Faithful irreducible representation

Groups G whose centre is cyclic (and only these) admit a faithful irreducible representation ρ: G→GL_n(ℂ). In the table below the groups are sorted by the smallest dimension n and the Frobenius-Schur indicator + if ρ is orthogonal, - if ρ is symplectic, and nothing otherwise.

Jump to: 1,1+ (cyclic) 2+ (dihedral) 2- (dicyclic+3 more) 2 3+ (symmetries of platonic solids) 3
4+ 4- 4 5+ 5 6+ 6- 6 7+ 7 8+ 8- 8 9+ 9 10+ 10- 10 11 12+ 12- 12 13 14+ 14- 14 15+ 15 16+ 18+ 20+

Dimension 1 (ρ=1,1+)

A group has a faithful 1-dimensional representation if and only if it is cyclic.

Orthogonal of dimension 2 (ρ=2+)

A group has a faithful 2-dimensional orthogonal irreducible representation if and only if it is dihedral.

Symplectic of dimension 2 (ρ=2-)

A group with a faithful 2-dimensional symplectic irreducible representation is either dicyclic (e.g. generalized quaternion) or one of the following groups (Klein 1876).

Groups of order 24

		d	ρ	Label	ID
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

Groups of order 48

		d	ρ	Label	ID
CSU₂(𝔽₃)	Conformal special unitary group on 𝔽₃²; = Q₈ .S₃ = 2O = <2,3,4>	16	2-	CSU(2,3)	48,28

Groups of order 120

		d	ρ	Label	ID
SL₂(𝔽₅)	Special linear group on 𝔽₅²; = C₂ .A₅ = 2I = <2,3,5>	24	2-	SL(2,5)	120,5

Complex of dimension 2 (ρ=2)

Groups of order 16

		d	ρ	Label	ID
M₄(2)	Modular maximal-cyclic group; = C₈ ⋊₃ C₂	8	2	M4(2)	16,6
SD₁₆	Semidihedral group; = Q₈ ⋊C₂ = QD₁₆	8	2	SD16	16,8
C₄○D₄	Pauli group = central product of C₄ and D₄	8	2	C4oD4	16,13

Groups of order 18

		d	ρ	Label	ID
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	6	2	C3xS3	18,3

Groups of order 24

		d	ρ	Label	ID
C₃⋊C₈	The semidirect product of C₃ and C₈ acting via C₈/C₄=C₂	24	2	C3:C8	24,1
C₄×S₃	Direct product of C₄ and S₃	12	2	C4xS3	24,5
C₃⋊D₄	The semidirect product of C₃ and D₄ acting via D₄/C₂²=C₂	12	2	C3:D4	24,8
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 30

		d	ρ	Label	ID
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 32

		d	ρ	Label	ID
C₄≀C₂	Wreath product of C₄ by C₂	8	2	C4wrC2	32,11
C₈.C₄	1^st non-split extension by C₈ of C₄ acting via C₄/C₂=C₂	16	2	C8.C4	32,15
M₅(2)	Modular maximal-cyclic group; = C₁₆ ⋊₃ C₂	16	2	M5(2)	32,17
SD₃₂	Semidihedral group; = C₁₆ ⋊₂ C₂ = QD₃₂	16	2	SD32	32,19
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

Groups of order 36

		d	ρ	Label	ID
C₃×Dic₃	Direct product of C₃ and Dic₃	12	2	C3xDic3	36,6
S₃×C₆	Direct product of C₆ and S₃	12	2	S3xC6	36,12

Groups of order 40

		d	ρ	Label	ID
C₅⋊₂C₈	The semidirect product of C₅ and C₈ acting via C₈/C₄=C₂	40	2	C5:2C8	40,1
C₄×D₅	Direct product of C₄ and D₅	20	2	C4xD5	40,5
C₅⋊D₄	The semidirect product of C₅ and D₄ acting via D₄/C₂²=C₂	20	2	C5:D4	40,8
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 42

		d	ρ	Label	ID
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

Groups of order 48

		d	ρ	Label	ID
C₃⋊C₁₆	The semidirect product of C₃ and C₁₆ acting via C₁₆/C₈=C₂	48	2	C3:C16	48,1
S₃×C₈	Direct product of C₈ and S₃	24	2	S3xC8	48,4
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
C₄.Dic₃	The non-split extension by C₄ of Dic₃ acting via Dic₃/C₆=C₂	24	2	C4.Dic3	48,10
C₃×M₄(2)	Direct product of C₃ and M₄(2)	24	2	C3xM4(2)	48,24
C₃×D₈	Direct product of C₃ and D₈	24	2	C3xD8	48,25
C₃×SD₁₆	Direct product of C₃ and SD₁₆	24	2	C3xSD16	48,26
C₃×Q₁₆	Direct product of C₃ and Q₁₆	48	2	C3xQ16	48,27
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	8	2	GL(2,3)	48,29
C₄.A₄	The central extension by C₄ of A₄	16	2	C4.A4	48,33
C₄○D₁₂	Central product of C₄ and D₁₂	24	2	C4oD12	48,37
C₃×C₄○D₄	Direct product of C₃ and C₄○D₄	24	2	C3xC4oD4	48,47

Groups of order 50

		d	ρ	Label	ID
C₅×D₅	Direct product of C₅ and D₅; = AΣL₁(𝔽₂₅)	10	2	C5xD5	50,3

Groups of order 54

		d	ρ	Label	ID
C₃×D₉	Direct product of C₃ and D₉	18	2	C3xD9	54,3
S₃×C₉	Direct product of C₉ and S₃	18	2	S3xC9	54,4

Groups of order 56

		d	ρ	Label	ID
C₇⋊C₈	The semidirect product of C₇ and C₈ acting via C₈/C₄=C₂	56	2	C7:C8	56,1
C₄×D₇	Direct product of C₄ and D₇	28	2	C4xD7	56,4
C₇⋊D₄	The semidirect product of C₇ and D₄ acting via D₄/C₂²=C₂	28	2	C7:D4	56,7
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 60

		d	ρ	Label	ID
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
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

Groups of order 64

		d	ρ	Label	ID
D₄.C₈	The non-split extension by D₄ of C₈ acting via C₈/C₄=C₂	32	2	D4.C8	64,31
D₈.C₄	1^st non-split extension by D₈ of C₄ acting via C₄/C₂=C₂	32	2	D8.C4	64,40
C₈.C₈	1^st non-split extension by C₈ of C₈ acting via C₈/C₄=C₂	16	2	C8.C8	64,45
C₈.₄Q₈	3^rd non-split extension by C₈ of Q₈ acting via Q₈/C₄=C₂	32	2	C8.4Q8	64,49
M₆(2)	Modular maximal-cyclic group; = C₃₂ ⋊₃ C₂	32	2	M6(2)	64,51
SD₆₄	Semidihedral group; = C₃₂ ⋊₂ C₂ = QD₆₄	32	2	SD64	64,53
C₈○D₈	Central product of C₈ and D₈	16	2	C8oD8	64,124
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

Groups of order 66

		d	ρ	Label	ID
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 70

		d	ρ	Label	ID
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 72

		d	ρ	Label	ID
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
C₄×D₉	Direct product of C₄ and D₉	36	2	C4xD9	72,5
C₉⋊D₄	The semidirect product of C₉ and D₄ acting via D₄/C₂²=C₂	36	2	C9:D4	72,8
D₄×C₉	Direct product of C₉ and D₄	36	2	D4xC9	72,10
Q₈×C₉	Direct product of C₉ and Q₈	72	2	Q8xC9	72,11
C₃×C₃⋊C₈	Direct product of C₃ and C₃⋊C₈	24	2	C3xC3:C8	72,12
C₃×SL₂(𝔽₃)	Direct product of C₃ and SL₂(𝔽₃)	24	2	C3xSL(2,3)	72,25
C₃×Dic₆	Direct product of C₃ and Dic₆	24	2	C3xDic6	72,26
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
C₃×C₃⋊D₄	Direct product of C₃ and C₃⋊D₄	12	2	C3xC3:D4	72,30

Groups of order 78

		d	ρ	Label	ID
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

Groups of order 80

		d	ρ	Label	ID
C₅⋊₂C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₈=C₂	80	2	C5:2C16	80,1
C₈×D₅	Direct product of C₈ and D₅	40	2	C8xD5	80,4
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
C₄.Dic₅	The non-split extension by C₄ of Dic₅ acting via Dic₅/C₁₀=C₂	40	2	C4.Dic5	80,10
C₅×M₄(2)	Direct product of C₅ and M₄(2)	40	2	C5xM4(2)	80,24
C₅×D₈	Direct product of C₅ and D₈	40	2	C5xD8	80,25
C₅×SD₁₆	Direct product of C₅ and SD₁₆	40	2	C5xSD16	80,26
C₅×Q₁₆	Direct product of C₅ and Q₁₆	80	2	C5xQ16	80,27
C₄○D₂₀	Central product of C₄ and D₂₀	40	2	C4oD20	80,38
C₅×C₄○D₄	Direct product of C₅ and C₄○D₄	40	2	C5xC4oD4	80,48

Groups of order 84

		d	ρ	Label	ID
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
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

Groups of order 88

		d	ρ	Label	ID
C₁₁⋊C₈	The semidirect product of C₁₁ and C₈ acting via C₈/C₄=C₂	88	2	C11:C8	88,1
C₄×D₁₁	Direct product of C₄ and D₁₁	44	2	C4xD11	88,4
C₁₁⋊D₄	The semidirect product of C₁₁ and D₄ acting via D₄/C₂²=C₂	44	2	C11:D4	88,7
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 90

		d	ρ	Label	ID
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
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

Groups of order 96

		d	ρ	Label	ID
C₃⋊C₃₂	The semidirect product of C₃ and C₃₂ acting via C₃₂/C₁₆=C₂	96	2	C3:C32	96,1
S₃×C₁₆	Direct product of C₁₆ and S₃	48	2	S3xC16	96,4
D₆.C₈	The non-split extension by D₆ of C₈ acting via C₈/C₄=C₂	48	2	D6.C8	96,5
C₄₈⋊C₂	2^nd semidirect product of C₄₈ and C₂ acting faithfully	48	2	C48:C2	96,7
C₄²⋊₄S₃	3^rd semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	24	2	C4^2:4S3	96,12
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
C₃×C₄≀C₂	Direct product of C₃ and C₄≀C₂	24	2	C3xC4wrC2	96,54
C₃×C₈.C₄	Direct product of C₃ and C₈.C₄	48	2	C3xC8.C4	96,58
C₃×M₅(2)	Direct product of C₃ and M₅(2)	48	2	C3xM5(2)	96,60
C₃×D₁₆	Direct product of C₃ and D₁₆	48	2	C3xD16	96,61
C₃×SD₃₂	Direct product of C₃ and SD₃₂	48	2	C3xSD32	96,62
C₃×Q₃₂	Direct product of C₃ and Q₃₂	96	2	C3xQ32	96,63
U₂(𝔽₃)	Unitary group on 𝔽₃²; = SL₂(𝔽₃)⋊₂ C₄	24	2	U(2,3)	96,67
C₈.A₄	The central extension by C₈ of A₄	32	2	C8.A4	96,74
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
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
C₄.₆S₄	3^rd central extension by C₄ of S₄	16	2	C4.6S4	96,192

Groups of order 98

		d	ρ	Label	ID
C₇×D₇	Direct product of C₇ and D₇; = AΣL₁(𝔽₄₉)	14	2	C7xD7	98,3

Groups of order 100

		d	ρ	Label	ID
C₅×Dic₅	Direct product of C₅ and Dic₅	20	2	C5xDic5	100,6
D₅×C₁₀	Direct product of C₁₀ and D₅	20	2	D5xC10	100,14

Groups of order 102

		d	ρ	Label	ID
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 104

		d	ρ	Label	ID
C₁₃⋊₂C₈	The semidirect product of C₁₃ and C₈ acting via C₈/C₄=C₂	104	2	C13:2C8	104,1
C₄×D₁₃	Direct product of C₄ and D₁₃	52	2	C4xD13	104,5
C₁₃⋊D₄	The semidirect product of C₁₃ and D₄ acting via D₄/C₂²=C₂	52	2	C13:D4	104,8
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 108

		d	ρ	Label	ID
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
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

Groups of order 110

		d	ρ	Label	ID
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

Groups of order 112

		d	ρ	Label	ID
C₇⋊C₁₆	The semidirect product of C₇ and C₁₆ acting via C₁₆/C₈=C₂	112	2	C7:C16	112,1
C₈×D₇	Direct product of C₈ and D₇	56	2	C8xD7	112,3
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
C₄.Dic₇	The non-split extension by C₄ of Dic₇ acting via Dic₇/C₁₄=C₂	56	2	C4.Dic7	112,9
C₇×M₄(2)	Direct product of C₇ and M₄(2)	56	2	C7xM4(2)	112,23
C₇×D₈	Direct product of C₇ and D₈	56	2	C7xD8	112,24
C₇×SD₁₆	Direct product of C₇ and SD₁₆	56	2	C7xSD16	112,25
C₇×Q₁₆	Direct product of C₇ and Q₁₆	112	2	C7xQ16	112,26
C₄○D₂₈	Central product of C₄ and D₂₈	56	2	C4oD28	112,30
C₇×C₄○D₄	Direct product of C₇ and C₄○D₄	56	2	C7xC4oD4	112,40

Groups of order 114

		d	ρ	Label	ID
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

Groups of order 120

		d	ρ	Label	ID
C₅×C₃⋊C₈	Direct product of C₅ and C₃⋊C₈	120	2	C5xC3:C8	120,1
C₃×C₅⋊₂C₈	Direct product of C₃ and C₅⋊₂C₈	120	2	C3xC5:2C8	120,2
C₁₅⋊₃C₈	1^st semidirect product of C₁₅ and C₈ acting via C₈/C₄=C₂	120	2	C15:3C8	120,3
C₅×SL₂(𝔽₃)	Direct product of C₅ and SL₂(𝔽₃)	40	2	C5xSL(2,3)	120,15
C₃×Dic₁₀	Direct product of C₃ and Dic₁₀	120	2	C3xDic10	120,16
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
C₃×C₅⋊D₄	Direct product of C₃ and C₅⋊D₄	60	2	C3xC5:D4	120,20
C₅×Dic₆	Direct product of C₅ and Dic₆	120	2	C5xDic6	120,21
S₃×C₂₀	Direct product of C₂₀ and S₃	60	2	S3xC20	120,22
C₅×D₁₂	Direct product of C₅ and D₁₂	60	2	C5xD12	120,23
C₅×C₃⋊D₄	Direct product of C₅ and C₃⋊D₄	60	2	C5xC3:D4	120,25
C₄×D₁₅	Direct product of C₄ and D₁₅	60	2	C4xD15	120,27
C₁₅⋊₇D₄	1^st semidirect product of C₁₅ and D₄ acting via D₄/C₂²=C₂	60	2	C15:7D4	120,30
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

Groups of order 126

		d	ρ	Label	ID
C₇×D₉	Direct product of C₇ and D₉	63	2	C7xD9	126,3
C₉×D₇	Direct product of C₉ and D₇	63	2	C9xD7	126,4
S₃×C₂₁	Direct product of C₂₁ and S₃	42	2	S3xC21	126,12
C₃×D₂₁	Direct product of C₃ and D₂₁	42	2	C3xD21	126,13

Groups of order 128

		d	ρ	Label	ID
C₈≀C₂	Wreath product of C₈ by C₂	16	2	C8wrC2	128,67
C₁₆.₃C₈	1^st non-split extension by C₁₆ of C₈ acting via C₈/C₄=C₂	32	2	C16.3C8	128,105
D₄.C₁₆	The non-split extension by D₄ of C₁₆ acting via C₁₆/C₈=C₂	64	2	D4.C16	128,133
D₁₆.C₄	1^st non-split extension by D₁₆ of C₄ acting via C₄/C₂=C₂	64	2	D16.C4	128,149
C₈.C₁₆	1^st non-split extension by C₈ of C₁₆ acting via C₁₆/C₈=C₂	32	2	C8.C16	128,154
C₃₂.C₄	1^st non-split extension by C₃₂ of C₄ acting via C₄/C₂=C₂	64	2	C32.C4	128,157
M₇(2)	Modular maximal-cyclic group; = C₆₄ ⋊₃ C₂	64	2	M7(2)	128,160
SD₁₂₈	Semidihedral group; = C₆₄ ⋊₂ C₂ = QD₁₂₈	64	2	SD128	128,162
C₁₆○D₈	Central product of C₁₆ and D₈	32	2	C16oD8	128,902
C₈○D₁₆	Central product of C₈ and D₁₆	32	2	C8oD16	128,910
D₄○C₃₂	Central product of D₄ and C₃₂	64	2	D4oC32	128,990
C₄○D₃₂	Central product of C₄ and D₃₂	64	2	C4oD32	128,994

Groups of order 130

		d	ρ	Label	ID
D₅×C₁₃	Direct product of C₁₃ and D₅	65	2	D5xC13	130,1
C₅×D₁₃	Direct product of C₅ and D₁₃	65	2	C5xD13	130,2

Groups of order 132

		d	ρ	Label	ID
C₁₁×Dic₃	Direct product of C₁₁ and Dic₃	132	2	C11xDic3	132,1
C₃×Dic₁₁	Direct product of C₃ and Dic₁₁	132	2	C3xDic11	132,2
C₆×D₁₁	Direct product of C₆ and D₁₁	66	2	C6xD11	132,7
S₃×C₂₂	Direct product of C₂₂ and S₃	66	2	S3xC22	132,8

Groups of order 136

		d	ρ	Label	ID
C₁₇⋊₃C₈	The semidirect product of C₁₇ and C₈ acting via C₈/C₄=C₂	136	2	C17:3C8	136,1
C₄×D₁₇	Direct product of C₄ and D₁₇	68	2	C4xD17	136,5
C₁₇⋊D₄	The semidirect product of C₁₇ and D₄ acting via D₄/C₂²=C₂	68	2	C17:D4	136,8
D₄×C₁₇	Direct product of C₁₇ and D₄	68	2	D4xC17	136,10
Q₈×C₁₇	Direct product of C₁₇ and Q₈	136	2	Q8xC17	136,11

Groups of order 138

		d	ρ	Label	ID
S₃×C₂₃	Direct product of C₂₃ and S₃	69	2	S3xC23	138,1
C₃×D₂₃	Direct product of C₃ and D₂₃	69	2	C3xD23	138,2

Groups of order 140

		d	ρ	Label	ID
C₇×Dic₅	Direct product of C₇ and Dic₅	140	2	C7xDic5	140,1
C₅×Dic₇	Direct product of C₅ and Dic₇	140	2	C5xDic7	140,2
C₁₀×D₇	Direct product of C₁₀ and D₇	70	2	C10xD7	140,8
D₅×C₁₄	Direct product of C₁₄ and D₅	70	2	D5xC14	140,9

Groups of order 144

		d	ρ	Label	ID
C₉⋊C₁₆	The semidirect product of C₉ and C₁₆ acting via C₁₆/C₈=C₂	144	2	C9:C16	144,1
C₈×D₉	Direct product of C₈ and D₉	72	2	C8xD9	144,5
C₈⋊D₉	3^rd semidirect product of C₈ and D₉ acting via D₉/C₉=C₂	72	2	C8:D9	144,6
C₇₂⋊C₂	2^nd semidirect product of C₇₂ and C₂ acting faithfully	72	2	C72:C2	144,7
C₄.Dic₉	The non-split extension by C₄ of Dic₉ acting via Dic₉/C₁₈=C₂	72	2	C4.Dic9	144,10
C₉×M₄(2)	Direct product of C₉ and M₄(2)	72	2	C9xM4(2)	144,24
C₉×D₈	Direct product of C₉ and D₈	72	2	C9xD8	144,25
C₉×SD₁₆	Direct product of C₉ and SD₁₆	72	2	C9xSD16	144,26
C₉×Q₁₆	Direct product of C₉ and Q₁₆	144	2	C9xQ16	144,27
C₃×C₃⋊C₁₆	Direct product of C₃ and C₃⋊C₁₆	48	2	C3xC3:C16	144,28
Q₈.C₁₈	The non-split extension by Q₈ of C₁₈ acting via C₁₈/C₆=C₃	72	2	Q8.C18	144,36
D₃₆⋊₅C₂	The semidirect product of D₃₆ and C₂ acting through Inn(D₃₆)	72	2	D36:5C2	144,40
C₉×C₄○D₄	Direct product of C₉ and C₄○D₄	72	2	C9xC4oD4	144,50
S₃×C₂₄	Direct product of C₂₄ and S₃	48	2	S3xC24	144,69
C₃×C₈⋊S₃	Direct product of C₃ and C₈⋊S₃	48	2	C3xC8:S3	144,70
C₃×C₂₄⋊C₂	Direct product of C₃ and C₂₄⋊C₂	48	2	C3xC24:C2	144,71
C₃×D₂₄	Direct product of C₃ and D₂₄	48	2	C3xD24	144,72
C₃×Dic₁₂	Direct product of C₃ and Dic₁₂	48	2	C3xDic12	144,73
C₃×C₄.Dic₃	Direct product of C₃ and C₄.Dic₃	24	2	C3xC4.Dic3	144,75
C₃×CSU₂(𝔽₃)	Direct product of C₃ and CSU₂(𝔽₃)	48	2	C3xCSU(2,3)	144,121
C₃×GL₂(𝔽₃)	Direct product of C₃ and GL₂(𝔽₃)	24	2	C3xGL(2,3)	144,122
C₃×C₄.A₄	Direct product of C₃ and C₄.A₄	48	2	C3xC4.A4	144,157
C₃×C₄○D₁₂	Direct product of C₃ and C₄○D₁₂	24	2	C3xC4oD12	144,161

Groups of order 150

		d	ρ	Label	ID
S₃×C₂₅	Direct product of C₂₅ and S₃	75	2	S3xC25	150,1
C₃×D₂₅	Direct product of C₃ and D₂₅	75	2	C3xD25	150,2
D₅×C₁₅	Direct product of C₁₅ and D₅	30	2	D5xC15	150,8
C₅×D₁₅	Direct product of C₅ and D₁₅	30	2	C5xD15	150,11

Groups of order 152

		d	ρ	Label	ID
C₁₉⋊C₈	The semidirect product of C₁₉ and C₈ acting via C₈/C₄=C₂	152	2	C19:C8	152,1
C₄×D₁₉	Direct product of C₄ and D₁₉	76	2	C4xD19	152,4
C₁₉⋊D₄	The semidirect product of C₁₉ and D₄ acting via D₄/C₂²=C₂	76	2	C19:D4	152,7
D₄×C₁₉	Direct product of C₁₉ and D₄	76	2	D4xC19	152,9
Q₈×C₁₉	Direct product of C₁₉ and Q₈	152	2	Q8xC19	152,10

Groups of order 154

		d	ρ	Label	ID
C₁₁×D₇	Direct product of C₁₁ and D₇	77	2	C11xD7	154,1
C₇×D₁₁	Direct product of C₇ and D₁₁	77	2	C7xD11	154,2

Groups of order 156

		d	ρ	Label	ID
Dic₃×C₁₃	Direct product of C₁₃ and Dic₃	156	2	Dic3xC13	156,3
C₃×Dic₁₃	Direct product of C₃ and Dic₁₃	156	2	C3xDic13	156,4
C₆×D₁₃	Direct product of C₆ and D₁₃	78	2	C6xD13	156,15
S₃×C₂₆	Direct product of C₂₆ and S₃	78	2	S3xC26	156,16

Groups of order 160

		d	ρ	Label	ID
C₅⋊₂C₃₂	The semidirect product of C₅ and C₃₂ acting via C₃₂/C₁₆=C₂	160	2	C5:2C32	160,1
D₅×C₁₆	Direct product of C₁₆ and D₅	80	2	D5xC16	160,4
C₈₀⋊C₂	5^th semidirect product of C₈₀ and C₂ acting faithfully	80	2	C80:C2	160,5
C₁₆⋊D₅	2^nd semidirect product of C₁₆ and D₅ acting via D₅/C₅=C₂	80	2	C16:D5	160,7
D₂₀⋊₄C₄	1^st semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	40	2	D20:4C4	160,12
C₂₀.₄C₈	1^st non-split extension by C₂₀ of C₈ acting via C₈/C₄=C₂	80	2	C20.4C8	160,19
C₄₀.₆C₄	1^st non-split extension by C₄₀ of C₄ acting via C₄/C₂=C₂	80	2	C40.6C4	160,26
C₅×C₄≀C₂	Direct product of C₅ and C₄≀C₂	40	2	C5xC4wrC2	160,54
C₅×C₈.C₄	Direct product of C₅ and C₈.C₄	80	2	C5xC8.C4	160,58
C₅×M₅(2)	Direct product of C₅ and M₅(2)	80	2	C5xM5(2)	160,60
C₅×D₁₆	Direct product of C₅ and D₁₆	80	2	C5xD16	160,61
C₅×SD₃₂	Direct product of C₅ and SD₃₂	80	2	C5xSD32	160,62
C₅×Q₃₂	Direct product of C₅ and Q₃₂	160	2	C5xQ32	160,63
D₂₀.₃C₄	The non-split extension by D₂₀ of C₄ acting through Inn(D₂₀)	80	2	D20.3C4	160,122
D₄₀⋊₇C₂	The semidirect product of D₄₀ and C₂ acting through Inn(D₄₀)	80	2	D40:7C2	160,125
C₅×C₈○D₄	Direct product of C₅ and C₈○D₄	80	2	C5xC8oD4	160,192
C₅×C₄○D₈	Direct product of C₅ and C₄○D₈	80	2	C5xC4oD8	160,196

Groups of order 162

		d	ρ	Label	ID
C₉×D₉	Direct product of C₉ and D₉	18	2	C9xD9	162,3
C₃×D₂₇	Direct product of C₃ and D₂₇	54	2	C3xD27	162,7
S₃×C₂₇	Direct product of C₂₇ and S₃	54	2	S3xC27	162,8

Groups of order 168

		d	ρ	Label	ID
C₇×C₃⋊C₈	Direct product of C₇ and C₃⋊C₈	168	2	C7xC3:C8	168,3
C₃×C₇⋊C₈	Direct product of C₃ and C₇⋊C₈	168	2	C3xC7:C8	168,4
C₂₁⋊C₈	1^st semidirect product of C₂₁ and C₈ acting via C₈/C₄=C₂	168	2	C21:C8	168,5
C₇×SL₂(𝔽₃)	Direct product of C₇ and SL₂(𝔽₃)	56	2	C7xSL(2,3)	168,22
C₃×Dic₁₄	Direct product of C₃ and Dic₁₄	168	2	C3xDic14	168,24
C₁₂×D₇	Direct product of C₁₂ and D₇	84	2	C12xD7	168,25
C₃×D₂₈	Direct product of C₃ and D₂₈	84	2	C3xD28	168,26
C₃×C₇⋊D₄	Direct product of C₃ and C₇⋊D₄	84	2	C3xC7:D4	168,28
C₇×Dic₆	Direct product of C₇ and Dic₆	168	2	C7xDic6	168,29
S₃×C₂₈	Direct product of C₂₈ and S₃	84	2	S3xC28	168,30
C₇×D₁₂	Direct product of C₇ and D₁₂	84	2	C7xD12	168,31
C₇×C₃⋊D₄	Direct product of C₇ and C₃⋊D₄	84	2	C7xC3:D4	168,33
C₄×D₂₁	Direct product of C₄ and D₂₁	84	2	C4xD21	168,35
C₂₁⋊₇D₄	1^st semidirect product of C₂₁ and D₄ acting via D₄/C₂²=C₂	84	2	C21:7D4	168,38
D₄×C₂₁	Direct product of C₂₁ and D₄	84	2	D4xC21	168,40
Q₈×C₂₁	Direct product of C₂₁ and Q₈	168	2	Q8xC21	168,41

Groups of order 170

		d	ρ	Label	ID
D₅×C₁₇	Direct product of C₁₇ and D₅	85	2	D5xC17	170,1
C₅×D₁₇	Direct product of C₅ and D₁₇	85	2	C5xD17	170,2

Groups of order 174

		d	ρ	Label	ID
S₃×C₂₉	Direct product of C₂₉ and S₃	87	2	S3xC29	174,1
C₃×D₂₉	Direct product of C₃ and D₂₉	87	2	C3xD29	174,2

