Nilpotent groups

A finite group G is nilpotent if it is a direct product of p-groups. Equivalently, all Sylow subgroups of G are normal. Equivalently, G has a central series

{1}=G₀ ◃ G₁ ◃ N₂ ◃...◃ G_k = G, a nested sequence of normal subgroups with [G,G_i+1]≤G_i. The smallest such k is the nilpotency class of G. It is 0 for C₁, 1 for non-trivial abelian groups, and ≥2 for all other nilpotent groups. Nilpotent groups are closed under subgroups and quotients (but not extensions), and are soluble, supersoluble and monomial. See also non-nilpotent 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

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

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
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

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
C₃×C₆	Abelian group of type [3,6]	18		C3xC6	18,5

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
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

Groups of order 22

		d	ρ	Label	ID
C₂₂	Cyclic group	22	1	C22	22,2

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
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
C₃×D₄	Direct product of C₃ and D₄	12	2	C3xD4	24,10
C₃×Q₈	Direct product of C₃ and Q₈	24	2	C3xQ8	24,11

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

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
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

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

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
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

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

Groups of order 39

		d	ρ	Label	ID
C₃₉	Cyclic group	39	1	C39	39,2

Groups of order 40

		d	ρ	Label	ID
C₄₀	Cyclic group	40	1	C40	40,2
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
C₅×D₄	Direct product of C₅ and D₄	20	2	C5xD4	40,10
C₅×Q₈	Direct product of C₅ and Q₈	40	2	C5xQ8	40,11

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

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
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

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
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
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
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
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
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
C₅×C₁₀	Abelian group of type [5,10]	50		C5xC10	50,5

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
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
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
C₂×He₃	Direct product of C₂ and He₃	18	3	C2xHe3	54,10
C₂×3_-¹⁺²	Direct product of C₂ and 3_-¹⁺²	18	3	C2xES-(3,1)	54,11

Groups of order 55

		d	ρ	Label	ID
C₅₅	Cyclic group	55	1	C55	55,2

Groups of order 56

		d	ρ	Label	ID
C₅₆	Cyclic group	56	1	C56	56,2
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
C₇×D₄	Direct product of C₇ and D₄	28	2	C7xD4	56,9
C₇×Q₈	Direct product of C₇ and Q₈	56	2	C7xQ8	56,10

Groups of order 57

		d	ρ	Label	ID
C₅₇	Cyclic group	57	1	C57	57,2

Groups of order 58

		d	ρ	Label	ID
C₅₈	Cyclic group	58	1	C58	58,2

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
C₂×C₃₀	Abelian group of type [2,30]	60		C2xC30	60,13

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

Groups of order 63

		d	ρ	Label	ID
C₆₃	Cyclic group	63	1	C63	63,2
C₃×C₂₁	Abelian group of type [3,21]	63		C3xC21	63,4

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

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
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

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
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
D₄×C₉	Direct product of C₉ and D₄	36	2	D4xC9	72,10
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
Q₈×C₃²	Direct product of C₃² and Q₈	72		Q8xC3^2	72,38

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

Groups of order 75

		d	ρ	Label	ID
C₇₅	Cyclic group	75	1	C75	75,1
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
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

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
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
C₅×D₈	Direct product of C₅ and D₈	40	2	C5xD8	80,25
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
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
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
C₅×C₄⋊C₄	Direct product of C₅ and C₄⋊C₄	80		C5xC4:C4	80,22

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

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
C₂×C₄₂	Abelian group of type [2,42]	84		C2xC42	84,15

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

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
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
D₄×C₁₁	Direct product of C₁₁ and D₄	44	2	D4xC11	88,9
Q₈×C₁₁	Direct product of C₁₁ and Q₈	88	2	Q8xC11	88,10

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
C₃×C₃₀	Abelian group of type [3,30]	90		C3xC30	90,10

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
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

Groups of order 94

		d	ρ	Label	ID
C₉₄	Cyclic group	94	1	C94	94,2

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
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
C₃×2₊¹⁺⁴	Direct product of C₃ and 2₊¹⁺⁴	24	4	C3xES+(2,2)	96,224
C₆×D₈	Direct product of C₆ and D₈	48		C6xD8	96,179
C₃×D₁₆	Direct product of C₃ and D₁₆	48	2	C3xD16	96,61
D₄×C₁₂	Direct product of C₁₂ and D₄	48		D4xC12	96,165
C₃×SD₃₂	Direct product of C₃ and SD₃₂	48	2	C3xSD32	96,62
C₆×SD₁₆	Direct product of C₆ and SD₁₆	48		C6xSD16	96,180
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
C₃×C₄≀C₂	Direct product of C₃ and C₄≀C₂	24	2	C3xC4wrC2	96,54
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	24	4	C3xC2^3:C4	96,49
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
D₄×C₂×C₆	Direct product of C₂×C₆ and D₄	48		D4xC2xC6	96,221
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
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
C₃×C₂²⋊Q₈	Direct product of C₃ and C₂²⋊Q₈	48		C3xC2^2:Q8	96,169
C₃×C₄²⋊C₂	Direct product of C₃ and C₄²⋊C₂	48		C3xC4^2:C2	96,164
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
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
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
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
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
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
C₇×C₁₄	Abelian group of type [7,14]	98		C7xC14	98,5

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
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

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

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
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
D₄×C₁₃	Direct product of C₁₃ and D₄	52	2	D4xC13	104,10
Q₈×C₁₃	Direct product of C₁₃ and Q₈	104	2	Q8xC13	104,11

Groups of order 105

		d	ρ	Label	ID
C₁₀₅	Cyclic group	105	1	C105	105,2

Groups of order 106

		d	ρ	Label	ID
C₁₀₆	Cyclic group	106	1	C106	106,2

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
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
C₄×He₃	Direct product of C₄ and He₃	36	3	C4xHe3	108,13
C₂²×He₃	Direct product of C₂² and He₃	36		C2^2xHe3	108,30
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

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

Groups of order 111

		d	ρ	Label	ID
C₁₁₁	Cyclic group	111	1	C111	111,2

Groups of order 112

		d	ρ	Label	ID
C₁₁₂	Cyclic group	112	1	C112	112,2
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
C₇×D₈	Direct product of C₇ and D₈	56	2	C7xD8	112,24
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
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
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
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

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
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
C₃×C₃₉	Abelian group of type [3,39]	117		C3xC39	117,4

Groups of order 118

		d	ρ	Label	ID
C₁₁₈	Cyclic group	118	1	C118	118,2

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
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
D₄×C₁₅	Direct product of C₁₅ and D₄	60	2	D4xC15	120,32
Q₈×C₁₅	Direct product of C₁₅ and Q₈	120	2	Q8xC15	120,33

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