Soluble groups

A group is soluble or solvable if there are nested normal subgroups N_i◃G

{1}=N₀ < N₁ < N₂ <...< N_k = G with all successive quotients N_i+1/N_i abelian. All abelian, nilpotent, monomial, supersoluble, metabelian groups, p-groups, Z-groups and A-groups are soluble, and the class of soluble groups is closed under subgroups, quotients and extensions. Among all groups of order <120 only A₅ is not soluble. See also non-soluble 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
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
D₆₀	Dihedral group	60	2+	D60	120,28
Dic₃₀	Dicyclic group; = C₁₅ ⋊₂ Q₈	120	2-	Dic30	120,26
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
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

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