5xQ32	160,63
Q₈×C₂₀	Direct product of C₂₀ and Q₈	160		Q8xC20	160,180
C₁₀×Q₁₆	Direct product of C₁₀ and Q₁₆	160		C10xQ16	160,195
C₈×Dic₅	Direct product of C₈ and Dic₅	160		C8xDic5	160,20
Q₈×Dic₅	Direct product of Q₈ and Dic₅	160		Q8xDic5	160,166
C₄×Dic₁₀	Direct product of C₄ and Dic₁₀	160		C4xDic10	160,89
C₂×Dic₂₀	Direct product of C₂ and Dic₂₀	160		C2xDic20	160,126
C₂³×Dic₅	Direct product of C₂³ and Dic₅	160		C2^3xDic5	160,226
C₂²×Dic₁₀	Direct product of C₂² and Dic₁₀	160		C2^2xDic10	160,213
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	10	5+	C2xC2^4:C5	160,235
C₂×D₄×D₅	Direct product of C₂, D₄ and D₅	40		C2xD4xD5	160,217
C₂×C₄×F₅	Direct product of C₂×C₄ and F₅	40		C2xC4xF5	160,203
C₅×C₄≀C₂	Direct product of C₅ and C₄≀C₂	40	2	C5xC4wrC2	160,54
C₂×C₄⋊F₅	Direct product of C₂ and C₄⋊F₅	40		C2xC4:F5	160,204
D₅×C₄○D₄	Direct product of D₅ and C₄○D₄	40	4	D5xC4oD4	160,223
C₅×C₂³⋊C₄	Direct product of C₅ and C₂³⋊C₄	40	4	C5xC2^3:C4	160,49
C₅×C₈⋊C₂²	Direct product of C₅ and C₈⋊C₂²	40	4	C5xC8:C2^2	160,197
D₅×C₂²⋊C₄	Direct product of D₅ and C₂²⋊C₄	40		D5xC2^2:C4	160,101
C₅×C₄.D₄	Direct product of C₅ and C₄.D₄	40	4	C5xC4.D4	160,50
C₂×C₂²⋊F₅	Direct product of C₂ and C₂²⋊F₅	40		C2xC2^2:F5	160,212
C₅×C₂²≀C₂	Direct product of C₅ and C₂²≀C₂	40		C5xC2^2wrC2	160,181
D₅×C₂×C₈	Direct product of C₂×C₈ and D₅	80		D5xC2xC8	160,120
C₂×Q₈×D₅	Direct product of C₂, Q₈ and D₅	80		C2xQ8xD5	160,220
D₅×C₄⋊C₄	Direct product of D₅ and C₄⋊C₄	80		D5xC4:C4	160,112
D₄×C₂×C₁₀	Direct product of C₂×C₁₀ and D₄	80		D4xC2xC10	160,229
C₄×C₅⋊D₄	Direct product of C₄ and C₅⋊D₄	80		C4xC5:D4	160,149
C₂×D₄⋊D₅	Direct product of C₂ and D₄⋊D₅	80		C2xD4:D5	160,152
C₂×D₅⋊C₈	Direct product of C₂ and D₅⋊C₈	80		C2xD5:C8	160,200
C₅×C₈○D₄	Direct product of C₅ and C₈○D₄	80	2	C5xC8oD4	160,192
C₅×C₄○D₈	Direct product of C₅ and C₄○D₈	80	2	C5xC4oD8	160,196
C₂×C₈⋊D₅	Direct product of C₂ and C₈⋊D₅	80		C2xC8:D5	160,121
C₅×C₄⋊D₄	Direct product of C₅ and C₄⋊D₄	80		C5xC4:D4	160,182
C₂×Q₈⋊D₅	Direct product of C₂ and Q₈⋊D₅	80		C2xQ8:D5	160,162
C₂×C₄₀⋊C₂	Direct product of C₂ and C₄₀⋊C₂	80		C2xC40:C2	160,123
D₅×C₂²×C₄	Direct product of C₂²×C₄ and D₅	80		D5xC2^2xC4	160,214
C₂×C₄.F₅	Direct product of C₂ and C₄.F₅	80		C2xC4.F5	160,201
C₂×C₄○D₂₀	Direct product of C₂ and C₄○D₂₀	80		C2xC4oD20	160,216
C₁₀×C₄○D₄	Direct product of C₁₀ and C₄○D₄	80		C10xC4oD4	160,231
C₅×D₄⋊C₄	Direct product of C₅ and D₄⋊C₄	80		C5xD4:C4	160,52
C₅×C₈.C₄	Direct product of C₅ and C₈.C₄	80	2	C5xC8.C4	160,58
C₅×C₄⋊₁D₄	Direct product of C₅ and C₄⋊₁D₄	80		C5xC4:1D4	160,188
C₅×C₂²⋊C₈	Direct product of C₅ and C₂²⋊C₈	80		C5xC2^2:C8	160,48
C₂×D₄.D₅	Direct product of C₂ and D₄.D₅	80		C2xD4.D5	160,154
C₂²×C₅⋊D₄	Direct product of C₂² and C₅⋊D₄	80		C2^2xC5:D4	160,227
C₅×C₂²⋊Q₈	Direct product of C₅ and C₂²⋊Q₈	80		C5xC2^2:Q8	160,183
C₂×D₁₀⋊C₄	Direct product of C₂ and D₁₀⋊C₄	80		C2xD10:C4	160,148
C₂×D₄⋊₂D₅	Direct product of C₂ and D₄⋊₂D₅	80		C2xD4:2D5	160,218
C₁₀×C₂²⋊C₄	Direct product of C₁₀ and C₂²⋊C₄	80		C10xC2^2:C4	160,176
C₅×C₄²⋊C₂	Direct product of C₅ and C₄²⋊C₂	80		C5xC4^2:C2	160,178
C₂×Q₈⋊₂D₅	Direct product of C₂ and Q₈⋊₂D₅	80		C2xQ8:2D5	160,221
C₅×C₄.₄D₄	Direct product of C₅ and C₄.₄D₄	80		C5xC4.4D4	160,185
C₅×C₈.C₂²	Direct product of C₅ and C₈.C₂²	80	4	C5xC8.C2^2	160,198
C₂×C₄.Dic₅	Direct product of C₂ and C₄.Dic₅	80		C2xC4.Dic5	160,142
C₂×C₂³.D₅	Direct product of C₂ and C₂³.D₅	80		C2xC2^3.D5	160,173
C₂×C₂².F₅	Direct product of C₂ and C₂².F₅	80		C2xC2^2.F5	160,211
C₅×C₄²⋊₂C₂	Direct product of C₅ and C₄²⋊₂C₂	80		C5xC4^2:2C2	160,187
C₅×C₄.₁₀D₄	Direct product of C₅ and C₄.₁₀D₄	80	4	C5xC4.10D4	160,51
C₅×C₂².D₄	Direct product of C₅ and C₂².D₄	80		C5xC2^2.D4	160,184
C₄×C₅⋊C₈	Direct product of C₄ and C₅⋊C₈	160		C4xC5:C8	160,75
C₅×C₄⋊C₈	Direct product of C₅ and C₄⋊C₈	160		C5xC4:C8	160,55
C₂×C₅⋊C₁₆	Direct product of C₂ and C₅⋊C₁₆	160		C2xC5:C16	160,72
C₅×C₄⋊Q₈	Direct product of C₅ and C₄⋊Q₈	160		C5xC4:Q8	160,189
C₁₀×C₄⋊C₄	Direct product of C₁₀ and C₄⋊C₄	160		C10xC4:C4	160,177
Q₈×C₂×C₁₀	Direct product of C₂×C₁₀ and Q₈	160		Q8xC2xC10	160,230
C₅×C₈⋊C₄	Direct product of C₅ and C₈⋊C₄	160		C5xC8:C4	160,47
C₄×C₅⋊₂C₈	Direct product of C₄ and C₅⋊₂C₈	160		C4xC5:2C8	160,9
C₂²×C₅⋊C₈	Direct product of C₂² and C₅⋊C₈	160		C2^2xC5:C8	160,210
C₂×C₄×Dic₅	Direct product of C₂×C₄ and Dic₅	160		C2xC4xDic5	160,143
C₂×C₅⋊Q₁₆	Direct product of C₂ and C₅⋊Q₁₆	160		C2xC5:Q16	160,164
C₂×C₅⋊₂C₁₆	Direct product of C₂ and C₅⋊₂C₁₆	160		C2xC5:2C16	160,18
C₂×C₄⋊Dic₅	Direct product of C₂ and C₄⋊Dic₅	160		C2xC4:Dic5	160,146
C₅×Q₈⋊C₄	Direct product of C₅ and Q₈⋊C₄	160		C5xQ8:C4	160,53
C₅×C₂.D₈	Direct product of C₅ and C₂.D₈	160		C5xC2.D8	160,57
C₅×C₄.Q₈	Direct product of C₅ and C₄.Q₈	160		C5xC4.Q8	160,56
C₂²×C₅⋊₂C₈	Direct product of C₂² and C₅⋊₂C₈	160		C2^2xC5:2C8	160,141
C₂×C₁₀.D₄	Direct product of C₂ and C₁₀.D₄	160		C2xC10.D4	160,144
C₅×C₂.C₄²	Direct product of C₅ and C₂.C₄²	160		C5xC2.C4^2	160,45
C₅×C₄².C₂	Direct product of C₅ and C₄².C₂	160		C5xC4^2.C2	160,186

Groups of order 161

		d	ρ	Label	ID
C₁₆₁	Cyclic group	161	1	C161	161,1

Groups of order 162

		d	ρ	Label	ID
C₁₆₂	Cyclic group	162	1	C162	162,2
D₈₁	Dihedral group	81	2+	D81	162,1
C₃≀S₃	Wreath product of C₃ by S₃	9	3	C3wrS3	162,10
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	9	6+	C3^3:C6	162,11
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	9	6+	C3^3:S3	162,19
C₉⋊C₁₈	The semidirect product of C₉ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C9:C18	162,6
C₃²⋊C₁₈	The semidirect product of C₃² and C₁₈ acting via C₁₈/C₃=C₆	18	6	C3^2:C18	162,4
He₃⋊₅S₃	2^nd semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	18	6	He3:5S3	162,46
C₃²⋊₂D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	18	6	C3^2:2D9	162,17
C₂₇⋊C₆	The semidirect product of C₂₇ and C₆ acting faithfully	27	6+	C27:C6	162,9
He₃⋊S₃	3^rd semidirect product of He₃ and S₃ acting faithfully	27	6+	He3:S3	162,21
He₃⋊₄S₃	1^st semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	27		He3:4S3	162,40
C₃²⋊D₉	1^st semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	27		C3^2:D9	162,5
C₉⋊D₉	The semidirect product of C₉ and D₉ acting via D₉/C₉=C₂	81		C9:D9	162,16
C₂₇⋊S₃	The semidirect product of C₂₇ and S₃ acting via S₃/C₃=C₂	81		C27:S3	162,18
C₃⁴⋊C₂	4^th semidirect product of C₃⁴ and C₂ acting faithfully	81		C3^4:C2	162,54
C₃²⋊₄D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₉=C₂	81		C3^2:4D9	162,45
He₃.C₆	1^st non-split extension by He₃ of C₆ acting faithfully	27	3	He3.C6	162,12
He₃.S₃	1^st non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.S3	162,13
He₃.₂C₆	2^nd non-split extension by He₃ of C₆ acting faithfully	27	3	He3.2C6	162,14
He₃.₂S₃	2^nd non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.2S3	162,15
He₃.₃S₃	3^rd non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.3S3	162,20
He₃.₄S₃	The non-split extension by He₃ of S₃ acting via S₃/C₃=C₂	27	6+	He3.4S3	162,43
He₃.₄C₆	The non-split extension by He₃ of C₆ acting via C₆/C₃=C₂	27	3	He3.4C6	162,44
C₃³.S₃	4^th non-split extension by C₃³ of S₃ acting faithfully	27		C3^3.S3	162,42
3_-¹⁺².S₃	The non-split extension by 3_-¹⁺² of S₃ acting faithfully	27	6+	ES-(3,1).S3	162,22
C₉×C₁₈	Abelian group of type [9,18]	162		C9xC18	162,23
C₃×C₅₄	Abelian group of type [3,54]	162		C3xC54	162,26
C₃³×C₆	Abelian group of type [3,3,3,6]	162		C3^3xC6	162,55
C₃²×C₁₈	Abelian group of type [3,3,18]	162		C3^2xC18	162,47
C₉×D₉	Direct product of C₉ and D₉	18	2	C9xD9	162,3
S₃×He₃	Direct product of S₃ and He₃	18	6	S3xHe3	162,35
S₃×3_-¹⁺²	Direct product of S₃ and 3_-¹⁺²	18	6	S3xES-(3,1)	162,37
S₃×C₂₇	Direct product of C₂₇ and S₃	54	2	S3xC27	162,8
C₃×D₂₇	Direct product of C₃ and D₂₇	54	2	C3xD27	162,7
C₆×He₃	Direct product of C₆ and He₃	54		C6xHe3	162,48
S₃×C₃³	Direct product of C₃³ and S₃	54		S3xC3^3	162,51
C₃²×D₉	Direct product of C₃² and D₉	54		C3^2xD9	162,32
C₆×3_-¹⁺²	Direct product of C₆ and 3_-¹⁺²	54		C6xES-(3,1)	162,49
C₃×C₉⋊C₆	Direct product of C₃ and C₉⋊C₆	18	6	C3xC9:C6	162,36
C₂×C₃≀C₃	Direct product of C₂ and C₃≀C₃	18	3	C2xC3wrC3	162,28
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	18	6	C3xC3^2:C6	162,34
C₃²×C₃⋊S₃	Direct product of C₃² and C₃⋊S₃	18		C3^2xC3:S3	162,52
C₃×He₃⋊C₂	Direct product of C₃ and He₃⋊C₂	27		C3xHe3:C2	162,41
S₃×C₃×C₉	Direct product of C₃×C₉ and S₃	54		S3xC3xC9	162,33
C₃×C₉⋊S₃	Direct product of C₃ and C₉⋊S₃	54		C3xC9:S3	162,38
C₉×C₃⋊S₃	Direct product of C₉ and C₃⋊S₃	54		C9xC3:S3	162,39
C₂×C₂₇⋊C₃	Direct product of C₂ and C₂₇⋊C₃	54	3	C2xC27:C3	162,27
C₂×C₃²⋊C₉	Direct product of C₂ and C₃²⋊C₉	54		C2xC3^2:C9	162,24
C₂×C₉○He₃	Direct product of C₂ and C₉○He₃	54	3	C2xC9oHe3	162,50
C₃×C₃³⋊C₂	Direct product of C₃ and C₃³⋊C₂	54		C3xC3^3:C2	162,53
C₂×He₃⋊C₃	Direct product of C₂ and He₃⋊C₃	54	3	C2xHe3:C3	162,30
C₂×He₃.C₃	Direct product of C₂ and He₃.C₃	54	3	C2xHe3.C3	162,29
C₂×C₃.He₃	Direct product of C₂ and C₃.He₃	54	3	C2xC3.He3	162,31
C₂×C₉⋊C₉	Direct product of C₂ and C₉⋊C₉	162		C2xC9:C9	162,25

Groups of order 163

		d	ρ	Label	ID
C₁₆₃	Cyclic group	163	1	C163	163,1

Groups of order 164

		d	ρ	Label	ID
C₁₆₄	Cyclic group	164	1	C164	164,2
D₈₂	Dihedral group; = C₂×D₄₁	82	2+	D82	164,4
Dic₄₁	Dicyclic group; = C₄₁ ⋊₂ C₄	164	2-	Dic41	164,1
C₄₁⋊C₄	The semidirect product of C₄₁ and C₄ acting faithfully	41	4+	C41:C4	164,3
C₂×C₈₂	Abelian group of type [2,82]	164		C2xC82	164,5

Groups of order 165

		d	ρ	Label	ID
C₁₆₅	Cyclic group	165	1	C165	165,2
C₃×C₁₁⋊C₅	Direct product of C₃ and C₁₁⋊C₅	33	5	C3xC11:C5	165,1

Groups of order 166

		d	ρ	Label	ID
C₁₆₆	Cyclic group	166	1	C166	166,2
D₈₃	Dihedral group	83	2+	D83	166,1

Groups of order 167

		d	ρ	Label	ID
C₁₆₇	Cyclic group	167	1	C167	167,1

Groups of order 168

		d	ρ	Label	ID
C₁₆₈	Cyclic group	168	1	C168	168,6
D₈₄	Dihedral group	84	2+	D84	168,36
Dic₄₂	Dicyclic group; = C₂₁ ⋊₂ Q₈	168	2-	Dic42	168,34
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	7	3	GL(3,2)	168,42
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	8	7+	AGammaL(1,8)	168,43
C₇⋊S₄	The semidirect product of C₇ and S₄ acting via S₄/A₄=C₂	28	6+	C7:S4	168,46
C₄⋊F₇	The semidirect product of C₄ and F₇ acting via F₇/C₇⋊C₃=C₂	28	6+	C4:F7	168,9
D₇⋊A₄	The semidirect product of D₇ and A₄ acting via A₄/C₂²=C₃	28	6+	D7:A4	168,49
Dic₇⋊C₆	The semidirect product of Dic₇ and C₆ acting faithfully	28	6	Dic7:C6	168,11
C₇⋊C₂₄	The semidirect product of C₇ and C₂₄ acting via C₂₄/C₄=C₆	56	6	C7:C24	168,1
D₂₁⋊C₄	The semidirect product of D₂₁ and C₄ acting via C₄/C₂=C₂	84	4+	D21:C4	168,14
C₂₁⋊D₄	1^st semidirect product of C₂₁ and D₄ acting via D₄/C₂=C₂²	84	4-	C21:D4	168,15
C₃⋊D₂₈	The semidirect product of C₃ and D₂₈ acting via D₂₈/D₁₄=C₂	84	4+	C3:D28	168,16
C₇⋊D₁₂	The semidirect product of C₇ and D₁₂ acting via D₁₂/D₆=C₂	84	4+	C7:D12	168,17
C₂₁⋊₇D₄	1^st semidirect product of C₂₁ and D₄ acting via D₄/C₂²=C₂	84	2	C21:7D4	168,38
C₂₁⋊Q₈	The semidirect product of C₂₁ and Q₈ acting via Q₈/C₂=C₂²	168	4-	C21:Q8	168,18
C₂₁⋊C₈	1^st semidirect product of C₂₁ and C₈ acting via C₈/C₄=C₂	168	2	C21:C8	168,5
C₄.F₇	The non-split extension by C₄ of F₇ acting via F₇/C₇⋊C₃=C₂	56	6-	C4.F7	168,7
C₁₄.A₄	The non-split extension by C₁₄ of A₄ acting via A₄/C₂²=C₃	56	6	C14.A4	168,23
C₂×C₈₄	Abelian group of type [2,84]	168		C2xC84	168,39
C₂²×C₄₂	Abelian group of type [2,2,42]	168		C2^2xC42	168,57
C₃×F₈	Direct product of C₃ and F₈	24	7	C3xF8	168,44
C₇×S₄	Direct product of C₇ and S₄	28	3	C7xS4	168,45
A₄×D₇	Direct product of A₄ and D₇	28	6+	A4xD7	168,48
C₄×F₇	Direct product of C₄ and F₇	28	6	C4xF7	168,8
C₂²×F₇	Direct product of C₂² and F₇	28		C2^2xF7	168,47
A₄×C₁₄	Direct product of C₁₄ and A₄	42	3	A4xC14	168,52
C₇×SL₂(𝔽₃)	Direct product of C₇ and SL₂(𝔽₃)	56	2	C7xSL(2,3)	168,22
S₃×C₂₈	Direct product of C₂₈ and S₃	84	2	S3xC28	168,30
C₁₂×D₇	Direct product of C₁₂ and D₇	84	2	C12xD7	168,25
C₃×D₂₈	Direct product of C₃ and D₂₈	84	2	C3xD28	168,26
C₇×D₁₂	Direct product of C₇ and D₁₂	84	2	C7xD12	168,31
C₄×D₂₁	Direct product of C₄ and D₂₁	84	2	C4xD21	168,35
D₄×C₂₁	Direct product of C₂₁ and D₄	84	2	D4xC21	168,40
Dic₃×D₇	Direct product of Dic₃ and D₇	84	4-	Dic3xD7	168,12
S₃×Dic₇	Direct product of S₃ and Dic₇	84	4-	S3xDic7	168,13
C₂²×D₂₁	Direct product of C₂² and D₂₁	84		C2^2xD21	168,56
Q₈×C₂₁	Direct product of C₂₁ and Q₈	168	2	Q8xC21	168,41
C₆×Dic₇	Direct product of C₆ and Dic₇	168		C6xDic7	168,27
C₇×Dic₆	Direct product of C₇ and Dic₆	168	2	C7xDic6	168,29
C₃×Dic₁₄	Direct product of C₃ and Dic₁₄	168	2	C3xDic14	168,24
Dic₃×C₁₄	Direct product of C₁₄ and Dic₃	168		Dic3xC14	168,32
C₂×Dic₂₁	Direct product of C₂ and Dic₂₁	168		C2xDic21	168,37
D₄×C₇⋊C₃	Direct product of D₄ and C₇⋊C₃	28	6	D4xC7:C3	168,20
C₂×C₇⋊A₄	Direct product of C₂ and C₇⋊A₄	42	3	C2xC7:A4	168,53
C₂×S₃×D₇	Direct product of C₂, S₃ and D₇	42	4+	C2xS3xD7	168,50
C₈×C₇⋊C₃	Direct product of C₈ and C₇⋊C₃	56	3	C8xC7:C3	168,2
Q₈×C₇⋊C₃	Direct product of Q₈ and C₇⋊C₃	56	6	Q8xC7:C3	168,21
C₂×C₇⋊C₁₂	Direct product of C₂ and C₇⋊C₁₂	56		C2xC7:C12	168,10
C₂³×C₇⋊C₃	Direct product of C₂³ and C₇⋊C₃	56		C2^3xC7:C3	168,51
C₂×C₆×D₇	Direct product of C₂×C₆ and D₇	84		C2xC6xD7	168,54
S₃×C₂×C₁₄	Direct product of C₂×C₁₄ and S₃	84		S3xC2xC14	168,55
C₃×C₇⋊D₄	Direct product of C₃ and C₇⋊D₄	84	2	C3xC7:D4	168,28
C₇×C₃⋊D₄	Direct product of C₇ and C₃⋊D₄	84	2	C7xC3:D4	168,33
C₇×C₃⋊C₈	Direct product of C₇ and C₃⋊C₈	168	2	C7xC3:C8	168,3
C₃×C₇⋊C₈	Direct product of C₃ and C₇⋊C₈	168	2	C3xC7:C8	168,4
C₂×C₄×C₇⋊C₃	Direct product of C₂×C₄ and C₇⋊C₃	56		C2xC4xC7:C3	168,19

Groups of order 169

		d	ρ	Label	ID
C₁₆₉	Cyclic group	169	1	C169	169,1
C₁₃²	Elementary abelian group of type [13,13]	169		C13^2	169,2

Groups of order 170

		d	ρ	Label	ID
C₁₇₀	Cyclic group	170	1	C170	170,4
D₈₅	Dihedral group	85	2+	D85	170,3
D₅×C₁₇	Direct product of C₁₇ and D₅	85	2	D5xC17	170,1
C₅×D₁₇	Direct product of C₅ and D₁₇	85	2	C5xD17	170,2

Groups of order 171

		d	ρ	Label	ID
C₁₇₁	Cyclic group	171	1	C171	171,2
C₁₉⋊C₉	The semidirect product of C₁₉ and C₉ acting faithfully	19	9	C19:C9	171,3
C₁₉⋊₂C₉	The semidirect product of C₁₉ and C₉ acting via C₉/C₃=C₃	171	3	C19:2C9	171,1
C₃×C₅₇	Abelian group of type [3,57]	171		C3xC57	171,5
C₃×C₁₉⋊C₃	Direct product of C₃ and C₁₉⋊C₃	57	3	C3xC19:C3	171,4

Groups of order 172

		d	ρ	Label	ID
C₁₇₂	Cyclic group	172	1	C172	172,2
D₈₆	Dihedral group; = C₂×D₄₃	86	2+	D86	172,3
Dic₄₃	Dicyclic group; = C₄₃ ⋊C₄	172	2-	Dic43	172,1
C₂×C₈₆	Abelian group of type [2,86]	172		C2xC86	172,4

Groups of order 173

		d	ρ	Label	ID
C₁₇₃	Cyclic group	173	1	C173	173,1

Groups of order 174

		d	ρ	Label	ID
C₁₇₄	Cyclic group	174	1	C174	174,4
D₈₇	Dihedral group	87	2+	D87	174,3
S₃×C₂₉	Direct product of C₂₉ and S₃	87	2	S3xC29	174,1
C₃×D₂₉	Direct product of C₃ and D₂₉	87	2	C3xD29	174,2

Groups of order 175

		d	ρ	Label	ID
C₁₇₅	Cyclic group	175	1	C175	175,1
C₅×C₃₅	Abelian group of type [5,35]	175		C5xC35	175,2

Groups of order 176

		d	ρ	Label	ID
C₁₇₆	Cyclic group	176	1	C176	176,2
D₈₈	Dihedral group	88	2+	D88	176,6
Dic₄₄	Dicyclic group; = C₁₁ ⋊₁ Q₁₆	176	2-	Dic44	176,7
D₂₂⋊C₄	The semidirect product of D₂₂ and C₄ acting via C₄/C₂=C₂	88		D22:C4	176,13
D₄⋊D₁₁	The semidirect product of D₄ and D₁₁ acting via D₁₁/C₁₁=C₂	88	4+	D4:D11	176,14
Q₈⋊D₁₁	The semidirect product of Q₈ and D₁₁ acting via D₁₁/C₁₁=C₂	88	4+	Q8:D11	176,16
C₈₈⋊C₂	4^th semidirect product of C₈₈ and C₂ acting faithfully	88	2	C88:C2	176,4
C₈⋊D₁₁	2^nd semidirect product of C₈ and D₁₁ acting via D₁₁/C₁₁=C₂	88	2	C8:D11	176,5
D₄₄⋊₅C₂	The semidirect product of D₄₄ and C₂ acting through Inn(D₄₄)	88	2	D44:5C2	176,30
D₄⋊₂D₁₁	The semidirect product of D₄ and D₁₁ acting through Inn(D₄)	88	4-	D4:2D11	176,32
D₄₄⋊C₂	4^th semidirect product of D₄₄ and C₂ acting faithfully	88	4+	D44:C2	176,34
C₁₁⋊C₁₆	The semidirect product of C₁₁ and C₁₆ acting via C₁₆/C₈=C₂	176	2	C11:C16	176,1
C₄₄⋊C₄	1^st semidirect product of C₄₄ and C₄ acting via C₄/C₂=C₂	176		C44:C4	176,12
C₁₁⋊Q₁₆	The semidirect product of C₁₁ and Q₁₆ acting via Q₁₆/Q₈=C₂	176	4-	C11:Q16	176,17
Dic₁₁⋊C₄	The semidirect product of Dic₁₁ and C₄ acting via C₄/C₂=C₂	176		Dic11:C4	176,11
D₄.D₁₁	The non-split extension by D₄ of D₁₁ acting via D₁₁/C₁₁=C₂	88	4-	D4.D11	176,15
C₄₄.C₄	1^st non-split extension by C₄₄ of C₄ acting via C₄/C₂=C₂	88	2	C44.C4	176,9
C₂³.D₁₁	The non-split extension by C₂³ of D₁₁ acting via D₁₁/C₁₁=C₂	88		C2^3.D11	176,18
C₄×C₄₄	Abelian group of type [4,44]	176		C4xC44	176,19
C₂×C₈₈	Abelian group of type [2,88]	176		C2xC88	176,22
C₂²×C₄₄	Abelian group of type [2,2,44]	176		C2^2xC44	176,37
C₂³×C₂₂	Abelian group of type [2,2,2,22]	176		C2^3xC22	176,42
D₄×D₁₁	Direct product of D₄ and D₁₁	44	4+	D4xD11	176,31
C₈×D₁₁	Direct product of C₈ and D₁₁	88	2	C8xD11	176,3
C₁₁×D₈	Direct product of C₁₁ and D₈	88	2	C11xD8	176,24
C₂×D₄₄	Direct product of C₂ and D₄₄	88		C2xD44	176,29
D₄×C₂₂	Direct product of C₂₂ and D₄	88		D4xC22	176,38
Q₈×D₁₁	Direct product of Q₈ and D₁₁	88	4-	Q8xD11	176,33
C₁₁×SD₁₆	Direct product of C₁₁ and SD₁₆	88	2	C11xSD16	176,25
C₂³×D₁₁	Direct product of C₂³ and D₁₁	88		C2^3xD11	176,41
C₁₁×M₄(2)	Direct product of C₁₁ and M₄(2)	88	2	C11xM4(2)	176,23
Q₈×C₂₂	Direct product of C₂₂ and Q₈	176		Q8xC22	176,39
C₁₁×Q₁₆	Direct product of C₁₁ and Q₁₆	176	2	C11xQ16	176,26
C₄×Dic₁₁	Direct product of C₄ and Dic₁₁	176		C4xDic11	176,10
C₂×Dic₂₂	Direct product of C₂ and Dic₂₂	176		C2xDic22	176,27
C₂²×Dic₁₁	Direct product of C₂² and Dic₁₁	176		C2^2xDic11	176,35
C₂×C₄×D₁₁	Direct product of C₂×C₄ and D₁₁	88		C2xC4xD11	176,28
C₂×C₁₁⋊D₄	Direct product of C₂ and C₁₁⋊D₄	88		C2xC11:D4	176,36
C₁₁×C₄○D₄	Direct product of C₁₁ and C₄○D₄	88	2	C11xC4oD4	176,40
C₁₁×C₂²⋊C₄	Direct product of C₁₁ and C₂²⋊C₄	88		C11xC2^2:C4	176,20
C₂×C₁₁⋊C₈	Direct product of C₂ and C₁₁⋊C₈	176		C2xC11:C8	176,8
C₁₁×C₄⋊C₄	Direct product of C₁₁ and C₄⋊C₄	176		C11xC4:C4	176,21

Groups of order 177

		d	ρ	Label	ID
C₁₇₇	Cyclic group	177	1	C177	177,1

Groups of order 178

		d	ρ	Label	ID
C₁₇₈	Cyclic group	178	1	C178	178,2
D₈₉	Dihedral group	89	2+	D89	178,1

Groups of order 179

		d	ρ	Label	ID
C₁₇₉	Cyclic group	179	1	C179	179,1

Groups of order 180

		d	ρ	Label	ID
C₁₈₀	Cyclic group	180	1	C180	180,4
D₉₀	Dihedral group; = C₂×D₄₅	90	2+	D90	180,11
Dic₄₅	Dicyclic group; = C₉ ⋊Dic₅	180	2-	Dic45	180,3
C₃²⋊F₅	The semidirect product of C₃² and F₅ acting via F₅/C₅=C₄	30	4+	C3^2:F5	180,25
D₁₅⋊S₃	The semidirect product of D₁₅ and S₃ acting via S₃/C₃=C₂	30	4	D15:S3	180,30
C₃²⋊Dic₅	The semidirect product of C₃² and Dic₅ acting via Dic₅/C₅=C₄	30	4	C3^2:Dic5	180,24
C₉⋊F₅	The semidirect product of C₉ and F₅ acting via F₅/D₅=C₂	45	4	C9:F5	180,6
C₃²⋊₃F₅	2^nd semidirect product of C₃² and F₅ acting via F₅/D₅=C₂	45		C3^2:3F5	180,22
C₃⋊Dic₁₅	The semidirect product of C₃ and Dic₁₅ acting via Dic₁₅/C₃₀=C₂	180		C3:Dic15	180,17
C₂×C₉₀	Abelian group of type [2,90]	180		C2xC90	180,12
C₃×C₆₀	Abelian group of type [3,60]	180		C3xC60	180,18
C₆×C₃₀	Abelian group of type [6,30]	180		C6xC30	180,37
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	15	3	C3xA5	180,19
S₃×D₁₅	Direct product of S₃ and D₁₅	30	4+	S3xD15	180,29
D₅×D₉	Direct product of D₅ and D₉	45	4+	D5xD9	180,7
C₉×F₅	Direct product of C₉ and F₅	45	4	C9xF5	180,5
C₃²×F₅	Direct product of C₃² and F₅	45		C3^2xF5	180,20
S₃×C₃₀	Direct product of C₃₀ and S₃	60	2	S3xC30	180,33
A₄×C₁₅	Direct product of C₁₅ and A₄	60	3	A4xC15	180,31
C₆×D₁₅	Direct product of C₆ and D₁₅	60	2	C6xD15	180,34
Dic₃×C₁₅	Direct product of C₁₅ and Dic₃	60	2	Dic3xC15	180,14
C₃×Dic₁₅	Direct product of C₃ and Dic₁₅	60	2	C3xDic15	180,15
D₅×C₁₈	Direct product of C₁₈ and D₅	90	2	D5xC18	180,9
C₁₀×D₉	Direct product of C₁₀ and D₉	90	2	C10xD9	180,10
C₅×Dic₉	Direct product of C₅ and Dic₉	180	2	C5xDic9	180,1
C₉×Dic₅	Direct product of C₉ and Dic₅	180	2	C9xDic5	180,2
C₃²×Dic₅	Direct product of C₃² and Dic₅	180		C3^2xDic5	180,13
C₅×S₃²	Direct product of C₅, S₃ and S₃	30	4	C5xS3^2	180,28
C₃×S₃×D₅	Direct product of C₃, S₃ and D₅	30	4	C3xS3xD5	180,26
C₃×C₃⋊F₅	Direct product of C₃ and C₃⋊F₅	30	4	C3xC3:F5	180,21
C₅×C₃²⋊C₄	Direct product of C₅ and C₃²⋊C₄	30	4	C5xC3^2:C4	180,23
D₅×C₃⋊S₃	Direct product of D₅ and C₃⋊S₃	45		D5xC3:S3	180,27
D₅×C₃×C₆	Direct product of C₃×C₆ and D₅	90		D5xC3xC6	180,32
C₁₀×C₃⋊S₃	Direct product of C₁₀ and C₃⋊S₃	90		C10xC3:S3	180,35
C₂×C₃⋊D₁₅	Direct product of C₂ and C₃⋊D₁₅	90		C2xC3:D15	180,36
C₅×C₃.A₄	Direct product of C₅ and C₃.A₄	90	3	C5xC3.A4	180,8
C₅×C₃⋊Dic₃	Direct product of C₅ and C₃⋊Dic₃	180		C5xC3:Dic3	180,16

Groups of order 181

		d	ρ	Label	ID
C₁₈₁	Cyclic group	181	1	C181	181,1

Groups of order 182

		d	ρ	Label	ID
C₁₈₂	Cyclic group	182	1	C182	182,4
D₉₁	Dihedral group	91	2+	D91	182,3
C₁₃×D₇	Direct product of C₁₃ and D₇	91	2	C13xD7	182,1
C₇×D₁₃	Direct product of C₇ and D₁₃	91	2	C7xD13	182,2

Groups of order 183

		d	ρ	Label	ID
C₁₈₃	Cyclic group	183	1	C183	183,2
C₆₁⋊C₃	The semidirect product of C₆₁ and C₃ acting faithfully	61	3	C61:C3	183,1

Groups of order 184

		d	ρ	Label	ID
C₁₈₄	Cyclic group	184	1	C184	184,2
D₉₂	Dihedral group	92	2+	D92	184,5
Dic₄₆	Dicyclic group; = C₂₃ ⋊Q₈	184	2-	Dic46	184,3
C₂₃⋊D₄	The semidirect product of C₂₃ and D₄ acting via D₄/C₂²=C₂	92	2	C23:D4	184,7
C₂₃⋊C₈	The semidirect product of C₂₃ and C₈ acting via C₈/C₄=C₂	184	2	C23:C8	184,1
C₂×C₉₂	Abelian group of type [2,92]	184		C2xC92	184,8
C₂²×C₄₆	Abelian group of type [2,2,46]	184		C2^2xC46	184,12
C₄×D₂₃	Direct product of C₄ and D₂₃	92	2	C4xD23	184,4
D₄×C₂₃	Direct product of C₂₃ and D₄	92	2	D4xC23	184,9
C₂²×D₂₃	Direct product of C₂² and D₂₃	92		C2^2xD23	184,11
Q₈×C₂₃	Direct product of C₂₃ and Q₈	184	2	Q8xC23	184,10
C₂×Dic₂₃	Direct product of C₂ and Dic₂₃	184		C2xDic23	184,6

Groups of order 185

		d	ρ	Label	ID
C₁₈₅	Cyclic group	185	1	C185	185,1

Groups of order 186

		d	ρ	Label	ID
C₁₈₆	Cyclic group	186	1	C186	186,6
D₉₃	Dihedral group	93	2+	D93	186,5
C₃₁⋊C₆	The semidirect product of C₃₁ and C₆ acting faithfully	31	6+	C31:C6	186,1
S₃×C₃₁	Direct product of C₃₁ and S₃	93	2	S3xC31	186,3
C₃×D₃₁	Direct product of C₃ and D₃₁	93	2	C3xD31	186,4
C₂×C₃₁⋊C₃	Direct product of C₂ and C₃₁⋊C₃	62	3	C2xC31:C3	186,2

Groups of order 187

		d	ρ	Label	ID
C₁₈₇	Cyclic group	187	1	C187	187,1

Groups of order 188

		d	ρ	Label	ID
C₁₈₈	Cyclic group	188	1	C188	188,2
D₉₄	Dihedral group; = C₂×D₄₇	94	2+	D94	188,3
Dic₄₇	Dicyclic group; = C₄₇ ⋊C₄	188	2-	Dic47	188,1
C₂×C₉₄	Abelian group of type [2,94]	188		C2xC94	188,4

Groups of order 189

		d	ρ	Label	ID
C₁₈₉	Cyclic group	189	1	C189	189,2
C₇⋊He₃	The semidirect product of C₇ and He₃ acting via He₃/C₃²=C₃	63	3	C7:He3	189,8
C₆₃⋊C₃	2^nd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:C3	189,4
C₆₃⋊₃C₃	3^rd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:3C3	189,5
C₇⋊C₂₇	The semidirect product of C₇ and C₂₇ acting via C₂₇/C₉=C₃	189	3	C7:C27	189,1
C₂₁.C₃²	5^th non-split extension by C₂₁ of C₃² acting via C₃²/C₃=C₃	63	3	C21.C3^2	189,7
C₃×C₆₃	Abelian group of type [3,63]	189		C3xC63	189,9
C₃²×C₂₁	Abelian group of type [3,3,21]	189		C3^2xC21	189,13
C₇×He₃	Direct product of C₇ and He₃	63	3	C7xHe3	189,10
C₇×3_-¹⁺²	Direct product of C₇ and 3_-¹⁺²	63	3	C7xES-(3,1)	189,11
C₉×C₇⋊C₃	Direct product of C₉ and C₇⋊C₃	63	3	C9xC7:C3	189,3
C₃²×C₇⋊C₃	Direct product of C₃² and C₇⋊C₃	63		C3^2xC7:C3	189,12
C₃×C₇⋊C₉	Direct product of C₃ and C₇⋊C₉	189		C3xC7:C9	189,6

Groups of order 190

		d	ρ	Label	ID
C₁₉₀	Cyclic group	190	1	C190	190,4
D₉₅	Dihedral group	95	2+	D95	190,3
D₅×C₁₉	Direct product of C₁₉ and D₅	95	2	D5xC19	190,1
C₅×D₁₉	Direct product of C₅ and D₁₉	95	2	C5xD19	190,2

Groups of order 191

		d	ρ	Label	ID
C₁₉₁	Cyclic group	191	1	C191	191,1

Groups of order 192

		d	ρ	Label	ID
C₁₉₂	Cyclic group	192	1	C192	192,2
D₉₆	Dihedral group	96	2+	D96	192,7
Dic₄₈	Dicyclic group; = C₃ ⋊₁ Q₆₄	192	2-	Dic48	192,9
CU₂(𝔽₃)	Conformal unitary group on 𝔽₃²; = U₂(𝔽₃)⋊₇ C₂	32	2	CU(2,3)	192,963
C₂≀A₄	Wreath product of C₂ by A₄	8	4+	C2wrA4	192,201
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	8	4+	Q8:2S4	192,1494
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	8	4+	C2^3:S4	192,1493
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	8	6+	C2^4:D6	192,955
C₄²⋊D₆	The semidirect product of C₄² and D₆ acting faithfully	12	6+	C4^2:D6	192,956
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	12	6+	C2^4:C12	192,191
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	12	6+	C2^4:4Dic3	192,1495
C₄²⋊A₄	The semidirect product of C₄² and A₄ acting faithfully	16	12+	C4^2:A4	192,1023
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	16	12+	C2^4:A4	192,1009
C₂⁴⋊₅A₄	5^th semidirect product of C₂⁴ and A₄ acting faithfully	16		C2^4:5A4	192,1024
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	16	12+	C2^4:Dic3	192,184
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	16	12+	C4^2:Dic3	192,185
D₄⋊S₄	The semidirect product of D₄ and S₄ acting via S₄/A₄=C₂	24	6+	D4:S4	192,974
C₈²⋊C₃	The semidirect product of C₈² and C₃ acting faithfully	24	3	C8^2:C3	192,3
C₈⋊S₄	3^rd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	24	6	C8:S4	192,959
C₈⋊₂S₄	2^nd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	24	6	C8:2S4	192,960
A₄⋊D₈	The semidirect product of A₄ and D₈ acting via D₈/C₈=C₂	24	6+	A4:D8	192,961
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	24	6	D4:2S4	192,1473
C₂⁶⋊C₃	3^rd semidirect product of C₂⁶ and C₃ acting faithfully	24		C2^6:C3	192,1541
Q₈⋊₃S₄	The semidirect product of Q₈ and S₄ acting via S₄/A₄=C₂	24	6	Q8:3S4	192,976
Q₈⋊₄S₄	The semidirect product of Q₈ and S₄ acting through Inn(Q₈)	24	6	Q8:4S4	192,1478
Q₈⋊S₄	1^st semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃	24	6	Q8:S4	192,1490
C₂³⋊D₁₂	The semidirect product of C₂³ and D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3:D12	192,300
D₁₂⋊₁D₄	1^st semidirect product of D₁₂ and D₄ acting via D₄/C₂=C₂²	24	8+	D12:1D4	192,306
C₄²⋊₂A₄	The semidirect product of C₄² and A₄ acting via A₄/C₂²=C₃	24		C4^2:2A4	192,1020
Q₈⋊₅D₁₂	3^rd semidirect product of Q₈ and D₁₂ acting via D₁₂/D₆=C₂	24	4+	Q8:5D12	192,381
C₂⁴⋊₆D₆	1^st semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	24	4	C2^4:6D6	192,591
C₄²⋊₈D₆	6^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	24	4	C4^2:8D6	192,636
D₁₂⋊₁₈D₄	6^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	24	8+	D12:18D4	192,757
C₄²⋊C₁₂	1^st semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	24	6	C4^2:C12	192,192
C₄²⋊₂C₁₂	2^nd semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	24	6-	C4^2:2C12	192,193
A₄⋊SD₁₆	The semidirect product of A₄ and SD₁₆ acting via SD₁₆/D₄=C₂	24	6	A4:SD16	192,973
A₄⋊M₄(2)	The semidirect product of A₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	24	6	A4:M4(2)	192,968
C₂⁴⋊₅Dic₃	1^st semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₃=C₄	24	4	C2^4:5Dic3	192,95
C₄²⋊₅Dic₃	3^rd semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	24	4	C4^2:5Dic3	192,104
2₊¹⁺⁴⋊₆S₃	1^st semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	24	8+	ES+(2,2):6S3	192,800
2₊¹⁺⁴⋊₇S₃	2^nd semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	24	8+	ES+(2,2):7S3	192,803
Q₈⋊D₁₂	The semidirect product of Q₈ and D₁₂ acting via D₁₂/C₄=S₃	32		Q8:D12	192,952
U₂(𝔽₃)⋊C₂	6^th semidirect product of U₂(𝔽₃) and C₂ acting faithfully	32	4	U(2,3):C2	192,982
GL₂(𝔽₃)⋊C₄	1^st semidirect product of GL₂(𝔽₃) and C₄ acting via C₄/C₂=C₂	32		GL(2,3):C4	192,953
SL₂(𝔽₃)⋊D₄	2^nd semidirect product of SL₂(𝔽₃) and D₄ acting via D₄/C₂²=C₂	32		SL(2,3):D4	192,986
SL₂(𝔽₃)⋊₅D₄	1^st semidirect product of SL₂(𝔽₃) and D₄ acting through Inn(SL₂(𝔽₃))	32		SL(2,3):5D4	192,1003
2_-¹⁺⁴⋊₃C₆	2^nd semidirect product of 2_-¹⁺⁴ and C₆ acting via C₆/C₂=C₃	32	4	ES-(2,2):3C6	192,1504
GL₂(𝔽₃)⋊C₂²	3^rd semidirect product of GL₂(𝔽₃) and C₂² acting via C₂²/C₂=C₂	32	4	GL(2,3):C2^2	192,1482
A₄⋊C₁₆	The semidirect product of A₄ and C₁₆ acting via C₁₆/C₈=C₂	48	3	A4:C16	192,186
C₄₈⋊C₄	2^nd semidirect product of C₄₈ and C₄ acting faithfully	48	4	C48:C4	192,71

Full list: Groups of order 192 (1543 groups)

Groups of order 193

		d	ρ	Label	ID
C₁₉₃	Cyclic group	193	1	C193	193,1

Groups of order 194

		d	ρ	Label	ID
C₁₉₄	Cyclic group	194	1	C194	194,2
D₉₇	Dihedral group	97	2+	D97	194,1

Groups of order 195

		d	ρ	Label	ID
C₁₉₅	Cyclic group	195	1	C195	195,2
C₅×C₁₃⋊C₃	Direct product of C₅ and C₁₃⋊C₃	65	3	C5xC13:C3	195,1

Groups of order 196

		d	ρ	Label	ID
C₁₉₆	Cyclic group	196	1	C196	196,2
D₉₈	Dihedral group; = C₂×D₄₉	98	2+	D98	196,3
Dic₄₉	Dicyclic group; = C₄₉ ⋊C₄	196	2-	Dic49	196,1
C₇²⋊C₄	The semidirect product of C₇² and C₄ acting faithfully	14	4+	C7^2:C4	196,8
C₇⋊Dic₇	The semidirect product of C₇ and Dic₇ acting via Dic₇/C₁₄=C₂	196		C7:Dic7	196,6
C₁₄²	Abelian group of type [14,14]	196		C14^2	196,12
C₂×C₉₈	Abelian group of type [2,98]	196		C2xC98	196,4
C₇×C₂₈	Abelian group of type [7,28]	196		C7xC28	196,7
D₇²	Direct product of D₇ and D₇	14	4+	D7^2	196,9
D₇×C₁₄	Direct product of C₁₄ and D₇	28	2	D7xC14	196,10
C₇×Dic₇	Direct product of C₇ and Dic₇	28	2	C7xDic7	196,5
C₂×C₇⋊D₇	Direct product of C₂ and C₇⋊D₇	98		C2xC7:D7	196,11

Groups of order 197

		d	ρ	Label	ID
C₁₉₇	Cyclic group	197	1	C197	197,1

Groups of order 198

		d	ρ	Label	ID
C₁₉₈	Cyclic group	198	1	C198	198,4
D₉₉	Dihedral group	99	2+	D99	198,3
C₃⋊D₃₃	The semidirect product of C₃ and D₃₃ acting via D₃₃/C₃₃=C₂	99		C3:D33	198,9
C₃×C₆₆	Abelian group of type [3,66]	198		C3xC66	198,10
S₃×C₃₃	Direct product of C₃₃ and S₃	66	2	S3xC33	198,6
C₃×D₃₃	Direct product of C₃ and D₃₃	66	2	C3xD33	198,7
C₁₁×D₉	Direct product of C₁₁ and D₉	99	2	C11xD9	198,1
C₉×D₁₁	Direct product of C₉ and D₁₁	99	2	C9xD11	198,2
C₃²×D₁₁	Direct product of C₃² and D₁₁	99		C3^2xD11	198,5
C₁₁×C₃⋊S₃	Direct product of C₁₁ and C₃⋊S₃	99		C11xC3:S3	198,8

Groups of order 199

		d	ρ	Label	ID
C₁₉₉	Cyclic group	199	1	C199	199,1

Groups of order 200

		d	ρ	Label	ID
C₂₀₀	Cyclic group	200	1	C200	200,2
D₁₀₀	Dihedral group	100	2+	D100	200,6
Dic₅₀	Dicyclic group; = C₂₅ ⋊Q₈	200	2-	Dic50	200,4
D₅≀C₂	Wreath product of D₅ by C₂	10	4+	D5wrC2	200,43
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	10	8+	D5:F5	200,42
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	10	8+	C5^2:C8	200,40
C₅²⋊Q₈	The semidirect product of C₅² and Q₈ acting faithfully	10	8+	C5^2:Q8	200,44
C₅⋊D₂₀	The semidirect product of C₅ and D₂₀ acting via D₂₀/D₁₀=C₂	20	4+	C5:D20	200,25
Dic₅⋊₂D₅	The semidirect product of Dic₅ and D₅ acting through Inn(Dic₅)	20	4+	Dic5:2D5	200,23
C₅²⋊₃C₈	2^nd semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4	C5^2:3C8	200,19
C₅²⋊₅C₈	4^th semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4-	C5^2:5C8	200,21
C₅²⋊₂D₄	1^st semidirect product of C₅² and D₄ acting via D₄/C₂=C₂²	40	4-	C5^2:2D4	200,24
C₅²⋊₂Q₈	The semidirect product of C₅² and Q₈ acting via Q₈/C₂=C₂²	40	4-	C5^2:2Q8	200,26
C₂₅⋊D₄	The semidirect product of C₂₅ and D₄ acting via D₄/C₂²=C₂	100	2	C25:D4	200,8
C₂₀⋊D₅	1^st semidirect product of C₂₀ and D₅ acting via D₅/C₅=C₂	100		C20:D5	200,34
C₅²⋊₇D₄	2^nd semidirect product of C₅² and D₄ acting via D₄/C₂²=C₂	100		C5^2:7D4	200,36
C₂₅⋊C₈	The semidirect product of C₂₅ and C₈ acting via C₈/C₂=C₄	200	4-	C25:C8	200,3
C₂₅⋊₂C₈	The semidirect product of C₂₅ and C₈ acting via C₈/C₄=C₂	200	2	C25:2C8	200,1
C₅²⋊₇C₈	2^nd semidirect product of C₅² and C₈ acting via C₈/C₄=C₂	200		C5^2:7C8	200,16
C₅²⋊₄C₈	3^rd semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	200		C5^2:4C8	200,20
C₅²⋊₄Q₈	2^nd semidirect product of C₅² and Q₈ acting via Q₈/C₄=C₂	200		C5^2:4Q8	200,32
C₅×C₄₀	Abelian group of type [5,40]	200		C5xC40	200,17
C₂×C₁₀₀	Abelian group of type [2,100]	200		C2xC100	200,9
C₁₀×C₂₀	Abelian group of type [10,20]	200		C10xC20	200,37
C₂²×C₅₀	Abelian group of type [2,2,50]	200		C2^2xC50	200,14
C₂×C₁₀²	Abelian group of type [2,10,10]	200		C2xC10^2	200,52
D₅×F₅	Direct product of D₅ and F₅	20	8+	D5xF5	200,41
D₅×C₂₀	Direct product of C₂₀ and D₅	40	2	D5xC20	200,28
C₅×D₂₀	Direct product of C₅ and D₂₀	40	2	C5xD20	200,29
C₁₀×F₅	Direct product of C₁₀ and F₅	40	4	C10xF5	200,45
D₅×Dic₅	Direct product of D₅ and Dic₅	40	4-	D5xDic5	200,22
C₅×Dic₁₀	Direct product of C₅ and Dic₁₀	40	2	C5xDic10	200,27
C₁₀×Dic₅	Direct product of C₁₀ and Dic₅	40		C10xDic5	200,30
C₄×D₂₅	Direct product of C₄ and D₂₅	100	2	C4xD25	200,5
D₄×C₂₅	Direct product of C₂₅ and D₄	100	2	D4xC25	200,10
D₄×C₅²	Direct product of C₅² and D₄	100		D4xC5^2	200,38
C₂²×D₂₅	Direct product of C₂² and D₂₅	100		C2^2xD25	200,13
Q₈×C₂₅	Direct product of C₂₅ and Q₈	200	2	Q8xC25	200,11
Q₈×C₅²	Direct product of C₅² and Q₈	200		Q8xC5^2	200,39
C₂×Dic₂₅	Direct product of C₂ and Dic₂₅	200		C2xDic25	200,7
C₂×D₅²	Direct product of C₂, D₅ and D₅	20	4+	C2xD5^2	200,49
C₅×C₅⋊D₄	Direct product of C₅ and C₅⋊D₄	20	2	C5xC5:D4	200,31
C₂×C₅²⋊C₄	Direct product of C₂ and C₅²⋊C₄	20	4+	C2xC5^2:C4	200,48
C₅×C₅⋊C₈	Direct product of C₅ and C₅⋊C₈	40	4	C5xC5:C8	200,18
D₅×C₂×C₁₀	Direct product of C₂×C₁₀ and D₅	40		D5xC2xC10	200,50
C₅×C₅⋊₂C₈	Direct product of C₅ and C₅⋊₂C₈	40	2	C5xC5:2C8	200,15
C₂×D₅.D₅	Direct product of C₂ and D₅.D₅	40	4	C2xD5.D5	200,46
C₂×C₂₅⋊C₄	Direct product of C₂ and C₂₅⋊C₄	50	4+	C2xC25:C4	200,12
C₂×C₅⋊F₅	Direct product of C₂ and C₅⋊F₅	50		C2xC5:F5	200,47
C₄×C₅⋊D₅	Direct product of C₄ and C₅⋊D₅	100		C4xC5:D5	200,33
C₂²×C₅⋊D₅	Direct product of C₂² and C₅⋊D₅	100		C2^2xC5:D5	200,51
C₂×C₅²⋊₆C₄	Direct product of C₂ and C₅²⋊₆C₄	200		C2xC5^2:6C4	200,35

Groups of order 201

		d	ρ	Label	ID
C₂₀₁	Cyclic group	201	1	C201	201,2
C₆₇⋊C₃	The semidirect product of C₆₇ and C₃ acting faithfully	67	3	C67:C3	201,1

Groups of order 202

		d	ρ	Label	ID
C₂₀₂	Cyclic group	202	1	C202	202,2
D₁₀₁	Dihedral group	101	2+	D101	202,1

Groups of order 203

		d	ρ	Label	ID
C₂₀₃	Cyclic group	203	1	C203	203,2
C₂₉⋊C₇	The semidirect product of C₂₉ and C₇ acting faithfully	29	7	C29:C7	203,1

Groups of order 204

		d	ρ	Label	ID
C₂₀₄	Cyclic group	204	1	C204	204,4
D₁₀₂	Dihedral group; = C₂×D₅₁	102	2+	D102	204,11
Dic₅₁	Dicyclic group; = C₅₁ ⋊₃ C₄	204	2-	Dic51	204,3
C₅₁⋊C₄	1^st semidirect product of C₅₁ and C₄ acting faithfully	51	4	C51:C4	204,6
C₂×C₁₀₂	Abelian group of type [2,102]	204		C2xC102	204,12
S₃×D₁₇	Direct product of S₃ and D₁₇	51	4+	S3xD17	204,7
A₄×C₁₇	Direct product of C₁₇ and A₄	68	3	A4xC17	204,8
S₃×C₃₄	Direct product of C₃₄ and S₃	102	2	S3xC34	204,10
C₆×D₁₇	Direct product of C₆ and D₁₇	102	2	C6xD17	204,9
Dic₃×C₁₇	Direct product of C₁₇ and Dic₃	204	2	Dic3xC17	204,1
C₃×Dic₁₇	Direct product of C₃ and Dic₁₇	204	2	C3xDic17	204,2
C₃×C₁₇⋊C₄	Direct product of C₃ and C₁₇⋊C₄	51	4	C3xC17:C4	204,5

Groups of order 205

		d	ρ	Label	ID
C₂₀₅	Cyclic group	205	1	C205	205,2
C₄₁⋊C₅	The semidirect product of C₄₁ and C₅ acting faithfully	41	5	C41:C5	205,1

Groups of order 206

		d	ρ	Label	ID
C₂₀₆	Cyclic group	206	1	C206	206,2
D₁₀₃	Dihedral group	103	2+	D103	206,1

Groups of order 207

		d	ρ	Label	ID
C₂₀₇	Cyclic group	207	1	C207	207,1
C₃×C₆₉	Abelian group of type [3,69]	207		C3xC69	207,2

Groups of order 208

		d	ρ	Label	ID
C₂₀₈	Cyclic group	208	1	C208	208,2
D₁₀₄	Dihedral group	104	2+	D104	208,7
Dic₅₂	Dicyclic group; = C₁₃ ⋊₁ Q₁₆	208	2-	Dic52	208,8
C₅₂⋊C₄	1^st semidirect product of C₅₂ and C₄ acting faithfully	52	4	C52:C4	208,31
D₄⋊D₁₃	The semidirect product of D₄ and D₁₃ acting via D₁₃/C₁₃=C₂	104	4+	D4:D13	208,15
D₁₃⋊C₈	The semidirect product of D₁₃ and C₈ acting via C₈/C₄=C₂	104	4	D13:C8	208,28
Q₈⋊D₁₃	The semidirect product of Q₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	4+	Q8:D13	208,17
C₈⋊D₁₃	3^rd semidirect product of C₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	2	C8:D13	208,5
C₁₀₄⋊C₂	2^nd semidirect product of C₁₀₄ and C₂ acting faithfully	104	2	C104:C2	208,6
D₂₆⋊C₄	1^st semidirect product of D₂₆ and C₄ acting via C₄/C₂=C₂	104		D26:C4	208,14
D₅₂⋊₅C₂	The semidirect product of D₅₂ and C₂ acting through Inn(D₅₂)	104	2	D52:5C2	208,38
D₄⋊₂D₁₃	The semidirect product of D₄ and D₁₃ acting through Inn(D₄)	104	4-	D4:2D13	208,40
D₅₂⋊C₂	4^th semidirect product of D₅₂ and C₂ acting faithfully	104	4+	D52:C2	208,42
C₁₃⋊M₄(2)	The semidirect product of C₁₃ and M₄(2) acting via M₄(2)/C₂²=C₄	104	4-	C13:M4(2)	208,33
C₁₃⋊C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₄=C₄	208	4	C13:C16	208,3
C₅₂⋊₃C₄	1^st semidirect product of C₅₂ and C₄ acting via C₄/C₂=C₂	208		C52:3C4	208,13
C₁₃⋊₂C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	2	C13:2C16	208,1
C₁₃⋊Q₁₆	The semidirect product of C₁₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	208	4-	C13:Q16	208,18
D₁₃.D₄	The non-split extension by D₁₃ of D₄ acting via D₄/C₂²=C₂	52	4+	D13.D4	208,34
D₄.D₁₃	The non-split extension by D₄ of D₁₃ acting via D₁₃/C₁₃=C₂	104	4-	D4.D13	208,16
C₅₂.₄C₄	1^st non-split extension by C₅₂ of C₄ acting via C₄/C₂=C₂	104	2	C52.4C4	208,10
C₅₂.C₄	1^st non-split extension by C₅₂ of C₄ acting faithfully	104	4	C52.C4	208,29
C₂³.D₁₃	The non-split extension by C₂³ of D₁₃ acting via D₁₃/C₁₃=C₂	104		C2^3.D13	208,19
C₂₆.D₄	1^st non-split extension by C₂₆ of D₄ acting via D₄/C₂²=C₂	208		C26.D4	208,12
C₄×C₅₂	Abelian group of type [4,52]	208		C4xC52	208,20
C₂×C₁₀₄	Abelian group of type [2,104]	208		C2xC104	208,23
C₂²×C₅₂	Abelian group of type [2,2,52]	208		C2^2xC52	208,45
C₂³×C₂₆	Abelian group of type [2,2,2,26]	208		C2^3xC26	208,51
D₄×D₁₃	Direct product of D₄ and D₁₃	52	4+	D4xD13	208,39
C₈×D₁₃	Direct product of C₈ and D₁₃	104	2	C8xD13	208,4
C₁₃×D₈	Direct product of C₁₃ and D₈	104	2	C13xD8	208,25
C₂×D₅₂	Direct product of C₂ and D₅₂	104		C2xD52	208,37
D₄×C₂₆	Direct product of C₂₆ and D₄	104		D4xC26	208,46
Q₈×D₁₃	Direct product of Q₈ and D₁₃	104	4-	Q8xD13	208,41
C₁₃×SD₁₆	Direct product of C₁₃ and SD₁₆	104	2	C13xSD16	208,26
C₂³×D₁₃	Direct product of C₂³ and D₁₃	104		C2^3xD13	208,50
C₁₃×M₄(2)	Direct product of C₁₃ and M₄(2)	104	2	C13xM4(2)	208,24
Q₈×C₂₆	Direct product of C₂₆ and Q₈	208		Q8xC26	208,47
C₁₃×Q₁₆	Direct product of C₁₃ and Q₁₆	208	2	C13xQ16	208,27
C₄×Dic₁₃	Direct product of C₄ and Dic₁₃	208		C4xDic13	208,11
C₂×Dic₂₆	Direct product of C₂ and Dic₂₆	208		C2xDic26	208,35
C₂²×Dic₁₃	Direct product of C₂² and Dic₁₃	208		C2^2xDic13	208,43
C₄×C₁₃⋊C₄	Direct product of C₄ and C₁₃⋊C₄	52	4	C4xC13:C4	208,30
C₂²×C₁₃⋊C₄	Direct product of C₂² and C₁₃⋊C₄	52		C2^2xC13:C4	208,49
C₂×C₄×D₁₃	Direct product of C₂×C₄ and D₁₃	104		C2xC4xD13	208,36
C₂×C₁₃⋊D₄	Direct product of C₂ and C₁₃⋊D₄	104		C2xC13:D4	208,44
C₁₃×C₄○D₄	Direct product of C₁₃ and C₄○D₄	104	2	C13xC4oD4	208,48
C₁₃×C₂²⋊C₄	Direct product of C₁₃ and C₂²⋊C₄	104		C13xC2^2:C4	208,21
C₂×C₁₃⋊C₈	Direct product of C₂ and C₁₃⋊C₈	208		C2xC13:C8	208,32
C₁₃×C₄⋊C₄	Direct product of C₁₃ and C₄⋊C₄	208		C13xC4:C4	208,22
C₂×C₁₃⋊₂C₈	Direct product of C₂ and C₁₃⋊₂C₈	208		C2xC13:2C8	208,9

Groups of order 209

		d	ρ	Label	ID
C₂₀₉	Cyclic group	209	1	C209	209,1

Groups of order 210

		d	ρ	Label	ID
C₂₁₀	Cyclic group	210	1	C210	210,12
D₁₀₅	Dihedral group	105	2+	D105	210,11
C₅⋊F₇	The semidirect product of C₅ and F₇ acting via F₇/C₇⋊C₃=C₂	35	6+	C5:F7	210,3
C₅×F₇	Direct product of C₅ and F₇	35	6	C5xF7	210,1
S₃×C₃₅	Direct product of C₃₅ and S₃	105	2	S3xC35	210,8
D₇×C₁₅	Direct product of C₁₅ and D₇	105	2	D7xC15	210,5
D₅×C₂₁	Direct product of C₂₁ and D₅	105	2	D5xC21	210,6
C₃×D₃₅	Direct product of C₃ and D₃₅	105	2	C3xD35	210,7
C₅×D₂₁	Direct product of C₅ and D₂₁	105	2	C5xD21	210,9
C₇×D₁₅	Direct product of C₇ and D₁₅	105	2	C7xD15	210,10
D₅×C₇⋊C₃	Direct product of D₅ and C₇⋊C₃	35	6	D5xC7:C3	210,2
C₁₀×C₇⋊C₃	Direct product of C₁₀ and C₇⋊C₃	70	3	C10xC7:C3	210,4

Groups of order 211

		d	ρ	Label	ID
C₂₁₁	Cyclic group	211	1	C211	211,1

Groups of order 212

		d	ρ	Label	ID
C₂₁₂	Cyclic group	212	1	C212	212,2
D₁₀₆	Dihedral group; = C₂×D₅₃	106	2+	D106	212,4
Dic₅₃	Dicyclic group; = C₅₃ ⋊₂ C₄	212	2-	Dic53	212,1
C₅₃⋊C₄	The semidirect product of C₅₃ and C₄ acting faithfully	53	4+	C53:C4	212,3
C₂×C₁₀₆	Abelian group of type [2,106]	212		C2xC106	212,5

Groups of order 213

		d	ρ	Label	ID
C₂₁₃	Cyclic group	213	1	C213	213,1

Groups of order 214

		d	ρ	Label	ID
C₂₁₄	Cyclic group	214	1	C214	214,2
D₁₀₇	Dihedral group	107	2+	D107	214,1