Groups of order 176

		d	ρ	Label	ID
C₁₁⋊C₁₆	The semidirect product of C₁₁ and C₁₆ acting via C₁₆/C₈=C₂	176	2	C11:C16	176,1
C₈×D₁₁	Direct product of C₈ and D₁₁	88	2	C8xD11	176,3
C₈₈⋊C₂	4^th semidirect product of C₈₈ and C₂ acting faithfully	88	2	C88:C2	176,4
C₈⋊D₁₁	2^nd semidirect product of C₈ and D₁₁ acting via D₁₁/C₁₁=C₂	88	2	C8:D11	176,5
C₄₄.C₄	1^st non-split extension by C₄₄ of C₄ acting via C₄/C₂=C₂	88	2	C44.C4	176,9
C₁₁×M₄(2)	Direct product of C₁₁ and M₄(2)	88	2	C11xM4(2)	176,23
C₁₁×D₈	Direct product of C₁₁ and D₈	88	2	C11xD8	176,24
C₁₁×SD₁₆	Direct product of C₁₁ and SD₁₆	88	2	C11xSD16	176,25
C₁₁×Q₁₆	Direct product of C₁₁ and Q₁₆	176	2	C11xQ16	176,26
D₄₄⋊₅C₂	The semidirect product of D₄₄ and C₂ acting through Inn(D₄₄)	88	2	D44:5C2	176,30
C₁₁×C₄○D₄	Direct product of C₁₁ and C₄○D₄	88	2	C11xC4oD4	176,40

Groups of order 180

		d	ρ	Label	ID
C₅×Dic₉	Direct product of C₅ and Dic₉	180	2	C5xDic9	180,1
C₉×Dic₅	Direct product of C₉ and Dic₅	180	2	C9xDic5	180,2
D₅×C₁₈	Direct product of C₁₈ and D₅	90	2	D5xC18	180,9
C₁₀×D₉	Direct product of C₁₀ and D₉	90	2	C10xD9	180,10
Dic₃×C₁₅	Direct product of C₁₅ and Dic₃	60	2	Dic3xC15	180,14
C₃×Dic₁₅	Direct product of C₃ and Dic₁₅	60	2	C3xDic15	180,15
S₃×C₃₀	Direct product of C₃₀ and S₃	60	2	S3xC30	180,33
C₆×D₁₅	Direct product of C₆ and D₁₅	60	2	C6xD15	180,34

Groups of order 182

		d	ρ	Label	ID
C₁₃×D₇	Direct product of C₁₃ and D₇	91	2	C13xD7	182,1
C₇×D₁₃	Direct product of C₇ and D₁₃	91	2	C7xD13	182,2

Groups of order 184

		d	ρ	Label	ID
C₂₃⋊C₈	The semidirect product of C₂₃ and C₈ acting via C₈/C₄=C₂	184	2	C23:C8	184,1
C₄×D₂₃	Direct product of C₄ and D₂₃	92	2	C4xD23	184,4
C₂₃⋊D₄	The semidirect product of C₂₃ and D₄ acting via D₄/C₂²=C₂	92	2	C23:D4	184,7
D₄×C₂₃	Direct product of C₂₃ and D₄	92	2	D4xC23	184,9
Q₈×C₂₃	Direct product of C₂₃ and Q₈	184	2	Q8xC23	184,10

Groups of order 186

		d	ρ	Label	ID
S₃×C₃₁	Direct product of C₃₁ and S₃	93	2	S3xC31	186,3
C₃×D₃₁	Direct product of C₃ and D₃₁	93	2	C3xD31	186,4

Groups of order 190

		d	ρ	Label	ID
D₅×C₁₉	Direct product of C₁₉ and D₅	95	2	D5xC19	190,1
C₅×D₁₉	Direct product of C₅ and D₁₉	95	2	C5xD19	190,2

Groups of order 192

		d	ρ	Label	ID
C₃⋊C₆₄	The semidirect product of C₃ and C₆₄ acting via C₆₄/C₃₂=C₂	192	2	C3:C64	192,1
S₃×C₃₂	Direct product of C₃₂ and S₃	96	2	S3xC32	192,5
C₉₆⋊C₂	6^th semidirect product of C₉₆ and C₂ acting faithfully	96	2	C96:C2	192,6
C₃₂⋊S₃	2^nd semidirect product of C₃₂ and S₃ acting via S₃/C₃=C₂	96	2	C32:S3	192,8
C₂₄.₁C₈	1^st non-split extension by C₂₄ of C₈ acting via C₈/C₄=C₂	48	2	C24.1C8	192,22
C₃⋊M₆(2)	The semidirect product of C₃ and M₆(2) acting via M₆(2)/C₂×C₁₆=C₂	96	2	C3:M6(2)	192,58
C₄₈.C₄	1^st non-split extension by C₄₈ of C₄ acting via C₄/C₂=C₂	96	2	C48.C4	192,65
D₁₂.C₈	1^st non-split extension by D₁₂ of C₈ acting via C₈/C₄=C₂	96	2	D12.C8	192,67
D₂₄.₁C₄	1^st non-split extension by D₂₄ of C₄ acting via C₄/C₂=C₂	96	2	D24.1C4	192,69
C₃×D₄.C₈	Direct product of C₃ and D₄.C₈	96	2	C3xD4.C8	192,156
C₃×D₈.C₄	Direct product of C₃ and D₈.C₄	96	2	C3xD8.C4	192,165
C₃×C₈.C₈	Direct product of C₃ and C₈.C₈	48	2	C3xC8.C8	192,170
C₃×C₈.₄Q₈	Direct product of C₃ and C₈.₄Q₈	96	2	C3xC8.4Q8	192,174
C₃×M₆(2)	Direct product of C₃ and M₆(2)	96	2	C3xM6(2)	192,176
C₃×D₃₂	Direct product of C₃ and D₃₂	96	2	C3xD32	192,177
C₃×SD₆₄	Direct product of C₃ and SD₆₄	96	2	C3xSD64	192,178
C₃×Q₆₄	Direct product of C₃ and Q₆₄	192	2	C3xQ64	192,179
C₈.₇S₄	2^nd central extension by C₈ of S₄	64	2	C8.7S4	192,187
C₁₆.A₄	The central extension by C₁₆ of A₄	64	2	C16.A4	192,204
D₂₄⋊₁₁C₄	The semidirect product of D₂₄ and C₄ acting through Inn(D₂₄)	48	2	D24:11C4	192,259
D₁₂.₄C₈	The non-split extension by D₁₂ of C₈ acting through Inn(D₁₂)	96	2	D12.4C8	192,460
D₄₈⋊₇C₂	The semidirect product of D₄₈ and C₂ acting through Inn(D₄₈)	96	2	D48:7C2	192,463
C₃×C₈○D₈	Direct product of C₃ and C₈○D₈	48	2	C3xC8oD8	192,876
C₃×D₄○C₁₆	Direct product of C₃ and D₄○C₁₆	96	2	C3xD4oC16	192,937
C₃×C₄○D₁₆	Direct product of C₃ and C₄○D₁₆	96	2	C3xC4oD16	192,941
CU₂(𝔽₃)	Conformal unitary group on 𝔽₃²; = U₂(𝔽₃)⋊₇ C₂	32	2	CU(2,3)	192,963

Groups of order 196

		d	ρ	Label	ID
C₇×Dic₇	Direct product of C₇ and Dic₇	28	2	C7xDic7	196,5
D₇×C₁₄	Direct product of C₁₄ and D₇	28	2	D7xC14	196,10

Groups of order 198

		d	ρ	Label	ID
C₁₁×D₉	Direct product of C₁₁ and D₉	99	2	C11xD9	198,1
C₉×D₁₁	Direct product of C₉ and D₁₁	99	2	C9xD11	198,2
S₃×C₃₃	Direct product of C₃₃ and S₃	66	2	S3xC33	198,6
C₃×D₃₃	Direct product of C₃ and D₃₃	66	2	C3xD33	198,7

Groups of order 200

		d	ρ	Label	ID
C₂₅⋊₂C₈	The semidirect product of C₂₅ and C₈ acting via C₈/C₄=C₂	200	2	C25:2C8	200,1
C₄×D₂₅	Direct product of C₄ and D₂₅	100	2	C4xD25	200,5
C₂₅⋊D₄	The semidirect product of C₂₅ and D₄ acting via D₄/C₂²=C₂	100	2	C25:D4	200,8
D₄×C₂₅	Direct product of C₂₅ and D₄	100	2	D4xC25	200,10
Q₈×C₂₅	Direct product of C₂₅ and Q₈	200	2	Q8xC25	200,11
C₅×C₅⋊₂C₈	Direct product of C₅ and C₅⋊₂C₈	40	2	C5xC5:2C8	200,15
C₅×Dic₁₀	Direct product of C₅ and Dic₁₀	40	2	C5xDic10	200,27
D₅×C₂₀	Direct product of C₂₀ and D₅	40	2	D5xC20	200,28
C₅×D₂₀	Direct product of C₅ and D₂₀	40	2	C5xD20	200,29
C₅×C₅⋊D₄	Direct product of C₅ and C₅⋊D₄	20	2	C5xC5:D4	200,31

Groups of order 204

		d	ρ	Label	ID
Dic₃×C₁₇	Direct product of C₁₇ and Dic₃	204	2	Dic3xC17	204,1
C₃×Dic₁₇	Direct product of C₃ and Dic₁₇	204	2	C3xDic17	204,2
C₆×D₁₇	Direct product of C₆ and D₁₇	102	2	C6xD17	204,9
S₃×C₃₄	Direct product of C₃₄ and S₃	102	2	S3xC34	204,10

Groups of order 208

		d	ρ	Label	ID
C₁₃⋊₂C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	2	C13:2C16	208,1
C₈×D₁₃	Direct product of C₈ and D₁₃	104	2	C8xD13	208,4
C₈⋊D₁₃	3^rd semidirect product of C₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	2	C8:D13	208,5
C₁₀₄⋊C₂	2^nd semidirect product of C₁₀₄ and C₂ acting faithfully	104	2	C104:C2	208,6
C₅₂.₄C₄	1^st non-split extension by C₅₂ of C₄ acting via C₄/C₂=C₂	104	2	C52.4C4	208,10
C₁₃×M₄(2)	Direct product of C₁₃ and M₄(2)	104	2	C13xM4(2)	208,24
C₁₃×D₈	Direct product of C₁₃ and D₈	104	2	C13xD8	208,25
C₁₃×SD₁₆	Direct product of C₁₃ and SD₁₆	104	2	C13xSD16	208,26
C₁₃×Q₁₆	Direct product of C₁₃ and Q₁₆	208	2	C13xQ16	208,27
D₅₂⋊₅C₂	The semidirect product of D₅₂ and C₂ acting through Inn(D₅₂)	104	2	D52:5C2	208,38
C₁₃×C₄○D₄	Direct product of C₁₃ and C₄○D₄	104	2	C13xC4oD4	208,48

Groups of order 210

		d	ρ	Label	ID
D₇×C₁₅	Direct product of C₁₅ and D₇	105	2	D7xC15	210,5
D₅×C₂₁	Direct product of C₂₁ and D₅	105	2	D5xC21	210,6
C₃×D₃₅	Direct product of C₃ and D₃₅	105	2	C3xD35	210,7
S₃×C₃₅	Direct product of C₃₅ and S₃	105	2	S3xC35	210,8
C₅×D₂₁	Direct product of C₅ and D₂₁	105	2	C5xD21	210,9
C₇×D₁₅	Direct product of C₇ and D₁₅	105	2	C7xD15	210,10

Groups of order 216

		d	ρ	Label	ID
C₂₇⋊C₈	The semidirect product of C₂₇ and C₈ acting via C₈/C₄=C₂	216	2	C27:C8	216,1
Q₈⋊C₂₇	The semidirect product of Q₈ and C₂₇ acting via C₂₇/C₉=C₃	216	2	Q8:C27	216,3
C₄×D₂₇	Direct product of C₄ and D₂₇	108	2	C4xD27	216,5
C₂₇⋊D₄	The semidirect product of C₂₇ and D₄ acting via D₄/C₂²=C₂	108	2	C27:D4	216,8
D₄×C₂₇	Direct product of C₂₇ and D₄	108	2	D4xC27	216,10
Q₈×C₂₇	Direct product of C₂₇ and Q₈	216	2	Q8xC27	216,11
C₃×C₉⋊C₈	Direct product of C₃ and C₉⋊C₈	72	2	C3xC9:C8	216,12
C₉×C₃⋊C₈	Direct product of C₉ and C₃⋊C₈	72	2	C9xC3:C8	216,13
C₉×SL₂(𝔽₃)	Direct product of C₉ and SL₂(𝔽₃)	72	2	C9xSL(2,3)	216,38
C₃×Dic₁₈	Direct product of C₃ and Dic₁₈	72	2	C3xDic18	216,43
C₉×Dic₆	Direct product of C₉ and Dic₆	72	2	C9xDic6	216,44
C₁₂×D₉	Direct product of C₁₂ and D₉	72	2	C12xD9	216,45
C₃×D₃₆	Direct product of C₃ and D₃₆	72	2	C3xD36	216,46
S₃×C₃₆	Direct product of C₃₆ and S₃	72	2	S3xC36	216,47
C₉×D₁₂	Direct product of C₉ and D₁₂	72	2	C9xD12	216,48
C₃×C₉⋊D₄	Direct product of C₃ and C₉⋊D₄	36	2	C3xC9:D4	216,57
C₉×C₃⋊D₄	Direct product of C₉ and C₃⋊D₄	36	2	C9xC3:D4	216,58

Groups of order 220

		d	ρ	Label	ID
C₁₁×Dic₅	Direct product of C₁₁ and Dic₅	220	2	C11xDic5	220,3
C₅×Dic₁₁	Direct product of C₅ and Dic₁₁	220	2	C5xDic11	220,4
C₁₀×D₁₁	Direct product of C₁₀ and D₁₁	110	2	C10xD11	220,12
D₅×C₂₂	Direct product of C₂₂ and D₅	110	2	D5xC22	220,13

Groups of order 222

		d	ρ	Label	ID
S₃×C₃₇	Direct product of C₃₇ and S₃	111	2	S3xC37	222,3
C₃×D₃₇	Direct product of C₃ and D₃₇	111	2	C3xD37	222,4

Groups of order 224

		d	ρ	Label	ID
C₇⋊C₃₂	The semidirect product of C₇ and C₃₂ acting via C₃₂/C₁₆=C₂	224	2	C7:C32	224,1
D₇×C₁₆	Direct product of C₁₆ and D₇	112	2	D7xC16	224,3
C₁₆⋊D₇	3^rd semidirect product of C₁₆ and D₇ acting via D₇/C₇=C₂	112	2	C16:D7	224,4
C₁₁₂⋊C₂	2^nd semidirect product of C₁₁₂ and C₂ acting faithfully	112	2	C112:C2	224,6
Dic₁₄⋊C₄	1^st semidirect product of Dic₁₄ and C₄ acting via C₄/C₂=C₂	56	2	Dic14:C4	224,11
C₂₈.C₈	1^st non-split extension by C₂₈ of C₈ acting via C₈/C₄=C₂	112	2	C28.C8	224,18
C₅₆.C₄	1^st non-split extension by C₅₆ of C₄ acting via C₄/C₂=C₂	112	2	C56.C4	224,25
C₇×C₄≀C₂	Direct product of C₇ and C₄≀C₂	56	2	C7xC4wrC2	224,53
C₇×C₈.C₄	Direct product of C₇ and C₈.C₄	112	2	C7xC8.C4	224,57
C₇×M₅(2)	Direct product of C₇ and M₅(2)	112	2	C7xM5(2)	224,59
C₇×D₁₆	Direct product of C₇ and D₁₆	112	2	C7xD16	224,60
C₇×SD₃₂	Direct product of C₇ and SD₃₂	112	2	C7xSD32	224,61
C₇×Q₃₂	Direct product of C₇ and Q₃₂	224	2	C7xQ32	224,62
D₂₈.₂C₄	The non-split extension by D₂₈ of C₄ acting through Inn(D₂₈)	112	2	D28.2C4	224,96
D₅₆⋊₇C₂	The semidirect product of D₅₆ and C₂ acting through Inn(D₅₆)	112	2	D56:7C2	224,99
C₇×C₈○D₄	Direct product of C₇ and C₈○D₄	112	2	C7xC8oD4	224,166
C₇×C₄○D₈	Direct product of C₇ and C₄○D₈	112	2	C7xC4oD8	224,170

Groups of order 228

		d	ρ	Label	ID
Dic₃×C₁₉	Direct product of C₁₉ and Dic₃	228	2	Dic3xC19	228,3
C₃×Dic₁₉	Direct product of C₃ and Dic₁₉	228	2	C3xDic19	228,4
C₆×D₁₉	Direct product of C₆ and D₁₉	114	2	C6xD19	228,12
S₃×C₃₈	Direct product of C₃₈ and S₃	114	2	S3xC38	228,13

Groups of order 230

		d	ρ	Label	ID
D₅×C₂₃	Direct product of C₂₃ and D₅	115	2	D5xC23	230,1
C₅×D₂₃	Direct product of C₅ and D₂₃	115	2	C5xD23	230,2

Groups of order 232

		d	ρ	Label	ID
C₂₉⋊₂C₈	The semidirect product of C₂₉ and C₈ acting via C₈/C₄=C₂	232	2	C29:2C8	232,1
C₄×D₂₉	Direct product of C₄ and D₂₉	116	2	C4xD29	232,5
C₂₉⋊D₄	The semidirect product of C₂₉ and D₄ acting via D₄/C₂²=C₂	116	2	C29:D4	232,8
D₄×C₂₉	Direct product of C₂₉ and D₄	116	2	D4xC29	232,10
Q₈×C₂₉	Direct product of C₂₉ and Q₈	232	2	Q8xC29	232,11

Groups of order 234

		d	ρ	Label	ID
C₁₃×D₉	Direct product of C₁₃ and D₉	117	2	C13xD9	234,3
C₉×D₁₃	Direct product of C₉ and D₁₃	117	2	C9xD13	234,4
S₃×C₃₉	Direct product of C₃₉ and S₃	78	2	S3xC39	234,12
C₃×D₃₉	Direct product of C₃ and D₃₉	78	2	C3xD39	234,13

Groups of order 238

		d	ρ	Label	ID
D₇×C₁₇	Direct product of C₁₇ and D₇	119	2	D7xC17	238,1
C₇×D₁₇	Direct product of C₇ and D₁₇	119	2	C7xD17	238,2

Groups of order 240

		d	ρ	Label	ID
C₅×C₃⋊C₁₆	Direct product of C₅ and C₃⋊C₁₆	240	2	C5xC3:C16	240,1
C₃×C₅⋊₂C₁₆	Direct product of C₃ and C₅⋊₂C₁₆	240	2	C3xC5:2C16	240,2
C₁₅⋊₃C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₈=C₂	240	2	C15:3C16	240,3
D₅×C₂₄	Direct product of C₂₄ and D₅	120	2	D5xC24	240,33
C₃×C₈⋊D₅	Direct product of C₃ and C₈⋊D₅	120	2	C3xC8:D5	240,34
C₃×C₄₀⋊C₂	Direct product of C₃ and C₄₀⋊C₂	120	2	C3xC40:C2	240,35
C₃×D₄₀	Direct product of C₃ and D₄₀	120	2	C3xD40	240,36
C₃×Dic₂₀	Direct product of C₃ and Dic₂₀	240	2	C3xDic20	240,37
C₃×C₄.Dic₅	Direct product of C₃ and C₄.Dic₅	120	2	C3xC4.Dic5	240,39
S₃×C₄₀	Direct product of C₄₀ and S₃	120	2	S3xC40	240,49
C₅×C₈⋊S₃	Direct product of C₅ and C₈⋊S₃	120	2	C5xC8:S3	240,50
C₅×C₂₄⋊C₂	Direct product of C₅ and C₂₄⋊C₂	120	2	C5xC24:C2	240,51
C₅×D₂₄	Direct product of C₅ and D₂₄	120	2	C5xD24	240,52
C₅×Dic₁₂	Direct product of C₅ and Dic₁₂	240	2	C5xDic12	240,53
C₅×C₄.Dic₃	Direct product of C₅ and C₄.Dic₃	120	2	C5xC4.Dic3	240,55
C₈×D₁₅	Direct product of C₈ and D₁₅	120	2	C8xD15	240,65
C₄₀⋊S₃	4^th semidirect product of C₄₀ and S₃ acting via S₃/C₃=C₂	120	2	C40:S3	240,66
C₂₄⋊D₅	2^nd semidirect product of C₂₄ and D₅ acting via D₅/C₅=C₂	120	2	C24:D5	240,67
C₆₀.₇C₄	1^st non-split extension by C₆₀ of C₄ acting via C₄/C₂=C₂	120	2	C60.7C4	240,71
C₁₅×M₄(2)	Direct product of C₁₅ and M₄(2)	120	2	C15xM4(2)	240,85
C₁₅×D₈	Direct product of C₁₅ and D₈	120	2	C15xD8	240,86
C₁₅×SD₁₆	Direct product of C₁₅ and SD₁₆	120	2	C15xSD16	240,87
C₁₅×Q₁₆	Direct product of C₁₅ and Q₁₆	240	2	C15xQ16	240,88
C₄.A₅	The central extension by C₄ of A₅	24	2	C4.A5	240,93
C₅×CSU₂(𝔽₃)	Direct product of C₅ and CSU₂(𝔽₃)	80	2	C5xCSU(2,3)	240,102
C₅×GL₂(𝔽₃)	Direct product of C₅ and GL₂(𝔽₃)	40	2	C5xGL(2,3)	240,103
C₅×C₄.A₄	Direct product of C₅ and C₄.A₄	80	2	C5xC4.A4	240,154
C₃×C₄○D₂₀	Direct product of C₃ and C₄○D₂₀	120	2	C3xC4oD20	240,158
C₅×C₄○D₁₂	Direct product of C₅ and C₄○D₁₂	120	2	C5xC4oD12	240,168
D₆₀⋊₁₁C₂	The semidirect product of D₆₀ and C₂ acting through Inn(D₆₀)	120	2	D60:11C2	240,178
C₁₅×C₄○D₄	Direct product of C₁₅ and C₄○D₄	120	2	C15xC4oD4	240,188

Groups of order 242

		d	ρ	Label	ID
C₁₁×D₁₁	Direct product of C₁₁ and D₁₁; = AΣL₁(𝔽₁₂₁)	22	2	C11xD11	242,3

Groups of order 246

		d	ρ	Label	ID
S₃×C₄₁	Direct product of C₄₁ and S₃	123	2	S3xC41	246,1
C₃×D₄₁	Direct product of C₃ and D₄₁	123	2	C3xD41	246,2

Groups of order 248

		d	ρ	Label	ID
C₃₁⋊C₈	The semidirect product of C₃₁ and C₈ acting via C₈/C₄=C₂	248	2	C31:C8	248,1
C₄×D₃₁	Direct product of C₄ and D₃₁	124	2	C4xD31	248,4
C₃₁⋊D₄	The semidirect product of C₃₁ and D₄ acting via D₄/C₂²=C₂	124	2	C31:D4	248,7
D₄×C₃₁	Direct product of C₃₁ and D₄	124	2	D4xC31	248,9
Q₈×C₃₁	Direct product of C₃₁ and Q₈	248	2	Q8xC31	248,10

Groups of order 250

		d	ρ	Label	ID
C₅×D₂₅	Direct product of C₅ and D₂₅	50	2	C5xD25	250,3
D₅×C₂₅	Direct product of C₂₅ and D₅	50	2	D5xC25	250,4

Groups of order 252

		d	ρ	Label	ID
C₇×Dic₉	Direct product of C₇ and Dic₉	252	2	C7xDic9	252,3
C₉×Dic₇	Direct product of C₉ and Dic₇	252	2	C9xDic7	252,4
D₇×C₁₈	Direct product of C₁₈ and D₇	126	2	D7xC18	252,12
C₁₄×D₉	Direct product of C₁₄ and D₉	126	2	C14xD9	252,13
Dic₃×C₂₁	Direct product of C₂₁ and Dic₃	84	2	Dic3xC21	252,21
C₃×Dic₂₁	Direct product of C₃ and Dic₂₁	84	2	C3xDic21	252,22
S₃×C₄₂	Direct product of C₄₂ and S₃	84	2	S3xC42	252,42
C₆×D₂₁	Direct product of C₆ and D₂₁	84	2	C6xD21	252,43

Groups of order 258

		d	ρ	Label	ID
S₃×C₄₃	Direct product of C₄₃ and S₃	129	2	S3xC43	258,3
C₃×D₄₃	Direct product of C₃ and D₄₃	129	2	C3xD43	258,4

Groups of order 260

		d	ρ	Label	ID
C₁₃×Dic₅	Direct product of C₁₃ and Dic₅	260	2	C13xDic5	260,1
C₅×Dic₁₃	Direct product of C₅ and Dic₁₃	260	2	C5xDic13	260,2
C₁₀×D₁₃	Direct product of C₁₀ and D₁₃	130	2	C10xD13	260,12
D₅×C₂₆	Direct product of C₂₆ and D₅	130	2	D5xC26	260,13

Groups of order 264

		d	ρ	Label	ID
C₁₁×C₃⋊C₈	Direct product of C₁₁ and C₃⋊C₈	264	2	C11xC3:C8	264,1
C₃×C₁₁⋊C₈	Direct product of C₃ and C₁₁⋊C₈	264	2	C3xC11:C8	264,2
C₃₃⋊C₈	1^st semidirect product of C₃₃ and C₈ acting via C₈/C₄=C₂	264	2	C33:C8	264,3
C₁₁×SL₂(𝔽₃)	Direct product of C₁₁ and SL₂(𝔽₃)	88	2	C11xSL(2,3)	264,12
C₃×Dic₂₂	Direct product of C₃ and Dic₂₂	264	2	C3xDic22	264,13
C₁₂×D₁₁	Direct product of C₁₂ and D₁₁	132	2	C12xD11	264,14
C₃×D₄₄	Direct product of C₃ and D₄₄	132	2	C3xD44	264,15
C₃×C₁₁⋊D₄	Direct product of C₃ and C₁₁⋊D₄	132	2	C3xC11:D4	264,17
C₁₁×Dic₆	Direct product of C₁₁ and Dic₆	264	2	C11xDic6	264,18
S₃×C₄₄	Direct product of C₄₄ and S₃	132	2	S3xC44	264,19
C₁₁×D₁₂	Direct product of C₁₁ and D₁₂	132	2	C11xD12	264,20
C₁₁×C₃⋊D₄	Direct product of C₁₁ and C₃⋊D₄	132	2	C11xC3:D4	264,22
C₄×D₃₃	Direct product of C₄ and D₃₃	132	2	C4xD33	264,24
C₃₃⋊₇D₄	1^st semidirect product of C₃₃ and D₄ acting via D₄/C₂²=C₂	132	2	C33:7D4	264,27
D₄×C₃₃	Direct product of C₃₃ and D₄	132	2	D4xC33	264,29
Q₈×C₃₃	Direct product of C₃₃ and Q₈	264	2	Q8xC33	264,30

Groups of order 266

		d	ρ	Label	ID
D₇×C₁₉	Direct product of C₁₉ and D₇	133	2	D7xC19	266,1
C₇×D₁₉	Direct product of C₇ and D₁₉	133	2	C7xD19	266,2

Groups of order 270

		d	ρ	Label	ID
C₅×D₂₇	Direct product of C₅ and D₂₇	135	2	C5xD27	270,1
D₅×C₂₇	Direct product of C₂₇ and D₅	135	2	D5xC27	270,2
C₁₅×D₉	Direct product of C₁₅ and D₉	90	2	C15xD9	270,8
S₃×C₄₅	Direct product of C₄₅ and S₃	90	2	S3xC45	270,9
C₃×D₄₅	Direct product of C₃ and D₄₅	90	2	C3xD45	270,12
C₉×D₁₅	Direct product of C₉ and D₁₅	90	2	C9xD15	270,13

Groups of order 272

		d	ρ	Label	ID
C₁₇⋊₄C₁₆	The semidirect product of C₁₇ and C₁₆ acting via C₁₆/C₈=C₂	272	2	C17:4C16	272,1
C₈×D₁₇	Direct product of C₈ and D₁₇	136	2	C8xD17	272,4
C₈⋊D₁₇	3^rd semidirect product of C₈ and D₁₇ acting via D₁₇/C₁₇=C₂	136	2	C8:D17	272,5
C₁₃₆⋊C₂	2^nd semidirect product of C₁₃₆ and C₂ acting faithfully	136	2	C136:C2	272,6
C₆₈.₄C₄	1^st non-split extension by C₆₈ of C₄ acting via C₄/C₂=C₂	136	2	C68.4C4	272,10
M₄(2)×C₁₇	Direct product of C₁₇ and M₄(2)	136	2	M4(2)xC17	272,24
D₈×C₁₇	Direct product of C₁₇ and D₈	136	2	D8xC17	272,25
SD₁₆×C₁₇	Direct product of C₁₇ and SD₁₆	136	2	SD16xC17	272,26
Q₁₆×C₁₇	Direct product of C₁₇ and Q₁₆	272	2	Q16xC17	272,27
D₆₈⋊₅C₂	The semidirect product of D₆₈ and C₂ acting through Inn(D₆₈)	136	2	D68:5C2	272,39
C₄○D₄×C₁₇	Direct product of C₁₇ and C₄○D₄	136	2	C4oD4xC17	272,49

