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

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Group​Names [Beta]

Groups of order 1

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GroupNames [Beta]