Groups of order 215

		d	ρ	Label	ID
C₂₁₅	Cyclic group	215	1	C215	215,1

Groups of order 216

		d	ρ	Label	ID
C₂₁₆	Cyclic group	216	1	C216	216,2
D₁₀₈	Dihedral group	108	2+	D108	216,6
Dic₅₄	Dicyclic group; = C₂₇ ⋊Q₈	216	2-	Dic54	216,4
SU₃(𝔽₂)	Special unitary group on 𝔽₂³; = He₃ ⋊Q₈	27	3	SU(3,2)	216,88
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	9	8+	ASL(2,3)	216,153
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	12	4	C3^3:D4	216,158
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	12	8+	C3^2:2D12	216,159
He₃⋊D₄	The semidirect product of He₃ and D₄ acting faithfully	18	6+	He3:D4	216,87
C₆²⋊S₃	4^th semidirect product of C₆² and S₃ acting faithfully	18	6+	C6^2:S3	216,92
C₃²⋊S₄	2^nd semidirect product of C₃² and S₄ acting via S₄/C₂²=S₃	18	3	C3^2:S4	216,95
C₆²⋊C₆	3^rd semidirect product of C₆² and C₆ acting faithfully	18	6+	C6^2:C6	216,99
C₃⋊F₉	The semidirect product of C₃ and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8	C3:F9	216,155
C₃³⋊₄C₈	2^nd semidirect product of C₃³ and C₈ acting via C₈/C₂=C₄	24	4	C3^3:4C8	216,118
C₃³⋊₉D₄	6^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	24	4	C3^3:9D4	216,132
C₃³⋊₅Q₈	3^rd semidirect product of C₃³ and Q₈ acting via Q₈/C₂=C₂²	24	4	C3^3:5Q8	216,133
C₃³⋊Q₈	2^nd semidirect product of C₃³ and Q₈ acting faithfully	24	8	C3^3:Q8	216,161
He₃⋊C₈	The semidirect product of He₃ and C₈ acting faithfully	27	6+	He3:C8	216,86
C₉⋊S₄	The semidirect product of C₉ and S₄ acting via S₄/A₄=C₂	36	6+	C9:S4	216,93
D₉⋊A₄	The semidirect product of D₉ and A₄ acting via A₄/C₂²=C₃	36	6+	D9:A4	216,96
D₃₆⋊C₃	The semidirect product of D₃₆ and C₃ acting faithfully	36	6+	D36:C3	216,54
C₃⋊D₃₆	The semidirect product of C₃ and D₃₆ acting via D₃₆/D₁₈=C₂	36	4+	C3:D36	216,29
C₉⋊D₁₂	The semidirect product of C₉ and D₁₂ acting via D₁₂/D₆=C₂	36	4+	C9:D12	216,32
Dic₉⋊C₆	The semidirect product of Dic₉ and C₆ acting faithfully	36	6	Dic9:C6	216,62
He₃⋊₂D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₂=C₂²	36	6+	He3:2D4	216,35
He₃⋊₃D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₂=C₂²	36	6	He3:3D4	216,37
He₃⋊₄D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₄=C₂	36	6+	He3:4D4	216,51
He₃⋊₆D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₂²=C₂	36	6	He3:6D4	216,60
He₃⋊₅D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₄=C₂	36	6	He3:5D4	216,68
He₃⋊₇D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₂²=C₂	36	6	He3:7D4	216,72
C₃³⋊₇D₄	4^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	36		C3^3:7D4	216,128
C₃³⋊₈D₄	5^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	36		C3^3:8D4	216,129
C₃²⋊₄S₄	2^nd semidirect product of C₃² and S₄ acting via S₄/A₄=C₂	36		C3^2:4S4	216,165
C₉⋊C₂₄	The semidirect product of C₉ and C₂₄ acting via C₂₄/C₄=C₆	72	6	C9:C24	216,15
Q₈⋊He₃	The semidirect product of Q₈ and He₃ acting via He₃/C₃²=C₃	72	6	Q8:He3	216,42
D₆⋊D₉	1^st semidirect product of D₆ and D₉ acting via D₉/C₉=C₂	72	4-	D6:D9	216,31
He₃⋊₃C₈	1^st semidirect product of He₃ and C₈ acting via C₈/C₄=C₂	72	6	He3:3C8	216,14
He₃⋊₄C₈	2^nd semidirect product of He₃ and C₈ acting via C₈/C₄=C₂	72	3	He3:4C8	216,17
He₃⋊₂C₈	The semidirect product of He₃ and C₈ acting via C₈/C₂=C₄	72	3	He3:2C8	216,25
He₃⋊₂Q₈	The semidirect product of He₃ and Q₈ acting via Q₈/C₂=C₂²	72	6-	He3:2Q8	216,33
He₃⋊₃Q₈	1^st semidirect product of He₃ and Q₈ acting via Q₈/C₄=C₂	72	6-	He3:3Q8	216,49
He₃⋊₄Q₈	2^nd semidirect product of He₃ and Q₈ acting via Q₈/C₄=C₂	72	6	He3:4Q8	216,66
C₃³⋊₆D₄	3^rd semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	72		C3^3:6D4	216,127
C₃³⋊₄Q₈	2^nd semidirect product of C₃³ and Q₈ acting via Q₈/C₂=C₂²	72		C3^3:4Q8	216,130
C₉⋊Dic₆	The semidirect product of C₉ and Dic₆ acting via Dic₆/Dic₃=C₂	72	4-	C9:Dic6	216,26
Q₈⋊3_-¹⁺²	The semidirect product of Q₈ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	72	6	Q8:ES-(3,1)	216,41
C₂₇⋊D₄	The semidirect product of C₂₇ and D₄ acting via D₄/C₂²=C₂	108	2	C27:D4	216,8
C₃₆⋊S₃	1^st semidirect product of C₃₆ and S₃ acting via S₃/C₃=C₂	108		C36:S3	216,65
C₃³⋊₁₂D₄	3^rd semidirect product of C₃³ and D₄ acting via D₄/C₄=C₂	108		C3^3:12D4	216,147
C₃³⋊₁₅D₄	3^rd semidirect product of C₃³ and D₄ acting via D₄/C₂²=C₂	108		C3^3:15D4	216,149
C₂₇⋊C₈	The semidirect product of C₂₇ and C₈ acting via C₈/C₄=C₂	216	2	C27:C8	216,1
Q₈⋊C₂₇	The semidirect product of Q₈ and C₂₇ acting via C₂₇/C₉=C₃	216	2	Q8:C27	216,3
C₃³⋊₇C₈	3^rd semidirect product of C₃³ and C₈ acting via C₈/C₄=C₂	216		C3^3:7C8	216,84
C₃³⋊₈Q₈	3^rd semidirect product of C₃³ and Q₈ acting via Q₈/C₄=C₂	216		C3^3:8Q8	216,145
C₃³⋊₉(C₂×C₄)	6^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	24	4	C3^3:9(C2xC4)	216,131
He₃⋊(C₂×C₄)	2^nd semidirect product of He₃ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	36	6-	He3:(C2xC4)	216,36
C₃³⋊₈(C₂×C₄)	5^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	36		C3^3:8(C2xC4)	216,126
C₃².S₄	The non-split extension by C₃² of S₄ acting via S₄/C₂²=S₃	18	6+	C3^2.S4	216,90
C₁₈.D₆	3^rd non-split extension by C₁₈ of D₆ acting via D₆/S₃=C₂	36	4+	C18.D6	216,28
C₉.S₄	The non-split extension by C₉ of S₄ acting via S₄/A₄=C₂	54	6+	C9.S4	216,21
C₃².₃S₄	2^nd non-split extension by C₃² of S₄ acting via S₄/A₄=C₂	54		C3^2.3S4	216,94
C₁₈.A₄	The non-split extension by C₁₈ of A₄ acting via A₄/C₂²=C₃	72	6	C18.A4	216,39
C₃₆.C₆	1^st non-split extension by C₃₆ of C₆ acting faithfully	72	6-	C36.C6	216,52
C₆.D₁₈	11^st non-split extension by C₆ of D₁₈ acting via D₁₈/C₁₈=C₂	108		C6.D18	216,70
C₃₆.S₃	6^th non-split extension by C₃₆ of S₃ acting via S₃/C₃=C₂	216		C36.S3	216,16
C₁₂.D₉	3^rd non-split extension by C₁₂ of D₉ acting via D₉/C₉=C₂	216		C12.D9	216,63
C₆.S₃²	2^nd non-split extension by C₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	36	6	C6.S3^2	216,34
C₆³	Abelian group of type [6,6,6]	216		C6^3	216,177
C₃×C₇₂	Abelian group of type [3,72]	216		C3xC72	216,18
C₆×C₃₆	Abelian group of type [6,36]	216		C6xC36	216,73
C₂×C₁₀₈	Abelian group of type [2,108]	216		C2xC108	216,9
C₂²×C₅₄	Abelian group of type [2,2,54]	216		C2^2xC54	216,24
C₃²×C₂₄	Abelian group of type [3,3,24]	216		C3^2xC24	216,85
C₂×C₆×C₁₈	Abelian group of type [2,6,18]	216		C2xC6xC18	216,114
C₃×C₆×C₁₂	Abelian group of type [3,6,12]	216		C3xC6xC12	216,150
C₃×F₉	Direct product of C₃ and F₉	24	8	C3xF9	216,154
C₃×PSU₃(𝔽₂)	Direct product of C₃ and PSU₃(𝔽₂)	24	8	C3xPSU(3,2)	216,160
C₉×S₄	Direct product of C₉ and S₄	36	3	C9xS4	216,89
A₄×D₉	Direct product of A₄ and D₉	36	6+	A4xD9	216,97
D₄×He₃	Direct product of D₄ and He₃	36	6	D4xHe3	216,77
C₃²×S₄	Direct product of C₃² and S₄	36		C3^2xS4	216,163
D₄×3_-¹⁺²	Direct product of D₄ and 3_-¹⁺²	36	6	D4xES-(3,1)	216,78
A₄×C₁₈	Direct product of C₁₈ and A₄	54	3	A4xC18	216,103
S₃×C₃₆	Direct product of C₃₆ and S₃	72	2	S3xC36	216,47
C₁₂×D₉	Direct product of C₁₂ and D₉	72	2	C12xD9	216,45
C₃×D₃₆	Direct product of C₃ and D₃₆	72	2	C3xD36	216,46
C₉×D₁₂	Direct product of C₉ and D₁₂	72	2	C9xD12	216,48
C₈×He₃	Direct product of C₈ and He₃	72	3	C8xHe3	216,19
Q₈×He₃	Direct product of Q₈ and He₃	72	6	Q8xHe3	216,80
S₃×C₆²	Direct product of C₆² and S₃	72		S3xC6^2	216,174
Dic₃×D₉	Direct product of Dic₃ and D₉	72	4-	Dic3xD9	216,27
S₃×Dic₉	Direct product of S₃ and Dic₉	72	4-	S3xDic9	216,30
C₉×Dic₆	Direct product of C₉ and Dic₆	72	2	C9xDic6	216,44
C₆×Dic₉	Direct product of C₆ and Dic₉	72		C6xDic9	216,55
C₃×Dic₁₈	Direct product of C₃ and Dic₁₈	72	2	C3xDic18	216,43
Dic₃×C₁₈	Direct product of C₁₈ and Dic₃	72		Dic3xC18	216,56
C₃²×D₁₂	Direct product of C₃² and D₁₂	72		C3^2xD12	216,137
C₂³×He₃	Direct product of C₂³ and He₃	72		C2^3xHe3	216,115
C₃²×Dic₆	Direct product of C₃² and Dic₆	72		C3^2xDic6	216,135
C₉×SL₂(𝔽₃)	Direct product of C₉ and SL₂(𝔽₃)	72	2	C9xSL(2,3)	216,38
C₈×3_-¹⁺²	Direct product of C₈ and 3_-¹⁺²	72	3	C8xES-(3,1)	216,20
Q₈×3_-¹⁺²	Direct product of Q₈ and 3_-¹⁺²	72	6	Q8xES-(3,1)	216,81
C₃²×SL₂(𝔽₃)	Direct product of C₃² and SL₂(𝔽₃)	72		C3^2xSL(2,3)	216,134
C₂³×3_-¹⁺²	Direct product of C₂³ and 3_-¹⁺²	72		C2^3xES-(3,1)	216,116
C₄×D₂₇	Direct product of C₄ and D₂₇	108	2	C4xD27	216,5
D₄×C₂₇	Direct product of C₂₇ and D₄	108	2	D4xC27	216,10
D₄×C₃³	Direct product of C₃³ and D₄	108		D4xC3^3	216,151
C₂²×D₂₇	Direct product of C₂² and D₂₇	108		C2^2xD27	216,23
Q₈×C₂₇	Direct product of C₂₇ and Q₈	216	2	Q8xC27	216,11
Q₈×C₃³	Direct product of C₃³ and Q₈	216		Q8xC3^3	216,152
C₂×Dic₂₇	Direct product of C₂ and Dic₂₇	216		C2xDic27	216,7
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	12	8+	S3^3	216,162
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	12	4	C3xS3wrC2	216,157
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	12	8+	S3xC3^2:C4	216,156
C₂×C₃²⋊A₄	Direct product of C₂ and C₃²⋊A₄	18	3	C2xC3^2:A4	216,107
C₂×C₃²⋊D₆	Direct product of C₂ and C₃²⋊D₆	18	6+	C2xC3^2:D6	216,102
C₂×C₃².A₄	Direct product of C₂ and C₃².A₄	18	3	C2xC3^2.A4	216,106
S₃²×C₆	Direct product of C₆, S₃ and S₃	24	4	S3^2xC6	216,170
C₃×S₃×A₄	Direct product of C₃, S₃ and A₄	24	6	C3xS3xA4	216,166
C₃×C₃⋊S₄	Direct product of C₃ and C₃⋊S₄	24	6	C3xC3:S4	216,164
C₆×C₃²⋊C₄	Direct product of C₆ and C₃²⋊C₄	24	4	C6xC3^2:C4	216,168
C₃×S₃×Dic₃	Direct product of C₃, S₃ and Dic₃	24	4	C3xS3xDic3	216,119
C₃×D₆⋊S₃	Direct product of C₃ and D₆⋊S₃	24	4	C3xD6:S3	216,121
C₃×C₃⋊D₁₂	Direct product of C₃ and C₃⋊D₁₂	24	4	C3xC3:D12	216,122
C₂×C₃³⋊C₄	Direct product of C₂ and C₃³⋊C₄	24	4	C2xC3^3:C4	216,169
C₃×C₆.D₆	Direct product of C₃ and C₆.D₆	24	4	C3xC6.D6	216,120
C₃×C₃²⋊₂C₈	Direct product of C₃ and C₃²⋊₂C₈	24	4	C3xC3^2:2C8	216,117
C₃×C₃²⋊₂Q₈	Direct product of C₃ and C₃²⋊₂Q₈	24	4	C3xC3^2:2Q8	216,123
C₂×C₃²⋊₄D₆	Direct product of C₂ and C₃²⋊₄D₆	24	4	C2xC3^2:4D6	216,172
C₂×S₃×D₉	Direct product of C₂, S₃ and D₉	36	4+	C2xS3xD9	216,101
C₄×C₉⋊C₆	Direct product of C₄ and C₉⋊C₆	36	6	C4xC9:C6	216,53
A₄×C₃⋊S₃	Direct product of A₄ and C₃⋊S₃	36		A4xC3:S3	216,167
C₃×C₉⋊D₄	Direct product of C₃ and C₉⋊D₄	36	2	C3xC9:D4	216,57
C₉×C₃⋊D₄	Direct product of C₉ and C₃⋊D₄	36	2	C9xC3:D4	216,58
C₃×C₃.S₄	Direct product of C₃ and C₃.S₄	36	6	C3xC3.S4	216,91
S₃×C₃.A₄	Direct product of S₃ and C₃.A₄	36	6	S3xC3.A4	216,98
C₂×He₃⋊C₄	Direct product of C₂ and He₃⋊C₄	36	3	C2xHe3:C4	216,100
C₄×C₃²⋊C₆	Direct product of C₄ and C₃²⋊C₆	36	6	C4xC3^2:C6	216,50
C₂²×C₉⋊C₆	Direct product of C₂² and C₉⋊C₆	36		C2^2xC9:C6	216,111
C₄×He₃⋊C₂	Direct product of C₄ and He₃⋊C₂	36	3	C4xHe3:C2	216,67
C₃²×C₃⋊D₄	Direct product of C₃² and C₃⋊D₄	36		C3^2xC3:D4	216,139
C₃×C₃²⋊₇D₄	Direct product of C₃ and C₃²⋊₇D₄	36		C3xC3^2:7D4	216,144
C₂²×C₃²⋊C₆	Direct product of C₂² and C₃²⋊C₆	36		C2^2xC3^2:C6	216,110
C₂²×He₃⋊C₂	Direct product of C₂² and He₃⋊C₂	36		C2^2xHe3:C2	216,113
A₄×C₃×C₆	Direct product of C₃×C₆ and A₄	54		A4xC3xC6	216,173
C₂×C₉⋊A₄	Direct product of C₂ and C₉⋊A₄	54	3	C2xC9:A4	216,104
C₂×C₉.A₄	Direct product of C₂ and C₉.A₄	54	3	C2xC9.A4	216,22
C₆×C₃.A₄	Direct product of C₆ and C₃.A₄	54		C6xC3.A4	216,105
C₃×C₉⋊C₈	Direct product of C₃ and C₉⋊C₈	72	2	C3xC9:C8	216,12
C₉×C₃⋊C₈	Direct product of C₉ and C₃⋊C₈	72	2	C9xC3:C8	216,13
C₂×C₆×D₉	Direct product of C₂×C₆ and D₉	72		C2xC6xD9	216,108
S₃×C₂×C₁₈	Direct product of C₂×C₁₈ and S₃	72		S3xC2xC18	216,109
S₃×C₃×C₁₂	Direct product of C₃×C₁₂ and S₃	72		S3xC3xC12	216,136
C₂×C₉⋊C₁₂	Direct product of C₂ and C₉⋊C₁₂	72		C2xC9:C12	216,61
C₂×C₄×He₃	Direct product of C₂×C₄ and He₃	72		C2xC4xHe3	216,74
C₁₂×C₃⋊S₃	Direct product of C₁₂ and C₃⋊S₃	72		C12xC3:S3	216,141
C₃²×C₃⋊C₈	Direct product of C₃² and C₃⋊C₈	72		C3^2xC3:C8	216,82
Dic₃×C₃×C₆	Direct product of C₃×C₆ and Dic₃	72		Dic3xC3xC6	216,138
C₃×C₁₂⋊S₃	Direct product of C₃ and C₁₂⋊S₃	72		C3xC12:S3	216,142
S₃×C₃⋊Dic₃	Direct product of S₃ and C₃⋊Dic₃	72		S3xC3:Dic3	216,124
Dic₃×C₃⋊S₃	Direct product of Dic₃ and C₃⋊S₃	72		Dic3xC3:S3	216,125
C₆×C₃⋊Dic₃	Direct product of C₆ and C₃⋊Dic₃	72		C6xC3:Dic3	216,143
C₂×C₃²⋊C₁₂	Direct product of C₂ and C₃²⋊C₁₂	72		C2xC3^2:C12	216,59
C₂×He₃⋊₃C₄	Direct product of C₂ and He₃⋊₃C₄	72		C2xHe3:3C4	216,71
C₃×C₃²⋊₄C₈	Direct product of C₃ and C₃²⋊₄C₈	72		C3xC3^2:4C8	216,83
C₃×C₃²⋊₄Q₈	Direct product of C₃ and C₃²⋊₄Q₈	72		C3xC3^2:4Q8	216,140
C₂×C₄×3_-¹⁺²	Direct product of C₂×C₄ and 3_-¹⁺²	72		C2xC4xES-(3,1)	216,75
D₄×C₃×C₉	Direct product of C₃×C₉ and D₄	108		D4xC3xC9	216,76
C₄×C₉⋊S₃	Direct product of C₄ and C₉⋊S₃	108		C4xC9:S3	216,64
C₂²×C₉⋊S₃	Direct product of C₂² and C₉⋊S₃	108		C2^2xC9:S3	216,112
C₄×C₃³⋊C₂	Direct product of C₄ and C₃³⋊C₂	108		C4xC3^3:C2	216,146
C₂²×C₃³⋊C₂	Direct product of C₂² and C₃³⋊C₂	108		C2^2xC3^3:C2	216,176
Q₈×C₃×C₉	Direct product of C₃×C₉ and Q₈	216		Q8xC3xC9	216,79
C₃×Q₈⋊C₉	Direct product of C₃ and Q₈⋊C₉	216		C3xQ8:C9	216,40
C₂×C₉⋊Dic₃	Direct product of C₂ and C₉⋊Dic₃	216		C2xC9:Dic3	216,69
C₂×C₃³⋊₅C₄	Direct product of C₂ and C₃³⋊₅C₄	216		C2xC3^3:5C4	216,148
C₂×S₃×C₃⋊S₃	Direct product of C₂, S₃ and C₃⋊S₃	36		C2xS3xC3:S3	216,171
C₂×C₆×C₃⋊S₃	Direct product of C₂×C₆ and C₃⋊S₃	72		C2xC6xC3:S3	216,175

Groups of order 217

		d	ρ	Label	ID
C₂₁₇	Cyclic group	217	1	C217	217,1

Groups of order 218

		d	ρ	Label	ID
C₂₁₈	Cyclic group	218	1	C218	218,2
D₁₀₉	Dihedral group	109	2+	D109	218,1

Groups of order 219

		d	ρ	Label	ID
C₂₁₉	Cyclic group	219	1	C219	219,2
C₇₃⋊C₃	The semidirect product of C₇₃ and C₃ acting faithfully	73	3	C73:C3	219,1

Groups of order 220

		d	ρ	Label	ID
C₂₂₀	Cyclic group	220	1	C220	220,6
D₁₁₀	Dihedral group; = C₂×D₅₅	110	2+	D110	220,14
Dic₅₅	Dicyclic group; = C₅₅ ⋊₃ C₄	220	2-	Dic55	220,5
C₁₁⋊C₂₀	The semidirect product of C₁₁ and C₂₀ acting via C₂₀/C₂=C₁₀	44	10-	C11:C20	220,1
C₁₁⋊F₅	The semidirect product of C₁₁ and F₅ acting via F₅/D₅=C₂	55	4	C11:F5	220,10
C₂×C₁₁₀	Abelian group of type [2,110]	220		C2xC110	220,15
C₂×F₁₁	Direct product of C₂ and F₁₁; = Aut(D₂₂) = Hol(C₂₂)	22	10+	C2xF11	220,7
D₅×D₁₁	Direct product of D₅ and D₁₁	55	4+	D5xD11	220,11
C₁₁×F₅	Direct product of C₁₁ and F₅	55	4	C11xF5	220,9
D₅×C₂₂	Direct product of C₂₂ and D₅	110	2	D5xC22	220,13
C₁₀×D₁₁	Direct product of C₁₀ and D₁₁	110	2	C10xD11	220,12
C₁₁×Dic₅	Direct product of C₁₁ and Dic₅	220	2	C11xDic5	220,3
C₅×Dic₁₁	Direct product of C₅ and Dic₁₁	220	2	C5xDic11	220,4
C₄×C₁₁⋊C₅	Direct product of C₄ and C₁₁⋊C₅	44	5	C4xC11:C5	220,2
C₂²×C₁₁⋊C₅	Direct product of C₂² and C₁₁⋊C₅	44		C2^2xC11:C5	220,8

Groups of order 221

		d	ρ	Label	ID
C₂₂₁	Cyclic group	221	1	C221	221,1

Groups of order 222

		d	ρ	Label	ID
C₂₂₂	Cyclic group	222	1	C222	222,6
D₁₁₁	Dihedral group	111	2+	D111	222,5
C₃₇⋊C₆	The semidirect product of C₃₇ and C₆ acting faithfully	37	6+	C37:C6	222,1
S₃×C₃₇	Direct product of C₃₇ and S₃	111	2	S3xC37	222,3
C₃×D₃₇	Direct product of C₃ and D₃₇	111	2	C3xD37	222,4
C₂×C₃₇⋊C₃	Direct product of C₂ and C₃₇⋊C₃	74	3	C2xC37:C3	222,2

Groups of order 223

		d	ρ	Label	ID
C₂₂₃	Cyclic group	223	1	C223	223,1

Groups of order 224

		d	ρ	Label	ID
C₂₂₄	Cyclic group	224	1	C224	224,2
D₁₁₂	Dihedral group	112	2+	D112	224,5
Dic₅₆	Dicyclic group; = C₇ ⋊₁ Q₃₂	224	2-	Dic56	224,7
D₈⋊D₇	2^nd semidirect product of D₈ and D₇ acting via D₇/C₇=C₂	56	4	D8:D7	224,106
C₈⋊D₁₄	1^st semidirect product of C₈ and D₁₄ acting via D₁₄/C₇=C₂²	56	4+	C8:D14	224,103
D₂₈⋊₄C₄	4^th semidirect product of D₂₈ and C₄ acting via C₄/C₂=C₂	56	4	D28:4C4	224,31
D₅₆⋊C₂	6^th semidirect product of D₅₆ and C₂ acting faithfully	56	4+	D56:C2	224,109
D₄⋊D₁₄	2^nd semidirect product of D₄ and D₁₄ acting via D₁₄/C₁₄=C₂	56	4+	D4:D14	224,144
D₄⋊₆D₁₄	2^nd semidirect product of D₄ and D₁₄ acting through Inn(D₄)	56	4	D4:6D14	224,180
D₄⋊₈D₁₄	4^th semidirect product of D₄ and D₁₄ acting through Inn(D₄)	56	4+	D4:8D14	224,185
C₂⁴⋊D₇	1^st semidirect product of C₂⁴ and D₇ acting via D₇/C₇=C₂	56		C2^4:D7	224,148
C₂³⋊Dic₇	The semidirect product of C₂³ and Dic₇ acting via Dic₇/C₇=C₄	56	4	C2^3:Dic7	224,40
D₄⋊₂Dic₇	2^nd semidirect product of D₄ and Dic₇ acting via Dic₇/C₁₄=C₂	56	4	D4:2Dic7	224,43
C₂²⋊D₂₈	The semidirect product of C₂² and D₂₈ acting via D₂₈/D₁₄=C₂	56		C2^2:D28	224,77
C₂³⋊D₁₄	1^st semidirect product of C₂³ and D₁₄ acting via D₁₄/C₇=C₂²	56		C2^3:D14	224,132
Dic₁₄⋊C₄	1^st semidirect product of Dic₁₄ and C₄ acting via C₄/C₂=C₂	56	2	Dic14:C4	224,11
D₁₄⋊C₈	The semidirect product of D₁₄ and C₈ acting via C₈/C₄=C₂	112		D14:C8	224,26
C₇⋊D₁₆	The semidirect product of C₇ and D₁₆ acting via D₁₆/D₈=C₂	112	4+	C7:D16	224,32
D₈⋊₃D₇	The semidirect product of D₈ and D₇ acting through Inn(D₈)	112	4-	D8:3D7	224,107
C₁₆⋊D₇	3^rd semidirect product of C₁₆ and D₇ acting via D₇/C₇=C₂	112	2	C16:D7	224,4
C₂₈⋊₄D₄	1^st semidirect product of C₂₈ and D₄ acting via D₄/C₄=C₂	112		C28:4D4	224,69
C₄⋊D₂₈	The semidirect product of C₄ and D₂₈ acting via D₂₈/D₁₄=C₂	112		C4:D28	224,90
C₂₈⋊₇D₄	1^st semidirect product of C₂₈ and D₄ acting via D₄/C₂²=C₂	112		C28:7D4	224,125
C₂₈⋊₂D₄	2^nd semidirect product of C₂₈ and D₄ acting via D₄/C₂=C₂²	112		C28:2D4	224,133
C₂₈⋊D₄	3^rd semidirect product of C₂₈ and D₄ acting via D₄/C₂=C₂²	112		C28:D4	224,135
C₁₁₂⋊C₂	2^nd semidirect product of C₁₁₂ and C₂ acting faithfully	112	2	C112:C2	224,6
C₇⋊SD₃₂	The semidirect product of C₇ and SD₃₂ acting via SD₃₂/Q₁₆=C₂	112	4+	C7:SD32	224,34
D₁₄⋊D₄	1^st semidirect product of D₁₄ and D₄ acting via D₄/C₄=C₂	112		D14:D4	224,79
D₂₈⋊C₄	5^th semidirect product of D₂₈ and C₄ acting via C₄/C₂=C₂	112		D28:C4	224,88
D₅₆⋊₇C₂	The semidirect product of D₅₆ and C₂ acting through Inn(D₅₆)	112	2	D56:7C2	224,99
D₁₄⋊Q₈	1^st semidirect product of D₁₄ and Q₈ acting via Q₈/C₄=C₂	112		D14:Q8	224,91
D₁₄⋊₂Q₈	2^nd semidirect product of D₁₄ and Q₈ acting via Q₈/C₄=C₂	112		D14:2Q8	224,92
Q₁₆⋊D₇	2^nd semidirect product of Q₁₆ and D₇ acting via D₇/C₇=C₂	112	4	Q16:D7	224,113
D₁₄⋊₃Q₈	3^rd semidirect product of D₁₄ and Q₈ acting via Q₈/C₄=C₂	112		D14:3Q8	224,141
C₄²⋊D₇	1^st semidirect product of C₄² and D₇ acting via D₇/C₇=C₂	112		C4^2:D7	224,67
C₄²⋊₂D₇	2^nd semidirect product of C₄² and D₇ acting via D₇/C₇=C₂	112		C4^2:2D7	224,71
D₄⋊Dic₇	1^st semidirect product of D₄ and Dic₇ acting via Dic₇/C₁₄=C₂	112		D4:Dic7	224,38
Dic₇⋊₄D₄	1^st semidirect product of Dic₇ and D₄ acting through Inn(Dic₇)	112		Dic7:4D4	224,76
SD₁₆⋊D₇	2^nd semidirect product of SD₁₆ and D₇ acting via D₇/C₇=C₂	112	4-	SD16:D7	224,110
SD₁₆⋊₃D₇	The semidirect product of SD₁₆ and D₇ acting through Inn(SD₁₆)	112	4	SD16:3D7	224,111
Dic₇⋊D₄	2^nd semidirect product of Dic₇ and D₄ acting via D₄/C₂²=C₂	112		Dic7:D4	224,134
C₂²⋊Dic₁₄	The semidirect product of C₂² and Dic₁₄ acting via Dic₁₄/Dic₇=C₂	112		C2^2:Dic14	224,73
C₇⋊C₃₂	The semidirect product of C₇ and C₃₂ acting via C₃₂/C₁₆=C₂	224	2	C7:C32	224,1
C₂₈⋊Q₈	The semidirect product of C₂₈ and Q₈ acting via Q₈/C₂=C₂²	224		C28:Q8	224,83
C₂₈⋊C₈	1^st semidirect product of C₂₈ and C₈ acting via C₈/C₄=C₂	224		C28:C8	224,10
C₅₆⋊C₄	4^th semidirect product of C₅₆ and C₄ acting via C₄/C₂=C₂	224		C56:C4	224,21
C₅₆⋊₁C₄	1^st semidirect product of C₅₆ and C₄ acting via C₄/C₂=C₂	224		C56:1C4	224,24
C₇⋊Q₃₂	The semidirect product of C₇ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	224	4-	C7:Q32	224,35
Dic₇⋊C₈	The semidirect product of Dic₇ and C₈ acting via C₈/C₄=C₂	224		Dic7:C8	224,20
C₂₈⋊₂Q₈	1^st semidirect product of C₂₈ and Q₈ acting via Q₈/C₄=C₂	224		C28:2Q8	224,64
C₈⋊Dic₇	2^nd semidirect product of C₈ and Dic₇ acting via Dic₇/C₁₄=C₂	224		C8:Dic7	224,23
Q₈⋊Dic₇	1^st semidirect product of Q₈ and Dic₇ acting via Dic₇/C₁₄=C₂	224		Q8:Dic7	224,41
Dic₇⋊₃Q₈	The semidirect product of Dic₇ and Q₈ acting through Inn(Dic₇)	224		Dic7:3Q8	224,82
Dic₇⋊Q₈	2^nd semidirect product of Dic₇ and Q₈ acting via Q₈/C₄=C₂	224		Dic7:Q8	224,139
C₄⋊C₄⋊₇D₇	1^st semidirect product of C₄⋊C₄ and D₇ acting through Inn(C₄⋊C₄)	112		C4:C4:7D7	224,87
C₄⋊C₄⋊D₇	6^th semidirect product of C₄⋊C₄ and D₇ acting via D₇/C₇=C₂	112		C4:C4:D7	224,93
C₂₈.D₄	8^th non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	56	4	C28.D4	224,39
D₄.D₁₄	1^st non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	56	4	D4.D14	224,127
C₂₈.₄₆D₄	3^rd non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	56	4+	C28.46D4	224,29
C₂³.₁D₁₄	1^st non-split extension by C₂³ of D₁₄ acting via D₁₄/C₇=C₂²	56	4	C2^3.1D14	224,12
D₈.D₇	The non-split extension by D₈ of D₇ acting via D₇/C₇=C₂	112	4-	D8.D7	224,33
D₂₈.C₄	The non-split extension by D₂₈ of C₄ acting via C₄/C₂=C₂	112	4	D28.C4	224,102
C₂₈.C₈	1^st non-split extension by C₂₈ of C₈ acting via C₈/C₄=C₂	112	2	C28.C8	224,18
C₅₆.C₄	1^st non-split extension by C₅₆ of C₄ acting via C₄/C₂=C₂	112	2	C56.C4	224,25
C₁₄.D₈	2^nd non-split extension by C₁₄ of D₈ acting via D₈/D₄=C₂	112		C14.D8	224,15
C₂.D₅₆	2^nd central extension by C₂ of D₅₆	112		C2.D56	224,27
C₄.D₂₈	5^th non-split extension by C₄ of D₂₈ acting via D₂₈/C₂₈=C₂	112		C4.D28	224,70
C₈.D₁₄	1^st non-split extension by C₈ of D₁₄ acting via D₁₄/C₇=C₂²	112	4-	C8.D14	224,104
Q₈.Dic₇	The non-split extension by Q₈ of Dic₇ acting through Inn(Q₈)	112	4	Q8.Dic7	224,143
D₁₄.D₄	1^st non-split extension by D₁₄ of D₄ acting via D₄/C₂²=C₂	112		D14.D4	224,78
D₁₄.₅D₄	2^nd non-split extension by D₁₄ of D₄ acting via D₄/C₂²=C₂	112		D14.5D4	224,89
D₂₈.₂C₄	The non-split extension by D₂₈ of C₄ acting through Inn(D₂₈)	112	2	D28.2C4	224,96
D₄.₈D₁₄	3^rd non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D4.8D14	224,145
D₄.₉D₁₄	4^th non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	112	4-	D4.9D14	224,146
C₂₈.₅₃D₄	10^th non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	112	4	C28.53D4	224,28
C₄.₁₂D₂₈	4^th non-split extension by C₄ of D₂₈ acting via D₂₈/D₁₄=C₂	112	4-	C4.12D28	224,30
C₂₈.₅₅D₄	12^nd non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	112		C28.55D4	224,36
C₂₈.₁₀D₄	10^th non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	112	4	C28.10D4	224,42
C₂₈.₄₈D₄	5^th non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	112		C28.48D4	224,119
C₂₈.₁₇D₄	17^th non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	112		C28.17D4	224,131
C₂₈.₂₃D₄	23^rd non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	112		C28.23D4	224,142
Q₈.D₁₄	5^th non-split extension by Q₈ of D₁₄ acting via D₁₄/D₇=C₂	112	4+	Q8.D14	224,114
D₄.₁₀D₁₄	The non-split extension by D₄ of D₁₄ acting through Inn(D₄)	112	4-	D4.10D14	224,186
Q₈.₁₀D₁₄	1^st non-split extension by Q₈ of D₁₄ acting through Inn(Q₈)	112	4	Q8.10D14	224,183
Dic₇.D₄	1^st non-split extension by Dic₇ of D₄ acting via D₄/C₄=C₂	112		Dic7.D4	224,80
C₂³.D₁₄	3^rd non-split extension by C₂³ of D₁₄ acting via D₁₄/C₇=C₂²	112		C2^3.D14	224,74
C₂².D₂₈	3^rd non-split extension by C₂² of D₂₈ acting via D₂₈/D₁₄=C₂	112		C2^2.D28	224,81
C₂₈.C₂³	15^th non-split extension by C₂₈ of C₂³ acting via C₂³/C₂=C₂²	112	4	C28.C2^3	224,137
C₂³.₁₁D₁₄	1^st non-split extension by C₂³ of D₁₄ acting via D₁₄/D₇=C₂	112		C2^3.11D14	224,72
C₂³.₂₁D₁₄	2^nd non-split extension by C₂³ of D₁₄ acting via D₁₄/C₁₄=C₂	112		C2^3.21D14	224,121
C₂³.₂₃D₁₄	4^th non-split extension by C₂³ of D₁₄ acting via D₁₄/C₁₄=C₂	112		C2^3.23D14	224,124
C₂³.₁₈D₁₄	8^th non-split extension by C₂³ of D₁₄ acting via D₁₄/D₇=C₂	112		C2^3.18D14	224,130
Dic₇.Q₈	The non-split extension by Dic₇ of Q₈ acting via Q₈/C₄=C₂	224		Dic7.Q8	224,84
C₂₈.Q₈	1^st non-split extension by C₂₈ of Q₈ acting via Q₈/C₂=C₂²	224		C28.Q8	224,13
C₂₈.₆Q₈	3^rd non-split extension by C₂₈ of Q₈ acting via Q₈/C₄=C₂	224		C28.6Q8	224,65
C₂₈.₃Q₈	3^rd non-split extension by C₂₈ of Q₈ acting via Q₈/C₂=C₂²	224		C28.3Q8	224,85
C₂₈.₄₄D₄	1^st non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	224		C28.44D4	224,22
C₁₄.Q₁₆	2^nd non-split extension by C₁₄ of Q₁₆ acting via Q₁₆/Q₈=C₂	224		C14.Q16	224,16
C₄².D₇	1^st non-split extension by C₄² of D₇ acting via D₇/C₇=C₂	224		C4^2.D7	224,9
C₁₄.C₄²	5^th non-split extension by C₁₄ of C₄² acting via C₄²/C₂×C₄=C₂	224		C14.C4^2	224,37
C₄.Dic₁₄	2^nd non-split extension by C₄ of Dic₁₄ acting via Dic₁₄/Dic₇=C₂	224		C4.Dic14	224,14
C₄×C₅₆	Abelian group of type [4,56]	224		C4xC56	224,45
C₂×C₁₁₂	Abelian group of type [2,112]	224		C2xC112	224,58
C₂²×C₅₆	Abelian group of type [2,2,56]	224		C2^2xC56	224,164
C₂³×C₂₈	Abelian group of type [2,2,2,28]	224		C2^3xC28	224,189
C₂⁴×C₁₄	Abelian group of type [2,2,2,2,14]	224		C2^4xC14	224,197
C₂×C₄×C₂₈	Abelian group of type [2,4,28]	224		C2xC4xC28	224,149
C₄×F₈	Direct product of C₄ and F₈	28	7	C4xF8	224,173
C₂²×F₈	Direct product of C₂² and F₈	28		C2^2xF8	224,195
D₇×D₈	Direct product of D₇ and D₈	56	4+	D7xD8	224,105
D₇×SD₁₆	Direct product of D₇ and SD₁₆	56	4	D7xSD16	224,108
D₇×M₄(2)	Direct product of D₇ and M₄(2)	56	4	D7xM4(2)	224,101
C₇×2₊¹⁺⁴	Direct product of C₇ and 2₊¹⁺⁴	56	4	C7xES+(2,2)	224,193
D₇×C₁₆	Direct product of C₁₆ and D₇	112	2	D7xC16	224,3
C₇×D₁₆	Direct product of C₇ and D₁₆	112	2	C7xD16	224,60
C₄×D₂₈	Direct product of C₄ and D₂₈	112		C4xD28	224,68
C₂×D₅₆	Direct product of C₂ and D₅₆	112		C2xD56	224,98
D₄×C₂₈	Direct product of C₂₈ and D₄	112		D4xC28	224,153
C₁₄×D₈	Direct product of C₁₄ and D₈	112		C14xD8	224,167
D₇×Q₁₆	Direct product of D₇ and Q₁₆	112	4-	D7xQ16	224,112
C₇×SD₃₂	Direct product of C₇ and SD₃₂	112	2	C7xSD32	224,61
D₄×Dic₇	Direct product of D₄ and Dic₇	112		D4xDic7	224,129
D₇×C₄²	Direct product of C₄² and D₇	112		D7xC4^2	224,66
D₇×C₂⁴	Direct product of C₂⁴ and D₇	112		D7xC2^4	224,196
C₁₄×SD₁₆	Direct product of C₁₄ and SD₁₆	112		C14xSD16	224,168
C₂²×D₂₈	Direct product of C₂² and D₂₈	112		C2^2xD28	224,176
C₇×M₅(2)	Direct product of C₇ and M₅(2)	112	2	C7xM5(2)	224,59
C₁₄×M₄(2)	Direct product of C₁₄ and M₄(2)	112		C14xM4(2)	224,165
C₇×2_-¹⁺⁴	Direct product of C₇ and 2_-¹⁺⁴	112	4	C7xES-(2,2)	224,194
C₇×Q₃₂	Direct product of C₇ and Q₃₂	224	2	C7xQ32	224,62
Q₈×C₂₈	Direct product of C₂₈ and Q₈	224		Q8xC28	224,154
C₁₄×Q₁₆	Direct product of C₁₄ and Q₁₆	224		C14xQ16	224,169
C₈×Dic₇	Direct product of C₈ and Dic₇	224		C8xDic7	224,19
Q₈×Dic₇	Direct product of Q₈ and Dic₇	224		Q8xDic7	224,140
C₄×Dic₁₄	Direct product of C₄ and Dic₁₄	224		C4xDic14	224,63
C₂×Dic₂₈	Direct product of C₂ and Dic₂₈	224		C2xDic28	224,100
C₂³×Dic₇	Direct product of C₂³ and Dic₇	224		C2^3xDic7	224,187
C₂²×Dic₁₄	Direct product of C₂² and Dic₁₄	224		C2^2xDic14	224,174
C₂×D₄×D₇	Direct product of C₂, D₄ and D₇	56		C2xD4xD7	224,178
C₇×C₄≀C₂	Direct product of C₇ and C₄≀C₂	56	2	C7xC4wrC2	224,53
D₇×C₄○D₄	Direct product of D₇ and C₄○D₄	56	4	D7xC4oD4	224,184
C₇×C₂³⋊C₄	Direct product of C₇ and C₂³⋊C₄	56	4	C7xC2^3:C4	224,48
C₇×C₈⋊C₂²	Direct product of C₇ and C₈⋊C₂²	56	4	C7xC8:C2^2	224,171
D₇×C₂²⋊C₄	Direct product of D₇ and C₂²⋊C₄	56		D7xC2^2:C4	224,75
C₇×C₄.D₄	Direct product of C₇ and C₄.D₄	56	4	C7xC4.D4	224,49
C₇×C₂²≀C₂	Direct product of C₇ and C₂²≀C₂	56		C7xC2^2wrC2	224,155
D₇×C₂×C₈	Direct product of C₂×C₈ and D₇	112		D7xC2xC8	224,94
C₂×Q₈×D₇	Direct product of C₂, Q₈ and D₇	112		C2xQ8xD7	224,181
D₇×C₄⋊C₄	Direct product of D₇ and C₄⋊C₄	112		D7xC4:C4	224,86
D₄×C₂×C₁₄	Direct product of C₂×C₁₄ and D₄	112		D4xC2xC14	224,190
C₄×C₇⋊D₄	Direct product of C₄ and C₇⋊D₄	112		C4xC7:D4	224,123
C₂×D₄⋊D₇	Direct product of C₂ and D₄⋊D₇	112		C2xD4:D7	224,126
C₇×C₈○D₄	Direct product of C₇ and C₈○D₄	112	2	C7xC8oD4	224,166
C₇×C₄○D₈	Direct product of C₇ and C₄○D₈	112	2	C7xC4oD8	224,170
C₂×C₈⋊D₇	Direct product of C₂ and C₈⋊D₇	112		C2xC8:D7	224,95
C₇×C₄⋊D₄	Direct product of C₇ and C₄⋊D₄	112		C7xC4:D4	224,156
C₂×Q₈⋊D₇	Direct product of C₂ and Q₈⋊D₇	112		C2xQ8:D7	224,136
C₂×C₅₆⋊C₂	Direct product of C₂ and C₅₆⋊C₂	112		C2xC56:C2	224,97
D₇×C₂²×C₄	Direct product of C₂²×C₄ and D₇	112		D7xC2^2xC4	224,175
C₂×D₁₄⋊C₄	Direct product of C₂ and D₁₄⋊C₄	112		C2xD14:C4	224,122
C₂×C₄○D₂₈	Direct product of C₂ and C₄○D₂₈	112		C2xC4oD28	224,177
C₁₄×C₄○D₄	Direct product of C₁₄ and C₄○D₄	112		C14xC4oD4	224,192
C₇×D₄⋊C₄	Direct product of C₇ and D₄⋊C₄	112		C7xD4:C4	224,51
C₇×C₈.C₄	Direct product of C₇ and C₈.C₄	112	2	C7xC8.C4	224,57
C₇×C₄⋊₁D₄	Direct product of C₇ and C₄⋊₁D₄	112		C7xC4:1D4	224,162
C₇×C₂²⋊C₈	Direct product of C₇ and C₂²⋊C₈	112		C7xC2^2:C8	224,47
C₂×D₄.D₇	Direct product of C₂ and D₄.D₇	112		C2xD4.D7	224,128
C₂²×C₇⋊D₄	Direct product of C₂² and C₇⋊D₄	112		C2^2xC7:D4	224,188
C₇×C₂²⋊Q₈	Direct product of C₇ and C₂²⋊Q₈	112		C7xC2^2:Q8	224,157
C₂×D₄⋊₂D₇	Direct product of C₂ and D₄⋊₂D₇	112		C2xD4:2D7	224,179
C₁₄×C₂²⋊C₄	Direct product of C₁₄ and C₂²⋊C₄	112		C14xC2^2:C4	224,150
C₇×C₄²⋊C₂	Direct product of C₇ and C₄²⋊C₂	112		C7xC4^2:C2	224,152
C₂×Q₈⋊₂D₇	Direct product of C₂ and Q₈⋊₂D₇	112		C2xQ8:2D7	224,182
C₇×C₄.₄D₄	Direct product of C₇ and C₄.₄D₄	112		C7xC4.4D4	224,159
C₇×C₈.C₂²	Direct product of C₇ and C₈.C₂²	112	4	C7xC8.C2^2	224,172
C₂×C₄.Dic₇	Direct product of C₂ and C₄.Dic₇	112		C2xC4.Dic7	224,116
C₂×C₂³.D₇	Direct product of C₂ and C₂³.D₇	112		C2xC2^3.D7	224,147
C₇×C₄²⋊₂C₂	Direct product of C₇ and C₄²⋊₂C₂	112		C7xC4^2:2C2	224,161
C₇×C₄.₁₀D₄	Direct product of C₇ and C₄.₁₀D₄	112	4	C7xC4.10D4	224,50
C₇×C₂².D₄	Direct product of C₇ and C₂².D₄	112		C7xC2^2.D4	224,158
C₄×C₇⋊C₈	Direct product of C₄ and C₇⋊C₈	224		C4xC7:C8	224,8
C₇×C₄⋊C₈	Direct product of C₇ and C₄⋊C₈	224		C7xC4:C8	224,54
C₂×C₇⋊C₁₆	Direct product of C₂ and C₇⋊C₁₆	224		C2xC7:C16	224,17
C₇×C₄⋊Q₈	Direct product of C₇ and C₄⋊Q₈	224		C7xC4:Q8	224,163
C₁₄×C₄⋊C₄	Direct product of C₁₄ and C₄⋊C₄	224		C14xC4:C4	224,151
Q₈×C₂×C₁₄	Direct product of C₂×C₁₄ and Q₈	224		Q8xC2xC14	224,191
C₇×C₈⋊C₄	Direct product of C₇ and C₈⋊C₄	224		C7xC8:C4	224,46
C₂²×C₇⋊C₈	Direct product of C₂² and C₇⋊C₈	224		C2^2xC7:C8	224,115
C₂×C₄×Dic₇	Direct product of C₂×C₄ and Dic₇	224		C2xC4xDic7	224,117
C₂×C₇⋊Q₁₆	Direct product of C₂ and C₇⋊Q₁₆	224		C2xC7:Q16	224,138
C₂×C₄⋊Dic₇	Direct product of C₂ and C₄⋊Dic₇	224		C2xC4:Dic7	224,120
C₇×Q₈⋊C₄	Direct product of C₇ and Q₈⋊C₄	224		C7xQ8:C4	224,52
C₇×C₂.D₈	Direct product of C₇ and C₂.D₈	224		C7xC2.D8	224,56
C₇×C₄.Q₈	Direct product of C₇ and C₄.Q₈	224		C7xC4.Q8	224,55
C₂×Dic₇⋊C₄	Direct product of C₂ and Dic₇⋊C₄	224		C2xDic7:C4	224,118
C₇×C₂.C₄²	Direct product of C₇ and C₂.C₄²	224		C7xC2.C4^2	224,44
C₇×C₄².C₂	Direct product of C₇ and C₄².C₂	224		C7xC4^2.C2	224,160

Groups of order 225

		d	ρ	Label	ID
C₂₂₅	Cyclic group	225	1	C225	225,1
C₅²⋊C₉	The semidirect product of C₅² and C₉ acting via C₉/C₃=C₃	45	3	C5^2:C9	225,3
C₁₅²	Abelian group of type [15,15]	225		C15^2	225,6
C₃×C₇₅	Abelian group of type [3,75]	225		C3xC75	225,2
C₅×C₄₅	Abelian group of type [5,45]	225		C5xC45	225,4
C₃×C₅²⋊C₃	Direct product of C₃ and C₅²⋊C₃	45	3	C3xC5^2:C3	225,5

Groups of order 226

		d	ρ	Label	ID
C₂₂₆	Cyclic group	226	1	C226	226,2
D₁₁₃	Dihedral group	113	2+	D113	226,1

Groups of order 227

		d	ρ	Label	ID
C₂₂₇	Cyclic group	227	1	C227	227,1

Groups of order 228

		d	ρ	Label	ID
C₂₂₈	Cyclic group	228	1	C228	228,6
D₁₁₄	Dihedral group; = C₂×D₅₇	114	2+	D114	228,14
Dic₅₇	Dicyclic group; = C₅₇ ⋊₁ C₄	228	2-	Dic57	228,5
C₁₉⋊A₄	The semidirect product of C₁₉ and A₄ acting via A₄/C₂²=C₃	76	3	C19:A4	228,11
C₁₉⋊C₁₂	The semidirect product of C₁₉ and C₁₂ acting via C₁₂/C₂=C₆	76	6-	C19:C12	228,1
C₂×C₁₁₄	Abelian group of type [2,114]	228		C2xC114	228,15
S₃×D₁₉	Direct product of S₃ and D₁₉	57	4+	S3xD19	228,8
A₄×C₁₉	Direct product of C₁₉ and A₄	76	3	A4xC19	228,10
S₃×C₃₈	Direct product of C₃₈ and S₃	114	2	S3xC38	228,13
C₆×D₁₉	Direct product of C₆ and D₁₉	114	2	C6xD19	228,12
Dic₃×C₁₉	Direct product of C₁₉ and Dic₃	228	2	Dic3xC19	228,3
C₃×Dic₁₉	Direct product of C₃ and Dic₁₉	228	2	C3xDic19	228,4
C₂×C₁₉⋊C₆	Direct product of C₂ and C₁₉⋊C₆	38	6+	C2xC19:C6	228,7
C₄×C₁₉⋊C₃	Direct product of C₄ and C₁₉⋊C₃	76	3	C4xC19:C3	228,2
C₂²×C₁₉⋊C₃	Direct product of C₂² and C₁₉⋊C₃	76		C2^2xC19:C3	228,9

Groups of order 229

		d	ρ	Label	ID
C₂₂₉	Cyclic group	229	1	C229	229,1

Groups of order 230

		d	ρ	Label	ID
C₂₃₀	Cyclic group	230	1	C230	230,4
D₁₁₅	Dihedral group	115	2+	D115	230,3
D₅×C₂₃	Direct product of C₂₃ and D₅	115	2	D5xC23	230,1
C₅×D₂₃	Direct product of C₅ and D₂₃	115	2	C5xD23	230,2

Groups of order 231

		d	ρ	Label	ID
C₂₃₁	Cyclic group	231	1	C231	231,2
C₁₁×C₇⋊C₃	Direct product of C₁₁ and C₇⋊C₃	77	3	C11xC7:C3	231,1

Groups of order 232

		d	ρ	Label	ID
C₂₃₂	Cyclic group	232	1	C232	232,2
D₁₁₆	Dihedral group	116	2+	D116	232,6
Dic₅₈	Dicyclic group; = C₂₉ ⋊Q₈	232	2-	Dic58	232,4
C₂₉⋊D₄	The semidirect product of C₂₉ and D₄ acting via D₄/C₂²=C₂	116	2	C29:D4	232,8
C₂₉⋊C₈	The semidirect product of C₂₉ and C₈ acting via C₈/C₂=C₄	232	4-	C29:C8	232,3
C₂₉⋊₂C₈	The semidirect product of C₂₉ and C₈ acting via C₈/C₄=C₂	232	2	C29:2C8	232,1
C₂×C₁₁₆	Abelian group of type [2,116]	232		C2xC116	232,9
C₂²×C₅₈	Abelian group of type [2,2,58]	232		C2^2xC58	232,14
C₄×D₂₉	Direct product of C₄ and D₂₉	116	2	C4xD29	232,5
D₄×C₂₉	Direct product of C₂₉ and D₄	116	2	D4xC29	232,10
C₂²×D₂₉	Direct product of C₂² and D₂₉	116		C2^2xD29	232,13
Q₈×C₂₉	Direct product of C₂₉ and Q₈	232	2	Q8xC29	232,11
C₂×Dic₂₉	Direct product of C₂ and Dic₂₉	232		C2xDic29	232,7
C₂×C₂₉⋊C₄	Direct product of C₂ and C₂₉⋊C₄	58	4+	C2xC29:C4	232,12

Groups of order 233

		d	ρ	Label	ID
C₂₃₃	Cyclic group	233	1	C233	233,1

Groups of order 234

		d	ρ	Label	ID
C₂₃₄	Cyclic group	234	1	C234	234,6
D₁₁₇	Dihedral group	117	2+	D117	234,5
D₃₉⋊C₃	The semidirect product of D₃₉ and C₃ acting faithfully	39	6+	D39:C3	234,9
C₁₃⋊C₁₈	The semidirect product of C₁₃ and C₁₈ acting via C₁₈/C₃=C₆	117	6	C13:C18	234,1
C₃⋊D₃₉	The semidirect product of C₃ and D₃₉ acting via D₃₉/C₃₉=C₂	117		C3:D39	234,15
C₃×C₇₈	Abelian group of type [3,78]	234		C3xC78	234,16
S₃×C₃₉	Direct product of C₃₉ and S₃	78	2	S3xC39	234,12
C₃×D₃₉	Direct product of C₃ and D₃₉	78	2	C3xD39	234,13
C₁₃×D₉	Direct product of C₁₃ and D₉	117	2	C13xD9	234,3
C₉×D₁₃	Direct product of C₉ and D₁₃	117	2	C9xD13	234,4
C₃²×D₁₃	Direct product of C₃² and D₁₃	117		C3^2xD13	234,11
C₃×C₁₃⋊C₆	Direct product of C₃ and C₁₃⋊C₆	39	6	C3xC13:C6	234,7
S₃×C₁₃⋊C₃	Direct product of S₃ and C₁₃⋊C₃	39	6	S3xC13:C3	234,8
C₆×C₁₃⋊C₃	Direct product of C₆ and C₁₃⋊C₃	78	3	C6xC13:C3	234,10
C₁₃×C₃⋊S₃	Direct product of C₁₃ and C₃⋊S₃	117		C13xC3:S3	234,14
C₂×C₁₃⋊C₉	Direct product of C₂ and C₁₃⋊C₉	234	3	C2xC13:C9	234,2

Groups of order 235

		d	ρ	Label	ID
C₂₃₅	Cyclic group	235	1	C235	235,1

Groups of order 236

		d	ρ	Label	ID
C₂₃₆	Cyclic group	236	1	C236	236,2
D₁₁₈	Dihedral group; = C₂×D₅₉	118	2+	D118	236,3
Dic₅₉	Dicyclic group; = C₅₉ ⋊C₄	236	2-	Dic59	236,1
C₂×C₁₁₈	Abelian group of type [2,118]	236		C2xC118	236,4

Groups of order 237

		d	ρ	Label	ID
C₂₃₇	Cyclic group	237	1	C237	237,2
C₇₉⋊C₃	The semidirect product of C₇₉ and C₃ acting faithfully	79	3	C79:C3	237,1

Groups of order 238

		d	ρ	Label	ID
C₂₃₈	Cyclic group	238	1	C238	238,4
D₁₁₉	Dihedral group	119	2+	D119	238,3
D₇×C₁₇	Direct product of C₁₇ and D₇	119	2	D7xC17	238,1
C₇×D₁₇	Direct product of C₇ and D₁₇	119	2	C7xD17	238,2

Groups of order 239

		d	ρ	Label	ID
C₂₃₉	Cyclic group	239	1	C239	239,1

Groups of order 240

		d	ρ	Label	ID
C₂₄₀	Cyclic group	240	1	C240	240,4
D₁₂₀	Dihedral group	120	2+	D120	240,68
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	16	15+	F16	240,191
Dic₆₀	Dicyclic group; = C₁₅ ⋊₄ Q₁₆	240	2-	Dic60	240,69
CSU₂(𝔽₅)	Conformal special unitary group on 𝔽₅²; = C₂ .₂ S₅	48	4-	CSU(2,5)	240,89
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	12	4	A5:C4	240,91
A₄⋊F₅	The semidirect product of A₄ and F₅ acting via F₅/D₅=C₂	20	12+	A4:F5	240,192
Q₈⋊D₁₅	The semidirect product of Q₈ and D₁₅ acting via D₁₅/C₅=S₃	40	4+	Q8:D15	240,106
D₆⋊F₅	The semidirect product of D₆ and F₅ acting via F₅/D₅=C₂	60	8+	D6:F5	240,96
C₆₀⋊C₄	1^st semidirect product of C₆₀ and C₄ acting faithfully	60	4	C60:C4	240,121
C₂₀⋊D₆	2^nd semidirect product of C₂₀ and D₆ acting via D₆/C₃=C₂²	60	4	C20:D6	240,138
Dic₃⋊F₅	The semidirect product of Dic₃ and F₅ acting via F₅/D₅=C₂	60	8-	Dic3:F5	240,97
A₄⋊Dic₅	The semidirect product of A₄ and Dic₅ acting via Dic₅/C₁₀=C₂	60	6-	A4:Dic5	240,107
D₁₀⋊D₆	4^th semidirect product of D₁₀ and D₆ acting via D₆/S₃=C₂	60	4+	D10:D6	240,151
D₄⋊D₁₅	The semidirect product of D₄ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4+	D4:D15	240,76
D₁₅⋊C₈	The semidirect product of D₁₅ and C₈ acting via C₈/C₂=C₄	120	8+	D15:C8	240,99
C₁₅⋊D₈	1^st semidirect product of C₁₅ and D₈ acting via D₈/C₄=C₂²	120	4	C15:D8	240,13
C₃⋊D₄₀	The semidirect product of C₃ and D₄₀ acting via D₄₀/D₂₀=C₂	120	4+	C3:D40	240,14
C₅⋊D₂₄	The semidirect product of C₅ and D₂₄ acting via D₂₄/D₁₂=C₂	120	4+	C5:D24	240,15
D₁₅⋊Q₈	The semidirect product of D₁₅ and Q₈ acting via Q₈/C₄=C₂	120	4	D15:Q8	240,131
C₄₀⋊S₃	4^th semidirect product of C₄₀ and S₃ acting via S₃/C₃=C₂	120	2	C40:S3	240,66
C₂₄⋊D₅	2^nd semidirect product of C₂₄ and D₅ acting via D₅/C₅=C₂	120	2	C24:D5	240,67
D₆⋊Dic₅	The semidirect product of D₆ and Dic₅ acting via Dic₅/C₁₀=C₂	120		D6:Dic5	240,27
D₁₅⋊₂C₈	The semidirect product of D₁₅ and C₈ acting via C₈/C₄=C₂	120	4	D15:2C8	240,9
D₃₀⋊₄C₄	2^nd semidirect product of D₃₀ and C₄ acting via C₄/C₂=C₂	120		D30:4C4	240,28
D₃₀⋊₃C₄	1^st semidirect product of D₃₀ and C₄ acting via C₄/C₂=C₂	120		D30:3C4	240,75
D₂₀⋊₅S₃	The semidirect product of D₂₀ and S₃ acting through Inn(D₂₀)	120	4-	D20:5S3	240,126
D₂₀⋊S₃	3^rd semidirect product of D₂₀ and S₃ acting via S₃/C₃=C₂	120	4	D20:S3	240,127
D₁₂⋊D₅	3^rd semidirect product of D₁₂ and D₅ acting via D₅/C₅=C₂	120	4	D12:D5	240,129
D₆₀⋊C₂	6^th semidirect product of D₆₀ and C₂ acting faithfully	120	4+	D60:C2	240,130
D₁₂⋊₅D₅	The semidirect product of D₁₂ and D₅ acting through Inn(D₁₂)	120	4-	D12:5D5	240,133
D₄⋊₂D₁₅	The semidirect product of D₄ and D₁₅ acting through Inn(D₄)	120	4-	D4:2D15	240,180
Q₈⋊₂D₁₅	The semidirect product of Q₈ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4+	Q8:2D15	240,78
Q₈⋊₃D₁₅	The semidirect product of Q₈ and D₁₅ acting through Inn(Q₈)	120	4+	Q8:3D15	240,182
C₁₅⋊SD₁₆	4^th semidirect product of C₁₅ and SD₁₆ acting via SD₁₆/C₄=C₂²	120	4+	C15:SD16	240,19
D₆₀⋊₁₁C₂	The semidirect product of D₆₀ and C₂ acting through Inn(D₆₀)	120	2	D60:11C2	240,178
Dic₆⋊D₅	1^st semidirect product of Dic₆ and D₅ acting via D₅/C₅=C₂	120	4+	Dic6:D5	240,21
C₁₅⋊₈M₄(2)	1^st semidirect product of C₁₅ and M₄(2) acting via M₄(2)/C₂²=C₄	120	4	C15:8M4(2)	240,123
D₁₀⋊Dic₃	1^st semidirect product of D₁₀ and Dic₃ acting via Dic₃/C₆=C₂	120		D10:Dic3	240,26
C₆₀⋊₅C₄	1^st semidirect product of C₆₀ and C₄ acting via C₄/C₂=C₂	240		C60:5C4	240,74
C₁₅⋊₃C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₈=C₂	240	2	C15:3C16	240,3
C₁₅⋊C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₄=C₄	240	4	C15:C16	240,6
C₁₅⋊Q₁₆	1^st semidirect product of C₁₅ and Q₁₆ acting via Q₁₆/C₄=C₂²	240	4	C15:Q16	240,22
C₁₅⋊₇Q₁₆	1^st semidirect product of C₁₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	240	4-	C15:7Q16	240,79
C₃⋊Dic₂₀	The semidirect product of C₃ and Dic₂₀ acting via Dic₂₀/Dic₁₀=C₂	240	4-	C3:Dic20	240,23
C₅⋊Dic₁₂	The semidirect product of C₅ and Dic₁₂ acting via Dic₁₂/Dic₆=C₂	240	4-	C5:Dic12	240,24
Dic₁₅⋊₅C₄	3^rd semidirect product of Dic₁₅ and C₄ acting via C₄/C₂=C₂	240		Dic15:5C4	240,30
C₄.A₅	The central extension by C₄ of A₅	24	2	C4.A5	240,93
C₂.S₅	2^nd central stem extension by C₂ of S₅	40	4-	C2.S5	240,90
D₁₀.D₆	6^th non-split extension by D₁₀ of D₆ acting via D₆/C₆=C₂	60	4	D10.D6	240,124
Q₈.D₁₅	The non-split extension by Q₈ of D₁₅ acting via D₁₅/C₅=S₃	80	4-	Q8.D15	240,105
Dic₅.A₄	The non-split extension by Dic₅ of A₄ acting through Inn(Dic₅)	80	4+	Dic5.A4	240,108
D₆.F₅	The non-split extension by D₆ of F₅ acting via F₅/D₅=C₂	120	8-	D6.F5	240,100
D₄.D₁₅	The non-split extension by D₄ of D₁₅ acting via D₁₅/C₁₅=C₂	120	4-	D4.D15	240,77
C₆₀.₇C₄	1^st non-split extension by C₆₀ of C₄ acting via C₄/C₂=C₂	120	2	C60.7C4	240,71
C₆₀.C₄	3^rd non-split extension by C₆₀ of C₄ acting faithfully	120	4	C60.C4	240,118
C₃₀.D₄	4^th non-split extension by C₃₀ of D₄ acting via D₄/C₂=C₂²	120	4	C30.D4	240,16
C₂₀.D₆	4^th non-split extension by C₂₀ of D₆ acting via D₆/C₃=C₂²	120	4	C20.D6	240,17
C₆.D₂₀	2^nd non-split extension by C₆ of D₂₀ acting via D₂₀/D₁₀=C₂	120	4-	C6.D20	240,18
D₆.Dic₅	The non-split extension by D₆ of Dic₅ acting via Dic₅/C₁₀=C₂	120	4	D6.Dic5	240,11
Dic₃.F₅	The non-split extension by Dic₃ of F₅ acting via F₅/D₅=C₂	120	8+	Dic3.F5	240,101
C₁₂.F₅	1^st non-split extension by C₁₂ of F₅ acting via F₅/D₅=C₂	120	4	C12.F5	240,119
D₃₀.₅C₄	3^rd non-split extension by D₃₀ of C₄ acting via C₄/C₂=C₂	120	4	D30.5C4	240,12
D₁₂.D₅	1^st non-split extension by D₁₂ of D₅ acting via D₅/C₅=C₂	120	4-	D12.D5	240,20
D₆.D₁₀	3^rd non-split extension by D₆ of D₁₀ acting via D₁₀/C₁₀=C₂	120	4	D6.D10	240,132
C₂₀.₃₂D₆	11^st non-split extension by C₂₀ of D₆ acting via D₆/S₃=C₂	120	4	C20.32D6	240,10
C₃₀.₃₈D₄	7^th non-split extension by C₃₀ of D₄ acting via D₄/C₂²=C₂	120		C30.38D4	240,80
C₁₂.₂₈D₁₀	7^th non-split extension by C₁₂ of D₁₀ acting via D₁₀/D₅=C₂	120	4+	C12.28D10	240,134
Dic₅.D₆	5^th non-split extension by Dic₅ of D₆ acting via D₆/S₃=C₂	120	4	Dic5.D6	240,140
C₃₀.C₂³	17^th non-split extension by C₃₀ of C₂³ acting via C₂³/C₂=C₂²	120	4-	C30.C2^3	240,141
Dic₃.D₁₀	6^th non-split extension by Dic₃ of D₁₀ acting via D₁₀/D₅=C₂	120	4	Dic3.D10	240,143
C₃₀.Q₈	1^st non-split extension by C₃₀ of Q₈ acting via Q₈/C₂=C₂²	240		C30.Q8	240,29
C₃₀.₄Q₈	1^st non-split extension by C₃₀ of Q₈ acting via Q₈/C₄=C₂	240		C30.4Q8	240,73
C₆.Dic₁₀	3^rd non-split extension by C₆ of Dic₁₀ acting via Dic₁₀/Dic₅=C₂	240		C6.Dic10	240,31
C₄×C₆₀	Abelian group of type [4,60]	240		C4xC60	240,81
C₂×C₁₂₀	Abelian group of type [2,120]	240		C2xC120	240,84
C₂²×C₆₀	Abelian group of type [2,2,60]	240		C2^2xC60	240,185
C₂³×C₃₀	Abelian group of type [2,2,2,30]	240		C2^3xC30	240,208
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	10	4+	C2xS5	240,189
C₄×A₅	Direct product of C₄ and A₅	20	3	C4xA5	240,92
D₅×S₄	Direct product of D₅ and S₄	20	6+	D5xS4	240,194
A₄×F₅	Direct product of A₄ and F₅	20	12+	A4xF5	240,193
C₂²×A₅	Direct product of C₂² and A₅	20		C2^2xA5	240,190
C₁₀×S₄	Direct product of C₁₀ and S₄	30	3	C10xS4	240,196
C₅×GL₂(𝔽₃)	Direct product of C₅ and GL₂(𝔽₃)	40	2	C5xGL(2,3)	240,103
D₅×SL₂(𝔽₃)	Direct product of D₅ and SL₂(𝔽₃)	40	4-	D5xSL(2,3)	240,109
C₂×SL₂(𝔽₅)	Direct product of C₂ and SL₂(𝔽₅)	48		C2xSL(2,5)	240,94
A₄×C₂₀	Direct product of C₂₀ and A₄	60	3	A4xC20	240,152
D₅×D₁₂	Direct product of D₅ and D₁₂	60	4+	D5xD12	240,136
S₃×D₂₀	Direct product of S₃ and D₂₀	60	4+	S3xD20	240,137
D₄×D₁₅	Direct product of D₄ and D₁₅	60	4+	D4xD15	240,179
C₁₂×F₅	Direct product of C₁₂ and F₅	60	4	C12xF5	240,113
Dic₃×F₅	Direct product of Dic₃ and F₅	60	8-	Dic3xF5	240,95
A₄×Dic₅	Direct product of A₄ and Dic₅	60	6-	A4xDic5	240,110
C₅×CSU₂(𝔽₃)	Direct product of C₅ and CSU₂(𝔽₃)	80	2	C5xCSU(2,3)	240,102
C₁₀×SL₂(𝔽₃)	Direct product of C₁₀ and SL₂(𝔽₃)	80		C10xSL(2,3)	240,153
S₃×C₄₀	Direct product of C₄₀ and S₃	120	2	S3xC40	240,49
D₅×C₂₄	Direct product of C₂₄ and D₅	120	2	D5xC24	240,33
C₃×D₄₀	Direct product of C₃ and D₄₀	120	2	C3xD40	240,36
C₅×D₂₄	Direct product of C₅ and D₂₄	120	2	C5xD24	240,52
C₈×D₁₅	Direct product of C₈ and D₁₅	120	2	C8xD15	240,65
C₁₅×D₈	Direct product of C₁₅ and D₈	120	2	C15xD8	240,86
C₆×D₂₀	Direct product of C₆ and D₂₀	120		C6xD20	240,157
C₂×D₆₀	Direct product of C₂ and D₆₀	120		C2xD60	240,177
D₄×C₃₀	Direct product of C₃₀ and D₄	120		D4xC30	240,186
Q₈×D₁₅	Direct product of Q₈ and D₁₅	120	4-	Q8xD15	240,181
C₁₀×D₁₂	Direct product of C₁₀ and D₁₂	120		C10xD12	240,167
D₅×Dic₆	Direct product of D₅ and Dic₆	120	4-	D5xDic6	240,125
C₁₅×SD₁₆	Direct product of C₁₅ and SD₁₆	120	2	C15xSD16	240,87
S₃×Dic₁₀	Direct product of S₃ and Dic₁₀	120	4-	S3xDic10	240,128
C₂³×D₁₅	Direct product of C₂³ and D₁₅	120		C2^3xD15	240,207
C₁₅×M₄(2)	Direct product of C₁₅ and M₄(2)	120	2	C15xM4(2)	240,85
Q₈×C₃₀	Direct product of C₃₀ and Q₈	240		Q8xC30	240,187
C₁₅×Q₁₆	Direct product of C₁₅ and Q₁₆	240	2	C15xQ16	240,88
C₃×Dic₂₀	Direct product of C₃ and Dic₂₀	240	2	C3xDic20	240,37
C₁₂×Dic₅	Direct product of C₁₂ and Dic₅	240		C12xDic5	240,40
C₅×Dic₁₂	Direct product of C₅ and Dic₁₂	240	2	C5xDic12	240,53
Dic₃×C₂₀	Direct product of C₂₀ and Dic₃	240		Dic3xC20	240,56
C₄×Dic₁₅	Direct product of C₄ and Dic₁₅	240		C4xDic15	240,72
C₆×Dic₁₀	Direct product of C₆ and Dic₁₀	240		C6xDic10	240,155
C₁₀×Dic₆	Direct product of C₁₀ and Dic₆	240		C10xDic6	240,165
C₂×Dic₃₀	Direct product of C₂ and Dic₃₀	240		C2xDic30	240,175
Dic₃×Dic₅	Direct product of Dic₃ and Dic₅	240		Dic3xDic5	240,25
C₂²×Dic₁₅	Direct product of C₂² and Dic₁₅	240		C2^2xDic15	240,183
C₂×C₅⋊S₄	Direct product of C₂ and C₅⋊S₄	30	6+	C2xC5:S4	240,197
C₂×D₅×A₄	Direct product of C₂, D₅ and A₄	30	6+	C2xD5xA4	240,198
C₂×S₃×F₅	Direct product of C₂, S₃ and F₅; = Aut(D₃₀) = Hol(C₃₀)	30	8+	C2xS3xF5	240,195
C₃×C₂⁴⋊C₅	Direct product of C₃ and C₂⁴⋊C₅	30	5	C3xC2^4:C5	240,199
C₄×S₃×D₅	Direct product of C₄, S₃ and D₅	60	4	C4xS3xD5	240,135
C₃×D₄×D₅	Direct product of C₃, D₄ and D₅	60	4	C3xD4xD5	240,159
C₅×S₃×D₄	Direct product of C₅, S₃ and D₄	60	4	C5xS3xD4	240,169
C₄×C₃⋊F₅	Direct product of C₄ and C₃⋊F₅	60	4	C4xC3:F5	240,120
C₂×C₆×F₅	Direct product of C₂×C₆ and F₅	60		C2xC6xF5	240,200
A₄×C₂×C₁₀	Direct product of C₂×C₁₀ and A₄	60		A4xC2xC10	240,203
D₅×C₃⋊D₄	Direct product of D₅ and C₃⋊D₄	60	4	D5xC3:D4	240,149
S₃×C₅⋊D₄	Direct product of S₃ and C₅⋊D₄	60	4	S3xC5:D4	240,150
C₃×C₄⋊F₅	Direct product of C₃ and C₄⋊F₅	60	4	C3xC4:F5	240,114
C₅×A₄⋊C₄	Direct product of C₅ and A₄⋊C₄	60	3	C5xA4:C4	240,104
C₅×C₄²⋊C₃	Direct product of C₅ and C₄²⋊C₃	60	3	C5xC4^2:C3	240,32
C₂²×S₃×D₅	Direct product of C₂², S₃ and D₅	60		C2^2xS3xD5	240,202
C₂²×C₃⋊F₅	Direct product of C₂² and C₃⋊F₅	60		C2^2xC3:F5	240,201
C₅×C₂²⋊A₄	Direct product of C₅ and C₂²⋊A₄	60		C5xC2^2:A4	240,204
C₃×C₂²⋊F₅	Direct product of C₃ and C₂²⋊F₅	60	4	C3xC2^2:F5	240,117
C₅×C₄.A₄	Direct product of C₅ and C₄.A₄	80	2	C5xC4.A4	240,154
S₃×C₅⋊C₈	Direct product of S₃ and C₅⋊C₈	120	8-	S3xC5:C8	240,98
D₅×C₃⋊C₈	Direct product of D₅ and C₃⋊C₈	120	4	D5xC3:C8	240,7
C₃×Q₈×D₅	Direct product of C₃, Q₈ and D₅	120	4	C3xQ8xD5	240,161
C₅×S₃×Q₈	Direct product of C₅, S₃ and Q₈	120	4	C5xS3xQ8	240,171
S₃×C₂×C₂₀	Direct product of C₂×C₂₀ and S₃	120		S3xC2xC20	240,166
D₅×C₂×C₁₂	Direct product of C₂×C₁₂ and D₅	120		D5xC2xC12	240,156
C₂×C₄×D₁₅	Direct product of C₂×C₄ and D₁₅	120		C2xC4xD15	240,176
C₆×C₅⋊D₄	Direct product of C₆ and C₅⋊D₄	120		C6xC5:D4	240,164
C₅×C₈⋊S₃	Direct product of C₅ and C₈⋊S₃	120	2	C5xC8:S3	240,50
S₃×C₅⋊₂C₈	Direct product of S₃ and C₅⋊₂C₈	120	4	S3xC5:2C8	240,8
C₃×D₄⋊D₅	Direct product of C₃ and D₄⋊D₅	120	4	C3xD4:D5	240,44
C₅×D₆⋊C₄	Direct product of C₅ and D₆⋊C₄	120		C5xD6:C4	240,59
C₅×D₄⋊S₃	Direct product of C₅ and D₄⋊S₃	120	4	C5xD4:S3	240,60
C₃×D₅⋊C₈	Direct product of C₃ and D₅⋊C₈	120	4	C3xD5:C8	240,111
C₃×C₈⋊D₅	Direct product of C₃ and C₈⋊D₅	120	2	C3xC8:D5	240,34
C₂×C₁₅⋊D₄	Direct product of C₂ and C₁₅⋊D₄	120		C2xC15:D4	240,145
C₂×C₃⋊D₂₀	Direct product of C₂ and C₃⋊D₂₀	120		C2xC3:D20	240,146
C₂×C₅⋊D₁₂	Direct product of C₂ and C₅⋊D₁₂	120		C2xC5:D12	240,147
C₁₀×C₃⋊D₄	Direct product of C₁₀ and C₃⋊D₄	120		C10xC3:D4	240,174
C₃×Q₈⋊D₅	Direct product of C₃ and Q₈⋊D₅	120	4	C3xQ8:D5	240,46
C₂×D₅×Dic₃	Direct product of C₂, D₅ and Dic₃	120		C2xD5xDic3	240,139
C₂×S₃×Dic₅	Direct product of C₂, S₃ and Dic₅	120		C2xS3xDic5	240,142
C₃×C₄₀⋊C₂	Direct product of C₃ and C₄₀⋊C₂	120	2	C3xC40:C2	240,35
C₅×C₂₄⋊C₂	Direct product of C₅ and C₂₄⋊C₂	120	2	C5xC24:C2	240,51
D₅×C₂²×C₆	Direct product of C₂²×C₆ and D₅	120		D5xC2^2xC6	240,205
C₃×C₄.F₅	Direct product of C₃ and C₄.F₅	120	4	C3xC4.F5	240,112
C₃×C₄○D₂₀	Direct product of C₃ and C₄○D₂₀	120	2	C3xC4oD20	240,158
C₅×C₄○D₁₂	Direct product of C₅ and C₄○D₁₂	120	2	C5xC4oD12	240,168
C₁₅×C₄○D₄	Direct product of C₁₅ and C₄○D₄	120	2	C15xC4oD4	240,188
C₂×C₁₅⋊₇D₄	Direct product of C₂ and C₁₅⋊₇D₄	120		C2xC15:7D4	240,184
C₃×D₄.D₅	Direct product of C₃ and D₄.D₅	120	4	C3xD4.D5	240,45
C₅×D₄.S₃	Direct product of C₅ and D₄.S₃	120	4	C5xD4.S3	240,61
S₃×C₂²×C₁₀	Direct product of C₂²×C₁₀ and S₃	120		S3xC2^2xC10	240,206
C₅×C₆.D₄	Direct product of C₅ and C₆.D₄	120		C5xC6.D4	240,64
C₃×D₁₀⋊C₄	Direct product of C₃ and D₁₀⋊C₄	120		C3xD10:C4	240,43
C₃×D₄⋊₂D₅	Direct product of C₃ and D₄⋊₂D₅	120	4	C3xD4:2D5	240,160
C₅×D₄⋊₂S₃	Direct product of C₅ and D₄⋊₂S₃	120	4	C5xD4:2S3	240,170
C₁₅×C₂²⋊C₄	Direct product of C₁₅ and C₂²⋊C₄	120		C15xC2^2:C4	240,82
C₂×D₃₀.C₂	Direct product of C₂ and D₃₀.C₂	120		C2xD30.C2	240,144
C₅×Q₈⋊₂S₃	Direct product of C₅ and Q₈⋊₂S₃	120	4	C5xQ8:2S3	240,62
C₃×Q₈⋊₂D₅	Direct product of C₃ and Q₈⋊₂D₅	120	4	C3xQ8:2D5	240,162
C₅×Q₈⋊₃S₃	Direct product of C₅ and Q₈⋊₃S₃	120	4	C5xQ8:3S3	240,172
C₃×C₄.Dic₅	Direct product of C₃ and C₄.Dic₅	120	2	C3xC4.Dic5	240,39
C₅×C₄.Dic₃	Direct product of C₅ and C₄.Dic₃	120	2	C5xC4.Dic3	240,55
C₃×C₂³.D₅	Direct product of C₃ and C₂³.D₅	120		C3xC2^3.D5	240,48
C₃×C₂².F₅	Direct product of C₃ and C₂².F₅	120	4	C3xC2^2.F5	240,116
C₆×C₅⋊C₈	Direct product of C₆ and C₅⋊C₈	240		C6xC5:C8	240,115
C₅×C₃⋊C₁₆	Direct product of C₅ and C₃⋊C₁₆	240	2	C5xC3:C16	240,1
C₃×C₅⋊C₁₆	Direct product of C₃ and C₅⋊C₁₆	240	4	C3xC5:C16	240,5
C₁₀×C₃⋊C₈	Direct product of C₁₀ and C₃⋊C₈	240		C10xC3:C8	240,54
C₁₅×C₄⋊C₄	Direct product of C₁₅ and C₄⋊C₄	240		C15xC4:C4	240,83
C₂×C₁₅⋊Q₈	Direct product of C₂ and C₁₅⋊Q₈	240		C2xC15:Q8	240,148
C₆×C₅⋊₂C₈	Direct product of C₆ and C₅⋊₂C₈	240		C6xC5:2C8	240,38
C₂×C₁₅⋊C₈	Direct product of C₂ and C₁₅⋊C₈	240		C2xC15:C8	240,122
C₂×C₆×Dic₅	Direct product of C₂×C₆ and Dic₅	240		C2xC6xDic5	240,163
C₃×C₅⋊Q₁₆	Direct product of C₃ and C₅⋊Q₁₆	240	4	C3xC5:Q16	240,47
C₅×C₃⋊Q₁₆	Direct product of C₅ and C₃⋊Q₁₆	240	4	C5xC3:Q16	240,63
C₃×C₅⋊₂C₁₆	Direct product of C₃ and C₅⋊₂C₁₆	240	2	C3xC5:2C16	240,2
C₂×C₁₅⋊₃C₈	Direct product of C₂ and C₁₅⋊₃C₈	240		C2xC15:3C8	240,70
C₃×C₄⋊Dic₅	Direct product of C₃ and C₄⋊Dic₅	240		C3xC4:Dic5	240,42
C₅×C₄⋊Dic₃	Direct product of C₅ and C₄⋊Dic₃	240		C5xC4:Dic3	240,58
Dic₃×C₂×C₁₀	Direct product of C₂×C₁₀ and Dic₃	240		Dic3xC2xC10	240,173
C₅×Dic₃⋊C₄	Direct product of C₅ and Dic₃⋊C₄	240		C5xDic3:C4	240,57
C₃×C₁₀.D₄	Direct product of C₃ and C₁₀.D₄	240		C3xC10.D4	240,41