Groups of order 276

		d	ρ	Label	ID
Dic₃×C₂₃	Direct product of C₂₃ and Dic₃	276	2	Dic3xC23	276,1
C₃×Dic₂₃	Direct product of C₃ and Dic₂₃	276	2	C3xDic23	276,2
C₆×D₂₃	Direct product of C₆ and D₂₃	138	2	C6xD23	276,7
S₃×C₄₆	Direct product of C₄₆ and S₃	138	2	S3xC46	276,8

Groups of order 280

		d	ρ	Label	ID
C₇×C₅⋊₂C₈	Direct product of C₇ and C₅⋊₂C₈	280	2	C7xC5:2C8	280,1
C₅×C₇⋊C₈	Direct product of C₅ and C₇⋊C₈	280	2	C5xC7:C8	280,2
C₃₅⋊₃C₈	1^st semidirect product of C₃₅ and C₈ acting via C₈/C₄=C₂	280	2	C35:3C8	280,3
C₅×Dic₁₄	Direct product of C₅ and Dic₁₄	280	2	C5xDic14	280,14
D₇×C₂₀	Direct product of C₂₀ and D₇	140	2	D7xC20	280,15
C₅×D₂₈	Direct product of C₅ and D₂₈	140	2	C5xD28	280,16
C₅×C₇⋊D₄	Direct product of C₅ and C₇⋊D₄	140	2	C5xC7:D4	280,18
C₇×Dic₁₀	Direct product of C₇ and Dic₁₀	280	2	C7xDic10	280,19
D₅×C₂₈	Direct product of C₂₈ and D₅	140	2	D5xC28	280,20
C₇×D₂₀	Direct product of C₇ and D₂₀	140	2	C7xD20	280,21
C₇×C₅⋊D₄	Direct product of C₇ and C₅⋊D₄	140	2	C7xC5:D4	280,23
C₄×D₃₅	Direct product of C₄ and D₃₅	140	2	C4xD35	280,25
C₃₅⋊₇D₄	1^st semidirect product of C₃₅ and D₄ acting via D₄/C₂²=C₂	140	2	C35:7D4	280,28
D₄×C₃₅	Direct product of C₃₅ and D₄	140	2	D4xC35	280,30
Q₈×C₃₅	Direct product of C₃₅ and Q₈	280	2	Q8xC35	280,31

Groups of order 282

		d	ρ	Label	ID
S₃×C₄₇	Direct product of C₄₇ and S₃	141	2	S3xC47	282,1
C₃×D₄₇	Direct product of C₃ and D₄₇	141	2	C3xD47	282,2

Groups of order 286

		d	ρ	Label	ID
C₁₃×D₁₁	Direct product of C₁₃ and D₁₁	143	2	C13xD11	286,1
C₁₁×D₁₃	Direct product of C₁₁ and D₁₃	143	2	C11xD13	286,2

Groups of order 288

		d	ρ	Label	ID
C₉⋊C₃₂	The semidirect product of C₉ and C₃₂ acting via C₃₂/C₁₆=C₂	288	2	C9:C32	288,1
C₁₆×D₉	Direct product of C₁₆ and D₉	144	2	C16xD9	288,4
C₁₆⋊D₉	3^rd semidirect product of C₁₆ and D₉ acting via D₉/C₉=C₂	144	2	C16:D9	288,5
C₁₄₄⋊C₂	2^nd semidirect product of C₁₄₄ and C₂ acting faithfully	144	2	C144:C2	288,7
C₄²⋊₄D₉	3^rd semidirect product of C₄² and D₉ acting via D₉/C₉=C₂	72	2	C4^2:4D9	288,12
C₃₆.C₈	1^st non-split extension by C₃₆ of C₈ acting via C₈/C₄=C₂	144	2	C36.C8	288,19
C₇₂.C₄	1^st non-split extension by C₇₂ of C₄ acting via C₄/C₂=C₂	144	2	C72.C4	288,20
C₉×C₄≀C₂	Direct product of C₉ and C₄≀C₂	72	2	C9xC4wrC2	288,54
C₉×C₈.C₄	Direct product of C₉ and C₈.C₄	144	2	C9xC8.C4	288,58
C₉×M₅(2)	Direct product of C₉ and M₅(2)	144	2	C9xM5(2)	288,60
C₉×D₁₆	Direct product of C₉ and D₁₆	144	2	C9xD16	288,61
C₉×SD₃₂	Direct product of C₉ and SD₃₂	144	2	C9xSD32	288,62
C₉×Q₃₂	Direct product of C₉ and Q₃₂	288	2	C9xQ32	288,63
C₃×C₃⋊C₃₂	Direct product of C₃ and C₃⋊C₃₂	96	2	C3xC3:C32	288,64
Q₈.C₃₆	The non-split extension by Q₈ of C₃₆ acting via C₃₆/C₁₂=C₃	144	2	Q8.C36	288,77
D₃₆.₂C₄	The non-split extension by D₃₆ of C₄ acting through Inn(D₃₆)	144	2	D36.2C4	288,112
D₇₂⋊₇C₂	The semidirect product of D₇₂ and C₂ acting through Inn(D₇₂)	144	2	D72:7C2	288,115
C₉×C₈○D₄	Direct product of C₉ and C₈○D₄	144	2	C9xC8oD4	288,181
C₉×C₄○D₈	Direct product of C₉ and C₄○D₈	144	2	C9xC4oD8	288,185
S₃×C₄₈	Direct product of C₄₈ and S₃	96	2	S3xC48	288,231
C₃×D₆.C₈	Direct product of C₃ and D₆.C₈	96	2	C3xD6.C8	288,232
C₃×D₄₈	Direct product of C₃ and D₄₈	96	2	C3xD48	288,233
C₃×C₄₈⋊C₂	Direct product of C₃ and C₄₈⋊C₂	96	2	C3xC48:C2	288,234
C₃×Dic₂₄	Direct product of C₃ and Dic₂₄	96	2	C3xDic24	288,235
C₃×C₄²⋊₄S₃	Direct product of C₃ and C₄²⋊₄S₃	24	2	C3xC4^2:4S3	288,239
C₃×C₁₂.C₈	Direct product of C₃ and C₁₂.C₈	48	2	C3xC12.C8	288,246
C₃×C₂₄.C₄	Direct product of C₃ and C₂₄.C₄	48	2	C3xC24.C4	288,253
C₃×U₂(𝔽₃)	Direct product of C₃ and U₂(𝔽₃)	72	2	C3xU(2,3)	288,400
C₃×C₈.A₄	Direct product of C₃ and C₈.A₄	96	2	C3xC8.A4	288,638
C₃×C₈○D₁₂	Direct product of C₃ and C₈○D₁₂	48	2	C3xC8oD12	288,672
C₃×C₄○D₂₄	Direct product of C₃ and C₄○D₂₄	48	2	C3xC4oD24	288,675
C₃×C₄.₆S₄	Direct product of C₃ and C₄.₆S₄	48	2	C3xC4.6S4	288,903

Groups of order 290

		d	ρ	Label	ID
D₅×C₂₉	Direct product of C₂₉ and D₅	145	2	D5xC29	290,1
C₅×D₂₉	Direct product of C₅ and D₂₉	145	2	C5xD29	290,2

Groups of order 294

		d	ρ	Label	ID
S₃×C₄₉	Direct product of C₄₉ and S₃	147	2	S3xC49	294,3
C₃×D₄₉	Direct product of C₃ and D₄₉	147	2	C3xD49	294,4
D₇×C₂₁	Direct product of C₂₁ and D₇	42	2	D7xC21	294,18
C₇×D₂₁	Direct product of C₇ and D₂₁	42	2	C7xD21	294,21

Groups of order 296

		d	ρ	Label	ID
C₃₇⋊₂C₈	The semidirect product of C₃₇ and C₈ acting via C₈/C₄=C₂	296	2	C37:2C8	296,1
C₄×D₃₇	Direct product of C₄ and D₃₇	148	2	C4xD37	296,5
C₃₇⋊D₄	The semidirect product of C₃₇ and D₄ acting via D₄/C₂²=C₂	148	2	C37:D4	296,8
D₄×C₃₇	Direct product of C₃₇ and D₄	148	2	D4xC37	296,10
Q₈×C₃₇	Direct product of C₃₇ and Q₈	296	2	Q8xC37	296,11

Groups of order 300

		d	ρ	Label	ID
Dic₃×C₂₅	Direct product of C₂₅ and Dic₃	300	2	Dic3xC25	300,1
C₃×Dic₂₅	Direct product of C₃ and Dic₂₅	300	2	C3xDic25	300,2
C₆×D₂₅	Direct product of C₆ and D₂₅	150	2	C6xD25	300,9
S₃×C₅₀	Direct product of C₅₀ and S₃	150	2	S3xC50	300,10
C₁₅×Dic₅	Direct product of C₁₅ and Dic₅	60	2	C15xDic5	300,16
C₅×Dic₁₅	Direct product of C₅ and Dic₁₅	60	2	C5xDic15	300,19
D₅×C₃₀	Direct product of C₃₀ and D₅	60	2	D5xC30	300,44
C₁₀×D₁₅	Direct product of C₁₀ and D₁₅	60	2	C10xD15	300,47

Groups of order 304

		d	ρ	Label	ID
C₁₉⋊C₁₆	The semidirect product of C₁₉ and C₁₆ acting via C₁₆/C₈=C₂	304	2	C19:C16	304,1
C₈×D₁₉	Direct product of C₈ and D₁₉	152	2	C8xD19	304,3
C₈⋊D₁₉	3^rd semidirect product of C₈ and D₁₉ acting via D₁₉/C₁₉=C₂	152	2	C8:D19	304,4
C₁₅₂⋊C₂	2^nd semidirect product of C₁₅₂ and C₂ acting faithfully	152	2	C152:C2	304,5
C₇₆.C₄	1^st non-split extension by C₇₆ of C₄ acting via C₄/C₂=C₂	152	2	C76.C4	304,9
M₄(2)×C₁₉	Direct product of C₁₉ and M₄(2)	152	2	M4(2)xC19	304,23
D₈×C₁₉	Direct product of C₁₉ and D₈	152	2	D8xC19	304,24
SD₁₆×C₁₉	Direct product of C₁₉ and SD₁₆	152	2	SD16xC19	304,25
Q₁₆×C₁₉	Direct product of C₁₉ and Q₁₆	304	2	Q16xC19	304,26
D₇₆⋊₅C₂	The semidirect product of D₇₆ and C₂ acting through Inn(D₇₆)	152	2	D76:5C2	304,30
C₄○D₄×C₁₉	Direct product of C₁₉ and C₄○D₄	152	2	C4oD4xC19	304,40

Groups of order 306

		d	ρ	Label	ID
C₁₇×D₉	Direct product of C₁₇ and D₉	153	2	C17xD9	306,1
C₉×D₁₇	Direct product of C₉ and D₁₇	153	2	C9xD17	306,2
S₃×C₅₁	Direct product of C₅₁ and S₃	102	2	S3xC51	306,6
C₃×D₅₁	Direct product of C₃ and D₅₁	102	2	C3xD51	306,7

Groups of order 308

		d	ρ	Label	ID
C₁₁×Dic₇	Direct product of C₁₁ and Dic₇	308	2	C11xDic7	308,1
C₇×Dic₁₁	Direct product of C₇ and Dic₁₁	308	2	C7xDic11	308,2
C₁₄×D₁₁	Direct product of C₁₄ and D₁₁	154	2	C14xD11	308,6
D₇×C₂₂	Direct product of C₂₂ and D₇	154	2	D7xC22	308,7

Groups of order 310

		d	ρ	Label	ID
D₅×C₃₁	Direct product of C₃₁ and D₅	155	2	D5xC31	310,3
C₅×D₃₁	Direct product of C₅ and D₃₁	155	2	C5xD31	310,4

Groups of order 312

		d	ρ	Label	ID
C₁₃×C₃⋊C₈	Direct product of C₁₃ and C₃⋊C₈	312	2	C13xC3:C8	312,3
C₃×C₁₃⋊₂C₈	Direct product of C₃ and C₁₃⋊₂C₈	312	2	C3xC13:2C8	312,4
C₃₉⋊₃C₈	1^st semidirect product of C₃₉ and C₈ acting via C₈/C₄=C₂	312	2	C39:3C8	312,5
C₁₃×SL₂(𝔽₃)	Direct product of C₁₃ and SL₂(𝔽₃)	104	2	C13xSL(2,3)	312,25
C₃×Dic₂₆	Direct product of C₃ and Dic₂₆	312	2	C3xDic26	312,27
C₁₂×D₁₃	Direct product of C₁₂ and D₁₃	156	2	C12xD13	312,28
C₃×D₅₂	Direct product of C₃ and D₅₂	156	2	C3xD52	312,29
C₃×C₁₃⋊D₄	Direct product of C₃ and C₁₃⋊D₄	156	2	C3xC13:D4	312,31
C₁₃×Dic₆	Direct product of C₁₃ and Dic₆	312	2	C13xDic6	312,32
S₃×C₅₂	Direct product of C₅₂ and S₃	156	2	S3xC52	312,33
C₁₃×D₁₂	Direct product of C₁₃ and D₁₂	156	2	C13xD12	312,34
C₁₃×C₃⋊D₄	Direct product of C₁₃ and C₃⋊D₄	156	2	C13xC3:D4	312,36
C₄×D₃₉	Direct product of C₄ and D₃₉	156	2	C4xD39	312,38
C₃₉⋊₇D₄	1^st semidirect product of C₃₉ and D₄ acting via D₄/C₂²=C₂	156	2	C39:7D4	312,41
D₄×C₃₉	Direct product of C₃₉ and D₄	156	2	D4xC39	312,43
Q₈×C₃₉	Direct product of C₃₉ and Q₈	312	2	Q8xC39	312,44

Groups of order 318

		d	ρ	Label	ID
S₃×C₅₃	Direct product of C₅₃ and S₃	159	2	S3xC53	318,1
C₃×D₅₃	Direct product of C₃ and D₅₃	159	2	C3xD53	318,2

Groups of order 320

		d	ρ	Label	ID
C₅⋊₂C₆₄	The semidirect product of C₅ and C₆₄ acting via C₆₄/C₃₂=C₂	320	2	C5:2C64	320,1
D₅×C₃₂	Direct product of C₃₂ and D₅	160	2	D5xC32	320,4
C₃₂⋊D₅	3^rd semidirect product of C₃₂ and D₅ acting via D₅/C₅=C₂	160	2	C32:D5	320,5
C₁₆₀⋊C₂	2^nd semidirect product of C₁₆₀ and C₂ acting faithfully	160	2	C160:C2	320,7
C₄₀.₇C₈	1^st non-split extension by C₄₀ of C₈ acting via C₈/C₄=C₂	80	2	C40.7C8	320,21
C₈₀.₉C₄	4^th non-split extension by C₈₀ of C₄ acting via C₄/C₂=C₂	160	2	C80.9C4	320,57
C₈₀.₆C₄	1^st non-split extension by C₈₀ of C₄ acting via C₄/C₂=C₂	160	2	C80.6C4	320,64
D₂₀.₃C₈	1^st non-split extension by D₂₀ of C₈ acting via C₈/C₄=C₂	160	2	D20.3C8	320,66
D₄₀.₃C₄	1^st non-split extension by D₄₀ of C₄ acting via C₄/C₂=C₂	160	2	D40.3C4	320,68
C₅×D₄.C₈	Direct product of C₅ and D₄.C₈	160	2	C5xD4.C8	320,155
C₅×D₈.C₄	Direct product of C₅ and D₈.C₄	160	2	C5xD8.C4	320,164
C₅×C₈.C₈	Direct product of C₅ and C₈.C₈	80	2	C5xC8.C8	320,169
C₅×C₈.₄Q₈	Direct product of C₅ and C₈.₄Q₈	160	2	C5xC8.4Q8	320,173
C₅×M₆(2)	Direct product of C₅ and M₆(2)	160	2	C5xM6(2)	320,175
C₅×D₃₂	Direct product of C₅ and D₃₂	160	2	C5xD32	320,176
C₅×SD₆₄	Direct product of C₅ and SD₆₄	160	2	C5xSD64	320,177
C₅×Q₆₄	Direct product of C₅ and Q₆₄	320	2	C5xQ64	320,178
D₄₀⋊₁₇C₄	The semidirect product of D₄₀ and C₄ acting through Inn(D₄₀)	80	2	D40:17C4	320,327
D₂₀.₆C₈	The non-split extension by D₂₀ of C₈ acting through Inn(D₂₀)	160	2	D20.6C8	320,528
D₈₀⋊₇C₂	The semidirect product of D₈₀ and C₂ acting through Inn(D₈₀)	160	2	D80:7C2	320,531
C₅×C₈○D₈	Direct product of C₅ and C₈○D₈	80	2	C5xC8oD8	320,944
C₅×D₄○C₁₆	Direct product of C₅ and D₄○C₁₆	160	2	C5xD4oC16	320,1005
C₅×C₄○D₁₆	Direct product of C₅ and C₄○D₁₆	160	2	C5xC4oD16	320,1009

Groups of order 322

		d	ρ	Label	ID
D₇×C₂₃	Direct product of C₂₃ and D₇	161	2	D7xC23	322,1
C₇×D₂₃	Direct product of C₇ and D₂₃	161	2	C7xD23	322,2

Groups of order 324

		d	ρ	Label	ID
C₉×Dic₉	Direct product of C₉ and Dic₉	36	2	C9xDic9	324,6
C₃×Dic₂₇	Direct product of C₃ and Dic₂₇	108	2	C3xDic27	324,10
Dic₃×C₂₇	Direct product of C₂₇ and Dic₃	108	2	Dic3xC27	324,11
D₉×C₁₈	Direct product of C₁₈ and D₉	36	2	D9xC18	324,61
C₆×D₂₇	Direct product of C₆ and D₂₇	108	2	C6xD27	324,65
S₃×C₅₄	Direct product of C₅₄ and S₃	108	2	S3xC54	324,66

Groups of order 328

		d	ρ	Label	ID
C₄₁⋊₃C₈	The semidirect product of C₄₁ and C₈ acting via C₈/C₄=C₂	328	2	C41:3C8	328,1
C₄×D₄₁	Direct product of C₄ and D₄₁	164	2	C4xD41	328,5
C₄₁⋊D₄	The semidirect product of C₄₁ and D₄ acting via D₄/C₂²=C₂	164	2	C41:D4	328,8
D₄×C₄₁	Direct product of C₄₁ and D₄	164	2	D4xC41	328,10
Q₈×C₄₁	Direct product of C₄₁ and Q₈	328	2	Q8xC41	328,11

Groups of order 330

		d	ρ	Label	ID
C₁₅×D₁₁	Direct product of C₁₅ and D₁₁	165	2	C15xD11	330,5
D₅×C₃₃	Direct product of C₃₃ and D₅	165	2	D5xC33	330,6
C₃×D₅₅	Direct product of C₃ and D₅₅	165	2	C3xD55	330,7
S₃×C₅₅	Direct product of C₅₅ and S₃	165	2	S3xC55	330,8
C₅×D₃₃	Direct product of C₅ and D₃₃	165	2	C5xD33	330,9
C₁₁×D₁₅	Direct product of C₁₁ and D₁₅	165	2	C11xD15	330,10

Groups of order 336

		d	ρ	Label	ID
C₇×C₃⋊C₁₆	Direct product of C₇ and C₃⋊C₁₆	336	2	C7xC3:C16	336,3
C₃×C₇⋊C₁₆	Direct product of C₃ and C₇⋊C₁₆	336	2	C3xC7:C16	336,4
C₂₁⋊C₁₆	1^st semidirect product of C₂₁ and C₁₆ acting via C₁₆/C₈=C₂	336	2	C21:C16	336,5
D₇×C₂₄	Direct product of C₂₄ and D₇	168	2	D7xC24	336,58
C₃×C₈⋊D₇	Direct product of C₃ and C₈⋊D₇	168	2	C3xC8:D7	336,59
C₃×C₅₆⋊C₂	Direct product of C₃ and C₅₆⋊C₂	168	2	C3xC56:C2	336,60
C₃×D₅₆	Direct product of C₃ and D₅₆	168	2	C3xD56	336,61
C₃×Dic₂₈	Direct product of C₃ and Dic₂₈	336	2	C3xDic28	336,62
C₃×C₄.Dic₇	Direct product of C₃ and C₄.Dic₇	168	2	C3xC4.Dic7	336,64
S₃×C₅₆	Direct product of C₅₆ and S₃	168	2	S3xC56	336,74
C₇×C₈⋊S₃	Direct product of C₇ and C₈⋊S₃	168	2	C7xC8:S3	336,75
C₇×C₂₄⋊C₂	Direct product of C₇ and C₂₄⋊C₂	168	2	C7xC24:C2	336,76
C₇×D₂₄	Direct product of C₇ and D₂₄	168	2	C7xD24	336,77
C₇×Dic₁₂	Direct product of C₇ and Dic₁₂	336	2	C7xDic12	336,78
C₇×C₄.Dic₃	Direct product of C₇ and C₄.Dic₃	168	2	C7xC4.Dic3	336,80
C₈×D₂₁	Direct product of C₈ and D₂₁	168	2	C8xD21	336,90
C₅₆⋊S₃	4^th semidirect product of C₅₆ and S₃ acting via S₃/C₃=C₂	168	2	C56:S3	336,91
C₈⋊D₂₁	2^nd semidirect product of C₈ and D₂₁ acting via D₂₁/C₂₁=C₂	168	2	C8:D21	336,92
C₈₄.C₄	1^st non-split extension by C₈₄ of C₄ acting via C₄/C₂=C₂	168	2	C84.C4	336,96
M₄(2)×C₂₁	Direct product of C₂₁ and M₄(2)	168	2	M4(2)xC21	336,110
D₈×C₂₁	Direct product of C₂₁ and D₈	168	2	D8xC21	336,111
SD₁₆×C₂₁	Direct product of C₂₁ and SD₁₆	168	2	SD16xC21	336,112
Q₁₆×C₂₁	Direct product of C₂₁ and Q₁₆	336	2	Q16xC21	336,113
C₇×CSU₂(𝔽₃)	Direct product of C₇ and CSU₂(𝔽₃)	112	2	C7xCSU(2,3)	336,115
C₇×GL₂(𝔽₃)	Direct product of C₇ and GL₂(𝔽₃)	56	2	C7xGL(2,3)	336,116
C₇×C₄.A₄	Direct product of C₇ and C₄.A₄	112	2	C7xC4.A4	336,170
C₃×C₄○D₂₈	Direct product of C₃ and C₄○D₂₈	168	2	C3xC4oD28	336,177
C₇×C₄○D₁₂	Direct product of C₇ and C₄○D₁₂	168	2	C7xC4oD12	336,187
D₈₄⋊₁₁C₂	The semidirect product of D₈₄ and C₂ acting through Inn(D₈₄)	168	2	D84:11C2	336,197
C₄○D₄×C₂₁	Direct product of C₂₁ and C₄○D₄	168	2	C4oD4xC21	336,207

Groups of order 338

		d	ρ	Label	ID
C₁₃×D₁₃	Direct product of C₁₃ and D₁₃; = AΣL₁(𝔽₁₆₉)	26	2	C13xD13	338,3

Groups of order 340

		d	ρ	Label	ID
C₁₇×Dic₅	Direct product of C₁₇ and Dic₅	340	2	C17xDic5	340,1
C₅×Dic₁₇	Direct product of C₅ and Dic₁₇	340	2	C5xDic17	340,2
C₁₀×D₁₇	Direct product of C₁₀ and D₁₇	170	2	C10xD17	340,12
D₅×C₃₄	Direct product of C₃₄ and D₅	170	2	D5xC34	340,13

Groups of order 342

		d	ρ	Label	ID
D₉×C₁₉	Direct product of C₁₉ and D₉	171	2	D9xC19	342,3
C₉×D₁₉	Direct product of C₉ and D₁₉	171	2	C9xD19	342,4
S₃×C₅₇	Direct product of C₅₇ and S₃	114	2	S3xC57	342,14
C₃×D₅₇	Direct product of C₃ and D₅₇	114	2	C3xD57	342,15

Groups of order 344

		d	ρ	Label	ID
C₄₃⋊C₈	The semidirect product of C₄₃ and C₈ acting via C₈/C₄=C₂	344	2	C43:C8	344,1
C₄×D₄₃	Direct product of C₄ and D₄₃	172	2	C4xD43	344,4
C₄₃⋊D₄	The semidirect product of C₄₃ and D₄ acting via D₄/C₂²=C₂	172	2	C43:D4	344,7
D₄×C₄₃	Direct product of C₄₃ and D₄	172	2	D4xC43	344,9
Q₈×C₄₃	Direct product of C₄₃ and Q₈	344	2	Q8xC43	344,10

Groups of order 348

		d	ρ	Label	ID
Dic₃×C₂₉	Direct product of C₂₉ and Dic₃	348	2	Dic3xC29	348,1
C₃×Dic₂₉	Direct product of C₃ and Dic₂₉	348	2	C3xDic29	348,2
C₆×D₂₉	Direct product of C₆ and D₂₉	174	2	C6xD29	348,9
S₃×C₅₈	Direct product of C₅₈ and S₃	174	2	S3xC58	348,10

Groups of order 350

		d	ρ	Label	ID
C₇×D₂₅	Direct product of C₇ and D₂₅	175	2	C7xD25	350,1
D₇×C₂₅	Direct product of C₂₅ and D₇	175	2	D7xC25	350,2
D₅×C₃₅	Direct product of C₃₅ and D₅	70	2	D5xC35	350,6
C₅×D₃₅	Direct product of C₅ and D₃₅	70	2	C5xD35	350,7

Groups of order 352

		d	ρ	Label	ID
C₁₁⋊C₃₂	The semidirect product of C₁₁ and C₃₂ acting via C₃₂/C₁₆=C₂	352	2	C11:C32	352,1
C₁₆×D₁₁	Direct product of C₁₆ and D₁₁	176	2	C16xD11	352,3
D₂₂.C₈	The non-split extension by D₂₂ of C₈ acting via C₈/C₄=C₂	176	2	D22.C8	352,4
C₁₇₆⋊C₂	2^nd semidirect product of C₁₇₆ and C₂ acting faithfully	176	2	C176:C2	352,6
D₄₄⋊₁C₄	1^st semidirect product of D₄₄ and C₄ acting via C₄/C₂=C₂	88	2	D44:1C4	352,11
C₄₄.C₈	1^st non-split extension by C₄₄ of C₈ acting via C₈/C₄=C₂	176	2	C44.C8	352,18
C₈₈.C₄	1^st non-split extension by C₈₈ of C₄ acting via C₄/C₂=C₂	176	2	C88.C4	352,25
C₁₁×C₄≀C₂	Direct product of C₁₁ and C₄≀C₂	88	2	C11xC4wrC2	352,53
C₁₁×C₈.C₄	Direct product of C₁₁ and C₈.C₄	176	2	C11xC8.C4	352,57
C₁₁×M₅(2)	Direct product of C₁₁ and M₅(2)	176	2	C11xM5(2)	352,59
C₁₁×D₁₆	Direct product of C₁₁ and D₁₆	176	2	C11xD16	352,60
C₁₁×SD₃₂	Direct product of C₁₁ and SD₃₂	176	2	C11xSD32	352,61
C₁₁×Q₃₂	Direct product of C₁₁ and Q₃₂	352	2	C11xQ32	352,62
D₄₄.₂C₄	The non-split extension by D₄₄ of C₄ acting through Inn(D₄₄)	176	2	D44.2C4	352,96
D₈₈⋊₇C₂	The semidirect product of D₈₈ and C₂ acting through Inn(D₈₈)	176	2	D88:7C2	352,99
C₁₁×C₈○D₄	Direct product of C₁₁ and C₈○D₄	176	2	C11xC8oD4	352,166
C₁₁×C₄○D₈	Direct product of C₁₁ and C₄○D₈	176	2	C11xC4oD8	352,170

Groups of order 354

		d	ρ	Label	ID
S₃×C₅₉	Direct product of C₅₉ and S₃	177	2	S3xC59	354,1
C₃×D₅₉	Direct product of C₃ and D₅₉	177	2	C3xD59	354,2