Groups of order 241

		d	ρ	Label	ID
C₂₄₁	Cyclic group	241	1	C241	241,1

Groups of order 242

		d	ρ	Label	ID
C₂₄₂	Cyclic group	242	1	C242	242,2
D₁₂₁	Dihedral group	121	2+	D121	242,1
C₁₁⋊D₁₁	The semidirect product of C₁₁ and D₁₁ acting via D₁₁/C₁₁=C₂	121		C11:D11	242,4
C₁₁×C₂₂	Abelian group of type [11,22]	242		C11xC22	242,5
C₁₁×D₁₁	Direct product of C₁₁ and D₁₁; = AΣL₁(𝔽₁₂₁)	22	2	C11xD11	242,3

Groups of order 243

		d	ρ	Label	ID
C₂₄₃	Cyclic group	243	1	C243	243,1
3₊¹⁺⁴	Extraspecial group; = He₃ ○He₃	27	9	ES+(3,2)	243,65
3_-¹⁺⁴	Extraspecial group; = He₃ ○3_-¹⁺²	27	9	ES-(3,2)	243,66
C₂₇○He₃	Central product of C₂₇ and He₃	81	3	C27oHe3	243,50
C₂₇⋊C₉	The semidirect product of C₂₇ and C₉ acting faithfully	27	9	C27:C9	243,22
C₃²⋊He₃	The semidirect product of C₃² and He₃ acting via He₃/C₃²=C₃	27		C3^2:He3	243,37
C₃³⋊C₉	1^st semidirect product of C₃³ and C₉ acting via C₉/C₃=C₃	27		C3^3:C9	243,13
C₉²⋊C₃	1^st semidirect product of C₉² and C₃ acting faithfully	27	3	C9^2:C3	243,25
C₉²⋊₂C₃	2^nd semidirect product of C₉² and C₃ acting faithfully	27	3	C9^2:2C3	243,26
He₃⋊C₃²	3^rd semidirect product of He₃ and C₃² acting via C₃²/C₃=C₃	27	9	He3:C3^2	243,58
C₃³⋊C₃²	2^nd semidirect product of C₃³ and C₃² acting faithfully	27	9	C3^3:C3^2	243,56
C₈₁⋊C₃	The semidirect product of C₈₁ and C₃ acting faithfully	81	3	C81:C3	243,24
C₉⋊He₃	The semidirect product of C₉ and He₃ acting via He₃/C₃²=C₃	81		C9:He3	243,39
He₃⋊C₉	The semidirect product of He₃ and C₉ acting via C₉/C₃=C₃	81		He3:C9	243,17
C₃²⋊C₂₇	The semidirect product of C₃² and C₂₇ acting via C₂₇/C₉=C₃	81		C3^2:C27	243,12
C₉²⋊₃C₃	3^rd semidirect product of C₉² and C₃ acting faithfully	81		C9^2:3C3	243,34
C₉²⋊₇C₃	7^th semidirect product of C₉² and C₃ acting faithfully	81		C9^2:7C3	243,43
C₉²⋊₄C₃	4^th semidirect product of C₉² and C₃ acting faithfully	81		C9^2:4C3	243,44
C₉²⋊₅C₃	5^th semidirect product of C₉² and C₃ acting faithfully	81		C9^2:5C3	243,45
C₉²⋊₈C₃	8^th semidirect product of C₉² and C₃ acting faithfully	81		C9^2:8C3	243,46
C₉²⋊₉C₃	9^th semidirect product of C₉² and C₃ acting faithfully	81		C9^2:9C3	243,47
3_-¹⁺²⋊C₉	The semidirect product of 3_-¹⁺² and C₉ acting via C₉/C₃=C₃	81		ES-(3,1):C9	243,18
C₉⋊3_-¹⁺²	The semidirect product of C₉ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	81		C9:ES-(3,1)	243,41
C₉⋊C₂₇	The semidirect product of C₉ and C₂₇ acting via C₂₇/C₉=C₃	243		C9:C27	243,21
C₂₇⋊₂C₉	The semidirect product of C₂₇ and C₉ acting via C₉/C₃=C₃	243		C27:2C9	243,11
C₉.₄He₃	2^nd central extension by C₉ of He₃	27	3	C9.4He3	243,16
C₉.He₃	1^st non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	27	3	C9.He3	243,55
C₉.₂He₃	2^nd non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	27	9	C9.2He3	243,60
C₉².C₃	2^nd non-split extension by C₉² of C₃ acting faithfully	27	3	C9^2.C3	243,27
C₃⁴.C₃	3^rd non-split extension by C₃⁴ of C₃ acting faithfully	27		C3^4.C3	243,38
C₃².He₃	4^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.He3	243,28
C₃².₅He₃	5^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.5He3	243,29
C₃².₆He₃	6^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.6He3	243,30
He₃.C₃²	4^th non-split extension by He₃ of C₃² acting via C₃²/C₃=C₃	27	9	He3.C3^2	243,57
C₃².C₃³	9^th non-split extension by C₃² of C₃³ acting via C₃³/C₃²=C₃	27	9	C3^2.C3^3	243,59
C₉.₅He₃	3^rd central extension by C₉ of He₃	81	3	C9.5He3	243,19
C₉.₆He₃	4^th central extension by C₉ of He₃	81	3	C9.6He3	243,20
C₃².₂₄He₃	1^st central stem extension by C₃² of He₃	81		C3^2.24He3	243,3
C₃³.C₃²	2^nd non-split extension by C₃³ of C₃² acting faithfully	81		C3^3.C3^2	243,4
C₃³.₃C₃²	3^rd non-split extension by C₃³ of C₃² acting faithfully	81		C3^3.3C3^2	243,5
C₃².₂₇He₃	4^th central stem extension by C₃² of He₃	81		C3^2.27He3	243,6
C₃².₂₈He₃	5^th central stem extension by C₃² of He₃	81		C3^2.28He3	243,7
C₃².₂₉He₃	6^th central stem extension by C₃² of He₃	81		C3^2.29He3	243,8
C₃³.₇C₃²	7^th non-split extension by C₃³ of C₃² acting faithfully	81		C3^3.7C3^2	243,9
C₃².₁₉He₃	3^rd central extension by C₃² of He₃	81		C3^2.19He3	243,14
C₃².₂₀He₃	4^th central extension by C₃² of He₃	81		C3^2.20He3	243,15
C₃².₂₃C₃³	4^th central stem extension by C₃² of C₃³	81		C3^2.23C3^3	243,40
C₃³.₃₁C₃²	14^th non-split extension by C₃³ of C₃² acting via C₃²/C₃=C₃	81		C3^3.31C3^2	243,42
C₃.C₉²	1^st central stem extension by C₃ of C₉²	243		C3.C9^2	243,2
C₃⁵	Elementary abelian group of type [3,3,3,3,3]	243		C3^5	243,67
C₉×C₂₇	Abelian group of type [9,27]	243		C9xC27	243,10
C₃×C₈₁	Abelian group of type [3,81]	243		C3xC81	243,23
C₃×C₉²	Abelian group of type [3,9,9]	243		C3xC9^2	243,31
C₃³×C₉	Abelian group of type [3,3,3,9]	243		C3^3xC9	243,61
C₃²×C₂₇	Abelian group of type [3,3,27]	243		C3^2xC27	243,48
C₉×He₃	Direct product of C₉ and He₃	81		C9xHe3	243,35
C₃²×He₃	Direct product of C₃² and He₃	81		C3^2xHe3	243,62
C₉×3_-¹⁺²	Direct product of C₉ and 3_-¹⁺²	81		C9xES-(3,1)	243,36
C₃²×3_-¹⁺²	Direct product of C₃² and 3_-¹⁺²	81		C3^2xES-(3,1)	243,63
C₃×C₃≀C₃	Direct product of C₃ and C₃≀C₃	27		C3xC3wrC3	243,51
C₃×C₂₇⋊C₃	Direct product of C₃ and C₂₇⋊C₃	81		C3xC27:C3	243,49
C₃×C₃²⋊C₉	Direct product of C₃ and C₃²⋊C₉	81		C3xC3^2:C9	243,32
C₃×C₉○He₃	Direct product of C₃ and C₉○He₃	81		C3xC9oHe3	243,64
C₃×He₃⋊C₃	Direct product of C₃ and He₃⋊C₃	81		C3xHe3:C3	243,53
C₃×He₃.C₃	Direct product of C₃ and He₃.C₃	81		C3xHe3.C3	243,52
C₃×C₃.He₃	Direct product of C₃ and C₃.He₃	81		C3xC3.He3	243,54
C₃×C₉⋊C₉	Direct product of C₃ and C₉⋊C₉	243		C3xC9:C9	243,33

Groups of order 244

		d	ρ	Label	ID
C₂₄₄	Cyclic group	244	1	C244	244,2
D₁₂₂	Dihedral group; = C₂×D₆₁	122	2+	D122	244,4
Dic₆₁	Dicyclic group; = C₆₁ ⋊₂ C₄	244	2-	Dic61	244,1
C₆₁⋊C₄	The semidirect product of C₆₁ and C₄ acting faithfully	61	4+	C61:C4	244,3
C₂×C₁₂₂	Abelian group of type [2,122]	244		C2xC122	244,5

Groups of order 245

		d	ρ	Label	ID
C₂₄₅	Cyclic group	245	1	C245	245,1
C₇×C₃₅	Abelian group of type [7,35]	245		C7xC35	245,2

Groups of order 246

		d	ρ	Label	ID
C₂₄₆	Cyclic group	246	1	C246	246,4
D₁₂₃	Dihedral group	123	2+	D123	246,3
S₃×C₄₁	Direct product of C₄₁ and S₃	123	2	S3xC41	246,1
C₃×D₄₁	Direct product of C₃ and D₄₁	123	2	C3xD41	246,2

Groups of order 247

		d	ρ	Label	ID
C₂₄₇	Cyclic group	247	1	C247	247,1

Groups of order 248

		d	ρ	Label	ID
C₂₄₈	Cyclic group	248	1	C248	248,2
D₁₂₄	Dihedral group	124	2+	D124	248,5
Dic₆₂	Dicyclic group; = C₃₁ ⋊Q₈	248	2-	Dic62	248,3
C₃₁⋊D₄	The semidirect product of C₃₁ and D₄ acting via D₄/C₂²=C₂	124	2	C31:D4	248,7
C₃₁⋊C₈	The semidirect product of C₃₁ and C₈ acting via C₈/C₄=C₂	248	2	C31:C8	248,1
C₂×C₁₂₄	Abelian group of type [2,124]	248		C2xC124	248,8
C₂²×C₆₂	Abelian group of type [2,2,62]	248		C2^2xC62	248,12
C₄×D₃₁	Direct product of C₄ and D₃₁	124	2	C4xD31	248,4
D₄×C₃₁	Direct product of C₃₁ and D₄	124	2	D4xC31	248,9
C₂²×D₃₁	Direct product of C₂² and D₃₁	124		C2^2xD31	248,11
Q₈×C₃₁	Direct product of C₃₁ and Q₈	248	2	Q8xC31	248,10
C₂×Dic₃₁	Direct product of C₂ and Dic₃₁	248		C2xDic31	248,6

Groups of order 249

		d	ρ	Label	ID
C₂₄₉	Cyclic group	249	1	C249	249,1

Groups of order 250

		d	ρ	Label	ID
C₂₅₀	Cyclic group	250	1	C250	250,2
D₁₂₅	Dihedral group	125	2+	D125	250,1
C₂₅⋊C₁₀	The semidirect product of C₂₅ and C₁₀ acting faithfully	25	10+	C25:C10	250,6
C₅²⋊C₁₀	The semidirect product of C₅² and C₁₀ acting faithfully	25	10+	C5^2:C10	250,5
He₅⋊C₂	2^nd semidirect product of He₅ and C₂ acting faithfully	25	5	He5:C2	250,8
C₂₅⋊D₅	The semidirect product of C₂₅ and D₅ acting via D₅/C₅=C₂	125		C25:D5	250,7
C₅³⋊C₂	3^rd semidirect product of C₅³ and C₂ acting faithfully	125		C5^3:C2	250,14
C₅×C₅₀	Abelian group of type [5,50]	250		C5xC50	250,9
C₅²×C₁₀	Abelian group of type [5,5,10]	250		C5^2xC10	250,15
C₅×D₂₅	Direct product of C₅ and D₂₅	50	2	C5xD25	250,3
D₅×C₂₅	Direct product of C₂₅ and D₅	50	2	D5xC25	250,4
C₂×He₅	Direct product of C₂ and He₅	50	5	C2xHe5	250,10
D₅×C₅²	Direct product of C₅² and D₅	50		D5xC5^2	250,12
C₂×5_-¹⁺²	Direct product of C₂ and 5_-¹⁺²	50	5	C2xES-(5,1)	250,11
C₅×C₅⋊D₅	Direct product of C₅ and C₅⋊D₅	50		C5xC5:D5	250,13

Groups of order 251

		d	ρ	Label	ID
C₂₅₁	Cyclic group	251	1	C251	251,1

Groups of order 252

		d	ρ	Label	ID
C₂₅₂	Cyclic group	252	1	C252	252,6
D₁₂₆	Dihedral group; = C₂×D₆₃	126	2+	D126	252,14
Dic₆₃	Dicyclic group; = C₉ ⋊Dic₇	252	2-	Dic63	252,5
D₂₁⋊S₃	The semidirect product of D₂₁ and S₃ acting via S₃/C₃=C₂	42	4	D21:S3	252,37
C₃²⋊Dic₇	The semidirect product of C₃² and Dic₇ acting via Dic₇/C₇=C₄	42	4	C3^2:Dic7	252,32
C₇⋊C₃₆	The semidirect product of C₇ and C₃₆ acting via C₃₆/C₆=C₆	252	6	C7:C36	252,1
C₃⋊Dic₂₁	The semidirect product of C₃ and Dic₂₁ acting via Dic₂₁/C₄₂=C₂	252		C3:Dic21	252,24
C₆.F₇	The non-split extension by C₆ of F₇ acting via F₇/C₇⋊C₃=C₂	84	6-	C6.F7	252,18
C₂₁.A₄	The non-split extension by C₂₁ of A₄ acting via A₄/C₂²=C₃	126	3	C21.A4	252,11
C₃×C₈₄	Abelian group of type [3,84]	252		C3xC84	252,25
C₆×C₄₂	Abelian group of type [6,42]	252		C6xC42	252,46
C₂×C₁₂₆	Abelian group of type [2,126]	252		C2xC126	252,15
S₃×F₇	Direct product of S₃ and F₇; = Aut(D₂₁) = Hol(C₂₁)	21	12+	S3xF7	252,26
C₆×F₇	Direct product of C₆ and F₇	42	6	C6xF7	252,28
S₃×D₂₁	Direct product of S₃ and D₂₁	42	4+	S3xD21	252,36
D₇×D₉	Direct product of D₇ and D₉	63	4+	D7xD9	252,8
S₃×C₄₂	Direct product of C₄₂ and S₃	84	2	S3xC42	252,42
A₄×C₂₁	Direct product of C₂₁ and A₄	84	3	A4xC21	252,39
C₆×D₂₁	Direct product of C₆ and D₂₁	84	2	C6xD21	252,43
Dic₃×C₂₁	Direct product of C₂₁ and Dic₃	84	2	Dic3xC21	252,21
C₃×Dic₂₁	Direct product of C₃ and Dic₂₁	84	2	C3xDic21	252,22
D₇×C₁₈	Direct product of C₁₈ and D₇	126	2	D7xC18	252,12
C₁₄×D₉	Direct product of C₁₄ and D₉	126	2	C14xD9	252,13
C₇×Dic₉	Direct product of C₇ and Dic₉	252	2	C7xDic9	252,3
C₉×Dic₇	Direct product of C₉ and Dic₇	252	2	C9xDic7	252,4
C₃²×Dic₇	Direct product of C₃² and Dic₇	252		C3^2xDic7	252,20
A₄×C₇⋊C₃	Direct product of A₄ and C₇⋊C₃	28	9	A4xC7:C3	252,27
S₃²×C₇	Direct product of C₇, S₃ and S₃	42	4	S3^2xC7	252,35
C₃×S₃×D₇	Direct product of C₃, S₃ and D₇	42	4	C3xS3xD7	252,33
C₂×C₃⋊F₇	Direct product of C₂ and C₃⋊F₇	42	6+	C2xC3:F7	252,30
C₇×C₃²⋊C₄	Direct product of C₇ and C₃²⋊C₄	42	4	C7xC3^2:C4	252,31
D₇×C₃⋊S₃	Direct product of D₇ and C₃⋊S₃	63		D7xC3:S3	252,34
C₃×C₇⋊A₄	Direct product of C₃ and C₇⋊A₄	84	3	C3xC7:A4	252,40
C₃×C₇⋊C₁₂	Direct product of C₃ and C₇⋊C₁₂	84	6	C3xC7:C12	252,16
C₁₂×C₇⋊C₃	Direct product of C₁₂ and C₇⋊C₃	84	3	C12xC7:C3	252,19
Dic₃×C₇⋊C₃	Direct product of Dic₃ and C₇⋊C₃	84	6	Dic3xC7:C3	252,17
D₇×C₃×C₆	Direct product of C₃×C₆ and D₇	126		D7xC3xC6	252,41
C₂×C₇⋊C₁₈	Direct product of C₂ and C₇⋊C₁₈	126	6	C2xC7:C18	252,7
C₁₄×C₃⋊S₃	Direct product of C₁₄ and C₃⋊S₃	126		C14xC3:S3	252,44
C₂×C₃⋊D₂₁	Direct product of C₂ and C₃⋊D₂₁	126		C2xC3:D21	252,45
C₇×C₃.A₄	Direct product of C₇ and C₃.A₄	126	3	C7xC3.A4	252,10
C₄×C₇⋊C₉	Direct product of C₄ and C₇⋊C₉	252	3	C4xC7:C9	252,2
C₂²×C₇⋊C₉	Direct product of C₂² and C₇⋊C₉	252		C2^2xC7:C9	252,9
C₇×C₃⋊Dic₃	Direct product of C₇ and C₃⋊Dic₃	252		C7xC3:Dic3	252,23
C₂×S₃×C₇⋊C₃	Direct product of C₂, S₃ and C₇⋊C₃	42	6	C2xS3xC7:C3	252,29
C₂×C₆×C₇⋊C₃	Direct product of C₂×C₆ and C₇⋊C₃	84		C2xC6xC7:C3	252,38

Groups of order 253

		d	ρ	Label	ID
C₂₅₃	Cyclic group	253	1	C253	253,2
C₂₃⋊C₁₁	The semidirect product of C₂₃ and C₁₁ acting faithfully	23	11	C23:C11	253,1

Groups of order 254

		d	ρ	Label	ID
C₂₅₄	Cyclic group	254	1	C254	254,2
D₁₂₇	Dihedral group	127	2+	D127	254,1

Groups of order 255

		d	ρ	Label	ID
C₂₅₅	Cyclic group	255	1	C255	255,1

Groups of order 257

		d	ρ	Label	ID
C₂₅₇	Cyclic group	257	1	C257	257,1

Groups of order 258

		d	ρ	Label	ID
C₂₅₈	Cyclic group	258	1	C258	258,6
D₁₂₉	Dihedral group	129	2+	D129	258,5
C₄₃⋊C₆	The semidirect product of C₄₃ and C₆ acting faithfully	43	6+	C43:C6	258,1
S₃×C₄₃	Direct product of C₄₃ and S₃	129	2	S3xC43	258,3
C₃×D₄₃	Direct product of C₃ and D₄₃	129	2	C3xD43	258,4
C₂×C₄₃⋊C₃	Direct product of C₂ and C₄₃⋊C₃	86	3	C2xC43:C3	258,2

Groups of order 259

		d	ρ	Label	ID
C₂₅₉	Cyclic group	259	1	C259	259,1

Groups of order 260

		d	ρ	Label	ID
C₂₆₀	Cyclic group	260	1	C260	260,4
D₁₃₀	Dihedral group; = C₂×D₆₅	130	2+	D130	260,14
Dic₆₅	Dicyclic group; = C₆₅ ⋊₇ C₄	260	2-	Dic65	260,3
C₆₅⋊C₄	3^rd semidirect product of C₆₅ and C₄ acting faithfully	65	4	C65:C4	260,6
C₆₅⋊₂C₄	2^nd semidirect product of C₆₅ and C₄ acting faithfully	65	4+	C65:2C4	260,10
C₁₃⋊₃F₅	The semidirect product of C₁₃ and F₅ acting via F₅/D₅=C₂	65	4	C13:3F5	260,8
C₁₃⋊F₅	1^st semidirect product of C₁₃ and F₅ acting via F₅/C₅=C₄	65	4+	C13:F5	260,9
C₂×C₁₃₀	Abelian group of type [2,130]	260		C2xC130	260,15
D₅×D₁₃	Direct product of D₅ and D₁₃	65	4+	D5xD13	260,11
C₁₃×F₅	Direct product of C₁₃ and F₅	65	4	C13xF5	260,7
D₅×C₂₆	Direct product of C₂₆ and D₅	130	2	D5xC26	260,13
C₁₀×D₁₃	Direct product of C₁₀ and D₁₃	130	2	C10xD13	260,12
C₁₃×Dic₅	Direct product of C₁₃ and Dic₅	260	2	C13xDic5	260,1
C₅×Dic₁₃	Direct product of C₅ and Dic₁₃	260	2	C5xDic13	260,2
C₅×C₁₃⋊C₄	Direct product of C₅ and C₁₃⋊C₄	65	4	C5xC13:C4	260,5

Groups of order 261

		d	ρ	Label	ID
C₂₆₁	Cyclic group	261	1	C261	261,1
C₃×C₈₇	Abelian group of type [3,87]	261		C3xC87	261,2

Groups of order 262

		d	ρ	Label	ID
C₂₆₂	Cyclic group	262	1	C262	262,2
D₁₃₁	Dihedral group	131	2+	D131	262,1

Groups of order 263

		d	ρ	Label	ID
C₂₆₃	Cyclic group	263	1	C263	263,1

Groups of order 264

		d	ρ	Label	ID
C₂₆₄	Cyclic group	264	1	C264	264,4
D₁₃₂	Dihedral group	132	2+	D132	264,25
Dic₆₆	Dicyclic group; = C₃₃ ⋊₂ Q₈	264	2-	Dic66	264,23
C₁₁⋊S₄	The semidirect product of C₁₁ and S₄ acting via S₄/A₄=C₂	44	6+	C11:S4	264,32
D₃₃⋊C₄	The semidirect product of D₃₃ and C₄ acting via C₄/C₂=C₂	132	4+	D33:C4	264,7
C₃₃⋊D₄	1^st semidirect product of C₃₃ and D₄ acting via D₄/C₂=C₂²	132	4-	C33:D4	264,8
C₃⋊D₄₄	The semidirect product of C₃ and D₄₄ acting via D₄₄/D₂₂=C₂	132	4+	C3:D44	264,9
C₃₃⋊₇D₄	1^st semidirect product of C₃₃ and D₄ acting via D₄/C₂²=C₂	132	2	C33:7D4	264,27
C₁₁⋊D₁₂	The semidirect product of C₁₁ and D₁₂ acting via D₁₂/D₆=C₂	132	4+	C11:D12	264,10
C₃₃⋊Q₈	The semidirect product of C₃₃ and Q₈ acting via Q₈/C₂=C₂²	264	4-	C33:Q8	264,11
C₃₃⋊C₈	1^st semidirect product of C₃₃ and C₈ acting via C₈/C₄=C₂	264	2	C33:C8	264,3
C₂×C₁₃₂	Abelian group of type [2,132]	264		C2xC132	264,28
C₂²×C₆₆	Abelian group of type [2,2,66]	264		C2^2xC66	264,39
C₁₁×S₄	Direct product of C₁₁ and S₄	44	3	C11xS4	264,31
A₄×D₁₁	Direct product of A₄ and D₁₁	44	6+	A4xD11	264,33
A₄×C₂₂	Direct product of C₂₂ and A₄	66	3	A4xC22	264,35
C₁₁×SL₂(𝔽₃)	Direct product of C₁₁ and SL₂(𝔽₃)	88	2	C11xSL(2,3)	264,12
S₃×C₄₄	Direct product of C₄₄ and S₃	132	2	S3xC44	264,19
C₃×D₄₄	Direct product of C₃ and D₄₄	132	2	C3xD44	264,15
C₄×D₃₃	Direct product of C₄ and D₃₃	132	2	C4xD33	264,24
D₄×C₃₃	Direct product of C₃₃ and D₄	132	2	D4xC33	264,29
C₁₂×D₁₁	Direct product of C₁₂ and D₁₁	132	2	C12xD11	264,14
C₁₁×D₁₂	Direct product of C₁₁ and D₁₂	132	2	C11xD12	264,20
Dic₃×D₁₁	Direct product of Dic₃ and D₁₁	132	4-	Dic3xD11	264,5
S₃×Dic₁₁	Direct product of S₃ and Dic₁₁	132	4-	S3xDic11	264,6
C₂²×D₃₃	Direct product of C₂² and D₃₃	132		C2^2xD33	264,38
Q₈×C₃₃	Direct product of C₃₃ and Q₈	264	2	Q8xC33	264,30
C₃×Dic₂₂	Direct product of C₃ and Dic₂₂	264	2	C3xDic22	264,13
C₆×Dic₁₁	Direct product of C₆ and Dic₁₁	264		C6xDic11	264,16
C₁₁×Dic₆	Direct product of C₁₁ and Dic₆	264	2	C11xDic6	264,18
Dic₃×C₂₂	Direct product of C₂₂ and Dic₃	264		Dic3xC22	264,21
C₂×Dic₃₃	Direct product of C₂ and Dic₃₃	264		C2xDic33	264,26
C₂×S₃×D₁₁	Direct product of C₂, S₃ and D₁₁	66	4+	C2xS3xD11	264,34
S₃×C₂×C₂₂	Direct product of C₂×C₂₂ and S₃	132		S3xC2xC22	264,37
C₂×C₆×D₁₁	Direct product of C₂×C₆ and D₁₁	132		C2xC6xD11	264,36
C₃×C₁₁⋊D₄	Direct product of C₃ and C₁₁⋊D₄	132	2	C3xC11:D4	264,17
C₁₁×C₃⋊D₄	Direct product of C₁₁ and C₃⋊D₄	132	2	C11xC3:D4	264,22
C₁₁×C₃⋊C₈	Direct product of C₁₁ and C₃⋊C₈	264	2	C11xC3:C8	264,1
C₃×C₁₁⋊C₈	Direct product of C₃ and C₁₁⋊C₈	264	2	C3xC11:C8	264,2

Groups of order 265

		d	ρ	Label	ID
C₂₆₅	Cyclic group	265	1	C265	265,1

Groups of order 266

		d	ρ	Label	ID
C₂₆₆	Cyclic group	266	1	C266	266,4
D₁₃₃	Dihedral group	133	2+	D133	266,3
D₇×C₁₉	Direct product of C₁₉ and D₇	133	2	D7xC19	266,1
C₇×D₁₉	Direct product of C₇ and D₁₉	133	2	C7xD19	266,2

Groups of order 267

		d	ρ	Label	ID
C₂₆₇	Cyclic group	267	1	C267	267,1

Groups of order 268

		d	ρ	Label	ID
C₂₆₈	Cyclic group	268	1	C268	268,2
D₁₃₄	Dihedral group; = C₂×D₆₇	134	2+	D134	268,3
Dic₆₇	Dicyclic group; = C₆₇ ⋊C₄	268	2-	Dic67	268,1
C₂×C₁₃₄	Abelian group of type [2,134]	268		C2xC134	268,4

Groups of order 269

		d	ρ	Label	ID
C₂₆₉	Cyclic group	269	1	C269	269,1

Groups of order 270

		d	ρ	Label	ID
C₂₇₀	Cyclic group	270	1	C270	270,4
D₁₃₅	Dihedral group	135	2+	D135	270,3
D₄₅⋊C₃	The semidirect product of D₄₅ and C₃ acting faithfully	45	6+	D45:C3	270,15
He₃⋊D₅	1^st semidirect product of He₃ and D₅ acting via D₅/C₅=C₂	45	6+	He3:D5	270,14
C₃²⋊D₁₅	2^nd semidirect product of C₃² and D₁₅ acting via D₁₅/C₅=S₃	45	6	C3^2:D15	270,19
C₃⋊D₄₅	The semidirect product of C₃ and D₄₅ acting via D₄₅/C₄₅=C₂	135		C3:D45	270,18
C₃³⋊D₅	3^rd semidirect product of C₃³ and D₅ acting via D₅/C₅=C₂	135		C3^3:D5	270,29
C₃×C₉₀	Abelian group of type [3,90]	270		C3xC90	270,20
C₃²×C₃₀	Abelian group of type [3,3,30]	270		C3^2xC30	270,30
D₅×He₃	Direct product of D₅ and He₃	45	6	D5xHe3	270,6
D₅×3_-¹⁺²	Direct product of D₅ and 3_-¹⁺²	45	6	D5xES-(3,1)	270,7
S₃×C₄₅	Direct product of C₄₅ and S₃	90	2	S3xC45	270,9
C₁₅×D₉	Direct product of C₁₅ and D₉	90	2	C15xD9	270,8
C₃×D₄₅	Direct product of C₃ and D₄₅	90	2	C3xD45	270,12
C₉×D₁₅	Direct product of C₉ and D₁₅	90	2	C9xD15	270,13
C₁₀×He₃	Direct product of C₁₀ and He₃	90	3	C10xHe3	270,21
C₃²×D₁₅	Direct product of C₃² and D₁₅	90		C3^2xD15	270,25
C₁₀×3_-¹⁺²	Direct product of C₁₀ and 3_-¹⁺²	90	3	C10xES-(3,1)	270,22
C₅×D₂₇	Direct product of C₅ and D₂₇	135	2	C5xD27	270,1
D₅×C₂₇	Direct product of C₂₇ and D₅	135	2	D5xC27	270,2
D₅×C₃³	Direct product of C₃³ and D₅	135		D5xC3^3	270,23
C₅×C₉⋊C₆	Direct product of C₅ and C₉⋊C₆	45	6	C5xC9:C6	270,11
C₅×C₃²⋊C₆	Direct product of C₅ and C₃²⋊C₆	45	6	C5xC3^2:C6	270,10
C₅×He₃⋊C₂	Direct product of C₅ and He₃⋊C₂	45	3	C5xHe3:C2	270,17
S₃×C₃×C₁₅	Direct product of C₃×C₁₅ and S₃	90		S3xC3xC15	270,24
C₁₅×C₃⋊S₃	Direct product of C₁₅ and C₃⋊S₃	90		C15xC3:S3	270,26
C₃×C₃⋊D₁₅	Direct product of C₃ and C₃⋊D₁₅	90		C3xC3:D15	270,27
D₅×C₃×C₉	Direct product of C₃×C₉ and D₅	135		D5xC3xC9	270,5
C₅×C₉⋊S₃	Direct product of C₅ and C₉⋊S₃	135		C5xC9:S3	270,16
C₅×C₃³⋊C₂	Direct product of C₅ and C₃³⋊C₂	135		C5xC3^3:C2	270,28

Groups of order 271

		d	ρ	Label	ID
C₂₇₁	Cyclic group	271	1	C271	271,1

Groups of order 272

		d	ρ	Label	ID
C₂₇₂	Cyclic group	272	1	C272	272,2
D₁₃₆	Dihedral group	136	2+	D136	272,7
F₁₇	Frobenius group; = C₁₇ ⋊C₁₆ = AGL₁(𝔽₁₇) = Aut(D₁₇) = Hol(C₁₇)	17	16+	F17	272,50
Dic₆₈	Dicyclic group; = C₁₇ ⋊₁ Q₁₆	272	2-	Dic68	272,8
C₆₈⋊C₄	1^st semidirect product of C₆₈ and C₄ acting faithfully	68	4	C68:C4	272,32
D₄⋊D₁₇	The semidirect product of D₄ and D₁₇ acting via D₁₇/C₁₇=C₂	136	4+	D4:D17	272,15
Q₈⋊D₁₇	The semidirect product of Q₈ and D₁₇ acting via D₁₇/C₁₇=C₂	136	4+	Q8:D17	272,17
C₈⋊D₁₇	3^rd semidirect product of C₈ and D₁₇ acting via D₁₇/C₁₇=C₂	136	2	C8:D17	272,5
C₁₃₆⋊C₂	2^nd semidirect product of C₁₃₆ and C₂ acting faithfully	136	2	C136:C2	272,6
D₃₄⋊C₄	1^st semidirect product of D₃₄ and C₄ acting via C₄/C₂=C₂	136		D34:C4	272,14
D₆₈⋊₅C₂	The semidirect product of D₆₈ and C₂ acting through Inn(D₆₈)	136	2	D68:5C2	272,39
D₄⋊₂D₁₇	The semidirect product of D₄ and D₁₇ acting through Inn(D₄)	136	4-	D4:2D17	272,41
D₆₈⋊C₂	4^th semidirect product of D₆₈ and C₂ acting faithfully	136	4+	D68:C2	272,43
C₁₇⋊M₄(2)	The semidirect product of C₁₇ and M₄(2) acting via M₄(2)/C₂²=C₄	136	4-	C17:M4(2)	272,34
C₆₈⋊₃C₄	1^st semidirect product of C₆₈ and C₄ acting via C₄/C₂=C₂	272		C68:3C4	272,13
C₁₇⋊₄C₁₆	The semidirect product of C₁₇ and C₁₆ acting via C₁₆/C₈=C₂	272	2	C17:4C16	272,1
C₁₇⋊₃C₁₆	The semidirect product of C₁₇ and C₁₆ acting via C₁₆/C₄=C₄	272	4	C17:3C16	272,3
C₁₇⋊Q₁₆	The semidirect product of C₁₇ and Q₁₆ acting via Q₁₆/Q₈=C₂	272	4-	C17:Q16	272,18
D₁₇.D₄	The non-split extension by D₁₇ of D₄ acting via D₄/C₂²=C₂	68	4+	D17.D4	272,35
D₄.D₁₇	The non-split extension by D₄ of D₁₇ acting via D₁₇/C₁₇=C₂	136	4-	D4.D17	272,16
C₆₈.₄C₄	1^st non-split extension by C₆₈ of C₄ acting via C₄/C₂=C₂	136	2	C68.4C4	272,10
C₆₈.C₄	3^rd non-split extension by C₆₈ of C₄ acting faithfully	136	4	C68.C4	272,29
C₂³.D₁₇	The non-split extension by C₂³ of D₁₇ acting via D₁₇/C₁₇=C₂	136		C2^3.D17	272,19
D₃₄.₄C₄	3^rd non-split extension by D₃₄ of C₄ acting via C₄/C₂=C₂	136	4	D34.4C4	272,30
C₃₄.C₈	The non-split extension by C₃₄ of C₈ acting faithfully	272	8-	C34.C8	272,28
C₃₄.D₄	1^st non-split extension by C₃₄ of D₄ acting via D₄/C₂²=C₂	272		C34.D4	272,12
C₄×C₆₈	Abelian group of type [4,68]	272		C4xC68	272,20
C₂×C₁₃₆	Abelian group of type [2,136]	272		C2xC136	272,23
C₂²×C₆₈	Abelian group of type [2,2,68]	272		C2^2xC68	272,46
C₂³×C₃₄	Abelian group of type [2,2,2,34]	272		C2^3xC34	272,54
D₄×D₁₇	Direct product of D₄ and D₁₇	68	4+	D4xD17	272,40
C₈×D₁₇	Direct product of C₈ and D₁₇	136	2	C8xD17	272,4
D₈×C₁₇	Direct product of C₁₇ and D₈	136	2	D8xC17	272,25
C₂×D₆₈	Direct product of C₂ and D₆₈	136		C2xD68	272,38
D₄×C₃₄	Direct product of C₃₄ and D₄	136		D4xC34	272,47
Q₈×D₁₇	Direct product of Q₈ and D₁₇	136	4-	Q8xD17	272,42
SD₁₆×C₁₇	Direct product of C₁₇ and SD₁₆	136	2	SD16xC17	272,26
C₂³×D₁₇	Direct product of C₂³ and D₁₇	136		C2^3xD17	272,53
M₄(2)×C₁₇	Direct product of C₁₇ and M₄(2)	136	2	M4(2)xC17	272,24
Q₈×C₃₄	Direct product of C₃₄ and Q₈	272		Q8xC34	272,48
Q₁₆×C₁₇	Direct product of C₁₇ and Q₁₆	272	2	Q16xC17	272,27
C₄×Dic₁₇	Direct product of C₄ and Dic₁₇	272		C4xDic17	272,11
C₂×Dic₃₄	Direct product of C₂ and Dic₃₄	272		C2xDic34	272,36
C₂²×Dic₁₇	Direct product of C₂² and Dic₁₇	272		C2^2xDic17	272,44
C₂×C₁₇⋊C₈	Direct product of C₂ and C₁₇⋊C₈	34	8+	C2xC17:C8	272,51
C₄×C₁₇⋊C₄	Direct product of C₄ and C₁₇⋊C₄	68	4	C4xC17:C4	272,31
C₂²×C₁₇⋊C₄	Direct product of C₂² and C₁₇⋊C₄	68		C2^2xC17:C4	272,52
C₂×C₄×D₁₇	Direct product of C₂×C₄ and D₁₇	136		C2xC4xD17	272,37
C₂×C₁₇⋊D₄	Direct product of C₂ and C₁₇⋊D₄	136		C2xC17:D4	272,45
C₄○D₄×C₁₇	Direct product of C₁₇ and C₄○D₄	136	2	C4oD4xC17	272,49
C₂²⋊C₄×C₁₇	Direct product of C₁₇ and C₂²⋊C₄	136		C2^2:C4xC17	272,21
C₄⋊C₄×C₁₇	Direct product of C₁₇ and C₄⋊C₄	272		C4:C4xC17	272,22
C₂×C₁₇⋊₃C₈	Direct product of C₂ and C₁₇⋊₃C₈	272		C2xC17:3C8	272,9
C₂×C₁₇⋊₂C₈	Direct product of C₂ and C₁₇⋊₂C₈	272		C2xC17:2C8	272,33

Groups of order 273

		d	ρ	Label	ID
C₂₇₃	Cyclic group	273	1	C273	273,5
C₉₁⋊C₃	3^rd semidirect product of C₉₁ and C₃ acting faithfully	91	3	C91:C3	273,3
C₉₁⋊₄C₃	4^th semidirect product of C₉₁ and C₃ acting faithfully	91	3	C91:4C3	273,4
C₁₃×C₇⋊C₃	Direct product of C₁₃ and C₇⋊C₃	91	3	C13xC7:C3	273,1
C₇×C₁₃⋊C₃	Direct product of C₇ and C₁₃⋊C₃	91	3	C7xC13:C3	273,2

Groups of order 274

		d	ρ	Label	ID
C₂₇₄	Cyclic group	274	1	C274	274,2
D₁₃₇	Dihedral group	137	2+	D137	274,1

Groups of order 275

		d	ρ	Label	ID
C₂₇₅	Cyclic group	275	1	C275	275,2
C₁₁⋊C₂₅	The semidirect product of C₁₁ and C₂₅ acting via C₂₅/C₅=C₅	275	5	C11:C25	275,1
C₅×C₅₅	Abelian group of type [5,55]	275		C5xC55	275,4
C₅×C₁₁⋊C₅	Direct product of C₅ and C₁₁⋊C₅	55	5	C5xC11:C5	275,3

Groups of order 276

		d	ρ	Label	ID
C₂₇₆	Cyclic group	276	1	C276	276,4
D₁₃₈	Dihedral group; = C₂×D₆₉	138	2+	D138	276,9
Dic₆₉	Dicyclic group; = C₆₉ ⋊₁ C₄	276	2-	Dic69	276,3
C₂×C₁₃₈	Abelian group of type [2,138]	276		C2xC138	276,10
S₃×D₂₃	Direct product of S₃ and D₂₃	69	4+	S3xD23	276,5
A₄×C₂₃	Direct product of C₂₃ and A₄	92	3	A4xC23	276,6
S₃×C₄₆	Direct product of C₄₆ and S₃	138	2	S3xC46	276,8
C₆×D₂₃	Direct product of C₆ and D₂₃	138	2	C6xD23	276,7
Dic₃×C₂₃	Direct product of C₂₃ and Dic₃	276	2	Dic3xC23	276,1
C₃×Dic₂₃	Direct product of C₃ and Dic₂₃	276	2	C3xDic23	276,2

Groups of order 277

		d	ρ	Label	ID
C₂₇₇	Cyclic group	277	1	C277	277,1

Groups of order 278

		d	ρ	Label	ID
C₂₇₈	Cyclic group	278	1	C278	278,2
D₁₃₉	Dihedral group	139	2+	D139	278,1

Groups of order 279

		d	ρ	Label	ID
C₂₇₉	Cyclic group	279	1	C279	279,2
C₃₁⋊C₉	The semidirect product of C₃₁ and C₉ acting via C₉/C₃=C₃	279	3	C31:C9	279,1
C₃×C₉₃	Abelian group of type [3,93]	279		C3xC93	279,4
C₃×C₃₁⋊C₃	Direct product of C₃ and C₃₁⋊C₃	93	3	C3xC31:C3	279,3

Groups of order 280

		d	ρ	Label	ID
C₂₈₀	Cyclic group	280	1	C280	280,4
D₁₄₀	Dihedral group	140	2+	D140	280,26
Dic₇₀	Dicyclic group; = C₃₅ ⋊₂ Q₈	280	2-	Dic70	280,24
C₃₅⋊D₄	1^st semidirect product of C₃₅ and D₄ acting via D₄/C₂=C₂²	140	4-	C35:D4	280,10
C₅⋊D₂₈	The semidirect product of C₅ and D₂₈ acting via D₂₈/D₁₄=C₂	140	4+	C5:D28	280,11
C₇⋊D₂₀	The semidirect product of C₇ and D₂₀ acting via D₂₀/D₁₀=C₂	140	4+	C7:D20	280,12
C₃₅⋊₇D₄	1^st semidirect product of C₃₅ and D₄ acting via D₄/C₂²=C₂	140	2	C35:7D4	280,28
C₃₅⋊Q₈	The semidirect product of C₃₅ and Q₈ acting via Q₈/C₂=C₂²	280	4-	C35:Q8	280,13
C₃₅⋊₃C₈	1^st semidirect product of C₃₅ and C₈ acting via C₈/C₄=C₂	280	2	C35:3C8	280,3
C₃₅⋊C₈	1^st semidirect product of C₃₅ and C₈ acting via C₈/C₂=C₄	280	4	C35:C8	280,6
D₇₀.C₂	The non-split extension by D₇₀ of C₂ acting faithfully	140	4+	D70.C2	280,9
C₂×C₁₄₀	Abelian group of type [2,140]	280		C2xC140	280,29
C₂²×C₇₀	Abelian group of type [2,2,70]	280		C2^2xC70	280,40
D₇×F₅	Direct product of D₇ and F₅	35	8+	D7xF5	280,32
C₅×F₈	Direct product of C₅ and F₈	40	7	C5xF8	280,33
C₁₄×F₅	Direct product of C₁₄ and F₅	70	4	C14xF5	280,34
D₇×C₂₀	Direct product of C₂₀ and D₇	140	2	D7xC20	280,15
C₅×D₂₈	Direct product of C₅ and D₂₈	140	2	C5xD28	280,16
D₅×C₂₈	Direct product of C₂₈ and D₅	140	2	D5xC28	280,20
C₇×D₂₀	Direct product of C₇ and D₂₀	140	2	C7xD20	280,21
C₄×D₃₅	Direct product of C₄ and D₃₅	140	2	C4xD35	280,25
D₄×C₃₅	Direct product of C₃₅ and D₄	140	2	D4xC35	280,30
D₇×Dic₅	Direct product of D₇ and Dic₅	140	4-	D7xDic5	280,7
D₅×Dic₇	Direct product of D₅ and Dic₇	140	4-	D5xDic7	280,8
C₂²×D₃₅	Direct product of C₂² and D₃₅	140		C2^2xD35	280,39
Q₈×C₃₅	Direct product of C₃₅ and Q₈	280	2	Q8xC35	280,31
C₅×Dic₁₄	Direct product of C₅ and Dic₁₄	280	2	C5xDic14	280,14
C₁₀×Dic₇	Direct product of C₁₀ and Dic₇	280		C10xDic7	280,17
C₇×Dic₁₀	Direct product of C₇ and Dic₁₀	280	2	C7xDic10	280,19
C₁₄×Dic₅	Direct product of C₁₄ and Dic₅	280		C14xDic5	280,22
C₂×Dic₃₅	Direct product of C₂ and Dic₃₅	280		C2xDic35	280,27
C₂×D₅×D₇	Direct product of C₂, D₅ and D₇	70	4+	C2xD5xD7	280,36
C₂×C₇⋊F₅	Direct product of C₂ and C₇⋊F₅	70	4	C2xC7:F5	280,35
D₇×C₂×C₁₀	Direct product of C₂×C₁₀ and D₇	140		D7xC2xC10	280,37
D₅×C₂×C₁₄	Direct product of C₂×C₁₄ and D₅	140		D5xC2xC14	280,38
C₅×C₇⋊D₄	Direct product of C₅ and C₇⋊D₄	140	2	C5xC7:D4	280,18
C₇×C₅⋊D₄	Direct product of C₇ and C₅⋊D₄	140	2	C7xC5:D4	280,23
C₅×C₇⋊C₈	Direct product of C₅ and C₇⋊C₈	280	2	C5xC7:C8	280,2
C₇×C₅⋊C₈	Direct product of C₇ and C₅⋊C₈	280	4	C7xC5:C8	280,5
C₇×C₅⋊₂C₈	Direct product of C₇ and C₅⋊₂C₈	280	2	C7xC5:2C8	280,1

Groups of order 281

		d	ρ	Label	ID
C₂₈₁	Cyclic group	281	1	C281	281,1

Groups of order 282

		d	ρ	Label	ID
C₂₈₂	Cyclic group	282	1	C282	282,4
D₁₄₁	Dihedral group	141	2+	D141	282,3
S₃×C₄₇	Direct product of C₄₇ and S₃	141	2	S3xC47	282,1
C₃×D₄₇	Direct product of C₃ and D₄₇	141	2	C3xD47	282,2

Groups of order 283

		d	ρ	Label	ID
C₂₈₃	Cyclic group	283	1	C283	283,1

Groups of order 284

		d	ρ	Label	ID
C₂₈₄	Cyclic group	284	1	C284	284,2
D₁₄₂	Dihedral group; = C₂×D₇₁	142	2+	D142	284,3
Dic₇₁	Dicyclic group; = C₇₁ ⋊C₄	284	2-	Dic71	284,1
C₂×C₁₄₂	Abelian group of type [2,142]	284		C2xC142	284,4

Groups of order 285

		d	ρ	Label	ID
C₂₈₅	Cyclic group	285	1	C285	285,2
C₅×C₁₉⋊C₃	Direct product of C₅ and C₁₉⋊C₃	95	3	C5xC19:C3	285,1

Groups of order 286

		d	ρ	Label	ID
C₂₈₆	Cyclic group	286	1	C286	286,4
D₁₄₃	Dihedral group	143	2+	D143	286,3
C₁₃×D₁₁	Direct product of C₁₃ and D₁₁	143	2	C13xD11	286,1
C₁₁×D₁₃	Direct product of C₁₁ and D₁₃	143	2	C11xD13	286,2

Groups of order 287

		d	ρ	Label	ID
C₂₈₇	Cyclic group	287	1	C287	287,1

Groups of order 288

		d	ρ	Label	ID
C₂₈₈	Cyclic group	288	1	C288	288,2
D₁₄₄	Dihedral group	144	2+	D144	288,6
Dic₇₂	Dicyclic group; = C₉ ⋊₁ Q₃₂	288	2-	Dic72	288,8
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	12	9+	PSO+(4,3)	288,1026
Ω₄⁺ (𝔽₃)	Omega group of + type on 𝔽₃⁴; = SL₂(𝔽₃)⋊A₄	24	4+	Omega+(4,3)	288,860
A₄≀C₂	Wreath product of A₄ by C₂	8	6+	A4wrC2	288,1025
D₆≀C₂	Wreath product of D₆ by C₂	12	4+	D6wrC2	288,889
Dic₃≀C₂	Wreath product of Dic₃ by C₂	24	4-	Dic3wrC2	288,389
C₂²⋊F₉	The semidirect product of C₂² and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8+	C2^2:F9	288,867
D₁₂⋊D₆	4^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	24	8+	D12:D6	288,574
D₁₂⋊₅D₆	5^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	24	8+	D12:5D6	288,585
C₆²⋊₈D₄	5^th semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	24		C6^2:8D4	288,629
C₆²⋊D₄	2^nd semidirect product of C₆² and D₄ acting faithfully	24	8+	C6^2:D4	288,890
D₁₂⋊₁₈D₆	2^nd semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	24	4+	D12:18D6	288,473
D₁₂⋊₂₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	24	4	D12:23D6	288,954
D₁₂⋊₂₇D₆	3^rd semidirect product of D₁₂ and D₆ acting through Inn(D₁₂)	24	4+	D12:27D6	288,956
D₁₂⋊₁₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	24	8+	D12:13D6	288,962
C₆²⋊Q₈	1^st semidirect product of C₆² and Q₈ acting faithfully	24	8+	C6^2:Q8	288,895
Dic₆⋊D₆	4^th semidirect product of Dic₆ and D₆ acting via D₆/C₃=C₂²	24	8+	Dic6:D6	288,578
D₁₂⋊₄Dic₃	4^th semidirect product of D₁₂ and Dic₃ acting via Dic₃/C₆=C₂	24	4	D12:4Dic3	288,216
Dic₆⋊₁₂D₆	6^th semidirect product of Dic₆ and D₆ acting via D₆/S₃=C₂	24	8+	Dic6:12D6	288,960
C₃²⋊2₊¹⁺⁴	The semidirect product of C₃² and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂³=C₂²	24	4	C3^2:ES+(2,2)	288,978
C₄⋊F₉	The semidirect product of C₄ and F₉ acting via F₉/C₃²⋊C₄=C₂	36	8	C4:F9	288,864
F₉⋊C₄	The semidirect product of F₉ and C₄ acting via C₄/C₂=C₂	36	8	F9:C4	288,843
C₄²⋊D₉	The semidirect product of C₄² and D₉ acting via D₉/C₃=S₃	36	6+	C4^2:D9	288,67
C₁₂⋊S₄	1^st semidirect product of C₁₂ and S₄ acting via S₄/A₄=C₂	36	6+	C12:S4	288,909
D₆⋊S₄	1^st semidirect product of D₆ and S₄ acting via S₄/A₄=C₂	36	6	D6:S4	288,857
Dic₃⋊S₄	The semidirect product of Dic₃ and S₄ acting via S₄/A₄=C₂	36	6	Dic3:S4	288,855
C₂²⋊D₃₆	The semidirect product of C₂² and D₃₆ acting via D₃₆/C₁₂=S₃	36	6+	C2^2:D36	288,334
A₄⋊D₁₂	The semidirect product of A₄ and D₁₂ acting via D₁₂/D₆=C₂	36	6+	A4:D12	288,858
C₂⁴⋊D₉	3^rd semidirect product of C₂⁴ and D₉ acting via D₉/C₃=S₃	36	6	C2^4:D9	288,836
C₂⁴⋊C₁₈	1^st semidirect product of C₂⁴ and C₁₈ acting via C₁₈/C₃=C₆	36	6	C2^4:C18	288,73
C₄²⋊₂C₁₈	2^nd semidirect product of C₄² and C₁₈ acting via C₁₈/C₃=C₆	36	6	C4^2:2C18	288,75
Dic₃⋊₂S₄	The semidirect product of Dic₃ and S₄ acting through Inn(Dic₃)	36	6	Dic3:2S4	288,854
C₄⋊PSU₃(𝔽₂)	The semidirect product of C₄ and PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	36	8	C4:PSU(3,2)	288,893
PSU₃(𝔽₂)⋊C₄	The semidirect product of PSU₃(𝔽₂) and C₄ acting via C₄/C₂=C₂	36	8	PSU(3,2):C4	288,842
C₃²⋊D₁₆	The semidirect product of C₃² and D₁₆ acting via D₁₆/C₄=D₄	48	8+	C3^2:D16	288,382
C₃⋊D₄₈	The semidirect product of C₃ and D₄₈ acting via D₄₈/D₂₄=C₂	48	4+	C3:D48	288,194
C₂₄⋊₁D₆	1^st semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4+	C24:1D6	288,442
C₂₄⋊₉D₆	9^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:9D6	288,444
C₂₄⋊₄D₆	4^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:4D6	288,445
C₂₄⋊₆D₆	6^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:6D6	288,446
C₃²⋊SD₃₂	The semidirect product of C₃² and SD₃₂ acting via SD₃₂/C₄=D₄	48	8+	C3^2:SD32	288,383
D₂₄⋊S₃	2^nd semidirect product of D₂₄ and S₃ acting via S₃/C₃=C₂	48	4	D24:S3	288,443
D₂₄⋊₅S₃	5^th semidirect product of D₂₄ and S₃ acting via S₃/C₃=C₂	48	4	D24:5S3	288,458
D₆⋊D₁₂	1^st semidirect product of D₆ and D₁₂ acting via D₁₂/C₁₂=C₂	48		D6:D12	288,554
D₆⋊₄D₁₂	1^st semidirect product of D₆ and D₁₂ acting via D₁₂/D₆=C₂	48		D6:4D12	288,570
D₆⋊₅D₁₂	2^nd semidirect product of D₆ and D₁₂ acting via D₁₂/D₆=C₂	48		D6:5D12	288,571
D₁₂⋊₉D₆	3^rd semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:9D6	288,580
D₁₂⋊₆D₆	6^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	48	8+	D12:6D6	288,587

Full list: Groups of order 288 (1045 groups)

Groups of order 289

		d	ρ	Label	ID
C₂₈₉	Cyclic group	289	1	C289	289,1
C₁₇²	Elementary abelian group of type [17,17]	289		C17^2	289,2

Groups of order 290

		d	ρ	Label	ID
C₂₉₀	Cyclic group	290	1	C290	290,4
D₁₄₅	Dihedral group	145	2+	D145	290,3
D₅×C₂₉	Direct product of C₂₉ and D₅	145	2	D5xC29	290,1
C₅×D₂₉	Direct product of C₅ and D₂₉	145	2	C5xD29	290,2

Groups of order 291

		d	ρ	Label	ID
C₂₉₁	Cyclic group	291	1	C291	291,2
C₉₇⋊C₃	The semidirect product of C₉₇ and C₃ acting faithfully	97	3	C97:C3	291,1

Groups of order 292

		d	ρ	Label	ID
C₂₉₂	Cyclic group	292	1	C292	292,2
D₁₄₆	Dihedral group; = C₂×D₇₃	146	2+	D146	292,4
Dic₇₃	Dicyclic group; = C₇₃ ⋊₂ C₄	292	2-	Dic73	292,1
C₇₃⋊C₄	The semidirect product of C₇₃ and C₄ acting faithfully	73	4+	C73:C4	292,3
C₂×C₁₄₆	Abelian group of type [2,146]	292		C2xC146	292,5

Groups of order 293

		d	ρ	Label	ID
C₂₉₃	Cyclic group	293	1	C293	293,1

Groups of order 294

		d	ρ	Label	ID
C₂₉₄	Cyclic group	294	1	C294	294,6
D₁₄₇	Dihedral group	147	2+	D147	294,5
C₇²⋊S₃	The semidirect product of C₇² and S₃ acting faithfully	14	3	C7^2:S3	294,7
C₇⋊₄F₇	2^nd semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	14	6	C7:4F7	294,12
C₇⋊₅F₇	The semidirect product of C₇ and F₇ acting via F₇/C₇⋊C₃=C₂	21	6+	C7:5F7	294,10
C₇²⋊C₆	7^th semidirect product of C₇² and C₆ acting faithfully	21	6+	C7^2:C6	294,14
C₇⋊₃F₇	1^st semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	42	6	C7:3F7	294,11
C₄₉⋊C₆	The semidirect product of C₄₉ and C₆ acting faithfully	49	6+	C49:C6	294,1
C₇⋊F₇	1^st semidirect product of C₇ and F₇ acting via F₇/C₇=C₆	49		C7:F7	294,13
C₇⋊D₂₁	The semidirect product of C₇ and D₂₁ acting via D₂₁/C₂₁=C₂	147		C7:D21	294,22
C₇×C₄₂	Abelian group of type [7,42]	294		C7xC42	294,23
C₇×F₇	Direct product of C₇ and F₇	42	6	C7xF7	294,8
D₇×C₂₁	Direct product of C₂₁ and D₇	42	2	D7xC21	294,18
C₇×D₂₁	Direct product of C₇ and D₂₁	42	2	C7xD21	294,21
S₃×C₄₉	Direct product of C₄₉ and S₃	147	2	S3xC49	294,3
C₃×D₄₉	Direct product of C₃ and D₄₉	147	2	C3xD49	294,4
S₃×C₇²	Direct product of C₇² and S₃	147		S3xC7^2	294,20
D₇×C₇⋊C₃	Direct product of D₇ and C₇⋊C₃	42	6	D7xC7:C3	294,9
C₁₄×C₇⋊C₃	Direct product of C₁₄ and C₇⋊C₃	42	3	C14xC7:C3	294,15
C₂×C₇²⋊₃C₃	Direct product of C₂ and C₇²⋊₃C₃	42	3	C2xC7^2:3C3	294,17
C₂×C₄₉⋊C₃	Direct product of C₂ and C₄₉⋊C₃	98	3	C2xC49:C3	294,2
C₂×C₇²⋊C₃	Direct product of C₂ and C₇²⋊C₃	98		C2xC7^2:C3	294,16
C₃×C₇⋊D₇	Direct product of C₃ and C₇⋊D₇	147		C3xC7:D7	294,19

Groups of order 295

		d	ρ	Label	ID
C₂₉₅	Cyclic group	295	1	C295	295,1

Groups of order 296

		d	ρ	Label	ID
C₂₉₆	Cyclic group	296	1	C296	296,2
D₁₄₈	Dihedral group	148	2+	D148	296,6
Dic₇₄	Dicyclic group; = C₃₇ ⋊Q₈	296	2-	Dic74	296,4
C₃₇⋊D₄	The semidirect product of C₃₇ and D₄ acting via D₄/C₂²=C₂	148	2	C37:D4	296,8
C₃₇⋊C₈	The semidirect product of C₃₇ and C₈ acting via C₈/C₂=C₄	296	4-	C37:C8	296,3
C₃₇⋊₂C₈	The semidirect product of C₃₇ and C₈ acting via C₈/C₄=C₂	296	2	C37:2C8	296,1
C₂×C₁₄₈	Abelian group of type [2,148]	296		C2xC148	296,9
C₂²×C₇₄	Abelian group of type [2,2,74]	296		C2^2xC74	296,14
C₄×D₃₇	Direct product of C₄ and D₃₇	148	2	C4xD37	296,5
D₄×C₃₇	Direct product of C₃₇ and D₄	148	2	D4xC37	296,10
C₂²×D₃₇	Direct product of C₂² and D₃₇	148		C2^2xD37	296,13
Q₈×C₃₇	Direct product of C₃₇ and Q₈	296	2	Q8xC37	296,11
C₂×Dic₃₇	Direct product of C₂ and Dic₃₇	296		C2xDic37	296,7
C₂×C₃₇⋊C₄	Direct product of C₂ and C₃₇⋊C₄	74	4+	C2xC37:C4	296,12

Groups of order 297

		d	ρ	Label	ID
C₂₉₇	Cyclic group	297	1	C297	297,1
C₃×C₉₉	Abelian group of type [3,99]	297		C3xC99	297,2
C₃²×C₃₃	Abelian group of type [3,3,33]	297		C3^2xC33	297,5
C₁₁×He₃	Direct product of C₁₁ and He₃	99	3	C11xHe3	297,3
C₁₁×3_-¹⁺²	Direct product of C₁₁ and 3_-¹⁺²	99	3	C11xES-(3,1)	297,4

Groups of order 298

		d	ρ	Label	ID
C₂₉₈	Cyclic group	298	1	C298	298,2
D₁₄₉	Dihedral group	149	2+	D149	298,1

Groups of order 299

		d	ρ	Label	ID
C₂₉₉	Cyclic group	299	1	C299	299,1

Groups of order 300

		d	ρ	Label	ID
C₃₀₀	Cyclic group	300	1	C300	300,4
D₁₅₀	Dihedral group; = C₂×D₇₅	150	2+	D150	300,11
Dic₇₅	Dicyclic group; = C₇₅ ⋊₃ C₄	300	2-	Dic75	300,3
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	15	6+	C5^2:D6	300,25
C₅²⋊C₁₂	The semidirect product of C₅² and C₁₂ acting faithfully	15	12+	C5^2:C12	300,24
C₅²⋊Dic₃	The semidirect product of C₅² and Dic₃ acting faithfully	15	12+	C5^2:Dic3	300,23
C₅²⋊A₄	The semidirect product of C₅² and A₄ acting via A₄/C₂²=C₃	30	3	C5^2:A4	300,43
D₁₅⋊D₅	The semidirect product of D₁₅ and D₅ acting via D₅/C₅=C₂	30	4	D15:D5	300,40
C₁₅⋊₂F₅	2^nd semidirect product of C₁₅ and F₅ acting via F₅/C₅=C₄	30	4	C15:2F5	300,35
C₅²⋊₂C₁₂	The semidirect product of C₅² and C₁₂ acting via C₁₂/C₂=C₆	60	6-	C5^2:2C12	300,14
C₅²⋊₂Dic₃	The semidirect product of C₅² and Dic₃ acting via Dic₃/C₂=S₃	60	3	C5^2:2Dic3	300,13
C₇₅⋊C₄	1^st semidirect product of C₇₅ and C₄ acting faithfully	75	4	C75:C4	300,6
C₁₅⋊F₅	1^st semidirect product of C₁₅ and F₅ acting via F₅/C₅=C₄	75		C15:F5	300,34
D₅.D₁₅	The non-split extension by D₅ of D₁₅ acting via D₁₅/C₁₅=C₂	60	4	D5.D15	300,33
C₃₀.D₅	3^rd non-split extension by C₃₀ of D₅ acting via D₅/C₅=C₂	300		C30.D5	300,20
C₅×C₆₀	Abelian group of type [5,60]	300		C5xC60	300,21
C₂×C₁₅₀	Abelian group of type [2,150]	300		C2xC150	300,12
C₁₀×C₃₀	Abelian group of type [10,30]	300		C10xC30	300,49
C₅×A₅	Direct product of C₅ and A₅; = U₂(𝔽₄)	25	3	C5xA5	300,22
D₅×D₁₅	Direct product of D₅ and D₁₅	30	4+	D5xD15	300,39
D₅×C₃₀	Direct product of C₃₀ and D₅	60	2	D5xC30	300,44
C₁₅×F₅	Direct product of C₁₅ and F₅	60	4	C15xF5	300,28
C₁₀×D₁₅	Direct product of C₁₀ and D₁₅	60	2	C10xD15	300,47
C₁₅×Dic₅	Direct product of C₁₅ and Dic₅	60	2	C15xDic5	300,16
C₅×Dic₁₅	Direct product of C₅ and Dic₁₅	60	2	C5xDic15	300,19
S₃×D₂₅	Direct product of S₃ and D₂₅	75	4+	S3xD25	300,7
A₄×C₂₅	Direct product of C₂₅ and A₄	100	3	A4xC25	300,8
A₄×C₅²	Direct product of C₅² and A₄	100		A4xC5^2	300,42
S₃×C₅₀	Direct product of C₅₀ and S₃	150	2	S3xC50	300,10
C₆×D₂₅	Direct product of C₆ and D₂₅	150	2	C6xD25	300,9
Dic₃×C₂₅	Direct product of C₂₅ and Dic₃	300	2	Dic3xC25	300,1
C₃×Dic₂₅	Direct product of C₃ and Dic₂₅	300	2	C3xDic25	300,2
Dic₃×C₅²	Direct product of C₅² and Dic₃	300		Dic3xC5^2	300,18
C₃×D₅²	Direct product of C₃, D₅ and D₅	30	4	C3xD5^2	300,36
C₅×S₃×D₅	Direct product of C₅, S₃ and D₅	30	4	C5xS3xD5	300,37
C₂×C₅²⋊S₃	Direct product of C₂ and C₅²⋊S₃	30	3	C2xC5^2:S3	300,26
C₂×C₅²⋊C₆	Direct product of C₂ and C₅²⋊C₆	30	6+	C2xC5^2:C6	300,27
C₃×C₅²⋊C₄	Direct product of C₃ and C₅²⋊C₄	30	4	C3xC5^2:C4	300,31
C₅×C₃⋊F₅	Direct product of C₅ and C₃⋊F₅	60	4	C5xC3:F5	300,32
C₄×C₅²⋊C₃	Direct product of C₄ and C₅²⋊C₃	60	3	C4xC5^2:C3	300,15
C₃×D₅.D₅	Direct product of C₃ and D₅.D₅	60	4	C3xD5.D5	300,29
C₂²×C₅²⋊C₃	Direct product of C₂² and C₅²⋊C₃	60		C2^2xC5^2:C3	300,41
C₃×C₂₅⋊C₄	Direct product of C₃ and C₂₅⋊C₄	75	4	C3xC25:C4	300,5
S₃×C₅⋊D₅	Direct product of S₃ and C₅⋊D₅	75		S3xC5:D5	300,38
C₃×C₅⋊F₅	Direct product of C₃ and C₅⋊F₅	75		C3xC5:F5	300,30
S₃×C₅×C₁₀	Direct product of C₅×C₁₀ and S₃	150		S3xC5xC10	300,46
C₆×C₅⋊D₅	Direct product of C₆ and C₅⋊D₅	150		C6xC5:D5	300,45
C₂×C₅⋊D₁₅	Direct product of C₂ and C₅⋊D₁₅	150		C2xC5:D15	300,48
C₃×C₅²⋊₆C₄	Direct product of C₃ and C₅²⋊₆C₄	300		C3xC5^2:6C4	300,17

Groups of order 301

		d	ρ	Label	ID
C₃₀₁	Cyclic group	301	1	C301	301,2
C₄₃⋊C₇	The semidirect product of C₄₃ and C₇ acting faithfully	43	7	C43:C7	301,1

Groups of order 302

		d	ρ	Label	ID
C₃₀₂	Cyclic group	302	1	C302	302,2
D₁₅₁	Dihedral group	151	2+	D151	302,1

Groups of order 303

		d	ρ	Label	ID
C₃₀₃	Cyclic group	303	1	C303	303,1

Groups of order 304

		d	ρ	Label	ID
C₃₀₄	Cyclic group	304	1	C304	304,2
D₁₅₂	Dihedral group	152	2+	D152	304,6
Dic₇₆	Dicyclic group; = C₁₉ ⋊₁ Q₁₆	304	2-	Dic76	304,7
D₃₈⋊C₄	The semidirect product of D₃₈ and C₄ acting via C₄/C₂=C₂	152		D38:C4	304,13
D₄⋊D₁₉	The semidirect product of D₄ and D₁₉ acting via D₁₉/C₁₉=C₂	152	4+	D4:D19	304,14
Q₈⋊D₁₉	The semidirect product of Q₈ and D₁₉ acting via D₁₉/C₁₉=C₂	152	4+	Q8:D19	304,16
C₈⋊D₁₉	3^rd semidirect product of C₈ and D₁₉ acting via D₁₉/C₁₉=C₂	152	2	C8:D19	304,4
C₁₅₂⋊C₂	2^nd semidirect product of C₁₅₂ and C₂ acting faithfully	152	2	C152:C2	304,5
D₇₆⋊₅C₂	The semidirect product of D₇₆ and C₂ acting through Inn(D₇₆)	152	2	D76:5C2	304,30
D₄⋊₂D₁₉	The semidirect product of D₄ and D₁₉ acting through Inn(D₄)	152	4-	D4:2D19	304,32
D₇₆⋊C₂	4^th semidirect product of D₇₆ and C₂ acting faithfully	152	4+	D76:C2	304,34
C₁₉⋊C₁₆	The semidirect product of C₁₉ and C₁₆ acting via C₁₆/C₈=C₂	304	2	C19:C16	304,1
C₇₆⋊C₄	1^st semidirect product of C₇₆ and C₄ acting via C₄/C₂=C₂	304		C76:C4	304,12
C₁₉⋊Q₁₆	The semidirect product of C₁₉ and Q₁₆ acting via Q₁₆/Q₈=C₂	304	4-	C19:Q16	304,17
Dic₁₉⋊C₄	The semidirect product of Dic₁₉ and C₄ acting via C₄/C₂=C₂	304		Dic19:C4	304,11
D₄.D₁₉	The non-split extension by D₄ of D₁₉ acting via D₁₉/C₁₉=C₂	152	4-	D4.D19	304,15
C₇₆.C₄	1^st non-split extension by C₇₆ of C₄ acting via C₄/C₂=C₂	152	2	C76.C4	304,9
C₂³.D₁₉	The non-split extension by C₂³ of D₁₉ acting via D₁₉/C₁₉=C₂	152		C2^3.D19	304,18
C₄×C₇₆	Abelian group of type [4,76]	304		C4xC76	304,19
C₂×C₁₅₂	Abelian group of type [2,152]	304		C2xC152	304,22
C₂²×C₇₆	Abelian group of type [2,2,76]	304		C2^2xC76	304,37
C₂³×C₃₈	Abelian group of type [2,2,2,38]	304		C2^3xC38	304,42
D₄×D₁₉	Direct product of D₄ and D₁₉	76	4+	D4xD19	304,31
C₈×D₁₉	Direct product of C₈ and D₁₉	152	2	C8xD19	304,3
D₈×C₁₉	Direct product of C₁₉ and D₈	152	2	D8xC19	304,24
C₂×D₇₆	Direct product of C₂ and D₇₆	152		C2xD76	304,29
D₄×C₃₈	Direct product of C₃₈ and D₄	152		D4xC38	304,38
Q₈×D₁₉	Direct product of Q₈ and D₁₉	152	4-	Q8xD19	304,33
SD₁₆×C₁₉	Direct product of C₁₉ and SD₁₆	152	2	SD16xC19	304,25
C₂³×D₁₉	Direct product of C₂³ and D₁₉	152		C2^3xD19	304,41
M₄(2)×C₁₉	Direct product of C₁₉ and M₄(2)	152	2	M4(2)xC19	304,23
Q₈×C₃₈	Direct product of C₃₈ and Q₈	304		Q8xC38	304,39
Q₁₆×C₁₉	Direct product of C₁₉ and Q₁₆	304	2	Q16xC19	304,26
C₄×Dic₁₉	Direct product of C₄ and Dic₁₉	304		C4xDic19	304,10
C₂×Dic₃₈	Direct product of C₂ and Dic₃₈	304		C2xDic38	304,27
C₂²×Dic₁₉	Direct product of C₂² and Dic₁₉	304		C2^2xDic19	304,35
C₂×C₄×D₁₉	Direct product of C₂×C₄ and D₁₉	152		C2xC4xD19	304,28
C₂×C₁₉⋊D₄	Direct product of C₂ and C₁₉⋊D₄	152		C2xC19:D4	304,36
C₄○D₄×C₁₉	Direct product of C₁₉ and C₄○D₄	152	2	C4oD4xC19	304,40
C₂²⋊C₄×C₁₉	Direct product of C₁₉ and C₂²⋊C₄	152		C2^2:C4xC19	304,20
C₂×C₁₉⋊C₈	Direct product of C₂ and C₁₉⋊C₈	304		C2xC19:C8	304,8
C₄⋊C₄×C₁₉	Direct product of C₁₉ and C₄⋊C₄	304		C4:C4xC19	304,21

Groups of order 305

		d	ρ	Label	ID
C₃₀₅	Cyclic group	305	1	C305	305,2
C₆₁⋊C₅	The semidirect product of C₆₁ and C₅ acting faithfully	61	5	C61:C5	305,1

Groups of order 306

		d	ρ	Label	ID
C₃₀₆	Cyclic group	306	1	C306	306,4
D₁₅₃	Dihedral group	153	2+	D153	306,3
C₃⋊D₅₁	The semidirect product of C₃ and D₅₁ acting via D₅₁/C₅₁=C₂	153		C3:D51	306,9
C₃×C₁₀₂	Abelian group of type [3,102]	306		C3xC102	306,10
S₃×C₅₁	Direct product of C₅₁ and S₃	102	2	S3xC51	306,6
C₃×D₅₁	Direct product of C₃ and D₅₁	102	2	C3xD51	306,7
C₁₇×D₉	Direct product of C₁₇ and D₉	153	2	C17xD9	306,1
C₉×D₁₇	Direct product of C₉ and D₁₇	153	2	C9xD17	306,2
C₃²×D₁₇	Direct product of C₃² and D₁₇	153		C3^2xD17	306,5
C₁₇×C₃⋊S₃	Direct product of C₁₇ and C₃⋊S₃	153		C17xC3:S3	306,8

Groups of order 307

		d	ρ	Label	ID
C₃₀₇	Cyclic group	307	1	C307	307,1

Groups of order 308

		d	ρ	Label	ID
C₃₀₈	Cyclic group	308	1	C308	308,4
D₁₅₄	Dihedral group; = C₂×D₇₇	154	2+	D154	308,8
Dic₇₇	Dicyclic group; = C₇₇ ⋊₁ C₄	308	2-	Dic77	308,3
C₂×C₁₅₄	Abelian group of type [2,154]	308		C2xC154	308,9
D₇×D₁₁	Direct product of D₇ and D₁₁	77	4+	D7xD11	308,5
D₇×C₂₂	Direct product of C₂₂ and D₇	154	2	D7xC22	308,7
C₁₄×D₁₁	Direct product of C₁₄ and D₁₁	154	2	C14xD11	308,6
C₁₁×Dic₇	Direct product of C₁₁ and Dic₇	308	2	C11xDic7	308,1
C₇×Dic₁₁	Direct product of C₇ and Dic₁₁	308	2	C7xDic11	308,2

Groups of order 309

		d	ρ	Label	ID
C₃₀₉	Cyclic group	309	1	C309	309,2
C₁₀₃⋊C₃	The semidirect product of C₁₀₃ and C₃ acting faithfully	103	3	C103:C3	309,1

Groups of order 310

		d	ρ	Label	ID
C₃₁₀	Cyclic group	310	1	C310	310,6
D₁₅₅	Dihedral group	155	2+	D155	310,5
C₃₁⋊C₁₀	The semidirect product of C₃₁ and C₁₀ acting faithfully	31	10+	C31:C10	310,1
D₅×C₃₁	Direct product of C₃₁ and D₅	155	2	D5xC31	310,3
C₅×D₃₁	Direct product of C₅ and D₃₁	155	2	C5xD31	310,4
C₂×C₃₁⋊C₅	Direct product of C₂ and C₃₁⋊C₅	62	5	C2xC31:C5	310,2

Groups of order 311

		d	ρ	Label	ID
C₃₁₁	Cyclic group	311	1	C311	311,1

Groups of order 312

		d	ρ	Label	ID
C₃₁₂	Cyclic group	312	1	C312	312,6
D₁₅₆	Dihedral group	156	2+	D156	312,39
Dic₇₈	Dicyclic group; = C₃₉ ⋊₂ Q₈	312	2-	Dic78	312,37
C₁₃⋊S₄	The semidirect product of C₁₃ and S₄ acting via S₄/A₄=C₂	52	6+	C13:S4	312,48
D₅₂⋊C₃	The semidirect product of D₅₂ and C₃ acting faithfully	52	6+	D52:C3	312,10
D₁₃⋊A₄	The semidirect product of D₁₃ and A₄ acting via A₄/C₂²=C₃	52	6+	D13:A4	312,51
D₂₆⋊C₆	2^nd semidirect product of D₂₆ and C₆ acting faithfully	52	6	D26:C6	312,12
C₁₃⋊C₂₄	The semidirect product of C₁₃ and C₂₄ acting via C₂₄/C₂=C₁₂	104	12-	C13:C24	312,7
C₁₃⋊₂C₂₄	The semidirect product of C₁₃ and C₂₄ acting via C₂₄/C₄=C₆	104	6	C13:2C24	312,1
Dic₂₆⋊C₃	The semidirect product of Dic₂₆ and C₃ acting faithfully	104	6-	Dic26:C3	312,8
C₃₉⋊D₄	1^st semidirect product of C₃₉ and D₄ acting via D₄/C₂=C₂²	156	4-	C39:D4	312,18
C₃⋊D₅₂	The semidirect product of C₃ and D₅₂ acting via D₅₂/D₂₆=C₂	156	4+	C3:D52	312,19
C₃₉⋊₇D₄	1^st semidirect product of C₃₉ and D₄ acting via D₄/C₂²=C₂	156	2	C39:7D4	312,41
C₁₃⋊D₁₂	The semidirect product of C₁₃ and D₁₂ acting via D₁₂/D₆=C₂	156	4+	C13:D12	312,20
C₃₉⋊Q₈	The semidirect product of C₃₉ and Q₈ acting via Q₈/C₂=C₂²	312	4-	C39:Q8	312,21
C₃₉⋊₃C₈	1^st semidirect product of C₃₉ and C₈ acting via C₈/C₄=C₂	312	2	C39:3C8	312,5
C₃₉⋊C₈	1^st semidirect product of C₃₉ and C₈ acting via C₈/C₂=C₄	312	4	C39:C8	312,14
C₂₆.A₄	The non-split extension by C₂₆ of A₄ acting via A₄/C₂²=C₃	104	6	C26.A4	312,26
D₇₈.C₂	The non-split extension by D₇₈ of C₂ acting faithfully	156	4+	D78.C2	312,17
C₂×C₁₅₆	Abelian group of type [2,156]	312		C2xC156	312,42
C₂²×C₇₈	Abelian group of type [2,2,78]	312		C2^2xC78	312,61
C₂×F₁₃	Direct product of C₂ and F₁₃; = Aut(D₂₆) = Hol(C₂₆)	26	12+	C2xF13	312,45
C₁₃×S₄	Direct product of C₁₃ and S₄	52	3	C13xS4	312,47
A₄×D₁₃	Direct product of A₄ and D₁₃	52	6+	A4xD13	312,50
A₄×C₂₆	Direct product of C₂₆ and A₄	78	3	A4xC26	312,56
C₁₃×SL₂(𝔽₃)	Direct product of C₁₃ and SL₂(𝔽₃)	104	2	C13xSL(2,3)	312,25
S₃×C₅₂	Direct product of C₅₂ and S₃	156	2	S3xC52	312,33
C₃×D₅₂	Direct product of C₃ and D₅₂	156	2	C3xD52	312,29
C₄×D₃₉	Direct product of C₄ and D₃₉	156	2	C4xD39	312,38
D₄×C₃₉	Direct product of C₃₉ and D₄	156	2	D4xC39	312,43
C₁₂×D₁₃	Direct product of C₁₂ and D₁₃	156	2	C12xD13	312,28
C₁₃×D₁₂	Direct product of C₁₃ and D₁₂	156	2	C13xD12	312,34
Dic₃×D₁₃	Direct product of Dic₃ and D₁₃	156	4-	Dic3xD13	312,15
S₃×Dic₁₃	Direct product of S₃ and Dic₁₃	156	4-	S3xDic13	312,16
C₂²×D₃₉	Direct product of C₂² and D₃₉	156		C2^2xD39	312,60
Q₈×C₃₉	Direct product of C₃₉ and Q₈	312	2	Q8xC39	312,44
C₃×Dic₂₆	Direct product of C₃ and Dic₂₆	312	2	C3xDic26	312,27
C₆×Dic₁₃	Direct product of C₆ and Dic₁₃	312		C6xDic13	312,30
C₁₃×Dic₆	Direct product of C₁₃ and Dic₆	312	2	C13xDic6	312,32
Dic₃×C₂₆	Direct product of C₂₆ and Dic₃	312		Dic3xC26	312,35
C₂×Dic₃₉	Direct product of C₂ and Dic₃₉	312		C2xDic39	312,40
S₃×C₁₃⋊C₄	Direct product of S₃ and C₁₃⋊C₄	39	8+	S3xC13:C4	312,46
C₄×C₁₃⋊C₆	Direct product of C₄ and C₁₃⋊C₆	52	6	C4xC13:C6	312,9
D₄×C₁₃⋊C₃	Direct product of D₄ and C₁₃⋊C₃	52	6	D4xC13:C3	312,23
C₂²×C₁₃⋊C₆	Direct product of C₂² and C₁₃⋊C₆	52		C2^2xC13:C6	312,49
C₆×C₁₃⋊C₄	Direct product of C₆ and C₁₃⋊C₄	78	4	C6xC13:C4	312,52
C₂×C₁₃⋊A₄	Direct product of C₂ and C₁₃⋊A₄	78	3	C2xC13:A4	312,57
C₂×S₃×D₁₃	Direct product of C₂, S₃ and D₁₃	78	4+	C2xS3xD13	312,54
C₂×C₃₉⋊C₄	Direct product of C₂ and C₃₉⋊C₄	78	4	C2xC39:C4	312,53
C₈×C₁₃⋊C₃	Direct product of C₈ and C₁₃⋊C₃	104	3	C8xC13:C3	312,2
Q₈×C₁₃⋊C₃	Direct product of Q₈ and C₁₃⋊C₃	104	6	Q8xC13:C3	312,24
C₂×C₂₆.C₆	Direct product of C₂ and C₂₆.C₆	104		C2xC26.C6	312,11
C₂³×C₁₃⋊C₃	Direct product of C₂³ and C₁₃⋊C₃	104		C2^3xC13:C3	312,55
S₃×C₂×C₂₆	Direct product of C₂×C₂₆ and S₃	156		S3xC2xC26	312,59
C₂×C₆×D₁₃	Direct product of C₂×C₆ and D₁₃	156		C2xC6xD13	312,58
C₃×C₁₃⋊D₄	Direct product of C₃ and C₁₃⋊D₄	156	2	C3xC13:D4	312,31
C₁₃×C₃⋊D₄	Direct product of C₁₃ and C₃⋊D₄	156	2	C13xC3:D4	312,36
C₁₃×C₃⋊C₈	Direct product of C₁₃ and C₃⋊C₈	312	2	C13xC3:C8	312,3
C₃×C₁₃⋊C₈	Direct product of C₃ and C₁₃⋊C₈	312	4	C3xC13:C8	312,13
C₃×C₁₃⋊₂C₈	Direct product of C₃ and C₁₃⋊₂C₈	312	2	C3xC13:2C8	312,4
C₂×C₄×C₁₃⋊C₃	Direct product of C₂×C₄ and C₁₃⋊C₃	104		C2xC4xC13:C3	312,22

Groups of order 313

		d	ρ	Label	ID
C₃₁₃	Cyclic group	313	1	C313	313,1

Groups of order 314

		d	ρ	Label	ID
C₃₁₄	Cyclic group	314	1	C314	314,2
D₁₅₇	Dihedral group	157	2+	D157	314,1

Groups of order 315

		d	ρ	Label	ID
C₃₁₅	Cyclic group	315	1	C315	315,2
C₃×C₁₀₅	Abelian group of type [3,105]	315		C3xC105	315,4
C₁₅×C₇⋊C₃	Direct product of C₁₅ and C₇⋊C₃	105	3	C15xC7:C3	315,3
C₅×C₇⋊C₉	Direct product of C₅ and C₇⋊C₉	315	3	C5xC7:C9	315,1

Groups of order 316

		d	ρ	Label	ID
C₃₁₆	Cyclic group	316	1	C316	316,2
D₁₅₈	Dihedral group; = C₂×D₇₉	158	2+	D158	316,3
Dic₇₉	Dicyclic group; = C₇₉ ⋊C₄	316	2-	Dic79	316,1
C₂×C₁₅₈	Abelian group of type [2,158]	316		C2xC158	316,4

Groups of order 317

		d	ρ	Label	ID
C₃₁₇	Cyclic group	317	1	C317	317,1

Groups of order 318

		d	ρ	Label	ID
C₃₁₈	Cyclic group	318	1	C318	318,4
D₁₅₉	Dihedral group	159	2+	D159	318,3
S₃×C₅₃	Direct product of C₅₃ and S₃	159	2	S3xC53	318,1
C₃×D₅₃	Direct product of C₃ and D₅₃	159	2	C3xD53	318,2

Groups of order 319

		d	ρ	Label	ID
C₃₁₉	Cyclic group	319	1	C319	319,1

Groups of order 320

		d	ρ	Label	ID
C₃₂₀	Cyclic group	320	1	C320	320,2
D₁₆₀	Dihedral group	160	2+	D160	320,6
Dic₈₀	Dicyclic group; = C₅ ⋊₁ Q₆₄	320	2-	Dic80	320,8
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	10	5+	C2^4:F5	320,1635
2_-¹⁺⁴⋊D₅	The semidirect product of 2_-¹⁺⁴ and D₅ acting faithfully	32	4	ES-(2,2):D5	320,1582
C₂³⋊D₂₀	The semidirect product of C₂³ and D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3:D20	320,368
D₂₀⋊₁D₄	1^st semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	40	8+	D20:1D4	320,374
D₄⋊₄D₂₀	3^rd semidirect product of D₄ and D₂₀ acting via D₂₀/D₁₀=C₂	40	4+	D4:4D20	320,449
D₂₀⋊₅D₄	5^th semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	40	4	D20:5D4	320,704
D₄₀⋊C₄	2^nd semidirect product of D₄₀ and C₄ acting faithfully	40	8+	D40:C4	320,1069
C₄²⋊F₅	1^st semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	40	4+	C4^2:F5	320,191
C₄²⋊₆F₅	3^rd semidirect product of C₄² and F₅ acting via F₅/D₅=C₂	40	4	C4^2:6F5	320,200
C₂⁴⋊₂F₅	1^st semidirect product of C₂⁴ and F₅ acting via F₅/C₅=C₄	40	4	C2^4:2F5	320,272
C₂⁴⋊₄F₅	1^st semidirect product of C₂⁴ and F₅ acting via F₅/D₅=C₂	40		C2^4:4F5	320,1138
D₂₀⋊₁₈D₄	6^th semidirect product of D₂₀ and D₄ acting via D₄/C₂²=C₂	40	8+	D20:18D4	320,825
SD₁₆⋊F₅	1^st semidirect product of SD₁₆ and F₅ acting via F₅/D₅=C₂	40	8	SD16:F5	320,1073
C₂⁴⋊₂D₁₀	1^st semidirect product of C₂⁴ and D₁₀ acting via D₁₀/C₅=C₂²	40	4	C2^4:2D10	320,659
M₄(2)⋊F₅	2^nd semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):F5	320,237
M₄(2)⋊₃F₅	3^rd semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):3F5	320,238
M₄(2)⋊₁F₅	1^st semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):1F5	320,1065
C₂⁴⋊₂Dic₅	1^st semidirect product of C₂⁴ and Dic₅ acting via Dic₅/C₅=C₄	40	4	C2^4:2Dic5	320,94
C₄²⋊₃Dic₅	3^rd semidirect product of C₄² and Dic₅ acting via Dic₅/C₅=C₄	40	4	C4^2:3Dic5	320,103
2₊¹⁺⁴⋊D₅	1^st semidirect product of 2₊¹⁺⁴ and D₅ acting via D₅/C₅=C₂	40	8+	ES+(2,2):D5	320,868
2₊¹⁺⁴⋊₂D₅	2^nd semidirect product of 2₊¹⁺⁴ and D₅ acting via D₅/C₅=C₂	40	8+	ES+(2,2):2D5	320,871
C₈₀⋊C₄	6^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:C4	320,70
C₈₀⋊₄C₄	4^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:4C4	320,185
C₈₀⋊₅C₄	5^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:5C4	320,186
C₈₀⋊₂C₄	2^nd semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:2C4	320,187
C₈₀⋊₃C₄	3^rd semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:3C4	320,188
D₈⋊₅F₅	The semidirect product of D₈ and F₅ acting through Inn(D₈)	80	8-	D8:5F5	320,1070
D₈⋊F₅	4^th semidirect product of D₈ and F₅ acting via F₅/D₅=C₂	80	8-	D8:F5	320,1071
C₁₆⋊₇F₅	3^rd semidirect product of C₁₆ and F₅ acting via F₅/D₅=C₂	80	4	C16:7F5	320,182
C₁₆⋊F₅	3^rd semidirect product of C₁₆ and F₅ acting via F₅/C₅=C₄	80	4	C16:F5	320,183
C₁₆⋊₄F₅	4^th semidirect product of C₁₆ and F₅ acting via F₅/C₅=C₄	80	4	C16:4F5	320,184
D₄₀⋊₈C₄	2^nd semidirect product of D₄₀ and C₄ acting via C₄/C₂=C₂	80	4	D40:8C4	320,76
D₄₀⋊₁C₄	1^st semidirect product of D₄₀ and C₄ acting faithfully	80	8+	D40:1C4	320,245
D₄⋊D₂₀	1^st semidirect product of D₄ and D₂₀ acting via D₂₀/D₁₀=C₂	80		D4:D20	320,400
D₈₀⋊C₂	2^nd semidirect product of D₈₀ and C₂ acting faithfully	80	4+	D80:C2	320,535
D₁₆⋊D₅	2^nd semidirect product of D₁₆ and D₅ acting via D₅/C₅=C₂	80	4	D16:D5	320,538
D₂₀⋊D₄	6^th semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	80		D20:D4	320,783
D₈⋊D₁₀	2^nd semidirect product of D₈ and D₁₀ acting via D₁₀/C₁₀=C₂	80	4+	D8:D10	320,820
D₄⋊₅D₂₀	1^st semidirect product of D₄ and D₂₀ acting through Inn(D₄)	80		D4:5D20	320,1226
D₈⋊₅D₁₀	5^th semidirect product of D₈ and D₁₀ acting via D₁₀/D₅=C₂	80	8+	D8:5D10	320,1446
D₈⋊₆D₁₀	6^th semidirect product of D₈ and D₁₀ acting via D₁₀/D₅=C₂	80	8-	D8:6D10	320,1447
C₁₆⋊D₁₀	3^rd semidirect product of C₁₆ and D₁₀ acting via D₁₀/C₅=C₂²	80	4+	C16:D10	320,541
Q₁₆⋊₅F₅	The semidirect product of Q₁₆ and F₅ acting through Inn(Q₁₆)	80	8+	Q16:5F5	320,1078
Q₁₆⋊F₅	4^th semidirect product of Q₁₆ and F₅ acting via F₅/D₅=C₂	80	8+	Q16:F5	320,1079
D₅⋊M₅(2)	The semidirect product of D₅ and M₅(2) acting via M₅(2)/C₂×C₈=C₂	80	4	D5:M5(2)	320,1053
C₄²⋊₂F₅	2^nd semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	80	4	C4^2:2F5	320,192
C₄²⋊₃F₅	3^rd semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	80	4	C4^2:3F5	320,201

Full list: Groups of order 320 (1640 groups)

Groups of order 321

		d	ρ	Label	ID
C₃₂₁	Cyclic group	321	1	C321	321,1

Groups of order 322

		d	ρ	Label	ID
C₃₂₂	Cyclic group	322	1	C322	322,4
D₁₆₁	Dihedral group	161	2+	D161	322,3
D₇×C₂₃	Direct product of C₂₃ and D₇	161	2	D7xC23	322,1
C₇×D₂₃	Direct product of C₇ and D₂₃	161	2	C7xD23	322,2

Groups of order 323

		d	ρ	Label	ID
C₃₂₃	Cyclic group	323	1	C323	323,1

Groups of order 324

		d	ρ	Label	ID
C₃₂₄	Cyclic group	324	1	C324	324,2
D₁₆₂	Dihedral group; = C₂×D₈₁	162	2+	D162	324,4
Dic₈₁	Dicyclic group; = C₈₁ ⋊C₄	324	2-	Dic81	324,1
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	9	6+	He3:D6	324,39
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	9	4	C3^3:A4	324,160
C₉²⋊C₄	The semidirect product of C₉² and C₄ acting faithfully	18	4+	C9^2:C4	324,35
C₃⁴⋊₄C₄	4^th semidirect product of C₃⁴ and C₄ acting faithfully	18		C3^4:4C4	324,164
C₃²⋊D₁₈	The semidirect product of C₃² and D₁₈ acting via D₁₈/C₃=D₆	18	12+	C3^2:D18	324,37
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	18	12+	He3:5D6	324,121
C₃³⋊₂A₄	1^st semidirect product of C₃³ and A₄ acting via A₄/C₂²=C₃	18	3	C3^3:2A4	324,60
He₃⋊₄Dic₃	The semidirect product of He₃ and Dic₃ acting via Dic₃/C₃=C₄	18	6	He3:4Dic3	324,113
He₃⋊₆D₆	2^nd semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	27		He3:6D6	324,124
C₉⋊C₃₆	The semidirect product of C₉ and C₃₆ acting via C₃₆/C₆=C₆	36	6	C9:C36	324,9
He₃⋊C₁₂	The semidirect product of He₃ and C₁₂ acting via C₁₂/C₂=C₆	36	3	He3:C12	324,13
C₃²⋊C₃₆	The semidirect product of C₃² and C₃₆ acting via C₃₆/C₆=C₆	36	6	C3^2:C36	324,7
C₃⁴⋊C₄	3^rd semidirect product of C₃⁴ and C₄ acting faithfully	36		C3^4:C4	324,163
He₃⋊₂A₄	2^nd semidirect product of He₃ and A₄ acting via A₄/C₂²=C₃	36	9	He3:2A4	324,55
C₃³⋊C₁₂	1^st semidirect product of C₃³ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C3^3:C12	324,14
C₃²⋊₅D₁₈	2^nd semidirect product of C₃² and D₁₈ acting via D₁₈/C₉=C₂²	36	4	C3^2:5D18	324,123
C₃³⋊₁₇D₆	5^th semidirect product of C₃³ and D₆ acting via D₆/C₃=C₂²	36		C3^3:17D6	324,170
He₃⋊₆Dic₃	2^nd semidirect product of He₃ and Dic₃ acting via Dic₃/C₆=C₂	36	6	He3:6Dic3	324,104
C₃²⋊₂Dic₉	2^nd semidirect product of C₃² and Dic₉ acting via Dic₉/C₆=S₃	36	6	C3^2:2Dic9	324,20
C₃³⋊Dic₃	2^nd semidirect product of C₃³ and Dic₃ acting via Dic₃/C₂=S₃	36	6-	C3^3:Dic3	324,22
C₃²⋊₃Dic₉	The semidirect product of C₃² and Dic₉ acting via Dic₉/C₉=C₄	36	4	C3^2:3Dic9	324,112
He₃⋊A₄	1^st semidirect product of He₃ and A₄ acting via A₄/C₂²=C₃	54	9	He3:A4	324,54
C₆²⋊C₉	1^st semidirect product of C₆² and C₉ acting via C₉/C₃=C₃	54		C6^2:C9	324,59
3_-¹⁺²⋊A₄	1^st semidirect product of 3_-¹⁺² and A₄ acting via A₄/C₂²=C₃	54	9	ES-(3,1):A4	324,57
C₂₇⋊A₄	The semidirect product of C₂₇ and A₄ acting via A₄/C₂²=C₃	108	3	C27:A4	324,43
C₂₇⋊C₁₂	The semidirect product of C₂₇ and C₁₂ acting via C₁₂/C₂=C₆	108	6-	C27:C12	324,12
C₃³⋊₄C₁₂	4^th semidirect product of C₃³ and C₁₂ acting via C₁₂/C₂=C₆	108		C3^3:4C12	324,98
He₃⋊Dic₃	3^rd semidirect product of He₃ and Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3:Dic3	324,24
C₃²⋊Dic₉	1^st semidirect product of C₃² and Dic₉ acting via Dic₉/C₆=S₃	108		C3^2:Dic9	324,8
C₉⋊Dic₉	The semidirect product of C₉ and Dic₉ acting via Dic₉/C₁₈=C₂	324		C9:Dic9	324,19
C₂₇⋊Dic₃	The semidirect product of C₂₇ and Dic₃ acting via Dic₃/C₆=C₂	324		C27:Dic3	324,21
C₃⁴⋊₈C₄	4^th semidirect product of C₃⁴ and C₄ acting via C₄/C₂=C₂	324		C3^4:8C4	324,158
C₃²⋊₅Dic₉	2^nd semidirect product of C₃² and Dic₉ acting via Dic₉/C₁₈=C₂	324		C3^2:5Dic9	324,103
He₃.D₆	1^st non-split extension by He₃ of D₆ acting faithfully	27	6+	He3.D6	324,40
He₃.₂D₆	2^nd non-split extension by He₃ of D₆ acting faithfully	27	6+	He3.2D6	324,41
He₃.₆D₆	The non-split extension by He₃ of D₆ acting via D₆/C₃=C₂²	27	6+	He3.6D6	324,125
C₆².₆C₃²	6^th non-split extension by C₆² of C₃² acting faithfully	36	9	C6^2.6C3^2	324,58
He₃.A₄	The non-split extension by He₃ of A₄ acting via A₄/C₂²=C₃	54	9	He3.A4	324,53
He₃.₂A₄	The non-split extension by He₃ of A₄ acting through Inn(He₃)	54	9	He3.2A4	324,129
C₆².C₉	2^nd non-split extension by C₆² of C₉ acting via C₉/C₃=C₃	54	3	C6^2.C9	324,45
He₃.₃C₁₂	The non-split extension by He₃ of C₁₂ acting via C₁₂/C₃=C₄	54	3	He3.3C12	324,111
C₆².C₃²	4^th non-split extension by C₆² of C₃² acting faithfully	54	9	C6^2.C3^2	324,56
C₆².₉C₃²	9^th non-split extension by C₆² of C₃² acting faithfully	54	9	C6^2.9C3^2	324,132
C₆².₁₃C₃²	4^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.13C3^2	324,49
C₆².₁₄C₃²	5^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.14C3^2	324,50
C₆².₁₅C₃²	6^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.15C3^2	324,51
C₆².₂₅C₃²	16^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.25C3^2	324,128
He₃.C₁₂	1^st non-split extension by He₃ of C₁₂ acting via C₁₂/C₂=C₆	108	3	He3.C12	324,15
He₃.₂C₁₂	2^nd non-split extension by He₃ of C₁₂ acting via C₁₂/C₂=C₆	108	3	He3.2C12	324,17
He₃.₅C₁₂	The non-split extension by He₃ of C₁₂ acting via C₁₂/C₆=C₂	108	3	He3.5C12	324,102
He₃.Dic₃	1^st non-split extension by He₃ of Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3.Dic3	324,16
He₃.₂Dic₃	2^nd non-split extension by He₃ of Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3.2Dic3	324,18
He₃.₃Dic₃	3^rd non-split extension by He₃ of Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3.3Dic3	324,23
He₃.₄Dic₃	The non-split extension by He₃ of Dic₃ acting via Dic₃/C₆=C₂	108	6-	He3.4Dic3	324,101
C₃³.Dic₃	4^th non-split extension by C₃³ of Dic₃ acting via Dic₃/C₂=S₃	108		C3^3.Dic3	324,100
C₆².₁₆C₃²	7^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	108		C6^2.16C3^2	324,52
3_-¹⁺².Dic₃	The non-split extension by 3_-¹⁺² of Dic₃ acting via Dic₃/C₂=S₃	108	6-	ES-(3,1).Dic3	324,25
C₂₇.A₄	The central extension by C₂₇ of A₄	162	3	C27.A4	324,3
C₆².₁₁C₃²	2^nd non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	162		C6^2.11C3^2	324,47
C₆².₁₂C₃²	3^rd non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	162		C6^2.12C3^2	324,48
C₁₈²	Abelian group of type [18,18]	324		C18^2	324,81
C₉×C₃₆	Abelian group of type [9,36]	324		C9xC36	324,26
C₆×C₅₄	Abelian group of type [6,54]	324		C6xC54	324,84
C₂×C₁₆₂	Abelian group of type [2,162]	324		C2xC162	324,5
C₃×C₁₀₈	Abelian group of type [3,108]	324		C3xC108	324,29
C₃²×C₃₆	Abelian group of type [3,3,36]	324		C3^2xC36	324,105
C₃³×C₁₂	Abelian group of type [3,3,3,12]	324		C3^3xC12	324,159
C₃²×C₆²	Abelian group of type [3,3,6,6]	324		C3^2xC6^2	324,176
C₃×C₆×C₁₈	Abelian group of type [3,6,18]	324		C3xC6xC18	324,151
D₉²	Direct product of D₉ and D₉	18	4+	D9^2	324,36
D₉×C₁₈	Direct product of C₁₈ and D₉	36	2	D9xC18	324,61
A₄×He₃	Direct product of A₄ and He₃	36	9	A4xHe3	324,130
C₉×Dic₉	Direct product of C₉ and Dic₉	36	2	C9xDic9	324,6
Dic₃×He₃	Direct product of Dic₃ and He₃	36	6	Dic3xHe3	324,93
A₄×3_-¹⁺²	Direct product of A₄ and 3_-¹⁺²	36	9	A4xES-(3,1)	324,131
Dic₃×3_-¹⁺²	Direct product of Dic₃ and 3_-¹⁺²	36	6	Dic3xES-(3,1)	324,95
S₃×D₂₇	Direct product of S₃ and D₂₇	54	4+	S3xD27	324,38
S₃×C₅₄	Direct product of C₅₄ and S₃	108	2	S3xC54	324,66
A₄×C₂₇	Direct product of C₂₇ and A₄	108	3	A4xC27	324,42
C₆×D₂₇	Direct product of C₆ and D₂₇	108	2	C6xD27	324,65
C₁₂×He₃	Direct product of C₁₂ and He₃	108		C12xHe3	324,106
A₄×C₃³	Direct product of C₃³ and A₄	108		A4xC3^3	324,171
C₃×Dic₂₇	Direct product of C₃ and Dic₂₇	108	2	C3xDic27	324,10
Dic₃×C₂₇	Direct product of C₂₇ and Dic₃	108	2	Dic3xC27	324,11
C₃²×Dic₉	Direct product of C₃² and Dic₉	108		C3^2xDic9	324,90
Dic₃×C₃³	Direct product of C₃³ and Dic₃	108		Dic3xC3^3	324,155
C₁₂×3_-¹⁺²	Direct product of C₁₂ and 3_-¹⁺²	108		C12xES-(3,1)	324,107
C₃×C₃³⋊C₄	Direct product of C₃ and C₃³⋊C₄; = AΣL₁(𝔽₈₁)	12	4	C3xC3^3:C4	324,162
C₃×C₃²⋊₄D₆	Direct product of C₃ and C₃²⋊₄D₆	12	4	C3xC3^2:4D6	324,167
S₃×C₉⋊C₆	Direct product of S₃ and C₉⋊C₆	18	12+	S3xC9:C6	324,118
C₂×C₃≀S₃	Direct product of C₂ and C₃≀S₃	18	3	C2xC3wrS3	324,68
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	18	12+	S3xC3^2:C6	324,116
S₃×He₃⋊C₂	Direct product of S₃ and He₃⋊C₂	18	6	S3xHe3:C2	324,122
C₃×C₃²⋊D₆	Direct product of C₃ and C₃²⋊D₆	18	6	C3xC3^2:D6	324,117
C₂×C₃³⋊C₆	Direct product of C₂ and C₃³⋊C₆	18	6+	C2xC3^3:C6	324,69
C₂×C₃³⋊S₃	Direct product of C₂ and C₃³⋊S₃	18	6+	C2xC3^3:S3	324,77
S₃²×C₉	Direct product of C₉, S₃ and S₃	36	4	S3^2xC9	324,115
C₃×S₃×D₉	Direct product of C₃, S₃ and D₉	36	4	C3xS3xD9	324,114
C₆×C₉⋊C₆	Direct product of C₆ and C₉⋊C₆	36	6	C6xC9:C6	324,140
C₄×C₃≀C₃	Direct product of C₄ and C₃≀C₃	36	3	C4xC3wrC3	324,31
C₂×C₉⋊C₁₈	Direct product of C₂ and C₉⋊C₁₈	36	6	C2xC9:C18	324,64
C₃×C₉⋊C₁₂	Direct product of C₃ and C₉⋊C₁₂	36	6	C3xC9:C12	324,94
C₂×S₃×He₃	Direct product of C₂, S₃ and He₃	36	6	C2xS3xHe3	324,139
S₃²×C₃²	Direct product of C₃², S₃ and S₃	36		S3^2xC3^2	324,165
C₉×C₃²⋊C₄	Direct product of C₉ and C₃²⋊C₄	36	4	C9xC3^2:C4	324,109
C₆×C₃²⋊C₆	Direct product of C₆ and C₃²⋊C₆	36	6	C6xC3^2:C6	324,138
C₂²×C₃≀C₃	Direct product of C₂² and C₃≀C₃	36		C2^2xC3wrC3	324,86
C₂×C₃²⋊C₁₈	Direct product of C₂ and C₃²⋊C₁₈	36	6	C2xC3^2:C18	324,62
C₃×C₃²⋊C₁₂	Direct product of C₃ and C₃²⋊C₁₂	36	6	C3xC3^2:C12	324,92
C₃²×C₃²⋊C₄	Direct product of C₃² and C₃²⋊C₄	36		C3^2xC3^2:C4	324,161
C₂×He₃⋊₅S₃	Direct product of C₂ and He₃⋊₅S₃	36	6	C2xHe3:5S3	324,150
C₂×C₃²⋊₂D₉	Direct product of C₂ and C₃²⋊₂D₉	36	6	C2xC3^2:2D9	324,75
C₃²×C₃⋊Dic₃	Direct product of C₃² and C₃⋊Dic₃	36		C3^2xC3:Dic3	324,156
C₂×S₃×3_-¹⁺²	Direct product of C₂, S₃ and 3_-¹⁺²	36	6	C2xS3xES-(3,1)	324,141
S₃×C₉⋊S₃	Direct product of S₃ and C₉⋊S₃	54		S3xC9:S3	324,120
D₉×C₃⋊S₃	Direct product of D₉ and C₃⋊S₃	54		D9xC3:S3	324,119
C₂×C₂₇⋊C₆	Direct product of C₂ and C₂₇⋊C₆	54	6+	C2xC27:C6	324,67
C₃×He₃⋊C₄	Direct product of C₃ and He₃⋊C₄	54		C3xHe3:C4	324,110
C₃×C₃²⋊A₄	Direct product of C₃ and C₃²⋊A₄	54		C3xC3^2:A4	324,135
C₆×He₃⋊C₂	Direct product of C₆ and He₃⋊C₂	54		C6xHe3:C2	324,145
S₃×C₃³⋊C₂	Direct product of S₃ and C₃³⋊C₂	54		S3xC3^3:C2	324,168
C₂×He₃⋊S₃	Direct product of C₂ and He₃⋊S₃	54	6+	C2xHe3:S3	324,79
C₂×C₃²⋊D₉	Direct product of C₂ and C₃²⋊D₉	54		C2xC3^2:D9	324,63
C₃×C₃².A₄	Direct product of C₃ and C₃².A₄	54		C3xC3^2.A4	324,134
C₂×He₃⋊₄S₃	Direct product of C₂ and He₃⋊₄S₃	54		C2xHe3:4S3	324,144
C₂×He₃.C₆	Direct product of C₂ and He₃.C₆	54	3	C2xHe3.C6	324,70
C₂×He₃.S₃	Direct product of C₂ and He₃.S₃	54	6+	C2xHe3.S3	324,71
C₂×C₃³.S₃	Direct product of C₂ and C₃³.S₃	54		C2xC3^3.S3	324,146
C₂×He₃.₂C₆	Direct product of C₂ and He₃.₂C₆	54	3	C2xHe3.2C6	324,72
C₂×He₃.₂S₃	Direct product of C₂ and He₃.₂S₃	54	6+	C2xHe3.2S3	324,73
C₂×He₃.₃S₃	Direct product of C₂ and He₃.₃S₃	54	6+	C2xHe3.3S3	324,78
C₂×He₃.₄S₃	Direct product of C₂ and He₃.₄S₃	54	6+	C2xHe3.4S3	324,147
C₂×He₃.₄C₆	Direct product of C₂ and He₃.₄C₆	54	3	C2xHe3.4C6	324,148
C₂×3_-¹⁺².S₃	Direct product of C₂ and 3_-¹⁺².S₃	54	6+	C2xES-(3,1).S3	324,80
A₄×C₃×C₉	Direct product of C₃×C₉ and A₄	108		A4xC3xC9	324,126
D₉×C₃×C₆	Direct product of C₃×C₆ and D₉	108		D9xC3xC6	324,136
C₆×C₉⋊S₃	Direct product of C₆ and C₉⋊S₃	108		C6xC9:S3	324,142
C₃×C₉⋊A₄	Direct product of C₃ and C₉⋊A₄	108		C3xC9:A4	324,127
S₃×C₃×C₁₈	Direct product of C₃×C₁₈ and S₃	108		S3xC3xC18	324,137
C₄×C₂₇⋊C₃	Direct product of C₄ and C₂₇⋊C₃	108	3	C4xC27:C3	324,30
C₂×C₆×He₃	Direct product of C₂×C₆ and He₃	108		C2xC6xHe3	324,152
C₁₈×C₃⋊S₃	Direct product of C₁₈ and C₃⋊S₃	108		C18xC3:S3	324,143
S₃×C₃²×C₆	Direct product of C₃²×C₆ and S₃	108		S3xC3^2xC6	324,172
Dic₃×C₃×C₉	Direct product of C₃×C₉ and Dic₃	108		Dic3xC3xC9	324,91
C₄×C₃²⋊C₉	Direct product of C₄ and C₃²⋊C₉	108		C4xC3^2:C9	324,27
C₄×C₉○He₃	Direct product of C₄ and C₉○He₃	108	3	C4xC9oHe3	324,108
C₃×C₉⋊Dic₃	Direct product of C₃ and C₉⋊Dic₃	108		C3xC9:Dic3	324,96
C₉×C₃⋊Dic₃	Direct product of C₉ and C₃⋊Dic₃	108		C9xC3:Dic3	324,97
C₆×C₃³⋊C₂	Direct product of C₆ and C₃³⋊C₂	108		C6xC3^3:C2	324,174
C₂²×C₂₇⋊C₃	Direct product of C₂² and C₂₇⋊C₃	108		C2^2xC27:C3	324,85
C₄×He₃⋊C₃	Direct product of C₄ and He₃⋊C₃	108	3	C4xHe3:C3	324,33
C₃×He₃⋊₃C₄	Direct product of C₃ and He₃⋊₃C₄	108		C3xHe3:3C4	324,99
C₃×C₃³⋊₅C₄	Direct product of C₃ and C₃³⋊₅C₄	108		C3xC3^3:5C4	324,157
C₄×He₃.C₃	Direct product of C₄ and He₃.C₃	108	3	C4xHe3.C3	324,32
C₄×C₃.He₃	Direct product of C₄ and C₃.He₃	108	3	C4xC3.He3	324,34
C₂²×C₃²⋊C₉	Direct product of C₂² and C₃²⋊C₉	108		C2^2xC3^2:C9	324,82
C₂²×C₉○He₃	Direct product of C₂² and C₉○He₃	108		C2^2xC9oHe3	324,154
C₂×C₆×3_-¹⁺²	Direct product of C₂×C₆ and 3_-¹⁺²	108		C2xC6xES-(3,1)	324,153
C₂²×He₃⋊C₃	Direct product of C₂² and He₃⋊C₃	108		C2^2xHe3:C3	324,88
C₂²×He₃.C₃	Direct product of C₂² and He₃.C₃	108		C2^2xHe3.C3	324,87
C₂²×C₃.He₃	Direct product of C₂² and C₃.He₃	108		C2^2xC3.He3	324,89
C₂×C₉⋊D₉	Direct product of C₂ and C₉⋊D₉	162		C2xC9:D9	324,74
C₂×C₂₇⋊S₃	Direct product of C₂ and C₂₇⋊S₃	162		C2xC27:S3	324,76
C₃×C₉.A₄	Direct product of C₃ and C₉.A₄	162		C3xC9.A4	324,44
C₉×C₃.A₄	Direct product of C₉ and C₃.A₄	162		C9xC3.A4	324,46
C₂×C₃⁴⋊C₂	Direct product of C₂ and C₃⁴⋊C₂	162		C2xC3^4:C2	324,175
C₃²×C₃.A₄	Direct product of C₃² and C₃.A₄	162		C3^2xC3.A4	324,133
C₂×C₃²⋊₄D₉	Direct product of C₂ and C₃²⋊₄D₉	162		C2xC3^2:4D9	324,149
C₄×C₉⋊C₉	Direct product of C₄ and C₉⋊C₉	324		C4xC9:C9	324,28
C₂²×C₉⋊C₉	Direct product of C₂² and C₉⋊C₉	324		C2^2xC9:C9	324,83
C₃⋊S₃²	Direct product of C₃⋊S₃ and C₃⋊S₃	18		C3:S3^2	324,169
C₃×S₃×C₃⋊S₃	Direct product of C₃, S₃ and C₃⋊S₃	36		C3xS3xC3:S3	324,166
C₃⋊S₃×C₃×C₆	Direct product of C₃×C₆ and C₃⋊S₃	36		C3:S3xC3xC6	324,173

Groups of order 325

		d	ρ	Label	ID
C₃₂₅	Cyclic group	325	1	C325	325,1
C₅×C₆₅	Abelian group of type [5,65]	325		C5xC65	325,2

Groups of order 326

		d	ρ	Label	ID
C₃₂₆	Cyclic group	326	1	C326	326,2
D₁₆₃	Dihedral group	163	2+	D163	326,1

Groups of order 327

		d	ρ	Label	ID
C₃₂₇	Cyclic group	327	1	C327	327,2
C₁₀₉⋊C₃	The semidirect product of C₁₀₉ and C₃ acting faithfully	109	3	C109:C3	327,1

Groups of order 328

		d	ρ	Label	ID
C₃₂₈	Cyclic group	328	1	C328	328,2
D₁₆₄	Dihedral group	164	2+	D164	328,6
Dic₈₂	Dicyclic group; = C₄₁ ⋊Q₈	328	2-	Dic82	328,4
C₄₁⋊C₈	The semidirect product of C₄₁ and C₈ acting faithfully	41	8+	C41:C8	328,12
C₄₁⋊D₄	The semidirect product of C₄₁ and D₄ acting via D₄/C₂²=C₂	164	2	C41:D4	328,8
C₄₁⋊₃C₈	The semidirect product of C₄₁ and C₈ acting via C₈/C₄=C₂	328	2	C41:3C8	328,1
C₄₁⋊₂C₈	The semidirect product of C₄₁ and C₈ acting via C₈/C₂=C₄	328	4-	C41:2C8	328,3
C₂×C₁₆₄	Abelian group of type [2,164]	328		C2xC164	328,9
C₂²×C₈₂	Abelian group of type [2,2,82]	328		C2^2xC82	328,15
C₄×D₄₁	Direct product of C₄ and D₄₁	164	2	C4xD41	328,5
D₄×C₄₁	Direct product of C₄₁ and D₄	164	2	D4xC41	328,10
C₂²×D₄₁	Direct product of C₂² and D₄₁	164		C2^2xD41	328,14
Q₈×C₄₁	Direct product of C₄₁ and Q₈	328	2	Q8xC41	328,11
C₂×Dic₄₁	Direct product of C₂ and Dic₄₁	328		C2xDic41	328,7
C₂×C₄₁⋊C₄	Direct product of C₂ and C₄₁⋊C₄	82	4+	C2xC41:C4	328,13

Groups of order 329

		d	ρ	Label	ID
C₃₂₉	Cyclic group	329	1	C329	329,1

Groups of order 330

		d	ρ	Label	ID
C₃₃₀	Cyclic group	330	1	C330	330,12
D₁₆₅	Dihedral group	165	2+	D165	330,11
C₃⋊F₁₁	The semidirect product of C₃ and F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	33	10+	C3:F11	330,3
C₃×F₁₁	Direct product of C₃ and F₁₁	33	10	C3xF11	330,1
S₃×C₅₅	Direct product of C₅₅ and S₃	165	2	S3xC55	330,8
D₅×C₃₃	Direct product of C₃₃ and D₅	165	2	D5xC33	330,6
C₃×D₅₅	Direct product of C₃ and D₅₅	165	2	C3xD55	330,7
C₅×D₃₃	Direct product of C₅ and D₃₃	165	2	C5xD33	330,9
C₁₅×D₁₁	Direct product of C₁₅ and D₁₁	165	2	C15xD11	330,5
C₁₁×D₁₅	Direct product of C₁₁ and D₁₅	165	2	C11xD15	330,10
S₃×C₁₁⋊C₅	Direct product of S₃ and C₁₁⋊C₅	33	10	S3xC11:C5	330,2
C₆×C₁₁⋊C₅	Direct product of C₆ and C₁₁⋊C₅	66	5	C6xC11:C5	330,4

Groups of order 331

		d	ρ	Label	ID
C₃₃₁	Cyclic group	331	1	C331	331,1

Groups of order 332

		d	ρ	Label	ID
C₃₃₂	Cyclic group	332	1	C332	332,2
D₁₆₆	Dihedral group; = C₂×D₈₃	166	2+	D166	332,3
Dic₈₃	Dicyclic group; = C₈₃ ⋊C₄	332	2-	Dic83	332,1
C₂×C₁₆₆	Abelian group of type [2,166]	332		C2xC166	332,4

Groups of order 333

		d	ρ	Label	ID
C₃₃₃	Cyclic group	333	1	C333	333,2
C₃₇⋊C₉	The semidirect product of C₃₇ and C₉ acting faithfully	37	9	C37:C9	333,3
C₃₇⋊₂C₉	The semidirect product of C₃₇ and C₉ acting via C₉/C₃=C₃	333	3	C37:2C9	333,1
C₃×C₁₁₁	Abelian group of type [3,111]	333		C3xC111	333,5
C₃×C₃₇⋊C₃	Direct product of C₃ and C₃₇⋊C₃	111	3	C3xC37:C3	333,4

Groups of order 334

		d	ρ	Label	ID
C₃₃₄	Cyclic group	334	1	C334	334,2
D₁₆₇	Dihedral group	167	2+	D167	334,1

Groups of order 335

		d	ρ	Label	ID
C₃₃₅	Cyclic group	335	1	C335	335,1

Groups of order 336

		d	ρ	Label	ID
C₃₃₆	Cyclic group	336	1	C336	336,6
D₁₆₈	Dihedral group	168	2+	D168	336,93
Dic₈₄	Dicyclic group; = C₂₁ ⋊₄ Q₁₆	336	2-	Dic84	336,94
SL₂(𝔽₇)	Special linear group on 𝔽₇²; = C₂ .GL₃(𝔽₂)	16	4	SL(2,7)	336,114
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	8	6+	PGL(2,7)	336,208
D₅₆⋊C₃	The semidirect product of D₅₆ and C₃ acting faithfully	56	6+	D56:C3	336,10
D₄⋊F₇	The semidirect product of D₄ and F₇ acting via F₇/C₇⋊C₃=C₂	56	12+	D4:F7	336,18
Q₈⋊F₇	The semidirect product of Q₈ and F₇ acting via F₇/D₇=C₃	56	12-	Q8:F7	336,135
Q₈⋊D₂₁	The semidirect product of Q₈ and D₂₁ acting via D₂₁/C₇=S₃	56	4+	Q8:D21	336,119
C₈⋊F₇	3^rd semidirect product of C₈ and F₇ acting via F₇/C₇⋊C₃=C₂	56	6	C8:F7	336,8
C₅₆⋊C₆	2^nd semidirect product of C₅₆ and C₆ acting faithfully	56	6	C56:C6	336,9
D₁₄⋊C₁₂	The semidirect product of D₁₄ and C₁₂ acting via C₁₂/C₂=C₆	56		D14:C12	336,17
D₄⋊₂F₇	The semidirect product of D₄ and F₇ acting through Inn(D₄)	56	12-	D4:2F7	336,126
Q₈⋊₂F₇	The semidirect product of Q₈ and F₇ acting via F₇/C₇⋊C₃=C₂	56	12+	Q8:2F7	336,20
Q₈⋊₃F₇	The semidirect product of Q₈ and F₇ acting through Inn(Q₈)	56	12+	Q8:3F7	336,128
D₂₈⋊₆C₆	2^nd semidirect product of D₂₈ and C₆ acting via C₆/C₂=C₃	56	6	D28:6C6	336,124
C₂₈⋊D₆	2^nd semidirect product of C₂₈ and D₆ acting via D₆/C₃=C₂²	84	4	C28:D6	336,150
A₄⋊Dic₇	The semidirect product of A₄ and Dic₇ acting via Dic₇/C₁₄=C₂	84	6-	A4:Dic7	336,120
Dic₇⋊A₄	The semidirect product of Dic₇ and A₄ acting via A₄/C₂²=C₃	84	6-	Dic7:A4	336,136
D₆⋊D₁₄	4^th semidirect product of D₆ and D₁₄ acting via D₁₄/D₇=C₂	84	4+	D6:D14	336,163
C₇⋊C₄₈	The semidirect product of C₇ and C₄₈ acting via C₄₈/C₈=C₆	112	6	C7:C48	336,1
C₂₈⋊C₁₂	1^st semidirect product of C₂₈ and C₁₂ acting via C₁₂/C₂=C₆	112		C28:C12	336,16
Dic₇⋊C₁₂	The semidirect product of Dic₇ and C₁₂ acting via C₁₂/C₂=C₆	112		Dic7:C12	336,15
D₂₁⋊C₈	The semidirect product of D₂₁ and C₈ acting via C₈/C₄=C₂	168	4	D21:C8	336,25
D₄⋊D₂₁	The semidirect product of D₄ and D₂₁ acting via D₂₁/C₂₁=C₂	168	4+	D4:D21	336,101
C₂₁⋊D₈	1^st semidirect product of C₂₁ and D₈ acting via D₈/C₄=C₂²	168	4	C21:D8	336,29
C₃⋊D₅₆	The semidirect product of C₃ and D₅₆ acting via D₅₆/D₂₈=C₂	168	4+	C3:D56	336,30
C₇⋊D₂₄	The semidirect product of C₇ and D₂₄ acting via D₂₄/D₁₂=C₂	168	4+	C7:D24	336,31
D₂₁⋊Q₈	The semidirect product of D₂₁ and Q₈ acting via Q₈/C₄=C₂	168	4	D21:Q8	336,143
C₅₆⋊S₃	4^th semidirect product of C₅₆ and S₃ acting via S₃/C₃=C₂	168	2	C56:S3	336,91
C₈⋊D₂₁	2^nd semidirect product of C₈ and D₂₁ acting via D₂₁/C₂₁=C₂	168	2	C8:D21	336,92
D₆⋊Dic₇	The semidirect product of D₆ and Dic₇ acting via Dic₇/C₁₄=C₂	168		D6:Dic7	336,43
D₄₂⋊C₄	2^nd semidirect product of D₄₂ and C₄ acting via C₄/C₂=C₂	168		D42:C4	336,44
D₂₈⋊₅S₃	The semidirect product of D₂₈ and S₃ acting through Inn(D₂₈)	168	4-	D28:5S3	336,138
D₂₈⋊S₃	3^rd semidirect product of D₂₈ and S₃ acting via S₃/C₃=C₂	168	4	D28:S3	336,139
D₁₂⋊D₇	3^rd semidirect product of D₁₂ and D₇ acting via D₇/C₇=C₂	168	4	D12:D7	336,141
D₈₄⋊C₂	6^th semidirect product of D₈₄ and C₂ acting faithfully	168	4+	D84:C2	336,142
D₁₂⋊₅D₇	The semidirect product of D₁₂ and D₇ acting through Inn(D₁₂)	168	4-	D12:5D7	336,145
D₄⋊₂D₂₁	The semidirect product of D₄ and D₂₁ acting through Inn(D₄)	168	4-	D4:2D21	336,199
D₁₄⋊Dic₃	The semidirect product of D₁₄ and Dic₃ acting via Dic₃/C₆=C₂	168		D14:Dic3	336,42
Q₈⋊₂D₂₁	The semidirect product of Q₈ and D₂₁ acting via D₂₁/C₂₁=C₂	168	4+	Q8:2D21	336,103
Q₈⋊₃D₂₁	The semidirect product of Q₈ and D₂₁ acting through Inn(Q₈)	168	4+	Q8:3D21	336,201
C₂₁⋊SD₁₆	4^th semidirect product of C₂₁ and SD₁₆ acting via SD₁₆/C₄=C₂²	168	4+	C21:SD16	336,35
D₈₄⋊₁₁C₂	The semidirect product of D₈₄ and C₂ acting through Inn(D₈₄)	168	2	D84:11C2	336,197
Dic₆⋊D₇	1^st semidirect product of Dic₆ and D₇ acting via D₇/C₇=C₂	168	4+	Dic6:D7	336,37
C₈₄⋊C₄	1^st semidirect product of C₈₄ and C₄ acting via C₄/C₂=C₂	336		C84:C4	336,99
C₂₁⋊C₁₆	1^st semidirect product of C₂₁ and C₁₆ acting via C₁₆/C₈=C₂	336	2	C21:C16	336,5
C₂₁⋊Q₁₆	1^st semidirect product of C₂₁ and Q₁₆ acting via Q₁₆/C₄=C₂²	336	4	C21:Q16	336,38
C₂₁⋊₇Q₁₆	1^st semidirect product of C₂₁ and Q₁₆ acting via Q₁₆/Q₈=C₂	336	4-	C21:7Q16	336,104
C₃⋊Dic₂₈	The semidirect product of C₃ and Dic₂₈ acting via Dic₂₈/Dic₁₄=C₂	336	4-	C3:Dic28	336,39
C₇⋊Dic₁₂	The semidirect product of C₇ and Dic₁₂ acting via Dic₁₂/Dic₆=C₂	336	4-	C7:Dic12	336,40
Dic₂₁⋊C₄	3^rd semidirect product of Dic₂₁ and C₄ acting via C₄/C₂=C₂	336		Dic21:C4	336,46
C₄²⋊(C₇⋊C₃)	The semidirect product of C₄² and C₇⋊C₃ acting via C₇⋊C₃/C₇=C₃	84	3	C4^2:(C7:C3)	336,57
C₇⋊(C₂²⋊A₄)	The semidirect product of C₇ and C₂²⋊A₄ acting via C₂²⋊A₄/C₂⁴=C₃	84		C7:(C2^2:A4)	336,224
D₄.F₇	The non-split extension by D₄ of F₇ acting via F₇/C₇⋊C₃=C₂	56	12-	D4.F7	336,19
C₂₈.C₁₂	1^st non-split extension by C₂₈ of C₁₂ acting via C₁₂/C₂=C₆	56	6	C28.C12	336,13
C₂³.₂F₇	The non-split extension by C₂³ of F₇ acting via F₇/C₇⋊C₃=C₂	56		C2^3.2F7	336,22
C₈.F₇	The non-split extension by C₈ of F₇ acting via F₇/C₇⋊C₃=C₂	112	6-	C8.F7	336,11
C₂₈.A₄	The non-split extension by C₂₈ of A₄ acting via A₄/C₂²=C₃	112	6	C28.A4	336,173
Q₈.F₇	The non-split extension by Q₈ of F₇ acting via F₇/D₇=C₃	112	12+	Q8.F7	336,134
Q₈.D₂₁	The non-split extension by Q₈ of D₂₁ acting via D₂₁/C₇=S₃	112	4-	Q8.D21	336,118
Q₈.₂F₇	The non-split extension by Q₈ of F₇ acting via F₇/C₇⋊C₃=C₂	112	12-	Q8.2F7	336,21
Dic₇.₂A₄	The non-split extension by Dic₇ of A₄ acting through Inn(Dic₇)	112	4+	Dic7.2A4	336,131
D₄.D₂₁	The non-split extension by D₄ of D₂₁ acting via D₂₁/C₂₁=C₂	168	4-	D4.D21	336,102
C₈₄.C₄	1^st non-split extension by C₈₄ of C₄ acting via C₄/C₂=C₂	168	2	C84.C4	336,96
C₂₈.D₆	3^rd non-split extension by C₂₈ of D₆ acting via D₆/C₃=C₂²	168	4	C28.D6	336,32
C₄₂.D₄	5^th non-split extension by C₄₂ of D₄ acting via D₄/C₂=C₂²	168	4	C42.D4	336,33
C₆.D₂₈	2^nd non-split extension by C₆ of D₂₈ acting via D₂₈/D₁₄=C₂	168	4-	C6.D28	336,34
C₂.D₈₄	2^nd central extension by C₂ of D₈₄	168		C2.D84	336,100
D₆.Dic₇	The non-split extension by D₆ of Dic₇ acting via Dic₇/C₁₄=C₂	168	4	D6.Dic7	336,27
D₄₂.C₄	3^rd non-split extension by D₄₂ of C₄ acting via C₄/C₂=C₂	168	4	D42.C4	336,28
D₁₂.D₇	1^st non-split extension by D₁₂ of D₇ acting via D₇/C₇=C₂	168	4-	D12.D7	336,36
D₆.D₁₄	3^rd non-split extension by D₆ of D₁₄ acting via D₁₄/C₁₄=C₂	168	4	D6.D14	336,144
D₁₄.D₆	3^rd non-split extension by D₁₄ of D₆ acting via D₆/C₆=C₂	168	4+	D14.D6	336,146
C₂₈.₃₂D₆	11^st non-split extension by C₂₈ of D₆ acting via D₆/S₃=C₂	168	4	C28.32D6	336,26
C₄₂.₃₈D₄	7^th non-split extension by C₄₂ of D₄ acting via D₄/C₂²=C₂	168		C42.38D4	336,105
Dic₇.D₆	5^th non-split extension by Dic₇ of D₆ acting via D₆/S₃=C₂	168	4	Dic7.D6	336,152
C₄₂.C₂³	17^th non-split extension by C₄₂ of C₂³ acting via C₂³/C₂=C₂²	168	4-	C42.C2^3	336,153
Dic₃.D₁₄	6^th non-split extension by Dic₃ of D₁₄ acting via D₁₄/D₇=C₂	168	4	Dic3.D14	336,155
C₄₂.Q₈	1^st non-split extension by C₄₂ of Q₈ acting via Q₈/C₂=C₂²	336		C42.Q8	336,45
C₄₂.₄Q₈	1^st non-split extension by C₄₂ of Q₈ acting via Q₈/C₄=C₂	336		C42.4Q8	336,98
C₁₄.Dic₆	3^rd non-split extension by C₁₄ of Dic₆ acting via Dic₆/Dic₃=C₂	336		C14.Dic6	336,47
C₄×C₈₄	Abelian group of type [4,84]	336		C4xC84	336,106
C₂×C₁₆₈	Abelian group of type [2,168]	336		C2xC168	336,109
C₂²×C₈₄	Abelian group of type [2,2,84]	336		C2^2xC84	336,204
C₂³×C₄₂	Abelian group of type [2,2,2,42]	336		C2^3xC42	336,228
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	14	3	C2xGL(3,2)	336,209
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	14	7+	C2xAGammaL(1,8)	336,210
S₃×F₈	Direct product of S₃ and F₈	24	14+	S3xF8	336,211
D₇×S₄	Direct product of D₇ and S₄	28	6+	D7xS4	336,212
D₄×F₇	Direct product of D₄ and F₇; = Aut(D₂₈) = Hol(C₂₈)	28	12+	D4xF7	336,125
C₆×F₈	Direct product of C₆ and F₈	42	7	C6xF8	336,213
C₁₄×S₄	Direct product of C₁₄ and S₄	42	3	C14xS4	336,214
C₈×F₇	Direct product of C₈ and F₇	56	6	C8xF7	336,7
Q₈×F₇	Direct product of Q₈ and F₇	56	12-	Q8xF7	336,127
C₂³×F₇	Direct product of C₂³ and F₇	56		C2^3xF7	336,216
C₇×GL₂(𝔽₃)	Direct product of C₇ and GL₂(𝔽₃)	56	2	C7xGL(2,3)	336,116
D₇×SL₂(𝔽₃)	Direct product of D₇ and SL₂(𝔽₃)	56	4-	D7xSL(2,3)	336,132
A₄×C₂₈	Direct product of C₂₈ and A₄	84	3	A4xC28	336,168
D₇×D₁₂	Direct product of D₇ and D₁₂	84	4+	D7xD12	336,148
S₃×D₂₈	Direct product of S₃ and D₂₈	84	4+	S3xD28	336,149
D₄×D₂₁	Direct product of D₄ and D₂₁	84	4+	D4xD21	336,198
A₄×Dic₇	Direct product of A₄ and Dic₇	84	6-	A4xDic7	336,133
C₇×CSU₂(𝔽₃)	Direct product of C₇ and CSU₂(𝔽₃)	112	2	C7xCSU(2,3)	336,115
C₁₄×SL₂(𝔽₃)	Direct product of C₁₄ and SL₂(𝔽₃)	112		C14xSL(2,3)	336,169
S₃×C₅₆	Direct product of C₅₆ and S₃	168	2	S3xC56	336,74
D₇×C₂₄	Direct product of C₂₄ and D₇	168	2	D7xC24	336,58
C₃×D₅₆	Direct product of C₃ and D₅₆	168	2	C3xD56	336,61
C₇×D₂₄	Direct product of C₇ and D₂₄	168	2	C7xD24	336,77
C₈×D₂₁	Direct product of C₈ and D₂₁	168	2	C8xD21	336,90
D₈×C₂₁	Direct product of C₂₁ and D₈	168	2	D8xC21	336,111
C₆×D₂₈	Direct product of C₆ and D₂₈	168		C6xD28	336,176
C₂×D₈₄	Direct product of C₂ and D₈₄	168		C2xD84	336,196
D₄×C₄₂	Direct product of C₄₂ and D₄	168		D4xC42	336,205
Q₈×D₂₁	Direct product of Q₈ and D₂₁	168	4-	Q8xD21	336,200
C₁₄×D₁₂	Direct product of C₁₄ and D₁₂	168		C14xD12	336,186
D₇×Dic₆	Direct product of D₇ and Dic₆	168	4-	D7xDic6	336,137
SD₁₆×C₂₁	Direct product of C₂₁ and SD₁₆	168	2	SD16xC21	336,112
S₃×Dic₁₄	Direct product of S₃ and Dic₁₄	168	4-	S3xDic14	336,140
C₂³×D₂₁	Direct product of C₂³ and D₂₁	168		C2^3xD21	336,227
M₄(2)×C₂₁	Direct product of C₂₁ and M₄(2)	168	2	M4(2)xC21	336,110
Q₈×C₄₂	Direct product of C₄₂ and Q₈	336		Q8xC42	336,206
Q₁₆×C₂₁	Direct product of C₂₁ and Q₁₆	336	2	Q16xC21	336,113
C₃×Dic₂₈	Direct product of C₃ and Dic₂₈	336	2	C3xDic28	336,62
C₁₂×Dic₇	Direct product of C₁₂ and Dic₇	336		C12xDic7	336,65
C₇×Dic₁₂	Direct product of C₇ and Dic₁₂	336	2	C7xDic12	336,78
Dic₃×C₂₈	Direct product of C₂₈ and Dic₃	336		Dic3xC28	336,81
C₄×Dic₂₁	Direct product of C₄ and Dic₂₁	336		C4xDic21	336,97
C₆×Dic₁₄	Direct product of C₆ and Dic₁₄	336		C6xDic14	336,174
C₁₄×Dic₆	Direct product of C₁₄ and Dic₆	336		C14xDic6	336,184
C₂×Dic₄₂	Direct product of C₂ and Dic₄₂	336		C2xDic42	336,194
Dic₃×Dic₇	Direct product of Dic₃ and Dic₇	336		Dic3xDic7	336,41
C₂²×Dic₂₁	Direct product of C₂² and Dic₂₁	336		C2^2xDic21	336,202
C₂×C₇⋊S₄	Direct product of C₂ and C₇⋊S₄	42	6+	C2xC7:S4	336,215
C₂×A₄×D₇	Direct product of C₂, A₄ and D₇	42	6+	C2xA4xD7	336,217
C₂×D₇⋊A₄	Direct product of C₂ and D₇⋊A₄	42	6+	C2xD7:A4	336,218
D₈×C₇⋊C₃	Direct product of D₈ and C₇⋊C₃	56	6	D8xC7:C3	336,53
C₂×C₄×F₇	Direct product of C₂×C₄ and F₇	56		C2xC4xF7	336,122
C₂×C₄⋊F₇	Direct product of C₂ and C₄⋊F₇	56		C2xC4:F7	336,123
SD₁₆×C₇⋊C₃	Direct product of SD₁₆ and C₇⋊C₃	56	6	SD16xC7:C3	336,54
M₄(2)×C₇⋊C₃	Direct product of M₄(2) and C₇⋊C₃	56	6	M4(2)xC7:C3	336,52
C₂×Dic₇⋊C₆	Direct product of C₂ and Dic₇⋊C₆	56		C2xDic7:C6	336,130
C₄×C₇⋊A₄	Direct product of C₄ and C₇⋊A₄	84	3	C4xC7:A4	336,171
C₄×S₃×D₇	Direct product of C₄, S₃ and D₇	84	4	C4xS3xD7	336,147
C₃×D₄×D₇	Direct product of C₃, D₄ and D₇	84	4	C3xD4xD7	336,178
S₃×C₇×D₄	Direct product of C₇, S₃ and D₄	84	4	S3xC7xD4	336,188
A₄×C₂×C₁₄	Direct product of C₂×C₁₄ and A₄	84		A4xC2xC14	336,221
D₇×C₃⋊D₄	Direct product of D₇ and C₃⋊D₄	84	4	D7xC3:D4	336,161
S₃×C₇⋊D₄	Direct product of S₃ and C₇⋊D₄	84	4	S3xC7:D4	336,162
C₇×A₄⋊C₄	Direct product of C₇ and A₄⋊C₄	84	3	C7xA4:C4	336,117
C₇×C₄²⋊C₃	Direct product of C₇ and C₄²⋊C₃	84	3	C7xC4^2:C3	336,56
C₂²×C₇⋊A₄	Direct product of C₂² and C₇⋊A₄	84		C2^2xC7:A4	336,222
C₂²×S₃×D₇	Direct product of C₂², S₃ and D₇	84		C2^2xS3xD7	336,219
C₇×C₂²⋊A₄	Direct product of C₇ and C₂²⋊A₄	84		C7xC2^2:A4	336,223
C₁₆×C₇⋊C₃	Direct product of C₁₆ and C₇⋊C₃	112	3	C16xC7:C3	336,2
C₂×C₇⋊C₂₄	Direct product of C₂ and C₇⋊C₂₄	112		C2xC7:C24	336,12
C₄×C₇⋊C₁₂	Direct product of C₄ and C₇⋊C₁₂	112		C4xC7:C12	336,14
Q₁₆×C₇⋊C₃	Direct product of Q₁₆ and C₇⋊C₃	112	6	Q16xC7:C3	336,55
C₇×C₄.A₄	Direct product of C₇ and C₄.A₄	112	2	C7xC4.A4	336,170
C₄²×C₇⋊C₃	Direct product of C₄² and C₇⋊C₃	112		C4^2xC7:C3	336,48
C₂⁴×C₇⋊C₃	Direct product of C₂⁴ and C₇⋊C₃	112		C2^4xC7:C3	336,220
C₂×C₄.F₇	Direct product of C₂ and C₄.F₇	112		C2xC4.F7	336,121
C₂×C₁₄.A₄	Direct product of C₂ and C₁₄.A₄	112		C2xC14.A4	336,172
C₂²×C₇⋊C₁₂	Direct product of C₂² and C₇⋊C₁₂	112		C2^2xC7:C12	336,129
S₃×C₇⋊C₈	Direct product of S₃ and C₇⋊C₈	168	4	S3xC7:C8	336,24
D₇×C₃⋊C₈	Direct product of D₇ and C₃⋊C₈	168	4	D7xC3:C8	336,23
C₃×Q₈×D₇	Direct product of C₃, Q₈ and D₇	168	4	C3xQ8xD7	336,180
S₃×C₇×Q₈	Direct product of C₇, S₃ and Q₈	168	4	S3xC7xQ8	336,190
S₃×C₂×C₂₈	Direct product of C₂×C₂₈ and S₃	168		S3xC2xC28	336,185
D₇×C₂×C₁₂	Direct product of C₂×C₁₂ and D₇	168		D7xC2xC12	336,175
C₂×C₄×D₂₁	Direct product of C₂×C₄ and D₂₁	168		C2xC4xD21	336,195
C₆×C₇⋊D₄	Direct product of C₆ and C₇⋊D₄	168		C6xC7:D4	336,183
C₇×C₈⋊S₃	Direct product of C₇ and C₈⋊S₃	168	2	C7xC8:S3	336,75
C₃×D₄⋊D₇	Direct product of C₃ and D₄⋊D₇	168	4	C3xD4:D7	336,69
C₇×D₆⋊C₄	Direct product of C₇ and D₆⋊C₄	168		C7xD6:C4	336,84
C₇×D₄⋊S₃	Direct product of C₇ and D₄⋊S₃	168	4	C7xD4:S3	336,85
C₃×C₈⋊D₇	Direct product of C₃ and C₈⋊D₇	168	2	C3xC8:D7	336,59
C₂×C₂₁⋊D₄	Direct product of C₂ and C₂₁⋊D₄	168		C2xC21:D4	336,157
C₂×C₃⋊D₂₈	Direct product of C₂ and C₃⋊D₂₈	168		C2xC3:D28	336,158
C₂×C₇⋊D₁₂	Direct product of C₂ and C₇⋊D₁₂	168		C2xC7:D12	336,159
C₁₄×C₃⋊D₄	Direct product of C₁₄ and C₃⋊D₄	168		C14xC3:D4	336,193
C₃×Q₈⋊D₇	Direct product of C₃ and Q₈⋊D₇	168	4	C3xQ8:D7	336,71
C₂×Dic₃×D₇	Direct product of C₂, Dic₃ and D₇	168		C2xDic3xD7	336,151
C₂×S₃×Dic₇	Direct product of C₂, S₃ and Dic₇	168		C2xS3xDic7	336,154
C₃×C₅₆⋊C₂	Direct product of C₃ and C₅₆⋊C₂	168	2	C3xC56:C2	336,60
C₇×C₂₄⋊C₂	Direct product of C₇ and C₂₄⋊C₂	168	2	C7xC24:C2	336,76
D₇×C₂²×C₆	Direct product of C₂²×C₆ and D₇	168		D7xC2^2xC6	336,225
C₃×D₁₄⋊C₄	Direct product of C₃ and D₁₄⋊C₄	168		C3xD14:C4	336,68
C₂×D₂₁⋊C₄	Direct product of C₂ and D₂₁⋊C₄	168		C2xD21:C4	336,156
C₃×C₄○D₂₈	Direct product of C₃ and C₄○D₂₈	168	2	C3xC4oD28	336,177
C₇×C₄○D₁₂	Direct product of C₇ and C₄○D₁₂	168	2	C7xC4oD12	336,187
C₄○D₄×C₂₁	Direct product of C₂₁ and C₄○D₄	168	2	C4oD4xC21	336,207
C₂×C₂₁⋊₇D₄	Direct product of C₂ and C₂₁⋊₇D₄	168		C2xC21:7D4	336,203
C₃×D₄.D₇	Direct product of C₃ and D₄.D₇	168	4	C3xD4.D7	336,70
C₇×D₄.S₃	Direct product of C₇ and D₄.S₃	168	4	C7xD4.S3	336,86
S₃×C₂²×C₁₄	Direct product of C₂²×C₁₄ and S₃	168		S3xC2^2xC14	336,226
C₇×C₆.D₄	Direct product of C₇ and C₆.D₄	168		C7xC6.D4	336,89
C₃×D₄⋊₂D₇	Direct product of C₃ and D₄⋊₂D₇	168	4	C3xD4:2D7	336,179
C₇×D₄⋊₂S₃	Direct product of C₇ and D₄⋊₂S₃	168	4	C7xD4:2S3	336,189
C₂²⋊C₄×C₂₁	Direct product of C₂₁ and C₂²⋊C₄	168		C2^2:C4xC21	336,107
C₇×Q₈⋊₂S₃	Direct product of C₇ and Q₈⋊₂S₃	168	4	C7xQ8:2S3	336,87
C₃×Q₈⋊₂D₇	Direct product of C₃ and Q₈⋊₂D₇	168	4	C3xQ8:2D7	336,181
C₇×Q₈⋊₃S₃	Direct product of C₇ and Q₈⋊₃S₃	168	4	C7xQ8:3S3	336,191
C₃×C₄.Dic₇	Direct product of C₃ and C₄.Dic₇	168	2	C3xC4.Dic7	336,64
C₇×C₄.Dic₃	Direct product of C₇ and C₄.Dic₃	168	2	C7xC4.Dic3	336,80
C₃×C₂³.D₇	Direct product of C₃ and C₂³.D₇	168		C3xC2^3.D7	336,73
C₆×C₇⋊C₈	Direct product of C₆ and C₇⋊C₈	336		C6xC7:C8	336,63
C₇×C₃⋊C₁₆	Direct product of C₇ and C₃⋊C₁₆	336	2	C7xC3:C16	336,3
C₃×C₇⋊C₁₆	Direct product of C₃ and C₇⋊C₁₆	336	2	C3xC7:C16	336,4
C₁₄×C₃⋊C₈	Direct product of C₁₄ and C₃⋊C₈	336		C14xC3:C8	336,79
C₄⋊C₄×C₂₁	Direct product of C₂₁ and C₄⋊C₄	336		C4:C4xC21	336,108
C₂×C₂₁⋊Q₈	Direct product of C₂ and C₂₁⋊Q₈	336		C2xC21:Q8	336,160
C₂×C₂₁⋊C₈	Direct product of C₂ and C₂₁⋊C₈	336		C2xC21:C8	336,95
C₂×C₆×Dic₇	Direct product of C₂×C₆ and Dic₇	336		C2xC6xDic7	336,182
C₃×C₇⋊Q₁₆	Direct product of C₃ and C₇⋊Q₁₆	336	4	C3xC7:Q16	336,72
C₇×C₃⋊Q₁₆	Direct product of C₇ and C₃⋊Q₁₆	336	4	C7xC3:Q16	336,88
C₃×C₄⋊Dic₇	Direct product of C₃ and C₄⋊Dic₇	336		C3xC4:Dic7	336,67
C₇×C₄⋊Dic₃	Direct product of C₇ and C₄⋊Dic₃	336		C7xC4:Dic3	336,83
Dic₃×C₂×C₁₄	Direct product of C₂×C₁₄ and Dic₃	336		Dic3xC2xC14	336,192
C₃×Dic₇⋊C₄	Direct product of C₃ and Dic₇⋊C₄	336		C3xDic7:C4	336,66
C₇×Dic₃⋊C₄	Direct product of C₇ and Dic₃⋊C₄	336		C7xDic3:C4	336,82
C₂×D₄×C₇⋊C₃	Direct product of C₂, D₄ and C₇⋊C₃	56		C2xD4xC7:C3	336,165
C₄○D₄×C₇⋊C₃	Direct product of C₄○D₄ and C₇⋊C₃	56	6	C4oD4xC7:C3	336,167
C₂²⋊C₄×C₇⋊C₃	Direct product of C₂²⋊C₄ and C₇⋊C₃	56		C2^2:C4xC7:C3	336,49
C₂×C₈×C₇⋊C₃	Direct product of C₂×C₈ and C₇⋊C₃	112		C2xC8xC7:C3	336,51
C₄⋊C₄×C₇⋊C₃	Direct product of C₄⋊C₄ and C₇⋊C₃	112		C4:C4xC7:C3	336,50
C₂×Q₈×C₇⋊C₃	Direct product of C₂, Q₈ and C₇⋊C₃	112		C2xQ8xC7:C3	336,166
C₂²×C₄×C₇⋊C₃	Direct product of C₂²×C₄ and C₇⋊C₃	112		C2^2xC4xC7:C3	336,164

Groups of order 337

		d	ρ	Label	ID
C₃₃₇	Cyclic group	337	1	C337	337,1

Groups of order 338

		d	ρ	Label	ID
C₃₃₈	Cyclic group	338	1	C338	338,2
D₁₆₉	Dihedral group	169	2+	D169	338,1
C₁₃⋊D₁₃	The semidirect product of C₁₃ and D₁₃ acting via D₁₃/C₁₃=C₂	169		C13:D13	338,4
C₁₃×C₂₆	Abelian group of type [13,26]	338		C13xC26	338,5
C₁₃×D₁₃	Direct product of C₁₃ and D₁₃; = AΣL₁(𝔽₁₆₉)	26	2	C13xD13	338,3