Groups of order 360

		d	ρ	Label	ID
C₅×C₉⋊C₈	Direct product of C₅ and C₉⋊C₈	360	2	C5xC9:C8	360,1
C₉×C₅⋊₂C₈	Direct product of C₉ and C₅⋊₂C₈	360	2	C9xC5:2C8	360,2
C₄₅⋊₃C₈	1^st semidirect product of C₄₅ and C₈ acting via C₈/C₄=C₂	360	2	C45:3C8	360,3
C₅×Q₈⋊C₉	Direct product of C₅ and Q₈⋊C₉	360	2	C5xQ8:C9	360,14
C₉×Dic₁₀	Direct product of C₉ and Dic₁₀	360	2	C9xDic10	360,15
D₅×C₃₆	Direct product of C₃₆ and D₅	180	2	D5xC36	360,16
C₉×D₂₀	Direct product of C₉ and D₂₀	180	2	C9xD20	360,17
C₉×C₅⋊D₄	Direct product of C₉ and C₅⋊D₄	180	2	C9xC5:D4	360,19
C₅×Dic₁₈	Direct product of C₅ and Dic₁₈	360	2	C5xDic18	360,20
D₉×C₂₀	Direct product of C₂₀ and D₉	180	2	D9xC20	360,21
C₅×D₃₆	Direct product of C₅ and D₃₆	180	2	C5xD36	360,22
C₅×C₉⋊D₄	Direct product of C₅ and C₉⋊D₄	180	2	C5xC9:D4	360,24
C₄×D₄₅	Direct product of C₄ and D₄₅	180	2	C4xD45	360,26
C₄₅⋊₇D₄	1^st semidirect product of C₄₅ and D₄ acting via D₄/C₂²=C₂	180	2	C45:7D4	360,29
D₄×C₄₅	Direct product of C₄₅ and D₄	180	2	D4xC45	360,31
Q₈×C₄₅	Direct product of C₄₅ and Q₈	360	2	Q8xC45	360,32
C₁₅×C₃⋊C₈	Direct product of C₁₅ and C₃⋊C₈	120	2	C15xC3:C8	360,34
C₃×C₁₅⋊₃C₈	Direct product of C₃ and C₁₅⋊₃C₈	120	2	C3xC15:3C8	360,35
C₃×SL₂(𝔽₅)	Direct product of C₃ and SL₂(𝔽₅)	72	2	C3xSL(2,5)	360,51
C₁₅×SL₂(𝔽₃)	Direct product of C₁₅ and SL₂(𝔽₃)	120	2	C15xSL(2,3)	360,89
C₁₅×Dic₆	Direct product of C₁₅ and Dic₆	120	2	C15xDic6	360,95
S₃×C₆₀	Direct product of C₆₀ and S₃	120	2	S3xC60	360,96
C₁₅×D₁₂	Direct product of C₁₅ and D₁₂	120	2	C15xD12	360,97
C₁₅×C₃⋊D₄	Direct product of C₁₅ and C₃⋊D₄	60	2	C15xC3:D4	360,99
C₃×Dic₃₀	Direct product of C₃ and Dic₃₀	120	2	C3xDic30	360,100
C₁₂×D₁₅	Direct product of C₁₂ and D₁₅	120	2	C12xD15	360,101
C₃×D₆₀	Direct product of C₃ and D₆₀	120	2	C3xD60	360,102
C₃×C₁₅⋊₇D₄	Direct product of C₃ and C₁₅⋊₇D₄	60	2	C3xC15:7D4	360,104

Groups of order 364

		d	ρ	Label	ID
C₁₃×Dic₇	Direct product of C₁₃ and Dic₇	364	2	C13xDic7	364,1
C₇×Dic₁₃	Direct product of C₇ and Dic₁₃	364	2	C7xDic13	364,2
C₁₄×D₁₃	Direct product of C₁₄ and D₁₃	182	2	C14xD13	364,8
D₇×C₂₆	Direct product of C₂₆ and D₇	182	2	D7xC26	364,9

Groups of order 366

		d	ρ	Label	ID
S₃×C₆₁	Direct product of C₆₁ and S₃	183	2	S3xC61	366,3
C₃×D₆₁	Direct product of C₃ and D₆₁	183	2	C3xD61	366,4

Groups of order 368

		d	ρ	Label	ID
C₂₃⋊C₁₆	The semidirect product of C₂₃ and C₁₆ acting via C₁₆/C₈=C₂	368	2	C23:C16	368,1
C₈×D₂₃	Direct product of C₈ and D₂₃	184	2	C8xD23	368,3
C₈⋊D₂₃	3^rd semidirect product of C₈ and D₂₃ acting via D₂₃/C₂₃=C₂	184	2	C8:D23	368,4
C₁₈₄⋊C₂	2^nd semidirect product of C₁₈₄ and C₂ acting faithfully	184	2	C184:C2	368,5
C₉₂.C₄	1^st non-split extension by C₉₂ of C₄ acting via C₄/C₂=C₂	184	2	C92.C4	368,9
M₄(2)×C₂₃	Direct product of C₂₃ and M₄(2)	184	2	M4(2)xC23	368,23
D₈×C₂₃	Direct product of C₂₃ and D₈	184	2	D8xC23	368,24
SD₁₆×C₂₃	Direct product of C₂₃ and SD₁₆	184	2	SD16xC23	368,25
Q₁₆×C₂₃	Direct product of C₂₃ and Q₁₆	368	2	Q16xC23	368,26
D₉₂⋊₅C₂	The semidirect product of D₉₂ and C₂ acting through Inn(D₉₂)	184	2	D92:5C2	368,30
C₄○D₄×C₂₃	Direct product of C₂₃ and C₄○D₄	184	2	C4oD4xC23	368,40

Groups of order 370

		d	ρ	Label	ID
D₅×C₃₇	Direct product of C₃₇ and D₅	185	2	D5xC37	370,1
C₅×D₃₇	Direct product of C₅ and D₃₇	185	2	C5xD37	370,2

Groups of order 372

		d	ρ	Label	ID
Dic₃×C₃₁	Direct product of C₃₁ and Dic₃	372	2	Dic3xC31	372,3
C₃×Dic₃₁	Direct product of C₃ and Dic₃₁	372	2	C3xDic31	372,4
C₆×D₃₁	Direct product of C₆ and D₃₁	186	2	C6xD31	372,12
S₃×C₆₂	Direct product of C₆₂ and S₃	186	2	S3xC62	372,13

Groups of order 374

		d	ρ	Label	ID
C₁₇×D₁₁	Direct product of C₁₇ and D₁₁	187	2	C17xD11	374,1
C₁₁×D₁₇	Direct product of C₁₁ and D₁₇	187	2	C11xD17	374,2

Groups of order 376

		d	ρ	Label	ID
C₄₇⋊C₈	The semidirect product of C₄₇ and C₈ acting via C₈/C₄=C₂	376	2	C47:C8	376,1
C₄×D₄₇	Direct product of C₄ and D₄₇	188	2	C4xD47	376,4
C₄₇⋊D₄	The semidirect product of C₄₇ and D₄ acting via D₄/C₂²=C₂	188	2	C47:D4	376,7
D₄×C₄₇	Direct product of C₄₇ and D₄	188	2	D4xC47	376,9
Q₈×C₄₇	Direct product of C₄₇ and Q₈	376	2	Q8xC47	376,10

Groups of order 378

		d	ρ	Label	ID
C₇×D₂₇	Direct product of C₇ and D₂₇	189	2	C7xD27	378,3
D₇×C₂₇	Direct product of C₂₇ and D₇	189	2	D7xC27	378,4
D₉×C₂₁	Direct product of C₂₁ and D₉	126	2	D9xC21	378,32
S₃×C₆₃	Direct product of C₆₃ and S₃	126	2	S3xC63	378,33
C₃×D₆₃	Direct product of C₃ and D₆₃	126	2	C3xD63	378,36
C₉×D₂₁	Direct product of C₉ and D₂₁	126	2	C9xD21	378,37

Groups of order 380

		d	ρ	Label	ID
C₁₉×Dic₅	Direct product of C₁₉ and Dic₅	380	2	C19xDic5	380,1
C₅×Dic₁₉	Direct product of C₅ and Dic₁₉	380	2	C5xDic19	380,2
C₁₀×D₁₉	Direct product of C₁₀ and D₁₉	190	2	C10xD19	380,8
D₅×C₃₈	Direct product of C₃₈ and D₅	190	2	D5xC38	380,9

Groups of order 390

		d	ρ	Label	ID
C₁₅×D₁₃	Direct product of C₁₅ and D₁₃	195	2	C15xD13	390,5
D₅×C₃₉	Direct product of C₃₉ and D₅	195	2	D5xC39	390,6
C₃×D₆₅	Direct product of C₃ and D₆₅	195	2	C3xD65	390,7
S₃×C₆₅	Direct product of C₆₅ and S₃	195	2	S3xC65	390,8
C₅×D₃₉	Direct product of C₅ and D₃₉	195	2	C5xD39	390,9
C₁₃×D₁₅	Direct product of C₁₃ and D₁₅	195	2	C13xD15	390,10

Groups of order 392

		d	ρ	Label	ID
C₄₉⋊C₈	The semidirect product of C₄₉ and C₈ acting via C₈/C₄=C₂	392	2	C49:C8	392,1
C₄×D₄₉	Direct product of C₄ and D₄₉	196	2	C4xD49	392,4
C₄₉⋊D₄	The semidirect product of C₄₉ and D₄ acting via D₄/C₂²=C₂	196	2	C49:D4	392,7
D₄×C₄₉	Direct product of C₄₉ and D₄	196	2	D4xC49	392,9
Q₈×C₄₉	Direct product of C₄₉ and Q₈	392	2	Q8xC49	392,10
C₇×C₇⋊C₈	Direct product of C₇ and C₇⋊C₈	56	2	C7xC7:C8	392,14
C₇×Dic₁₄	Direct product of C₇ and Dic₁₄	56	2	C7xDic14	392,23
D₇×C₂₈	Direct product of C₂₈ and D₇	56	2	D7xC28	392,24
C₇×D₂₈	Direct product of C₇ and D₂₈	56	2	C7xD28	392,25
C₇×C₇⋊D₄	Direct product of C₇ and C₇⋊D₄	28	2	C7xC7:D4	392,27

Groups of order 396

		d	ρ	Label	ID
C₁₁×Dic₉	Direct product of C₁₁ and Dic₉	396	2	C11xDic9	396,1
C₉×Dic₁₁	Direct product of C₉ and Dic₁₁	396	2	C9xDic11	396,2
C₁₈×D₁₁	Direct product of C₁₈ and D₁₁	198	2	C18xD11	396,7
D₉×C₂₂	Direct product of C₂₂ and D₉	198	2	D9xC22	396,8
Dic₃×C₃₃	Direct product of C₃₃ and Dic₃	132	2	Dic3xC33	396,12
C₃×Dic₃₃	Direct product of C₃ and Dic₃₃	132	2	C3xDic33	396,13
S₃×C₆₆	Direct product of C₆₆ and S₃	132	2	S3xC66	396,26
C₆×D₃₃	Direct product of C₆ and D₃₃	132	2	C6xD33	396,27

Groups of order 400

		d	ρ	Label	ID
C₂₅⋊₂C₁₆	The semidirect product of C₂₅ and C₁₆ acting via C₁₆/C₈=C₂	400	2	C25:2C16	400,1
C₈×D₂₅	Direct product of C₈ and D₂₅	200	2	C8xD25	400,5
C₈⋊D₂₅	3^rd semidirect product of C₈ and D₂₅ acting via D₂₅/C₂₅=C₂	200	2	C8:D25	400,6
C₂₀₀⋊C₂	2^nd semidirect product of C₂₀₀ and C₂ acting faithfully	200	2	C200:C2	400,7
C₄.Dic₂₅	The non-split extension by C₄ of Dic₂₅ acting via Dic₂₅/C₅₀=C₂	200	2	C4.Dic25	400,10
M₄(2)×C₂₅	Direct product of C₂₅ and M₄(2)	200	2	M4(2)xC25	400,24
D₈×C₂₅	Direct product of C₂₅ and D₈	200	2	D8xC25	400,25
SD₁₆×C₂₅	Direct product of C₂₅ and SD₁₆	200	2	SD16xC25	400,26
Q₁₆×C₂₅	Direct product of C₂₅ and Q₁₆	400	2	Q16xC25	400,27
D₁₀₀⋊₅C₂	The semidirect product of D₁₀₀ and C₂ acting through Inn(D₁₀₀)	200	2	D100:5C2	400,38
C₄○D₄×C₂₅	Direct product of C₂₅ and C₄○D₄	200	2	C4oD4xC25	400,48
C₅×C₅⋊₂C₁₆	Direct product of C₅ and C₅⋊₂C₁₆	80	2	C5xC5:2C16	400,49
D₅×C₄₀	Direct product of C₄₀ and D₅	80	2	D5xC40	400,76
C₅×C₈⋊D₅	Direct product of C₅ and C₈⋊D₅	80	2	C5xC8:D5	400,77
C₅×C₄₀⋊C₂	Direct product of C₅ and C₄₀⋊C₂	80	2	C5xC40:C2	400,78
C₅×D₄₀	Direct product of C₅ and D₄₀	80	2	C5xD40	400,79
C₅×Dic₂₀	Direct product of C₅ and Dic₂₀	80	2	C5xDic20	400,80
C₅×C₄.Dic₅	Direct product of C₅ and C₄.Dic₅	40	2	C5xC4.Dic5	400,82
C₅×C₄○D₂₀	Direct product of C₅ and C₄○D₂₀	40	2	C5xC4oD20	400,184

Groups of order 402

		d	ρ	Label	ID
S₃×C₆₇	Direct product of C₆₇ and S₃	201	2	S3xC67	402,3
C₃×D₆₇	Direct product of C₃ and D₆₇	201	2	C3xD67	402,4

Groups of order 406

		d	ρ	Label	ID
D₇×C₂₉	Direct product of C₂₉ and D₇	203	2	D7xC29	406,3
C₇×D₂₉	Direct product of C₇ and D₂₉	203	2	C7xD29	406,4

Groups of order 408

		d	ρ	Label	ID
C₁₇×C₃⋊C₈	Direct product of C₁₇ and C₃⋊C₈	408	2	C17xC3:C8	408,1
C₃×C₁₇⋊₃C₈	Direct product of C₃ and C₁₇⋊₃C₈	408	2	C3xC17:3C8	408,2
C₅₁⋊₅C₈	1^st semidirect product of C₅₁ and C₈ acting via C₈/C₄=C₂	408	2	C51:5C8	408,3
C₁₇×SL₂(𝔽₃)	Direct product of C₁₇ and SL₂(𝔽₃)	136	2	C17xSL(2,3)	408,14
C₃×Dic₃₄	Direct product of C₃ and Dic₃₄	408	2	C3xDic34	408,15
C₁₂×D₁₇	Direct product of C₁₂ and D₁₇	204	2	C12xD17	408,16
C₃×D₆₈	Direct product of C₃ and D₆₈	204	2	C3xD68	408,17
C₃×C₁₇⋊D₄	Direct product of C₃ and C₁₇⋊D₄	204	2	C3xC17:D4	408,19
C₁₇×Dic₆	Direct product of C₁₇ and Dic₆	408	2	C17xDic6	408,20
S₃×C₆₈	Direct product of C₆₈ and S₃	204	2	S3xC68	408,21
C₁₇×D₁₂	Direct product of C₁₇ and D₁₂	204	2	C17xD12	408,22
C₁₇×C₃⋊D₄	Direct product of C₁₇ and C₃⋊D₄	204	2	C17xC3:D4	408,24
C₄×D₅₁	Direct product of C₄ and D₅₁	204	2	C4xD51	408,26
C₅₁⋊₇D₄	1^st semidirect product of C₅₁ and D₄ acting via D₄/C₂²=C₂	204	2	C51:7D4	408,29
D₄×C₅₁	Direct product of C₅₁ and D₄	204	2	D4xC51	408,31
Q₈×C₅₁	Direct product of C₅₁ and Q₈	408	2	Q8xC51	408,32

Groups of order 410

		d	ρ	Label	ID
D₅×C₄₁	Direct product of C₄₁ and D₅	205	2	D5xC41	410,3
C₅×D₄₁	Direct product of C₅ and D₄₁	205	2	C5xD41	410,4

Groups of order 414

		d	ρ	Label	ID
D₉×C₂₃	Direct product of C₂₃ and D₉	207	2	D9xC23	414,1
C₉×D₂₃	Direct product of C₉ and D₂₃	207	2	C9xD23	414,2
S₃×C₆₉	Direct product of C₆₉ and S₃	138	2	S3xC69	414,6
C₃×D₆₉	Direct product of C₃ and D₆₉	138	2	C3xD69	414,7

Groups of order 416

		d	ρ	Label	ID
C₁₃⋊₂C₃₂	The semidirect product of C₁₃ and C₃₂ acting via C₃₂/C₁₆=C₂	416	2	C13:2C32	416,1
C₁₆×D₁₃	Direct product of C₁₆ and D₁₃	208	2	C16xD13	416,4
C₂₀₈⋊C₂	4^th semidirect product of C₂₀₈ and C₂ acting faithfully	208	2	C208:C2	416,5
C₁₆⋊D₁₃	2^nd semidirect product of C₁₆ and D₁₃ acting via D₁₃/C₁₃=C₂	208	2	C16:D13	416,7
D₅₂⋊₄C₄	1^st semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	104	2	D52:4C4	416,12
C₅₂.₄C₈	1^st non-split extension by C₅₂ of C₈ acting via C₈/C₄=C₂	208	2	C52.4C8	416,19
C₁₀₄.₆C₄	1^st non-split extension by C₁₀₄ of C₄ acting via C₄/C₂=C₂	208	2	C104.6C4	416,26
C₁₃×C₄≀C₂	Direct product of C₁₃ and C₄≀C₂	104	2	C13xC4wrC2	416,54
C₁₃×C₈.C₄	Direct product of C₁₃ and C₈.C₄	208	2	C13xC8.C4	416,58
C₁₃×M₅(2)	Direct product of C₁₃ and M₅(2)	208	2	C13xM5(2)	416,60
C₁₃×D₁₆	Direct product of C₁₃ and D₁₆	208	2	C13xD16	416,61
C₁₃×SD₃₂	Direct product of C₁₃ and SD₃₂	208	2	C13xSD32	416,62
C₁₃×Q₃₂	Direct product of C₁₃ and Q₃₂	416	2	C13xQ32	416,63
D₅₂.₃C₄	The non-split extension by D₅₂ of C₄ acting through Inn(D₅₂)	208	2	D52.3C4	416,122
D₁₀₄⋊₇C₂	The semidirect product of D₁₀₄ and C₂ acting through Inn(D₁₀₄)	208	2	D104:7C2	416,125
C₁₃×C₈○D₄	Direct product of C₁₃ and C₈○D₄	208	2	C13xC8oD4	416,192
C₁₃×C₄○D₈	Direct product of C₁₃ and C₄○D₈	208	2	C13xC4oD8	416,196

Groups of order 418

		d	ρ	Label	ID
C₁₉×D₁₁	Direct product of C₁₉ and D₁₁	209	2	C19xD11	418,1
C₁₁×D₁₉	Direct product of C₁₁ and D₁₉	209	2	C11xD19	418,2

Groups of order 420

		d	ρ	Label	ID
C₁₅×Dic₇	Direct product of C₁₅ and Dic₇	420	2	C15xDic7	420,5
Dic₅×C₂₁	Direct product of C₂₁ and Dic₅	420	2	Dic5xC21	420,6
C₃×Dic₃₅	Direct product of C₃ and Dic₃₅	420	2	C3xDic35	420,7
Dic₃×C₃₅	Direct product of C₃₅ and Dic₃	420	2	Dic3xC35	420,8
C₅×Dic₂₁	Direct product of C₅ and Dic₂₁	420	2	C5xDic21	420,9
C₇×Dic₁₅	Direct product of C₇ and Dic₁₅	420	2	C7xDic15	420,10
D₇×C₃₀	Direct product of C₃₀ and D₇	210	2	D7xC30	420,34
D₅×C₄₂	Direct product of C₄₂ and D₅	210	2	D5xC42	420,35
C₆×D₃₅	Direct product of C₆ and D₃₅	210	2	C6xD35	420,36
S₃×C₇₀	Direct product of C₇₀ and S₃	210	2	S3xC70	420,37
C₁₀×D₂₁	Direct product of C₁₀ and D₂₁	210	2	C10xD21	420,38
C₁₄×D₁₅	Direct product of C₁₄ and D₁₅	210	2	C14xD15	420,39

Groups of order 424

		d	ρ	Label	ID
C₅₃⋊₂C₈	The semidirect product of C₅₃ and C₈ acting via C₈/C₄=C₂	424	2	C53:2C8	424,1
C₄×D₅₃	Direct product of C₄ and D₅₃	212	2	C4xD53	424,5
C₅₃⋊D₄	The semidirect product of C₅₃ and D₄ acting via D₄/C₂²=C₂	212	2	C53:D4	424,8
D₄×C₅₃	Direct product of C₅₃ and D₄	212	2	D4xC53	424,10
Q₈×C₅₃	Direct product of C₅₃ and Q₈	424	2	Q8xC53	424,11

Groups of order 426

		d	ρ	Label	ID
S₃×C₇₁	Direct product of C₇₁ and S₃	213	2	S3xC71	426,1
C₃×D₇₁	Direct product of C₃ and D₇₁	213	2	C3xD71	426,2

Groups of order 430

		d	ρ	Label	ID
D₅×C₄₃	Direct product of C₄₃ and D₅	215	2	D5xC43	430,1
C₅×D₄₃	Direct product of C₅ and D₄₃	215	2	C5xD43	430,2

Groups of order 432

		d	ρ	Label	ID
C₂₇⋊C₁₆	The semidirect product of C₂₇ and C₁₆ acting via C₁₆/C₈=C₂	432	2	C27:C16	432,1
C₈×D₂₇	Direct product of C₈ and D₂₇	216	2	C8xD27	432,5
C₈⋊D₂₇	3^rd semidirect product of C₈ and D₂₇ acting via D₂₇/C₂₇=C₂	216	2	C8:D27	432,6
C₂₁₆⋊C₂	2^nd semidirect product of C₂₁₆ and C₂ acting faithfully	216	2	C216:C2	432,7
C₄.Dic₂₇	The non-split extension by C₄ of Dic₂₇ acting via Dic₂₇/C₅₄=C₂	216	2	C4.Dic27	432,10
M₄(2)×C₂₇	Direct product of C₂₇ and M₄(2)	216	2	M4(2)xC27	432,24
D₈×C₂₇	Direct product of C₂₇ and D₈	216	2	D8xC27	432,25
SD₁₆×C₂₇	Direct product of C₂₇ and SD₁₆	216	2	SD16xC27	432,26
Q₁₆×C₂₇	Direct product of C₂₇ and Q₁₆	432	2	Q16xC27	432,27
C₃×C₉⋊C₁₆	Direct product of C₃ and C₉⋊C₁₆	144	2	C3xC9:C16	432,28
C₉×C₃⋊C₁₆	Direct product of C₉ and C₃⋊C₁₆	144	2	C9xC3:C16	432,29
Q₈.C₅₄	The non-split extension by Q₈ of C₅₄ acting via C₅₄/C₁₈=C₃	216	2	Q8.C54	432,42
D₁₀₈⋊₅C₂	The semidirect product of D₁₀₈ and C₂ acting through Inn(D₁₀₈)	216	2	D108:5C2	432,46
C₄○D₄×C₂₇	Direct product of C₂₇ and C₄○D₄	216	2	C4oD4xC27	432,56
C₃×Dic₃₆	Direct product of C₃ and Dic₃₆	144	2	C3xDic36	432,104
D₉×C₂₄	Direct product of C₂₄ and D₉	144	2	D9xC24	432,105
C₃×C₈⋊D₉	Direct product of C₃ and C₈⋊D₉	144	2	C3xC8:D9	432,106
C₃×C₇₂⋊C₂	Direct product of C₃ and C₇₂⋊C₂	144	2	C3xC72:C2	432,107
C₃×D₇₂	Direct product of C₃ and D₇₂	144	2	C3xD72	432,108
S₃×C₇₂	Direct product of C₇₂ and S₃	144	2	S3xC72	432,109
C₉×C₈⋊S₃	Direct product of C₉ and C₈⋊S₃	144	2	C9xC8:S3	432,110
C₉×C₂₄⋊C₂	Direct product of C₉ and C₂₄⋊C₂	144	2	C9xC24:C2	432,111
C₉×D₂₄	Direct product of C₉ and D₂₄	144	2	C9xD24	432,112
C₉×Dic₁₂	Direct product of C₉ and Dic₁₂	144	2	C9xDic12	432,113
C₃×C₄.Dic₉	Direct product of C₃ and C₄.Dic₉	72	2	C3xC4.Dic9	432,125
C₉×C₄.Dic₃	Direct product of C₉ and C₄.Dic₃	72	2	C9xC4.Dic3	432,127
C₉×CSU₂(𝔽₃)	Direct product of C₉ and CSU₂(𝔽₃)	144	2	C9xCSU(2,3)	432,240
C₉×GL₂(𝔽₃)	Direct product of C₉ and GL₂(𝔽₃)	72	2	C9xGL(2,3)	432,241
C₉×C₄.A₄	Direct product of C₉ and C₄.A₄	144	2	C9xC4.A4	432,329
C₃×D₃₆⋊₅C₂	Direct product of C₃ and D₃₆⋊₅C₂	72	2	C3xD36:5C2	432,344
C₉×C₄○D₁₂	Direct product of C₉ and C₄○D₁₂	72	2	C9xC4oD12	432,347

Groups of order 434

		d	ρ	Label	ID
D₇×C₃₁	Direct product of C₃₁ and D₇	217	2	D7xC31	434,1
C₇×D₃₁	Direct product of C₇ and D₃₁	217	2	C7xD31	434,2

Groups of order 438

		d	ρ	Label	ID
S₃×C₇₃	Direct product of C₇₃ and S₃	219	2	S3xC73	438,3
C₃×D₇₃	Direct product of C₃ and D₇₃	219	2	C3xD73	438,4

Groups of order 440

		d	ρ	Label	ID
C₁₁×C₅⋊₂C₈	Direct product of C₁₁ and C₅⋊₂C₈	440	2	C11xC5:2C8	440,3
C₅×C₁₁⋊C₈	Direct product of C₅ and C₁₁⋊C₈	440	2	C5xC11:C8	440,4
C₅₅⋊₃C₈	1^st semidirect product of C₅₅ and C₈ acting via C₈/C₄=C₂	440	2	C55:3C8	440,5
C₅×Dic₂₂	Direct product of C₅ and Dic₂₂	440	2	C5xDic22	440,24
C₂₀×D₁₁	Direct product of C₂₀ and D₁₁	220	2	C20xD11	440,25
C₅×D₄₄	Direct product of C₅ and D₄₄	220	2	C5xD44	440,26
C₅×C₁₁⋊D₄	Direct product of C₅ and C₁₁⋊D₄	220	2	C5xC11:D4	440,28
C₁₁×Dic₁₀	Direct product of C₁₁ and Dic₁₀	440	2	C11xDic10	440,29
D₅×C₄₄	Direct product of C₄₄ and D₅	220	2	D5xC44	440,30
C₁₁×D₂₀	Direct product of C₁₁ and D₂₀	220	2	C11xD20	440,31
C₁₁×C₅⋊D₄	Direct product of C₁₁ and C₅⋊D₄	220	2	C11xC5:D4	440,33
C₄×D₅₅	Direct product of C₄ and D₅₅	220	2	C4xD55	440,35
C₅₅⋊₇D₄	1^st semidirect product of C₅₅ and D₄ acting via D₄/C₂²=C₂	220	2	C55:7D4	440,38
D₄×C₅₅	Direct product of C₅₅ and D₄	220	2	D4xC55	440,40
Q₈×C₅₅	Direct product of C₅₅ and Q₈	440	2	Q8xC55	440,41

Groups of order 442

		d	ρ	Label	ID
C₁₇×D₁₃	Direct product of C₁₇ and D₁₃	221	2	C17xD13	442,1
C₁₃×D₁₇	Direct product of C₁₃ and D₁₇	221	2	C13xD17	442,2

Groups of order 444

		d	ρ	Label	ID
Dic₃×C₃₇	Direct product of C₃₇ and Dic₃	444	2	Dic3xC37	444,3
C₃×Dic₃₇	Direct product of C₃ and Dic₃₇	444	2	C3xDic37	444,4
C₆×D₃₇	Direct product of C₆ and D₃₇	222	2	C6xD37	444,15
S₃×C₇₄	Direct product of C₇₄ and S₃	222	2	S3xC74	444,16