Groups of order 339

		d	ρ	Label	ID
C₃₃₉	Cyclic group	339	1	C339	339,1

Groups of order 340

		d	ρ	Label	ID
C₃₄₀	Cyclic group	340	1	C340	340,4
D₁₇₀	Dihedral group; = C₂×D₈₅	170	2+	D170	340,14
Dic₈₅	Dicyclic group; = C₈₅ ⋊₇ C₄	340	2-	Dic85	340,3
C₈₅⋊C₄	3^rd semidirect product of C₈₅ and C₄ acting faithfully	85	4	C85:C4	340,6
C₈₅⋊₂C₄	2^nd semidirect product of C₈₅ and C₄ acting faithfully	85	4+	C85:2C4	340,10
C₁₇⋊₃F₅	The semidirect product of C₁₇ and F₅ acting via F₅/D₅=C₂	85	4	C17:3F5	340,8
C₁₇⋊F₅	1^st semidirect product of C₁₇ and F₅ acting via F₅/C₅=C₄	85	4+	C17:F5	340,9
C₂×C₁₇₀	Abelian group of type [2,170]	340		C2xC170	340,15
D₅×D₁₇	Direct product of D₅ and D₁₇	85	4+	D5xD17	340,11
C₁₇×F₅	Direct product of C₁₇ and F₅	85	4	C17xF5	340,7
D₅×C₃₄	Direct product of C₃₄ and D₅	170	2	D5xC34	340,13
C₁₀×D₁₇	Direct product of C₁₀ and D₁₇	170	2	C10xD17	340,12
C₁₇×Dic₅	Direct product of C₁₇ and Dic₅	340	2	C17xDic5	340,1
C₅×Dic₁₇	Direct product of C₅ and Dic₁₇	340	2	C5xDic17	340,2
C₅×C₁₇⋊C₄	Direct product of C₅ and C₁₇⋊C₄	85	4	C5xC17:C4	340,5

Groups of order 341

		d	ρ	Label	ID
C₃₄₁	Cyclic group	341	1	C341	341,1

Groups of order 342

		d	ρ	Label	ID
C₃₄₂	Cyclic group	342	1	C342	342,6
D₁₇₁	Dihedral group	171	2+	D171	342,5
F₁₉	Frobenius group; = C₁₉ ⋊C₁₈ = AGL₁(𝔽₁₉) = Aut(D₁₉) = Hol(C₁₉)	19	18+	F19	342,7
D₅₇⋊C₃	The semidirect product of D₅₇ and C₃ acting faithfully	57	6+	D57:C3	342,11
C₃⋊D₅₇	The semidirect product of C₃ and D₅₇ acting via D₅₇/C₅₇=C₂	171		C3:D57	342,17
C₅₇.C₆	The non-split extension by C₅₇ of C₆ acting faithfully	171	6	C57.C6	342,1
C₃×C₁₁₄	Abelian group of type [3,114]	342		C3xC114	342,18
S₃×C₅₇	Direct product of C₅₇ and S₃	114	2	S3xC57	342,14
C₃×D₅₇	Direct product of C₃ and D₅₇	114	2	C3xD57	342,15
D₉×C₁₉	Direct product of C₁₉ and D₉	171	2	D9xC19	342,3
C₉×D₁₉	Direct product of C₉ and D₁₉	171	2	C9xD19	342,4
C₃²×D₁₉	Direct product of C₃² and D₁₉	171		C3^2xD19	342,13
C₂×C₁₉⋊C₉	Direct product of C₂ and C₁₉⋊C₉	38	9	C2xC19:C9	342,8
C₃×C₁₉⋊C₆	Direct product of C₃ and C₁₉⋊C₆	57	6	C3xC19:C6	342,9
S₃×C₁₉⋊C₃	Direct product of S₃ and C₁₉⋊C₃	57	6	S3xC19:C3	342,10
C₆×C₁₉⋊C₃	Direct product of C₆ and C₁₉⋊C₃	114	3	C6xC19:C3	342,12
C₃⋊S₃×C₁₉	Direct product of C₁₉ and C₃⋊S₃	171		C3:S3xC19	342,16
C₂×C₁₉⋊₂C₉	Direct product of C₂ and C₁₉⋊₂C₉	342	3	C2xC19:2C9	342,2

Groups of order 343

		d	ρ	Label	ID
C₃₄₃	Cyclic group	343	1	C343	343,1
He₇	Heisenberg group; = C₇² ⋊C₇ = 7₊¹⁺²	49	7	He7	343,3
7_-¹⁺²	Extraspecial group	49	7	ES-(7,1)	343,4
C₇³	Elementary abelian group of type [7,7,7]	343		C7^3	343,5
C₇×C₄₉	Abelian group of type [7,49]	343		C7xC49	343,2

Groups of order 344

		d	ρ	Label	ID
C₃₄₄	Cyclic group	344	1	C344	344,2
D₁₇₂	Dihedral group	172	2+	D172	344,5
Dic₈₆	Dicyclic group; = C₄₃ ⋊Q₈	344	2-	Dic86	344,3
C₄₃⋊D₄	The semidirect product of C₄₃ and D₄ acting via D₄/C₂²=C₂	172	2	C43:D4	344,7
C₄₃⋊C₈	The semidirect product of C₄₃ and C₈ acting via C₈/C₄=C₂	344	2	C43:C8	344,1
C₂×C₁₇₂	Abelian group of type [2,172]	344		C2xC172	344,8
C₂²×C₈₆	Abelian group of type [2,2,86]	344		C2^2xC86	344,12
C₄×D₄₃	Direct product of C₄ and D₄₃	172	2	C4xD43	344,4
D₄×C₄₃	Direct product of C₄₃ and D₄	172	2	D4xC43	344,9
C₂²×D₄₃	Direct product of C₂² and D₄₃	172		C2^2xD43	344,11
Q₈×C₄₃	Direct product of C₄₃ and Q₈	344	2	Q8xC43	344,10
C₂×Dic₄₃	Direct product of C₂ and Dic₄₃	344		C2xDic43	344,6

Groups of order 345

		d	ρ	Label	ID
C₃₄₅	Cyclic group	345	1	C345	345,1

Groups of order 346

		d	ρ	Label	ID
C₃₄₆	Cyclic group	346	1	C346	346,2
D₁₇₃	Dihedral group	173	2+	D173	346,1

Groups of order 347

		d	ρ	Label	ID
C₃₄₇	Cyclic group	347	1	C347	347,1

Groups of order 348

		d	ρ	Label	ID
C₃₄₈	Cyclic group	348	1	C348	348,4
D₁₇₄	Dihedral group; = C₂×D₈₇	174	2+	D174	348,11
Dic₈₇	Dicyclic group; = C₈₇ ⋊₃ C₄	348	2-	Dic87	348,3
C₈₇⋊C₄	1^st semidirect product of C₈₇ and C₄ acting faithfully	87	4	C87:C4	348,6
C₂×C₁₇₄	Abelian group of type [2,174]	348		C2xC174	348,12
S₃×D₂₉	Direct product of S₃ and D₂₉	87	4+	S3xD29	348,7
A₄×C₂₉	Direct product of C₂₉ and A₄	116	3	A4xC29	348,8
S₃×C₅₈	Direct product of C₅₈ and S₃	174	2	S3xC58	348,10
C₆×D₂₉	Direct product of C₆ and D₂₉	174	2	C6xD29	348,9
Dic₃×C₂₉	Direct product of C₂₉ and Dic₃	348	2	Dic3xC29	348,1
C₃×Dic₂₉	Direct product of C₃ and Dic₂₉	348	2	C3xDic29	348,2
C₃×C₂₉⋊C₄	Direct product of C₃ and C₂₉⋊C₄	87	4	C3xC29:C4	348,5

Groups of order 349

		d	ρ	Label	ID
C₃₄₉	Cyclic group	349	1	C349	349,1

Groups of order 350

		d	ρ	Label	ID
C₃₅₀	Cyclic group	350	1	C350	350,4
D₁₇₅	Dihedral group	175	2+	D175	350,3
C₅⋊D₃₅	The semidirect product of C₅ and D₃₅ acting via D₃₅/C₃₅=C₂	175		C5:D35	350,9
C₅×C₇₀	Abelian group of type [5,70]	350		C5xC70	350,10
D₅×C₃₅	Direct product of C₃₅ and D₅	70	2	D5xC35	350,6
C₅×D₃₅	Direct product of C₅ and D₃₅	70	2	C5xD35	350,7
C₇×D₂₅	Direct product of C₇ and D₂₅	175	2	C7xD25	350,1
D₇×C₂₅	Direct product of C₂₅ and D₇	175	2	D7xC25	350,2
D₇×C₅²	Direct product of C₅² and D₇	175		D7xC5^2	350,5
C₇×C₅⋊D₅	Direct product of C₇ and C₅⋊D₅	175		C7xC5:D5	350,8

Groups of order 351

		d	ρ	Label	ID
C₃₅₁	Cyclic group	351	1	C351	351,2
C₃³⋊C₁₃	The semidirect product of C₃³ and C₁₃ acting faithfully	27	13	C3^3:C13	351,12
C₁₃⋊He₃	The semidirect product of C₁₃ and He₃ acting via He₃/C₃²=C₃	117	3	C13:He3	351,8
C₁₁₇⋊C₃	2^nd semidirect product of C₁₁₇ and C₃ acting faithfully	117	3	C117:C3	351,4
C₁₁₇⋊₃C₃	3^rd semidirect product of C₁₁₇ and C₃ acting faithfully	117	3	C117:3C3	351,5
C₁₃⋊C₂₇	The semidirect product of C₁₃ and C₂₇ acting via C₂₇/C₉=C₃	351	3	C13:C27	351,1
C₃₉.C₃²	5^th non-split extension by C₃₉ of C₃² acting via C₃²/C₃=C₃	117	3	C39.C3^2	351,7
C₃×C₁₁₇	Abelian group of type [3,117]	351		C3xC117	351,9
C₃²×C₃₉	Abelian group of type [3,3,39]	351		C3^2xC39	351,14
C₁₃×He₃	Direct product of C₁₃ and He₃	117	3	C13xHe3	351,10
C₁₃×3_-¹⁺²	Direct product of C₁₃ and 3_-¹⁺²	117	3	C13xES-(3,1)	351,11
C₉×C₁₃⋊C₃	Direct product of C₉ and C₁₃⋊C₃	117	3	C9xC13:C3	351,3
C₃²×C₁₃⋊C₃	Direct product of C₃² and C₁₃⋊C₃	117		C3^2xC13:C3	351,13
C₃×C₁₃⋊C₉	Direct product of C₃ and C₁₃⋊C₉	351		C3xC13:C9	351,6

Groups of order 352

		d	ρ	Label	ID
C₃₅₂	Cyclic group	352	1	C352	352,2
D₁₇₆	Dihedral group	176	2+	D176	352,5
Dic₈₈	Dicyclic group; = C₁₁ ⋊₁ Q₃₂	352	2-	Dic88	352,7
C₈⋊D₂₂	1^st semidirect product of C₈ and D₂₂ acting via D₂₂/C₁₁=C₂²	88	4+	C8:D22	352,103
D₄₄⋊₁C₄	1^st semidirect product of D₄₄ and C₄ acting via C₄/C₂=C₂	88	2	D44:1C4	352,11
D₄₄⋊₄C₄	4^th semidirect product of D₄₄ and C₄ acting via C₄/C₂=C₂	88	4	D44:4C4	352,31
D₄⋊D₂₂	2^nd semidirect product of D₄ and D₂₂ acting via D₂₂/D₁₁=C₂	88	4	D4:D22	352,106
D₈₈⋊C₂	6^th semidirect product of D₈₈ and C₂ acting faithfully	88	4+	D88:C2	352,109
D₄⋊₆D₂₂	2^nd semidirect product of D₄ and D₂₂ acting through Inn(D₄)	88	4	D4:6D22	352,179
D₄⋊₈D₂₂	4^th semidirect product of D₄ and D₂₂ acting through Inn(D₄)	88	4+	D4:8D22	352,184
Q₈⋊D₂₂	2^nd semidirect product of Q₈ and D₂₂ acting via D₂₂/C₂₂=C₂	88	4+	Q8:D22	352,144
C₂²⋊D₄₄	The semidirect product of C₂² and D₄₄ acting via D₄₄/D₂₂=C₂	88		C2^2:D44	352,77
C₂³⋊D₂₂	1^st semidirect product of C₂³ and D₂₂ acting via D₂₂/C₁₁=C₂²	88		C2^3:D22	352,132
C₂⁴⋊D₁₁	1^st semidirect product of C₂⁴ and D₁₁ acting via D₁₁/C₁₁=C₂	88		C2^4:D11	352,148
C₂³⋊Dic₁₁	The semidirect product of C₂³ and Dic₁₁ acting via Dic₁₁/C₁₁=C₄	88	4	C2^3:Dic11	352,40
D₄₄⋊₆C₂²	4^th semidirect product of D₄₄ and C₂² acting via C₂²/C₂=C₂	88	4	D44:6C2^2	352,127
D₂₂⋊C₈	The semidirect product of D₂₂ and C₈ acting via C₈/C₄=C₂	176		D22:C8	352,26
C₄⋊D₄₄	The semidirect product of C₄ and D₄₄ acting via D₄₄/C₄₄=C₂	176		C4:D44	352,69
C₄⋊₂D₄₄	The semidirect product of C₄ and D₄₄ acting via D₄₄/D₂₂=C₂	176		C4:2D44	352,90
C₄₄⋊₇D₄	1^st semidirect product of C₄₄ and D₄ acting via D₄/C₂²=C₂	176		C44:7D4	352,125
C₄₄⋊₂D₄	2^nd semidirect product of C₄₄ and D₄ acting via D₄/C₂=C₂²	176		C44:2D4	352,133
C₄₄⋊D₄	3^rd semidirect product of C₄₄ and D₄ acting via D₄/C₂=C₂²	176		C44:D4	352,135
C₁₁⋊D₁₆	The semidirect product of C₁₁ and D₁₆ acting via D₁₆/D₈=C₂	176	4+	C11:D16	352,32
C₁₇₆⋊C₂	2^nd semidirect product of C₁₇₆ and C₂ acting faithfully	176	2	C176:C2	352,6
D₂₂⋊D₄	1^st semidirect product of D₂₂ and D₄ acting via D₄/C₄=C₂	176		D22:D4	352,79
D₄₄⋊C₄	5^th semidirect product of D₄₄ and C₄ acting via C₄/C₂=C₂	176		D44:C4	352,88
D₈₈⋊₇C₂	The semidirect product of D₈₈ and C₂ acting through Inn(D₈₈)	176	2	D88:7C2	352,99
D₈⋊₃D₁₁	The semidirect product of D₈ and D₁₁ acting through Inn(D₈)	176	4-	D8:3D11	352,107
D₈₈⋊₅C₂	5^th semidirect product of D₈₈ and C₂ acting faithfully	176	4+	D88:5C2	352,114
D₂₂⋊Q₈	1^st semidirect product of D₂₂ and Q₈ acting via Q₈/C₄=C₂	176		D22:Q8	352,91
D₂₂⋊₂Q₈	2^nd semidirect product of D₂₂ and Q₈ acting via Q₈/C₄=C₂	176		D22:2Q8	352,92
D₂₂⋊₃Q₈	3^rd semidirect product of D₂₂ and Q₈ acting via Q₈/C₄=C₂	176		D22:3Q8	352,141
Q₁₆⋊D₁₁	2^nd semidirect product of Q₁₆ and D₁₁ acting via D₁₁/C₁₁=C₂	176	4	Q16:D11	352,113
C₄²⋊D₁₁	1^st semidirect product of C₄² and D₁₁ acting via D₁₁/C₁₁=C₂	176		C4^2:D11	352,67
C₄²⋊₂D₁₁	2^nd semidirect product of C₄² and D₁₁ acting via D₁₁/C₁₁=C₂	176		C4^2:2D11	352,71
D₄⋊Dic₁₁	1^st semidirect product of D₄ and Dic₁₁ acting via Dic₁₁/C₂₂=C₂	176		D4:Dic11	352,38
Dic₁₁⋊₄D₄	1^st semidirect product of Dic₁₁ and D₄ acting through Inn(Dic₁₁)	176		Dic11:4D4	352,76
Dic₁₁⋊D₄	2^nd semidirect product of Dic₁₁ and D₄ acting via D₄/C₂²=C₂	176		Dic11:D4	352,134
C₂²⋊Dic₂₂	The semidirect product of C₂² and Dic₂₂ acting via Dic₂₂/Dic₁₁=C₂	176		C2^2:Dic22	352,73
C₁₁⋊C₃₂	The semidirect product of C₁₁ and C₃₂ acting via C₃₂/C₁₆=C₂	352	2	C11:C32	352,1
C₄₄⋊Q₈	The semidirect product of C₄₄ and Q₈ acting via Q₈/C₂=C₂²	352		C44:Q8	352,83
C₄₄⋊C₈	1^st semidirect product of C₄₄ and C₈ acting via C₈/C₄=C₂	352		C44:C8	352,10
C₈₈⋊C₄	4^th semidirect product of C₈₈ and C₄ acting via C₄/C₂=C₂	352		C88:C4	352,21
C₄₄⋊₂Q₈	1^st semidirect product of C₄₄ and Q₈ acting via Q₈/C₄=C₂	352		C44:2Q8	352,64
C₁₁⋊Q₃₂	The semidirect product of C₁₁ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	352	4-	C11:Q32	352,35
Dic₁₁⋊C₈	The semidirect product of Dic₁₁ and C₈ acting via C₈/C₄=C₂	352		Dic11:C8	352,20
Q₈⋊Dic₁₁	1^st semidirect product of Q₈ and Dic₁₁ acting via Dic₁₁/C₂₂=C₂	352		Q8:Dic11	352,41
Dic₂₂⋊C₄	5^th semidirect product of Dic₂₂ and C₄ acting via C₄/C₂=C₂	352		Dic22:C4	352,82
Dic₁₁⋊Q₈	2^nd semidirect product of Dic₁₁ and Q₈ acting via Q₈/C₄=C₂	352		Dic11:Q8	352,139
C₄⋊C₄⋊₇D₁₁	1^st semidirect product of C₄⋊C₄ and D₁₁ acting through Inn(C₄⋊C₄)	176		C4:C4:7D11	352,87
C₄⋊C₄⋊D₁₁	6^th semidirect product of C₄⋊C₄ and D₁₁ acting via D₁₁/C₁₁=C₂	176		C4:C4:D11	352,93
C₄₄.D₄	8^th non-split extension by C₄₄ of D₄ acting via D₄/C₂=C₂²	88	4	C44.D4	352,39
C₄₄.₄₆D₄	3^rd non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	88	4+	C44.46D4	352,29
C₄₄.₅₆D₄	13^rd non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	88	4	C44.56D4	352,43
C₂².₂D₄₄	1^st non-split extension by C₂² of D₄₄ acting via D₄₄/D₂₂=C₂	88	4	C2^2.2D44	352,12
D₂₂.C₈	The non-split extension by D₂₂ of C₈ acting via C₈/C₄=C₂	176	2	D22.C8	352,4
D₈.D₁₁	The non-split extension by D₈ of D₁₁ acting via D₁₁/C₁₁=C₂	176	4-	D8.D11	352,33
D₄₄.C₄	The non-split extension by D₄₄ of C₄ acting via C₄/C₂=C₂	176	4	D44.C4	352,102
C₄₄.C₈	1^st non-split extension by C₄₄ of C₈ acting via C₈/C₄=C₂	176	2	C44.C8	352,18
C₈₈.C₄	1^st non-split extension by C₈₈ of C₄ acting via C₄/C₂=C₂	176	2	C88.C4	352,25
C₂₂.D₈	2^nd non-split extension by C₂₂ of D₈ acting via D₈/D₄=C₂	176		C22.D8	352,15
C₂.D₈₈	2^nd central extension by C₂ of D₈₈	176		C2.D88	352,27
C₈.₆D₂₂	3^rd non-split extension by C₈ of D₂₂ acting via D₂₂/D₁₁=C₂	176	4+	C8.6D22	352,34
C₄.D₄₄	5^th non-split extension by C₄ of D₄₄ acting via D₄₄/C₄₄=C₂	176		C4.D44	352,70
C₈.D₂₂	1^st non-split extension by C₈ of D₂₂ acting via D₂₂/C₁₁=C₂²	176	4-	C8.D22	352,104
D₂₂.D₄	1^st non-split extension by D₂₂ of D₄ acting via D₄/C₂²=C₂	176		D22.D4	352,78
D₂₂.₅D₄	2^nd non-split extension by D₂₂ of D₄ acting via D₄/C₂²=C₂	176		D22.5D4	352,89
D₄₄.₂C₄	The non-split extension by D₄₄ of C₄ acting through Inn(D₄₄)	176	2	D44.2C4	352,96
D₄.D₂₂	4^th non-split extension by D₄ of D₂₂ acting via D₂₂/D₁₁=C₂	176	4-	D4.D22	352,110
D₄.₈D₂₂	3^rd non-split extension by D₄ of D₂₂ acting via D₂₂/C₂₂=C₂	176	4	D4.8D22	352,145
D₄.₉D₂₂	4^th non-split extension by D₄ of D₂₂ acting via D₂₂/C₂₂=C₂	176	4-	D4.9D22	352,146
C₄₄.₅₃D₄	10^th non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	176	4	C44.53D4	352,28
C₄₄.₄₇D₄	4^th non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	176	4-	C44.47D4	352,30
C₄₄.₅₅D₄	12^nd non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	176		C44.55D4	352,36
C₄₄.₁₀D₄	10^th non-split extension by C₄₄ of D₄ acting via D₄/C₂=C₂²	176	4	C44.10D4	352,42
C₄₄.₄₈D₄	5^th non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	176		C44.48D4	352,119
C₄₄.₁₇D₄	17^th non-split extension by C₄₄ of D₄ acting via D₄/C₂=C₂²	176		C44.17D4	352,131
C₄₄.₂₃D₄	23^rd non-split extension by C₄₄ of D₄ acting via D₄/C₂=C₂²	176		C44.23D4	352,142
Q₈.Dic₁₁	The non-split extension by Q₈ of Dic₁₁ acting through Inn(Q₈)	176	4	Q8.Dic11	352,143
Q₈.D₂₂	2^nd non-split extension by Q₈ of D₂₂ acting via D₂₂/D₁₁=C₂	176	4	Q8.D22	352,111
D₄.₁₀D₂₂	The non-split extension by D₄ of D₂₂ acting through Inn(D₄)	176	4-	D4.10D22	352,185
Q₈.₁₀D₂₂	1^st non-split extension by Q₈ of D₂₂ acting through Inn(Q₈)	176	4	Q8.10D22	352,182
C₂³.D₂₂	3^rd non-split extension by C₂³ of D₂₂ acting via D₂₂/C₁₁=C₂²	176		C2^3.D22	352,74
C₂².D₄₄	3^rd non-split extension by C₂² of D₄₄ acting via D₄₄/D₂₂=C₂	176		C2^2.D44	352,81
C₄₄.C₂³	15^th non-split extension by C₄₄ of C₂³ acting via C₂³/C₂=C₂²	176	4	C44.C2^3	352,137
Dic₁₁.D₄	1^st non-split extension by Dic₁₁ of D₄ acting via D₄/C₄=C₂	176		Dic11.D4	352,80
C₂³.₁₁D₂₂	1^st non-split extension by C₂³ of D₂₂ acting via D₂₂/D₁₁=C₂	176		C2^3.11D22	352,72
C₂³.₂₁D₂₂	2^nd non-split extension by C₂³ of D₂₂ acting via D₂₂/C₂₂=C₂	176		C2^3.21D22	352,121
C₂³.₂₃D₂₂	4^th non-split extension by C₂³ of D₂₂ acting via D₂₂/C₂₂=C₂	176		C2^3.23D22	352,124
C₂³.₁₈D₂₂	8^th non-split extension by C₂³ of D₂₂ acting via D₂₂/D₁₁=C₂	176		C2^3.18D22	352,130
C₄₄.Q₈	1^st non-split extension by C₄₄ of Q₈ acting via Q₈/C₂=C₂²	352		C44.Q8	352,13
C₄₄.₄Q₈	1^st non-split extension by C₄₄ of Q₈ acting via Q₈/C₄=C₂	352		C44.4Q8	352,23
C₄₄.₅Q₈	2^nd non-split extension by C₄₄ of Q₈ acting via Q₈/C₄=C₂	352		C44.5Q8	352,24
C₄₄.₆Q₈	3^rd non-split extension by C₄₄ of Q₈ acting via Q₈/C₄=C₂	352		C44.6Q8	352,65
C₄₄.₃Q₈	3^rd non-split extension by C₄₄ of Q₈ acting via Q₈/C₂=C₂²	352		C44.3Q8	352,85
C₄₄.₄₄D₄	1^st non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	352		C44.44D4	352,22
Dic₁₁.Q₈	The non-split extension by Dic₁₁ of Q₈ acting via Q₈/C₄=C₂	352		Dic11.Q8	352,84
C₂₂.Q₁₆	2^nd non-split extension by C₂₂ of Q₁₆ acting via Q₁₆/Q₈=C₂	352		C22.Q16	352,16
C₂₂.C₄²	5^th non-split extension by C₂₂ of C₄² acting via C₄²/C₂×C₄=C₂	352		C22.C4^2	352,37
C₄.Dic₂₂	2^nd non-split extension by C₄ of Dic₂₂ acting via Dic₂₂/Dic₁₁=C₂	352		C4.Dic22	352,14
C₄².D₁₁	1^st non-split extension by C₄² of D₁₁ acting via D₁₁/C₁₁=C₂	352		C4^2.D11	352,9
C₄×C₈₈	Abelian group of type [4,88]	352		C4xC88	352,45
C₂×C₁₇₆	Abelian group of type [2,176]	352		C2xC176	352,58
C₂²×C₈₈	Abelian group of type [2,2,88]	352		C2^2xC88	352,164
C₂³×C₄₄	Abelian group of type [2,2,2,44]	352		C2^3xC44	352,188
C₂⁴×C₂₂	Abelian group of type [2,2,2,2,22]	352		C2^4xC22	352,195
C₂×C₄×C₄₄	Abelian group of type [2,4,44]	352		C2xC4xC44	352,149
D₈×D₁₁	Direct product of D₈ and D₁₁	88	4+	D8xD11	352,105
SD₁₆×D₁₁	Direct product of SD₁₆ and D₁₁	88	4	SD16xD11	352,108
M₄(2)×D₁₁	Direct product of M₄(2) and D₁₁	88	4	M4(2)xD11	352,101
C₁₁×2₊¹⁺⁴	Direct product of C₁₁ and 2₊¹⁺⁴	88	4	C11xES+(2,2)	352,192
C₄×D₄₄	Direct product of C₄ and D₄₄	176		C4xD44	352,68
C₂×D₈₈	Direct product of C₂ and D₈₈	176		C2xD88	352,98
D₄×C₄₄	Direct product of C₄₄ and D₄	176		D4xC44	352,153
D₈×C₂₂	Direct product of C₂₂ and D₈	176		D8xC22	352,167
C₁₆×D₁₁	Direct product of C₁₆ and D₁₁	176	2	C16xD11	352,3
C₁₁×D₁₆	Direct product of C₁₁ and D₁₆	176	2	C11xD16	352,60
Q₁₆×D₁₁	Direct product of Q₁₆ and D₁₁	176	4-	Q16xD11	352,112
C₁₁×SD₃₂	Direct product of C₁₁ and SD₃₂	176	2	C11xSD32	352,61
D₄×Dic₁₁	Direct product of D₄ and Dic₁₁	176		D4xDic11	352,129
SD₁₆×C₂₂	Direct product of C₂₂ and SD₁₆	176		SD16xC22	352,168
C₄²×D₁₁	Direct product of C₄² and D₁₁	176		C4^2xD11	352,66
C₂²×D₄₄	Direct product of C₂² and D₄₄	176		C2^2xD44	352,175
C₂⁴×D₁₁	Direct product of C₂⁴ and D₁₁	176		C2^4xD11	352,194
C₁₁×M₅(2)	Direct product of C₁₁ and M₅(2)	176	2	C11xM5(2)	352,59
M₄(2)×C₂₂	Direct product of C₂₂ and M₄(2)	176		M4(2)xC22	352,165
C₁₁×2_-¹⁺⁴	Direct product of C₁₁ and 2_-¹⁺⁴	176	4	C11xES-(2,2)	352,193
Q₈×C₄₄	Direct product of C₄₄ and Q₈	352		Q8xC44	352,154
C₁₁×Q₃₂	Direct product of C₁₁ and Q₃₂	352	2	C11xQ32	352,62
Q₁₆×C₂₂	Direct product of C₂₂ and Q₁₆	352		Q16xC22	352,169
C₈×Dic₁₁	Direct product of C₈ and Dic₁₁	352		C8xDic11	352,19
C₄×Dic₂₂	Direct product of C₄ and Dic₂₂	352		C4xDic22	352,63
C₂×Dic₄₄	Direct product of C₂ and Dic₄₄	352		C2xDic44	352,100
Q₈×Dic₁₁	Direct product of Q₈ and Dic₁₁	352		Q8xDic11	352,140
C₂²×Dic₂₂	Direct product of C₂² and Dic₂₂	352		C2^2xDic22	352,173
C₂³×Dic₁₁	Direct product of C₂³ and Dic₁₁	352		C2^3xDic11	352,186
C₂×D₄×D₁₁	Direct product of C₂, D₄ and D₁₁	88		C2xD4xD11	352,177
C₁₁×C₄≀C₂	Direct product of C₁₁ and C₄≀C₂	88	2	C11xC4wrC2	352,53
C₄○D₄×D₁₁	Direct product of C₄○D₄ and D₁₁	88	4	C4oD4xD11	352,183
C₁₁×C₂³⋊C₄	Direct product of C₁₁ and C₂³⋊C₄	88	4	C11xC2^3:C4	352,48
C₁₁×C₈⋊C₂²	Direct product of C₁₁ and C₈⋊C₂²	88	4	C11xC8:C2^2	352,171
C₂²⋊C₄×D₁₁	Direct product of C₂²⋊C₄ and D₁₁	88		C2^2:C4xD11	352,75
C₁₁×C₄.D₄	Direct product of C₁₁ and C₄.D₄	88	4	C11xC4.D4	352,49
C₁₁×C₂²≀C₂	Direct product of C₁₁ and C₂²≀C₂	88		C11xC2^2wrC2	352,155
C₂×C₈×D₁₁	Direct product of C₂×C₈ and D₁₁	176		C2xC8xD11	352,94
D₄×C₂×C₂₂	Direct product of C₂×C₂₂ and D₄	176		D4xC2xC22	352,189
C₂×Q₈×D₁₁	Direct product of C₂, Q₈ and D₁₁	176		C2xQ8xD11	352,180
C₄⋊C₄×D₁₁	Direct product of C₄⋊C₄ and D₁₁	176		C4:C4xD11	352,86
C₄×C₁₁⋊D₄	Direct product of C₄ and C₁₁⋊D₄	176		C4xC11:D4	352,123
C₂×C₈₈⋊C₂	Direct product of C₂ and C₈₈⋊C₂	176		C2xC88:C2	352,95
C₂×D₂₂⋊C₄	Direct product of C₂ and D₂₂⋊C₄	176		C2xD22:C4	352,122
C₂×D₄⋊D₁₁	Direct product of C₂ and D₄⋊D₁₁	176		C2xD4:D11	352,126
C₁₁×C₈○D₄	Direct product of C₁₁ and C₈○D₄	176	2	C11xC8oD4	352,166
C₁₁×C₄○D₈	Direct product of C₁₁ and C₄○D₈	176	2	C11xC4oD8	352,170
C₄○D₄×C₂₂	Direct product of C₂₂ and C₄○D₄	176		C4oD4xC22	352,191
C₂×C₈⋊D₁₁	Direct product of C₂ and C₈⋊D₁₁	176		C2xC8:D11	352,97
C₁₁×C₄⋊D₄	Direct product of C₁₁ and C₄⋊D₄	176		C11xC4:D4	352,156
C₂×Q₈⋊D₁₁	Direct product of C₂ and Q₈⋊D₁₁	176		C2xQ8:D11	352,136
C₂²×C₄×D₁₁	Direct product of C₂²×C₄ and D₁₁	176		C2^2xC4xD11	352,174
C₁₁×D₄⋊C₄	Direct product of C₁₁ and D₄⋊C₄	176		C11xD4:C4	352,51
C₁₁×C₈.C₄	Direct product of C₁₁ and C₈.C₄	176	2	C11xC8.C4	352,57
C₂×C₄₄.C₄	Direct product of C₂ and C₄₄.C₄	176		C2xC44.C4	352,116
C₂×D₄₄⋊C₂	Direct product of C₂ and D₄₄⋊C₂	176		C2xD44:C2	352,181
C₁₁×C₄⋊₁D₄	Direct product of C₁₁ and C₄⋊₁D₄	176		C11xC4:1D4	352,162
C₁₁×C₂²⋊C₈	Direct product of C₁₁ and C₂²⋊C₈	176		C11xC2^2:C8	352,47
C₂²⋊C₄×C₂₂	Direct product of C₂₂ and C₂²⋊C₄	176		C2^2:C4xC22	352,150
C₂×D₄.D₁₁	Direct product of C₂ and D₄.D₁₁	176		C2xD4.D11	352,128
C₂²×C₁₁⋊D₄	Direct product of C₂² and C₁₁⋊D₄	176		C2^2xC11:D4	352,187
C₁₁×C₂²⋊Q₈	Direct product of C₁₁ and C₂²⋊Q₈	176		C11xC2^2:Q8	352,157
C₂×D₄₄⋊₅C₂	Direct product of C₂ and D₄₄⋊₅C₂	176		C2xD44:5C2	352,176
C₂×D₄⋊₂D₁₁	Direct product of C₂ and D₄⋊₂D₁₁	176		C2xD4:2D11	352,178
C₁₁×C₄²⋊C₂	Direct product of C₁₁ and C₄²⋊C₂	176		C11xC4^2:C2	352,152
C₁₁×C₄.₄D₄	Direct product of C₁₁ and C₄.₄D₄	176		C11xC4.4D4	352,159
C₁₁×C₈.C₂²	Direct product of C₁₁ and C₈.C₂²	176	4	C11xC8.C2^2	352,172
C₂×C₂³.D₁₁	Direct product of C₂ and C₂³.D₁₁	176		C2xC2^3.D11	352,147
C₁₁×C₄²⋊₂C₂	Direct product of C₁₁ and C₄²⋊₂C₂	176		C11xC4^2:2C2	352,161
C₁₁×C₄.₁₀D₄	Direct product of C₁₁ and C₄.₁₀D₄	176	4	C11xC4.10D4	352,50
C₁₁×C₂².D₄	Direct product of C₁₁ and C₂².D₄	176		C11xC2^2.D4	352,158
C₄×C₁₁⋊C₈	Direct product of C₄ and C₁₁⋊C₈	352		C4xC11:C8	352,8
C₁₁×C₄⋊C₈	Direct product of C₁₁ and C₄⋊C₈	352		C11xC4:C8	352,54
C₄⋊C₄×C₂₂	Direct product of C₂₂ and C₄⋊C₄	352		C4:C4xC22	352,151
C₂×C₁₁⋊C₁₆	Direct product of C₂ and C₁₁⋊C₁₆	352		C2xC11:C16	352,17
Q₈×C₂×C₂₂	Direct product of C₂×C₂₂ and Q₈	352		Q8xC2xC22	352,190
C₁₁×C₄⋊Q₈	Direct product of C₁₁ and C₄⋊Q₈	352		C11xC4:Q8	352,163
C₁₁×C₈⋊C₄	Direct product of C₁₁ and C₈⋊C₄	352		C11xC8:C4	352,46
C₂×C₄₄⋊C₄	Direct product of C₂ and C₄₄⋊C₄	352		C2xC44:C4	352,120
C₂²×C₁₁⋊C₈	Direct product of C₂² and C₁₁⋊C₈	352		C2^2xC11:C8	352,115
C₂×C₄×Dic₁₁	Direct product of C₂×C₄ and Dic₁₁	352		C2xC4xDic11	352,117
C₂×C₁₁⋊Q₁₆	Direct product of C₂ and C₁₁⋊Q₁₆	352		C2xC11:Q16	352,138
C₁₁×Q₈⋊C₄	Direct product of C₁₁ and Q₈⋊C₄	352		C11xQ8:C4	352,52
C₁₁×C₂.D₈	Direct product of C₁₁ and C₂.D₈	352		C11xC2.D8	352,56
C₁₁×C₄.Q₈	Direct product of C₁₁ and C₄.Q₈	352		C11xC4.Q8	352,55
C₂×Dic₁₁⋊C₄	Direct product of C₂ and Dic₁₁⋊C₄	352		C2xDic11:C4	352,118
C₁₁×C₂.C₄²	Direct product of C₁₁ and C₂.C₄²	352		C11xC2.C4^2	352,44
C₁₁×C₄².C₂	Direct product of C₁₁ and C₄².C₂	352		C11xC4^2.C2	352,160

Groups of order 353

		d	ρ	Label	ID
C₃₅₃	Cyclic group	353	1	C353	353,1

Groups of order 354

		d	ρ	Label	ID
C₃₅₄	Cyclic group	354	1	C354	354,4
D₁₇₇	Dihedral group	177	2+	D177	354,3
S₃×C₅₉	Direct product of C₅₉ and S₃	177	2	S3xC59	354,1
C₃×D₅₉	Direct product of C₃ and D₅₉	177	2	C3xD59	354,2

Groups of order 355

		d	ρ	Label	ID
C₃₅₅	Cyclic group	355	1	C355	355,2
C₇₁⋊C₅	The semidirect product of C₇₁ and C₅ acting faithfully	71	5	C71:C5	355,1

Groups of order 356

		d	ρ	Label	ID
C₃₅₆	Cyclic group	356	1	C356	356,2
D₁₇₈	Dihedral group; = C₂×D₈₉	178	2+	D178	356,4
Dic₈₉	Dicyclic group; = C₈₉ ⋊₂ C₄	356	2-	Dic89	356,1
C₈₉⋊C₄	The semidirect product of C₈₉ and C₄ acting faithfully	89	4+	C89:C4	356,3
C₂×C₁₇₈	Abelian group of type [2,178]	356		C2xC178	356,5

Groups of order 357

		d	ρ	Label	ID
C₃₅₇	Cyclic group	357	1	C357	357,2
C₁₇×C₇⋊C₃	Direct product of C₁₇ and C₇⋊C₃	119	3	C17xC7:C3	357,1

Groups of order 358

		d	ρ	Label	ID
C₃₅₈	Cyclic group	358	1	C358	358,2
D₁₇₉	Dihedral group	179	2+	D179	358,1

Groups of order 359

		d	ρ	Label	ID
C₃₅₉	Cyclic group	359	1	C359	359,1

Groups of order 360

		d	ρ	Label	ID
C₃₆₀	Cyclic group	360	1	C360	360,4
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	6	5+	A6	360,118
D₁₈₀	Dihedral group	180	2+	D180	360,27
Dic₉₀	Dicyclic group; = C₄₅ ⋊₂ Q₈	360	2-	Dic90	360,25
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	15	6	GammaL(2,4)	360,120
C₃²⋊D₂₀	The semidirect product of C₃² and D₂₀ acting via D₂₀/C₅=D₄	30	8+	C3^2:D20	360,134
C₅⋊F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃⋊S₃=C₄	45	8	C5:F9	360,125
C₅⋊₂F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃²⋊C₄=C₂	45	8	C5:2F9	360,124
C₃²⋊Dic₁₀	The semidirect product of C₃² and Dic₁₀ acting via Dic₁₀/C₅=Q₈	45	8	C3^2:Dic10	360,136
A₄⋊D₁₅	The semidirect product of A₄ and D₁₅ acting via D₁₅/C₁₅=C₂	60	6+	A4:D15	360,141
C₃⋊D₆₀	The semidirect product of C₃ and D₆₀ acting via D₆₀/D₃₀=C₂	60	4+	C3:D60	360,81
D₆⋊₂D₁₅	2^nd semidirect product of D₆ and D₁₅ acting via D₁₅/C₁₅=C₂	60	4+	D6:2D15	360,82
D₃₀⋊S₃	3^rd semidirect product of D₃₀ and S₃ acting via S₃/C₃=C₂	60	4	D30:S3	360,86
Dic₁₅⋊S₃	3^rd semidirect product of Dic₁₅ and S₃ acting via S₃/C₃=C₂	60	4	Dic15:S3	360,85
C₂²⋊D₄₅	The semidirect product of C₂² and D₄₅ acting via D₄₅/C₁₅=S₃	90	6+	C2^2:D45	360,41
D₆⋊D₁₅	1^st semidirect product of D₆ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4-	D6:D15	360,80
C₃²⋊₃D₂₀	2^nd semidirect product of C₃² and D₂₀ acting via D₂₀/C₁₀=C₂²	120	4	C3^2:3D20	360,87
C₃⋊Dic₃₀	The semidirect product of C₃ and Dic₃₀ acting via Dic₃₀/Dic₁₅=C₂	120	4-	C3:Dic30	360,83
C₃²⋊₃Dic₁₀	2^nd semidirect product of C₃² and Dic₁₀ acting via Dic₁₀/C₁₀=C₂²	120	4	C3^2:3Dic10	360,88
C₅⋊D₃₆	The semidirect product of C₅ and D₃₆ acting via D₃₆/D₁₈=C₂	180	4+	C5:D36	360,10
C₄₅⋊D₄	2^nd semidirect product of C₄₅ and D₄ acting via D₄/C₂=C₂²	180	4-	C45:D4	360,12
C₉⋊D₂₀	The semidirect product of C₉ and D₂₀ acting via D₂₀/D₁₀=C₂	180	4+	C9:D20	360,13
C₄₅⋊₇D₄	1^st semidirect product of C₄₅ and D₄ acting via D₄/C₂²=C₂	180	2	C45:7D4	360,29
C₆₀⋊S₃	1^st semidirect product of C₆₀ and S₃ acting via S₃/C₃=C₂	180		C60:S3	360,112
C₁₅⋊D₁₂	1^st semidirect product of C₁₅ and D₁₂ acting via D₁₂/C₆=C₂²	180		C15:D12	360,70
C₆²⋊D₅	3^rd semidirect product of C₆² and D₅ acting via D₅/C₅=C₂	180		C6^2:D5	360,114
C₃²⋊₇D₂₀	2^nd semidirect product of C₃² and D₂₀ acting via D₂₀/D₁₀=C₂	180		C3^2:7D20	360,69
C₄₅⋊Q₈	The semidirect product of C₄₅ and Q₈ acting via Q₈/C₂=C₂²	360	4-	C45:Q8	360,7
C₄₅⋊₃C₈	1^st semidirect product of C₄₅ and C₈ acting via C₈/C₄=C₂	360	2	C45:3C8	360,3
C₄₅⋊C₈	1^st semidirect product of C₄₅ and C₈ acting via C₈/C₂=C₄	360	4	C45:C8	360,6
C₁₅⋊Dic₆	1^st semidirect product of C₁₅ and Dic₆ acting via Dic₆/C₆=C₂²	360		C15:Dic6	360,71
S₃²⋊D₅	The semidirect product of S₃² and D₅ acting via D₅/C₅=C₂	30	4	S3^2:D5	360,133
C₃⋊F₅⋊S₃	The semidirect product of C₃⋊F₅ and S₃ acting via S₃/C₃=C₂	30	8+	C3:F5:S3	360,129
C₃²⋊F₅⋊C₂	The semidirect product of C₃²⋊F₅ and C₂ acting faithfully	30	8+	C3^2:F5:C2	360,131
(C₃×C₁₅)⋊₉C₈	6^th semidirect product of C₃×C₁₅ and C₈ acting via C₈/C₂=C₄	120	4	(C3xC15):9C8	360,56
C₆.D₃₀	3^rd non-split extension by C₆ of D₃₀ acting via D₃₀/D₁₅=C₂	60	4+	C6.D30	360,79
D₃₀.S₃	The non-split extension by D₃₀ of S₃ acting via S₃/C₃=C₂	120	4	D30.S3	360,84
D₉₀.C₂	The non-split extension by D₉₀ of C₂ acting faithfully	180	4+	D90.C2	360,9
C₃₀.D₆	11^st non-split extension by C₃₀ of D₆ acting via D₆/C₃=C₂²	180		C30.D6	360,67
C₃₀.₁₂D₆	12^nd non-split extension by C₃₀ of D₆ acting via D₆/C₃=C₂²	180		C30.12D6	360,68
C₆₀.S₃	6^th non-split extension by C₆₀ of S₃ acting via S₃/C₃=C₂	360		C60.S3	360,37
C₁₂.D₁₅	3^rd non-split extension by C₁₂ of D₁₅ acting via D₁₅/C₁₅=C₂	360		C12.D15	360,110
C₃₀.Dic₃	3^rd non-split extension by C₃₀ of Dic₃ acting via Dic₃/C₃=C₄	360		C30.Dic3	360,54
(C₃×C₆).F₅	The non-split extension by C₃×C₆ of F₅ acting via F₅/C₅=C₄	120	4-	(C3xC6).F5	360,57
C₆×C₆₀	Abelian group of type [6,60]	360		C6xC60	360,115
C₂×C₁₈₀	Abelian group of type [2,180]	360		C2xC180	360,30
C₃×C₁₂₀	Abelian group of type [3,120]	360		C3xC120	360,38
C₂²×C₉₀	Abelian group of type [2,2,90]	360		C2^2xC90	360,50
C₂×C₆×C₃₀	Abelian group of type [2,6,30]	360		C2xC6xC30	360,162
C₃×S₅	Direct product of C₃ and S₅	15	4	C3xS5	360,119
S₃×A₅	Direct product of S₃ and A₅	15	6+	S3xA5	360,121
C₆×A₅	Direct product of C₆ and A₅	30	3	C6xA5	360,122
D₉×F₅	Direct product of D₉ and F₅	45	8+	D9xF5	360,39
C₅×F₉	Direct product of C₅ and F₉	45	8	C5xF9	360,123
C₅×PSU₃(𝔽₂)	Direct product of C₅ and PSU₃(𝔽₂)	45	8	C5xPSU(3,2)	360,135
C₁₅×S₄	Direct product of C₁₅ and S₄	60	3	C15xS4	360,138
A₄×D₁₅	Direct product of A₄ and D₁₅	60	6+	A4xD15	360,144
C₃×SL₂(𝔽₅)	Direct product of C₃ and SL₂(𝔽₅)	72	2	C3xSL(2,5)	360,51
A₄×C₃₀	Direct product of C₃₀ and A₄	90	3	A4xC30	360,156
C₁₈×F₅	Direct product of C₁₈ and F₅	90	4	C18xF5	360,43
S₃×C₆₀	Direct product of C₆₀ and S₃	120	2	S3xC60	360,96
C₃×D₆₀	Direct product of C₃ and D₆₀	120	2	C3xD60	360,102
C₁₅×D₁₂	Direct product of C₁₅ and D₁₂	120	2	C15xD12	360,97
C₁₂×D₁₅	Direct product of C₁₂ and D₁₅	120	2	C12xD15	360,101
Dic₃×D₁₅	Direct product of Dic₃ and D₁₅	120	4-	Dic3xD15	360,77
S₃×Dic₁₅	Direct product of S₃ and Dic₁₅	120	4-	S3xDic15	360,78
C₁₅×Dic₆	Direct product of C₁₅ and Dic₆	120	2	C15xDic6	360,95
Dic₃×C₃₀	Direct product of C₃₀ and Dic₃	120		Dic3xC30	360,98
C₃×Dic₃₀	Direct product of C₃ and Dic₃₀	120	2	C3xDic30	360,100
C₆×Dic₁₅	Direct product of C₆ and Dic₁₅	120		C6xDic15	360,103
C₁₅×SL₂(𝔽₃)	Direct product of C₁₅ and SL₂(𝔽₃)	120	2	C15xSL(2,3)	360,89
D₅×C₃₆	Direct product of C₃₆ and D₅	180	2	D5xC36	360,16
C₉×D₂₀	Direct product of C₉ and D₂₀	180	2	C9xD20	360,17
D₉×C₂₀	Direct product of C₂₀ and D₉	180	2	D9xC20	360,21
C₅×D₃₆	Direct product of C₅ and D₃₆	180	2	C5xD36	360,22
C₄×D₄₅	Direct product of C₄ and D₄₅	180	2	C4xD45	360,26
D₄×C₄₅	Direct product of C₄₅ and D₄	180	2	D4xC45	360,31
D₉×Dic₅	Direct product of D₉ and Dic₅	180	4-	D9xDic5	360,8
D₅×Dic₉	Direct product of D₅ and Dic₉	180	4-	D5xDic9	360,11
D₅×C₆²	Direct product of C₆² and D₅	180		D5xC6^2	360,157
C₂²×D₄₅	Direct product of C₂² and D₄₅	180		C2^2xD45	360,49
C₃²×D₂₀	Direct product of C₃² and D₂₀	180		C3^2xD20	360,92
Q₈×C₄₅	Direct product of C₄₅ and Q₈	360	2	Q8xC45	360,32
C₉×Dic₁₀	Direct product of C₉ and Dic₁₀	360	2	C9xDic10	360,15
C₁₈×Dic₅	Direct product of C₁₈ and Dic₅	360		C18xDic5	360,18
C₅×Dic₁₈	Direct product of C₅ and Dic₁₈	360	2	C5xDic18	360,20
C₁₀×Dic₉	Direct product of C₁₀ and Dic₉	360		C10xDic9	360,23
C₂×Dic₄₅	Direct product of C₂ and Dic₄₅	360		C2xDic45	360,28
C₃²×Dic₁₀	Direct product of C₃² and Dic₁₀	360		C3^2xDic10	360,90
S₃²×D₅	Direct product of S₃, S₃ and D₅	30	8+	S3^2xD5	360,137
S₃×C₃⋊F₅	Direct product of S₃ and C₃⋊F₅	30	8	S3xC3:F5	360,128
C₃×S₃×F₅	Direct product of C₃, S₃ and F₅	30	8	C3xS3xF5	360,126
C₅×S₃≀C₂	Direct product of C₅ and S₃≀C₂	30	4	C5xS3wrC2	360,132
D₅×C₃²⋊C₄	Direct product of D₅ and C₃²⋊C₄	30	8+	D5xC3^2:C4	360,130
C₃⋊S₃×F₅	Direct product of C₃⋊S₃ and F₅	45		C3:S3xF5	360,127
C₃×C₅⋊S₄	Direct product of C₃ and C₅⋊S₄	60	6	C3xC5:S4	360,139
C₅×S₃×A₄	Direct product of C₅, S₃ and A₄	60	6	C5xS3xA4	360,143
C₃×D₅×A₄	Direct product of C₃, D₅ and A₄	60	6	C3xD5xA4	360,142
S₃×C₆×D₅	Direct product of C₆, S₃ and D₅	60	4	S3xC6xD5	360,151
C₆×C₃⋊F₅	Direct product of C₆ and C₃⋊F₅	60	4	C6xC3:F5	360,146
S₃²×C₁₀	Direct product of C₁₀, S₃ and S₃	60	4	S3^2xC10	360,153
C₅×C₃⋊S₄	Direct product of C₅ and C₃⋊S₄	60	6	C5xC3:S4	360,140
C₂×S₃×D₁₅	Direct product of C₂, S₃ and D₁₅	60	4+	C2xS3xD15	360,154
C₃×C₁₅⋊D₄	Direct product of C₃ and C₁₅⋊D₄	60	4	C3xC15:D4	360,61
C₃×C₃⋊D₂₀	Direct product of C₃ and C₃⋊D₂₀	60	4	C3xC3:D20	360,62
C₁₅×C₃⋊D₄	Direct product of C₁₅ and C₃⋊D₄	60	2	C15xC3:D4	360,99
C₃×D₅×Dic₃	Direct product of C₃, D₅ and Dic₃	60	4	C3xD5xDic3	360,58
C₂×C₃²⋊F₅	Direct product of C₂ and C₃²⋊F₅	60	4+	C2xC3^2:F5	360,150
C₂×D₁₅⋊S₃	Direct product of C₂ and D₁₅⋊S₃	60	4	C2xD15:S3	360,155
C₅×C₃⋊D₁₂	Direct product of C₅ and C₃⋊D₁₂	60	4	C5xC3:D12	360,75
C₃×C₁₅⋊₇D₄	Direct product of C₃ and C₁₅⋊₇D₄	60	2	C3xC15:7D4	360,104
C₁₀×C₃²⋊C₄	Direct product of C₁₀ and C₃²⋊C₄	60	4	C10xC3^2:C4	360,148
C₅×C₆.D₆	Direct product of C₅ and C₆.D₆	60	4	C5xC6.D6	360,73
C₂×C₃²⋊Dic₅	Direct product of C₂ and C₃²⋊Dic₅	60	4	C2xC3^2:Dic5	360,149
C₂×D₅×D₉	Direct product of C₂, D₅ and D₉	90	4+	C2xD5xD9	360,45
C₂×C₉⋊F₅	Direct product of C₂ and C₉⋊F₅	90	4	C2xC9:F5	360,44
C₃×C₆×F₅	Direct product of C₃×C₆ and F₅	90		C3xC6xF5	360,145
C₅×C₃.S₄	Direct product of C₅ and C₃.S₄	90	6	C5xC3.S4	360,40
D₅×C₃.A₄	Direct product of D₅ and C₃.A₄	90	6	D5xC3.A4	360,42
C₁₀×C₃.A₄	Direct product of C₁₀ and C₃.A₄	90	3	C10xC3.A4	360,46
C₂×C₃²⋊₃F₅	Direct product of C₂ and C₃²⋊₃F₅	90		C2xC3^2:3F5	360,147
C₁₅×C₃⋊C₈	Direct product of C₁₅ and C₃⋊C₈	120	2	C15xC3:C8	360,34
S₃×C₂×C₃₀	Direct product of C₂×C₃₀ and S₃	120		S3xC2xC30	360,158
C₂×C₆×D₁₅	Direct product of C₂×C₆ and D₁₅	120		C2xC6xD15	360,159
C₃×C₁₅⋊Q₈	Direct product of C₃ and C₁₅⋊Q₈	120	4	C3xC15:Q8	360,64
C₃×C₁₅⋊C₈	Direct product of C₃ and C₁₅⋊C₈	120	4	C3xC15:C8	360,53
C₃×C₅⋊D₁₂	Direct product of C₃ and C₅⋊D₁₂	120	4	C3xC5:D12	360,63
C₃×S₃×Dic₅	Direct product of C₃, S₃ and Dic₅	120	4	C3xS3xDic5	360,59
C₅×S₃×Dic₃	Direct product of C₅, S₃ and Dic₃	120	4	C5xS3xDic3	360,72
C₃×C₁₅⋊₃C₈	Direct product of C₃ and C₁₅⋊₃C₈	120	2	C3xC15:3C8	360,35
C₅×D₆⋊S₃	Direct product of C₅ and D₆⋊S₃	120	4	C5xD6:S3	360,74
C₃×D₃₀.C₂	Direct product of C₃ and D₃₀.C₂	120	4	C3xD30.C2	360,60
C₅×C₃²⋊₂C₈	Direct product of C₅ and C₃²⋊₂C₈	120	4	C5xC3^2:2C8	360,55
C₅×C₃²⋊₂Q₈	Direct product of C₅ and C₃²⋊₂Q₈	120	4	C5xC3^2:2Q8	360,76
D₅×C₂×C₁₈	Direct product of C₂×C₁₈ and D₅	180		D5xC2xC18	360,47
D₉×C₂×C₁₀	Direct product of C₂×C₁₀ and D₉	180		D9xC2xC10	360,48
D₅×C₃×C₁₂	Direct product of C₃×C₁₂ and D₅	180		D5xC3xC12	360,91
D₄×C₃×C₁₅	Direct product of C₃×C₁₅ and D₄	180		D4xC3xC15	360,116
C₉×C₅⋊D₄	Direct product of C₉ and C₅⋊D₄	180	2	C9xC5:D4	360,19
C₅×C₉⋊D₄	Direct product of C₅ and C₉⋊D₄	180	2	C5xC9:D4	360,24
C₃⋊S₃×C₂₀	Direct product of C₂₀ and C₃⋊S₃	180		C3:S3xC20	360,106
C₄×C₃⋊D₁₅	Direct product of C₄ and C₃⋊D₁₅	180		C4xC3:D15	360,111
C₅×C₁₂⋊S₃	Direct product of C₅ and C₁₂⋊S₃	180		C5xC12:S3	360,107
D₅×C₃⋊Dic₃	Direct product of D₅ and C₃⋊Dic₃	180		D5xC3:Dic3	360,65
C₃⋊S₃×Dic₅	Direct product of C₃⋊S₃ and Dic₅	180		C3:S3xDic5	360,66
C₃²×C₅⋊D₄	Direct product of C₃² and C₅⋊D₄	180		C3^2xC5:D4	360,94
C₂²×C₃⋊D₁₅	Direct product of C₂² and C₃⋊D₁₅	180		C2^2xC3:D15	360,161
C₅×C₃²⋊₇D₄	Direct product of C₅ and C₃²⋊₇D₄	180		C5xC3^2:7D4	360,109
C₅×C₉⋊C₈	Direct product of C₅ and C₉⋊C₈	360	2	C5xC9:C8	360,1
C₉×C₅⋊C₈	Direct product of C₉ and C₅⋊C₈	360	4	C9xC5:C8	360,5
C₅×Q₈⋊C₉	Direct product of C₅ and Q₈⋊C₉	360	2	C5xQ8:C9	360,14
Q₈×C₃×C₁₅	Direct product of C₃×C₁₅ and Q₈	360		Q8xC3xC15	360,117
C₉×C₅⋊₂C₈	Direct product of C₉ and C₅⋊₂C₈	360	2	C9xC5:2C8	360,2
C₃²×C₅⋊C₈	Direct product of C₃² and C₅⋊C₈	360		C3^2xC5:C8	360,52
C₃×C₆×Dic₅	Direct product of C₃×C₆ and Dic₅	360		C3xC6xDic5	360,93
C₁₀×C₃⋊Dic₃	Direct product of C₁₀ and C₃⋊Dic₃	360		C10xC3:Dic3	360,108
C₂×C₃⋊Dic₁₅	Direct product of C₂ and C₃⋊Dic₁₅	360		C2xC3:Dic15	360,113
C₃²×C₅⋊₂C₈	Direct product of C₃² and C₅⋊₂C₈	360		C3^2xC5:2C8	360,33
C₅×C₃²⋊₄C₈	Direct product of C₅ and C₃²⋊₄C₈	360		C5xC3^2:4C8	360,36
C₅×C₃²⋊₄Q₈	Direct product of C₅ and C₃²⋊₄Q₈	360		C5xC3^2:4Q8	360,105
C₂×D₅×C₃⋊S₃	Direct product of C₂, D₅ and C₃⋊S₃	90		C2xD5xC3:S3	360,152
C₃⋊S₃×C₂×C₁₀	Direct product of C₂×C₁₀ and C₃⋊S₃	180		C3:S3xC2xC10	360,160

Groups of order 361

		d	ρ	Label	ID
C₃₆₁	Cyclic group	361	1	C361	361,1
C₁₉²	Elementary abelian group of type [19,19]	361		C19^2	361,2

Groups of order 362

		d	ρ	Label	ID
C₃₆₂	Cyclic group	362	1	C362	362,2
D₁₈₁	Dihedral group	181	2+	D181	362,1

Groups of order 363

		d	ρ	Label	ID
C₃₆₃	Cyclic group	363	1	C363	363,1
C₁₁²⋊C₃	The semidirect product of C₁₁² and C₃ acting faithfully	33	3	C11^2:C3	363,2
C₁₁×C₃₃	Abelian group of type [11,33]	363		C11xC33	363,3

Groups of order 364

		d	ρ	Label	ID
C₃₆₄	Cyclic group	364	1	C364	364,4
D₁₈₂	Dihedral group; = C₂×D₉₁	182	2+	D182	364,10
Dic₉₁	Dicyclic group; = C₉₁ ⋊₃ C₄	364	2-	Dic91	364,3
C₉₁⋊C₄	1^st semidirect product of C₉₁ and C₄ acting faithfully	91	4	C91:C4	364,6
C₂×C₁₈₂	Abelian group of type [2,182]	364		C2xC182	364,11
D₇×D₁₃	Direct product of D₇ and D₁₃	91	4+	D7xD13	364,7
D₇×C₂₆	Direct product of C₂₆ and D₇	182	2	D7xC26	364,9
C₁₄×D₁₃	Direct product of C₁₄ and D₁₃	182	2	C14xD13	364,8
C₁₃×Dic₇	Direct product of C₁₃ and Dic₇	364	2	C13xDic7	364,1
C₇×Dic₁₃	Direct product of C₇ and Dic₁₃	364	2	C7xDic13	364,2
C₇×C₁₃⋊C₄	Direct product of C₇ and C₁₃⋊C₄	91	4	C7xC13:C4	364,5

Groups of order 365

		d	ρ	Label	ID
C₃₆₅	Cyclic group	365	1	C365	365,1

Groups of order 366

		d	ρ	Label	ID
C₃₆₆	Cyclic group	366	1	C366	366,6
D₁₈₃	Dihedral group	183	2+	D183	366,5
C₆₁⋊C₆	The semidirect product of C₆₁ and C₆ acting faithfully	61	6+	C61:C6	366,1
S₃×C₆₁	Direct product of C₆₁ and S₃	183	2	S3xC61	366,3
C₃×D₆₁	Direct product of C₃ and D₆₁	183	2	C3xD61	366,4
C₂×C₆₁⋊C₃	Direct product of C₂ and C₆₁⋊C₃	122	3	C2xC61:C3	366,2

Groups of order 367

		d	ρ	Label	ID
C₃₆₇	Cyclic group	367	1	C367	367,1

Groups of order 368

		d	ρ	Label	ID
C₃₆₈	Cyclic group	368	1	C368	368,2
D₁₈₄	Dihedral group	184	2+	D184	368,6
Dic₉₂	Dicyclic group; = C₂₃ ⋊₁ Q₁₆	368	2-	Dic92	368,7
D₄₆⋊C₄	The semidirect product of D₄₆ and C₄ acting via C₄/C₂=C₂	184		D46:C4	368,13
D₄⋊D₂₃	The semidirect product of D₄ and D₂₃ acting via D₂₃/C₂₃=C₂	184	4+	D4:D23	368,14
Q₈⋊D₂₃	The semidirect product of Q₈ and D₂₃ acting via D₂₃/C₂₃=C₂	184	4+	Q8:D23	368,16
C₈⋊D₂₃	3^rd semidirect product of C₈ and D₂₃ acting via D₂₃/C₂₃=C₂	184	2	C8:D23	368,4
C₁₈₄⋊C₂	2^nd semidirect product of C₁₈₄ and C₂ acting faithfully	184	2	C184:C2	368,5
D₉₂⋊₅C₂	The semidirect product of D₉₂ and C₂ acting through Inn(D₉₂)	184	2	D92:5C2	368,30
D₄⋊₂D₂₃	The semidirect product of D₄ and D₂₃ acting through Inn(D₄)	184	4-	D4:2D23	368,32
D₉₂⋊C₂	4^th semidirect product of D₉₂ and C₂ acting faithfully	184	4+	D92:C2	368,34
C₂₃⋊C₁₆	The semidirect product of C₂₃ and C₁₆ acting via C₁₆/C₈=C₂	368	2	C23:C16	368,1
C₉₂⋊C₄	1^st semidirect product of C₉₂ and C₄ acting via C₄/C₂=C₂	368		C92:C4	368,12
C₂₃⋊Q₁₆	The semidirect product of C₂₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	368	4-	C23:Q16	368,17
Dic₂₃⋊C₄	The semidirect product of Dic₂₃ and C₄ acting via C₄/C₂=C₂	368		Dic23:C4	368,11
D₄.D₂₃	The non-split extension by D₄ of D₂₃ acting via D₂₃/C₂₃=C₂	184	4-	D4.D23	368,15
C₉₂.C₄	1^st non-split extension by C₉₂ of C₄ acting via C₄/C₂=C₂	184	2	C92.C4	368,9
C₂³.D₂₃	The non-split extension by C₂³ of D₂₃ acting via D₂₃/C₂₃=C₂	184		C2^3.D23	368,18
C₄×C₉₂	Abelian group of type [4,92]	368		C4xC92	368,19
C₂×C₁₈₄	Abelian group of type [2,184]	368		C2xC184	368,22
C₂²×C₉₂	Abelian group of type [2,2,92]	368		C2^2xC92	368,37
C₂³×C₄₆	Abelian group of type [2,2,2,46]	368		C2^3xC46	368,42
D₄×D₂₃	Direct product of D₄ and D₂₃	92	4+	D4xD23	368,31
C₈×D₂₃	Direct product of C₈ and D₂₃	184	2	C8xD23	368,3
D₈×C₂₃	Direct product of C₂₃ and D₈	184	2	D8xC23	368,24
C₂×D₉₂	Direct product of C₂ and D₉₂	184		C2xD92	368,29
D₄×C₄₆	Direct product of C₄₆ and D₄	184		D4xC46	368,38
Q₈×D₂₃	Direct product of Q₈ and D₂₃	184	4-	Q8xD23	368,33
SD₁₆×C₂₃	Direct product of C₂₃ and SD₁₆	184	2	SD16xC23	368,25
C₂³×D₂₃	Direct product of C₂³ and D₂₃	184		C2^3xD23	368,41
M₄(2)×C₂₃	Direct product of C₂₃ and M₄(2)	184	2	M4(2)xC23	368,23
Q₈×C₄₆	Direct product of C₄₆ and Q₈	368		Q8xC46	368,39
Q₁₆×C₂₃	Direct product of C₂₃ and Q₁₆	368	2	Q16xC23	368,26
C₄×Dic₂₃	Direct product of C₄ and Dic₂₃	368		C4xDic23	368,10
C₂×Dic₄₆	Direct product of C₂ and Dic₄₆	368		C2xDic46	368,27
C₂²×Dic₂₃	Direct product of C₂² and Dic₂₃	368		C2^2xDic23	368,35
C₂×C₄×D₂₃	Direct product of C₂×C₄ and D₂₃	184		C2xC4xD23	368,28
C₂×C₂₃⋊D₄	Direct product of C₂ and C₂₃⋊D₄	184		C2xC23:D4	368,36
C₄○D₄×C₂₃	Direct product of C₂₃ and C₄○D₄	184	2	C4oD4xC23	368,40
C₂²⋊C₄×C₂₃	Direct product of C₂₃ and C₂²⋊C₄	184		C2^2:C4xC23	368,20
C₂×C₂₃⋊C₈	Direct product of C₂ and C₂₃⋊C₈	368		C2xC23:C8	368,8
C₄⋊C₄×C₂₃	Direct product of C₂₃ and C₄⋊C₄	368		C4:C4xC23	368,21

Groups of order 369

		d	ρ	Label	ID
C₃₆₉	Cyclic group	369	1	C369	369,1
C₃×C₁₂₃	Abelian group of type [3,123]	369		C3xC123	369,2

Groups of order 370

		d	ρ	Label	ID
C₃₇₀	Cyclic group	370	1	C370	370,4
D₁₈₅	Dihedral group	185	2+	D185	370,3
D₅×C₃₇	Direct product of C₃₇ and D₅	185	2	D5xC37	370,1
C₅×D₃₇	Direct product of C₅ and D₃₇	185	2	C5xD37	370,2

Groups of order 371

		d	ρ	Label	ID
C₃₇₁	Cyclic group	371	1	C371	371,1

Groups of order 372

		d	ρ	Label	ID
C₃₇₂	Cyclic group	372	1	C372	372,6
D₁₈₆	Dihedral group; = C₂×D₉₃	186	2+	D186	372,14
Dic₉₃	Dicyclic group; = C₉₃ ⋊₁ C₄	372	2-	Dic93	372,5
C₃₁⋊A₄	The semidirect product of C₃₁ and A₄ acting via A₄/C₂²=C₃	124	3	C31:A4	372,11
C₃₁⋊C₁₂	The semidirect product of C₃₁ and C₁₂ acting via C₁₂/C₂=C₆	124	6-	C31:C12	372,1
C₂×C₁₈₆	Abelian group of type [2,186]	372		C2xC186	372,15
S₃×D₃₁	Direct product of S₃ and D₃₁	93	4+	S3xD31	372,8
A₄×C₃₁	Direct product of C₃₁ and A₄	124	3	A4xC31	372,10
S₃×C₆₂	Direct product of C₆₂ and S₃	186	2	S3xC62	372,13
C₆×D₃₁	Direct product of C₆ and D₃₁	186	2	C6xD31	372,12
Dic₃×C₃₁	Direct product of C₃₁ and Dic₃	372	2	Dic3xC31	372,3
C₃×Dic₃₁	Direct product of C₃ and Dic₃₁	372	2	C3xDic31	372,4
C₂×C₃₁⋊C₆	Direct product of C₂ and C₃₁⋊C₆	62	6+	C2xC31:C6	372,7
C₄×C₃₁⋊C₃	Direct product of C₄ and C₃₁⋊C₃	124	3	C4xC31:C3	372,2
C₂²×C₃₁⋊C₃	Direct product of C₂² and C₃₁⋊C₃	124		C2^2xC31:C3	372,9

Groups of order 373

		d	ρ	Label	ID
C₃₇₃	Cyclic group	373	1	C373	373,1

Groups of order 374

		d	ρ	Label	ID
C₃₇₄	Cyclic group	374	1	C374	374,4
D₁₈₇	Dihedral group	187	2+	D187	374,3
C₁₇×D₁₁	Direct product of C₁₇ and D₁₁	187	2	C17xD11	374,1
C₁₁×D₁₇	Direct product of C₁₁ and D₁₇	187	2	C11xD17	374,2

Groups of order 375

		d	ρ	Label	ID
C₃₇₅	Cyclic group	375	1	C375	375,1
He₅⋊C₃	The semidirect product of He₅ and C₃ acting faithfully	75	5	He5:C3	375,2
C₅×C₇₅	Abelian group of type [5,75]	375		C5xC75	375,3
C₅²×C₁₅	Abelian group of type [5,5,15]	375		C5^2xC15	375,7
C₃×He₅	Direct product of C₃ and He₅	75	5	C3xHe5	375,4
C₃×5_-¹⁺²	Direct product of C₃ and 5_-¹⁺²	75	5	C3xES-(5,1)	375,5
C₅×C₅²⋊C₃	Direct product of C₅ and C₅²⋊C₃; = AΣL₁(𝔽₁₂₅)	15	3	C5xC5^2:C3	375,6

Groups of order 376

		d	ρ	Label	ID
C₃₇₆	Cyclic group	376	1	C376	376,2
D₁₈₈	Dihedral group	188	2+	D188	376,5
Dic₉₄	Dicyclic group; = C₄₇ ⋊Q₈	376	2-	Dic94	376,3
C₄₇⋊D₄	The semidirect product of C₄₇ and D₄ acting via D₄/C₂²=C₂	188	2	C47:D4	376,7
C₄₇⋊C₈	The semidirect product of C₄₇ and C₈ acting via C₈/C₄=C₂	376	2	C47:C8	376,1
C₂×C₁₈₈	Abelian group of type [2,188]	376		C2xC188	376,8
C₂²×C₉₄	Abelian group of type [2,2,94]	376		C2^2xC94	376,12
C₄×D₄₇	Direct product of C₄ and D₄₇	188	2	C4xD47	376,4
D₄×C₄₇	Direct product of C₄₇ and D₄	188	2	D4xC47	376,9
C₂²×D₄₇	Direct product of C₂² and D₄₇	188		C2^2xD47	376,11
Q₈×C₄₇	Direct product of C₄₇ and Q₈	376	2	Q8xC47	376,10
C₂×Dic₄₇	Direct product of C₂ and Dic₄₇	376		C2xDic47	376,6