Groups of order 448

		d	ρ	Label	ID
C₇⋊C₆₄	The semidirect product of C₇ and C₆₄ acting via C₆₄/C₃₂=C₂	448	2	C7:C64	448,1
D₇×C₃₂	Direct product of C₃₂ and D₇	224	2	D7xC32	448,3
C₃₂⋊D₇	3^rd semidirect product of C₃₂ and D₇ acting via D₇/C₇=C₂	224	2	C32:D7	448,4
C₂₂₄⋊C₂	2^nd semidirect product of C₂₂₄ and C₂ acting faithfully	224	2	C224:C2	448,6
C₅₆.₁₆Q₈	6^th non-split extension by C₅₆ of Q₈ acting via Q₈/C₄=C₂	112	2	C56.16Q8	448,20
C₇⋊M₆(2)	The semidirect product of C₇ and M₆(2) acting via M₆(2)/C₂×C₁₆=C₂	224	2	C7:M6(2)	448,56
C₁₁₂.C₄	1^st non-split extension by C₁₁₂ of C₄ acting via C₄/C₂=C₂	224	2	C112.C4	448,63
D₂₈.C₈	1^st non-split extension by D₂₈ of C₈ acting via C₈/C₄=C₂	224	2	D28.C8	448,65
D₅₆.₁C₄	1^st non-split extension by D₅₆ of C₄ acting via C₄/C₂=C₂	224	2	D56.1C4	448,67
C₇×D₄.C₈	Direct product of C₇ and D₄.C₈	224	2	C7xD4.C8	448,154
C₇×D₈.C₄	Direct product of C₇ and D₈.C₄	224	2	C7xD8.C4	448,163
C₇×C₈.C₈	Direct product of C₇ and C₈.C₈	112	2	C7xC8.C8	448,168
C₇×C₈.₄Q₈	Direct product of C₇ and C₈.₄Q₈	224	2	C7xC8.4Q8	448,172
C₇×M₆(2)	Direct product of C₇ and M₆(2)	224	2	C7xM6(2)	448,174
C₇×D₃₂	Direct product of C₇ and D₃₂	224	2	C7xD32	448,175
C₇×SD₆₄	Direct product of C₇ and SD₆₄	224	2	C7xSD64	448,176
C₇×Q₆₄	Direct product of C₇ and Q₆₄	448	2	C7xQ64	448,177
D₅₆⋊₁₁C₄	The semidirect product of D₅₆ and C₄ acting through Inn(D₅₆)	112	2	D56:11C4	448,234
D₂₈.₄C₈	The non-split extension by D₂₈ of C₈ acting through Inn(D₂₈)	224	2	D28.4C8	448,435
D₁₁₂⋊₇C₂	The semidirect product of D₁₁₂ and C₂ acting through Inn(D₁₁₂)	224	2	D112:7C2	448,438
C₇×C₈○D₈	Direct product of C₇ and C₈○D₈	112	2	C7xC8oD8	448,851
C₇×D₄○C₁₆	Direct product of C₇ and D₄○C₁₆	224	2	C7xD4oC16	448,912
C₇×C₄○D₁₆	Direct product of C₇ and C₄○D₁₆	224	2	C7xC4oD16	448,916

Groups of order 450

		d	ρ	Label	ID
D₉×C₂₅	Direct product of C₂₅ and D₉	225	2	D9xC25	450,1
C₉×D₂₅	Direct product of C₉ and D₂₅	225	2	C9xD25	450,2
S₃×C₇₅	Direct product of C₇₅ and S₃	150	2	S3xC75	450,6
C₃×D₇₅	Direct product of C₃ and D₇₅	150	2	C3xD75	450,7
D₅×C₄₅	Direct product of C₄₅ and D₅	90	2	D5xC45	450,14
C₅×D₄₅	Direct product of C₅ and D₄₅	90	2	C5xD45	450,17
C₁₅×D₁₅	Direct product of C₁₅ and D₁₅	30	2	C15xD15	450,29

Groups of order 456

		d	ρ	Label	ID
C₁₉×C₃⋊C₈	Direct product of C₁₉ and C₃⋊C₈	456	2	C19xC3:C8	456,3
C₃×C₁₉⋊C₈	Direct product of C₃ and C₁₉⋊C₈	456	2	C3xC19:C8	456,4
C₅₇⋊C₈	1^st semidirect product of C₅₇ and C₈ acting via C₈/C₄=C₂	456	2	C57:C8	456,5
C₁₉×SL₂(𝔽₃)	Direct product of C₁₉ and SL₂(𝔽₃)	152	2	C19xSL(2,3)	456,22
C₃×Dic₃₈	Direct product of C₃ and Dic₃₈	456	2	C3xDic38	456,24
C₁₂×D₁₉	Direct product of C₁₂ and D₁₉	228	2	C12xD19	456,25
C₃×D₇₆	Direct product of C₃ and D₇₆	228	2	C3xD76	456,26
C₃×C₁₉⋊D₄	Direct product of C₃ and C₁₉⋊D₄	228	2	C3xC19:D4	456,28
C₁₉×Dic₆	Direct product of C₁₉ and Dic₆	456	2	C19xDic6	456,29
S₃×C₇₆	Direct product of C₇₆ and S₃	228	2	S3xC76	456,30
C₁₉×D₁₂	Direct product of C₁₉ and D₁₂	228	2	C19xD12	456,31
C₁₉×C₃⋊D₄	Direct product of C₁₉ and C₃⋊D₄	228	2	C19xC3:D4	456,33
C₄×D₅₇	Direct product of C₄ and D₅₇	228	2	C4xD57	456,35
C₅₇⋊₇D₄	1^st semidirect product of C₅₇ and D₄ acting via D₄/C₂²=C₂	228	2	C57:7D4	456,38
D₄×C₅₇	Direct product of C₅₇ and D₄	228	2	D4xC57	456,40
Q₈×C₅₇	Direct product of C₅₇ and Q₈	456	2	Q8xC57	456,41

Groups of order 460

		d	ρ	Label	ID
Dic₅×C₂₃	Direct product of C₂₃ and Dic₅	460	2	Dic5xC23	460,1
C₅×Dic₂₃	Direct product of C₅ and Dic₂₃	460	2	C5xDic23	460,2
C₁₀×D₂₃	Direct product of C₁₀ and D₂₃	230	2	C10xD23	460,8
D₅×C₄₆	Direct product of C₄₆ and D₅	230	2	D5xC46	460,9

Groups of order 462

		d	ρ	Label	ID
C₂₁×D₁₁	Direct product of C₂₁ and D₁₁	231	2	C21xD11	462,5
D₇×C₃₃	Direct product of C₃₃ and D₇	231	2	D7xC33	462,6
C₃×D₇₇	Direct product of C₃ and D₇₇	231	2	C3xD77	462,7
S₃×C₇₇	Direct product of C₇₇ and S₃	231	2	S3xC77	462,8
C₇×D₃₃	Direct product of C₇ and D₃₃	231	2	C7xD33	462,9
C₁₁×D₂₁	Direct product of C₁₁ and D₂₁	231	2	C11xD21	462,10

Groups of order 464

		d	ρ	Label	ID
C₂₉⋊₂C₁₆	The semidirect product of C₂₉ and C₁₆ acting via C₁₆/C₈=C₂	464	2	C29:2C16	464,1
C₈×D₂₉	Direct product of C₈ and D₂₉	232	2	C8xD29	464,4
C₈⋊D₂₉	3^rd semidirect product of C₈ and D₂₉ acting via D₂₉/C₂₉=C₂	232	2	C8:D29	464,5
C₂₃₂⋊C₂	2^nd semidirect product of C₂₃₂ and C₂ acting faithfully	232	2	C232:C2	464,6
C₄.Dic₂₉	The non-split extension by C₄ of Dic₂₉ acting via Dic₂₉/C₅₈=C₂	232	2	C4.Dic29	464,10
M₄(2)×C₂₉	Direct product of C₂₉ and M₄(2)	232	2	M4(2)xC29	464,24
D₈×C₂₉	Direct product of C₂₉ and D₈	232	2	D8xC29	464,25
SD₁₆×C₂₉	Direct product of C₂₉ and SD₁₆	232	2	SD16xC29	464,26
Q₁₆×C₂₉	Direct product of C₂₉ and Q₁₆	464	2	Q16xC29	464,27
D₁₁₆⋊₅C₂	The semidirect product of D₁₁₆ and C₂ acting through Inn(D₁₁₆)	232	2	D116:5C2	464,38
C₄○D₄×C₂₉	Direct product of C₂₉ and C₄○D₄	232	2	C4oD4xC29	464,48

Groups of order 468

		d	ρ	Label	ID
C₁₃×Dic₉	Direct product of C₁₃ and Dic₉	468	2	C13xDic9	468,3
C₉×Dic₁₃	Direct product of C₉ and Dic₁₃	468	2	C9xDic13	468,4
C₁₈×D₁₃	Direct product of C₁₈ and D₁₃	234	2	C18xD13	468,15
D₉×C₂₆	Direct product of C₂₆ and D₉	234	2	D9xC26	468,16
Dic₃×C₃₉	Direct product of C₃₉ and Dic₃	156	2	Dic3xC39	468,24
C₃×Dic₃₉	Direct product of C₃ and Dic₃₉	156	2	C3xDic39	468,25
S₃×C₇₈	Direct product of C₇₈ and S₃	156	2	S3xC78	468,51
C₆×D₃₉	Direct product of C₆ and D₃₉	156	2	C6xD39	468,52

Groups of order 470

		d	ρ	Label	ID
D₅×C₄₇	Direct product of C₄₇ and D₅	235	2	D5xC47	470,1
C₅×D₄₇	Direct product of C₅ and D₄₇	235	2	C5xD47	470,2

Groups of order 472

		d	ρ	Label	ID
C₅₉⋊C₈	The semidirect product of C₅₉ and C₈ acting via C₈/C₄=C₂	472	2	C59:C8	472,1
C₄×D₅₉	Direct product of C₄ and D₅₉	236	2	C4xD59	472,4
C₅₉⋊D₄	The semidirect product of C₅₉ and D₄ acting via D₄/C₂²=C₂	236	2	C59:D4	472,7
D₄×C₅₉	Direct product of C₅₉ and D₄	236	2	D4xC59	472,9
Q₈×C₅₉	Direct product of C₅₉ and Q₈	472	2	Q8xC59	472,10

Groups of order 474

		d	ρ	Label	ID
S₃×C₇₉	Direct product of C₇₉ and S₃	237	2	S3xC79	474,3
C₃×D₇₉	Direct product of C₃ and D₇₉	237	2	C3xD79	474,4

Groups of order 476

		d	ρ	Label	ID
C₁₇×Dic₇	Direct product of C₁₇ and Dic₇	476	2	C17xDic7	476,1
C₇×Dic₁₇	Direct product of C₇ and Dic₁₇	476	2	C7xDic17	476,2
C₁₄×D₁₇	Direct product of C₁₄ and D₁₇	238	2	C14xD17	476,8
D₇×C₃₄	Direct product of C₃₄ and D₇	238	2	D7xC34	476,9

Groups of order 480

		d	ρ	Label	ID
C₅×C₃⋊C₃₂	Direct product of C₅ and C₃⋊C₃₂	480	2	C5xC3:C32	480,1
C₃×C₅⋊₂C₃₂	Direct product of C₃ and C₅⋊₂C₃₂	480	2	C3xC5:2C32	480,2
C₁₅⋊₃C₃₂	1^st semidirect product of C₁₅ and C₃₂ acting via C₃₂/C₁₆=C₂	480	2	C15:3C32	480,3
D₅×C₄₈	Direct product of C₄₈ and D₅	240	2	D5xC48	480,75
C₃×C₈₀⋊C₂	Direct product of C₃ and C₈₀⋊C₂	240	2	C3xC80:C2	480,76
C₃×D₈₀	Direct product of C₃ and D₈₀	240	2	C3xD80	480,77
C₃×C₁₆⋊D₅	Direct product of C₃ and C₁₆⋊D₅	240	2	C3xC16:D5	480,78
C₃×Dic₄₀	Direct product of C₃ and Dic₄₀	480	2	C3xDic40	480,79
C₃×D₂₀⋊₄C₄	Direct product of C₃ and D₂₀⋊₄C₄	120	2	C3xD20:4C4	480,83
C₃×C₂₀.₄C₈	Direct product of C₃ and C₂₀.₄C₈	240	2	C3xC20.4C8	480,90
C₃×C₄₀.₆C₄	Direct product of C₃ and C₄₀.₆C₄	240	2	C3xC40.6C4	480,97
S₃×C₈₀	Direct product of C₈₀ and S₃	240	2	S3xC80	480,116
C₅×D₆.C₈	Direct product of C₅ and D₆.C₈	240	2	C5xD6.C8	480,117
C₅×D₄₈	Direct product of C₅ and D₄₈	240	2	C5xD48	480,118
C₅×C₄₈⋊C₂	Direct product of C₅ and C₄₈⋊C₂	240	2	C5xC48:C2	480,119
C₅×Dic₂₄	Direct product of C₅ and Dic₂₄	480	2	C5xDic24	480,120
C₅×C₄²⋊₄S₃	Direct product of C₅ and C₄²⋊₄S₃	120	2	C5xC4^2:4S3	480,124
C₅×C₁₂.C₈	Direct product of C₅ and C₁₂.C₈	240	2	C5xC12.C8	480,131
C₅×C₂₄.C₄	Direct product of C₅ and C₂₄.C₄	240	2	C5xC24.C4	480,138
C₁₆×D₁₅	Direct product of C₁₆ and D₁₅	240	2	C16xD15	480,157
C₈₀⋊S₃	5^th semidirect product of C₈₀ and S₃ acting via S₃/C₃=C₂	240	2	C80:S3	480,158
C₄₈⋊D₅	2^nd semidirect product of C₄₈ and D₅ acting via D₅/C₅=C₂	240	2	C48:D5	480,160
D₆₀⋊₇C₄	1^st semidirect product of D₆₀ and C₄ acting via C₄/C₂=C₂	120	2	D60:7C4	480,165
C₆₀.₇C₈	1^st non-split extension by C₆₀ of C₈ acting via C₈/C₄=C₂	240	2	C60.7C8	480,172
C₄.₁₈D₆₀	3^rd central extension by C₄ of D₆₀	240	2	C4.18D60	480,179
C₁₅×C₄≀C₂	Direct product of C₁₅ and C₄≀C₂	120	2	C15xC4wrC2	480,207
C₁₅×C₈.C₄	Direct product of C₁₅ and C₈.C₄	240	2	C15xC8.C4	480,211
C₁₅×M₅(2)	Direct product of C₁₅ and M₅(2)	240	2	C15xM5(2)	480,213
C₁₅×D₁₆	Direct product of C₁₅ and D₁₆	240	2	C15xD16	480,214
C₁₅×SD₃₂	Direct product of C₁₅ and SD₃₂	240	2	C15xSD32	480,215
C₁₅×Q₃₂	Direct product of C₁₅ and Q₃₂	480	2	C15xQ32	480,216
C₈.A₅	The central extension by C₈ of A₅	48	2	C8.A5	480,221
C₅×U₂(𝔽₃)	Direct product of C₅ and U₂(𝔽₃)	120	2	C5xU(2,3)	480,257
C₅×C₈.A₄	Direct product of C₅ and C₈.A₄	160	2	C5xC8.A4	480,660
C₃×D₂₀.₃C₄	Direct product of C₃ and D₂₀.₃C₄	240	2	C3xD20.3C4	480,694
C₃×D₄₀⋊₇C₂	Direct product of C₃ and D₄₀⋊₇C₂	240	2	C3xD40:7C2	480,697
C₅×C₈○D₁₂	Direct product of C₅ and C₈○D₁₂	240	2	C5xC8oD12	480,780
C₅×C₄○D₂₄	Direct product of C₅ and C₄○D₂₄	240	2	C5xC4oD24	480,783
D₆₀.₆C₄	The non-split extension by D₆₀ of C₄ acting through Inn(D₆₀)	240	2	D60.6C4	480,866
C₄₀.₆₉D₆	5^th non-split extension by C₄₀ of D₆ acting via D₆/C₆=C₂	240	2	C40.69D6	480,869
C₁₅×C₈○D₄	Direct product of C₁₅ and C₈○D₄	240	2	C15xC8oD4	480,936
C₁₅×C₄○D₈	Direct product of C₁₅ and C₄○D₈	240	2	C15xC4oD8	480,940
C₅×C₄.₆S₄	Direct product of C₅ and C₄.₆S₄	80	2	C5xC4.6S4	480,1020

Groups of order 484

		d	ρ	Label	ID
C₁₁×Dic₁₁	Direct product of C₁₁ and Dic₁₁	44	2	C11xDic11	484,5
D₁₁×C₂₂	Direct product of C₂₂ and D₁₁	44	2	D11xC22	484,10

Groups of order 486

		d	ρ	Label	ID
C₉×D₂₇	Direct product of C₉ and D₂₇	54	2	C9xD27	486,13
D₉×C₂₇	Direct product of C₂₇ and D₉	54	2	D9xC27	486,14
C₃×D₈₁	Direct product of C₃ and D₈₁	162	2	C3xD81	486,32
S₃×C₈₁	Direct product of C₈₁ and S₃	162	2	S3xC81	486,33

Groups of order 488

		d	ρ	Label	ID
C₆₁⋊₂C₈	The semidirect product of C₆₁ and C₈ acting via C₈/C₄=C₂	488	2	C61:2C8	488,1
C₄×D₆₁	Direct product of C₄ and D₆₁	244	2	C4xD61	488,5
C₆₁⋊D₄	The semidirect product of C₆₁ and D₄ acting via D₄/C₂²=C₂	244	2	C61:D4	488,8
D₄×C₆₁	Direct product of C₆₁ and D₄	244	2	D4xC61	488,10
Q₈×C₆₁	Direct product of C₆₁ and Q₈	488	2	Q8xC61	488,11

Groups of order 490

		d	ρ	Label	ID
D₅×C₄₉	Direct product of C₄₉ and D₅	245	2	D5xC49	490,1
C₅×D₄₉	Direct product of C₅ and D₄₉	245	2	C5xD49	490,2
D₇×C₃₅	Direct product of C₃₅ and D₇	70	2	D7xC35	490,5
C₇×D₃₅	Direct product of C₇ and D₃₅	70	2	C7xD35	490,8

Groups of order 492

		d	ρ	Label	ID
Dic₃×C₄₁	Direct product of C₄₁ and Dic₃	492	2	Dic3xC41	492,1
C₃×Dic₄₁	Direct product of C₃ and Dic₄₁	492	2	C3xDic41	492,2
C₆×D₄₁	Direct product of C₆ and D₄₁	246	2	C6xD41	492,9
S₃×C₈₂	Direct product of C₈₂ and S₃	246	2	S3xC82	492,10

Groups of order 494

		d	ρ	Label	ID
C₁₉×D₁₃	Direct product of C₁₉ and D₁₃	247	2	C19xD13	494,1
C₁₃×D₁₉	Direct product of C₁₃ and D₁₉	247	2	C13xD19	494,2

Groups of order 496

		d	ρ	Label	ID
C₃₁⋊C₁₆	The semidirect product of C₃₁ and C₁₆ acting via C₁₆/C₈=C₂	496	2	C31:C16	496,1
C₈×D₃₁	Direct product of C₈ and D₃₁	248	2	C8xD31	496,3
C₈⋊D₃₁	3^rd semidirect product of C₈ and D₃₁ acting via D₃₁/C₃₁=C₂	248	2	C8:D31	496,4
C₂₄₈⋊C₂	2^nd semidirect product of C₂₄₈ and C₂ acting faithfully	248	2	C248:C2	496,5
C₄.Dic₃₁	The non-split extension by C₄ of Dic₃₁ acting via Dic₃₁/C₆₂=C₂	248	2	C4.Dic31	496,9
M₄(2)×C₃₁	Direct product of C₃₁ and M₄(2)	248	2	M4(2)xC31	496,23
D₈×C₃₁	Direct product of C₃₁ and D₈	248	2	D8xC31	496,24
SD₁₆×C₃₁	Direct product of C₃₁ and SD₁₆	248	2	SD16xC31	496,25
Q₁₆×C₃₁	Direct product of C₃₁ and Q₁₆	496	2	Q16xC31	496,26
D₁₂₄⋊₅C₂	The semidirect product of D₁₂₄ and C₂ acting through Inn(D₁₂₄)	248	2	D124:5C2	496,30
C₄○D₄×C₃₁	Direct product of C₃₁ and C₄○D₄	248	2	C4oD4xC31	496,40

Groups of order 498

		d	ρ	Label	ID
S₃×C₈₃	Direct product of C₈₃ and S₃	249	2	S3xC83	498,1
C₃×D₈₃	Direct product of C₃ and D₈₃	249	2	C3xD83	498,2

Groups of order 500

		d	ρ	Label	ID
C₅×Dic₂₅	Direct product of C₅ and Dic₂₅	100	2	C5xDic25	500,6
Dic₅×C₂₅	Direct product of C₂₅ and Dic₅	100	2	Dic5xC25	500,7
C₁₀×D₂₅	Direct product of C₁₀ and D₂₅	100	2	C10xD25	500,28
D₅×C₅₀	Direct product of C₅₀ and D₅	100	2	D5xC50	500,29

Orthogonal of dimension 3 (ρ=3+)

Groups of order 12

		d	ρ	Label	ID
A₄	Alternating group on 4 letters; = PSL₂(𝔽₃) = L₂(3) = tetrahedron rotations	4	3+	A4	12,3

Groups of order 24

		d	ρ	Label	ID
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	4	3+	S4	24,12
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	6	3+	C2xA4	24,13

Groups of order 48

		d	ρ	Label	ID
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	6	3+	C2xS4	48,48

Groups of order 60

		d	ρ	Label	ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	5	3+	A5	60,5

Groups of order 120

		d	ρ	Label	ID
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35

Complex of dimension 3 (ρ=3)

Groups of order 21

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

Groups of order 27

		d	ρ	Label	ID
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

Groups of order 36

		d	ρ	Label	ID
C₃.A₄	The central extension by C₃ of A₄	18	3	C3.A4	36,3
C₃×A₄	Direct product of C₃ and A₄	12	3	C3xA4	36,11

Groups of order 39

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

Groups of order 42

		d	ρ	Label	ID
C₂×C₇⋊C₃	Direct product of C₂ and C₇⋊C₃	14	3	C2xC7:C3	42,2

Groups of order 48

		d	ρ	Label	ID
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	12	3	C4^2:C3	48,3
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	12	3	A4:C4	48,30
C₄×A₄	Direct product of C₄ and A₄	12	3	C4xA4	48,31

Groups of order 54

		d	ρ	Label	ID
He₃⋊C₂	2^nd semidirect product of He₃ and C₂ acting faithfully; = Aut(3_-¹⁺²)	9	3	He3:C2	54,8
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 57

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

Groups of order 60

		d	ρ	Label	ID
C₅×A₄	Direct product of C₅ and A₄	20	3	C5xA4	60,9

Groups of order 63

		d	ρ	Label	ID
C₇⋊C₉	The semidirect product of C₇ and C₉ acting via C₉/C₃=C₃	63	3	C7:C9	63,1
C₃×C₇⋊C₃	Direct product of C₃ and C₇⋊C₃	21	3	C3xC7:C3	63,3

Groups of order 72

		d	ρ	Label	ID
C₂×C₃.A₄	Direct product of C₂ and C₃.A₄	18	3	C2xC3.A4	72,16
C₃×S₄	Direct product of C₃ and S₄	12	3	C3xS4	72,42
C₆×A₄	Direct product of C₆ and A₄	18	3	C6xA4	72,47

Groups of order 75

		d	ρ	Label	ID
C₅²⋊C₃	The semidirect product of C₅² and C₃ acting faithfully	15	3	C5^2:C3	75,2

Groups of order 78

		d	ρ	Label	ID
C₂×C₁₃⋊C₃	Direct product of C₂ and C₁₃⋊C₃	26	3	C2xC13:C3	78,2

Groups of order 81

		d	ρ	Label	ID
C₂₇⋊C₃	The semidirect product of C₂₇ and C₃ acting faithfully	27	3	C27:C3	81,6
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	9	3	C3wrC3	81,7
He₃.C₃	The non-split extension by He₃ of C₃ acting faithfully	27	3	He3.C3	81,8
He₃⋊C₃	2^nd semidirect product of He₃ and C₃ acting faithfully	27	3	He3:C3	81,9
C₃.He₃	4^th central stem extension by C₃ of He₃	27	3	C3.He3	81,10
C₉○He₃	Central product of C₉ and He₃	27	3	C9oHe3	81,14

Groups of order 84

		d	ρ	Label	ID
C₄×C₇⋊C₃	Direct product of C₄ and C₇⋊C₃	28	3	C4xC7:C3	84,2
C₇×A₄	Direct product of C₇ and A₄	28	3	C7xA4	84,10
C₇⋊A₄	The semidirect product of C₇ and A₄ acting via A₄/C₂²=C₃	28	3	C7:A4	84,11

Groups of order 93

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

Groups of order 96

		d	ρ	Label	ID
C₄²⋊S₃	The semidirect product of C₄² and S₃ acting faithfully	12	3	C4^2:S3	96,64
A₄⋊C₈	The semidirect product of A₄ and C₈ acting via C₈/C₄=C₂	24	3	A4:C8	96,65
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	12	3	C2xC4^2:C3	96,68
C₈×A₄	Direct product of C₈ and A₄	24	3	C8xA4	96,73
C₄×S₄	Direct product of C₄ and S₄	12	3	C4xS4	96,186

Groups of order 105

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

Groups of order 108

		d	ρ	Label	ID
C₉.A₄	The central extension by C₉ of A₄	54	3	C9.A4	108,3
He₃⋊₃C₄	2^nd semidirect product of He₃ and C₄ acting via C₄/C₂=C₂	36	3	He3:3C4	108,11
C₄×He₃	Direct product of C₄ and He₃	36	3	C4xHe3	108,13
C₄×3_-¹⁺²	Direct product of C₄ and 3_-¹⁺²	36	3	C4xES-(3,1)	108,14
He₃⋊C₄	The semidirect product of He₃ and C₄ acting faithfully	18	3	He3:C4	108,15
C₉×A₄	Direct product of C₉ and A₄	36	3	C9xA4	108,18
C₉⋊A₄	The semidirect product of C₉ and A₄ acting via A₄/C₂²=C₃	36	3	C9:A4	108,19
C₃².A₄	The non-split extension by C₃² of A₄ acting via A₄/C₂²=C₃	18	3	C3^2.A4	108,21
C₃²⋊A₄	The semidirect product of C₃² and A₄ acting via A₄/C₂²=C₃	18	3	C3^2:A4	108,22
C₂×He₃⋊C₂	Direct product of C₂ and He₃⋊C₂	18	3	C2xHe3:C2	108,28

Groups of order 111

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

Groups of order 114

		d	ρ	Label	ID
C₂×C₁₉⋊C₃	Direct product of C₂ and C₁₉⋊C₃	38	3	C2xC19:C3	114,2

Groups of order 117

		d	ρ	Label	ID
C₁₃⋊C₉	The semidirect product of C₁₃ and C₉ acting via C₉/C₃=C₃	117	3	C13:C9	117,1
C₃×C₁₃⋊C₃	Direct product of C₃ and C₁₃⋊C₃	39	3	C3xC13:C3	117,3

Groups of order 120

		d	ρ	Label	ID
C₅×S₄	Direct product of C₅ and S₄	20	3	C5xS4	120,37
C₁₀×A₄	Direct product of C₁₀ and A₄	30	3	C10xA4	120,43

Groups of order 126

		d	ρ	Label	ID
C₂×C₇⋊C₉	Direct product of C₂ and C₇⋊C₉	126	3	C2xC7:C9	126,2
C₆×C₇⋊C₃	Direct product of C₆ and C₇⋊C₃	42	3	C6xC7:C3	126,10

Groups of order 129

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

Groups of order 132

		d	ρ	Label	ID
C₁₁×A₄	Direct product of C₁₁ and A₄	44	3	C11xA4	132,6

Groups of order 135

		d	ρ	Label	ID
C₅×He₃	Direct product of C₅ and He₃	45	3	C5xHe3	135,3
C₅×3_-¹⁺²	Direct product of C₅ and 3_-¹⁺²	45	3	C5xES-(3,1)	135,4

Groups of order 144

		d	ρ	Label	ID
C₄²⋊C₉	The semidirect product of C₄² and C₉ acting via C₉/C₃=C₃	36	3	C4^2:C9	144,3
C₄×C₃.A₄	Direct product of C₄ and C₃.A₄	36	3	C4xC3.A4	144,34
C₃×C₄²⋊C₃	Direct product of C₃ and C₄²⋊C₃	36	3	C3xC4^2:C3	144,68
C₃×A₄⋊C₄	Direct product of C₃ and A₄⋊C₄	36	3	C3xA4:C4	144,123
C₁₂×A₄	Direct product of C₁₂ and A₄	36	3	C12xA4	144,155
C₆×S₄	Direct product of C₆ and S₄	18	3	C6xS4	144,188

Groups of order 147

		d	ρ	Label	ID
C₄₉⋊C₃	The semidirect product of C₄₉ and C₃ acting faithfully	49	3	C49:C3	147,1
C₇×C₇⋊C₃	Direct product of C₇ and C₇⋊C₃	21	3	C7xC7:C3	147,3
C₇²⋊₃C₃	3^rd semidirect product of C₇² and C₃ acting faithfully	21	3	C7^2:3C3	147,5

Groups of order 150

		d	ρ	Label	ID
C₅²⋊S₃	The semidirect product of C₅² and S₃ acting faithfully	15	3	C5^2:S3	150,5
C₂×C₅²⋊C₃	Direct product of C₂ and C₅²⋊C₃	30	3	C2xC5^2:C3	150,7

Groups of order 156

		d	ρ	Label	ID
C₄×C₁₃⋊C₃	Direct product of C₄ and C₁₃⋊C₃	52	3	C4xC13:C3	156,2
A₄×C₁₃	Direct product of C₁₃ and A₄	52	3	A4xC13	156,13
C₁₃⋊A₄	The semidirect product of C₁₃ and A₄ acting via A₄/C₂²=C₃	52	3	C13:A4	156,14

Groups of order 162

		d	ρ	Label	ID
C₃≀S₃	Wreath product of C₃ by S₃	9	3	C3wrS3	162,10
He₃.C₆	1^st non-split extension by He₃ of C₆ acting faithfully	27	3	He3.C6	162,12
He₃.₂C₆	2^nd non-split extension by He₃ of C₆ acting faithfully	27	3	He3.2C6	162,14
C₂×C₂₇⋊C₃	Direct product of C₂ and C₂₇⋊C₃	54	3	C2xC27:C3	162,27
C₂×C₃≀C₃	Direct product of C₂ and C₃≀C₃	18	3	C2xC3wrC3	162,28
C₂×He₃.C₃	Direct product of C₂ and He₃.C₃	54	3	C2xHe3.C3	162,29
C₂×He₃⋊C₃	Direct product of C₂ and He₃⋊C₃	54	3	C2xHe3:C3	162,30
C₂×C₃.He₃	Direct product of C₂ and C₃.He₃	54	3	C2xC3.He3	162,31
He₃.₄C₆	The non-split extension by He₃ of C₆ acting via C₆/C₃=C₂	27	3	He3.4C6	162,44
C₂×C₉○He₃	Direct product of C₂ and C₉○He₃	54	3	C2xC9oHe3	162,50

Groups of order 168

		d	ρ	Label	ID
C₈×C₇⋊C₃	Direct product of C₈ and C₇⋊C₃	56	3	C8xC7:C3	168,2
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	7	3	GL(3,2)	168,42
C₇×S₄	Direct product of C₇ and S₄	28	3	C7xS4	168,45
A₄×C₁₄	Direct product of C₁₄ and A₄	42	3	A4xC14	168,52
C₂×C₇⋊A₄	Direct product of C₂ and C₇⋊A₄	42	3	C2xC7:A4	168,53

Groups of order 171

		d	ρ	Label	ID
C₁₉⋊₂C₉	The semidirect product of C₁₉ and C₉ acting via C₉/C₃=C₃	171	3	C19:2C9	171,1
C₃×C₁₉⋊C₃	Direct product of C₃ and C₁₉⋊C₃	57	3	C3xC19:C3	171,4

Groups of order 180

		d	ρ	Label	ID
C₅×C₃.A₄	Direct product of C₅ and C₃.A₄	90	3	C5xC3.A4	180,8
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	15	3	C3xA5	180,19
A₄×C₁₅	Direct product of C₁₅ and A₄	60	3	A4xC15	180,31

Groups of order 183

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

Groups of order 186

		d	ρ	Label	ID
C₂×C₃₁⋊C₃	Direct product of C₂ and C₃₁⋊C₃	62	3	C2xC31:C3	186,2

Groups of order 189

		d	ρ	Label	ID
C₇⋊C₂₇	The semidirect product of C₇ and C₂₇ acting via C₂₇/C₉=C₃	189	3	C7:C27	189,1
C₉×C₇⋊C₃	Direct product of C₉ and C₇⋊C₃	63	3	C9xC7:C3	189,3
C₆₃⋊C₃	2^nd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:C3	189,4
C₆₃⋊₃C₃	3^rd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:3C3	189,5
C₂₁.C₃²	5^th non-split extension by C₂₁ of C₃² acting via C₃²/C₃=C₃	63	3	C21.C3^2	189,7
C₇⋊He₃	The semidirect product of C₇ and He₃ acting via He₃/C₃²=C₃	63	3	C7:He3	189,8
C₇×He₃	Direct product of C₇ and He₃	63	3	C7xHe3	189,10
C₇×3_-¹⁺²	Direct product of C₇ and 3_-¹⁺²	63	3	C7xES-(3,1)	189,11

Groups of order 192

		d	ρ	Label	ID
C₈²⋊C₃	The semidirect product of C₈² and C₃ acting faithfully	24	3	C8^2:C3	192,3
C₂³.₉S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	12	3	C2^3.9S4	192,182
A₄⋊C₁₆	The semidirect product of A₄ and C₁₆ acting via C₁₆/C₈=C₂	48	3	A4:C16	192,186
C₄×C₄²⋊C₃	Direct product of C₄ and C₄²⋊C₃	12	3	C4xC4^2:C3	192,188
A₄×C₁₆	Direct product of C₁₆ and A₄	48	3	A4xC16	192,203
C₂×C₄²⋊S₃	Direct product of C₂ and C₄²⋊S₃	12	3	C2xC4^2:S3	192,944
C₈×S₄	Direct product of C₈ and S₄	24	3	C8xS4	192,958

Groups of order 195

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

Groups of order 201

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

Groups of order 204

		d	ρ	Label	ID
A₄×C₁₇	Direct product of C₁₇ and A₄	68	3	A4xC17	204,8

Groups of order 210

		d	ρ	Label	ID
C₁₀×C₇⋊C₃	Direct product of C₁₀ and C₇⋊C₃	70	3	C10xC7:C3	210,4

Groups of order 216

		d	ρ	Label	ID
He₃⋊₄C₈	2^nd semidirect product of He₃ and C₈ acting via C₈/C₄=C₂	72	3	He3:4C8	216,17
C₈×He₃	Direct product of C₈ and He₃	72	3	C8xHe3	216,19
C₈×3_-¹⁺²	Direct product of C₈ and 3_-¹⁺²	72	3	C8xES-(3,1)	216,20
C₂×C₉.A₄	Direct product of C₂ and C₉.A₄	54	3	C2xC9.A4	216,22
He₃⋊₂C₈	The semidirect product of He₃ and C₈ acting via C₈/C₂=C₄	72	3	He3:2C8	216,25
C₄×He₃⋊C₂	Direct product of C₄ and He₃⋊C₂	36	3	C4xHe3:C2	216,67
SU₃(𝔽₂)	Special unitary group on 𝔽₂³; = He₃ ⋊Q₈	27	3	SU(3,2)	216,88
C₉×S₄	Direct product of C₉ and S₄	36	3	C9xS4	216,89
C₃²⋊S₄	2^nd semidirect product of C₃² and S₄ acting via S₄/C₂²=S₃	18	3	C3^2:S4	216,95
C₂×He₃⋊C₄	Direct product of C₂ and He₃⋊C₄	36	3	C2xHe3:C4	216,100
A₄×C₁₈	Direct product of C₁₈ and A₄	54	3	A4xC18	216,103
C₂×C₉⋊A₄	Direct product of C₂ and C₉⋊A₄	54	3	C2xC9:A4	216,104
C₂×C₃².A₄	Direct product of C₂ and C₃².A₄	18	3	C2xC3^2.A4	216,106
C₂×C₃²⋊A₄	Direct product of C₂ and C₃²⋊A₄	18	3	C2xC3^2:A4	216,107

Groups of order 219

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

Groups of order 222

		d	ρ	Label	ID
C₂×C₃₇⋊C₃	Direct product of C₂ and C₃₇⋊C₃	74	3	C2xC37:C3	222,2

Groups of order 225

		d	ρ	Label	ID
C₅²⋊C₉	The semidirect product of C₅² and C₉ acting via C₉/C₃=C₃	45	3	C5^2:C9	225,3
C₃×C₅²⋊C₃	Direct product of C₃ and C₅²⋊C₃	45	3	C3xC5^2:C3	225,5

Groups of order 228

		d	ρ	Label	ID
C₄×C₁₉⋊C₃	Direct product of C₄ and C₁₉⋊C₃	76	3	C4xC19:C3	228,2
A₄×C₁₉	Direct product of C₁₉ and A₄	76	3	A4xC19	228,10
C₁₉⋊A₄	The semidirect product of C₁₉ and A₄ acting via A₄/C₂²=C₃	76	3	C19:A4	228,11

Groups of order 231

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

Groups of order 234

		d	ρ	Label	ID
C₂×C₁₃⋊C₉	Direct product of C₂ and C₁₃⋊C₉	234	3	C2xC13:C9	234,2
C₆×C₁₃⋊C₃	Direct product of C₆ and C₁₃⋊C₃	78	3	C6xC13:C3	234,10

Groups of order 237

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

Groups of order 240

		d	ρ	Label	ID
C₅×C₄²⋊C₃	Direct product of C₅ and C₄²⋊C₃	60	3	C5xC4^2:C3	240,32
C₄×A₅	Direct product of C₄ and A₅	20	3	C4xA5	240,92
C₅×A₄⋊C₄	Direct product of C₅ and A₄⋊C₄	60	3	C5xA4:C4	240,104
A₄×C₂₀	Direct product of C₂₀ and A₄	60	3	A4xC20	240,152
C₁₀×S₄	Direct product of C₁₀ and S₄	30	3	C10xS4	240,196

Groups of order 243

		d	ρ	Label	ID
C₉.₄He₃	2^nd central extension by C₉ of He₃	27	3	C9.4He3	243,16
C₉.₅He₃	3^rd central extension by C₉ of He₃	81	3	C9.5He3	243,19
C₉.₆He₃	4^th central extension by C₉ of He₃	81	3	C9.6He3	243,20
C₈₁⋊C₃	The semidirect product of C₈₁ and C₃ acting faithfully	81	3	C81:C3	243,24
C₉²⋊C₃	1^st semidirect product of C₉² and C₃ acting faithfully	27	3	C9^2:C3	243,25
C₉²⋊₂C₃	2^nd semidirect product of C₉² and C₃ acting faithfully	27	3	C9^2:2C3	243,26
C₉².C₃	2^nd non-split extension by C₉² of C₃ acting faithfully	27	3	C9^2.C3	243,27
C₂₇○He₃	Central product of C₂₇ and He₃	81	3	C27oHe3	243,50
C₉.He₃	1^st non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	27	3	C9.He3	243,55

Groups of order 252

		d	ρ	Label	ID
C₄×C₇⋊C₉	Direct product of C₄ and C₇⋊C₉	252	3	C4xC7:C9	252,2
C₇×C₃.A₄	Direct product of C₇ and C₃.A₄	126	3	C7xC3.A4	252,10
C₂₁.A₄	The non-split extension by C₂₁ of A₄ acting via A₄/C₂²=C₃	126	3	C21.A4	252,11
C₁₂×C₇⋊C₃	Direct product of C₁₂ and C₇⋊C₃	84	3	C12xC7:C3	252,19
A₄×C₂₁	Direct product of C₂₁ and A₄	84	3	A4xC21	252,39
C₃×C₇⋊A₄	Direct product of C₃ and C₇⋊A₄	84	3	C3xC7:A4	252,40

Groups of order 258

		d	ρ	Label	ID
C₂×C₄₃⋊C₃	Direct product of C₂ and C₄₃⋊C₃	86	3	C2xC43:C3	258,2

Groups of order 264

		d	ρ	Label	ID
C₁₁×S₄	Direct product of C₁₁ and S₄	44	3	C11xS4	264,31
A₄×C₂₂	Direct product of C₂₂ and A₄	66	3	A4xC22	264,35

Groups of order 270

		d	ρ	Label	ID
C₅×He₃⋊C₂	Direct product of C₅ and He₃⋊C₂	45	3	C5xHe3:C2	270,17
C₁₀×He₃	Direct product of C₁₀ and He₃	90	3	C10xHe3	270,21
C₁₀×3_-¹⁺²	Direct product of C₁₀ and 3_-¹⁺²	90	3	C10xES-(3,1)	270,22

Groups of order 273

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

Groups of order 276

		d	ρ	Label	ID
A₄×C₂₃	Direct product of C₂₃ and A₄	92	3	A4xC23	276,6

Groups of order 279

		d	ρ	Label	ID
C₃₁⋊C₉	The semidirect product of C₃₁ and C₉ acting via C₉/C₃=C₃	279	3	C31:C9	279,1
C₃×C₃₁⋊C₃	Direct product of C₃ and C₃₁⋊C₃	93	3	C3xC31:C3	279,3

Groups of order 285

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

Groups of order 288

		d	ρ	Label	ID
C₂×C₄²⋊C₉	Direct product of C₂ and C₄²⋊C₉	36	3	C2xC4^2:C9	288,71
C₈×C₃.A₄	Direct product of C₈ and C₃.A₄	72	3	C8xC3.A4	288,76
C₃×C₄²⋊S₃	Direct product of C₃ and C₄²⋊S₃	36	3	C3xC4^2:S3	288,397
C₃×A₄⋊C₈	Direct product of C₃ and A₄⋊C₈	72	3	C3xA4:C8	288,398
C₆×C₄²⋊C₃	Direct product of C₆ and C₄²⋊C₃	36	3	C6xC4^2:C3	288,632
A₄×C₂₄	Direct product of C₂₄ and A₄	72	3	A4xC24	288,637
C₁₂×S₄	Direct product of C₁₂ and S₄	36	3	C12xS4	288,897

Groups of order 291

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

Groups of order 294

		d	ρ	Label	ID
C₂×C₄₉⋊C₃	Direct product of C₂ and C₄₉⋊C₃	98	3	C2xC49:C3	294,2
C₇²⋊S₃	The semidirect product of C₇² and S₃ acting faithfully	14	3	C7^2:S3	294,7
C₁₄×C₇⋊C₃	Direct product of C₁₄ and C₇⋊C₃	42	3	C14xC7:C3	294,15
C₂×C₇²⋊₃C₃	Direct product of C₂ and C₇²⋊₃C₃	42	3	C2xC7^2:3C3	294,17

Groups of order 297

		d	ρ	Label	ID
C₁₁×He₃	Direct product of C₁₁ and He₃	99	3	C11xHe3	297,3
C₁₁×3_-¹⁺²	Direct product of C₁₁ and 3_-¹⁺²	99	3	C11xES-(3,1)	297,4

Groups of order 300

		d	ρ	Label	ID
A₄×C₂₅	Direct product of C₂₅ and A₄	100	3	A4xC25	300,8
C₅²⋊₂Dic₃	The semidirect product of C₅² and Dic₃ acting via Dic₃/C₂=S₃	60	3	C5^2:2Dic3	300,13
C₄×C₅²⋊C₃	Direct product of C₄ and C₅²⋊C₃	60	3	C4xC5^2:C3	300,15
C₅×A₅	Direct product of C₅ and A₅; = U₂(𝔽₄)	25	3	C5xA5	300,22
C₂×C₅²⋊S₃	Direct product of C₂ and C₅²⋊S₃	30	3	C2xC5^2:S3	300,26
C₅²⋊A₄	The semidirect product of C₅² and A₄ acting via A₄/C₂²=C₃	30	3	C5^2:A4	300,43

Groups of order 309

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

Groups of order 312

		d	ρ	Label	ID
C₈×C₁₃⋊C₃	Direct product of C₈ and C₁₃⋊C₃	104	3	C8xC13:C3	312,2
C₁₃×S₄	Direct product of C₁₃ and S₄	52	3	C13xS4	312,47
A₄×C₂₆	Direct product of C₂₆ and A₄	78	3	A4xC26	312,56
C₂×C₁₃⋊A₄	Direct product of C₂ and C₁₃⋊A₄	78	3	C2xC13:A4	312,57

Groups of order 315

		d	ρ	Label	ID
C₅×C₇⋊C₉	Direct product of C₅ and C₇⋊C₉	315	3	C5xC7:C9	315,1
C₁₅×C₇⋊C₃	Direct product of C₁₅ and C₇⋊C₃	105	3	C15xC7:C3	315,3

Groups of order 324

		d	ρ	Label	ID
C₂₇.A₄	The central extension by C₂₇ of A₄	162	3	C27.A4	324,3
He₃⋊C₁₂	The semidirect product of He₃ and C₁₂ acting via C₁₂/C₂=C₆	36	3	He3:C12	324,13
He₃.C₁₂	1^st non-split extension by He₃ of C₁₂ acting via C₁₂/C₂=C₆	108	3	He3.C12	324,15
He₃.₂C₁₂	2^nd non-split extension by He₃ of C₁₂ acting via C₁₂/C₂=C₆	108	3	He3.2C12	324,17
C₄×C₂₇⋊C₃	Direct product of C₄ and C₂₇⋊C₃	108	3	C4xC27:C3	324,30
C₄×C₃≀C₃	Direct product of C₄ and C₃≀C₃	36	3	C4xC3wrC3	324,31
C₄×He₃.C₃	Direct product of C₄ and He₃.C₃	108	3	C4xHe3.C3	324,32
C₄×He₃⋊C₃	Direct product of C₄ and He₃⋊C₃	108	3	C4xHe3:C3	324,33
C₄×C₃.He₃	Direct product of C₄ and C₃.He₃	108	3	C4xC3.He3	324,34
A₄×C₂₇	Direct product of C₂₇ and A₄	108	3	A4xC27	324,42
C₂₇⋊A₄	The semidirect product of C₂₇ and A₄ acting via A₄/C₂²=C₃	108	3	C27:A4	324,43
C₆².C₉	2^nd non-split extension by C₆² of C₉ acting via C₉/C₃=C₃	54	3	C6^2.C9	324,45
C₆².₁₃C₃²	4^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.13C3^2	324,49
C₆².₁₄C₃²	5^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.14C3^2	324,50
C₆².₁₅C₃²	6^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.15C3^2	324,51
C₃³⋊₂A₄	1^st semidirect product of C₃³ and A₄ acting via A₄/C₂²=C₃	18	3	C3^3:2A4	324,60
C₂×C₃≀S₃	Direct product of C₂ and C₃≀S₃	18	3	C2xC3wrS3	324,68
C₂×He₃.C₆	Direct product of C₂ and He₃.C₆	54	3	C2xHe3.C6	324,70
C₂×He₃.₂C₆	Direct product of C₂ and He₃.₂C₆	54	3	C2xHe3.2C6	324,72
He₃.₅C₁₂	The non-split extension by He₃ of C₁₂ acting via C₁₂/C₆=C₂	108	3	He3.5C12	324,102
C₄×C₉○He₃	Direct product of C₄ and C₉○He₃	108	3	C4xC9oHe3	324,108
He₃.₃C₁₂	The non-split extension by He₃ of C₁₂ acting via C₁₂/C₃=C₄	54	3	He3.3C12	324,111
C₆².₂₅C₃²	16^th non-split extension by C₆² of C₃² acting via C₃²/C₃=C₃	54	3	C6^2.25C3^2	324,128
C₂×He₃.₄C₆	Direct product of C₂ and He₃.₄C₆	54	3	C2xHe3.4C6	324,148

Groups of order 327

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

Groups of order 333

		d	ρ	Label	ID
C₃₇⋊₂C₉	The semidirect product of C₃₇ and C₉ acting via C₉/C₃=C₃	333	3	C37:2C9	333,1
C₃×C₃₇⋊C₃	Direct product of C₃ and C₃₇⋊C₃	111	3	C3xC37:C3	333,4

Groups of order 336

		d	ρ	Label	ID
C₁₆×C₇⋊C₃	Direct product of C₁₆ and C₇⋊C₃	112	3	C16xC7:C3	336,2
C₇×C₄²⋊C₃	Direct product of C₇ and C₄²⋊C₃	84	3	C7xC4^2:C3	336,56
C₄²⋊(C₇⋊C₃)	The semidirect product of C₄² and C₇⋊C₃ acting via C₇⋊C₃/C₇=C₃	84	3	C4^2:(C7:C3)	336,57
C₇×A₄⋊C₄	Direct product of C₇ and A₄⋊C₄	84	3	C7xA4:C4	336,117
A₄×C₂₈	Direct product of C₂₈ and A₄	84	3	A4xC28	336,168
C₄×C₇⋊A₄	Direct product of C₄ and C₇⋊A₄	84	3	C4xC7:A4	336,171
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	14	3	C2xGL(3,2)	336,209
C₁₄×S₄	Direct product of C₁₄ and S₄	42	3	C14xS4	336,214

Groups of order 342

		d	ρ	Label	ID
C₂×C₁₉⋊₂C₉	Direct product of C₂ and C₁₉⋊₂C₉	342	3	C2xC19:2C9	342,2
C₆×C₁₉⋊C₃	Direct product of C₆ and C₁₉⋊C₃	114	3	C6xC19:C3	342,12

Groups of order 348

		d	ρ	Label	ID
A₄×C₂₉	Direct product of C₂₉ and A₄	116	3	A4xC29	348,8

Groups of order 351

		d	ρ	Label	ID
C₁₃⋊C₂₇	The semidirect product of C₁₃ and C₂₇ acting via C₂₇/C₉=C₃	351	3	C13:C27	351,1
C₉×C₁₃⋊C₃	Direct product of C₉ and C₁₃⋊C₃	117	3	C9xC13:C3	351,3
C₁₁₇⋊C₃	2^nd semidirect product of C₁₁₇ and C₃ acting faithfully	117	3	C117:C3	351,4
C₁₁₇⋊₃C₃	3^rd semidirect product of C₁₁₇ and C₃ acting faithfully	117	3	C117:3C3	351,5
C₃₉.C₃²	5^th non-split extension by C₃₉ of C₃² acting via C₃²/C₃=C₃	117	3	C39.C3^2	351,7
C₁₃⋊He₃	The semidirect product of C₁₃ and He₃ acting via He₃/C₃²=C₃	117	3	C13:He3	351,8
C₁₃×He₃	Direct product of C₁₃ and He₃	117	3	C13xHe3	351,10
C₁₃×3_-¹⁺²	Direct product of C₁₃ and 3_-¹⁺²	117	3	C13xES-(3,1)	351,11

Groups of order 357

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

Groups of order 360

		d	ρ	Label	ID
C₁₀×C₃.A₄	Direct product of C₁₀ and C₃.A₄	90	3	C10xC3.A4	360,46
C₆×A₅	Direct product of C₆ and A₅	30	3	C6xA5	360,122
C₁₅×S₄	Direct product of C₁₅ and S₄	60	3	C15xS4	360,138
A₄×C₃₀	Direct product of C₃₀ and A₄	90	3	A4xC30	360,156

Groups of order 363

		d	ρ	Label	ID
C₁₁²⋊C₃	The semidirect product of C₁₁² and C₃ acting faithfully	33	3	C11^2:C3	363,2

Groups of order 366

		d	ρ	Label	ID
C₂×C₆₁⋊C₃	Direct product of C₂ and C₆₁⋊C₃	122	3	C2xC61:C3	366,2

Groups of order 372

		d	ρ	Label	ID
C₄×C₃₁⋊C₃	Direct product of C₄ and C₃₁⋊C₃	124	3	C4xC31:C3	372,2
A₄×C₃₁	Direct product of C₃₁ and A₄	124	3	A4xC31	372,10
C₃₁⋊A₄	The semidirect product of C₃₁ and A₄ acting via A₄/C₂²=C₃	124	3	C31:A4	372,11

Groups of order 375

		d	ρ	Label	ID
C₅×C₅²⋊C₃	Direct product of C₅ and C₅²⋊C₃; = AΣL₁(𝔽₁₂₅)	15	3	C5xC5^2:C3	375,6

Groups of order 378

		d	ρ	Label	ID
C₂×C₇⋊C₂₇	Direct product of C₂ and C₇⋊C₂₇	378	3	C2xC7:C27	378,2
C₁₈×C₇⋊C₃	Direct product of C₁₈ and C₇⋊C₃	126	3	C18xC7:C3	378,23
C₂×C₆₃⋊C₃	Direct product of C₂ and C₆₃⋊C₃	126	3	C2xC63:C3	378,24
C₂×C₆₃⋊₃C₃	Direct product of C₂ and C₆₃⋊₃C₃	126	3	C2xC63:3C3	378,25
C₂×C₂₁.C₃²	Direct product of C₂ and C₂₁.C₃²	126	3	C2xC21.C3^2	378,27
C₂×C₇⋊He₃	Direct product of C₂ and C₇⋊He₃	126	3	C2xC7:He3	378,28
C₇×He₃⋊C₂	Direct product of C₇ and He₃⋊C₂	63	3	C7xHe3:C2	378,41
C₁₄×He₃	Direct product of C₁₄ and He₃	126	3	C14xHe3	378,45
C₁₄×3_-¹⁺²	Direct product of C₁₄ and 3_-¹⁺²	126	3	C14xES-(3,1)	378,46

Groups of order 381

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

Groups of order 387

		d	ρ	Label	ID
C₄₃⋊C₉	The semidirect product of C₄₃ and C₉ acting via C₉/C₃=C₃	387	3	C43:C9	387,1
C₃×C₄₃⋊C₃	Direct product of C₃ and C₄₃⋊C₃	129	3	C3xC43:C3	387,3

Groups of order 390

		d	ρ	Label	ID
C₁₀×C₁₃⋊C₃	Direct product of C₁₀ and C₁₃⋊C₃	130	3	C10xC13:C3	390,4

Groups of order 396

		d	ρ	Label	ID
C₁₁×C₃.A₄	Direct product of C₁₁ and C₃.A₄	198	3	C11xC3.A4	396,6
A₄×C₃₃	Direct product of C₃₃ and A₄	132	3	A4xC33	396,24

Groups of order 399

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

Groups of order 402

		d	ρ	Label	ID
C₂×C₆₇⋊C₃	Direct product of C₂ and C₆₇⋊C₃	134	3	C2xC67:C3	402,2

Groups of order 405

		d	ρ	Label	ID
C₅×C₂₇⋊C₃	Direct product of C₅ and C₂₇⋊C₃	135	3	C5xC27:C3	405,6
C₅×C₃≀C₃	Direct product of C₅ and C₃≀C₃	45	3	C5xC3wrC3	405,7
C₅×He₃.C₃	Direct product of C₅ and He₃.C₃	135	3	C5xHe3.C3	405,8
C₅×He₃⋊C₃	Direct product of C₅ and He₃⋊C₃	135	3	C5xHe3:C3	405,9
C₅×C₃.He₃	Direct product of C₅ and C₃.He₃	135	3	C5xC3.He3	405,10
C₅×C₉○He₃	Direct product of C₅ and C₉○He₃	135	3	C5xC9oHe3	405,14

Groups of order 408

		d	ρ	Label	ID
C₁₇×S₄	Direct product of C₁₇ and S₄	68	3	C17xS4	408,36
A₄×C₃₄	Direct product of C₃₄ and A₄	102	3	A4xC34	408,42

Groups of order 417

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

Groups of order 420

		d	ρ	Label	ID
C₂₀×C₇⋊C₃	Direct product of C₂₀ and C₇⋊C₃	140	3	C20xC7:C3	420,4
C₇×A₅	Direct product of C₇ and A₅	35	3	C7xA5	420,13
A₄×C₃₅	Direct product of C₃₅ and A₄	140	3	A4xC35	420,32
C₅×C₇⋊A₄	Direct product of C₅ and C₇⋊A₄	140	3	C5xC7:A4	420,33

Groups of order 429

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

Groups of order 432

		d	ρ	Label	ID
C₄²⋊C₂₇	The semidirect product of C₄² and C₂₇ acting via C₂₇/C₉=C₃	108	3	C4^2:C27	432,3
He₃⋊₄C₁₆	2^nd semidirect product of He₃ and C₁₆ acting via C₁₆/C₈=C₂	144	3	He3:4C16	432,33
C₁₆×He₃	Direct product of C₁₆ and He₃	144	3	C16xHe3	432,35
C₁₆×3_-¹⁺²	Direct product of C₁₆ and 3_-¹⁺²	144	3	C16xES-(3,1)	432,36
C₄×C₉.A₄	Direct product of C₄ and C₉.A₄	108	3	C4xC9.A4	432,40
He₃⋊₂C₁₆	The semidirect product of He₃ and C₁₆ acting via C₁₆/C₄=C₄	144	3	He3:2C16	432,57
C₉×C₄²⋊C₃	Direct product of C₉ and C₄²⋊C₃	108	3	C9xC4^2:C3	432,99
C₄²⋊3_-¹⁺²	The semidirect product of C₄² and 3_-¹⁺² acting via 3_-¹⁺²/C₉=C₃	108	3	C4^2:ES-(3,1)	432,100
C₁₂².C₃	2^nd non-split extension by C₁₂² of C₃ acting faithfully	36	3	C12^2.C3	432,102
C₄²⋊He₃	The semidirect product of C₄² and He₃ acting via He₃/C₃²=C₃	36	3	C4^2:He3	432,103
C₈×He₃⋊C₂	Direct product of C₈ and He₃⋊C₂	72	3	C8xHe3:C2	432,173
C₂.SU₃(𝔽₂)	The central extension by C₂ of SU₃(𝔽₂)	72	3	C2.SU(3,2)	432,239
C₉×A₄⋊C₄	Direct product of C₉ and A₄⋊C₄	108	3	C9xA4:C4	432,242
C₆²⋊₆Dic₃	5^th semidirect product of C₆² and Dic₃ acting via Dic₃/C₂=S₃	36	3	C6^2:6Dic3	432,260
He₃⋊₂(C₂×C₈)	The semidirect product of He₃ and C₂×C₈ acting via C₂×C₈/C₄=C₄	72	3	He3:2(C2xC8)	432,273
C₄×He₃⋊C₄	Direct product of C₄ and He₃⋊C₄	72	3	C4xHe3:C4	432,275
A₄×C₃₆	Direct product of C₃₆ and A₄	108	3	A4xC36	432,325
C₄×C₉⋊A₄	Direct product of C₄ and C₉⋊A₄	108	3	C4xC9:A4	432,326
C₄×C₃².A₄	Direct product of C₄ and C₃².A₄	36	3	C4xC3^2.A4	432,332
C₄×C₃²⋊A₄	Direct product of C₄ and C₃²⋊A₄	36	3	C4xC3^2:A4	432,333
C₂×SU₃(𝔽₂)	Direct product of C₂ and SU₃(𝔽₂)	54	3	C2xSU(3,2)	432,531
C₁₈×S₄	Direct product of C₁₈ and S₄	54	3	C18xS4	432,532
C₂×C₃²⋊S₄	Direct product of C₂ and C₃²⋊S₄	18	3	C2xC3^2:S4	432,538