Groups of order 377

		d	ρ	Label	ID
C₃₇₇	Cyclic group	377	1	C377	377,1

Groups of order 378

		d	ρ	Label	ID
C₃₇₈	Cyclic group	378	1	C378	378,6
D₁₈₉	Dihedral group	189	2+	D189	378,5
D₇⋊He₃	The semidirect product of D₇ and He₃ acting via He₃/C₃²=C₃	63	6	D7:He3	378,12
C₉⋊₃F₇	1^st semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:3F7	378,8
C₉⋊₄F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:4F7	378,9
C₉⋊F₇	1^st semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:F7	378,18
C₉⋊₂F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:2F7	378,19
C₉⋊₅F₇	The semidirect product of C₉ and F₇ acting via F₇/C₇⋊C₃=C₂	63	6+	C9:5F7	378,20
C₆₃⋊C₆	5^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:C6	378,13
C₆₃⋊₆C₆	6^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:6C6	378,14
C₃²⋊F₇	The semidirect product of C₃² and F₇ acting via F₇/C₇=C₆	63	6+	C3^2:F7	378,22
He₃⋊D₇	1^st semidirect product of He₃ and D₇ acting via D₇/C₇=C₂	63	6+	He3:D7	378,38
D₆₃⋊C₃	1^st semidirect product of D₆₃ and C₃ acting faithfully	63	6+	D63:C3	378,39
C₃²⋊₄F₇	2^nd semidirect product of C₃² and F₇ acting via F₇/C₇⋊C₃=C₂	63		C3^2:4F7	378,51
C₃²⋊D₂₁	2^nd semidirect product of C₃² and D₂₁ acting via D₂₁/C₇=S₃	63	6	C3^2:D21	378,43
D₂₁⋊C₉	The semidirect product of D₂₁ and C₉ acting via C₉/C₃=C₃	126	6	D21:C9	378,21
C₇⋊C₅₄	The semidirect product of C₇ and C₅₄ acting via C₅₄/C₉=C₆	189	6	C7:C54	378,1
C₃⋊D₆₃	The semidirect product of C₃ and D₆₃ acting via D₆₃/C₆₃=C₂	189		C3:D63	378,42
C₃³⋊D₇	3^rd semidirect product of C₃³ and D₇ acting via D₇/C₇=C₂	189		C3^3:D7	378,59
C₇⋊He₃⋊C₂	3^rd semidirect product of C₇⋊He₃ and C₂ acting faithfully	63	6	C7:He3:C2	378,17
C₃².F₇	The non-split extension by C₃² of F₇ acting via F₇/D₇=C₃	63	6	C3^2.F7	378,11
C₃×C₁₂₆	Abelian group of type [3,126]	378		C3xC126	378,44
C₃²×C₄₂	Abelian group of type [3,3,42]	378		C3^2xC42	378,60
C₉×F₇	Direct product of C₉ and F₇	63	6	C9xF7	378,7
D₇×He₃	Direct product of D₇ and He₃	63	6	D7xHe3	378,30
C₃²×F₇	Direct product of C₃² and F₇	63		C3^2xF7	378,47
D₇×3_-¹⁺²	Direct product of D₇ and 3_-¹⁺²	63	6	D7xES-(3,1)	378,31
S₃×C₆₃	Direct product of C₆₃ and S₃	126	2	S3xC63	378,33
D₉×C₂₁	Direct product of C₂₁ and D₉	126	2	D9xC21	378,32
C₃×D₆₃	Direct product of C₃ and D₆₃	126	2	C3xD63	378,36
C₉×D₂₁	Direct product of C₉ and D₂₁	126	2	C9xD21	378,37
C₁₄×He₃	Direct product of C₁₄ and He₃	126	3	C14xHe3	378,45
C₃²×D₂₁	Direct product of C₃² and D₂₁	126		C3^2xD21	378,55
C₁₄×3_-¹⁺²	Direct product of C₁₄ and 3_-¹⁺²	126	3	C14xES-(3,1)	378,46
C₇×D₂₇	Direct product of C₇ and D₂₇	189	2	C7xD27	378,3
D₇×C₂₇	Direct product of C₂₇ and D₇	189	2	D7xC27	378,4
D₇×C₃³	Direct product of C₃³ and D₇	189		D7xC3^3	378,53
C₃×C₃⋊F₇	Direct product of C₃ and C₃⋊F₇	42	6	C3xC3:F7	378,49
D₉×C₇⋊C₃	Direct product of D₉ and C₇⋊C₃	63	6	D9xC7:C3	378,15
C₇×C₉⋊C₆	Direct product of C₇ and C₉⋊C₆	63	6	C7xC9:C6	378,35
C₇×C₃²⋊C₆	Direct product of C₇ and C₃²⋊C₆	63	6	C7xC3^2:C6	378,34
C₇×He₃⋊C₂	Direct product of C₇ and He₃⋊C₂	63	3	C7xHe3:C2	378,41
S₃×C₇⋊C₉	Direct product of S₃ and C₇⋊C₉	126	6	S3xC7:C9	378,16
C₁₈×C₇⋊C₃	Direct product of C₁₈ and C₇⋊C₃	126	3	C18xC7:C3	378,23
S₃×C₃×C₂₁	Direct product of C₃×C₂₁ and S₃	126		S3xC3xC21	378,54
C₂×C₇⋊He₃	Direct product of C₂ and C₇⋊He₃	126	3	C2xC7:He3	378,28
C₃⋊S₃×C₂₁	Direct product of C₂₁ and C₃⋊S₃	126		C3:S3xC21	378,56
C₃×C₃⋊D₂₁	Direct product of C₃ and C₃⋊D₂₁	126		C3xC3:D21	378,57
C₂×C₆₃⋊C₃	Direct product of C₂ and C₆₃⋊C₃	126	3	C2xC63:C3	378,24
C₂×C₆₃⋊₃C₃	Direct product of C₂ and C₆₃⋊₃C₃	126	3	C2xC63:3C3	378,25
C₂×C₂₁.C₃²	Direct product of C₂ and C₂₁.C₃²	126	3	C2xC21.C3^2	378,27
D₇×C₃×C₉	Direct product of C₃×C₉ and D₇	189		D7xC3xC9	378,29
C₃×C₇⋊C₁₈	Direct product of C₃ and C₇⋊C₁₈	189		C3xC7:C18	378,10
C₇×C₉⋊S₃	Direct product of C₇ and C₉⋊S₃	189		C7xC9:S3	378,40
C₇×C₃³⋊C₂	Direct product of C₇ and C₃³⋊C₂	189		C7xC3^3:C2	378,58
C₆×C₇⋊C₉	Direct product of C₆ and C₇⋊C₉	378		C6xC7:C9	378,26
C₂×C₇⋊C₂₇	Direct product of C₂ and C₇⋊C₂₇	378	3	C2xC7:C27	378,2
C₃×S₃×C₇⋊C₃	Direct product of C₃, S₃ and C₇⋊C₃	42	6	C3xS3xC7:C3	378,48
C₃⋊S₃×C₇⋊C₃	Direct product of C₃⋊S₃ and C₇⋊C₃	63		C3:S3xC7:C3	378,50
C₃×C₆×C₇⋊C₃	Direct product of C₃×C₆ and C₇⋊C₃	126		C3xC6xC7:C3	378,52

Groups of order 379

		d	ρ	Label	ID
C₃₇₉	Cyclic group	379	1	C379	379,1

Groups of order 380

		d	ρ	Label	ID
C₃₈₀	Cyclic group	380	1	C380	380,4
D₁₉₀	Dihedral group; = C₂×D₉₅	190	2+	D190	380,10
Dic₉₅	Dicyclic group; = C₉₅ ⋊₃ C₄	380	2-	Dic95	380,3
C₁₉⋊F₅	The semidirect product of C₁₉ and F₅ acting via F₅/D₅=C₂	95	4	C19:F5	380,6
C₂×C₁₉₀	Abelian group of type [2,190]	380		C2xC190	380,11
D₅×D₁₉	Direct product of D₅ and D₁₉	95	4+	D5xD19	380,7
C₁₉×F₅	Direct product of C₁₉ and F₅	95	4	C19xF5	380,5
D₅×C₃₈	Direct product of C₃₈ and D₅	190	2	D5xC38	380,9
C₁₀×D₁₉	Direct product of C₁₀ and D₁₉	190	2	C10xD19	380,8
C₁₉×Dic₅	Direct product of C₁₉ and Dic₅	380	2	C19xDic5	380,1
C₅×Dic₁₉	Direct product of C₅ and Dic₁₉	380	2	C5xDic19	380,2

Groups of order 381

		d	ρ	Label	ID
C₃₈₁	Cyclic group	381	1	C381	381,2
C₁₂₇⋊C₃	The semidirect product of C₁₂₇ and C₃ acting faithfully	127	3	C127:C3	381,1

Groups of order 382

		d	ρ	Label	ID
C₃₈₂	Cyclic group	382	1	C382	382,2
D₁₉₁	Dihedral group	191	2+	D191	382,1

Groups of order 383

		d	ρ	Label	ID
C₃₈₃	Cyclic group	383	1	C383	383,1

Groups of order 385

		d	ρ	Label	ID
C₃₈₅	Cyclic group	385	1	C385	385,2
C₇×C₁₁⋊C₅	Direct product of C₇ and C₁₁⋊C₅	77	5	C7xC11:C5	385,1

Groups of order 386

		d	ρ	Label	ID
C₃₈₆	Cyclic group	386	1	C386	386,2
D₁₉₃	Dihedral group	193	2+	D193	386,1

Groups of order 387

		d	ρ	Label	ID
C₃₈₇	Cyclic group	387	1	C387	387,2
C₄₃⋊C₉	The semidirect product of C₄₃ and C₉ acting via C₉/C₃=C₃	387	3	C43:C9	387,1
C₃×C₁₂₉	Abelian group of type [3,129]	387		C3xC129	387,4
C₃×C₄₃⋊C₃	Direct product of C₃ and C₄₃⋊C₃	129	3	C3xC43:C3	387,3

Groups of order 388

		d	ρ	Label	ID
C₃₈₈	Cyclic group	388	1	C388	388,2
D₁₉₄	Dihedral group; = C₂×D₉₇	194	2+	D194	388,4
Dic₉₇	Dicyclic group; = C₉₇ ⋊₂ C₄	388	2-	Dic97	388,1
C₉₇⋊C₄	The semidirect product of C₉₇ and C₄ acting faithfully	97	4+	C97:C4	388,3
C₂×C₁₉₄	Abelian group of type [2,194]	388		C2xC194	388,5

Groups of order 389

		d	ρ	Label	ID
C₃₈₉	Cyclic group	389	1	C389	389,1

Groups of order 390

		d	ρ	Label	ID
C₃₉₀	Cyclic group	390	1	C390	390,12
D₁₉₅	Dihedral group	195	2+	D195	390,11
D₆₅⋊C₃	The semidirect product of D₆₅ and C₃ acting faithfully	65	6+	D65:C3	390,3
S₃×C₆₅	Direct product of C₆₅ and S₃	195	2	S3xC65	390,8
D₅×C₃₉	Direct product of C₃₉ and D₅	195	2	D5xC39	390,6
C₃×D₆₅	Direct product of C₃ and D₆₅	195	2	C3xD65	390,7
C₅×D₃₉	Direct product of C₅ and D₃₉	195	2	C5xD39	390,9
C₁₅×D₁₃	Direct product of C₁₅ and D₁₃	195	2	C15xD13	390,5
C₁₃×D₁₅	Direct product of C₁₃ and D₁₅	195	2	C13xD15	390,10
C₅×C₁₃⋊C₆	Direct product of C₅ and C₁₃⋊C₆	65	6	C5xC13:C6	390,1
D₅×C₁₃⋊C₃	Direct product of D₅ and C₁₃⋊C₃	65	6	D5xC13:C3	390,2
C₁₀×C₁₃⋊C₃	Direct product of C₁₀ and C₁₃⋊C₃	130	3	C10xC13:C3	390,4

Groups of order 391

		d	ρ	Label	ID
C₃₉₁	Cyclic group	391	1	C391	391,1

Groups of order 392

		d	ρ	Label	ID
C₃₉₂	Cyclic group	392	1	C392	392,2
D₁₉₆	Dihedral group	196	2+	D196	392,5
Dic₉₈	Dicyclic group; = C₄₉ ⋊Q₈	392	2-	Dic98	392,3
D₇≀C₂	Wreath product of D₇ by C₂	14	4+	D7wrC2	392,37
C₇²⋊C₈	The semidirect product of C₇² and C₈ acting faithfully	28	8+	C7^2:C8	392,36
C₇²⋊Q₈	The semidirect product of C₇² and Q₈ acting faithfully	28	8+	C7^2:Q8	392,38
C₇⋊D₂₈	The semidirect product of C₇ and D₂₈ acting via D₂₈/D₁₄=C₂	28	4+	C7:D28	392,21
Dic₇⋊₂D₇	The semidirect product of Dic₇ and D₇ acting through Inn(Dic₇)	28	4+	Dic7:2D7	392,19
C₇²⋊₂C₈	The semidirect product of C₇² and C₈ acting via C₈/C₂=C₄	56	4-	C7^2:2C8	392,17
C₇²⋊₂D₄	1^st semidirect product of C₇² and D₄ acting via D₄/C₂=C₂²	56	4-	C7^2:2D4	392,20
C₇²⋊₂Q₈	The semidirect product of C₇² and Q₈ acting via Q₈/C₂=C₂²	56	4-	C7^2:2Q8	392,22
C₄₉⋊D₄	The semidirect product of C₄₉ and D₄ acting via D₄/C₂²=C₂	196	2	C49:D4	392,7
C₂₈⋊D₇	1^st semidirect product of C₂₈ and D₇ acting via D₇/C₇=C₂	196		C28:D7	392,30
C₇²⋊₇D₄	2^nd semidirect product of C₇² and D₄ acting via D₄/C₂²=C₂	196		C7^2:7D4	392,32
C₄₉⋊C₈	The semidirect product of C₄₉ and C₈ acting via C₈/C₄=C₂	392	2	C49:C8	392,1
C₇²⋊₄C₈	2^nd semidirect product of C₇² and C₈ acting via C₈/C₄=C₂	392		C7^2:4C8	392,15
C₇²⋊₄Q₈	2^nd semidirect product of C₇² and Q₈ acting via Q₈/C₄=C₂	392		C7^2:4Q8	392,28
C₇.F₈	The central extension by C₇ of F₈	98	7	C7.F8	392,11
C₇×C₅₆	Abelian group of type [7,56]	392		C7xC56	392,16
C₂×C₁₉₆	Abelian group of type [2,196]	392		C2xC196	392,8
C₁₄×C₂₈	Abelian group of type [14,28]	392		C14xC28	392,33
C₂²×C₉₈	Abelian group of type [2,2,98]	392		C2^2xC98	392,13
C₂×C₁₄²	Abelian group of type [2,14,14]	392		C2xC14^2	392,44
C₇×F₈	Direct product of C₇ and F₈	56	7	C7xF8	392,39
D₇×C₂₈	Direct product of C₂₈ and D₇	56	2	D7xC28	392,24
C₇×D₂₈	Direct product of C₇ and D₂₈	56	2	C7xD28	392,25
D₇×Dic₇	Direct product of D₇ and Dic₇	56	4-	D7xDic7	392,18
C₇×Dic₁₄	Direct product of C₇ and Dic₁₄	56	2	C7xDic14	392,23
C₁₄×Dic₇	Direct product of C₁₄ and Dic₇	56		C14xDic7	392,26
C₄×D₄₉	Direct product of C₄ and D₄₉	196	2	C4xD49	392,4
D₄×C₄₉	Direct product of C₄₉ and D₄	196	2	D4xC49	392,9
D₄×C₇²	Direct product of C₇² and D₄	196		D4xC7^2	392,34
C₂²×D₄₉	Direct product of C₂² and D₄₉	196		C2^2xD49	392,12
Q₈×C₄₉	Direct product of C₄₉ and Q₈	392	2	Q8xC49	392,10
Q₈×C₇²	Direct product of C₇² and Q₈	392		Q8xC7^2	392,35
C₂×Dic₄₉	Direct product of C₂ and Dic₄₉	392		C2xDic49	392,6
C₂×D₇²	Direct product of C₂, D₇ and D₇	28	4+	C2xD7^2	392,41
C₇×C₇⋊D₄	Direct product of C₇ and C₇⋊D₄	28	2	C7xC7:D4	392,27
C₂×C₇²⋊C₄	Direct product of C₂ and C₇²⋊C₄	28	4+	C2xC7^2:C4	392,40
C₇×C₇⋊C₈	Direct product of C₇ and C₇⋊C₈	56	2	C7xC7:C8	392,14
D₇×C₂×C₁₄	Direct product of C₂×C₁₄ and D₇	56		D7xC2xC14	392,42
C₄×C₇⋊D₇	Direct product of C₄ and C₇⋊D₇	196		C4xC7:D7	392,29
C₂²×C₇⋊D₇	Direct product of C₂² and C₇⋊D₇	196		C2^2xC7:D7	392,43
C₂×C₇⋊Dic₇	Direct product of C₂ and C₇⋊Dic₇	392		C2xC7:Dic7	392,31

Groups of order 393

		d	ρ	Label	ID
C₃₉₃	Cyclic group	393	1	C393	393,1

Groups of order 394

		d	ρ	Label	ID
C₃₉₄	Cyclic group	394	1	C394	394,2
D₁₉₇	Dihedral group	197	2+	D197	394,1

Groups of order 395

		d	ρ	Label	ID
C₃₉₅	Cyclic group	395	1	C395	395,1

Groups of order 396

		d	ρ	Label	ID
C₃₉₆	Cyclic group	396	1	C396	396,4
D₁₉₈	Dihedral group; = C₂×D₉₉	198	2+	D198	396,9
Dic₉₉	Dicyclic group; = C₉₉ ⋊₁ C₄	396	2-	Dic99	396,3
D₃₃⋊S₃	The semidirect product of D₃₃ and S₃ acting via S₃/C₃=C₂	66	4	D33:S3	396,23
C₃²⋊Dic₁₁	The semidirect product of C₃² and Dic₁₁ acting via Dic₁₁/C₁₁=C₄	66	4	C3^2:Dic11	396,18
C₃⋊Dic₃₃	The semidirect product of C₃ and Dic₃₃ acting via Dic₃₃/C₆₆=C₂	396		C3:Dic33	396,15
C₆×C₆₆	Abelian group of type [6,66]	396		C6xC66	396,30
C₂×C₁₉₈	Abelian group of type [2,198]	396		C2xC198	396,10
C₃×C₁₃₂	Abelian group of type [3,132]	396		C3xC132	396,16
S₃×D₃₃	Direct product of S₃ and D₃₃	66	4+	S3xD33	396,22
D₉×D₁₁	Direct product of D₉ and D₁₁	99	4+	D9xD11	396,5
S₃×C₆₆	Direct product of C₆₆ and S₃	132	2	S3xC66	396,26
A₄×C₃₃	Direct product of C₃₃ and A₄	132	3	A4xC33	396,24
C₆×D₃₃	Direct product of C₆ and D₃₃	132	2	C6xD33	396,27
Dic₃×C₃₃	Direct product of C₃₃ and Dic₃	132	2	Dic3xC33	396,12
C₃×Dic₃₃	Direct product of C₃ and Dic₃₃	132	2	C3xDic33	396,13
D₉×C₂₂	Direct product of C₂₂ and D₉	198	2	D9xC22	396,8
C₁₈×D₁₁	Direct product of C₁₈ and D₁₁	198	2	C18xD11	396,7
C₁₁×Dic₉	Direct product of C₁₁ and Dic₉	396	2	C11xDic9	396,1
C₉×Dic₁₁	Direct product of C₉ and Dic₁₁	396	2	C9xDic11	396,2
C₃²×Dic₁₁	Direct product of C₃² and Dic₁₁	396		C3^2xDic11	396,11
S₃²×C₁₁	Direct product of C₁₁, S₃ and S₃	66	4	S3^2xC11	396,21
C₃×S₃×D₁₁	Direct product of C₃, S₃ and D₁₁	66	4	C3xS3xD11	396,19
C₁₁×C₃²⋊C₄	Direct product of C₁₁ and C₃²⋊C₄	66	4	C11xC3^2:C4	396,17
C₃⋊S₃×D₁₁	Direct product of C₃⋊S₃ and D₁₁	99		C3:S3xD11	396,20
C₃×C₆×D₁₁	Direct product of C₃×C₆ and D₁₁	198		C3xC6xD11	396,25
C₃⋊S₃×C₂₂	Direct product of C₂₂ and C₃⋊S₃	198		C3:S3xC22	396,28
C₂×C₃⋊D₃₃	Direct product of C₂ and C₃⋊D₃₃	198		C2xC3:D33	396,29
C₁₁×C₃.A₄	Direct product of C₁₁ and C₃.A₄	198	3	C11xC3.A4	396,6
C₁₁×C₃⋊Dic₃	Direct product of C₁₁ and C₃⋊Dic₃	396		C11xC3:Dic3	396,14

Groups of order 397

		d	ρ	Label	ID
C₃₉₇	Cyclic group	397	1	C397	397,1

Groups of order 398

		d	ρ	Label	ID
C₃₉₈	Cyclic group	398	1	C398	398,2
D₁₉₉	Dihedral group	199	2+	D199	398,1

Groups of order 399

		d	ρ	Label	ID
C₃₉₉	Cyclic group	399	1	C399	399,5
C₁₃₃⋊C₃	3^rd semidirect product of C₁₃₃ and C₃ acting faithfully	133	3	C133:C3	399,3
C₁₃₃⋊₄C₃	4^th semidirect product of C₁₃₃ and C₃ acting faithfully	133	3	C133:4C3	399,4
C₁₉×C₇⋊C₃	Direct product of C₁₉ and C₇⋊C₃	133	3	C19xC7:C3	399,1
C₇×C₁₉⋊C₃	Direct product of C₇ and C₁₉⋊C₃	133	3	C7xC19:C3	399,2

Groups of order 400

		d	ρ	Label	ID
C₄₀₀	Cyclic group	400	1	C400	400,2
D₂₀₀	Dihedral group	200	2+	D200	400,8
Dic₁₀₀	Dicyclic group; = C₂₅ ⋊₁ Q₁₆	400	2-	Dic100	400,4
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	10	8+	C5^2:M4(2)	400,206
D₁₀⋊F₅	2^nd semidirect product of D₁₀ and F₅ acting via F₅/D₅=C₂	20	8+	D10:F5	400,125
D₁₀⋊D₁₀	3^rd semidirect product of D₁₀ and D₁₀ acting via D₁₀/D₅=C₂	20	4+	D10:D10	400,180
C₁₀²⋊₄C₄	4^th semidirect product of C₁₀² and C₄ acting faithfully	20	4+	C10^2:4C4	400,162
Dic₅⋊F₅	3^rd semidirect product of Dic₅ and F₅ acting via F₅/D₅=C₂	20	8+	Dic5:F5	400,126
C₅²⋊₃C₄²	2^nd semidirect product of C₅² and C₄² acting via C₄²/C₂=C₂×C₄	20	8+	C5^2:3C4^2	400,124
C₅²⋊D₈	The semidirect product of C₅² and D₈ acting via D₈/C₂=D₄	40	4	C5^2:D8	400,131
C₅⋊D₄₀	The semidirect product of C₅ and D₄₀ acting via D₄₀/D₂₀=C₂	40	4+	C5:D40	400,65
C₂₀⋊₂F₅	2^nd semidirect product of C₂₀ and F₅ acting via F₅/C₅=C₄	40	4	C20:2F5	400,159
C₅²⋊SD₁₆	The semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₂=D₄	40	4-	C5^2:SD16	400,132
D₂₀⋊D₅	3^rd semidirect product of D₂₀ and D₅ acting via D₅/C₅=C₂	40	4	D20:D5	400,165
C₂₀⋊D₁₀	2^nd semidirect product of C₂₀ and D₁₀ acting via D₁₀/C₅=C₂²	40	4	C20:D10	400,171
C₅²⋊₄SD₁₆	3^rd semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₄=C₂²	40	4+	C5^2:4SD16	400,68
Dic₁₀⋊D₅	4^th semidirect product of Dic₁₀ and D₅ acting via D₅/C₅=C₂	40	4	Dic10:D5	400,166
Dic₁₀⋊₅D₅	The semidirect product of Dic₁₀ and D₅ acting through Inn(Dic₁₀)	40	4+	Dic10:5D5	400,168
C₅²⋊₈M₄(2)	4^th semidirect product of C₅² and M₄(2) acting via M₄(2)/C₄=C₄	40	4	C5^2:8M4(2)	400,157
C₅²⋊₁₄M₄(2)	4^th semidirect product of C₅² and M₄(2) acting via M₄(2)/C₂²=C₄	40	4-	C5^2:14M4(2)	400,161
C₂⁴⋊C₂₅	The semidirect product of C₂⁴ and C₂₅ acting via C₂₅/C₅=C₅	50	5	C2^4:C25	400,52
C₅²⋊C₁₆	The semidirect product of C₅² and C₁₆ acting via C₁₆/C₂=C₈	80	8-	C5^2:C16	400,116
C₅²⋊Q₁₆	The semidirect product of C₅² and Q₁₆ acting via Q₁₆/C₂=D₄	80	4-	C5^2:Q16	400,133
C₂₀⋊₅F₅	1^st semidirect product of C₂₀ and F₅ acting via F₅/D₅=C₂	80	4	C20:5F5	400,145
C₅²⋊₂D₈	1^st semidirect product of C₅² and D₈ acting via D₈/C₄=C₂²	80	4	C5^2:2D8	400,64
D₂₀⋊₅D₅	The semidirect product of D₂₀ and D₅ acting through Inn(D₂₀)	80	4-	D20:5D5	400,164
C₅²⋊₃C₁₆	2^nd semidirect product of C₅² and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5^2:3C16	400,57
C₅²⋊₅C₁₆	4^th semidirect product of C₅² and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5^2:5C16	400,59
C₅²⋊₂Q₁₆	1^st semidirect product of C₅² and Q₁₆ acting via Q₁₆/C₄=C₂²	80	4	C5^2:2Q16	400,69
C₅²⋊₃Q₁₆	2^nd semidirect product of C₅² and Q₁₆ acting via Q₁₆/C₄=C₂²	80	4-	C5^2:3Q16	400,70
C₅²⋊₃SD₁₆	2^nd semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₄=C₂²	80	4-	C5^2:3SD16	400,67
D₁₀⋊Dic₅	1^st semidirect product of D₁₀ and Dic₅ acting via Dic₅/C₁₀=C₂	80		D10:Dic5	400,72
C₅²⋊₄M₄(2)	3^rd semidirect product of C₅² and M₄(2) acting via M₄(2)/C₂=C₂×C₄	80	8-	C5^2:4M4(2)	400,128
Dic₅⋊Dic₅	1^st semidirect product of Dic₅ and Dic₅ acting via Dic₅/C₁₀=C₂	80		Dic5:Dic5	400,74
C₂₀⋊F₅	1^st semidirect product of C₂₀ and F₅ acting via F₅/C₅=C₄	100		C20:F5	400,152
C₁₀₀⋊C₄	1^st semidirect product of C₁₀₀ and C₄ acting faithfully	100	4	C100:C4	400,31
C₁₀²⋊C₄	3^rd semidirect product of C₁₀² and C₄ acting faithfully	100		C10^2:C4	400,155
D₄⋊D₂₅	The semidirect product of D₄ and D₂₅ acting via D₂₅/C₂₅=C₂	200	4+	D4:D25	400,16
D₂₅⋊C₈	The semidirect product of D₂₅ and C₈ acting via C₈/C₄=C₂	200	4	D25:C8	400,28
Q₈⋊D₂₅	The semidirect product of Q₈ and D₂₅ acting via D₂₅/C₂₅=C₂	200	4+	Q8:D25	400,18
C₈⋊D₂₅	3^rd semidirect product of C₈ and D₂₅ acting via D₂₅/C₂₅=C₂	200	2	C8:D25	400,6
C₄₀⋊D₅	4^th semidirect product of C₄₀ and D₅ acting via D₅/C₅=C₂	200		C40:D5	400,93
C₄₀⋊₂D₅	2^nd semidirect product of C₄₀ and D₅ acting via D₅/C₅=C₂	200		C40:2D5	400,94
C₂₀₀⋊C₂	2^nd semidirect product of C₂₀₀ and C₂ acting faithfully	200	2	C200:C2	400,7
C₅²⋊₅D₈	2^nd semidirect product of C₅² and D₈ acting via D₈/C₈=C₂	200		C5^2:5D8	400,95
C₅²⋊₇D₈	2^nd semidirect product of C₅² and D₈ acting via D₈/D₄=C₂	200		C5^2:7D8	400,103
D₅₀⋊C₄	1^st semidirect product of D₅₀ and C₄ acting via C₄/C₂=C₂	200		D50:C4	400,14
D₄⋊₂D₂₅	The semidirect product of D₄ and D₂₅ acting through Inn(D₄)	200	4-	D4:2D25	400,40
Q₈⋊₂D₂₅	The semidirect product of Q₈ and D₂₅ acting through Inn(Q₈)	200	4+	Q8:2D25	400,42
D₁₀₀⋊₅C₂	The semidirect product of D₁₀₀ and C₂ acting through Inn(D₁₀₀)	200	2	D100:5C2	400,38
C₂₅⋊M₄(2)	The semidirect product of C₂₅ and M₄(2) acting via M₄(2)/C₂²=C₄	200	4-	C25:M4(2)	400,33
C₅²⋊₈SD₁₆	2^nd semidirect product of C₅² and SD₁₆ acting via SD₁₆/D₄=C₂	200		C5^2:8SD16	400,104
C₁₀²⋊₁₁C₄	3^rd semidirect product of C₁₀² and C₄ acting via C₄/C₂=C₂	200		C10^2:11C4	400,107
C₅²⋊₁₀SD₁₆	2^nd semidirect product of C₅² and SD₁₆ acting via SD₁₆/Q₈=C₂	200		C5^2:10SD16	400,105
C₅²⋊₇M₄(2)	3^rd semidirect product of C₅² and M₄(2) acting via M₄(2)/C₄=C₄	200		C5^2:7M4(2)	400,150
C₅²⋊₁₃M₄(2)	3^rd semidirect product of C₅² and M₄(2) acting via M₄(2)/C₂²=C₄	200		C5^2:13M4(2)	400,154
C₂₅⋊C₁₆	The semidirect product of C₂₅ and C₁₆ acting via C₁₆/C₄=C₄	400	4	C25:C16	400,3
C₂₅⋊₂C₁₆	The semidirect product of C₂₅ and C₁₆ acting via C₁₆/C₈=C₂	400	2	C25:2C16	400,1
C₄⋊Dic₂₅	The semidirect product of C₄ and Dic₂₅ acting via Dic₂₅/C₅₀=C₂	400		C4:Dic25	400,13
C₂₅⋊Q₁₆	The semidirect product of C₂₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	400	4-	C25:Q16	400,17
C₅²⋊₇C₁₆	2^nd semidirect product of C₅² and C₁₆ acting via C₁₆/C₈=C₂	400		C5^2:7C16	400,50
C₅²⋊₄C₁₆	3^rd semidirect product of C₅² and C₁₆ acting via C₁₆/C₄=C₄	400		C5^2:4C16	400,58
C₅²⋊₇Q₁₆	2^nd semidirect product of C₅² and Q₁₆ acting via Q₁₆/Q₈=C₂	400		C5^2:7Q16	400,106
C₂₀⋊₃Dic₅	1^st semidirect product of C₂₀ and Dic₅ acting via Dic₅/C₁₀=C₂	400		C20:3Dic5	400,101
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	10	8+	D5wrC2:C2	400,207
D₅²⋊C₄	1^st semidirect product of D₅² and C₄ acting via C₄/C₂=C₂	20	4+	D5^2:C4	400,129
D₅.D₂₀	The non-split extension by D₅ of D₂₀ acting via D₂₀/D₁₀=C₂	40	8+	D5.D20	400,118
C₂₀.₁₁F₅	11^st non-split extension by C₂₀ of F₅ acting via F₅/C₅=C₄	40	4	C20.11F5	400,156
D₁₀.₉D₁₀	1^st non-split extension by D₁₀ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D10.9D10	400,167
D₁₀.₄D₁₀	4^th non-split extension by D₁₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4-	D10.4D10	400,174
C₂₀.₂₉D₁₀	3^rd non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.29D10	400,61
C₂₀.₃₁D₁₀	5^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.31D10	400,63
C₁₀.D₂₀	6^th non-split extension by C₁₀ of D₂₀ acting via D₂₀/D₁₀=C₂	40		C10.D20	400,73
C₁₀².C₄	4^th non-split extension by C₁₀² of C₄ acting faithfully	40	4	C10^2.C4	400,147
Dic₅.₄F₅	The non-split extension by Dic₅ of F₅ acting through Inn(Dic₅)	40	8+	Dic5.4F5	400,121
Dic₅.F₅	1^st non-split extension by Dic₅ of F₅ acting via F₅/D₅=C₂	40	8+	Dic5.F5	400,123
D₁₀.D₁₀	5^th non-split extension by D₁₀ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D10.D10	400,148
Dic₅.D₁₀	3^rd non-split extension by Dic₅ of D₁₀ acting via D₁₀/D₅=C₂	40	4	Dic5.D10	400,173
D₂₀.D₅	2^nd non-split extension by D₂₀ of D₅ acting via D₅/C₅=C₂	80	4	D20.D5	400,66
D₁₀.F₅	1^st non-split extension by D₁₀ of F₅ acting via F₅/D₅=C₂	80	8-	D10.F5	400,122
D₁₀.₂F₅	2^nd non-split extension by D₁₀ of F₅ acting via F₅/D₅=C₂	80	8-	D10.2F5	400,127
C₂₀.₁₄F₅	3^rd non-split extension by C₂₀ of F₅ acting via F₅/D₅=C₂	80	4	C20.14F5	400,142
C₂₀.₁₂F₅	1^st non-split extension by C₂₀ of F₅ acting via F₅/D₅=C₂	80	4	C20.12F5	400,143
C₂₀.₃₀D₁₀	4^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	80	4	C20.30D10	400,62
D₅.Dic₁₀	The non-split extension by D₅ of Dic₁₀ acting via Dic₁₀/Dic₅=C₂	80	8-	D5.Dic10	400,119
C₁₀.Dic₁₀	2^nd non-split extension by C₁₀ of Dic₁₀ acting via Dic₁₀/Dic₅=C₂	80		C10.Dic10	400,75
D₂₅.D₄	The non-split extension by D₂₅ of D₄ acting via D₄/C₂²=C₂	100	4+	D25.D4	400,34
D₄.D₂₅	The non-split extension by D₄ of D₂₅ acting via D₂₅/C₂₅=C₂	200	4-	D4.D25	400,15
C₄.Dic₂₅	The non-split extension by C₄ of Dic₂₅ acting via Dic₂₅/C₅₀=C₂	200	2	C4.Dic25	400,10
C₂³.D₂₅	The non-split extension by C₂³ of D₂₅ acting via D₂₅/C₂₅=C₂	200		C2^3.D25	400,19
C₁₀₀.C₄	1^st non-split extension by C₁₀₀ of C₄ acting faithfully	200	4	C100.C4	400,29
C₂₀.F₅	10^th non-split extension by C₂₀ of F₅ acting via F₅/C₅=C₄	200		C20.F5	400,149
C₂₀.₅₉D₁₀	20^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/C₁₀=C₂	200		C20.59D10	400,98
C₁₀.₁₁D₂₀	11^st non-split extension by C₁₀ of D₂₀ acting via D₂₀/C₂₀=C₂	200		C10.11D20	400,102
C₂₀.₅₀D₁₀	11^st non-split extension by C₂₀ of D₁₀ acting via D₁₀/C₁₀=C₂	200		C20.50D10	400,194
C₂₀.D₁₀	24^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/C₅=C₂²	200		C20.D10	400,196
C₂₀.₂₆D₁₀	26^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/C₅=C₂²	200		C20.26D10	400,198
C₅₀.D₄	1^st non-split extension by C₅₀ of D₄ acting via D₄/C₂²=C₂	400		C50.D4	400,12
C₄₀.D₅	3^rd non-split extension by C₄₀ of D₅ acting via D₅/C₅=C₂	400		C40.D5	400,96
C₁₀².₂₂C₂²	8^th non-split extension by C₁₀² of C₂² acting via C₂²/C₂=C₂	400		C10^2.22C2^2	400,100
(C₅×C₁₀).Q₈	The non-split extension by C₅×C₁₀ of Q₈ acting faithfully	20	8+	(C5xC10).Q8	400,134
C₂.D₅≀C₂	2^nd central extension by C₂ of D₅≀C₂	20	4	C2.D5wrC2	400,130
C₂₀²	Abelian group of type [20,20]	400		C20^2	400,108
C₅×C₈₀	Abelian group of type [5,80]	400		C5xC80	400,51
C₄×C₁₀₀	Abelian group of type [4,100]	400		C4xC100	400,20
C₂×C₂₀₀	Abelian group of type [2,200]	400		C2xC200	400,23
C₁₀×C₄₀	Abelian group of type [10,40]	400		C10xC40	400,111
C₂³×C₅₀	Abelian group of type [2,2,2,50]	400		C2^3xC50	400,55
C₂²×C₁₀₀	Abelian group of type [2,2,100]	400		C2^2xC100	400,45
C₂²×C₁₀²	Abelian group of type [2,2,10,10]	400		C2^2xC10^2	400,221
C₂×C₁₀×C₂₀	Abelian group of type [2,10,20]	400		C2xC10xC20	400,201
F₅²	Direct product of F₅ and F₅; = Hol(F₅)	20	16+	F5^2	400,205
D₅×D₂₀	Direct product of D₅ and D₂₀	40	4+	D5xD20	400,170
D₅×C₄₀	Direct product of C₄₀ and D₅	80	2	D5xC40	400,76
C₅×D₄₀	Direct product of C₅ and D₄₀	80	2	C5xD40	400,79
C₂₀×F₅	Direct product of C₂₀ and F₅	80	4	C20xF5	400,137
C₁₀×D₂₀	Direct product of C₁₀ and D₂₀	80		C10xD20	400,183
Dic₅²	Direct product of Dic₅ and Dic₅	80		Dic5^2	400,71
Dic₅×F₅	Direct product of Dic₅ and F₅	80	8-	Dic5xF5	400,117
C₅×Dic₂₀	Direct product of C₅ and Dic₂₀	80	2	C5xDic20	400,80
Dic₅×C₂₀	Direct product of C₂₀ and Dic₅	80		Dic5xC20	400,83
D₅×Dic₁₀	Direct product of D₅ and Dic₁₀	80	4-	D5xDic10	400,163
C₁₀×Dic₁₀	Direct product of C₁₀ and Dic₁₀	80		C10xDic10	400,181
D₄×D₂₅	Direct product of D₄ and D₂₅	100	4+	D4xD25	400,39
C₈×D₂₅	Direct product of C₈ and D₂₅	200	2	C8xD25	400,5
D₈×C₂₅	Direct product of C₂₅ and D₈	200	2	D8xC25	400,25
D₄×C₅₀	Direct product of C₅₀ and D₄	200		D4xC50	400,46
Q₈×D₂₅	Direct product of Q₈ and D₂₅	200	4-	Q8xD25	400,41
C₂×D₁₀₀	Direct product of C₂ and D₁₀₀	200		C2xD100	400,37
D₈×C₅²	Direct product of C₅² and D₈	200		D8xC5^2	400,113
SD₁₆×C₂₅	Direct product of C₂₅ and SD₁₆	200	2	SD16xC25	400,26
C₂³×D₂₅	Direct product of C₂³ and D₂₅	200		C2^3xD25	400,54
M₄(2)×C₂₅	Direct product of C₂₅ and M₄(2)	200	2	M4(2)xC25	400,24
SD₁₆×C₅²	Direct product of C₅² and SD₁₆	200		SD16xC5^2	400,114
M₄(2)×C₅²	Direct product of C₅² and M₄(2)	200		M4(2)xC5^2	400,112
Q₈×C₅₀	Direct product of C₅₀ and Q₈	400		Q8xC50	400,47
Q₁₆×C₂₅	Direct product of C₂₅ and Q₁₆	400	2	Q16xC25	400,27
C₄×Dic₂₅	Direct product of C₄ and Dic₂₅	400		C4xDic25	400,11
C₂×Dic₅₀	Direct product of C₂ and Dic₅₀	400		C2xDic50	400,35
Q₁₆×C₅²	Direct product of C₅² and Q₁₆	400		Q16xC5^2	400,115
C₂²×Dic₂₅	Direct product of C₂² and Dic₂₅	400		C2^2xDic25	400,43
C₂×D₅≀C₂	Direct product of C₂ and D₅≀C₂	20	4+	C2xD5wrC2	400,211
C₂×D₅⋊F₅	Direct product of C₂ and D₅⋊F₅	20	8+	C2xD5:F5	400,210
C₂×C₅²⋊C₈	Direct product of C₂ and C₅²⋊C₈	20	8+	C2xC5^2:C8	400,208
C₂×C₅²⋊Q₈	Direct product of C₂ and C₅²⋊Q₈	20	8+	C2xC5^2:Q8	400,212
C₄×D₅²	Direct product of C₄, D₅ and D₅	40	4	C4xD5^2	400,169
C₅×D₄×D₅	Direct product of C₅, D₄ and D₅	40	4	C5xD4xD5	400,185
C₂×D₅×F₅	Direct product of C₂, D₅ and F₅	40	8+	C2xD5xF5	400,209
D₅×C₅⋊D₄	Direct product of D₅ and C₅⋊D₄	40	4	D5xC5:D4	400,179
C₅×D₄⋊D₅	Direct product of C₅ and D₄⋊D₅	40	4	C5xD4:D5	400,87
C₁₀×C₅⋊D₄	Direct product of C₁₀ and C₅⋊D₄	40		C10xC5:D4	400,190
C₂²×D₅²	Direct product of C₂², D₅ and D₅	40		C2^2xD5^2	400,218
C₅×C₄○D₂₀	Direct product of C₅ and C₄○D₂₀	40	2	C5xC4oD20	400,184
C₂×C₅⋊D₂₀	Direct product of C₂ and C₅⋊D₂₀	40		C2xC5:D20	400,177
C₅×D₄.D₅	Direct product of C₅ and D₄.D₅	40	4	C5xD4.D5	400,88
C₄×C₅²⋊C₄	Direct product of C₄ and C₅²⋊C₄	40	4	C4xC5^2:C4	400,158
C₅×C₂²⋊F₅	Direct product of C₅ and C₂²⋊F₅	40	4	C5xC2^2:F5	400,141
C₅×D₄⋊₂D₅	Direct product of C₅ and D₄⋊₂D₅	40	4	C5xD4:2D5	400,186
C₅×C₄.Dic₅	Direct product of C₅ and C₄.Dic₅	40	2	C5xC4.Dic5	400,82
C₅×C₂³.D₅	Direct product of C₅ and C₂³.D₅	40		C5xC2^3.D5	400,91
C₅×C₂².F₅	Direct product of C₅ and C₂².F₅	40	4	C5xC2^2.F5	400,140
C₂²×C₅²⋊C₄	Direct product of C₂² and C₅²⋊C₄	40		C2^2xC5^2:C4	400,217
C₂×Dic₅⋊₂D₅	Direct product of C₂ and Dic₅⋊₂D₅	40		C2xDic5:2D5	400,175
C₅×C₂⁴⋊C₅	Direct product of C₅ and C₂⁴⋊C₅	50	5	C5xC2^4:C5	400,213
D₅×C₅⋊C₈	Direct product of D₅ and C₅⋊C₈	80	8-	D5xC5:C8	400,120
C₅×C₅⋊C₁₆	Direct product of C₅ and C₅⋊C₁₆	80	4	C5xC5:C16	400,56
C₁₀×C₅⋊C₈	Direct product of C₁₀ and C₅⋊C₈	80		C10xC5:C8	400,139
C₅×Q₈×D₅	Direct product of C₅, Q₈ and D₅	80	4	C5xQ8xD5	400,187
D₅×C₂×C₂₀	Direct product of C₂×C₂₀ and D₅	80		D5xC2xC20	400,182
C₅×C₄⋊F₅	Direct product of C₅ and C₄⋊F₅	80	4	C5xC4:F5	400,138
F₅×C₂×C₁₀	Direct product of C₂×C₁₀ and F₅	80		F5xC2xC10	400,214
C₅×D₅⋊C₈	Direct product of C₅ and D₅⋊C₈	80	4	C5xD5:C8	400,135
C₅×C₈⋊D₅	Direct product of C₅ and C₈⋊D₅	80	2	C5xC8:D5	400,77
D₅×C₅⋊₂C₈	Direct product of D₅ and C₅⋊₂C₈	80	4	D5xC5:2C8	400,60
C₅×Q₈⋊D₅	Direct product of C₅ and Q₈⋊D₅	80	4	C5xQ8:D5	400,89
C₂×D₅×Dic₅	Direct product of C₂, D₅ and Dic₅	80		C2xD5xDic5	400,172
C₅×C₄₀⋊C₂	Direct product of C₅ and C₄₀⋊C₂	80	2	C5xC40:C2	400,78
C₅×C₅⋊Q₁₆	Direct product of C₅ and C₅⋊Q₁₆	80	4	C5xC5:Q16	400,90
C₅×C₅⋊₂C₁₆	Direct product of C₅ and C₅⋊₂C₁₆	80	2	C5xC5:2C16	400,49
C₁₀×C₅⋊₂C₈	Direct product of C₁₀ and C₅⋊₂C₈	80		C10xC5:2C8	400,81
C₅×C₄.F₅	Direct product of C₅ and C₄.F₅	80	4	C5xC4.F5	400,136
C₄×D₅.D₅	Direct product of C₄ and D₅.D₅	80	4	C4xD5.D5	400,144
C₅×C₄⋊Dic₅	Direct product of C₅ and C₄⋊Dic₅	80		C5xC4:Dic5	400,85
Dic₅×C₂×C₁₀	Direct product of C₂×C₁₀ and Dic₅	80		Dic5xC2xC10	400,189
D₅×C₂²×C₁₀	Direct product of C₂²×C₁₀ and D₅	80		D5xC2^2xC10	400,219
C₅×D₁₀⋊C₄	Direct product of C₅ and D₁₀⋊C₄	80		C5xD10:C4	400,86
C₂×C₅²⋊₃C₈	Direct product of C₂ and C₅²⋊₃C₈	80		C2xC5^2:3C8	400,146
C₂×C₅²⋊₅C₈	Direct product of C₂ and C₅²⋊₅C₈	80		C2xC5^2:5C8	400,160
C₅×Q₈⋊₂D₅	Direct product of C₅ and Q₈⋊₂D₅	80	4	C5xQ8:2D5	400,188
C₅×C₁₀.D₄	Direct product of C₅ and C₁₀.D₄	80		C5xC10.D4	400,84
C₂×C₅²⋊₂D₄	Direct product of C₂ and C₅²⋊₂D₄	80		C2xC5^2:2D4	400,176
C₂×C₅²⋊₂Q₈	Direct product of C₂ and C₅²⋊₂Q₈	80		C2xC5^2:2Q8	400,178
C₂²×D₅.D₅	Direct product of C₂² and D₅.D₅	80		C2^2xD5.D5	400,215
C₄×C₂₅⋊C₄	Direct product of C₄ and C₂₅⋊C₄	100	4	C4xC25:C4	400,30
D₄×C₅⋊D₅	Direct product of D₄ and C₅⋊D₅	100		D4xC5:D5	400,195
C₄×C₅⋊F₅	Direct product of C₄ and C₅⋊F₅	100		C4xC5:F5	400,151
C₂²×C₂₅⋊C₄	Direct product of C₂² and C₂₅⋊C₄	100		C2^2xC25:C4	400,53
C₂²×C₅⋊F₅	Direct product of C₂² and C₅⋊F₅	100		C2^2xC5:F5	400,216
C₈×C₅⋊D₅	Direct product of C₈ and C₅⋊D₅	200		C8xC5:D5	400,92
C₂×C₄×D₂₅	Direct product of C₂×C₄ and D₂₅	200		C2xC4xD25	400,36
D₄×C₅×C₁₀	Direct product of C₅×C₁₀ and D₄	200		D4xC5xC10	400,202
Q₈×C₅⋊D₅	Direct product of Q₈ and C₅⋊D₅	200		Q8xC5:D5	400,197
C₂×C₂₅⋊D₄	Direct product of C₂ and C₂₅⋊D₄	200		C2xC25:D4	400,44
C₄○D₄×C₂₅	Direct product of C₂₅ and C₄○D₄	200	2	C4oD4xC25	400,48
C₂×C₂₀⋊D₅	Direct product of C₂ and C₂₀⋊D₅	200		C2xC20:D5	400,193
C₂³×C₅⋊D₅	Direct product of C₂³ and C₅⋊D₅	200		C2^3xC5:D5	400,220
C₂²⋊C₄×C₂₅	Direct product of C₂₅ and C₂²⋊C₄	200		C2^2:C4xC25	400,21
C₄○D₄×C₅²	Direct product of C₅² and C₄○D₄	200		C4oD4xC5^2	400,204
C₂×C₅²⋊₇D₄	Direct product of C₂ and C₅²⋊₇D₄	200		C2xC5^2:7D4	400,200
C₂²⋊C₄×C₅²	Direct product of C₅² and C₂²⋊C₄	200		C2^2:C4xC5^2	400,109
C₂×C₂₅⋊C₈	Direct product of C₂ and C₂₅⋊C₈	400		C2xC25:C8	400,32
C₄⋊C₄×C₂₅	Direct product of C₂₅ and C₄⋊C₄	400		C4:C4xC25	400,22
Q₈×C₅×C₁₀	Direct product of C₅×C₁₀ and Q₈	400		Q8xC5xC10	400,203
C₂×C₂₅⋊₂C₈	Direct product of C₂ and C₂₅⋊₂C₈	400		C2xC25:2C8	400,9
C₄⋊C₄×C₅²	Direct product of C₅² and C₄⋊C₄	400		C4:C4xC5^2	400,110
C₂×C₅²⋊₇C₈	Direct product of C₂ and C₅²⋊₇C₈	400		C2xC5^2:7C8	400,97
C₄×C₅²⋊₆C₄	Direct product of C₄ and C₅²⋊₆C₄	400		C4xC5^2:6C4	400,99
C₂×C₅²⋊₄C₈	Direct product of C₂ and C₅²⋊₄C₈	400		C2xC5^2:4C8	400,153
C₂×C₅²⋊₄Q₈	Direct product of C₂ and C₅²⋊₄Q₈	400		C2xC5^2:4Q8	400,191
C₂²×C₅²⋊₆C₄	Direct product of C₂² and C₅²⋊₆C₄	400		C2^2xC5^2:6C4	400,199
C₂×C₄×C₅⋊D₅	Direct product of C₂×C₄ and C₅⋊D₅	200		C2xC4xC5:D5	400,192

Groups of order 401

		d	ρ	Label	ID
C₄₀₁	Cyclic group	401	1	C401	401,1

Groups of order 402

		d	ρ	Label	ID
C₄₀₂	Cyclic group	402	1	C402	402,6
D₂₀₁	Dihedral group	201	2+	D201	402,5
C₆₇⋊C₆	The semidirect product of C₆₇ and C₆ acting faithfully	67	6+	C67:C6	402,1
S₃×C₆₇	Direct product of C₆₇ and S₃	201	2	S3xC67	402,3
C₃×D₆₇	Direct product of C₃ and D₆₇	201	2	C3xD67	402,4
C₂×C₆₇⋊C₃	Direct product of C₂ and C₆₇⋊C₃	134	3	C2xC67:C3	402,2

Groups of order 403

		d	ρ	Label	ID
C₄₀₃	Cyclic group	403	1	C403	403,1

Groups of order 404

		d	ρ	Label	ID
C₄₀₄	Cyclic group	404	1	C404	404,2
D₂₀₂	Dihedral group; = C₂×D₁₀₁	202	2+	D202	404,4
Dic₁₀₁	Dicyclic group; = C₁₀₁ ⋊₂ C₄	404	2-	Dic101	404,1
C₁₀₁⋊C₄	The semidirect product of C₁₀₁ and C₄ acting faithfully	101	4+	C101:C4	404,3
C₂×C₂₀₂	Abelian group of type [2,202]	404		C2xC202	404,5

Groups of order 405

		d	ρ	Label	ID
C₄₀₅	Cyclic group	405	1	C405	405,1
C₃⁴⋊C₅	The semidirect product of C₃⁴ and C₅ acting faithfully	15	5	C3^4:C5	405,15
C₉×C₄₅	Abelian group of type [9,45]	405		C9xC45	405,2
C₃×C₁₃₅	Abelian group of type [3,135]	405		C3xC135	405,5
C₃²×C₄₅	Abelian group of type [3,3,45]	405		C3^2xC45	405,11
C₃³×C₁₅	Abelian group of type [3,3,3,15]	405		C3^3xC15	405,16
C₁₅×He₃	Direct product of C₁₅ and He₃	135		C15xHe3	405,12
C₁₅×3_-¹⁺²	Direct product of C₁₅ and 3_-¹⁺²	135		C15xES-(3,1)	405,13
C₅×C₃≀C₃	Direct product of C₅ and C₃≀C₃	45	3	C5xC3wrC3	405,7
C₅×C₂₇⋊C₃	Direct product of C₅ and C₂₇⋊C₃	135	3	C5xC27:C3	405,6
C₅×C₃²⋊C₉	Direct product of C₅ and C₃²⋊C₉	135		C5xC3^2:C9	405,3
C₅×C₉○He₃	Direct product of C₅ and C₉○He₃	135	3	C5xC9oHe3	405,14
C₅×He₃⋊C₃	Direct product of C₅ and He₃⋊C₃	135	3	C5xHe3:C3	405,9
C₅×He₃.C₃	Direct product of C₅ and He₃.C₃	135	3	C5xHe3.C3	405,8
C₅×C₃.He₃	Direct product of C₅ and C₃.He₃	135	3	C5xC3.He3	405,10
C₅×C₉⋊C₉	Direct product of C₅ and C₉⋊C₉	405		C5xC9:C9	405,4

Groups of order 406

		d	ρ	Label	ID
C₄₀₆	Cyclic group	406	1	C406	406,6
D₂₀₃	Dihedral group	203	2+	D203	406,5
C₂₉⋊C₁₄	The semidirect product of C₂₉ and C₁₄ acting faithfully	29	14+	C29:C14	406,1
D₇×C₂₉	Direct product of C₂₉ and D₇	203	2	D7xC29	406,3
C₇×D₂₉	Direct product of C₇ and D₂₉	203	2	C7xD29	406,4
C₂×C₂₉⋊C₇	Direct product of C₂ and C₂₉⋊C₇	58	7	C2xC29:C7	406,2

Groups of order 407

		d	ρ	Label	ID
C₄₀₇	Cyclic group	407	1	C407	407,1

Groups of order 408

		d	ρ	Label	ID
C₄₀₈	Cyclic group	408	1	C408	408,4
D₂₀₄	Dihedral group	204	2+	D204	408,27
Dic₁₀₂	Dicyclic group; = C₅₁ ⋊₂ Q₈	408	2-	Dic102	408,25
C₅₁⋊C₈	1^st semidirect product of C₅₁ and C₈ acting faithfully	51	8	C51:C8	408,34
C₁₇⋊S₄	The semidirect product of C₁₇ and S₄ acting via S₄/A₄=C₂	68	6+	C17:S4	408,37
C₅₁⋊D₄	1^st semidirect product of C₅₁ and D₄ acting via D₄/C₂=C₂²	204	4-	C51:D4	408,10
C₃⋊D₆₈	The semidirect product of C₃ and D₆₈ acting via D₆₈/D₃₄=C₂	204	4+	C3:D68	408,11
C₅₁⋊₇D₄	1^st semidirect product of C₅₁ and D₄ acting via D₄/C₂²=C₂	204	2	C51:7D4	408,29
C₁₇⋊D₁₂	The semidirect product of C₁₇ and D₁₂ acting via D₁₂/D₆=C₂	204	4+	C17:D12	408,12
D₅₁⋊₂C₄	The semidirect product of D₅₁ and C₄ acting via C₄/C₂=C₂	204	4+	D51:2C4	408,9
C₅₁⋊Q₈	The semidirect product of C₅₁ and Q₈ acting via Q₈/C₂=C₂²	408	4-	C51:Q8	408,13
C₅₁⋊₅C₈	1^st semidirect product of C₅₁ and C₈ acting via C₈/C₄=C₂	408	2	C51:5C8	408,3
C₅₁⋊₃C₈	1^st semidirect product of C₅₁ and C₈ acting via C₈/C₂=C₄	408	4	C51:3C8	408,6
C₂×C₂₀₄	Abelian group of type [2,204]	408		C2xC204	408,30
C₂²×C₁₀₂	Abelian group of type [2,2,102]	408		C2^2xC102	408,46
C₁₇×S₄	Direct product of C₁₇ and S₄	68	3	C17xS4	408,36
A₄×D₁₇	Direct product of A₄ and D₁₇	68	6+	A4xD17	408,38
A₄×C₃₄	Direct product of C₃₄ and A₄	102	3	A4xC34	408,42
C₁₇×SL₂(𝔽₃)	Direct product of C₁₇ and SL₂(𝔽₃)	136	2	C17xSL(2,3)	408,14
S₃×C₆₈	Direct product of C₆₈ and S₃	204	2	S3xC68	408,21
C₃×D₆₈	Direct product of C₃ and D₆₈	204	2	C3xD68	408,17
C₄×D₅₁	Direct product of C₄ and D₅₁	204	2	C4xD51	408,26
D₄×C₅₁	Direct product of C₅₁ and D₄	204	2	D4xC51	408,31
C₁₂×D₁₇	Direct product of C₁₂ and D₁₇	204	2	C12xD17	408,16
C₁₇×D₁₂	Direct product of C₁₇ and D₁₂	204	2	C17xD12	408,22
Dic₃×D₁₇	Direct product of Dic₃ and D₁₇	204	4-	Dic3xD17	408,7
S₃×Dic₁₇	Direct product of S₃ and Dic₁₇	204	4-	S3xDic17	408,8
C₂²×D₅₁	Direct product of C₂² and D₅₁	204		C2^2xD51	408,45
Q₈×C₅₁	Direct product of C₅₁ and Q₈	408	2	Q8xC51	408,32
C₃×Dic₃₄	Direct product of C₃ and Dic₃₄	408	2	C3xDic34	408,15
C₆×Dic₁₇	Direct product of C₆ and Dic₁₇	408		C6xDic17	408,18
C₁₇×Dic₆	Direct product of C₁₇ and Dic₆	408	2	C17xDic6	408,20
Dic₃×C₃₄	Direct product of C₃₄ and Dic₃	408		Dic3xC34	408,23
C₂×Dic₅₁	Direct product of C₂ and Dic₅₁	408		C2xDic51	408,28
C₃×C₁₇⋊C₈	Direct product of C₃ and C₁₇⋊C₈	51	8	C3xC17:C8	408,33
S₃×C₁₇⋊C₄	Direct product of S₃ and C₁₇⋊C₄	51	8+	S3xC17:C4	408,35
C₆×C₁₇⋊C₄	Direct product of C₆ and C₁₇⋊C₄	102	4	C6xC17:C4	408,39
C₂×S₃×D₁₇	Direct product of C₂, S₃ and D₁₇	102	4+	C2xS3xD17	408,41
C₂×C₅₁⋊C₄	Direct product of C₂ and C₅₁⋊C₄	102	4	C2xC51:C4	408,40
S₃×C₂×C₃₄	Direct product of C₂×C₃₄ and S₃	204		S3xC2xC34	408,44
C₂×C₆×D₁₇	Direct product of C₂×C₆ and D₁₇	204		C2xC6xD17	408,43
C₃×C₁₇⋊D₄	Direct product of C₃ and C₁₇⋊D₄	204	2	C3xC17:D4	408,19
C₁₇×C₃⋊D₄	Direct product of C₁₇ and C₃⋊D₄	204	2	C17xC3:D4	408,24
C₁₇×C₃⋊C₈	Direct product of C₁₇ and C₃⋊C₈	408	2	C17xC3:C8	408,1
C₃×C₁₇⋊₃C₈	Direct product of C₃ and C₁₇⋊₃C₈	408	2	C3xC17:3C8	408,2
C₃×C₁₇⋊₂C₈	Direct product of C₃ and C₁₇⋊₂C₈	408	4	C3xC17:2C8	408,5

Groups of order 409

		d	ρ	Label	ID
C₄₀₉	Cyclic group	409	1	C409	409,1

Groups of order 410

		d	ρ	Label	ID
C₄₁₀	Cyclic group	410	1	C410	410,6
D₂₀₅	Dihedral group	205	2+	D205	410,5
C₄₁⋊C₁₀	The semidirect product of C₄₁ and C₁₀ acting faithfully	41	10+	C41:C10	410,1
D₅×C₄₁	Direct product of C₄₁ and D₅	205	2	D5xC41	410,3
C₅×D₄₁	Direct product of C₅ and D₄₁	205	2	C5xD41	410,4
C₂×C₄₁⋊C₅	Direct product of C₂ and C₄₁⋊C₅	82	5	C2xC41:C5	410,2

Groups of order 411

		d	ρ	Label	ID
C₄₁₁	Cyclic group	411	1	C411	411,1

Groups of order 412

		d	ρ	Label	ID
C₄₁₂	Cyclic group	412	1	C412	412,2
D₂₀₆	Dihedral group; = C₂×D₁₀₃	206	2+	D206	412,3
Dic₁₀₃	Dicyclic group; = C₁₀₃ ⋊C₄	412	2-	Dic103	412,1
C₂×C₂₀₆	Abelian group of type [2,206]	412		C2xC206	412,4

Groups of order 413

		d	ρ	Label	ID
C₄₁₃	Cyclic group	413	1	C413	413,1

Groups of order 414

		d	ρ	Label	ID
C₄₁₄	Cyclic group	414	1	C414	414,4
D₂₀₇	Dihedral group	207	2+	D207	414,3
C₃⋊D₆₉	The semidirect product of C₃ and D₆₉ acting via D₆₉/C₆₉=C₂	207		C3:D69	414,9
C₃×C₁₃₈	Abelian group of type [3,138]	414		C3xC138	414,10
S₃×C₆₉	Direct product of C₆₉ and S₃	138	2	S3xC69	414,6
C₃×D₆₉	Direct product of C₃ and D₆₉	138	2	C3xD69	414,7
D₉×C₂₃	Direct product of C₂₃ and D₉	207	2	D9xC23	414,1
C₉×D₂₃	Direct product of C₉ and D₂₃	207	2	C9xD23	414,2
C₃²×D₂₃	Direct product of C₃² and D₂₃	207		C3^2xD23	414,5
C₃⋊S₃×C₂₃	Direct product of C₂₃ and C₃⋊S₃	207		C3:S3xC23	414,8

Groups of order 415

		d	ρ	Label	ID
C₄₁₅	Cyclic group	415	1	C415	415,1

Groups of order 416

		d	ρ	Label	ID
C₄₁₆	Cyclic group	416	1	C416	416,2
D₂₀₈	Dihedral group	208	2+	D208	416,6
Dic₁₀₄	Dicyclic group; = C₁₃ ⋊₁ Q₃₂	416	2-	Dic104	416,8
C₈⋊D₂₆	1^st semidirect product of C₈ and D₂₆ acting via D₂₆/C₁₃=C₂²	104	4+	C8:D26	416,129
C₁₀₄⋊C₄	4^th semidirect product of C₁₀₄ and C₄ acting faithfully	104	4	C104:C4	416,67
D₅₂⋊₄C₄	1^st semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	104	2	D52:4C4	416,12
D₅₂⋊₇C₄	4^th semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	104	4	D52:7C4	416,32
D₅₂⋊₁C₄	1^st semidirect product of D₅₂ and C₄ acting faithfully	104	8+	D52:1C4	416,82
D₅₂⋊C₄	2^nd semidirect product of D₅₂ and C₄ acting faithfully	104	8+	D52:C4	416,85
D₈⋊D₁₃	2^nd semidirect product of D₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	4	D8:D13	416,132
D₄⋊D₂₆	2^nd semidirect product of D₄ and D₂₆ acting via D₂₆/C₂₆=C₂	104	4+	D4:D26	416,170
D₄⋊₆D₂₆	2^nd semidirect product of D₄ and D₂₆ acting through Inn(D₄)	104	4	D4:6D26	416,218
D₄⋊₈D₂₆	4^th semidirect product of D₄ and D₂₆ acting through Inn(D₄)	104	4+	D4:8D26	416,223
Q₈⋊D₂₆	2^nd semidirect product of Q₈ and D₂₆ acting via D₂₆/D₁₃=C₂	104	4+	Q8:D26	416,135
D₁₃⋊M₄(2)	The semidirect product of D₁₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	104	4	D13:M4(2)	416,201
C₂²⋊D₅₂	The semidirect product of C₂² and D₅₂ acting via D₅₂/D₂₆=C₂	104		C2^2:D52	416,103
C₂³⋊D₂₆	1^st semidirect product of C₂³ and D₂₆ acting via D₂₆/C₁₃=C₂²	104		C2^3:D26	416,158
C₂⁴⋊D₁₃	1^st semidirect product of C₂⁴ and D₁₃ acting via D₁₃/C₁₃=C₂	104		C2^4:D13	416,174
C₂³⋊Dic₁₃	The semidirect product of C₂³ and Dic₁₃ acting via Dic₁₃/C₁₃=C₄	104	4	C2^3:Dic13	416,41
Dic₂₆⋊C₄	1^st semidirect product of Dic₂₆ and C₄ acting faithfully	104	8-	Dic26:C4	416,83
D₅₂⋊₆C₂²	4^th semidirect product of D₅₂ and C₂² acting via C₂²/C₂=C₂	104	4	D52:6C2^2	416,153
D₁₃⋊C₁₆	The semidirect product of D₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	4	D13:C16	416,64
C₄⋊D₅₂	The semidirect product of C₄ and D₅₂ acting via D₅₂/C₅₂=C₂	208		C4:D52	416,95
C₄⋊₂D₅₂	The semidirect product of C₄ and D₅₂ acting via D₅₂/D₂₆=C₂	208		C4:2D52	416,116
C₅₂⋊₇D₄	1^st semidirect product of C₅₂ and D₄ acting via D₄/C₂²=C₂	208		C52:7D4	416,151
C₅₂⋊₂D₄	2^nd semidirect product of C₅₂ and D₄ acting via D₄/C₂=C₂²	208		C52:2D4	416,159
C₅₂⋊D₄	3^rd semidirect product of C₅₂ and D₄ acting via D₄/C₂=C₂²	208		C52:D4	416,161
C₁₃⋊D₁₆	The semidirect product of C₁₃ and D₁₆ acting via D₁₆/D₈=C₂	208	4+	C13:D16	416,33
C₂₀₈⋊C₂	4^th semidirect product of C₂₀₈ and C₂ acting faithfully	208	2	C208:C2	416,5
D₅₂⋊₆C₄	3^rd semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	208		D52:6C4	416,16
D₂₆⋊₁C₈	1^st semidirect product of D₂₆ and C₈ acting via C₈/C₄=C₂	208		D26:1C8	416,27
D₅₂⋊₅C₄	2^nd semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	208		D52:5C4	416,28
D₂₆⋊C₈	2^nd semidirect product of D₂₆ and C₈ acting via C₈/C₄=C₂	208		D26:C8	416,78
D₂₆⋊D₄	1^st semidirect product of D₂₆ and D₄ acting via D₄/C₄=C₂	208		D26:D4	416,105
D₅₂⋊₈C₄	5^th semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	208		D52:8C4	416,114
D₈⋊₃D₁₃	The semidirect product of D₈ and D₁₃ acting through Inn(D₈)	208	4-	D8:3D13	416,133
C₁₆⋊D₁₃	2^nd semidirect product of C₁₆ and D₁₃ acting via D₁₃/C₁₃=C₂	208	2	C16:D13	416,7
D₂₆⋊Q₈	1^st semidirect product of D₂₆ and Q₈ acting via Q₈/C₄=C₂	208		D26:Q8	416,117
D₂₆⋊₂Q₈	2^nd semidirect product of D₂₆ and Q₈ acting via Q₈/C₄=C₂	208		D26:2Q8	416,118
D₂₆⋊₃Q₈	3^rd semidirect product of D₂₆ and Q₈ acting via Q₈/C₄=C₂	208		D26:3Q8	416,167
D₁₀₄⋊₇C₂	The semidirect product of D₁₀₄ and C₂ acting through Inn(D₁₀₄)	208	2	D104:7C2	416,125
D₁₀₄⋊C₂	5^th semidirect product of D₁₀₄ and C₂ acting faithfully	208	4+	D104:C2	416,140
Q₁₆⋊D₁₃	2^nd semidirect product of Q₁₆ and D₁₃ acting via D₁₃/C₁₃=C₂	208	4	Q16:D13	416,139
C₄²⋊D₁₃	1^st semidirect product of C₄² and D₁₃ acting via D₁₃/C₁₃=C₂	208		C4^2:D13	416,93
C₄²⋊₂D₁₃	2^nd semidirect product of C₄² and D₁₃ acting via D₁₃/C₁₃=C₂	208		C4^2:2D13	416,97
D₄⋊Dic₁₃	1^st semidirect product of D₄ and Dic₁₃ acting via Dic₁₃/C₂₆=C₂	208		D4:Dic13	416,39
Dic₁₃⋊₄D₄	1^st semidirect product of Dic₁₃ and D₄ acting through Inn(Dic₁₃)	208		Dic13:4D4	416,102
Dic₁₃⋊D₄	2^nd semidirect product of Dic₁₃ and D₄ acting via D₄/C₂²=C₂	208		Dic13:D4	416,160
C₂²⋊Dic₂₆	The semidirect product of C₂² and Dic₂₆ acting via Dic₂₆/Dic₁₃=C₂	208		C2^2:Dic26	416,99
C₁₃⋊C₃₂	The semidirect product of C₁₃ and C₃₂ acting via C₃₂/C₈=C₄	416	4	C13:C32	416,3
C₅₂⋊Q₈	The semidirect product of C₅₂ and Q₈ acting via Q₈/C₂=C₂²	416		C52:Q8	416,109
C₅₂⋊₃C₈	1^st semidirect product of C₅₂ and C₈ acting via C₈/C₄=C₂	416		C52:3C8	416,11
C₅₂⋊C₈	1^st semidirect product of C₅₂ and C₈ acting via C₈/C₂=C₄	416		C52:C8	416,76
C₁₃⋊₂C₃₂	The semidirect product of C₁₃ and C₃₂ acting via C₃₂/C₁₆=C₂	416	2	C13:2C32	416,1
C₅₂⋊₂Q₈	1^st semidirect product of C₅₂ and Q₈ acting via Q₈/C₄=C₂	416		C52:2Q8	416,90
C₁₀₄⋊₈C₄	4^th semidirect product of C₁₀₄ and C₄ acting via C₄/C₂=C₂	416		C104:8C4	416,22
C₁₀₄⋊₆C₄	2^nd semidirect product of C₁₀₄ and C₄ acting via C₄/C₂=C₂	416		C104:6C4	416,24
C₁₀₄⋊₅C₄	1^st semidirect product of C₁₀₄ and C₄ acting via C₄/C₂=C₂	416		C104:5C4	416,25
C₁₃⋊Q₃₂	The semidirect product of C₁₃ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	416	4-	C13:Q32	416,36
Q₈⋊Dic₁₃	1^st semidirect product of Q₈ and Dic₁₃ acting via Dic₁₃/C₂₆=C₂	416		Q8:Dic13	416,42
Dic₁₃⋊C₈	3^rd semidirect product of Dic₁₃ and C₈ acting via C₈/C₄=C₂	416		Dic13:C8	416,79
Dic₁₃⋊₃Q₈	The semidirect product of Dic₁₃ and Q₈ acting through Inn(Dic₁₃)	416		Dic13:3Q8	416,108
Dic₁₃⋊Q₈	2^nd semidirect product of Dic₁₃ and Q₈ acting via Q₈/C₄=C₂	416		Dic13:Q8	416,165
C₄⋊C₄⋊₇D₁₃	1^st semidirect product of C₄⋊C₄ and D₁₃ acting through Inn(C₄⋊C₄)	208		C4:C4:7D13	416,113
C₄⋊C₄⋊D₁₃	6^th semidirect product of C₄⋊C₄ and D₁₃ acting via D₁₃/C₁₃=C₂	208		C4:C4:D13	416,119
C₅₂.D₄	8^th non-split extension by C₅₂ of D₄ acting via D₄/C₂=C₂²	104	4	C52.D4	416,40
D₂₆.₈D₄	4^th non-split extension by D₂₆ of D₄ acting via D₄/C₄=C₂	104	4	D26.8D4	416,68
D₁₃.D₈	The non-split extension by D₁₃ of D₈ acting via D₈/C₈=C₂	104	4	D13.D8	416,69
D₂₆.D₄	1^st non-split extension by D₂₆ of D₄ acting via D₄/C₂=C₂²	104	4+	D26.D4	416,74
D₂₆.₄D₄	4^th non-split extension by D₂₆ of D₄ acting via D₄/C₂=C₂²	104	4	D26.4D4	416,86
C₅₂.₄₆D₄	3^rd non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	104	4+	C52.46D4	416,30
C₅₂.₅₆D₄	13^rd non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	104	4	C52.56D4	416,44
D₂₆.Q₈	3^rd non-split extension by D₂₆ of Q₈ acting via Q₈/C₄=C₂	104		D26.Q8	416,81
D₁₃.Q₁₆	The non-split extension by D₁₃ of Q₁₆ acting via Q₁₆/Q₈=C₂	104	8-	D13.Q16	416,84
C₂².₂D₅₂	1^st non-split extension by C₂² of D₅₂ acting via D₅₂/D₂₆=C₂	104	4	C2^2.2D52	416,13
Dic₁₃.₄D₄	4^th non-split extension by Dic₁₃ of D₄ acting via D₄/C₂=C₂²	104	4	Dic13.4D4	416,88
D₂₆.C₂³	11^st non-split extension by D₂₆ of C₂³ acting via C₂³/C₂²=C₂	104	4	D26.C2^3	416,204
D₈.D₁₃	The non-split extension by D₈ of D₁₃ acting via D₁₃/C₁₃=C₂	208	4-	D8.D13	416,34
D₅₂.C₄	The non-split extension by D₅₂ of C₄ acting faithfully	208	8+	D52.C4	416,207
C₅₂.₄C₈	1^st non-split extension by C₅₂ of C₈ acting via C₈/C₄=C₂	208	2	C52.4C8	416,19
C₅₂.C₈	1^st non-split extension by C₅₂ of C₈ acting via C₈/C₂=C₄	208	4	C52.C8	416,73
C₈.₆D₂₆	3^rd non-split extension by C₈ of D₂₆ acting via D₂₆/D₁₃=C₂	208	4+	C8.6D26	416,35
C₄.D₅₂	5^th non-split extension by C₄ of D₅₂ acting via D₅₂/C₅₂=C₂	208		C4.D52	416,96
C₈.D₂₆	1^st non-split extension by C₈ of D₂₆ acting via D₂₆/C₁₃=C₂²	208	4-	C8.D26	416,130
C₁₀₄.₆C₄	1^st non-split extension by C₁₀₄ of C₄ acting via C₄/C₂=C₂	208	2	C104.6C4	416,26
C₁₀₄.C₄	2^nd non-split extension by C₁₀₄ of C₄ acting faithfully	208	4	C104.C4	416,70
C₁₀₄.₁C₄	1^st non-split extension by C₁₀₄ of C₄ acting faithfully	208	4	C104.1C4	416,71
D₂₆.C₈	3^rd non-split extension by D₂₆ of C₈ acting via C₈/C₄=C₂	208	4	D26.C8	416,65
D₅₂.₃C₄	The non-split extension by D₅₂ of C₄ acting through Inn(D₅₂)	208	2	D52.3C4	416,122
D₅₂.₂C₄	The non-split extension by D₅₂ of C₄ acting via C₄/C₂=C₂	208	4	D52.2C4	416,128
D₄.D₂₆	4^th non-split extension by D₄ of D₂₆ acting via D₂₆/D₁₃=C₂	208	4-	D4.D26	416,136
D₂₆.₆D₄	2^nd non-split extension by D₂₆ of D₄ acting via D₄/C₄=C₂	208	4	D26.6D4	416,137
D₄.₉D₂₆	4^th non-split extension by D₄ of D₂₆ acting via D₂₆/C₂₆=C₂	208	4-	D4.9D26	416,172
C₅₂.₅₃D₄	10^th non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	208	4	C52.53D4	416,29
C₄.₁₂D₅₂	4^th non-split extension by C₄ of D₅₂ acting via D₅₂/D₂₆=C₂	208	4-	C4.12D52	416,31
C₅₂.₅₅D₄	12^nd non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	208		C52.55D4	416,37
C₅₂.₁₀D₄	10^th non-split extension by C₅₂ of D₄ acting via D₄/C₂=C₂²	208	4	C52.10D4	416,43
C₅₂.₄₈D₄	5^th non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	208		C52.48D4	416,145
C₅₂.₁₇D₄	17^th non-split extension by C₅₂ of D₄ acting via D₄/C₂=C₂²	208		C52.17D4	416,157
C₅₂.₂₃D₄	23^rd non-split extension by C₅₂ of D₄ acting via D₄/C₂=C₂²	208		C52.23D4	416,168
D₄.Dic₁₃	The non-split extension by D₄ of Dic₁₃ acting through Inn(D₄)	208	4	D4.Dic13	416,169
Dic₂₆.C₄	The non-split extension by Dic₂₆ of C₄ acting faithfully	208	8-	Dic26.C4	416,205
Q₈.D₂₆	1^st non-split extension by Q₈ of D₂₆ acting via D₂₆/C₂₆=C₂	208	4	Q8.D26	416,163
D₂₆.₁₂D₄	1^st non-split extension by D₂₆ of D₄ acting via D₄/C₂²=C₂	208		D26.12D4	416,104
D₂₆.₁₃D₄	2^nd non-split extension by D₂₆ of D₄ acting via D₄/C₂²=C₂	208		D26.13D4	416,115
D₄.₁₀D₂₆	The non-split extension by D₄ of D₂₆ acting through Inn(D₄)	208	4-	D4.10D26	416,224
Q₈.₁₀D₂₆	1^st non-split extension by Q₈ of D₂₆ acting through Inn(Q₈)	208	4	Q8.10D26	416,221
C₂³.D₂₆	3^rd non-split extension by C₂³ of D₂₆ acting via D₂₆/C₁₃=C₂²	208		C2^3.D26	416,100
C₂³.₆D₂₆	6^th non-split extension by C₂³ of D₂₆ acting via D₂₆/C₁₃=C₂²	208		C2^3.6D26	416,106
C₂².D₅₂	3^rd non-split extension by C₂² of D₅₂ acting via D₅₂/D₂₆=C₂	208		C2^2.D52	416,107
C₅₂.C₂³	18^th non-split extension by C₅₂ of C₂³ acting via C₂³/C₂=C₂²	208	4	C52.C2^3	416,171
Dic₁₃.D₄	1^st non-split extension by Dic₁₃ of D₄ acting via D₄/C₂=C₂²	208	4-	Dic13.D4	416,80
C₂³.₁₁D₂₆	1^st non-split extension by C₂³ of D₂₆ acting via D₂₆/D₁₃=C₂	208		C2^3.11D26	416,98
C₂³.₂₁D₂₆	2^nd non-split extension by C₂³ of D₂₆ acting via D₂₆/C₂₆=C₂	208		C2^3.21D26	416,147
C₂³.₂₃D₂₆	4^th non-split extension by C₂³ of D₂₆ acting via D₂₆/C₂₆=C₂	208		C2^3.23D26	416,150
C₂³.₁₈D₂₆	8^th non-split extension by C₂³ of D₂₆ acting via D₂₆/D₁₃=C₂	208		C2^3.18D26	416,156
C₂₆.M₄(2)	2^nd non-split extension by C₂₆ of M₄(2) acting via M₄(2)/C₂²=C₄	208		C26.M4(2)	416,87
C₂₆.D₈	1^st non-split extension by C₂₆ of D₈ acting via D₈/D₄=C₂	416		C26.D8	416,14
C₅₂.Q₈	2^nd non-split extension by C₅₂ of Q₈ acting via Q₈/C₂=C₂²	416		C52.Q8	416,15
C₅₂.₈Q₈	5^th non-split extension by C₅₂ of Q₈ acting via Q₈/C₄=C₂	416		C52.8Q8	416,21
C₅₂.₆Q₈	3^rd non-split extension by C₅₂ of Q₈ acting via Q₈/C₄=C₂	416		C52.6Q8	416,91
C₅₂.₄₄D₄	1^st non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	416		C52.44D4	416,23
C₂₆.Q₁₆	2^nd non-split extension by C₂₆ of Q₁₆ acting via Q₁₆/Q₈=C₂	416		C26.Q16	416,17
C₂₆.₇C₄²	2^nd non-split extension by C₂₆ of C₄² acting via C₄²/C₂×C₄=C₂	416		C26.7C4^2	416,10
C₂₆.C₄²	4^th non-split extension by C₂₆ of C₄² acting via C₄²/C₄=C₄	416		C26.C4^2	416,77
C₄.Dic₂₆	3^rd non-split extension by C₄ of Dic₂₆ acting via Dic₂₆/Dic₁₃=C₂	416		C4.Dic26	416,111
C₂₆.₁₀C₄²	5^th non-split extension by C₂₆ of C₄² acting via C₄²/C₂×C₄=C₂	416		C26.10C4^2	416,38
Dic₁₃.Q₈	1^st non-split extension by Dic₁₃ of Q₈ acting via Q₈/C₄=C₂	416		Dic13.Q8	416,110
C₄×C₁₀₄	Abelian group of type [4,104]	416		C4xC104	416,46
C₂×C₂₀₈	Abelian group of type [2,208]	416		C2xC208	416,59
C₂³×C₅₂	Abelian group of type [2,2,2,52]	416		C2^3xC52	416,227
C₂⁴×C₂₆	Abelian group of type [2,2,2,2,26]	416		C2^4xC26	416,235
C₂²×C₁₀₄	Abelian group of type [2,2,104]	416		C2^2xC104	416,190
C₂×C₄×C₅₂	Abelian group of type [2,4,52]	416		C2xC4xC52	416,175
D₈×D₁₃	Direct product of D₈ and D₁₃	104	4+	D8xD13	416,131
SD₁₆×D₁₃	Direct product of SD₁₆ and D₁₃	104	4	SD16xD13	416,134
M₄(2)×D₁₃	Direct product of M₄(2) and D₁₃	104	4	M4(2)xD13	416,127
C₁₃×2₊¹⁺⁴	Direct product of C₁₃ and 2₊¹⁺⁴	104	4	C13xES+(2,2)	416,231
C₄×D₅₂	Direct product of C₄ and D₅₂	208		C4xD52	416,94
D₄×C₅₂	Direct product of C₅₂ and D₄	208		D4xC52	416,179
D₈×C₂₆	Direct product of C₂₆ and D₈	208		D8xC26	416,193
C₁₆×D₁₃	Direct product of C₁₆ and D₁₃	208	2	C16xD13	416,4
C₁₃×D₁₆	Direct product of C₁₃ and D₁₆	208	2	C13xD16	416,61
C₂×D₁₀₄	Direct product of C₂ and D₁₀₄	208		C2xD104	416,124
Q₁₆×D₁₃	Direct product of Q₁₆ and D₁₃	208	4-	Q16xD13	416,138
C₁₃×SD₃₂	Direct product of C₁₃ and SD₃₂	208	2	C13xSD32	416,62
D₄×Dic₁₃	Direct product of D₄ and Dic₁₃	208		D4xDic13	416,155
SD₁₆×C₂₆	Direct product of C₂₆ and SD₁₆	208		SD16xC26	416,194
C₄²×D₁₃	Direct product of C₄² and D₁₃	208		C4^2xD13	416,92
C₂²×D₅₂	Direct product of C₂² and D₅₂	208		C2^2xD52	416,214
C₂⁴×D₁₃	Direct product of C₂⁴ and D₁₃	208		C2^4xD13	416,234
C₁₃×M₅(2)	Direct product of C₁₃ and M₅(2)	208	2	C13xM5(2)	416,60
M₄(2)×C₂₆	Direct product of C₂₆ and M₄(2)	208		M4(2)xC26	416,191
C₁₃×2_-¹⁺⁴	Direct product of C₁₃ and 2_-¹⁺⁴	208	4	C13xES-(2,2)	416,232
Q₈×C₅₂	Direct product of C₅₂ and Q₈	416		Q8xC52	416,180
C₁₃×Q₃₂	Direct product of C₁₃ and Q₃₂	416	2	C13xQ32	416,63
Q₁₆×C₂₆	Direct product of C₂₆ and Q₁₆	416		Q16xC26	416,195
C₈×Dic₁₃	Direct product of C₈ and Dic₁₃	416		C8xDic13	416,20
C₄×Dic₂₆	Direct product of C₄ and Dic₂₆	416		C4xDic26	416,89
C₂×Dic₅₂	Direct product of C₂ and Dic₅₂	416		C2xDic52	416,126
Q₈×Dic₁₃	Direct product of Q₈ and Dic₁₃	416		Q8xDic13	416,166
C₂²×Dic₂₆	Direct product of C₂² and Dic₂₆	416		C2^2xDic26	416,212
C₂³×Dic₁₃	Direct product of C₂³ and Dic₁₃	416		C2^3xDic13	416,225
D₄×C₁₃⋊C₄	Direct product of D₄ and C₁₃⋊C₄	52	8+	D4xC13:C4	416,206
C₈×C₁₃⋊C₄	Direct product of C₈ and C₁₃⋊C₄	104	4	C8xC13:C4	416,66
C₂×D₄×D₁₃	Direct product of C₂, D₄ and D₁₃	104		C2xD4xD13	416,216
Q₈×C₁₃⋊C₄	Direct product of Q₈ and C₁₃⋊C₄	104	8-	Q8xC13:C4	416,208
C₁₃×C₄≀C₂	Direct product of C₁₃ and C₄≀C₂	104	2	C13xC4wrC2	416,54
C₂×C₅₂⋊C₄	Direct product of C₂ and C₅₂⋊C₄	104		C2xC52:C4	416,203
C₄○D₄×D₁₃	Direct product of C₄○D₄ and D₁₃	104	4	C4oD4xD13	416,222
C₂³×C₁₃⋊C₄	Direct product of C₂³ and C₁₃⋊C₄	104		C2^3xC13:C4	416,233
C₁₃×C₂³⋊C₄	Direct product of C₁₃ and C₂³⋊C₄	104	4	C13xC2^3:C4	416,49
C₁₃×C₈⋊C₂²	Direct product of C₁₃ and C₈⋊C₂²	104	4	C13xC8:C2^2	416,197
C₂²⋊C₄×D₁₃	Direct product of C₂²⋊C₄ and D₁₃	104		C2^2:C4xD13	416,101
C₁₃×C₄.D₄	Direct product of C₁₃ and C₄.D₄	104	4	C13xC4.D4	416,50
C₁₃×C₂²≀C₂	Direct product of C₁₃ and C₂²≀C₂	104		C13xC2^2wrC2	416,181
C₂×D₁₃.D₄	Direct product of C₂ and D₁₃.D₄	104		C2xD13.D4	416,211
C₂×C₈×D₁₃	Direct product of C₂×C₈ and D₁₃	208		C2xC8xD13	416,120
D₄×C₂×C₂₆	Direct product of C₂×C₂₆ and D₄	208		D4xC2xC26	416,228
C₂×Q₈×D₁₃	Direct product of C₂, Q₈ and D₁₃	208		C2xQ8xD13	416,219
C₄⋊C₄×D₁₃	Direct product of C₄⋊C₄ and D₁₃	208		C4:C4xD13	416,112
C₄×C₁₃⋊D₄	Direct product of C₄ and C₁₃⋊D₄	208		C4xC13:D4	416,149
C₂×D₄⋊D₁₃	Direct product of C₂ and D₄⋊D₁₃	208		C2xD4:D13	416,152
C₂×D₁₃⋊C₈	Direct product of C₂ and D₁₃⋊C₈	208		C2xD13:C8	416,199
C₁₃×C₈○D₄	Direct product of C₁₃ and C₈○D₄	208	2	C13xC8oD4	416,192
C₁₃×C₄○D₈	Direct product of C₁₃ and C₄○D₈	208	2	C13xC4oD8	416,196
C₄○D₄×C₂₆	Direct product of C₂₆ and C₄○D₄	208		C4oD4xC26	416,230
C₂×C₈⋊D₁₃	Direct product of C₂ and C₈⋊D₁₃	208		C2xC8:D13	416,121
C₁₃×C₄⋊D₄	Direct product of C₁₃ and C₄⋊D₄	208		C13xC4:D4	416,182
C₂×Q₈⋊D₁₃	Direct product of C₂ and Q₈⋊D₁₃	208		C2xQ8:D13	416,162
C₂×C₁₀₄⋊C₂	Direct product of C₂ and C₁₀₄⋊C₂	208		C2xC104:C2	416,123
C₂²×C₄×D₁₃	Direct product of C₂²×C₄ and D₁₃	208		C2^2xC4xD13	416,213
C₁₃×D₄⋊C₄	Direct product of C₁₃ and D₄⋊C₄	208		C13xD4:C4	416,52
C₁₃×C₈.C₄	Direct product of C₁₃ and C₈.C₄	208	2	C13xC8.C4	416,58
C₂×D₂₆⋊C₄	Direct product of C₂ and D₂₆⋊C₄	208		C2xD26:C4	416,148
C₂×C₅₂.C₄	Direct product of C₂ and C₅₂.C₄	208		C2xC52.C4	416,200
C₂×D₅₂⋊C₂	Direct product of C₂ and D₅₂⋊C₂	208		C2xD52:C2	416,220
C₁₃×C₄⋊₁D₄	Direct product of C₁₃ and C₄⋊₁D₄	208		C13xC4:1D4	416,188
C₁₃×C₂²⋊C₈	Direct product of C₁₃ and C₂²⋊C₈	208		C13xC2^2:C8	416,48
C₂²⋊C₄×C₂₆	Direct product of C₂₆ and C₂²⋊C₄	208		C2^2:C4xC26	416,176
C₂×D₄.D₁₃	Direct product of C₂ and D₄.D₁₃	208		C2xD4.D13	416,154
C₂²×C₁₃⋊D₄	Direct product of C₂² and C₁₃⋊D₄	208		C2^2xC13:D4	416,226
C₁₃×C₂²⋊Q₈	Direct product of C₁₃ and C₂²⋊Q₈	208		C13xC2^2:Q8	416,183
C₂×C₅₂.₄C₄	Direct product of C₂ and C₅₂.₄C₄	208		C2xC52.4C4	416,142
C₂×D₅₂⋊₅C₂	Direct product of C₂ and D₅₂⋊₅C₂	208		C2xD52:5C2	416,215
C₂×D₄⋊₂D₁₃	Direct product of C₂ and D₄⋊₂D₁₃	208		C2xD4:2D13	416,217
C₁₃×C₄²⋊C₂	Direct product of C₁₃ and C₄²⋊C₂	208		C13xC4^2:C2	416,178
C₁₃×C₄.₄D₄	Direct product of C₁₃ and C₄.₄D₄	208		C13xC4.4D4	416,185
C₁₃×C₈.C₂²	Direct product of C₁₃ and C₈.C₂²	208	4	C13xC8.C2^2	416,198
C₂×C₁₃⋊M₄(2)	Direct product of C₂ and C₁₃⋊M₄(2)	208		C2xC13:M4(2)	416,210
C₂×C₂³.D₁₃	Direct product of C₂ and C₂³.D₁₃	208		C2xC2^3.D13	416,173
C₁₃×C₄²⋊₂C₂	Direct product of C₁₃ and C₄²⋊₂C₂	208		C13xC4^2:2C2	416,187
C₁₃×C₄.₁₀D₄	Direct product of C₁₃ and C₄.₁₀D₄	208	4	C13xC4.10D4	416,51
C₁₃×C₂².D₄	Direct product of C₁₃ and C₂².D₄	208		C13xC2^2.D4	416,184
C₄×C₁₃⋊C₈	Direct product of C₄ and C₁₃⋊C₈	416		C4xC13:C8	416,75
C₁₃×C₄⋊C₈	Direct product of C₁₃ and C₄⋊C₈	416		C13xC4:C8	416,55
C₄⋊C₄×C₂₆	Direct product of C₂₆ and C₄⋊C₄	416		C4:C4xC26	416,177
C₂×C₁₃⋊C₁₆	Direct product of C₂ and C₁₃⋊C₁₆	416		C2xC13:C16	416,72
Q₈×C₂×C₂₆	Direct product of C₂×C₂₆ and Q₈	416		Q8xC2xC26	416,229
C₁₃×C₄⋊Q₈	Direct product of C₁₃ and C₄⋊Q₈	416		C13xC4:Q8	416,189
C₁₃×C₈⋊C₄	Direct product of C₁₃ and C₈⋊C₄	416		C13xC8:C4	416,47
C₄×C₁₃⋊₂C₈	Direct product of C₄ and C₁₃⋊₂C₈	416		C4xC13:2C8	416,9
C₂²×C₁₃⋊C₈	Direct product of C₂² and C₁₃⋊C₈	416		C2^2xC13:C8	416,209
C₂×C₄×Dic₁₃	Direct product of C₂×C₄ and Dic₁₃	416		C2xC4xDic13	416,143
C₂×C₅₂⋊₃C₄	Direct product of C₂ and C₅₂⋊₃C₄	416		C2xC52:3C4	416,146
C₂×C₁₃⋊Q₁₆	Direct product of C₂ and C₁₃⋊Q₁₆	416		C2xC13:Q16	416,164
C₂×C₁₃⋊₂C₁₆	Direct product of C₂ and C₁₃⋊₂C₁₆	416		C2xC13:2C16	416,18
C₁₃×Q₈⋊C₄	Direct product of C₁₃ and Q₈⋊C₄	416		C13xQ8:C4	416,53
C₁₃×C₂.D₈	Direct product of C₁₃ and C₂.D₈	416		C13xC2.D8	416,57
C₂×C₂₆.D₄	Direct product of C₂ and C₂₆.D₄	416		C2xC26.D4	416,144
C₁₃×C₄.Q₈	Direct product of C₁₃ and C₄.Q₈	416		C13xC4.Q8	416,56
C₂²×C₁₃⋊₂C₈	Direct product of C₂² and C₁₃⋊₂C₈	416		C2^2xC13:2C8	416,141
C₁₃×C₂.C₄²	Direct product of C₁₃ and C₂.C₄²	416		C13xC2.C4^2	416,45
C₁₃×C₄².C₂	Direct product of C₁₃ and C₄².C₂	416		C13xC4^2.C2	416,186
C₂×C₄×C₁₃⋊C₄	Direct product of C₂×C₄ and C₁₃⋊C₄	104		C2xC4xC13:C4	416,202

Groups of order 417

		d	ρ	Label	ID
C₄₁₇	Cyclic group	417	1	C417	417,2
C₁₃₉⋊C₃	The semidirect product of C₁₃₉ and C₃ acting faithfully	139	3	C139:C3	417,1

Groups of order 418

		d	ρ	Label	ID
C₄₁₈	Cyclic group	418	1	C418	418,4
D₂₀₉	Dihedral group	209	2+	D209	418,3
C₁₉×D₁₁	Direct product of C₁₉ and D₁₁	209	2	C19xD11	418,1
C₁₁×D₁₉	Direct product of C₁₁ and D₁₉	209	2	C11xD19	418,2

Groups of order 419

		d	ρ	Label	ID
C₄₁₉	Cyclic group	419	1	C419	419,1

Groups of order 420

		d	ρ	Label	ID
C₄₂₀	Cyclic group	420	1	C420	420,12
D₂₁₀	Dihedral group; = C₂×D₁₀₅	210	2+	D210	420,40
Dic₁₀₅	Dicyclic group; = C₃ ⋊Dic₃₅	420	2-	Dic105	420,11
C₃₅⋊C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting faithfully	35	12	C35:C12	420,15
D₁₅⋊D₇	The semidirect product of D₁₅ and D₇ acting via D₇/C₇=C₂	105	4	D15:D7	420,30
C₅⋊Dic₂₁	The semidirect product of C₅ and Dic₂₁ acting via Dic₂₁/C₂₁=C₄	105	4	C5:Dic21	420,23
C₃₅⋊₃C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting via C₁₂/C₂=C₆	140	6-	C35:3C12	420,3
C₂×C₂₁₀	Abelian group of type [2,210]	420		C2xC210	420,41
C₇×A₅	Direct product of C₇ and A₅	35	3	C7xA5	420,13
D₅×F₇	Direct product of D₅ and F₇	35	12+	D5xF7	420,16
C₁₀×F₇	Direct product of C₁₀ and F₇	70	6	C10xF7	420,17
D₇×D₁₅	Direct product of D₇ and D₁₅	105	4+	D7xD15	420,26
D₅×D₂₁	Direct product of D₅ and D₂₁	105	4+	D5xD21	420,28
S₃×D₃₅	Direct product of S₃ and D₃₅	105	4+	S3xD35	420,29
F₅×C₂₁	Direct product of C₂₁ and F₅	105	4	F5xC21	420,20
A₄×C₃₅	Direct product of C₃₅ and A₄	140	3	A4xC35	420,32
S₃×C₇₀	Direct product of C₇₀ and S₃	210	2	S3xC70	420,37
D₇×C₃₀	Direct product of C₃₀ and D₇	210	2	D7xC30	420,34
D₅×C₄₂	Direct product of C₄₂ and D₅	210	2	D5xC42	420,35
C₆×D₃₅	Direct product of C₆ and D₃₅	210	2	C6xD35	420,36
C₁₀×D₂₁	Direct product of C₁₀ and D₂₁	210	2	C10xD21	420,38
C₁₄×D₁₅	Direct product of C₁₄ and D₁₅	210	2	C14xD15	420,39
C₁₅×Dic₇	Direct product of C₁₅ and Dic₇	420	2	C15xDic7	420,5
Dic₅×C₂₁	Direct product of C₂₁ and Dic₅	420	2	Dic5xC21	420,6
C₃×Dic₃₅	Direct product of C₃ and Dic₃₅	420	2	C3xDic35	420,7
Dic₃×C₃₅	Direct product of C₃₅ and Dic₃	420	2	Dic3xC35	420,8
C₅×Dic₂₁	Direct product of C₅ and Dic₂₁	420	2	C5xDic21	420,9
C₇×Dic₁₅	Direct product of C₇ and Dic₁₅	420	2	C7xDic15	420,10
F₅×C₇⋊C₃	Direct product of F₅ and C₇⋊C₃	35	12	F5xC7:C3	420,14
C₂×C₅⋊F₇	Direct product of C₂ and C₅⋊F₇	70	6+	C2xC5:F7	420,19
C₃×D₅×D₇	Direct product of C₃, D₅ and D₇	105	4	C3xD5xD7	420,24
C₅×S₃×D₇	Direct product of C₅, S₃ and D₇	105	4	C5xS3xD7	420,25
S₃×C₇×D₅	Direct product of C₇, S₃ and D₅	105	4	S3xC7xD5	420,27
C₃×C₇⋊F₅	Direct product of C₃ and C₇⋊F₅	105	4	C3xC7:F5	420,21
C₇×C₃⋊F₅	Direct product of C₇ and C₃⋊F₅	105	4	C7xC3:F5	420,22
C₅×C₇⋊A₄	Direct product of C₅ and C₇⋊A₄	140	3	C5xC7:A4	420,33
C₅×C₇⋊C₁₂	Direct product of C₅ and C₇⋊C₁₂	140	6	C5xC7:C12	420,1
C₂₀×C₇⋊C₃	Direct product of C₂₀ and C₇⋊C₃	140	3	C20xC7:C3	420,4
Dic₅×C₇⋊C₃	Direct product of Dic₅ and C₇⋊C₃	140	6	Dic5xC7:C3	420,2
C₂×D₅×C₇⋊C₃	Direct product of C₂, D₅ and C₇⋊C₃	70	6	C2xD5xC7:C3	420,18
C₂×C₁₀×C₇⋊C₃	Direct product of C₂×C₁₀ and C₇⋊C₃	140		C2xC10xC7:C3	420,31

Groups of order 421

		d	ρ	Label	ID
C₄₂₁	Cyclic group	421	1	C421	421,1

Groups of order 422

		d	ρ	Label	ID
C₄₂₂	Cyclic group	422	1	C422	422,2
D₂₁₁	Dihedral group	211	2+	D211	422,1

Groups of order 423

		d	ρ	Label	ID
C₄₂₃	Cyclic group	423	1	C423	423,1
C₃×C₁₄₁	Abelian group of type [3,141]	423		C3xC141	423,2

Groups of order 424

		d	ρ	Label	ID
C₄₂₄	Cyclic group	424	1	C424	424,2
D₂₁₂	Dihedral group	212	2+	D212	424,6
Dic₁₀₆	Dicyclic group; = C₅₃ ⋊Q₈	424	2-	Dic106	424,4
C₅₃⋊D₄	The semidirect product of C₅₃ and D₄ acting via D₄/C₂²=C₂	212	2	C53:D4	424,8
C₅₃⋊C₈	The semidirect product of C₅₃ and C₈ acting via C₈/C₂=C₄	424	4-	C53:C8	424,3
C₅₃⋊₂C₈	The semidirect product of C₅₃ and C₈ acting via C₈/C₄=C₂	424	2	C53:2C8	424,1
C₂×C₂₁₂	Abelian group of type [2,212]	424		C2xC212	424,9
C₂²×C₁₀₆	Abelian group of type [2,2,106]	424		C2^2xC106	424,14
C₄×D₅₃	Direct product of C₄ and D₅₃	212	2	C4xD53	424,5
D₄×C₅₃	Direct product of C₅₃ and D₄	212	2	D4xC53	424,10
C₂²×D₅₃	Direct product of C₂² and D₅₃	212		C2^2xD53	424,13
Q₈×C₅₃	Direct product of C₅₃ and Q₈	424	2	Q8xC53	424,11
C₂×Dic₅₃	Direct product of C₂ and Dic₅₃	424		C2xDic53	424,7
C₂×C₅₃⋊C₄	Direct product of C₂ and C₅₃⋊C₄	106	4+	C2xC53:C4	424,12

Groups of order 425

		d	ρ	Label	ID
C₄₂₅	Cyclic group	425	1	C425	425,1
C₅×C₈₅	Abelian group of type [5,85]	425		C5xC85	425,2

Groups of order 426

		d	ρ	Label	ID
C₄₂₆	Cyclic group	426	1	C426	426,4
D₂₁₃	Dihedral group	213	2+	D213	426,3
S₃×C₇₁	Direct product of C₇₁ and S₃	213	2	S3xC71	426,1
C₃×D₇₁	Direct product of C₃ and D₇₁	213	2	C3xD71	426,2

Groups of order 427

		d	ρ	Label	ID
C₄₂₇	Cyclic group	427	1	C427	427,1

Groups of order 428

		d	ρ	Label	ID
C₄₂₈	Cyclic group	428	1	C428	428,2
D₂₁₄	Dihedral group; = C₂×D₁₀₇	214	2+	D214	428,3
Dic₁₀₇	Dicyclic group; = C₁₀₇ ⋊C₄	428	2-	Dic107	428,1
C₂×C₂₁₄	Abelian group of type [2,214]	428		C2xC214	428,4

Groups of order 429

		d	ρ	Label	ID
C₄₂₉	Cyclic group	429	1	C429	429,2
C₁₁×C₁₃⋊C₃	Direct product of C₁₁ and C₁₃⋊C₃	143	3	C11xC13:C3	429,1

Groups of order 430

		d	ρ	Label	ID
C₄₃₀	Cyclic group	430	1	C430	430,4
D₂₁₅	Dihedral group	215	2+	D215	430,3
D₅×C₄₃	Direct product of C₄₃ and D₅	215	2	D5xC43	430,1
C₅×D₄₃	Direct product of C₅ and D₄₃	215	2	C5xD43	430,2

Groups of order 431

		d	ρ	Label	ID
C₄₃₁	Cyclic group	431	1	C431	431,1

Groups of order 432

		d	ρ	Label	ID
C₄₃₂	Cyclic group	432	1	C432	432,2
D₂₁₆	Dihedral group	216	2+	D216	432,8
Dic₁₀₈	Dicyclic group; = C₂₇ ⋊₁ Q₁₆	432	2-	Dic108	432,4
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	9	8+	AGL(2,3)	432,734
C₆²⋊₅D₆	5^th semidirect product of C₆² and D₆ acting faithfully	18	6+	C6^2:5D6	432,523
F₉⋊S₃	The semidirect product of F₉ and S₃ acting via S₃/C₃=C₂	24	16+	F9:S3	432,740
C₃³⋊D₈	2^nd semidirect product of C₃³ and D₈ acting via D₈/C₂=D₄	24	4	C3^3:D8	432,582
C₆²⋊Dic₃	The semidirect product of C₆² and Dic₃ acting faithfully	24	12+	C6^2:Dic3	432,743
C₃²⋊₂D₂₄	The semidirect product of C₃² and D₂₄ acting via D₂₄/C₆=D₄	24	8+	C3^2:2D24	432,588
C₆²⋊₂₄D₆	5^th semidirect product of C₆² and D₆ acting via D₆/C₃=C₂²	24	4	C6^2:24D6	432,696
C₆²⋊₁₀D₆	10^th semidirect product of C₆² and D₆ acting faithfully	24	12+	C6^2:10D6	432,748
C₃³⋊₆SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	4	C3^3:6SD16	432,583
C₃³⋊₇SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	4	C3^3:7SD16	432,584
C₃³⋊₈SD₁₆	4^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	8+	C3^3:8SD16	432,589
C₃³⋊SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting faithfully	24	8	C3^3:SD16	432,738
C₃³⋊₃SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting faithfully	24	16+	C3^3:3SD16	432,739
C₃³⋊₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	24	8+	C3^3:2M4(2)	432,573
C₆²⋊₁₁Dic₃	1^st semidirect product of C₆² and Dic₃ acting via Dic₃/C₃=C₄	24	4	C6^2:11Dic3	432,641
C₃³⋊₁₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂²=C₄	24	4	C3^3:12M4(2)	432,640
He₃⋊SD₁₆	The semidirect product of He₃ and SD₁₆ acting faithfully	27	6+	He3:SD16	432,520
C₄²⋊He₃	The semidirect product of C₄² and He₃ acting via He₃/C₃²=C₃	36	3	C4^2:He3	432,103
C₂⁴⋊He₃	The semidirect product of C₂⁴ and He₃ acting via He₃/C₃=C₃²	36	9	C2^4:He3	432,526
D₁₈⋊D₆	4^th semidirect product of D₁₈ and D₆ acting via D₆/S₃=C₂	36	4+	D18:D6	432,315
C₆²⋊A₄	2^nd semidirect product of C₆² and A₄ acting via A₄/C₂²=C₃	36		C6^2:A4	432,555
C₆²⋊D₆	1^st semidirect product of C₆² and D₆ acting faithfully	36	12+	C6^2:D6	432,323
C₆²⋊₂D₆	2^nd semidirect product of C₆² and D₆ acting faithfully	36	6	C6^2:2D6	432,324
C₆²⋊₄C₁₂	3^rd semidirect product of C₆² and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C6^2:4C12	432,272
C₆²⋊₂₃D₆	4^th semidirect product of C₆² and D₆ acting via D₆/C₃=C₂²	36		C6^2:23D6	432,686
C₆²⋊₅Dic₃	4^th semidirect product of C₆² and Dic₃ acting via Dic₃/C₂=S₃	36	6-	C6^2:5Dic3	432,251
C₆²⋊₆Dic₃	5^th semidirect product of C₆² and Dic₃ acting via Dic₃/C₂=S₃	36	3	C6^2:6Dic3	432,260
C₂⁴⋊₂3_-¹⁺²	2^nd semidirect product of C₂⁴ and 3_-¹⁺² acting via 3_-¹⁺²/C₃=C₃²	36	9	C2^4:2ES-(3,1)	432,528
C₃³⋊₉D₈	6^th semidirect product of C₃³ and D₈ acting via D₈/C₄=C₂²	48	4	C3^3:9D8	432,457
C₃³⋊₄C₁₆	2^nd semidirect product of C₃³ and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^3:4C16	432,413
C₃³⋊₉Q₁₆	6^th semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3^3:9Q16	432,459
C₃³⋊Q₁₆	2^nd semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₂=D₄	48	4	C3^3:Q16	432,585
C₃³⋊₃Q₁₆	3^rd semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₂=D₄	48	8-	C3^3:3Q16	432,590
C₃³⋊₆C₄²	3^rd semidirect product of C₃³ and C₄² acting via C₄²/C₂²=C₂²	48		C3^3:6C4^2	432,460
C₃³⋊₁₈SD₁₆	10^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₄=C₂²	48	4	C3^3:18SD16	432,458
C₃³⋊M₄(2)	1^st semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	48	8-	C3^3:M4(2)	432,572
C₃³⋊₄M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₄=C₄	48	4	C3^3:4M4(2)	432,636
C₃³⋊₁₀M₄(2)	6^th semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₄=C₂²	48	4	C3^3:10M4(2)	432,456
C₂⁴⋊3_-¹⁺²	1^st semidirect product of C₂⁴ and 3_-¹⁺² acting via 3_-¹⁺²/C₃=C₃²	54	9	C2^4:ES-(3,1)	432,527
He₃⋊D₈	The semidirect product of He₃ and D₈ acting via D₈/C₂=D₄	72	6+	He3:D8	432,235
D₇₂⋊C₃	The semidirect product of D₇₂ and C₃ acting faithfully	72	6+	D72:C3	432,123
C₇₂⋊C₆	4^th semidirect product of C₇₂ and C₆ acting faithfully	72	6	C72:C6	432,121
C₇₂⋊₂C₆	2^nd semidirect product of C₇₂ and C₆ acting faithfully	72	6	C72:2C6	432,122
D₁₈⋊C₁₂	The semidirect product of D₁₈ and C₁₂ acting via C₁₂/C₂=C₆	72		D18:C12	432,147
C₃⋊D₇₂	The semidirect product of C₃ and D₇₂ acting via D₇₂/D₃₆=C₂	72	4+	C3:D72	432,64
C₉⋊D₂₄	The semidirect product of C₉ and D₂₄ acting via D₂₄/D₁₂=C₂	72	4+	C9:D24	432,69
C₃₆⋊D₆	2^nd semidirect product of C₃₆ and D₆ acting via D₆/C₃=C₂²	72	4	C36:D6	432,293

Full list: Groups of order 432 (775 groups)

Groups of order 433

		d	ρ	Label	ID
C₄₃₃	Cyclic group	433	1	C433	433,1

Groups of order 434

		d	ρ	Label	ID
C₄₃₄	Cyclic group	434	1	C434	434,4
D₂₁₇	Dihedral group	217	2+	D217	434,3
D₇×C₃₁	Direct product of C₃₁ and D₇	217	2	D7xC31	434,1
C₇×D₃₁	Direct product of C₇ and D₃₁	217	2	C7xD31	434,2

Groups of order 435

		d	ρ	Label	ID
C₄₃₅	Cyclic group	435	1	C435	435,1

Groups of order 436

		d	ρ	Label	ID
C₄₃₆	Cyclic group	436	1	C436	436,2
D₂₁₈	Dihedral group; = C₂×D₁₀₉	218	2+	D218	436,4
Dic₁₀₉	Dicyclic group; = C₁₀₉ ⋊₂ C₄	436	2-	Dic109	436,1
C₁₀₉⋊C₄	The semidirect product of C₁₀₉ and C₄ acting faithfully	109	4+	C109:C4	436,3
C₂×C₂₁₈	Abelian group of type [2,218]	436		C2xC218	436,5

Groups of order 437

		d	ρ	Label	ID
C₄₃₇	Cyclic group	437	1	C437	437,1

Groups of order 438

		d	ρ	Label	ID
C₄₃₈	Cyclic group	438	1	C438	438,6
D₂₁₉	Dihedral group	219	2+	D219	438,5
C₇₃⋊C₆	The semidirect product of C₇₃ and C₆ acting faithfully	73	6+	C73:C6	438,1
S₃×C₇₃	Direct product of C₇₃ and S₃	219	2	S3xC73	438,3
C₃×D₇₃	Direct product of C₃ and D₇₃	219	2	C3xD73	438,4
C₂×C₇₃⋊C₃	Direct product of C₂ and C₇₃⋊C₃	146	3	C2xC73:C3	438,2

Groups of order 439

		d	ρ	Label	ID
C₄₃₉	Cyclic group	439	1	C439	439,1

Groups of order 440

		d	ρ	Label	ID
C₄₄₀	Cyclic group	440	1	C440	440,6
D₂₂₀	Dihedral group	220	2+	D220	440,36
Dic₁₁₀	Dicyclic group; = C₅₅ ⋊₂ Q₈	440	2-	Dic110	440,34
D₄₄⋊C₅	The semidirect product of D₄₄ and C₅ acting faithfully	44	10+	D44:C5	440,9
C₂²⋊F₁₁	The semidirect product of C₂² and F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	44	10	C2^2:F11	440,11
C₁₁⋊C₄₀	The semidirect product of C₁₁ and C₄₀ acting via C₄₀/C₄=C₁₀	88	10	C11:C40	440,1
C₅₅⋊D₄	1^st semidirect product of C₅₅ and D₄ acting via D₄/C₂=C₂²	220	4-	C55:D4	440,20
C₅⋊D₄₄	The semidirect product of C₅ and D₄₄ acting via D₄₄/D₂₂=C₂	220	4+	C5:D44	440,21
C₅₅⋊₇D₄	1^st semidirect product of C₅₅ and D₄ acting via D₄/C₂²=C₂	220	2	C55:7D4	440,38
C₁₁⋊D₂₀	The semidirect product of C₁₁ and D₂₀ acting via D₂₀/D₁₀=C₂	220	4+	C11:D20	440,22
D₅₅⋊₂C₄	The semidirect product of D₅₅ and C₄ acting via C₄/C₂=C₂	220	4+	D55:2C4	440,19
C₅₅⋊Q₈	The semidirect product of C₅₅ and Q₈ acting via Q₈/C₂=C₂²	440	4-	C55:Q8	440,23
C₅₅⋊₃C₈	1^st semidirect product of C₅₅ and C₈ acting via C₈/C₄=C₂	440	2	C55:3C8	440,5
C₅₅⋊C₈	1^st semidirect product of C₅₅ and C₈ acting via C₈/C₂=C₄	440	4	C55:C8	440,16
C₄.F₁₁	The non-split extension by C₄ of F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	88	10-	C4.F11	440,7
C₂×C₂₂₀	Abelian group of type [2,220]	440		C2xC220	440,39
C₂²×C₁₁₀	Abelian group of type [2,2,110]	440		C2^2xC110	440,51
C₄×F₁₁	Direct product of C₄ and F₁₁	44	10	C4xF11	440,8
C₂²×F₁₁	Direct product of C₂² and F₁₁	44		C2^2xF11	440,42
F₅×D₁₁	Direct product of F₅ and D₁₁	55	8+	F5xD11	440,43
F₅×C₂₂	Direct product of C₂₂ and F₅	110	4	F5xC22	440,45
C₅×D₄₄	Direct product of C₅ and D₄₄	220	2	C5xD44	440,26
D₅×C₄₄	Direct product of C₄₄ and D₅	220	2	D5xC44	440,30
C₄×D₅₅	Direct product of C₄ and D₅₅	220	2	C4xD55	440,35
D₄×C₅₅	Direct product of C₅₅ and D₄	220	2	D4xC55	440,40
C₂₀×D₁₁	Direct product of C₂₀ and D₁₁	220	2	C20xD11	440,25
C₁₁×D₂₀	Direct product of C₁₁ and D₂₀	220	2	C11xD20	440,31
Dic₅×D₁₁	Direct product of Dic₅ and D₁₁	220	4-	Dic5xD11	440,17
D₅×Dic₁₁	Direct product of D₅ and Dic₁₁	220	4-	D5xDic11	440,18
C₂²×D₅₅	Direct product of C₂² and D₅₅	220		C2^2xD55	440,50
Q₈×C₅₅	Direct product of C₅₅ and Q₈	440	2	Q8xC55	440,41
C₅×Dic₂₂	Direct product of C₅ and Dic₂₂	440	2	C5xDic22	440,24
Dic₅×C₂₂	Direct product of C₂₂ and Dic₅	440		Dic5xC22	440,32
C₂×Dic₅₅	Direct product of C₂ and Dic₅₅	440		C2xDic55	440,37
C₁₀×Dic₁₁	Direct product of C₁₀ and Dic₁₁	440		C10xDic11	440,27
C₁₁×Dic₁₀	Direct product of C₁₁ and Dic₁₀	440	2	C11xDic10	440,29
D₄×C₁₁⋊C₅	Direct product of D₄ and C₁₁⋊C₅	44	10	D4xC11:C5	440,13
C₈×C₁₁⋊C₅	Direct product of C₈ and C₁₁⋊C₅	88	5	C8xC11:C5	440,2
Q₈×C₁₁⋊C₅	Direct product of Q₈ and C₁₁⋊C₅	88	10	Q8xC11:C5	440,14
C₂×C₁₁⋊C₂₀	Direct product of C₂ and C₁₁⋊C₂₀	88		C2xC11:C20	440,10
C₂³×C₁₁⋊C₅	Direct product of C₂³ and C₁₁⋊C₅	88		C2^3xC11:C5	440,44
C₂×D₅×D₁₁	Direct product of C₂, D₅ and D₁₁	110	4+	C2xD5xD11	440,47
C₂×C₁₁⋊F₅	Direct product of C₂ and C₁₁⋊F₅	110	4	C2xC11:F5	440,46
D₅×C₂×C₂₂	Direct product of C₂×C₂₂ and D₅	220		D5xC2xC22	440,49
C₂×C₁₀×D₁₁	Direct product of C₂×C₁₀ and D₁₁	220		C2xC10xD11	440,48
C₅×C₁₁⋊D₄	Direct product of C₅ and C₁₁⋊D₄	220	2	C5xC11:D4	440,28
C₁₁×C₅⋊D₄	Direct product of C₁₁ and C₅⋊D₄	220	2	C11xC5:D4	440,33
C₅×C₁₁⋊C₈	Direct product of C₅ and C₁₁⋊C₈	440	2	C5xC11:C8	440,4
C₁₁×C₅⋊C₈	Direct product of C₁₁ and C₅⋊C₈	440	4	C11xC5:C8	440,15
C₁₁×C₅⋊₂C₈	Direct product of C₁₁ and C₅⋊₂C₈	440	2	C11xC5:2C8	440,3
C₂×C₄×C₁₁⋊C₅	Direct product of C₂×C₄ and C₁₁⋊C₅	88		C2xC4xC11:C5	440,12

Groups of order 441

		d	ρ	Label	ID
C₄₄₁	Cyclic group	441	1	C441	441,2
C₇²⋊₃C₉	3^rd semidirect product of C₇² and C₉ acting via C₉/C₃=C₃	63	3	C7^2:3C9	441,7
C₄₉⋊C₉	The semidirect product of C₄₉ and C₉ acting via C₉/C₃=C₃	441	3	C49:C9	441,1
C₇²⋊C₉	2^nd semidirect product of C₇² and C₉ acting via C₉/C₃=C₃	441		C7^2:C9	441,6
C₂₁²	Abelian group of type [21,21]	441		C21^2	441,13
C₇×C₆₃	Abelian group of type [7,63]	441		C7xC63	441,8
C₃×C₁₄₇	Abelian group of type [3,147]	441		C3xC147	441,4
C₇×C₇⋊C₉	Direct product of C₇ and C₇⋊C₉	63	3	C7xC7:C9	441,5
C₇⋊C₃×C₂₁	Direct product of C₂₁ and C₇⋊C₃	63	3	C7:C3xC21	441,10
C₃×C₇²⋊₃C₃	Direct product of C₃ and C₇²⋊₃C₃	63	3	C3xC7^2:3C3	441,12
C₃×C₄₉⋊C₃	Direct product of C₃ and C₄₉⋊C₃	147	3	C3xC49:C3	441,3
C₃×C₇²⋊C₃	Direct product of C₃ and C₇²⋊C₃	147		C3xC7^2:C3	441,11
C₇⋊C₃²	Direct product of C₇⋊C₃ and C₇⋊C₃	21	9	C7:C3^2	441,9

Groups of order 442

		d	ρ	Label	ID
C₄₄₂	Cyclic group	442	1	C442	442,4
D₂₂₁	Dihedral group	221	2+	D221	442,3
C₁₇×D₁₃	Direct product of C₁₇ and D₁₃	221	2	C17xD13	442,1
C₁₃×D₁₇	Direct product of C₁₃ and D₁₇	221	2	C13xD17	442,2

Groups of order 443

		d	ρ	Label	ID
C₄₄₃	Cyclic group	443	1	C443	443,1

Groups of order 444

		d	ρ	Label	ID
C₄₄₄	Cyclic group	444	1	C444	444,6
D₂₂₂	Dihedral group; = C₂×D₁₁₁	222	2+	D222	444,17
Dic₁₁₁	Dicyclic group; = C₃ ⋊Dic₃₇	444	2-	Dic111	444,5
C₃₇⋊C₁₂	The semidirect product of C₃₇ and C₁₂ acting faithfully	37	12+	C37:C12	444,7
C₃₇⋊Dic₃	The semidirect product of C₃₇ and Dic₃ acting via Dic₃/C₃=C₄	111	4	C37:Dic3	444,10
C₃₇⋊A₄	The semidirect product of C₃₇ and A₄ acting via A₄/C₂²=C₃	148	3	C37:A4	444,14
C₇₄.C₆	The non-split extension by C₇₄ of C₆ acting faithfully	148	6-	C74.C6	444,1
C₂×C₂₂₂	Abelian group of type [2,222]	444		C2xC222	444,18
S₃×D₃₇	Direct product of S₃ and D₃₇	111	4+	S3xD37	444,11
A₄×C₃₇	Direct product of C₃₇ and A₄	148	3	A4xC37	444,13
S₃×C₇₄	Direct product of C₇₄ and S₃	222	2	S3xC74	444,16
C₆×D₃₇	Direct product of C₆ and D₃₇	222	2	C6xD37	444,15
Dic₃×C₃₇	Direct product of C₃₇ and Dic₃	444	2	Dic3xC37	444,3
C₃×Dic₃₇	Direct product of C₃ and Dic₃₇	444	2	C3xDic37	444,4
C₂×C₃₇⋊C₆	Direct product of C₂ and C₃₇⋊C₆	74	6+	C2xC37:C6	444,8
C₃×C₃₇⋊C₄	Direct product of C₃ and C₃₇⋊C₄	111	4	C3xC37:C4	444,9
C₄×C₃₇⋊C₃	Direct product of C₄ and C₃₇⋊C₃	148	3	C4xC37:C3	444,2
C₂²×C₃₇⋊C₃	Direct product of C₂² and C₃₇⋊C₃	148		C2^2xC37:C3	444,12

Groups of order 445

		d	ρ	Label	ID
C₄₄₅	Cyclic group	445	1	C445	445,1

Groups of order 446

		d	ρ	Label	ID
C₄₄₆	Cyclic group	446	1	C446	446,2
D₂₂₃	Dihedral group	223	2+	D223	446,1

Groups of order 447

		d	ρ	Label	ID
C₄₄₇	Cyclic group	447	1	C447	447,1

Groups of order 448

		d	ρ	Label	ID
C₄₄₈	Cyclic group	448	1	C448	448,2
D₂₂₄	Dihedral group	224	2+	D224	448,5
Dic₁₁₂	Dicyclic group; = C₇ ⋊₁ Q₆₄	448	2-	Dic112	448,7
C₂³⋊F₈	2^nd semidirect product of C₂³ and F₈ acting via F₈/C₂³=C₇	14	7+	C2^3:F8	448,1394
C₄³⋊C₇	The semidirect product of C₄³ and C₇ acting faithfully	28	7	C4^3:C7	448,178
C₂⁶⋊C₇	2^nd semidirect product of C₂⁶ and C₇ acting faithfully	28		C2^6:C7	448,1393
C₂³⋊D₂₈	The semidirect product of C₂³ and D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3:D28	448,275
D₂₈⋊₁D₄	1^st semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	56	8+	D28:1D4	448,281
D₄⋊₄D₂₈	3^rd semidirect product of D₄ and D₂₈ acting via D₂₈/D₁₄=C₂	56	4+	D4:4D28	448,356
D₂₈⋊₅D₄	5^th semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	56	4	D28:5D4	448,611
D₂₈⋊₁₈D₄	6^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	56	8+	D28:18D4	448,732
C₂⁴⋊D₁₄	1^st semidirect product of C₂⁴ and D₁₄ acting via D₁₄/C₇=C₂²	56	4	C2^4:D14	448,566
C₂⁴⋊Dic₇	1^st semidirect product of C₂⁴ and Dic₇ acting via Dic₇/C₇=C₄	56	4	C2^4:Dic7	448,93
C₄²⋊₃Dic₇	3^rd semidirect product of C₄² and Dic₇ acting via Dic₇/C₇=C₄	56	4	C4^2:3Dic7	448,102
2₊¹⁺⁴⋊D₇	1^st semidirect product of 2₊¹⁺⁴ and D₇ acting via D₇/C₇=C₂	56	8+	ES+(2,2):D7	448,775
2₊¹⁺⁴⋊₂D₇	2^nd semidirect product of 2₊¹⁺⁴ and D₇ acting via D₇/C₇=C₂	56	8+	ES+(2,2):2D7	448,778
C₁₁₂⋊C₄	2^nd semidirect product of C₁₁₂ and C₄ acting faithfully	112	4	C112:C4	448,69
D₅₆⋊₈C₄	8^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:8C4	448,45
D₅₆⋊₂C₄	2^nd semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:2C4	448,75
D₅₆⋊₄C₄	4^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:4C4	448,251
D₄⋊D₂₈	1^st semidirect product of D₄ and D₂₈ acting via D₂₈/D₁₄=C₂	112		D4:D28	448,307
D₅₆⋊₇C₄	7^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:7C4	448,429
D₈⋊D₁₄	2^nd semidirect product of D₈ and D₁₄ acting via D₁₄/D₇=C₂	112	4	D8:D14	448,445
D₂₈⋊D₄	6^th semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	112		D28:D4	448,690
D₄⋊₅D₂₈	1^st semidirect product of D₄ and D₂₈ acting through Inn(D₄)	112		D4:5D28	448,1007
D₈⋊₅D₁₄	5^th semidirect product of D₈ and D₁₄ acting via D₁₄/D₇=C₂	112	8+	D8:5D14	448,1227
D₈⋊₆D₁₄	6^th semidirect product of D₈ and D₁₄ acting via D₁₄/D₇=C₂	112	8-	D8:6D14	448,1228
C₁₆⋊D₁₄	1^st semidirect product of C₁₆ and D₁₄ acting via D₁₄/C₇=C₂²	112	4+	C16:D14	448,442
D₅₆⋊₁₁C₄	The semidirect product of D₅₆ and C₄ acting through Inn(D₅₆)	112	2	D56:11C4	448,234
D₂₈⋊₁₃D₄	1^st semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	112		D28:13D4	448,266
D₅₆⋊₁₀C₄	10^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:10C4	448,428
D₁₁₂⋊C₂	6^th semidirect product of D₁₁₂ and C₂ acting faithfully	112	4+	D112:C2	448,448
D₂₈⋊₁₆D₄	4^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	112		D28:16D4	448,570
D₂₈⋊₂₃D₄	1^st semidirect product of D₂₈ and D₄ acting through Inn(D₂₈)	112		D28:23D4	448,1003
D₂₈⋊₁₉D₄	7^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	112		D28:19D4	448,1062
D₂₈⋊₂₀D₄	8^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	112		D28:20D4	448,1065
D₂₈⋊₂₁D₄	9^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	112		D28:21D4	448,1083
D₂₈⋊₁₀D₄	3^rd semidirect product of D₂₈ and D₄ acting via D₄/C₄=C₂	112		D28:10D4	448,1129
D₂₈⋊₁₁D₄	4^th semidirect product of D₂₈ and D₄ acting via D₄/C₄=C₂	112		D28:11D4	448,1170
D₈⋊₁₃D₁₄	2^nd semidirect product of D₈ and D₁₄ acting through Inn(D₈)	112	4	D8:13D14	448,1210
D₈⋊₁₀D₁₄	4^th semidirect product of D₈ and D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D8:10D14	448,1221
D₈⋊₁₅D₁₄	4^th semidirect product of D₈ and D₁₄ acting through Inn(D₈)	112	4+	D8:15D14	448,1222
D₈⋊₁₁D₁₄	5^th semidirect product of D₈ and D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D8:11D14	448,1223
Q₁₆⋊D₁₄	2^nd semidirect product of Q₁₆ and D₁₄ acting via D₁₄/C₁₄=C₂	112	4+	Q16:D14	448,727
D₈⋊₂Dic₇	2^nd semidirect product of D₈ and Dic₇ acting via Dic₇/C₁₄=C₂	112	4	D8:2Dic7	448,123
D₈⋊₅Dic₇	The semidirect product of D₈ and Dic₇ acting through Inn(D₈)	112	4	D8:5Dic7	448,730
D₈⋊₄Dic₇	4^th semidirect product of D₈ and Dic₇ acting via Dic₇/C₁₄=C₂	112	4	D8:4Dic7	448,731
C₁₆⋊Dic₇	1^st semidirect product of C₁₆ and Dic₇ acting via Dic₇/C₇=C₄	112	4	C16:Dic7	448,70
C₄²⋊D₁₄	1^st semidirect product of C₄² and D₁₄ acting via D₁₄/C₇=C₂²	112	4	C4^2:D14	448,355
C₄²⋊₄D₁₄	4^th semidirect product of C₄² and D₁₄ acting via D₁₄/C₇=C₂²	112	4	C4^2:4D14	448,539

Full list: Groups of order 448 (1396 groups)

Groups of order 449

		d	ρ	Label	ID
C₄₄₉	Cyclic group	449	1	C449	449,1

Groups of order 450

		d	ρ	Label	ID
C₄₅₀	Cyclic group	450	1	C450	450,4
D₂₂₅	Dihedral group	225	2+	D225	450,3
C₅²⋊D₉	The semidirect product of C₅² and D₉ acting via D₉/C₃=S₃	45	6+	C5^2:D9	450,11
C₅²⋊C₁₈	The semidirect product of C₅² and C₁₈ acting via C₁₈/C₃=C₆	45	6	C5^2:C18	450,12
C₃⋊D₇₅	The semidirect product of C₃ and D₇₅ acting via D₇₅/C₇₅=C₂	225		C3:D75	450,9
C₅⋊D₄₅	The semidirect product of C₅ and D₄₅ acting via D₄₅/C₄₅=C₂	225		C5:D45	450,18
C₁₅⋊D₁₅	1^st semidirect product of C₁₅ and D₁₅ acting via D₁₅/C₁₅=C₂	225		C15:D15	450,33
C₅⋊D₁₅⋊C₃	The semidirect product of C₅⋊D₁₅ and C₃ acting faithfully	45	6+	C5:D15:C3	450,24
C₅²⋊(C₃⋊S₃)	The semidirect product of C₅² and C₃⋊S₃ acting via C₃⋊S₃/C₃=S₃	45	6+	C5^2:(C3:S3)	450,21
C₅×C₉₀	Abelian group of type [5,90]	450		C5xC90	450,19
C₃×C₁₅₀	Abelian group of type [3,150]	450		C3xC150	450,10
C₁₅×C₃₀	Abelian group of type [15,30]	450		C15xC30	450,34
C₁₅×D₁₅	Direct product of C₁₅ and D₁₅	30	2	C15xD15	450,29
D₅×C₄₅	Direct product of C₄₅ and D₅	90	2	D5xC45	450,14
C₅×D₄₅	Direct product of C₅ and D₄₅	90	2	C5xD45	450,17
S₃×C₇₅	Direct product of C₇₅ and S₃	150	2	S3xC75	450,6
C₃×D₇₅	Direct product of C₃ and D₇₅	150	2	C3xD75	450,7
D₉×C₂₅	Direct product of C₂₅ and D₉	225	2	D9xC25	450,1
C₉×D₂₅	Direct product of C₉ and D₂₅	225	2	C9xD25	450,2
D₉×C₅²	Direct product of C₅² and D₉	225		D9xC5^2	450,16
C₃²×D₂₅	Direct product of C₃² and D₂₅	225		C3^2xD25	450,5
C₃×C₅²⋊S₃	Direct product of C₃ and C₅²⋊S₃	45	3	C3xC5^2:S3	450,20
C₃×C₅²⋊C₆	Direct product of C₃ and C₅²⋊C₆	45	6	C3xC5^2:C6	450,22
S₃×C₅²⋊C₃	Direct product of S₃ and C₅²⋊C₃	45	6	S3xC5^2:C3	450,23
D₅×C₃×C₁₅	Direct product of C₃×C₁₅ and D₅	90		D5xC3xC15	450,26
C₅×C₃⋊D₁₅	Direct product of C₅ and C₃⋊D₁₅	90		C5xC3:D15	450,32
C₂×C₅²⋊C₉	Direct product of C₂ and C₅²⋊C₉	90	3	C2xC5^2:C9	450,13
C₆×C₅²⋊C₃	Direct product of C₆ and C₅²⋊C₃	90	3	C6xC5^2:C3	450,25
S₃×C₅×C₁₅	Direct product of C₅×C₁₅ and S₃	150		S3xC5xC15	450,28
C₃×C₅⋊D₁₅	Direct product of C₃ and C₅⋊D₁₅	150		C3xC5:D15	450,30
C₉×C₅⋊D₅	Direct product of C₉ and C₅⋊D₅	225		C9xC5:D5	450,15
C₃⋊S₃×C₂₅	Direct product of C₂₅ and C₃⋊S₃	225		C3:S3xC25	450,8
C₃⋊S₃×C₅²	Direct product of C₅² and C₃⋊S₃	225		C3:S3xC5^2	450,31
C₃²×C₅⋊D₅	Direct product of C₃² and C₅⋊D₅	225		C3^2xC5:D5	450,27

Groups of order 451

		d	ρ	Label	ID
C₄₅₁	Cyclic group	451	1	C451	451,1

Groups of order 452

		d	ρ	Label	ID
C₄₅₂	Cyclic group	452	1	C452	452,2
D₂₂₆	Dihedral group; = C₂×D₁₁₃	226	2+	D226	452,4
Dic₁₁₃	Dicyclic group; = C₁₁₃ ⋊₂ C₄	452	2-	Dic113	452,1
C₁₁₃⋊C₄	The semidirect product of C₁₁₃ and C₄ acting faithfully	113	4+	C113:C4	452,3
C₂×C₂₂₆	Abelian group of type [2,226]	452		C2xC226	452,5

Groups of order 453

		d	ρ	Label	ID
C₄₅₃	Cyclic group	453	1	C453	453,2
C₁₅₁⋊C₃	The semidirect product of C₁₅₁ and C₃ acting faithfully	151	3	C151:C3	453,1

Groups of order 454

		d	ρ	Label	ID
C₄₅₄	Cyclic group	454	1	C454	454,2
D₂₂₇	Dihedral group	227	2+	D227	454,1

Groups of order 455

		d	ρ	Label	ID
C₄₅₅	Cyclic group	455	1	C455	455,1

Groups of order 456

		d	ρ	Label	ID
C₄₅₆	Cyclic group	456	1	C456	456,6
D₂₂₈	Dihedral group	228	2+	D228	456,36
Dic₁₁₄	Dicyclic group; = C₅₇ ⋊₂ Q₈	456	2-	Dic114	456,34
C₁₉⋊S₄	The semidirect product of C₁₉ and S₄ acting via S₄/A₄=C₂	76	6+	C19:S4	456,43
D₇₆⋊C₃	The semidirect product of D₇₆ and C₃ acting faithfully	76	6+	D76:C3	456,9
D₁₉⋊A₄	The semidirect product of D₁₉ and A₄ acting via A₄/C₂²=C₃	76	6+	D19:A4	456,46
D₃₈⋊C₆	2^nd semidirect product of D₃₈ and C₆ acting faithfully	76	6	D38:C6	456,11
C₁₉⋊C₂₄	The semidirect product of C₁₉ and C₂₄ acting via C₂₄/C₄=C₆	152	6	C19:C24	456,1
Dic₃₈⋊C₃	The semidirect product of Dic₃₈ and C₃ acting faithfully	152	6-	Dic38:C3	456,7
D₅₇⋊C₄	The semidirect product of D₅₇ and C₄ acting via C₄/C₂=C₂	228	4+	D57:C4	456,14
C₅₇⋊D₄	1^st semidirect product of C₅₇ and D₄ acting via D₄/C₂=C₂²	228	4-	C57:D4	456,15
C₃⋊D₇₆	The semidirect product of C₃ and D₇₆ acting via D₇₆/D₃₈=C₂	228	4+	C3:D76	456,16
C₅₇⋊₇D₄	1^st semidirect product of C₅₇ and D₄ acting via D₄/C₂²=C₂	228	2	C57:7D4	456,38
C₁₉⋊D₁₂	The semidirect product of C₁₉ and D₁₂ acting via D₁₂/D₆=C₂	228	4+	C19:D12	456,17
C₅₇⋊Q₈	The semidirect product of C₅₇ and Q₈ acting via Q₈/C₂=C₂²	456	4-	C57:Q8	456,18
C₅₇⋊C₈	1^st semidirect product of C₅₇ and C₈ acting via C₈/C₄=C₂	456	2	C57:C8	456,5
C₃₈.A₄	The non-split extension by C₃₈ of A₄ acting via A₄/C₂²=C₃	152	6	C38.A4	456,23
C₂×C₂₂₈	Abelian group of type [2,228]	456		C2xC228	456,39
C₂²×C₁₁₄	Abelian group of type [2,2,114]	456		C2^2xC114	456,54
C₁₉×S₄	Direct product of C₁₉ and S₄	76	3	C19xS4	456,42
A₄×D₁₉	Direct product of A₄ and D₁₉	76	6+	A4xD19	456,45
A₄×C₃₈	Direct product of C₃₈ and A₄	114	3	A4xC38	456,49
C₁₉×SL₂(𝔽₃)	Direct product of C₁₉ and SL₂(𝔽₃)	152	2	C19xSL(2,3)	456,22
S₃×C₇₆	Direct product of C₇₆ and S₃	228	2	S3xC76	456,30
C₃×D₇₆	Direct product of C₃ and D₇₆	228	2	C3xD76	456,26
C₄×D₅₇	Direct product of C₄ and D₅₇	228	2	C4xD57	456,35
D₄×C₅₇	Direct product of C₅₇ and D₄	228	2	D4xC57	456,40
C₁₂×D₁₉	Direct product of C₁₂ and D₁₉	228	2	C12xD19	456,25
C₁₉×D₁₂	Direct product of C₁₉ and D₁₂	228	2	C19xD12	456,31
Dic₃×D₁₉	Direct product of Dic₃ and D₁₉	228	4-	Dic3xD19	456,12
S₃×Dic₁₉	Direct product of S₃ and Dic₁₉	228	4-	S3xDic19	456,13
C₂²×D₅₇	Direct product of C₂² and D₅₇	228		C2^2xD57	456,53
Q₈×C₅₇	Direct product of C₅₇ and Q₈	456	2	Q8xC57	456,41
C₃×Dic₃₈	Direct product of C₃ and Dic₃₈	456	2	C3xDic38	456,24
C₆×Dic₁₉	Direct product of C₆ and Dic₁₉	456		C6xDic19	456,27
C₁₉×Dic₆	Direct product of C₁₉ and Dic₆	456	2	C19xDic6	456,29
Dic₃×C₃₈	Direct product of C₃₈ and Dic₃	456		Dic3xC38	456,32
C₂×Dic₅₇	Direct product of C₂ and Dic₅₇	456		C2xDic57	456,37
C₄×C₁₉⋊C₆	Direct product of C₄ and C₁₉⋊C₆	76	6	C4xC19:C6	456,8
D₄×C₁₉⋊C₃	Direct product of D₄ and C₁₉⋊C₃	76	6	D4xC19:C3	456,20
C₂²×C₁₉⋊C₆	Direct product of C₂² and C₁₉⋊C₆	76		C2^2xC19:C6	456,44
C₂×C₁₉⋊A₄	Direct product of C₂ and C₁₉⋊A₄	114	3	C2xC19:A4	456,50
C₂×S₃×D₁₉	Direct product of C₂, S₃ and D₁₉	114	4+	C2xS3xD19	456,47
C₈×C₁₉⋊C₃	Direct product of C₈ and C₁₉⋊C₃	152	3	C8xC19:C3	456,2
Q₈×C₁₉⋊C₃	Direct product of Q₈ and C₁₉⋊C₃	152	6	Q8xC19:C3	456,21
C₂×C₁₉⋊C₁₂	Direct product of C₂ and C₁₉⋊C₁₂	152		C2xC19:C12	456,10
C₂³×C₁₉⋊C₃	Direct product of C₂³ and C₁₉⋊C₃	152		C2^3xC19:C3	456,48
S₃×C₂×C₃₈	Direct product of C₂×C₃₈ and S₃	228		S3xC2xC38	456,52
C₂×C₆×D₁₉	Direct product of C₂×C₆ and D₁₉	228		C2xC6xD19	456,51
C₃×C₁₉⋊D₄	Direct product of C₃ and C₁₉⋊D₄	228	2	C3xC19:D4	456,28
C₁₉×C₃⋊D₄	Direct product of C₁₉ and C₃⋊D₄	228	2	C19xC3:D4	456,33
C₁₉×C₃⋊C₈	Direct product of C₁₉ and C₃⋊C₈	456	2	C19xC3:C8	456,3
C₃×C₁₉⋊C₈	Direct product of C₃ and C₁₉⋊C₈	456	2	C3xC19:C8	456,4
C₂×C₄×C₁₉⋊C₃	Direct product of C₂×C₄ and C₁₉⋊C₃	152		C2xC4xC19:C3	456,19

Groups of order 457

		d	ρ	Label	ID
C₄₅₇	Cyclic group	457	1	C457	457,1

Groups of order 458

		d	ρ	Label	ID
C₄₅₈	Cyclic group	458	1	C458	458,2
D₂₂₉	Dihedral group	229	2+	D229	458,1

Groups of order 459

		d	ρ	Label	ID
C₄₅₉	Cyclic group	459	1	C459	459,1
C₃×C₁₅₃	Abelian group of type [3,153]	459		C3xC153	459,2
C₃²×C₅₁	Abelian group of type [3,3,51]	459		C3^2xC51	459,5
C₁₇×He₃	Direct product of C₁₇ and He₃	153	3	C17xHe3	459,3
C₁₇×3_-¹⁺²	Direct product of C₁₇ and 3_-¹⁺²	153	3	C17xES-(3,1)	459,4

Groups of order 460

		d	ρ	Label	ID
C₄₆₀	Cyclic group	460	1	C460	460,4
D₂₃₀	Dihedral group; = C₂×D₁₁₅	230	2+	D230	460,10
Dic₁₁₅	Dicyclic group; = C₂₃ ⋊Dic₅	460	2-	Dic115	460,3
C₂₃⋊F₅	The semidirect product of C₂₃ and F₅ acting via F₅/D₅=C₂	115	4	C23:F5	460,6
C₂×C₂₃₀	Abelian group of type [2,230]	460		C2xC230	460,11
D₅×D₂₃	Direct product of D₅ and D₂₃	115	4+	D5xD23	460,7
F₅×C₂₃	Direct product of C₂₃ and F₅	115	4	F5xC23	460,5
D₅×C₄₆	Direct product of C₄₆ and D₅	230	2	D5xC46	460,9
C₁₀×D₂₃	Direct product of C₁₀ and D₂₃	230	2	C10xD23	460,8
Dic₅×C₂₃	Direct product of C₂₃ and Dic₅	460	2	Dic5xC23	460,1
C₅×Dic₂₃	Direct product of C₅ and Dic₂₃	460	2	C5xDic23	460,2

Groups of order 461

		d	ρ	Label	ID
C₄₆₁	Cyclic group	461	1	C461	461,1

Groups of order 462

		d	ρ	Label	ID
C₄₆₂	Cyclic group	462	1	C462	462,12
D₂₃₁	Dihedral group	231	2+	D231	462,11
C₁₁⋊F₇	The semidirect product of C₁₁ and F₇ acting via F₇/C₇⋊C₃=C₂	77	6+	C11:F7	462,3
C₁₁×F₇	Direct product of C₁₁ and F₇	77	6	C11xF7	462,2
S₃×C₇₇	Direct product of C₇₇ and S₃	231	2	S3xC77	462,8
D₇×C₃₃	Direct product of C₃₃ and D₇	231	2	D7xC33	462,6
C₃×D₇₇	Direct product of C₃ and D₇₇	231	2	C3xD77	462,7
C₇×D₃₃	Direct product of C₇ and D₃₃	231	2	C7xD33	462,9
C₂₁×D₁₁	Direct product of C₂₁ and D₁₁	231	2	C21xD11	462,5
C₁₁×D₂₁	Direct product of C₁₁ and D₂₁	231	2	C11xD21	462,10
C₇⋊C₃×D₁₁	Direct product of C₇⋊C₃ and D₁₁	77	6	C7:C3xD11	462,1
C₇⋊C₃×C₂₂	Direct product of C₂₂ and C₇⋊C₃	154	3	C7:C3xC22	462,4

Groups of order 463

		d	ρ	Label	ID
C₄₆₃	Cyclic group	463	1	C463	463,1

Groups of order 464

		d	ρ	Label	ID
C₄₆₄	Cyclic group	464	1	C464	464,2
D₂₃₂	Dihedral group	232	2+	D232	464,7
Dic₁₁₆	Dicyclic group; = C₂₉ ⋊₁ Q₁₆	464	2-	Dic116	464,8
C₁₁₆⋊C₄	1^st semidirect product of C₁₁₆ and C₄ acting faithfully	116	4	C116:C4	464,31
D₄⋊D₂₉	The semidirect product of D₄ and D₂₉ acting via D₂₉/C₂₉=C₂	232	4+	D4:D29	464,15
D₂₉⋊C₈	The semidirect product of D₂₉ and C₈ acting via C₈/C₄=C₂	232	4	D29:C8	464,28
Q₈⋊D₂₉	The semidirect product of Q₈ and D₂₉ acting via D₂₉/C₂₉=C₂	232	4+	Q8:D29	464,17
C₈⋊D₂₉	3^rd semidirect product of C₈ and D₂₉ acting via D₂₉/C₂₉=C₂	232	2	C8:D29	464,5
C₂₃₂⋊C₂	2^nd semidirect product of C₂₃₂ and C₂ acting faithfully	232	2	C232:C2	464,6
D₅₈⋊C₄	1^st semidirect product of D₅₈ and C₄ acting via C₄/C₂=C₂	232		D58:C4	464,14
D₄⋊₂D₂₉	The semidirect product of D₄ and D₂₉ acting through Inn(D₄)	232	4-	D4:2D29	464,40
Q₈⋊₂D₂₉	The semidirect product of Q₈ and D₂₉ acting through Inn(Q₈)	232	4+	Q8:2D29	464,42
D₁₁₆⋊₅C₂	The semidirect product of D₁₁₆ and C₂ acting through Inn(D₁₁₆)	232	2	D116:5C2	464,38
C₂₉⋊M₄(2)	The semidirect product of C₂₉ and M₄(2) acting via M₄(2)/C₂²=C₄	232	4-	C29:M4(2)	464,33
C₂₉⋊C₁₆	The semidirect product of C₂₉ and C₁₆ acting via C₁₆/C₄=C₄	464	4	C29:C16	464,3
C₂₉⋊₂C₁₆	The semidirect product of C₂₉ and C₁₆ acting via C₁₆/C₈=C₂	464	2	C29:2C16	464,1
C₄⋊Dic₂₉	The semidirect product of C₄ and Dic₂₉ acting via Dic₂₉/C₅₈=C₂	464		C4:Dic29	464,13
C₂₉⋊Q₁₆	The semidirect product of C₂₉ and Q₁₆ acting via Q₁₆/Q₈=C₂	464	4-	C29:Q16	464,18
D₂₉.D₄	The non-split extension by D₂₉ of D₄ acting via D₄/C₂²=C₂	116	4+	D29.D4	464,34
D₄.D₂₉	The non-split extension by D₄ of D₂₉ acting via D₂₉/C₂₉=C₂	232	4-	D4.D29	464,16
C₄.Dic₂₉	The non-split extension by C₄ of Dic₂₉ acting via Dic₂₉/C₅₈=C₂	232	2	C4.Dic29	464,10
C₂³.D₂₉	The non-split extension by C₂³ of D₂₉ acting via D₂₉/C₂₉=C₂	232		C2^3.D29	464,19
C₁₁₆.C₄	1^st non-split extension by C₁₁₆ of C₄ acting faithfully	232	4	C116.C4	464,29
C₅₈.D₄	1^st non-split extension by C₅₈ of D₄ acting via D₄/C₂²=C₂	464		C58.D4	464,12
C₄×C₁₁₆	Abelian group of type [4,116]	464		C4xC116	464,20
C₂×C₂₃₂	Abelian group of type [2,232]	464		C2xC232	464,23
C₂³×C₅₈	Abelian group of type [2,2,2,58]	464		C2^3xC58	464,51
C₂²×C₁₁₆	Abelian group of type [2,2,116]	464		C2^2xC116	464,45
D₄×D₂₉	Direct product of D₄ and D₂₉	116	4+	D4xD29	464,39
C₈×D₂₉	Direct product of C₈ and D₂₉	232	2	C8xD29	464,4
D₈×C₂₉	Direct product of C₂₉ and D₈	232	2	D8xC29	464,25
D₄×C₅₈	Direct product of C₅₈ and D₄	232		D4xC58	464,46
Q₈×D₂₉	Direct product of Q₈ and D₂₉	232	4-	Q8xD29	464,41
C₂×D₁₁₆	Direct product of C₂ and D₁₁₆	232		C2xD116	464,37
SD₁₆×C₂₉	Direct product of C₂₉ and SD₁₆	232	2	SD16xC29	464,26
C₂³×D₂₉	Direct product of C₂³ and D₂₉	232		C2^3xD29	464,50
M₄(2)×C₂₉	Direct product of C₂₉ and M₄(2)	232	2	M4(2)xC29	464,24
Q₈×C₅₈	Direct product of C₅₈ and Q₈	464		Q8xC58	464,47
Q₁₆×C₂₉	Direct product of C₂₉ and Q₁₆	464	2	Q16xC29	464,27
C₄×Dic₂₉	Direct product of C₄ and Dic₂₉	464		C4xDic29	464,11
C₂×Dic₅₈	Direct product of C₂ and Dic₅₈	464		C2xDic58	464,35
C₂²×Dic₂₉	Direct product of C₂² and Dic₂₉	464		C2^2xDic29	464,43
C₄×C₂₉⋊C₄	Direct product of C₄ and C₂₉⋊C₄	116	4	C4xC29:C4	464,30
C₂²×C₂₉⋊C₄	Direct product of C₂² and C₂₉⋊C₄	116		C2^2xC29:C4	464,49
C₂×C₄×D₂₉	Direct product of C₂×C₄ and D₂₉	232		C2xC4xD29	464,36
C₂×C₂₉⋊D₄	Direct product of C₂ and C₂₉⋊D₄	232		C2xC29:D4	464,44
C₄○D₄×C₂₉	Direct product of C₂₉ and C₄○D₄	232	2	C4oD4xC29	464,48
C₂²⋊C₄×C₂₉	Direct product of C₂₉ and C₂²⋊C₄	232		C2^2:C4xC29	464,21
C₂×C₂₉⋊C₈	Direct product of C₂ and C₂₉⋊C₈	464		C2xC29:C8	464,32
C₄⋊C₄×C₂₉	Direct product of C₂₉ and C₄⋊C₄	464		C4:C4xC29	464,22
C₂×C₂₉⋊₂C₈	Direct product of C₂ and C₂₉⋊₂C₈	464		C2xC29:2C8	464,9