Groups of order 438

		d	ρ	Label	ID
C₂×C₇₃⋊C₃	Direct product of C₂ and C₇₃⋊C₃	146	3	C2xC73:C3	438,2

Groups of order 441

		d	ρ	Label	ID
C₄₉⋊C₉	The semidirect product of C₄₉ and C₉ acting via C₉/C₃=C₃	441	3	C49:C9	441,1
C₃×C₄₉⋊C₃	Direct product of C₃ and C₄₉⋊C₃	147	3	C3xC49:C3	441,3
C₇×C₇⋊C₉	Direct product of C₇ and C₇⋊C₉	63	3	C7xC7:C9	441,5
C₇²⋊₃C₉	3^rd semidirect product of C₇² and C₉ acting via C₉/C₃=C₃	63	3	C7^2:3C9	441,7
C₇⋊C₃×C₂₁	Direct product of C₂₁ and C₇⋊C₃	63	3	C7:C3xC21	441,10
C₃×C₇²⋊₃C₃	Direct product of C₃ and C₇²⋊₃C₃	63	3	C3xC7^2:3C3	441,12

Groups of order 444

		d	ρ	Label	ID
C₄×C₃₇⋊C₃	Direct product of C₄ and C₃₇⋊C₃	148	3	C4xC37:C3	444,2
A₄×C₃₇	Direct product of C₃₇ and A₄	148	3	A4xC37	444,13
C₃₇⋊A₄	The semidirect product of C₃₇ and A₄ acting via A₄/C₂²=C₃	148	3	C37:A4	444,14

Groups of order 450

		d	ρ	Label	ID
C₂×C₅²⋊C₉	Direct product of C₂ and C₅²⋊C₉	90	3	C2xC5^2:C9	450,13
C₃×C₅²⋊S₃	Direct product of C₃ and C₅²⋊S₃	45	3	C3xC5^2:S3	450,20
C₆×C₅²⋊C₃	Direct product of C₆ and C₅²⋊C₃	90	3	C6xC5^2:C3	450,25

Groups of order 453

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

Groups of order 456

		d	ρ	Label	ID
C₈×C₁₉⋊C₃	Direct product of C₈ and C₁₉⋊C₃	152	3	C8xC19:C3	456,2
C₁₉×S₄	Direct product of C₁₉ and S₄	76	3	C19xS4	456,42
A₄×C₃₈	Direct product of C₃₈ and A₄	114	3	A4xC38	456,49
C₂×C₁₉⋊A₄	Direct product of C₂ and C₁₉⋊A₄	114	3	C2xC19:A4	456,50

Groups of order 459

		d	ρ	Label	ID
C₁₇×He₃	Direct product of C₁₇ and He₃	153	3	C17xHe3	459,3
C₁₇×3_-¹⁺²	Direct product of C₁₇ and 3_-¹⁺²	153	3	C17xES-(3,1)	459,4

Groups of order 462

		d	ρ	Label	ID
C₇⋊C₃×C₂₂	Direct product of C₂₂ and C₇⋊C₃	154	3	C7:C3xC22	462,4

Groups of order 465

		d	ρ	Label	ID
C₅×C₃₁⋊C₃	Direct product of C₅ and C₃₁⋊C₃	155	3	C5xC31:C3	465,3

Groups of order 468

		d	ρ	Label	ID
C₄×C₁₃⋊C₉	Direct product of C₄ and C₁₃⋊C₉	468	3	C4xC13:C9	468,2
C₁₃×C₃.A₄	Direct product of C₁₃ and C₃.A₄	234	3	C13xC3.A4	468,13
C₃₉.A₄	The non-split extension by C₃₉ of A₄ acting via A₄/C₂²=C₃	234	3	C39.A4	468,14
C₁₂×C₁₃⋊C₃	Direct product of C₁₂ and C₁₃⋊C₃	156	3	C12xC13:C3	468,22
A₄×C₃₉	Direct product of C₃₉ and A₄	156	3	A4xC39	468,48
C₃×C₁₃⋊A₄	Direct product of C₃ and C₁₃⋊A₄	156	3	C3xC13:A4	468,49

Groups of order 471

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

Groups of order 474

		d	ρ	Label	ID
C₂×C₇₉⋊C₃	Direct product of C₂ and C₇₉⋊C₃	158	3	C2xC79:C3	474,2

Groups of order 480

		d	ρ	Label	ID
C₈×A₅	Direct product of C₈ and A₅	40	3	C8xA5	480,220
C₅×C₄²⋊S₃	Direct product of C₅ and C₄²⋊S₃	60	3	C5xC4^2:S3	480,254
C₅×A₄⋊C₈	Direct product of C₅ and A₄⋊C₈	120	3	C5xA4:C8	480,255
C₁₀×C₄²⋊C₃	Direct product of C₁₀ and C₄²⋊C₃	60	3	C10xC4^2:C3	480,654
A₄×C₄₀	Direct product of C₄₀ and A₄	120	3	A4xC40	480,659
C₂₀×S₄	Direct product of C₂₀ and S₄	60	3	C20xS4	480,1014

Groups of order 483

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

Groups of order 486

		d	ρ	Label	ID
He₃.C₁₈	1^st non-split extension by He₃ of C₁₈ acting via C₁₈/C₃=C₆	81	3	He3.C18	486,26
He₃.₂C₁₈	2^nd non-split extension by He₃ of C₁₈ acting via C₁₈/C₃=C₆	81	3	He3.2C18	486,28
C₉²⋊₂S₃	2^nd semidirect product of C₉² and S₃ acting faithfully	27	3	C9^2:2S3	486,61
C₂×C₉.₄He₃	Direct product of C₂ and C₉.₄He₃	54	3	C2xC9.4He3	486,76
C₂×C₉.₅He₃	Direct product of C₂ and C₉.₅He₃	162	3	C2xC9.5He3	486,79
C₂×C₉.₆He₃	Direct product of C₂ and C₉.₆He₃	162	3	C2xC9.6He3	486,80
C₂×C₈₁⋊C₃	Direct product of C₂ and C₈₁⋊C₃	162	3	C2xC81:C3	486,84
C₂×C₉²⋊C₃	Direct product of C₂ and C₉²⋊C₃	54	3	C2xC9^2:C3	486,85
C₂×C₉²⋊₂C₃	Direct product of C₂ and C₉²⋊₂C₃	54	3	C2xC9^2:2C3	486,86
C₂×C₉².C₃	Direct product of C₂ and C₉².C₃	54	3	C2xC9^2.C3	486,87
C₃≀S₃⋊₃C₃	The semidirect product of C₃≀S₃ and C₃ acting through Inn(C₃≀S₃)	27	3	C3wrS3:3C3	486,125
He₃.₅C₁₈	The non-split extension by He₃ of C₁₈ acting via C₁₈/C₉=C₂	81	3	He3.5C18	486,164
C₂×C₂₇○He₃	Direct product of C₂ and C₂₇○He₃	162	3	C2xC27oHe3	486,209
C₂×C₉.He₃	Direct product of C₂ and C₉.He₃	54	3	C2xC9.He3	486,214

Groups of order 489

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

Groups of order 492

		d	ρ	Label	ID
A₄×C₄₁	Direct product of C₄₁ and A₄	164	3	A4xC41	492,8

Orthogonal of dimension 4 (ρ=4+)

Groups of order 20

		d	ρ	Label	ID
F₅	Frobenius group; = C₅ ⋊C₄ = AGL₁(𝔽₅) = Aut(D₅) = Hol(C₅) = Sz(2)	5	4+	F5	20,3

Groups of order 32

		d	ρ	Label	ID
C₂³⋊C₄	The semidirect product of C₂³ and C₄ acting faithfully	8	4+	C2^3:C4	32,6
C₄.D₄	1^st non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	8	4+	C4.D4	32,7
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	8	4+	C8:C2^2	32,43
2₊¹⁺⁴	Extraspecial group; = D₄ ○D₄	8	4+	ES+(2,2)	32,49

Groups of order 36

		d	ρ	Label	ID
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	6	4+	C3^2:C4	36,9
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	6	4+	S3^2	36,10

Groups of order 40

		d	ρ	Label	ID
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	10	4+	C2xF5	40,12

Groups of order 48

		d	ρ	Label	ID
D₄⋊S₃	The semidirect product of D₄ and S₃ acting via S₃/C₃=C₂	24	4+	D4:S3	48,15
Q₈⋊₂S₃	The semidirect product of Q₈ and S₃ acting via S₃/C₃=C₂	24	4+	Q8:2S3	48,17
S₃×D₄	Direct product of S₃ and D₄; = Aut(D₁₂) = Hol(C₁₂)	12	4+	S3xD4	48,38
Q₈⋊₃S₃	The semidirect product of Q₈ and S₃ acting through Inn(Q₈)	24	4+	Q8:3S3	48,41

Groups of order 52

		d	ρ	Label	ID
C₁₃⋊C₄	The semidirect product of C₁₃ and C₄ acting faithfully	13	4+	C13:C4	52,3

Groups of order 60

		d	ρ	Label	ID
S₃×D₅	Direct product of S₃ and D₅	15	4+	S3xD5	60,8

Groups of order 64

		d	ρ	Label	ID
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	8	4+	C2wrC4	64,32
C₄²⋊C₄	2^nd semidirect product of C₄² and C₄ acting faithfully	8	4+	C4^2:C4	64,34
M₅(2)⋊C₂	6^th semidirect product of M₅(2) and C₂ acting faithfully	16	4+	M5(2):C2	64,42
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	8	4+	D4:4D4	64,134
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	8	4+	C2wrC2^2	64,138
D₄.₄D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	16	4+	D4.4D4	64,153
C₁₆⋊C₂²	The semidirect product of C₁₆ and C₂² acting faithfully	16	4+	C16:C2^2	64,190
D₄○D₈	Central product of D₄ and D₈	16	4+	D4oD8	64,257

Groups of order 68

		d	ρ	Label	ID
C₁₇⋊C₄	The semidirect product of C₁₇ and C₄ acting faithfully	17	4+	C17:C4	68,3

Groups of order 72

		d	ρ	Label	ID
C₆.D₆	2^nd non-split extension by C₆ of D₆ acting via D₆/S₃=C₂	12	4+	C6.D6	72,21
C₃⋊D₁₂	The semidirect product of C₃ and D₁₂ acting via D₁₂/D₆=C₂	12	4+	C3:D12	72,23
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	6	4+	S3wrC2	72,40
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	12	4+	C2xC3^2:C4	72,45
C₂×S₃²	Direct product of C₂, S₃ and S₃	12	4+	C2xS3^2	72,46

Groups of order 80

		d	ρ	Label	ID
D₄⋊D₅	The semidirect product of D₄ and D₅ acting via D₅/C₅=C₂	40	4+	D4:D5	80,15
Q₈⋊D₅	The semidirect product of Q₈ and D₅ acting via D₅/C₅=C₂	40	4+	Q8:D5	80,17
C₂²⋊F₅	The semidirect product of C₂² and F₅ acting via F₅/D₅=C₂	20	4+	C2^2:F5	80,34
D₄×D₅	Direct product of D₄ and D₅	20	4+	D4xD5	80,39
Q₈⋊₂D₅	The semidirect product of Q₈ and D₅ acting through Inn(Q₈)	40	4+	Q8:2D5	80,42

Groups of order 84

		d	ρ	Label	ID
S₃×D₇	Direct product of S₃ and D₇	21	4+	S3xD7	84,8

Groups of order 96

		d	ρ	Label	ID
C₁₂.₄₆D₄	3^rd non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	24	4+	C12.46D4	96,30
C₃⋊D₁₆	The semidirect product of C₃ and D₁₆ acting via D₁₆/D₈=C₂	48	4+	C3:D16	96,33
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 semidirect product of C₈ and D₆ acting via D₆/C₃=C₂²	24	4+	C8:D6	96,115
S₃×D₈	Direct product of S₃ and D₈	24	4+	S3xD8	96,117
Q₈⋊₃D₆	2^nd semidirect product of Q₈ and D₆ acting via D₆/S₃=C₂	24	4+	Q8:3D6	96,121
D₂₄⋊C₂	5^th semidirect product of D₂₄ and C₂ acting faithfully	48	4+	D24:C2	96,126
D₄⋊D₆	2^nd semidirect product of D₄ and D₆ acting via D₆/C₆=C₂	24	4+	D4:D6	96,156
C₄.₃S₄	3^rd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	16	4+	C4.3S4	96,193
Q₈.A₄	The non-split extension by Q₈ of A₄ acting through Inn(Q₈)	24	4+	Q8.A4	96,201
C₂³⋊A₄	2^nd semidirect product of C₂³ and A₄ acting faithfully	8	4+	C2^3:A4	96,204
D₄○D₁₂	Central product of D₄ and D₁₂	24	4+	D4oD12	96,216

Groups of order 100

		d	ρ	Label	ID
C₂₅⋊C₄	The semidirect product of C₂₅ and C₄ acting faithfully	25	4+	C25:C4	100,3
C₅²⋊C₄	4^th semidirect product of C₅² and C₄ acting faithfully	10	4+	C5^2:C4	100,12
D₅²	Direct product of D₅ and D₅	10	4+	D5^2	100,13

Groups of order 104

		d	ρ	Label	ID
C₂×C₁₃⋊C₄	Direct product of C₂ and C₁₃⋊C₄	26	4+	C2xC13:C4	104,12

Groups of order 108

		d	ρ	Label	ID
S₃×D₉	Direct product of S₃ and D₉	18	4+	S3xD9	108,16

Groups of order 112

		d	ρ	Label	ID
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
D₄×D₇	Direct product of D₄ and D₇	28	4+	D4xD7	112,31
Q₈⋊₂D₇	The semidirect product of Q₈ and D₇ acting through Inn(Q₈)	56	4+	Q8:2D7	112,34

Groups of order 116

		d	ρ	Label	ID
C₂₉⋊C₄	The semidirect product of C₂₉ and C₄ acting faithfully	29	4+	C29:C4	116,3

Groups of order 120

		d	ρ	Label	ID
D₃₀.C₂	The non-split extension by D₃₀ of C₂ acting faithfully	60	4+	D30.C2	120,10
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
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	5	4+	S5	120,34
C₂×S₃×D₅	Direct product of C₂, S₃ and D₅	30	4+	C2xS3xD5	120,42

Groups of order 128

		d	ρ	Label	ID
C₈.₂₄D₈	1^st non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	16	4+	C8.24D8	128,89
C₄².D₄	1^st non-split extension by C₄² of D₄ acting faithfully	16	4+	C4^2.D4	128,134
C₄⋊₁D₄⋊C₄	2^nd semidirect product of C₄⋊₁D₄ and C₄ acting faithfully	16	4+	C4:1D4:C4	128,140
M₆(2)⋊C₂	6^th semidirect product of M₆(2) and C₂ acting faithfully	32	4+	M6(2):C2	128,151
Q₁₆.₁₀D₄	3^rd non-split extension by Q₁₆ of D₄ acting via D₄/C₂²=C₂	32	4+	Q16.10D4	128,924
D₄≀C₂	Wreath product of D₄ by C₂	8	4+	D4wrC2	128,928
D₈⋊₃D₄	2^nd semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	16	4+	D8:3D4	128,945
D₄.₃D₈	3^rd non-split extension by D₄ of D₈ acting via D₈/C₈=C₂	32	4+	D4.3D8	128,953
C₃₂⋊C₂²	The semidirect product of C₃₂ and C₂² acting faithfully	32	4+	C32:C2^2	128,995
D₈○D₈	Central product of D₈ and D₈	16	4+	D8oD8	128,2024
D₄○D₁₆	Central product of D₄ and D₁₆	32	4+	D4oD16	128,2147

Groups of order 132

		d	ρ	Label	ID
S₃×D₁₁	Direct product of S₃ and D₁₁	33	4+	S3xD11	132,5

Groups of order 136

		d	ρ	Label	ID
C₂×C₁₇⋊C₄	Direct product of C₂ and C₁₇⋊C₄	34	4+	C2xC17:C4	136,13

Groups of order 140

		d	ρ	Label	ID
D₅×D₇	Direct product of D₅ and D₇	35	4+	D5xD7	140,7

Groups of order 144

		d	ρ	Label	ID
D₄⋊D₉	The semidirect product of D₄ and D₉ acting via D₉/C₉=C₂	72	4+	D4:D9	144,16
Q₈⋊₂D₉	The semidirect product of Q₈ and D₉ acting via D₉/C₉=C₂	72	4+	Q8:2D9	144,18
Q₈⋊D₉	The semidirect product of Q₈ and D₉ acting via D₉/C₃=S₃	72	4+	Q8:D9	144,32
D₄×D₉	Direct product of D₄ and D₉	36	4+	D4xD9	144,41
Q₈⋊₃D₉	The semidirect product of Q₈ and D₉ acting through Inn(Q₈)	72	4+	Q8:3D9	144,44
C₃⋊D₂₄	The semidirect product of C₃ and D₂₄ acting via D₂₄/D₁₂=C₂	24	4+	C3:D24	144,57
C₃²⋊₅SD₁₆	3^rd semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₄=C₂²	24	4+	C3^2:5SD16	144,60
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	12	4+	S3^2:C4	144,115
C₆.₆S₄	6^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	24	4+	C6.6S4	144,125
Dic₃.A₄	The non-split extension by Dic₃ of A₄ acting through Inn(Dic₃)	48	4+	Dic3.A4	144,127
C₆²⋊C₄	1^st semidirect product of C₆² and C₄ acting faithfully	12	4+	C6^2:C4	144,136
D₆.₆D₆	2^nd non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	24	4+	D6.6D6	144,142
S₃×D₁₂	Direct product of S₃ and D₁₂	24	4+	S3xD12	144,144
Dic₃⋊D₆	2^nd semidirect product of Dic₃ and D₆ acting via D₆/S₃=C₂; = Hol(Dic₃)	12	4+	Dic3:D6	144,154
C₂×S₃≀C₂	Direct product of C₂ and S₃≀C₂	12	4+	C2xS3wrC2	144,186

Groups of order 148

		d	ρ	Label	ID
C₃₇⋊C₄	The semidirect product of C₃₇ and C₄ acting faithfully	37	4+	C37:C4	148,3

Groups of order 156

		d	ρ	Label	ID
S₃×D₁₃	Direct product of S₃ and D₁₃	39	4+	S3xD13	156,11

Groups of order 160

		d	ρ	Label	ID
C₂₀.₄₆D₄	3^rd non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	40	4+	C20.46D4	160,30
C₅⋊D₁₆	The semidirect product of C₅ and D₁₆ acting via D₁₆/D₈=C₂	80	4+	C5:D16	160,33
C₅⋊SD₃₂	The semidirect product of C₅ and SD₃₂ acting via SD₃₂/Q₁₆=C₂	80	4+	C5:SD32	160,35
D₁₀.D₄	1^st non-split extension by D₁₀ of D₄ acting via D₄/C₂=C₂²	40	4+	D10.D4	160,74
C₈⋊D₁₀	1^st semidirect product of C₈ and D₁₀ acting via D₁₀/C₅=C₂²	40	4+	C8:D10	160,129
D₅×D₈	Direct product of D₅ and D₈	40	4+	D5xD8	160,131
D₄₀⋊C₂	6^th semidirect product of D₄₀ and C₂ acting faithfully	40	4+	D40:C2	160,135
Q₈.D₁₀	5^th non-split extension by Q₈ of D₁₀ acting via D₁₀/D₅=C₂	80	4+	Q8.D10	160,140
D₄⋊D₁₀	2^nd semidirect product of D₄ and D₁₀ acting via D₁₀/C₁₀=C₂	40	4+	D4:D10	160,170
D₄⋊₈D₁₀	4^th semidirect product of D₄ and D₁₀ acting through Inn(D₄)	40	4+	D4:8D10	160,224

Groups of order 164

		d	ρ	Label	ID
C₄₁⋊C₄	The semidirect product of C₄₁ and C₄ acting faithfully	41	4+	C41:C4	164,3

Groups of order 168

		d	ρ	Label	ID
D₂₁⋊C₄	The semidirect product of D₂₁ and C₄ acting via C₄/C₂=C₂	84	4+	D21:C4	168,14
C₃⋊D₂₈	The semidirect product of C₃ and D₂₈ acting via D₂₈/D₁₄=C₂	84	4+	C3:D28	168,16
C₇⋊D₁₂	The semidirect product of C₇ and D₁₂ acting via D₁₂/D₆=C₂	84	4+	C7:D12	168,17
C₂×S₃×D₇	Direct product of C₂, S₃ and D₇	42	4+	C2xS3xD7	168,50

Groups of order 176

		d	ρ	Label	ID
D₄⋊D₁₁	The semidirect product of D₄ and D₁₁ acting via D₁₁/C₁₁=C₂	88	4+	D4:D11	176,14
Q₈⋊D₁₁	The semidirect product of Q₈ and D₁₁ acting via D₁₁/C₁₁=C₂	88	4+	Q8:D11	176,16
D₄×D₁₁	Direct product of D₄ and D₁₁	44	4+	D4xD11	176,31
D₄₄⋊C₂	4^th semidirect product of D₄₄ and C₂ acting faithfully	88	4+	D44:C2	176,34

Groups of order 180

		d	ρ	Label	ID
D₅×D₉	Direct product of D₅ and D₉	45	4+	D5xD9	180,7
C₃²⋊F₅	The semidirect product of C₃² and F₅ acting via F₅/C₅=C₄	30	4+	C3^2:F5	180,25
S₃×D₁₅	Direct product of S₃ and D₁₅	30	4+	S3xD15	180,29

Groups of order 192

		d	ρ	Label	ID
D₂₄.C₄	4^th non-split extension by D₂₄ of C₄ acting via C₄/C₂=C₂	48	4+	D24.C4	192,54
M₅(2)⋊S₃	5^th semidirect product of M₅(2) and S₃ acting via S₃/C₃=C₂	48	4+	M5(2):S3	192,75
C₃⋊D₃₂	The semidirect product of C₃ and D₃₂ acting via D₃₂/D₁₆=C₂	96	4+	C3:D32	192,78
C₃⋊SD₆₄	The semidirect product of C₃ and SD₆₄ acting via SD₆₄/Q₃₂=C₂	96	4+	C3:SD64	192,80
C₂≀A₄	Wreath product of C₂ by A₄	8	4+	C2wrA4	192,201
Q₈⋊₅D₁₂	3^rd semidirect product of Q₈ and D₁₂ acting via D₁₂/D₆=C₂	24	4+	Q8:5D12	192,381
C₂₄.₁₉D₄	19^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4+	C24.19D4	192,456
C₁₆⋊D₆	1^st semidirect product of C₁₆ and D₆ acting via D₆/C₃=C₂²	48	4+	C16:D6	192,467
S₃×D₁₆	Direct product of S₃ and D₁₆	48	4+	S3xD16	192,469
D₄₈⋊C₂	6^th semidirect product of D₄₈ and C₂ acting faithfully	48	4+	D48:C2	192,473
D₄₈⋊₅C₂	5^th semidirect product of D₄₈ and C₂ acting faithfully	96	4+	D48:5C2	192,478
Q₈.₉D₁₂	4^th non-split extension by Q₈ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4+	Q8.9D12	192,701
Q₁₆⋊D₆	2^nd semidirect product of Q₁₆ and D₆ acting via D₆/C₆=C₂	48	4+	Q16:D6	192,752
C₈.₃S₄	3^rd non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4+	C8.3S4	192,966
Q₈.₅S₄	3^rd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	24	4+	Q8.5S4	192,988
Q₁₆.A₄	The non-split extension by Q₁₆ of A₄ acting through Inn(Q₁₆)	48	4+	Q16.A4	192,1017
D₄.₁₂D₁₂	2^nd non-split extension by D₄ of D₁₂ acting through Inn(D₄)	48	4+	D4.12D12	192,1311
D₈⋊₁₅D₆	4^th semidirect product of D₈ and D₆ acting through Inn(D₈)	48	4+	D8:15D6	192,1328
Q₈.₇S₄	2^nd non-split extension by Q₈ of S₄ acting through Inn(Q₈)	32	4+	Q8.7S4	192,1484
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	8	4+	C2^3:S4	192,1493
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	8	4+	Q8:2S4	192,1494

Groups of order 196

		d	ρ	Label	ID
C₇²⋊C₄	The semidirect product of C₇² and C₄ acting faithfully	14	4+	C7^2:C4	196,8
D₇²	Direct product of D₇ and D₇	14	4+	D7^2	196,9

Groups of order 200

		d	ρ	Label	ID
C₂×C₂₅⋊C₄	Direct product of C₂ and C₂₅⋊C₄	50	4+	C2xC25:C4	200,12
Dic₅⋊₂D₅	The semidirect product of Dic₅ and D₅ acting through Inn(Dic₅)	20	4+	Dic5:2D5	200,23
C₅⋊D₂₀	The semidirect product of C₅ and D₂₀ acting via D₂₀/D₁₀=C₂	20	4+	C5:D20	200,25
D₅≀C₂	Wreath product of D₅ by C₂	10	4+	D5wrC2	200,43
C₂×C₅²⋊C₄	Direct product of C₂ and C₅²⋊C₄	20	4+	C2xC5^2:C4	200,48
C₂×D₅²	Direct product of C₂, D₅ and D₅	20	4+	C2xD5^2	200,49

Groups of order 204

		d	ρ	Label	ID
S₃×D₁₇	Direct product of S₃ and D₁₇	51	4+	S3xD17	204,7

Groups of order 208

		d	ρ	Label	ID
D₄⋊D₁₃	The semidirect product of D₄ and D₁₃ acting via D₁₃/C₁₃=C₂	104	4+	D4:D13	208,15
Q₈⋊D₁₃	The semidirect product of Q₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	4+	Q8:D13	208,17
D₁₃.D₄	The non-split extension by D₁₃ of D₄ acting via D₄/C₂²=C₂	52	4+	D13.D4	208,34
D₄×D₁₃	Direct product of D₄ and D₁₃	52	4+	D4xD13	208,39
D₅₂⋊C₂	4^th semidirect product of D₅₂ and C₂ acting faithfully	104	4+	D52:C2	208,42

Groups of order 212

		d	ρ	Label	ID
C₅₃⋊C₄	The semidirect product of C₅₃ and C₄ acting faithfully	53	4+	C53:C4	212,3

Groups of order 216

		d	ρ	Label	ID
C₁₈.D₆	3^rd non-split extension by C₁₈ of D₆ acting via D₆/S₃=C₂	36	4+	C18.D6	216,28
C₃⋊D₃₆	The semidirect product of C₃ and D₃₆ acting via D₃₆/D₁₈=C₂	36	4+	C3:D36	216,29
C₉⋊D₁₂	The semidirect product of C₉ and D₁₂ acting via D₁₂/D₆=C₂	36	4+	C9:D12	216,32
C₂×S₃×D₉	Direct product of C₂, S₃ and D₉	36	4+	C2xS3xD9	216,101