Groups of order 465

		d	ρ	Label	ID
C₄₆₅	Cyclic group	465	1	C465	465,4
C₃₁⋊C₁₅	The semidirect product of C₃₁ and C₁₅ acting faithfully	31	15	C31:C15	465,1
C₃×C₃₁⋊C₅	Direct product of C₃ and C₃₁⋊C₅	93	5	C3xC31:C5	465,2
C₅×C₃₁⋊C₃	Direct product of C₅ and C₃₁⋊C₃	155	3	C5xC31:C3	465,3

Groups of order 466

		d	ρ	Label	ID
C₄₆₆	Cyclic group	466	1	C466	466,2
D₂₃₃	Dihedral group	233	2+	D233	466,1

Groups of order 467

		d	ρ	Label	ID
C₄₆₇	Cyclic group	467	1	C467	467,1

Groups of order 468

		d	ρ	Label	ID
C₄₆₈	Cyclic group	468	1	C468	468,6
D₂₃₄	Dihedral group; = C₂×D₁₁₇	234	2+	D234	468,17
Dic₁₁₇	Dicyclic group; = C₉ ⋊Dic₁₃	468	2-	Dic117	468,5
C₃⋊F₁₃	The semidirect product of C₃ and F₁₃ acting via F₁₃/C₁₃⋊C₆=C₂	39	12	C3:F13	468,30
D₃₉⋊S₃	The semidirect product of D₃₉ and S₃ acting via S₃/C₃=C₂	78	4	D39:S3	468,46
C₃²⋊Dic₁₃	The semidirect product of C₃² and Dic₁₃ acting via Dic₁₃/C₁₃=C₄	78	4	C3^2:Dic13	468,40
C₁₃⋊C₃₆	The semidirect product of C₁₃ and C₃₆ acting via C₃₆/C₃=C₁₂	117	12	C13:C36	468,7
C₁₃⋊Dic₉	The semidirect product of C₁₃ and Dic₉ acting via Dic₉/C₉=C₄	117	4	C13:Dic9	468,10
C₃₉⋊Dic₃	1^st semidirect product of C₃₉ and Dic₃ acting via Dic₃/C₃=C₄	117		C39:Dic3	468,38
C₃₉⋊₃C₁₂	1^st semidirect product of C₃₉ and C₁₂ acting via C₁₂/C₂=C₆	156	6-	C39:3C12	468,21
C₁₃⋊₂C₃₆	The semidirect product of C₁₃ and C₃₆ acting via C₃₆/C₆=C₆	468	6	C13:2C36	468,1
C₃⋊Dic₃₉	The semidirect product of C₃ and Dic₃₉ acting via Dic₃₉/C₇₈=C₂	468		C3:Dic39	468,27
(C₃×C₃₉)⋊C₄	1^st semidirect product of C₃×C₃₉ and C₄ acting faithfully	78	4+	(C3xC39):C4	468,41
C₃₉.A₄	The non-split extension by C₃₉ of A₄ acting via A₄/C₂²=C₃	234	3	C39.A4	468,14
C₆×C₇₈	Abelian group of type [6,78]	468		C6xC78	468,55
C₂×C₂₃₄	Abelian group of type [2,234]	468		C2xC234	468,18
C₃×C₁₅₆	Abelian group of type [3,156]	468		C3xC156	468,28
C₃×F₁₃	Direct product of C₃ and F₁₃	39	12	C3xF13	468,29
S₃×D₃₉	Direct product of S₃ and D₃₉	78	4+	S3xD39	468,45
D₉×D₁₃	Direct product of D₉ and D₁₃	117	4+	D9xD13	468,11
S₃×C₇₈	Direct product of C₇₈ and S₃	156	2	S3xC78	468,51
A₄×C₃₉	Direct product of C₃₉ and A₄	156	3	A4xC39	468,48
C₆×D₃₉	Direct product of C₆ and D₃₉	156	2	C6xD39	468,52
Dic₃×C₃₉	Direct product of C₃₉ and Dic₃	156	2	Dic3xC39	468,24
C₃×Dic₃₉	Direct product of C₃ and Dic₃₉	156	2	C3xDic39	468,25
D₉×C₂₆	Direct product of C₂₆ and D₉	234	2	D9xC26	468,16
C₁₈×D₁₃	Direct product of C₁₈ and D₁₃	234	2	C18xD13	468,15
C₁₃×Dic₉	Direct product of C₁₃ and Dic₉	468	2	C13xDic9	468,3
C₉×Dic₁₃	Direct product of C₉ and Dic₁₃	468	2	C9xDic13	468,4
C₃²×Dic₁₃	Direct product of C₃² and Dic₁₃	468		C3^2xDic13	468,23
S₃×C₁₃⋊C₆	Direct product of S₃ and C₁₃⋊C₆	39	12+	S3xC13:C6	468,31
A₄×C₁₃⋊C₃	Direct product of A₄ and C₁₃⋊C₃	52	9	A4xC13:C3	468,32
S₃²×C₁₃	Direct product of C₁₃, S₃ and S₃	78	4	S3^2xC13	468,44
C₆×C₁₃⋊C₆	Direct product of C₆ and C₁₃⋊C₆	78	6	C6xC13:C6	468,33
C₃×S₃×D₁₃	Direct product of C₃, S₃ and D₁₃	78	4	C3xS3xD13	468,42
C₃×C₃₉⋊C₄	Direct product of C₃ and C₃₉⋊C₄	78	4	C3xC39:C4	468,37
C₂×D₃₉⋊C₃	Direct product of C₂ and D₃₉⋊C₃	78	6+	C2xD39:C3	468,35
C₁₃×C₃²⋊C₄	Direct product of C₁₃ and C₃²⋊C₄	78	4	C13xC3^2:C4	468,39
C₉×C₁₃⋊C₄	Direct product of C₉ and C₁₃⋊C₄	117	4	C9xC13:C4	468,9
C₃⋊S₃×D₁₃	Direct product of C₃⋊S₃ and D₁₃	117		C3:S3xD13	468,43
C₃²×C₁₃⋊C₄	Direct product of C₃² and C₁₃⋊C₄	117		C3^2xC13:C4	468,36
C₃×C₁₃⋊A₄	Direct product of C₃ and C₁₃⋊A₄	156	3	C3xC13:A4	468,49
C₁₂×C₁₃⋊C₃	Direct product of C₁₂ and C₁₃⋊C₃	156	3	C12xC13:C3	468,22
C₃×C₂₆.C₆	Direct product of C₃ and C₂₆.C₆	156	6	C3xC26.C6	468,19
Dic₃×C₁₃⋊C₃	Direct product of Dic₃ and C₁₃⋊C₃	156	6	Dic3xC13:C3	468,20
C₃×C₆×D₁₃	Direct product of C₃×C₆ and D₁₃	234		C3xC6xD13	468,50
C₂×C₁₃⋊C₁₈	Direct product of C₂ and C₁₃⋊C₁₈	234	6	C2xC13:C18	468,8
C₃⋊S₃×C₂₆	Direct product of C₂₆ and C₃⋊S₃	234		C3:S3xC26	468,53
C₂×C₃⋊D₃₉	Direct product of C₂ and C₃⋊D₃₉	234		C2xC3:D39	468,54
C₁₃×C₃.A₄	Direct product of C₁₃ and C₃.A₄	234	3	C13xC3.A4	468,13
C₄×C₁₃⋊C₉	Direct product of C₄ and C₁₃⋊C₉	468	3	C4xC13:C9	468,2
C₂²×C₁₃⋊C₉	Direct product of C₂² and C₁₃⋊C₉	468		C2^2xC13:C9	468,12
C₁₃×C₃⋊Dic₃	Direct product of C₁₃ and C₃⋊Dic₃	468		C13xC3:Dic3	468,26
C₂×S₃×C₁₃⋊C₃	Direct product of C₂, S₃ and C₁₃⋊C₃	78	6	C2xS3xC13:C3	468,34
C₂×C₆×C₁₃⋊C₃	Direct product of C₂×C₆ and C₁₃⋊C₃	156		C2xC6xC13:C3	468,47

Groups of order 469

		d	ρ	Label	ID
C₄₆₉	Cyclic group	469	1	C469	469,1

Groups of order 470

		d	ρ	Label	ID
C₄₇₀	Cyclic group	470	1	C470	470,4
D₂₃₅	Dihedral group	235	2+	D235	470,3
D₅×C₄₇	Direct product of C₄₇ and D₅	235	2	D5xC47	470,1
C₅×D₄₇	Direct product of C₅ and D₄₇	235	2	C5xD47	470,2

Groups of order 471

		d	ρ	Label	ID
C₄₇₁	Cyclic group	471	1	C471	471,2
C₁₅₇⋊C₃	The semidirect product of C₁₅₇ and C₃ acting faithfully	157	3	C157:C3	471,1

Groups of order 472

		d	ρ	Label	ID
C₄₇₂	Cyclic group	472	1	C472	472,2
D₂₃₆	Dihedral group	236	2+	D236	472,5
Dic₁₁₈	Dicyclic group; = C₅₉ ⋊Q₈	472	2-	Dic118	472,3
C₅₉⋊D₄	The semidirect product of C₅₉ and D₄ acting via D₄/C₂²=C₂	236	2	C59:D4	472,7
C₅₉⋊C₈	The semidirect product of C₅₉ and C₈ acting via C₈/C₄=C₂	472	2	C59:C8	472,1
C₂×C₂₃₆	Abelian group of type [2,236]	472		C2xC236	472,8
C₂²×C₁₁₈	Abelian group of type [2,2,118]	472		C2^2xC118	472,12
C₄×D₅₉	Direct product of C₄ and D₅₉	236	2	C4xD59	472,4
D₄×C₅₉	Direct product of C₅₉ and D₄	236	2	D4xC59	472,9
C₂²×D₅₉	Direct product of C₂² and D₅₉	236		C2^2xD59	472,11
Q₈×C₅₉	Direct product of C₅₉ and Q₈	472	2	Q8xC59	472,10
C₂×Dic₅₉	Direct product of C₂ and Dic₅₉	472		C2xDic59	472,6

Groups of order 473

		d	ρ	Label	ID
C₄₇₃	Cyclic group	473	1	C473	473,1

Groups of order 474

		d	ρ	Label	ID
C₄₇₄	Cyclic group	474	1	C474	474,6
D₂₃₇	Dihedral group	237	2+	D237	474,5
C₇₉⋊C₆	The semidirect product of C₇₉ and C₆ acting faithfully	79	6+	C79:C6	474,1
S₃×C₇₉	Direct product of C₇₉ and S₃	237	2	S3xC79	474,3
C₃×D₇₉	Direct product of C₃ and D₇₉	237	2	C3xD79	474,4
C₂×C₇₉⋊C₃	Direct product of C₂ and C₇₉⋊C₃	158	3	C2xC79:C3	474,2

Groups of order 475

		d	ρ	Label	ID
C₄₇₅	Cyclic group	475	1	C475	475,1
C₅×C₉₅	Abelian group of type [5,95]	475		C5xC95	475,2

Groups of order 476

		d	ρ	Label	ID
C₄₇₆	Cyclic group	476	1	C476	476,4
D₂₃₈	Dihedral group; = C₂×D₁₁₉	238	2+	D238	476,10
Dic₁₁₉	Dicyclic group; = C₇ ⋊Dic₁₇	476	2-	Dic119	476,3
C₁₇⋊Dic₇	The semidirect product of C₁₇ and Dic₇ acting via Dic₇/C₇=C₄	119	4	C17:Dic7	476,6
C₂×C₂₃₈	Abelian group of type [2,238]	476		C2xC238	476,11
D₇×D₁₇	Direct product of D₇ and D₁₇	119	4+	D7xD17	476,7
D₇×C₃₄	Direct product of C₃₄ and D₇	238	2	D7xC34	476,9
C₁₄×D₁₇	Direct product of C₁₄ and D₁₇	238	2	C14xD17	476,8
C₁₇×Dic₇	Direct product of C₁₇ and Dic₇	476	2	C17xDic7	476,1
C₇×Dic₁₇	Direct product of C₇ and Dic₁₇	476	2	C7xDic17	476,2
C₇×C₁₇⋊C₄	Direct product of C₇ and C₁₇⋊C₄	119	4	C7xC17:C4	476,5

Groups of order 477

		d	ρ	Label	ID
C₄₇₇	Cyclic group	477	1	C477	477,1
C₃×C₁₅₉	Abelian group of type [3,159]	477		C3xC159	477,2

Groups of order 478

		d	ρ	Label	ID
C₄₇₈	Cyclic group	478	1	C478	478,2
D₂₃₉	Dihedral group	239	2+	D239	478,1

Groups of order 479

		d	ρ	Label	ID
C₄₇₉	Cyclic group	479	1	C479	479,1

Groups of order 480

		d	ρ	Label	ID
C₄₈₀	Cyclic group	480	1	C480	480,4
D₂₄₀	Dihedral group	240	2+	D240	480,159
Dic₁₂₀	Dicyclic group; = C₁₅ ⋊₄ Q₃₂	480	2-	Dic120	480,161
GL₂(𝔽₅)	General linear group on 𝔽₅²; = SL₂(𝔽₅)⋊₁ C₄ = Aut(C₅²)	24	4	GL(2,5)	480,218
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	16	15+	F16:C2	480,1188
C₄⋊S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	20	6	C4:S5	480,944
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	20	6+	C2^2:S5	480,951
A₅⋊Q₈	The semidirect product of A₅ and Q₈ acting via Q₈/C₄=C₂	24	6	A5:Q8	480,945
C₂⁴⋊D₁₅	The semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₃=D₅	30	10+	C2^4:D15	480,1195
A₅⋊C₈	The semidirect product of A₅ and C₈ acting via C₈/C₄=C₂	40	4	A5:C8	480,217
C₂⁴⋊₄D₁₅	3^rd semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₅=S₃	40	6	C2^4:4D15	480,1201
C₂₀⋊S₄	1^st semidirect product of C₂₀ and S₄ acting via S₄/A₄=C₂	60	6+	C20:S4	480,1026
Dic₅⋊S₄	The semidirect product of Dic₅ and S₄ acting via S₄/A₄=C₂	60	6	Dic5:S4	480,978
C₄²⋊D₁₅	The semidirect product of C₄² and D₁₅ acting via D₁₅/C₅=S₃	60	6+	C4^2:D15	480,258
D₁₀⋊S₄	1^st semidirect product of D₁₀ and S₄ acting via S₄/A₄=C₂	60	6	D10:S4	480,980
A₄⋊D₂₀	The semidirect product of A₄ and D₂₀ acting via D₂₀/D₁₀=C₂	60	6+	A4:D20	480,981
D₆₀⋊₃C₄	3^rd semidirect product of D₆₀ and C₄ acting faithfully	60	8+	D60:3C4	480,997
Dic₅⋊₂S₄	The semidirect product of Dic₅ and S₄ acting through Inn(Dic₅)	60	6	Dic5:2S4	480,977
C₂⁴⋊₂D₁₅	1^st semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₅=S₃	60	6	C2^4:2D15	480,1034
GL₂(𝔽₃)⋊D₅	1^st semidirect product of GL₂(𝔽₃) and D₅ acting via D₅/C₅=C₂	80	4+	GL(2,3):D5	480,970
C₄₀⋊₁D₆	1^st semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4+	C40:1D6	480,329
C₄₀⋊₅D₆	5^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:5D6	480,332
C₄₀⋊₈D₆	8^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:8D6	480,334
C₈⋊D₃₀	1^st semidirect product of C₈ and D₃₀ acting via D₃₀/C₁₅=C₂²	120	4+	C8:D30	480,873
C₅⋊U₂(𝔽₃)	The semidirect product of C₅ and U₂(𝔽₃) acting via U₂(𝔽₃)/SL₂(𝔽₃)=C₄	120	8+	C5:U(2,3)	480,961
C₂₄⋊F₅	5^th semidirect product of C₂₄ and F₅ acting via F₅/D₅=C₂	120	4	C24:F5	480,297
C₁₂₀⋊C₄	2^nd semidirect product of C₁₂₀ and C₄ acting faithfully	120	4	C120:C4	480,298
D₆₀⋊₇C₄	1^st semidirect product of D₆₀ and C₄ acting via C₄/C₂=C₂	120	2	D60:7C4	480,165
D₆₀⋊C₄	1^st semidirect product of D₆₀ and C₄ acting faithfully	120	8+	D60:C4	480,227
D₆₀⋊₂C₄	2^nd semidirect product of D₆₀ and C₄ acting faithfully	120	8+	D60:2C4	480,233
D₆₀⋊₅C₄	5^th semidirect product of D₆₀ and C₄ acting faithfully	120	8+	D60:5C4	480,234
D₂₄⋊D₅	2^nd semidirect product of D₂₄ and D₅ acting via D₅/C₅=C₂	120	4	D24:D5	480,326
D₄₀⋊S₃	2^nd semidirect product of D₄₀ and S₃ acting via S₃/C₃=C₂	120	4	D40:S3	480,330
D₂₄⋊₆D₅	6^th semidirect product of D₂₄ and D₅ acting via D₅/C₅=C₂	120	4	D24:6D5	480,333
D₆⋊₄D₂₀	1^st semidirect product of D₆ and D₂₀ acting via D₂₀/D₁₀=C₂	120		D6:4D20	480,550
D₃₀⋊₄D₄	4^th semidirect product of D₃₀ and D₄ acting via D₄/C₂=C₂²	120		D30:4D4	480,551
D₃₀⋊₅D₄	5^th semidirect product of D₃₀ and D₄ acting via D₄/C₂=C₂²	120		D30:5D4	480,552
D₁₅⋊D₈	The semidirect product of D₁₅ and D₈ acting via D₈/D₄=C₂	120	8+	D15:D8	480,557
D₂₀⋊D₆	6^th semidirect product of D₂₀ and D₆ acting via D₆/C₃=C₂²	120	8+	D20:D6	480,578
D₃₀⋊₈D₄	8^th semidirect product of D₃₀ and D₄ acting via D₄/C₂=C₂²	120		D30:8D4	480,653
D₈⋊D₁₅	2^nd semidirect product of D₈ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4	D8:D15	480,876
D₄⋊D₃₀	2^nd semidirect product of D₄ and D₃₀ acting via D₃₀/C₃₀=C₂	120	4+	D4:D30	480,914
D₄⋊₆D₃₀	2^nd semidirect product of D₄ and D₃₀ acting through Inn(D₄)	120	4	D4:6D30	480,1171
D₄⋊₈D₃₀	4^th semidirect product of D₄ and D₃₀ acting through Inn(D₄)	120	4+	D4:8D30	480,1176
C₄₀⋊D₆	17^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:D6	480,322
C₂₄⋊D₁₀	1^st semidirect product of C₂₄ and D₁₀ acting via D₁₀/C₅=C₂²	120	4+	C24:D10	480,325
C₄₀⋊₁₄D₆	14^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:14D6	480,331
D₁₂⋊F₅	1^st semidirect product of D₁₂ and F₅ acting via F₅/D₅=C₂	120	8+	D12:F5	480,228
D₁₂⋊₄F₅	4^th semidirect product of D₁₂ and F₅ acting via F₅/D₅=C₂	120	8-	D12:4F5	480,231
D₁₂⋊₂F₅	2^nd semidirect product of D₁₂ and F₅ acting via F₅/D₅=C₂	120	8-	D12:2F5	480,232

Full list: Groups of order 480 (1213 groups)

Groups of order 481

		d	ρ	Label	ID
C₄₈₁	Cyclic group	481	1	C481	481,1

Groups of order 482

		d	ρ	Label	ID
C₄₈₂	Cyclic group	482	1	C482	482,2
D₂₄₁	Dihedral group	241	2+	D241	482,1

Groups of order 483

		d	ρ	Label	ID
C₄₈₃	Cyclic group	483	1	C483	483,2
C₇⋊C₃×C₂₃	Direct product of C₂₃ and C₇⋊C₃	161	3	C7:C3xC23	483,1

Groups of order 484

		d	ρ	Label	ID
C₄₈₄	Cyclic group	484	1	C484	484,2
D₂₄₂	Dihedral group; = C₂×D₁₂₁	242	2+	D242	484,3
Dic₁₂₁	Dicyclic group; = C₁₂₁ ⋊C₄	484	2-	Dic121	484,1
C₁₁²⋊C₄	The semidirect product of C₁₁² and C₄ acting faithfully	22	4+	C11^2:C4	484,8
C₁₁⋊Dic₁₁	The semidirect product of C₁₁ and Dic₁₁ acting via Dic₁₁/C₂₂=C₂	484		C11:Dic11	484,6
C₂₂²	Abelian group of type [22,22]	484		C22^2	484,12
C₂×C₂₄₂	Abelian group of type [2,242]	484		C2xC242	484,4
C₁₁×C₄₄	Abelian group of type [11,44]	484		C11xC44	484,7
D₁₁²	Direct product of D₁₁ and D₁₁	22	4+	D11^2	484,9
D₁₁×C₂₂	Direct product of C₂₂ and D₁₁	44	2	D11xC22	484,10
C₁₁×Dic₁₁	Direct product of C₁₁ and Dic₁₁	44	2	C11xDic11	484,5
C₂×C₁₁⋊D₁₁	Direct product of C₂ and C₁₁⋊D₁₁	242		C2xC11:D11	484,11

Groups of order 485

		d	ρ	Label	ID
C₄₈₅	Cyclic group	485	1	C485	485,1

Groups of order 486

		d	ρ	Label	ID
C₄₈₆	Cyclic group	486	1	C486	486,2
D₂₄₃	Dihedral group	243	2+	D243	486,1
C₃⁴⋊C₆	1^st semidirect product of C₃⁴ and C₆ acting faithfully	18	6	C3^4:C6	486,102
C₉²⋊₈C₆	8^th semidirect product of C₉² and C₆ acting faithfully	18	6	C9^2:8C6	486,110
C₃⁴⋊₃S₃	3^rd semidirect product of C₃⁴ and S₃ acting faithfully	18	6	C3^4:3S3	486,145
C₉²⋊₆S₃	6^th semidirect product of C₉² and S₃ acting faithfully	18	6	C9^2:6S3	486,153
C₃⁴⋊₅S₃	5^th semidirect product of C₃⁴ and S₃ acting faithfully	18	6	C3^4:5S3	486,166
C₃³⋊₁D₉	1^st semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	18	6	C3^3:1D9	486,19
C₃³⋊₁C₁₈	1^st semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C3^3:1C18	486,18
C₂₇⋊C₁₈	The semidirect product of C₂₇ and C₁₈ acting faithfully; = Aut(D₂₇) = Hol(C₂₇)	27	18+	C27:C18	486,31
C₉²⋊C₆	1^st semidirect product of C₉² and C₆ acting faithfully	27	6+	C9^2:C6	486,35
C₉²⋊S₃	1^st semidirect product of C₉² and S₃ acting faithfully	27	6+	C9^2:S3	486,36
C₉²⋊₂C₆	2^nd semidirect product of C₉² and C₆ acting faithfully	27	6+	C9^2:2C6	486,37
C₉²⋊₂S₃	2^nd semidirect product of C₉² and S₃ acting faithfully	27	3	C9^2:2S3	486,61
C₃⁴⋊S₃	1^st semidirect product of C₃⁴ and S₃ acting faithfully	27		C3^4:S3	486,103
C₃⁴⋊₄C₆	4^th semidirect product of C₃⁴ and C₆ acting faithfully	27		C3^4:4C6	486,146
C₃⁴⋊₅C₆	5^th semidirect product of C₃⁴ and C₆ acting faithfully	27		C3^4:5C6	486,167
C₃⁴⋊₆S₃	6^th semidirect product of C₃⁴ and S₃ acting faithfully	27		C3^4:6S3	486,183
C₃⁴⋊₇S₃	7^th semidirect product of C₃⁴ and S₃ acting faithfully	27		C3^4:7S3	486,185
C₃³⋊₂D₉	2^nd semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	27		C3^3:2D9	486,52
3₊¹⁺⁴⋊C₂	1^st semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	18+	ES+(3,2):C2	486,236
3₊¹⁺⁴⋊₂C₂	2^nd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	9	ES+(3,2):2C2	486,237
3_-¹⁺⁴⋊C₂	1^st semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	27	18+	ES-(3,2):C2	486,238
3_-¹⁺⁴⋊₂C₂	2^nd semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	27	9	ES-(3,2):2C2	486,239
3₊¹⁺⁴⋊₃C₂	3^rd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	9	ES+(3,2):3C2	486,249
C₉⋊C₅₄	The semidirect product of C₉ and C₅₄ acting via C₅₄/C₉=C₆	54	6	C9:C54	486,30
D₉⋊He₃	The semidirect product of D₉ and He₃ acting via He₃/C₃²=C₃	54	6	D9:He3	486,106
C₃²⋊C₅₄	The semidirect product of C₃² and C₅₄ acting via C₅₄/C₉=C₆	54	6	C3^2:C54	486,16
C₂₇⋊₃C₁₈	The semidirect product of C₂₇ and C₁₈ acting via C₁₈/C₃=C₆	54	6	C27:3C18	486,15
He₃⋊₄D₉	2^nd semidirect product of He₃ and D₉ acting via D₉/C₉=C₂	54	6	He3:4D9	486,182
C₉²⋊₇C₆	7^th semidirect product of C₉² and C₆ acting faithfully	54	6	C9^2:7C6	486,109
C₉²⋊₃S₃	3^rd semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:3S3	486,139
C₉²⋊₄S₃	4^th semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:4S3	486,140
C₉²⋊₅S₃	5^th semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:5S3	486,156
C₃³⋊₆D₉	6^th semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	54		C3^3:6D9	486,181
C₃³⋊C₁₈	4^th semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	54		C3^3:C18	486,136
C₃⁴⋊₁₃S₃	13^rd semidirect product of C₃⁴ and S₃ acting faithfully	54		C3^4:13S3	486,248
C₃²⋊₂D₂₇	2^nd semidirect product of C₃² and D₂₇ acting via D₂₇/C₉=S₃	54	6	C3^2:2D27	486,51
D₉⋊3_-¹⁺²	The semidirect product of D₉ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	54	6	D9:ES-(3,1)	486,108
C₈₁⋊C₆	The semidirect product of C₈₁ and C₆ acting faithfully	81	6+	C81:C6	486,34
He₃⋊C₁₈	The semidirect product of He₃ and C₁₈ acting via C₁₈/C₃=C₆	81		He3:C18	486,24
He₃⋊D₉	1^st semidirect product of He₃ and D₉ acting via D₉/C₃=S₃	81		He3:D9	486,25
He₃⋊₂D₉	2^nd semidirect product of He₃ and D₉ acting via D₉/C₃=S₃	81		He3:2D9	486,56
He₃⋊₃D₉	1^st semidirect product of He₃ and D₉ acting via D₉/C₉=C₂	81		He3:3D9	486,142
C₉²⋊₃C₆	3^rd semidirect product of C₉² and C₆ acting faithfully	81		C9^2:3C6	486,141
C₉²⋊₉C₆	9^th semidirect product of C₉² and C₆ acting faithfully	81		C9^2:9C6	486,144
C₉²⋊₄C₆	4^th semidirect product of C₉² and C₆ acting faithfully	81		C9^2:4C6	486,155
C₉²⋊₅C₆	5^th semidirect product of C₉² and C₆ acting faithfully	81		C9^2:5C6	486,157
C₃³⋊D₉	5^th semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	81		C3^3:D9	486,137
C₉²⋊₁₀C₆	10^th semidirect product of C₉² and C₆ acting faithfully	81		C9^2:10C6	486,154
C₉²⋊₁₁C₆	11^st semidirect product of C₉² and C₆ acting faithfully	81		C9^2:11C6	486,158
C₉²⋊₁₂C₆	12^nd semidirect product of C₉² and C₆ acting faithfully	81		C9^2:12C6	486,159
C₃⁴⋊₁₀C₆	10^th semidirect product of C₃⁴ and C₆ acting faithfully	81		C3^4:10C6	486,242
C₃²⋊D₂₇	1^st semidirect product of C₃² and D₂₇ acting via D₂₇/C₉=S₃	81		C3^2:D27	486,17
3_-¹⁺²⋊D₉	The semidirect product of 3_-¹⁺² and D₉ acting via D₉/C₃=S₃	81		ES-(3,1):D9	486,57
C₈₁⋊S₃	The semidirect product of C₈₁ and S₃ acting via S₃/C₃=C₂	243		C81:S3	486,60
C₉⋊D₂₇	The semidirect product of C₉ and D₂₇ acting via D₂₇/C₂₇=C₂	243		C9:D27	486,50
C₃⁵⋊C₂	5^th semidirect product of C₃⁵ and C₂ acting faithfully	243		C3^5:C2	486,260
C₉²⋊₈S₃	2^nd semidirect product of C₉² and S₃ acting via S₃/C₃=C₂	243		C9^2:8S3	486,180
C₃³⋊₉D₉	3^rd semidirect product of C₃³ and D₉ acting via D₉/C₉=C₂	243		C3^3:9D9	486,247
C₃²⋊₄D₂₇	2^nd semidirect product of C₃² and D₂₇ acting via D₂₇/C₂₇=C₂	243		C3^2:4D27	486,184
C₃²⋊C₉⋊C₆	1^st semidirect product of C₃²⋊C₉ and C₆ acting faithfully	18	6	C3^2:C9:C6	486,6
C₃²⋊C₉⋊S₃	1^st semidirect product of C₃²⋊C₉ and S₃ acting faithfully	18	6	C3^2:C9:S3	486,7
C₉⋊C₉⋊S₃	1^st semidirect product of C₉⋊C₉ and S₃ acting faithfully	27	18+	C9:C9:S3	486,41
C₃≀C₃⋊C₆	2^nd semidirect product of C₃≀C₃ and C₆ acting faithfully	27	9	C3wrC3:C6	486,126
C₃≀S₃⋊₃C₃	The semidirect product of C₃≀S₃ and C₃ acting through Inn(C₃≀S₃)	27	3	C3wrS3:3C3	486,125
C₃≀C₃⋊S₃	2^nd semidirect product of C₃≀C₃ and S₃ acting via S₃/C₃=C₂	27	6+	C3wrC3:S3	486,189
C₃.He₃⋊C₆	The semidirect product of C₃.He₃ and C₆ acting faithfully	27	18+	C3.He3:C6	486,179
C₉⋊S₃⋊C₃²	2^nd semidirect product of C₉⋊S₃ and C₃² acting faithfully	27	18+	C9:S3:C3^2	486,129
(C₃×He₃)⋊C₆	8^th semidirect product of C₃×He₃ and C₆ acting faithfully	27	18+	(C3xHe3):C6	486,127
He₃⋊(C₃×S₃)	4^th semidirect product of He₃ and C₃×S₃ acting via C₃×S₃/C₃=S₃	27	18+	He3:(C3xS3)	486,178
C₃³⋊(C₃×S₃)	4^th semidirect product of C₃³ and C₃×S₃ acting faithfully	27	18+	C3^3:(C3xS3)	486,176
He₃.C₃⋊C₆	3^rd semidirect product of He₃.C₃ and C₆ acting faithfully	27	9	He3.C3:C6	486,128
He₃.C₃⋊₂C₆	2^nd semidirect product of He₃.C₃ and C₆ acting faithfully	27	18+	He3.C3:2C6	486,177
C₉⋊(S₃×C₉)	The semidirect product of C₉ and S₃×C₉ acting via S₃×C₉/C₃²=C₆	54		C9:(S3xC9)	486,138
C₉⋊S₃⋊C₉	1^st semidirect product of C₉⋊S₃ and C₉ acting via C₉/C₃=C₃	54		C9:S3:C9	486,3
C₉⋊S₃⋊₃C₉	3^rd semidirect product of C₉⋊S₃ and C₉ acting via C₉/C₃=C₃	54	6	C9:S3:3C9	486,22
C₉⋊C₉⋊₂S₃	2^nd semidirect product of C₉⋊C₉ and S₃ acting faithfully	54	6	C9:C9:2S3	486,152
(C₃×C₉)⋊D₉	2^nd semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	54	6	(C3xC9):D9	486,21
(C₃×C₉)⋊₃D₉	3^rd semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	54	6	(C3xC9):3D9	486,23
C₉⋊He₃⋊C₂	3^rd semidirect product of C₉⋊He₃ and C₂ acting faithfully	54	6	C9:He3:C2	486,107
(C₃×C₉)⋊C₁₈	2^nd semidirect product of C₃×C₉ and C₁₈ acting via C₁₈/C₃=C₆	54	6	(C3xC9):C18	486,20
C₉○He₃⋊₄S₃	2^nd semidirect product of C₉○He₃ and S₃ acting via S₃/C₃=C₂	54	6	C9oHe3:4S3	486,246
(C₃²×C₉)⋊₈S₃	8^th semidirect product of C₃²×C₉ and S₃ acting faithfully	54	6	(C3^2xC9):8S3	486,150
He₃⋊C₃⋊₂S₃	1^st semidirect product of He₃⋊C₃ and S₃ acting via S₃/C₃=C₂	54	6	He3:C3:2S3	486,172
(C₃²×C₉)⋊S₃	14^th semidirect product of C₃²×C₉ and S₃ acting faithfully	54	6	(C3^2xC9):S3	486,149
He₃.C₃⋊S₃	5^th semidirect product of He₃.C₃ and S₃ acting via S₃/C₃=C₂	54	6	He3.C3:S3	486,169
(C₃×C₉)⋊₅D₉	5^th semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	81		(C3xC9):5D9	486,53
(C₃×C₉)⋊₆D₉	6^th semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	81		(C3xC9):6D9	486,54
C₉⋊He₃⋊₂C₂	2^nd semidirect product of C₉⋊He₃ and C₂ acting faithfully	81		C9:He3:2C2	486,148
C₃²⋊C₉⋊₆S₃	6^th semidirect product of C₃²⋊C₉ and S₃ acting faithfully	81		C3^2:C9:6S3	486,46
C₃⋊(He₃⋊S₃)	The semidirect product of C₃ and He₃⋊S₃ acting via He₃⋊S₃/He₃⋊C₃=C₂	81		C3:(He3:S3)	486,187
C₉○He₃⋊₃S₃	1^st semidirect product of C₉○He₃ and S₃ acting via S₃/C₃=C₂	81		C9oHe3:3S3	486,245
(C₃×He₃)⋊S₃	2^nd semidirect product of C₃×He₃ and S₃ acting faithfully	81		(C3xHe3):S3	486,43
He₃⋊C₃⋊₃S₃	2^nd semidirect product of He₃⋊C₃ and S₃ acting via S₃/C₃=C₂	81		He3:C3:3S3	486,173
(C₃²×C₉)⋊C₆	12^nd semidirect product of C₃²×C₉ and C₆ acting faithfully	81		(C3^2xC9):C6	486,151
C₃²⋊₄D₉⋊C₃	5^th semidirect product of C₃²⋊₄D₉ and C₃ acting faithfully	81		C3^2:4D9:C3	486,170
C₃⁴.C₆	4^th non-split extension by C₃⁴ of C₆ acting faithfully	18	6	C3^4.C6	486,104
C₃⁴.₇S₃	7^th non-split extension by C₃⁴ of S₃ acting faithfully	18	6	C3^4.7S3	486,147
C₉².S₃	2^nd non-split extension by C₉² of S₃ acting faithfully	27	6+	C9^2.S3	486,38
C₃⁴.S₃	4^th non-split extension by C₃⁴ of S₃ acting faithfully	27		C3^4.S3	486,105
C₃³.D₉	3^rd non-split extension by C₃³ of D₉ acting via D₉/C₃=S₃	27	6+	C3^3.D9	486,55
He₃.D₉	1^st non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.D9	486,27
He₃.₂D₉	2^nd non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.2D9	486,29
He₃.₃D₉	3^rd non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.3D9	486,58
He₃.₄D₉	4^th non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.4D9	486,59
He₃.₅D₉	The non-split extension by He₃ of D₉ acting via D₉/C₉=C₂	81	6+	He3.5D9	486,163
C₃³.₅D₉	5^th non-split extension by C₃³ of D₉ acting via D₉/C₃=S₃	81		C3^3.5D9	486,162
He₃.C₁₈	1^st non-split extension by He₃ of C₁₈ acting via C₁₈/C₃=C₆	81	3	He3.C18	486,26
He₃.₂C₁₈	2^nd non-split extension by He₃ of C₁₈ acting via C₁₈/C₃=C₆	81	3	He3.2C18	486,28
He₃.₅C₁₈	The non-split extension by He₃ of C₁₈ acting via C₁₈/C₉=C₂	81	3	He3.5C18	486,164
C₃⁴.₁₁S₃	11^st non-split extension by C₃⁴ of S₃ acting faithfully	81		C3^4.11S3	486,244
C₃²⋊C₉.S₃	1^st non-split extension by C₃²⋊C₉ of S₃ acting faithfully	18	6	C3^2:C9.S3	486,5
C₃≀C₃.C₆	The non-split extension by C₃≀C₃ of C₆ acting faithfully	27	9	C3wrC3.C6	486,132
C₃≀C₃.S₃	The non-split extension by C₃≀C₃ of S₃ acting via S₃/C₃=C₂	27	6+	C3wrC3.S3	486,175
C₉⋊C₉.S₃	2^nd non-split extension by C₉⋊C₉ of S₃ acting faithfully	27	18+	C9:C9.S3	486,39
C₉⋊C₉.₃S₃	3^rd non-split extension by C₉⋊C₉ of S₃ acting faithfully	27	18+	C9:C9.3S3	486,40
He₃.(C₃×C₆)	6^th non-split extension by He₃ of C₃×C₆ acting via C₃×C₆/C₃=C₆	27	9	He3.(C3xC6)	486,130
He₃.(C₃×S₃)	5^th non-split extension by He₃ of C₃×S₃ acting via C₃×S₃/C₃=S₃	27	18+	He3.(C3xS3)	486,131
C₃.C₃≀S₃	1^st non-split extension by C₃ of C₃≀S₃ acting via C₃≀S₃/C₃≀C₃=C₂	54	6	C3.C3wrS3	486,4
C₃.₃C₃≀S₃	3^rd non-split extension by C₃ of C₃≀S₃ acting via C₃≀S₃/C₃≀C₃=C₂	54	6	C3.3C3wrS3	486,8
C₃²⋊C₉.C₆	2^nd non-split extension by C₃²⋊C₉ of C₆ acting faithfully	54	6	C3^2:C9.C6	486,10
(C₃×He₃).C₆	2^nd non-split extension by C₃×He₃ of C₆ acting faithfully	54	6	(C3xHe3).C6	486,9
C₃³.(C₃×S₃)	8^th non-split extension by C₃³ of C₃×S₃ acting faithfully	54	6	C3^3.(C3xS3)	486,11
C₃²⋊₂D₉.C₃	3^rd non-split extension by C₃²⋊₂D₉ of C₃ acting faithfully	54	6	C3^2:2D9.C3	486,12
(C₃×He₃).S₃	4^th non-split extension by C₃×He₃ of S₃ acting faithfully	81		(C3xHe3).S3	486,44
C₃²⋊C₉.₁₀S₃	10^th non-split extension by C₃²⋊C₉ of S₃ acting faithfully	81		C3^2:C9.10S3	486,49
He₃.(C₃⋊S₃)	4^th non-split extension by He₃ of C₃⋊S₃ acting via C₃⋊S₃/C₃=S₃	81		He3.(C3:S3)	486,186
C₃³.(C₃⋊S₃)	3^rd non-split extension by C₃³ of C₃⋊S₃ acting faithfully	81		C3^3.(C3:S3)	486,45
(C₃²×C₉).S₃	16^th non-split extension by C₃²×C₉ of S₃ acting faithfully	81		(C3^2xC9).S3	486,188
C₃.(He₃⋊S₃)	3^rd non-split extension by C₃ of He₃⋊S₃ acting via He₃⋊S₃/He₃⋊C₃=C₂	81		C3.(He3:S3)	486,48
C₃.(C₃³⋊S₃)	5^th non-split extension by C₃ of C₃³⋊S₃ acting via C₃³⋊S₃/C₃≀C₃=C₂	81		C3.(C3^3:S3)	486,47
C₃.₂(C₉⋊D₉)	The central stem extension by C₃ of C₉⋊D₉	162		C3.2(C9:D9)	486,42
C₉×C₅₄	Abelian group of type [9,54]	486		C9xC54	486,70
C₃×C₁₆₂	Abelian group of type [3,162]	486		C3xC162	486,83
C₃⁴×C₆	Abelian group of type [3,3,3,3,6]	486		C3^4xC6	486,261
C₃²×C₅₄	Abelian group of type [3,3,54]	486		C3^2xC54	486,207
C₃³×C₁₈	Abelian group of type [3,3,3,18]	486		C3^3xC18	486,250
C₃×C₉×C₁₈	Abelian group of type [3,9,18]	486		C3xC9xC18	486,190
C₉×D₂₇	Direct product of C₉ and D₂₇	54	2	C9xD27	486,13
D₉×C₂₇	Direct product of C₂₇ and D₉	54	2	D9xC27	486,14
D₉×He₃	Direct product of D₉ and He₃	54	6	D9xHe3	486,99
D₉×3_-¹⁺²	Direct product of D₉ and 3_-¹⁺²	54	6	D9xES-(3,1)	486,101
C₂×3₊¹⁺⁴	Direct product of C₂ and 3₊¹⁺⁴	54	9	C2xES+(3,2)	486,254
C₂×3_-¹⁺⁴	Direct product of C₂ and 3_-¹⁺⁴	54	9	C2xES-(3,2)	486,255
S₃×C₈₁	Direct product of C₈₁ and S₃	162	2	S3xC81	486,33
C₃×D₈₁	Direct product of C₃ and D₈₁	162	2	C3xD81	486,32
S₃×C₉²	Direct product of C₉² and S₃	162		S3xC9^2	486,92
C₁₈×He₃	Direct product of C₁₈ and He₃	162		C18xHe3	486,194
S₃×C₃⁴	Direct product of C₃⁴ and S₃	162		S3xC3^4	486,256
D₉×C₃³	Direct product of C₃³ and D₉	162		D9xC3^3	486,220
C₃²×D₂₇	Direct product of C₃² and D₂₇	162		C3^2xD27	486,111
C₁₈×3_-¹⁺²	Direct product of C₁₈ and 3_-¹⁺²	162		C18xES-(3,1)	486,195
S₃×C₃≀C₃	Direct product of S₃ and C₃≀C₃	18	6	S3xC3wrC3	486,117
C₃×C₃³⋊C₆	Direct product of C₃ and C₃³⋊C₆	18	6	C3xC3^3:C6	486,116
C₃×C₃³⋊S₃	Direct product of C₃ and C₃³⋊S₃	18	6	C3xC3^3:S3	486,165
C₃×C₃≀S₃	Direct product of C₃ and C₃≀S₃	27		C3xC3wrS3	486,115
D₉×C₃×C₉	Direct product of C₃×C₉ and D₉	54		D9xC3xC9	486,91
C₉×C₉⋊C₆	Direct product of C₉ and C₉⋊C₆	54	6	C9xC9:C6	486,100
C₉×C₉⋊S₃	Direct product of C₉ and C₉⋊S₃	54		C9xC9:S3	486,133
C₆×C₃≀C₃	Direct product of C₆ and C₃≀C₃	54		C6xC3wrC3	486,210
C₂×C₂₇⋊C₉	Direct product of C₂ and C₂₇⋊C₉	54	9	C2xC27:C9	486,82
C₃×C₉⋊C₁₈	Direct product of C₃ and C₉⋊C₁₈	54		C3xC9:C18	486,96
C₃×C₂₇⋊C₆	Direct product of C₃ and C₂₇⋊C₆	54	6	C3xC27:C6	486,113
C₃×S₃×He₃	Direct product of C₃, S₃ and He₃	54		C3xS3xHe3	486,223
S₃×C₂₇⋊C₃	Direct product of S₃ and C₂₇⋊C₃	54	6	S3xC27:C3	486,114
C₃⋊S₃×He₃	Direct product of C₃⋊S₃ and He₃	54		C3:S3xHe3	486,231
S₃×C₃²⋊C₉	Direct product of S₃ and C₃²⋊C₉	54		S3xC3^2:C9	486,95
C₉×C₃²⋊C₆	Direct product of C₉ and C₃²⋊C₆	54	6	C9xC3^2:C6	486,98
C₃²×C₉⋊C₆	Direct product of C₃² and C₉⋊C₆	54		C3^2xC9:C6	486,224
C₃²×C₉⋊S₃	Direct product of C₃² and C₉⋊S₃	54		C3^2xC9:S3	486,227
C₃⋊S₃×C₃³	Direct product of C₃³ and C₃⋊S₃	54		C3:S3xC3^3	486,257
S₃×C₉○He₃	Direct product of S₃ and C₉○He₃	54	6	S3xC9oHe3	486,226
C₃×C₃²⋊C₁₈	Direct product of C₃ and C₃²⋊C₁₈	54		C3xC3^2:C18	486,93
S₃×He₃⋊C₃	Direct product of S₃ and He₃⋊C₃	54	6	S3xHe3:C3	486,123
C₃×He₃⋊S₃	Direct product of C₃ and He₃⋊S₃	54	6	C3xHe3:S3	486,171
C₂×C₃³⋊C₉	Direct product of C₂ and C₃³⋊C₉	54		C2xC3^3:C9	486,73
C₂×C₉²⋊C₃	Direct product of C₂ and C₉²⋊C₃	54	3	C2xC9^2:C3	486,85
S₃×He₃.C₃	Direct product of S₃ and He₃.C₃	54	6	S3xHe3.C3	486,120
C₃×C₃²⋊D₉	Direct product of C₃ and C₃²⋊D₉	54		C3xC3^2:D9	486,94
C₂×C₃²⋊He₃	Direct product of C₂ and C₃²⋊He₃	54		C2xC3^2:He3	486,196
S₃×C₃.He₃	Direct product of S₃ and C₃.He₃	54	6	S3xC3.He3	486,124
C₂×C₉.He₃	Direct product of C₂ and C₉.He₃	54	3	C2xC9.He3	486,214
C₃×He₃⋊₄S₃	Direct product of C₃ and He₃⋊₄S₃	54		C3xHe3:4S3	486,229
C₃×He₃⋊₅S₃	Direct product of C₃ and He₃⋊₅S₃	54		C3xHe3:5S3	486,243
C₂×C₉²⋊₂C₃	Direct product of C₂ and C₉²⋊₂C₃	54	3	C2xC9^2:2C3	486,86
C₃×C₃²⋊₂D₉	Direct product of C₃ and C₃²⋊₂D₉	54		C3xC3^2:2D9	486,135
C₃²×C₃²⋊C₆	Direct product of C₃² and C₃²⋊C₆	54		C3^2xC3^2:C6	486,222
C₃×He₃.S₃	Direct product of C₃ and He₃.S₃	54	6	C3xHe3.S3	486,119
C₂×C₉.₄He₃	Direct product of C₂ and C₉.₄He₃	54	3	C2xC9.4He3	486,76
C₂×C₉².C₃	Direct product of C₂ and C₉².C₃	54	3	C2xC9^2.C3	486,87
C₂×C₃⁴.C₃	Direct product of C₂ and C₃⁴.C₃	54		C2xC3^4.C3	486,197
C₂×C₉.₂He₃	Direct product of C₂ and C₉.₂He₃	54	9	C2xC9.2He3	486,219
C₃×C₃³.S₃	Direct product of C₃ and C₃³.S₃	54		C3xC3^3.S3	486,232
C₃²×C₃³⋊C₂	Direct product of C₃² and C₃³⋊C₂	54		C3^2xC3^3:C2	486,258
C₃×S₃×3_-¹⁺²	Direct product of C₃, S₃ and 3_-¹⁺²	54		C3xS3xES-(3,1)	486,225
C₃×He₃.₂S₃	Direct product of C₃ and He₃.₂S₃	54	6	C3xHe3.2S3	486,122
C₃×He₃.₃S₃	Direct product of C₃ and He₃.₃S₃	54	6	C3xHe3.3S3	486,168
C₃×He₃.₄S₃	Direct product of C₃ and He₃.₄S₃	54	6	C3xHe3.4S3	486,234
C₂×He₃⋊C₃²	Direct product of C₂ and He₃⋊C₃²	54	9	C2xHe3:C3^2	486,217
C₂×C₃³⋊C₃²	Direct product of C₂ and C₃³⋊C₃²	54	9	C2xC3^3:C3^2	486,215
C₃⋊S₃×3_-¹⁺²	Direct product of C₃⋊S₃ and 3_-¹⁺²	54		C3:S3xES-(3,1)	486,233
C₂×C₃².He₃	Direct product of C₂ and C₃².He₃	54	9	C2xC3^2.He3	486,88
C₂×He₃.C₃²	Direct product of C₂ and He₃.C₃²	54	9	C2xHe3.C3^2	486,216
C₂×C₃².₅He₃	Direct product of C₂ and C₃².₅He₃	54	9	C2xC3^2.5He3	486,89
C₂×C₃².₆He₃	Direct product of C₂ and C₃².₆He₃	54	9	C2xC3^2.6He3	486,90
C₂×C₃².C₃³	Direct product of C₂ and C₃².C₃³	54	9	C2xC3^2.C3^3	486,218
C₃×3_-¹⁺².S₃	Direct product of C₃ and 3_-¹⁺².S₃	54	6	C3xES-(3,1).S3	486,174
C₉×He₃⋊C₂	Direct product of C₉ and He₃⋊C₂	81		C9xHe3:C2	486,143
C₃×He₃.C₆	Direct product of C₃ and He₃.C₆	81		C3xHe3.C6	486,118
C₃²×He₃⋊C₂	Direct product of C₃² and He₃⋊C₂	81		C3^2xHe3:C2	486,230
C₃×He₃.₂C₆	Direct product of C₃ and He₃.₂C₆	81		C3xHe3.2C6	486,121
C₃×He₃.₄C₆	Direct product of C₃ and He₃.₄C₆	81		C3xHe3.4C6	486,235
S₃×C₉⋊C₉	Direct product of S₃ and C₉⋊C₉	162		S3xC9:C9	486,97
S₃×C₃×C₂₇	Direct product of C₃×C₂₇ and S₃	162		S3xC3xC27	486,112
C₃×C₉⋊D₉	Direct product of C₃ and C₉⋊D₉	162		C3xC9:D9	486,134
C₂×C₈₁⋊C₃	Direct product of C₂ and C₈₁⋊C₃	162	3	C2xC81:C3	486,84
C₆×C₂₇⋊C₃	Direct product of C₆ and C₂₇⋊C₃	162		C6xC27:C3	486,208
C₃×C₆×He₃	Direct product of C₃×C₆ and He₃	162		C3xC6xHe3	486,251
C₃×C₂₇⋊S₃	Direct product of C₃ and C₂₇⋊S₃	162		C3xC27:S3	486,160
C₃⋊S₃×C₂₇	Direct product of C₂₇ and C₃⋊S₃	162		C3:S3xC27	486,161
C₂×C₉⋊He₃	Direct product of C₂ and C₉⋊He₃	162		C2xC9:He3	486,198
S₃×C₃²×C₉	Direct product of C₃²×C₉ and S₃	162		S3xC3^2xC9	486,221
C₂×He₃⋊C₉	Direct product of C₂ and He₃⋊C₉	162		C2xHe3:C9	486,77
C₆×C₃²⋊C₉	Direct product of C₆ and C₃²⋊C₉	162		C6xC3^2:C9	486,191
C₆×C₉○He₃	Direct product of C₆ and C₉○He₃	162		C6xC9oHe3	486,253
C₉×C₃³⋊C₂	Direct product of C₉ and C₃³⋊C₂	162		C9xC3^3:C2	486,241
C₃×C₃⁴⋊C₂	Direct product of C₃ and C₃⁴⋊C₂	162		C3xC3^4:C2	486,259
C₂×C₃²⋊C₂₇	Direct product of C₂ and C₃²⋊C₂₇	162		C2xC3^2:C27	486,72
C₂×C₂₇○He₃	Direct product of C₂ and C₂₇○He₃	162	3	C2xC27oHe3	486,209
C₆×He₃⋊C₃	Direct product of C₆ and He₃⋊C₃	162		C6xHe3:C3	486,212
C₆×He₃.C₃	Direct product of C₆ and He₃.C₃	162		C6xHe3.C3	486,211
C₆×C₃.He₃	Direct product of C₆ and C₃.He₃	162		C6xC3.He3	486,213
C₂×C₉²⋊₃C₃	Direct product of C₂ and C₉²⋊₃C₃	162		C2xC9^2:3C3	486,193
C₂×C₉²⋊₇C₃	Direct product of C₂ and C₉²⋊₇C₃	162		C2xC9^2:7C3	486,202
C₂×C₉²⋊₄C₃	Direct product of C₂ and C₉²⋊₄C₃	162		C2xC9^2:4C3	486,203
C₂×C₉²⋊₅C₃	Direct product of C₂ and C₉²⋊₅C₃	162		C2xC9^2:5C3	486,204
C₂×C₉²⋊₈C₃	Direct product of C₂ and C₉²⋊₈C₃	162		C2xC9^2:8C3	486,205
C₂×C₉²⋊₉C₃	Direct product of C₂ and C₉²⋊₉C₃	162		C2xC9^2:9C3	486,206
C₃×C₃²⋊₄D₉	Direct product of C₃ and C₃²⋊₄D₉	162		C3xC3^2:4D9	486,240
C₂×C₉.₅He₃	Direct product of C₂ and C₉.₅He₃	162	3	C2xC9.5He3	486,79
C₂×C₉.₆He₃	Direct product of C₂ and C₉.₆He₃	162	3	C2xC9.6He3	486,80
C₃×C₆×3_-¹⁺²	Direct product of C₃×C₆ and 3_-¹⁺²	162		C3xC6xES-(3,1)	486,252
C₂×3_-¹⁺²⋊C₉	Direct product of C₂ and 3_-¹⁺²⋊C₉	162		C2xES-(3,1):C9	486,78
C₂×C₃³.C₃²	Direct product of C₂ and C₃³.C₃²	162		C2xC3^3.C3^2	486,64
C₂×C₉⋊3_-¹⁺²	Direct product of C₂ and C₉⋊3_-¹⁺²	162		C2xC9:ES-(3,1)	486,200
C₂×C₃².₂₄He₃	Direct product of C₂ and C₃².₂₄He₃	162		C2xC3^2.24He3	486,63
C₂×C₃³.₃C₃²	Direct product of C₂ and C₃³.₃C₃²	162		C2xC3^3.3C3^2	486,65
C₂×C₃².₂₇He₃	Direct product of C₂ and C₃².₂₇He₃	162		C2xC3^2.27He3	486,66
C₂×C₃².₂₈He₃	Direct product of C₂ and C₃².₂₈He₃	162		C2xC3^2.28He3	486,67
C₂×C₃².₂₉He₃	Direct product of C₂ and C₃².₂₉He₃	162		C2xC3^2.29He3	486,68
C₂×C₃³.₇C₃²	Direct product of C₂ and C₃³.₇C₃²	162		C2xC3^3.7C3^2	486,69
C₂×C₃².₁₉He₃	Direct product of C₂ and C₃².₁₉He₃	162		C2xC3^2.19He3	486,74
C₂×C₃².₂₀He₃	Direct product of C₂ and C₃².₂₀He₃	162		C2xC3^2.20He3	486,75
C₂×C₃².₂₃C₃³	Direct product of C₂ and C₃².₂₃C₃³	162		C2xC3^2.23C3^3	486,199
C₂×C₃³.₃₁C₃²	Direct product of C₂ and C₃³.₃₁C₃²	162		C2xC3^3.31C3^2	486,201
C₆×C₉⋊C₉	Direct product of C₆ and C₉⋊C₉	486		C6xC9:C9	486,192
C₂×C₉⋊C₂₇	Direct product of C₂ and C₉⋊C₂₇	486		C2xC9:C27	486,81
C₂×C₂₇⋊₂C₉	Direct product of C₂ and C₂₇⋊₂C₉	486		C2xC27:2C9	486,71
C₂×C₃.C₉²	Direct product of C₂ and C₃.C₉²	486		C2xC3.C9^2	486,62
C₃⋊S₃×C₃×C₉	Direct product of C₃×C₉ and C₃⋊S₃	54		C3:S3xC3xC9	486,228

Groups of order 487

		d	ρ	Label	ID
C₄₈₇	Cyclic group	487	1	C487	487,1

Groups of order 488

		d	ρ	Label	ID
C₄₈₈	Cyclic group	488	1	C488	488,2
D₂₄₄	Dihedral group	244	2+	D244	488,6
Dic₁₂₂	Dicyclic group; = C₆₁ ⋊Q₈	488	2-	Dic122	488,4
C₆₁⋊D₄	The semidirect product of C₆₁ and D₄ acting via D₄/C₂²=C₂	244	2	C61:D4	488,8
C₆₁⋊C₈	The semidirect product of C₆₁ and C₈ acting via C₈/C₂=C₄	488	4-	C61:C8	488,3
C₆₁⋊₂C₈	The semidirect product of C₆₁ and C₈ acting via C₈/C₄=C₂	488	2	C61:2C8	488,1
C₂×C₂₄₄	Abelian group of type [2,244]	488		C2xC244	488,9
C₂²×C₁₂₂	Abelian group of type [2,2,122]	488		C2^2xC122	488,14
C₄×D₆₁	Direct product of C₄ and D₆₁	244	2	C4xD61	488,5
D₄×C₆₁	Direct product of C₆₁ and D₄	244	2	D4xC61	488,10
C₂²×D₆₁	Direct product of C₂² and D₆₁	244		C2^2xD61	488,13
Q₈×C₆₁	Direct product of C₆₁ and Q₈	488	2	Q8xC61	488,11
C₂×Dic₆₁	Direct product of C₂ and Dic₆₁	488		C2xDic61	488,7
C₂×C₆₁⋊C₄	Direct product of C₂ and C₆₁⋊C₄	122	4+	C2xC61:C4	488,12

Groups of order 489

		d	ρ	Label	ID
C₄₈₉	Cyclic group	489	1	C489	489,2
C₁₆₃⋊C₃	The semidirect product of C₁₆₃ and C₃ acting faithfully	163	3	C163:C3	489,1

Groups of order 490

		d	ρ	Label	ID
C₄₉₀	Cyclic group	490	1	C490	490,4
D₂₄₅	Dihedral group	245	2+	D245	490,3
C₇⋊D₃₅	The semidirect product of C₇ and D₃₅ acting via D₃₅/C₃₅=C₂	245		C7:D35	490,9
C₇×C₇₀	Abelian group of type [7,70]	490		C7xC70	490,10
D₇×C₃₅	Direct product of C₃₅ and D₇	70	2	D7xC35	490,5
C₇×D₃₅	Direct product of C₇ and D₃₅	70	2	C7xD35	490,8
D₅×C₄₉	Direct product of C₄₉ and D₅	245	2	D5xC49	490,1
C₅×D₄₉	Direct product of C₅ and D₄₉	245	2	C5xD49	490,2
D₅×C₇²	Direct product of C₇² and D₅	245		D5xC7^2	490,7
C₅×C₇⋊D₇	Direct product of C₅ and C₇⋊D₇	245		C5xC7:D7	490,6

Groups of order 491

		d	ρ	Label	ID
C₄₉₁	Cyclic group	491	1	C491	491,1

Groups of order 492

		d	ρ	Label	ID
C₄₉₂	Cyclic group	492	1	C492	492,4
D₂₄₆	Dihedral group; = C₂×D₁₂₃	246	2+	D246	492,11
Dic₁₂₃	Dicyclic group; = C₃ ⋊Dic₄₁	492	2-	Dic123	492,3
C₄₁⋊Dic₃	The semidirect product of C₄₁ and Dic₃ acting via Dic₃/C₃=C₄	123	4	C41:Dic3	492,6
C₂×C₂₄₆	Abelian group of type [2,246]	492		C2xC246	492,12
S₃×D₄₁	Direct product of S₃ and D₄₁	123	4+	S3xD41	492,7
A₄×C₄₁	Direct product of C₄₁ and A₄	164	3	A4xC41	492,8
S₃×C₈₂	Direct product of C₈₂ and S₃	246	2	S3xC82	492,10
C₆×D₄₁	Direct product of C₆ and D₄₁	246	2	C6xD41	492,9
Dic₃×C₄₁	Direct product of C₄₁ and Dic₃	492	2	Dic3xC41	492,1
C₃×Dic₄₁	Direct product of C₃ and Dic₄₁	492	2	C3xDic41	492,2
C₃×C₄₁⋊C₄	Direct product of C₃ and C₄₁⋊C₄	123	4	C3xC41:C4	492,5

Groups of order 493

		d	ρ	Label	ID
C₄₉₃	Cyclic group	493	1	C493	493,1

Groups of order 494

		d	ρ	Label	ID
C₄₉₄	Cyclic group	494	1	C494	494,4
D₂₄₇	Dihedral group	247	2+	D247	494,3
C₁₉×D₁₃	Direct product of C₁₉ and D₁₃	247	2	C19xD13	494,1
C₁₃×D₁₉	Direct product of C₁₃ and D₁₉	247	2	C13xD19	494,2

Groups of order 495

		d	ρ	Label	ID
C₄₉₅	Cyclic group	495	1	C495	495,2
C₃×C₁₆₅	Abelian group of type [3,165]	495		C3xC165	495,4
C₉×C₁₁⋊C₅	Direct product of C₉ and C₁₁⋊C₅	99	5	C9xC11:C5	495,1
C₃²×C₁₁⋊C₅	Direct product of C₃² and C₁₁⋊C₅	99		C3^2xC11:C5	495,3

Groups of order 496

		d	ρ	Label	ID
C₄₉₆	Cyclic group	496	1	C496	496,2
D₂₄₈	Dihedral group	248	2+	D248	496,6
Dic₁₂₄	Dicyclic group; = C₃₁ ⋊₁ Q₁₆	496	2-	Dic124	496,7
D₆₂⋊C₄	The semidirect product of D₆₂ and C₄ acting via C₄/C₂=C₂	248		D62:C4	496,13
D₄⋊D₃₁	The semidirect product of D₄ and D₃₁ acting via D₃₁/C₃₁=C₂	248	4+	D4:D31	496,14
Q₈⋊D₃₁	The semidirect product of Q₈ and D₃₁ acting via D₃₁/C₃₁=C₂	248	4+	Q8:D31	496,16
C₈⋊D₃₁	3^rd semidirect product of C₈ and D₃₁ acting via D₃₁/C₃₁=C₂	248	2	C8:D31	496,4
C₂₄₈⋊C₂	2^nd semidirect product of C₂₄₈ and C₂ acting faithfully	248	2	C248:C2	496,5
D₄⋊₂D₃₁	The semidirect product of D₄ and D₃₁ acting through Inn(D₄)	248	4-	D4:2D31	496,32
Q₈⋊₂D₃₁	The semidirect product of Q₈ and D₃₁ acting through Inn(Q₈)	248	4+	Q8:2D31	496,34
D₁₂₄⋊₅C₂	The semidirect product of D₁₂₄ and C₂ acting through Inn(D₁₂₄)	248	2	D124:5C2	496,30
C₃₁⋊C₁₆	The semidirect product of C₃₁ and C₁₆ acting via C₁₆/C₈=C₂	496	2	C31:C16	496,1
C₄⋊Dic₃₁	The semidirect product of C₄ and Dic₃₁ acting via Dic₃₁/C₆₂=C₂	496		C4:Dic31	496,12
C₃₁⋊Q₁₆	The semidirect product of C₃₁ and Q₁₆ acting via Q₁₆/Q₈=C₂	496	4-	C31:Q16	496,17
Dic₃₁⋊C₄	The semidirect product of Dic₃₁ and C₄ acting via C₄/C₂=C₂	496		Dic31:C4	496,11
D₄.D₃₁	The non-split extension by D₄ of D₃₁ acting via D₃₁/C₃₁=C₂	248	4-	D4.D31	496,15
C₄.Dic₃₁	The non-split extension by C₄ of Dic₃₁ acting via Dic₃₁/C₆₂=C₂	248	2	C4.Dic31	496,9
C₂³.D₃₁	The non-split extension by C₂³ of D₃₁ acting via D₃₁/C₃₁=C₂	248		C2^3.D31	496,18
C₄×C₁₂₄	Abelian group of type [4,124]	496		C4xC124	496,19
C₂×C₂₄₈	Abelian group of type [2,248]	496		C2xC248	496,22
C₂³×C₆₂	Abelian group of type [2,2,2,62]	496		C2^3xC62	496,42
C₂²×C₁₂₄	Abelian group of type [2,2,124]	496		C2^2xC124	496,37
D₄×D₃₁	Direct product of D₄ and D₃₁	124	4+	D4xD31	496,31
C₈×D₃₁	Direct product of C₈ and D₃₁	248	2	C8xD31	496,3
D₈×C₃₁	Direct product of C₃₁ and D₈	248	2	D8xC31	496,24
D₄×C₆₂	Direct product of C₆₂ and D₄	248		D4xC62	496,38
Q₈×D₃₁	Direct product of Q₈ and D₃₁	248	4-	Q8xD31	496,33
C₂×D₁₂₄	Direct product of C₂ and D₁₂₄	248		C2xD124	496,29
SD₁₆×C₃₁	Direct product of C₃₁ and SD₁₆	248	2	SD16xC31	496,25
C₂³×D₃₁	Direct product of C₂³ and D₃₁	248		C2^3xD31	496,41
M₄(2)×C₃₁	Direct product of C₃₁ and M₄(2)	248	2	M4(2)xC31	496,23
Q₈×C₆₂	Direct product of C₆₂ and Q₈	496		Q8xC62	496,39
Q₁₆×C₃₁	Direct product of C₃₁ and Q₁₆	496	2	Q16xC31	496,26
C₄×Dic₃₁	Direct product of C₄ and Dic₃₁	496		C4xDic31	496,10
C₂×Dic₆₂	Direct product of C₂ and Dic₆₂	496		C2xDic62	496,27
C₂²×Dic₃₁	Direct product of C₂² and Dic₃₁	496		C2^2xDic31	496,35
C₂×C₄×D₃₁	Direct product of C₂×C₄ and D₃₁	248		C2xC4xD31	496,28
C₂×C₃₁⋊D₄	Direct product of C₂ and C₃₁⋊D₄	248		C2xC31:D4	496,36
C₄○D₄×C₃₁	Direct product of C₃₁ and C₄○D₄	248	2	C4oD4xC31	496,40
C₂²⋊C₄×C₃₁	Direct product of C₃₁ and C₂²⋊C₄	248		C2^2:C4xC31	496,20
C₂×C₃₁⋊C₈	Direct product of C₂ and C₃₁⋊C₈	496		C2xC31:C8	496,8
C₄⋊C₄×C₃₁	Direct product of C₃₁ and C₄⋊C₄	496		C4:C4xC31	496,21

Groups of order 497

		d	ρ	Label	ID
C₄₉₇	Cyclic group	497	1	C497	497,2
C₇₁⋊C₇	The semidirect product of C₇₁ and C₇ acting faithfully	71	7	C71:C7	497,1

Groups of order 498

		d	ρ	Label	ID
C₄₉₈	Cyclic group	498	1	C498	498,4
D₂₄₉	Dihedral group	249	2+	D249	498,3
S₃×C₈₃	Direct product of C₈₃ and S₃	249	2	S3xC83	498,1
C₃×D₈₃	Direct product of C₃ and D₈₃	249	2	C3xD83	498,2

Groups of order 499

		d	ρ	Label	ID
C₄₉₉	Cyclic group	499	1	C499	499,1

Groups of order 500

		d	ρ	Label	ID
C₅₀₀	Cyclic group	500	1	C500	500,2
D₂₅₀	Dihedral group; = C₂×D₁₂₅	250	2+	D250	500,4
Dic₁₂₅	Dicyclic group; = C₁₂₅ ⋊₂ C₄	500	2-	Dic125	500,1
C₅³⋊₆C₄	6^th semidirect product of C₅³ and C₄ acting faithfully	20	4	C5^3:6C4	500,46
C₅²⋊₅D₁₀	2^nd semidirect product of C₅² and D₁₀ acting via D₁₀/C₅=C₂²	20	4	C5^2:5D10	500,52
C₂₅⋊C₂₀	The semidirect product of C₂₅ and C₂₀ acting faithfully; = Aut(D₂₅) = Hol(C₂₅)	25	20+	C25:C20	500,18
C₅²⋊C₂₀	The semidirect product of C₅² and C₂₀ acting faithfully	25	20+	C5^2:C20	500,17
He₅⋊C₄	2^nd semidirect product of He₅ and C₄ acting faithfully	25	20+	He5:C4	500,21
He₅⋊₄C₄	4^th semidirect product of He₅ and C₄ acting faithfully; = Aut(5_-¹⁺²)	25	5	He5:4C4	500,25
C₅²⋊D₁₀	The semidirect product of C₅² and D₁₀ acting faithfully	25	10+	C5^2:D10	500,27
C₅²⋊F₅	3^rd semidirect product of C₅² and F₅ acting faithfully	25	10+	C5^2:F5	500,23
C₂₅⋊₂F₅	2^nd semidirect product of C₂₅ and F₅ acting via F₅/C₅=C₄	50	4+	C25:2F5	500,24
C₅³⋊₉C₄	9^th semidirect product of C₅³ and C₄ acting faithfully	50		C5^3:9C4	500,49
He₅⋊₅C₄	1^st semidirect product of He₅ and C₄ acting via C₄/C₂=C₂	100	10-	He5:5C4	500,8
He₅⋊₆C₄	2^nd semidirect product of He₅ and C₄ acting via C₄/C₂=C₂	100	5	He5:6C4	500,11
C₅³⋊C₄	5^th semidirect product of C₅³ and C₄ acting faithfully	100		C5^3:C4	500,45
C₅³⋊₇C₄	7^th semidirect product of C₅³ and C₄ acting faithfully	100		C5^3:7C4	500,47
C₁₂₅⋊C₄	The semidirect product of C₁₂₅ and C₄ acting faithfully	125	4+	C125:C4	500,3
C₂₅⋊F₅	1^st semidirect product of C₂₅ and F₅ acting via F₅/C₅=C₄	125		C25:F5	500,22
C₅³⋊₈C₄	8^th semidirect product of C₅³ and C₄ acting faithfully	125		C5^3:8C4	500,48
C₅³⋊₁₂C₄	3^rd semidirect product of C₅³ and C₄ acting via C₄/C₂=C₂	500		C5^3:12C4	500,39
C₅₀.C₁₀	The non-split extension by C₅₀ of C₁₀ acting faithfully	100	10-	C50.C10	500,9
D₅.D₂₅	The non-split extension by D₅ of D₂₅ acting via D₂₅/C₂₅=C₂	100	4	D5.D25	500,19
D₂₅.D₅	The non-split extension by D₂₅ of D₅ acting via D₅/C₅=C₂	100	4	D25.D5	500,20
C₅₀.D₅	3^rd non-split extension by C₅₀ of D₅ acting via D₅/C₅=C₂	500		C50.D5	500,10
C₂×C₂₅₀	Abelian group of type [2,250]	500		C2xC250	500,5
C₅×C₁₀₀	Abelian group of type [5,100]	500		C5xC100	500,12
C₁₀×C₅₀	Abelian group of type [10,50]	500		C10xC50	500,34
C₅²×C₂₀	Abelian group of type [5,5,20]	500		C5^2xC20	500,40
C₅×C₁₀²	Abelian group of type [5,10,10]	500		C5xC10^2	500,56
D₅×D₂₅	Direct product of D₅ and D₂₅	50	4+	D5xD25	500,26
D₅×C₅₀	Direct product of C₅₀ and D₅	100	2	D5xC50	500,29
C₄×He₅	Direct product of C₄ and He₅	100	5	C4xHe5	500,13
F₅×C₂₅	Direct product of C₂₅ and F₅	100	4	F5xC25	500,15
C₁₀×D₂₅	Direct product of C₁₀ and D₂₅	100	2	C10xD25	500,28
F₅×C₅²	Direct product of C₅² and F₅	100		F5xC5^2	500,41
C₅×Dic₂₅	Direct product of C₅ and Dic₂₅	100	2	C5xDic25	500,6
Dic₅×C₂₅	Direct product of C₂₅ and Dic₅	100	2	Dic5xC25	500,7
C₂²×He₅	Direct product of C₂² and He₅	100		C2^2xHe5	500,35
Dic₅×C₅²	Direct product of C₅² and Dic₅	100		Dic5xC5^2	500,37
C₄×5_-¹⁺²	Direct product of C₄ and 5_-¹⁺²	100	5	C4xES-(5,1)	500,14
C₂²×5_-¹⁺²	Direct product of C₂² and 5_-¹⁺²	100		C2^2xES-(5,1)	500,36
C₅×D₅²	Direct product of C₅, D₅ and D₅	20	4	C5xD5^2	500,50
C₅×D₅.D₅	Direct product of C₅ and D₅.D₅	20	4	C5xD5.D5	500,42
C₅×C₅²⋊C₄	Direct product of C₅ and C₅²⋊C₄	20	4	C5xC5^2:C4	500,44
D₅×C₅⋊D₅	Direct product of D₅ and C₅⋊D₅	50		D5xC5:D5	500,51
C₂×C₂₅⋊C₁₀	Direct product of C₂ and C₂₅⋊C₁₀	50	10+	C2xC25:C10	500,31
C₂×He₅⋊C₂	Direct product of C₂ and He₅⋊C₂	50	5	C2xHe5:C2	500,33
C₂×C₅²⋊C₁₀	Direct product of C₂ and C₅²⋊C₁₀	50	10+	C2xC5^2:C10	500,30
C₅×C₂₅⋊C₄	Direct product of C₅ and C₂₅⋊C₄	100	4	C5xC25:C4	500,16
D₅×C₅×C₁₀	Direct product of C₅×C₁₀ and D₅	100		D5xC5xC10	500,53
C₁₀×C₅⋊D₅	Direct product of C₁₀ and C₅⋊D₅	100		C10xC5:D5	500,54
C₅×C₅⋊F₅	Direct product of C₅ and C₅⋊F₅	100		C5xC5:F5	500,43
C₅×C₅²⋊₆C₄	Direct product of C₅ and C₅²⋊₆C₄	100		C5xC5^2:6C4	500,38
C₂×C₂₅⋊D₅	Direct product of C₂ and C₂₅⋊D₅	250		C2xC25:D5	500,32
C₂×C₅³⋊C₂	Direct product of C₂ and C₅³⋊C₂	250		C2xC5^3:C2	500,55

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Group​Names [Beta]

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GroupNames [Beta]