Groups of order 220

		d	ρ	Label	ID
D₅×D₁₁	Direct product of D₅ and D₁₁	55	4+	D5xD11	220,11

Groups of order 224

		d	ρ	Label	ID
C₂₈.₄₆D₄	3^rd non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	56	4+	C28.46D4	224,29
C₇⋊D₁₆	The semidirect product of C₇ and D₁₆ acting via D₁₆/D₈=C₂	112	4+	C7:D16	224,32
C₇⋊SD₃₂	The semidirect product of C₇ and SD₃₂ acting via SD₃₂/Q₁₆=C₂	112	4+	C7:SD32	224,34
C₈⋊D₁₄	1^st semidirect product of C₈ and D₁₄ acting via D₁₄/C₇=C₂²	56	4+	C8:D14	224,103
D₇×D₈	Direct product of D₇ and D₈	56	4+	D7xD8	224,105
D₅₆⋊C₂	6^th semidirect product of D₅₆ and C₂ acting faithfully	56	4+	D56:C2	224,109
Q₈.D₁₄	5^th non-split extension by Q₈ of D₁₄ acting via D₁₄/D₇=C₂	112	4+	Q8.D14	224,114
D₄⋊D₁₄	2^nd semidirect product of D₄ and D₁₄ acting via D₁₄/C₁₄=C₂	56	4+	D4:D14	224,144
D₄⋊₈D₁₄	4^th semidirect product of D₄ and D₁₄ acting through Inn(D₄)	56	4+	D4:8D14	224,185

Groups of order 228

		d	ρ	Label	ID
S₃×D₁₉	Direct product of S₃ and D₁₉	57	4+	S3xD19	228,8

Groups of order 232

		d	ρ	Label	ID
C₂×C₂₉⋊C₄	Direct product of C₂ and C₂₉⋊C₄	58	4+	C2xC29:C4	232,12

Groups of order 240

		d	ρ	Label	ID
C₃⋊D₄₀	The semidirect product of C₃ and D₄₀ acting via D₄₀/D₂₀=C₂	120	4+	C3:D40	240,14
C₅⋊D₂₄	The semidirect product of C₅ and D₂₄ acting via D₂₄/D₁₂=C₂	120	4+	C5:D24	240,15
C₁₅⋊SD₁₆	4^th semidirect product of C₁₅ and SD₁₆ acting via SD₁₆/C₄=C₂²	120	4+	C15:SD16	240,19
Dic₆⋊D₅	1^st semidirect product of Dic₆ and D₅ acting via D₅/C₅=C₂	120	4+	Dic6:D5	240,21
D₄⋊D₁₅	The semidirect product of D₄ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4+	D4:D15	240,76
Q₈⋊₂D₁₅	The semidirect product of Q₈ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4+	Q8:2D15	240,78
Q₈⋊D₁₅	The semidirect product of Q₈ and D₁₅ acting via D₁₅/C₅=S₃	40	4+	Q8:D15	240,106
Dic₅.A₄	The non-split extension by Dic₅ of A₄ acting through Inn(Dic₅)	80	4+	Dic5.A4	240,108
D₆₀⋊C₂	6^th semidirect product of D₆₀ and C₂ acting faithfully	120	4+	D60:C2	240,130
C₁₂.₂₈D₁₀	7^th non-split extension by C₁₂ of D₁₀ acting via D₁₀/D₅=C₂	120	4+	C12.28D10	240,134
D₅×D₁₂	Direct product of D₅ and D₁₂	60	4+	D5xD12	240,136
S₃×D₂₀	Direct product of S₃ and D₂₀	60	4+	S3xD20	240,137
D₁₀⋊D₆	4^th semidirect product of D₁₀ and D₆ acting via D₆/S₃=C₂	60	4+	D10:D6	240,151
D₄×D₁₅	Direct product of D₄ and D₁₅	60	4+	D4xD15	240,179
Q₈⋊₃D₁₅	The semidirect product of Q₈ and D₁₅ acting through Inn(Q₈)	120	4+	Q8:3D15	240,182
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	10	4+	C2xS5	240,189

Groups of order 244

		d	ρ	Label	ID
C₆₁⋊C₄	The semidirect product of C₆₁ and C₄ acting faithfully	61	4+	C61:C4	244,3

Groups of order 252

		d	ρ	Label	ID
D₇×D₉	Direct product of D₇ and D₉	63	4+	D7xD9	252,8
S₃×D₂₁	Direct product of S₃ and D₂₁	42	4+	S3xD21	252,36

Groups of order 260

		d	ρ	Label	ID
C₁₃⋊F₅	1^st semidirect product of C₁₃ and F₅ acting via F₅/C₅=C₄	65	4+	C13:F5	260,9
C₆₅⋊₂C₄	2^nd semidirect product of C₆₅ and C₄ acting faithfully	65	4+	C65:2C4	260,10
D₅×D₁₃	Direct product of D₅ and D₁₃	65	4+	D5xD13	260,11

Groups of order 264

		d	ρ	Label	ID
D₃₃⋊C₄	The semidirect product of D₃₃ and C₄ acting via C₄/C₂=C₂	132	4+	D33:C4	264,7
C₃⋊D₄₄	The semidirect product of C₃ and D₄₄ acting via D₄₄/D₂₂=C₂	132	4+	C3:D44	264,9
C₁₁⋊D₁₂	The semidirect product of C₁₁ and D₁₂ acting via D₁₂/D₆=C₂	132	4+	C11:D12	264,10
C₂×S₃×D₁₁	Direct product of C₂, S₃ and D₁₁	66	4+	C2xS3xD11	264,34

Groups of order 272

		d	ρ	Label	ID
D₄⋊D₁₇	The semidirect product of D₄ and D₁₇ acting via D₁₇/C₁₇=C₂	136	4+	D4:D17	272,15
Q₈⋊D₁₇	The semidirect product of Q₈ and D₁₇ acting via D₁₇/C₁₇=C₂	136	4+	Q8:D17	272,17
D₁₇.D₄	The non-split extension by D₁₇ of D₄ acting via D₄/C₂²=C₂	68	4+	D17.D4	272,35
D₄×D₁₇	Direct product of D₄ and D₁₇	68	4+	D4xD17	272,40
D₆₈⋊C₂	4^th semidirect product of D₆₈ and C₂ acting faithfully	136	4+	D68:C2	272,43

Groups of order 276

		d	ρ	Label	ID
S₃×D₂₃	Direct product of S₃ and D₂₃	69	4+	S3xD23	276,5

Groups of order 280

		d	ρ	Label	ID
D₇₀.C₂	The non-split extension by D₇₀ of C₂ acting faithfully	140	4+	D70.C2	280,9
C₅⋊D₂₈	The semidirect product of C₅ and D₂₈ acting via D₂₈/D₁₄=C₂	140	4+	C5:D28	280,11
C₇⋊D₂₀	The semidirect product of C₇ and D₂₀ acting via D₂₀/D₁₀=C₂	140	4+	C7:D20	280,12
C₂×D₅×D₇	Direct product of C₂, D₅ and D₇	70	4+	C2xD5xD7	280,36

Groups of order 288

		d	ρ	Label	ID
C₃₆.₄₈D₄	4^th non-split extension by C₃₆ of D₄ acting via D₄/C₂²=C₂	72	4+	C36.48D4	288,31
C₉⋊D₁₆	The semidirect product of C₉ and D₁₆ acting via D₁₆/D₈=C₂	144	4+	C9:D16	288,33
C₉⋊SD₃₂	The semidirect product of C₉ and SD₃₂ acting via SD₃₂/Q₁₆=C₂	144	4+	C9:SD32	288,35
C₈⋊D₁₈	1^st semidirect product of C₈ and D₁₈ acting via D₁₈/C₉=C₂²	72	4+	C8:D18	288,118
D₈×D₉	Direct product of D₈ and D₉	72	4+	D8xD9	288,120
D₇₂⋊C₂	6^th semidirect product of D₇₂ and C₂ acting faithfully	72	4+	D72:C2	288,124
D₇₂⋊₅C₂	5^th semidirect product of D₇₂ and C₂ acting faithfully	144	4+	D72:5C2	288,129
D₄⋊D₁₈	2^nd semidirect product of D₄ and D₁₈ acting via D₁₈/C₁₈=C₂	72	4+	D4:D18	288,160
C₃⋊D₄₈	The semidirect product of C₃ and D₄₈ acting via D₄₈/D₂₄=C₂	48	4+	C3:D48	288,194
C₂₄.₄₉D₆	2^nd non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4+	C24.49D6	288,197
C₁₂.₇₀D₁₂	1^st non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	24	4+	C12.70D12	288,207
C₁₂.₄S₄	4^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	4+	C12.4S4	288,340
D₄⋊₈D₁₈	4^th semidirect product of D₄ and D₁₈ acting through Inn(D₄)	72	4+	D4:8D18	288,363
C₆².₂D₄	2^nd non-split extension by C₆² of D₄ acting faithfully	24	4+	C6^2.2D4	288,386
(C₆×C₁₂)⋊C₄	1^st semidirect product of C₆×C₁₂ and C₄ acting faithfully	24	4+	(C6xC12):C4	288,422
S₃×D₂₄	Direct product of S₃ and D₂₄	48	4+	S3xD24	288,441
C₂₄⋊₁D₆	1^st semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4+	C24:1D6	288,442
D₆.₃D₁₂	3^rd non-split extension by D₆ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4+	D6.3D12	288,456
D₁₂⋊₁₈D₆	2^nd semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	24	4+	D12:18D6	288,473
Dic₃.₅S₄	2^nd non-split extension by Dic₃ of S₄ acting through Inn(Dic₃)	48	4+	Dic3.5S4	288,846
GL₂(𝔽₃)⋊S₃	1^st semidirect product of GL₂(𝔽₃) and S₃ acting via S₃/C₃=C₂	48	4+	GL(2,3):S3	288,847
Ω₄⁺ (𝔽₃)	Omega group of + type on 𝔽₃⁴; = SL₂(𝔽₃)⋊A₄	24	4+	Omega+(4,3)	288,860
D₆≀C₂	Wreath product of D₆ by C₂	12	4+	D6wrC2	288,889
C₁₂.₇S₄	7^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	48	4+	C12.7S4	288,915
Dic₆.A₄	The non-split extension by Dic₆ of A₄ acting through Inn(Dic₆)	72	4+	Dic6.A4	288,924
D₁₂⋊₂₇D₆	3^rd semidirect product of D₁₂ and D₆ acting through Inn(D₁₂)	24	4+	D12:27D6	288,956

Groups of order 292

		d	ρ	Label	ID
C₇₃⋊C₄	The semidirect product of C₇₃ and C₄ acting faithfully	73	4+	C73:C4	292,3

Groups of order 296

		d	ρ	Label	ID
C₂×C₃₇⋊C₄	Direct product of C₂ and C₃₇⋊C₄	74	4+	C2xC37:C4	296,12

Groups of order 300

		d	ρ	Label	ID
S₃×D₂₅	Direct product of S₃ and D₂₅	75	4+	S3xD25	300,7
D₅×D₁₅	Direct product of D₅ and D₁₅	30	4+	D5xD15	300,39

Groups of order 304

		d	ρ	Label	ID
D₄⋊D₁₉	The semidirect product of D₄ and D₁₉ acting via D₁₉/C₁₉=C₂	152	4+	D4:D19	304,14
Q₈⋊D₁₉	The semidirect product of Q₈ and D₁₉ acting via D₁₉/C₁₉=C₂	152	4+	Q8:D19	304,16
D₄×D₁₉	Direct product of D₄ and D₁₉	76	4+	D4xD19	304,31
D₇₆⋊C₂	4^th semidirect product of D₇₆ and C₂ acting faithfully	152	4+	D76:C2	304,34

Groups of order 308

		d	ρ	Label	ID
D₇×D₁₁	Direct product of D₇ and D₁₁	77	4+	D7xD11	308,5

Groups of order 312

		d	ρ	Label	ID
D₇₈.C₂	The non-split extension by D₇₈ of C₂ acting faithfully	156	4+	D78.C2	312,17
C₃⋊D₅₂	The semidirect product of C₃ and D₅₂ acting via D₅₂/D₂₆=C₂	156	4+	C3:D52	312,19
C₁₃⋊D₁₂	The semidirect product of C₁₃ and D₁₂ acting via D₁₂/D₆=C₂	156	4+	C13:D12	312,20
C₂×S₃×D₁₃	Direct product of C₂, S₃ and D₁₃	78	4+	C2xS3xD13	312,54

Groups of order 320

		d	ρ	Label	ID
D₄₀.₆C₄	4^th non-split extension by D₄₀ of C₄ acting via C₄/C₂=C₂	80	4+	D40.6C4	320,53
D₄₀.₄C₄	2^nd non-split extension by D₄₀ of C₄ acting via C₄/C₂=C₂	80	4+	D40.4C4	320,74
C₅⋊D₃₂	The semidirect product of C₅ and D₃₂ acting via D₃₂/D₁₆=C₂	160	4+	C5:D32	320,77
C₅⋊SD₆₄	The semidirect product of C₅ and SD₆₄ acting via SD₆₄/Q₃₂=C₂	160	4+	C5:SD64	320,79
C₄²⋊F₅	1^st semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	40	4+	C4^2:F5	320,191
D₄⋊₄D₂₀	3^rd semidirect product of D₄ and D₂₀ acting via D₂₀/D₁₀=C₂	40	4+	D4:4D20	320,449
C₈.₂₁D₂₀	7^th non-split extension by C₈ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4+	C8.21D20	320,524
D₈₀⋊C₂	2^nd semidirect product of D₈₀ and C₂ acting faithfully	80	4+	D80:C2	320,535
D₅×D₁₆	Direct product of D₅ and D₁₆	80	4+	D5xD16	320,537
C₁₆⋊D₁₀	3^rd semidirect product of C₁₆ and D₁₀ acting via D₁₀/C₅=C₂²	80	4+	C16:D10	320,541
D₈₀⋊₅C₂	5^th semidirect product of D₈₀ and C₂ acting faithfully	160	4+	D80:5C2	320,546
D₄.₄D₂₀	4^th non-split extension by D₄ of D₂₀ acting via D₂₀/C₂₀=C₂	80	4+	D4.4D20	320,769
D₈⋊D₁₀	2^nd semidirect product of D₈ and D₁₀ acting via D₁₀/C₁₀=C₂	80	4+	D8:D10	320,820
D₄.₁₂D₂₀	2^nd non-split extension by D₄ of D₂₀ acting through Inn(D₄)	80	4+	D4.12D20	320,1424
D₈⋊₁₅D₁₀	4^th semidirect product of D₈ and D₁₀ acting through Inn(D₈)	80	4+	D8:15D10	320,1441

Groups of order 324

		d	ρ	Label	ID
C₉²⋊C₄	The semidirect product of C₉² and C₄ acting faithfully	18	4+	C9^2:C4	324,35
D₉²	Direct product of D₉ and D₉	18	4+	D9^2	324,36
S₃×D₂₇	Direct product of S₃ and D₂₇	54	4+	S3xD27	324,38

Groups of order 328

		d	ρ	Label	ID
C₂×C₄₁⋊C₄	Direct product of C₂ and C₄₁⋊C₄	82	4+	C2xC41:C4	328,13

Groups of order 336

		d	ρ	Label	ID
C₃⋊D₅₆	The semidirect product of C₃ and D₅₆ acting via D₅₆/D₂₈=C₂	168	4+	C3:D56	336,30
C₇⋊D₂₄	The semidirect product of C₇ and D₂₄ acting via D₂₄/D₁₂=C₂	168	4+	C7:D24	336,31
C₂₁⋊SD₁₆	4^th semidirect product of C₂₁ and SD₁₆ acting via SD₁₆/C₄=C₂²	168	4+	C21:SD16	336,35
Dic₆⋊D₇	1^st semidirect product of Dic₆ and D₇ acting via D₇/C₇=C₂	168	4+	Dic6:D7	336,37
D₄⋊D₂₁	The semidirect product of D₄ and D₂₁ acting via D₂₁/C₂₁=C₂	168	4+	D4:D21	336,101
Q₈⋊₂D₂₁	The semidirect product of Q₈ and D₂₁ acting via D₂₁/C₂₁=C₂	168	4+	Q8:2D21	336,103
Q₈⋊D₂₁	The semidirect product of Q₈ and D₂₁ acting via D₂₁/C₇=S₃	56	4+	Q8:D21	336,119
Dic₇.₂A₄	The non-split extension by Dic₇ of A₄ acting through Inn(Dic₇)	112	4+	Dic7.2A4	336,131
D₈₄⋊C₂	6^th semidirect product of D₈₄ and C₂ acting faithfully	168	4+	D84:C2	336,142
D₁₄.D₆	3^rd non-split extension by D₁₄ of D₆ acting via D₆/C₆=C₂	168	4+	D14.D6	336,146
D₇×D₁₂	Direct product of D₇ and D₁₂	84	4+	D7xD12	336,148
S₃×D₂₈	Direct product of S₃ and D₂₈	84	4+	S3xD28	336,149
D₆⋊D₁₄	4^th semidirect product of D₆ and D₁₄ acting via D₁₄/D₇=C₂	84	4+	D6:D14	336,163
D₄×D₂₁	Direct product of D₄ and D₂₁	84	4+	D4xD21	336,198
Q₈⋊₃D₂₁	The semidirect product of Q₈ and D₂₁ acting through Inn(Q₈)	168	4+	Q8:3D21	336,201

Groups of order 340

		d	ρ	Label	ID
C₁₇⋊F₅	1^st semidirect product of C₁₇ and F₅ acting via F₅/C₅=C₄	85	4+	C17:F5	340,9
C₈₅⋊₂C₄	2^nd semidirect product of C₈₅ and C₄ acting faithfully	85	4+	C85:2C4	340,10
D₅×D₁₇	Direct product of D₅ and D₁₇	85	4+	D5xD17	340,11

Groups of order 348

		d	ρ	Label	ID
S₃×D₂₉	Direct product of S₃ and D₂₉	87	4+	S3xD29	348,7

Groups of order 352

		d	ρ	Label	ID
C₄₄.₄₆D₄	3^rd non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	88	4+	C44.46D4	352,29
C₁₁⋊D₁₆	The semidirect product of C₁₁ and D₁₆ acting via D₁₆/D₈=C₂	176	4+	C11:D16	352,32
C₈.₆D₂₂	3^rd non-split extension by C₈ of D₂₂ acting via D₂₂/D₁₁=C₂	176	4+	C8.6D22	352,34
C₈⋊D₂₂	1^st semidirect product of C₈ and D₂₂ acting via D₂₂/C₁₁=C₂²	88	4+	C8:D22	352,103
D₈×D₁₁	Direct product of D₈ and D₁₁	88	4+	D8xD11	352,105
D₈₈⋊C₂	6^th semidirect product of D₈₈ and C₂ acting faithfully	88	4+	D88:C2	352,109
D₈₈⋊₅C₂	5^th semidirect product of D₈₈ and C₂ acting faithfully	176	4+	D88:5C2	352,114
Q₈⋊D₂₂	2^nd semidirect product of Q₈ and D₂₂ acting via D₂₂/C₂₂=C₂	88	4+	Q8:D22	352,144
D₄⋊₈D₂₂	4^th semidirect product of D₄ and D₂₂ acting through Inn(D₄)	88	4+	D4:8D22	352,184

Groups of order 356

		d	ρ	Label	ID
C₈₉⋊C₄	The semidirect product of C₈₉ and C₄ acting faithfully	89	4+	C89:C4	356,3

Groups of order 360

		d	ρ	Label	ID
D₉₀.C₂	The non-split extension by D₉₀ of C₂ acting faithfully	180	4+	D90.C2	360,9
C₅⋊D₃₆	The semidirect product of C₅ and D₃₆ acting via D₃₆/D₁₈=C₂	180	4+	C5:D36	360,10
C₉⋊D₂₀	The semidirect product of C₉ and D₂₀ acting via D₂₀/D₁₀=C₂	180	4+	C9:D20	360,13
C₂×D₅×D₉	Direct product of C₂, D₅ and D₉	90	4+	C2xD5xD9	360,45
C₆.D₃₀	3^rd non-split extension by C₆ of D₃₀ acting via D₃₀/D₁₅=C₂	60	4+	C6.D30	360,79
C₃⋊D₆₀	The semidirect product of C₃ and D₆₀ acting via D₆₀/D₃₀=C₂	60	4+	C3:D60	360,81
D₆⋊₂D₁₅	2^nd semidirect product of D₆ and D₁₅ acting via D₁₅/C₁₅=C₂	60	4+	D6:2D15	360,82
C₂×C₃²⋊F₅	Direct product of C₂ and C₃²⋊F₅	60	4+	C2xC3^2:F5	360,150
C₂×S₃×D₁₅	Direct product of C₂, S₃ and D₁₅	60	4+	C2xS3xD15	360,154

Groups of order 364

		d	ρ	Label	ID
D₇×D₁₃	Direct product of D₇ and D₁₃	91	4+	D7xD13	364,7

Groups of order 368

		d	ρ	Label	ID
D₄⋊D₂₃	The semidirect product of D₄ and D₂₃ acting via D₂₃/C₂₃=C₂	184	4+	D4:D23	368,14
Q₈⋊D₂₃	The semidirect product of Q₈ and D₂₃ acting via D₂₃/C₂₃=C₂	184	4+	Q8:D23	368,16
D₄×D₂₃	Direct product of D₄ and D₂₃	92	4+	D4xD23	368,31
D₉₂⋊C₂	4^th semidirect product of D₉₂ and C₂ acting faithfully	184	4+	D92:C2	368,34

Groups of order 372

		d	ρ	Label	ID
S₃×D₃₁	Direct product of S₃ and D₃₁	93	4+	S3xD31	372,8

Groups of order 380

		d	ρ	Label	ID
D₅×D₁₉	Direct product of D₅ and D₁₉	95	4+	D5xD19	380,7

Groups of order 388

		d	ρ	Label	ID
C₉₇⋊C₄	The semidirect product of C₉₇ and C₄ acting faithfully	97	4+	C97:C4	388,3

Groups of order 392

		d	ρ	Label	ID
Dic₇⋊₂D₇	The semidirect product of Dic₇ and D₇ acting through Inn(Dic₇)	28	4+	Dic7:2D7	392,19
C₇⋊D₂₈	The semidirect product of C₇ and D₂₈ acting via D₂₈/D₁₄=C₂	28	4+	C7:D28	392,21
D₇≀C₂	Wreath product of D₇ by C₂	14	4+	D7wrC2	392,37
C₂×C₇²⋊C₄	Direct product of C₂ and C₇²⋊C₄	28	4+	C2xC7^2:C4	392,40
C₂×D₇²	Direct product of C₂, D₇ and D₇	28	4+	C2xD7^2	392,41

Groups of order 396

		d	ρ	Label	ID
D₉×D₁₁	Direct product of D₉ and D₁₁	99	4+	D9xD11	396,5
S₃×D₃₃	Direct product of S₃ and D₃₃	66	4+	S3xD33	396,22

Groups of order 400

		d	ρ	Label	ID
D₄⋊D₂₅	The semidirect product of D₄ and D₂₅ acting via D₂₅/C₂₅=C₂	200	4+	D4:D25	400,16
Q₈⋊D₂₅	The semidirect product of Q₈ and D₂₅ acting via D₂₅/C₂₅=C₂	200	4+	Q8:D25	400,18
D₂₅.D₄	The non-split extension by D₂₅ of D₄ acting via D₄/C₂²=C₂	100	4+	D25.D4	400,34
D₄×D₂₅	Direct product of D₄ and D₂₅	100	4+	D4xD25	400,39
Q₈⋊₂D₂₅	The semidirect product of Q₈ and D₂₅ acting through Inn(Q₈)	200	4+	Q8:2D25	400,42
C₅⋊D₄₀	The semidirect product of C₅ and D₄₀ acting via D₄₀/D₂₀=C₂	40	4+	C5:D40	400,65
C₅²⋊₄SD₁₆	3^rd semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₄=C₂²	40	4+	C5^2:4SD16	400,68
D₅²⋊C₄	1^st semidirect product of D₅² and C₄ acting via C₄/C₂=C₂	20	4+	D5^2:C4	400,129
C₁₀²⋊₄C₄	4^th semidirect product of C₁₀² and C₄ acting faithfully	20	4+	C10^2:4C4	400,162
Dic₁₀⋊₅D₅	The semidirect product of Dic₁₀ and D₅ acting through Inn(Dic₁₀)	40	4+	Dic10:5D5	400,168
D₅×D₂₀	Direct product of D₅ and D₂₀	40	4+	D5xD20	400,170
D₁₀⋊D₁₀	3^rd semidirect product of D₁₀ and D₁₀ acting via D₁₀/D₅=C₂	20	4+	D10:D10	400,180
C₂×D₅≀C₂	Direct product of C₂ and D₅≀C₂	20	4+	C2xD5wrC2	400,211

Groups of order 404

		d	ρ	Label	ID
C₁₀₁⋊C₄	The semidirect product of C₁₀₁ and C₄ acting faithfully	101	4+	C101:C4	404,3

Groups of order 408

		d	ρ	Label	ID
D₅₁⋊₂C₄	The semidirect product of D₅₁ and C₄ acting via C₄/C₂=C₂	204	4+	D51:2C4	408,9
C₃⋊D₆₈	The semidirect product of C₃ and D₆₈ acting via D₆₈/D₃₄=C₂	204	4+	C3:D68	408,11
C₁₇⋊D₁₂	The semidirect product of C₁₇ and D₁₂ acting via D₁₂/D₆=C₂	204	4+	C17:D12	408,12
C₂×S₃×D₁₇	Direct product of C₂, S₃ and D₁₇	102	4+	C2xS3xD17	408,41

Groups of order 416

		d	ρ	Label	ID
C₅₂.₄₆D₄	3^rd non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	104	4+	C52.46D4	416,30
C₁₃⋊D₁₆	The semidirect product of C₁₃ and D₁₆ acting via D₁₆/D₈=C₂	208	4+	C13:D16	416,33
C₈.₆D₂₆	3^rd non-split extension by C₈ of D₂₆ acting via D₂₆/D₁₃=C₂	208	4+	C8.6D26	416,35
D₂₆.D₄	1^st non-split extension by D₂₆ of D₄ acting via D₄/C₂=C₂²	104	4+	D26.D4	416,74
C₈⋊D₂₆	1^st semidirect product of C₈ and D₂₆ acting via D₂₆/C₁₃=C₂²	104	4+	C8:D26	416,129
D₈×D₁₃	Direct product of D₈ and D₁₃	104	4+	D8xD13	416,131
Q₈⋊D₂₆	2^nd semidirect product of Q₈ and D₂₆ acting via D₂₆/D₁₃=C₂	104	4+	Q8:D26	416,135
D₁₀₄⋊C₂	5^th semidirect product of D₁₀₄ and C₂ acting faithfully	208	4+	D104:C2	416,140
D₄⋊D₂₆	2^nd semidirect product of D₄ and D₂₆ acting via D₂₆/C₂₆=C₂	104	4+	D4:D26	416,170
D₄⋊₈D₂₆	4^th semidirect product of D₄ and D₂₆ acting through Inn(D₄)	104	4+	D4:8D26	416,223

Groups of order 420

		d	ρ	Label	ID
D₇×D₁₅	Direct product of D₇ and D₁₅	105	4+	D7xD15	420,26
D₅×D₂₁	Direct product of D₅ and D₂₁	105	4+	D5xD21	420,28
S₃×D₃₅	Direct product of S₃ and D₃₅	105	4+	S3xD35	420,29

Groups of order 424

		d	ρ	Label	ID
C₂×C₅₃⋊C₄	Direct product of C₂ and C₅₃⋊C₄	106	4+	C2xC53:C4	424,12

Groups of order 432

		d	ρ	Label	ID
D₄⋊D₂₇	The semidirect product of D₄ and D₂₇ acting via D₂₇/C₂₇=C₂	216	4+	D4:D27	432,16
Q₈⋊₂D₂₇	The semidirect product of Q₈ and D₂₇ acting via D₂₇/C₂₇=C₂	216	4+	Q8:2D27	432,18
Q₈⋊D₂₇	The semidirect product of Q₈ and D₂₇ acting via D₂₇/C₉=S₃	216	4+	Q8:D27	432,38
D₄×D₂₇	Direct product of D₄ and D₂₇	108	4+	D4xD27	432,47
Q₈⋊₃D₂₇	The semidirect product of Q₈ and D₂₇ acting through Inn(Q₈)	216	4+	Q8:3D27	432,50
C₆.D₃₆	2^nd non-split extension by C₆ of D₃₆ acting via D₃₆/D₁₈=C₂	72	4+	C6.D36	432,63
C₃⋊D₇₂	The semidirect product of C₃ and D₇₂ acting via D₇₂/D₃₆=C₂	72	4+	C3:D72	432,64
C₉⋊D₂₄	The semidirect product of C₉ and D₂₄ acting via D₂₄/D₁₂=C₂	72	4+	C9:D24	432,69
C₁₈.D₁₂	3^rd non-split extension by C₁₈ of D₁₂ acting via D₁₂/D₆=C₂	72	4+	C18.D12	432,73
C₁₈.₆S₄	6^th non-split extension by C₁₈ of S₄ acting via S₄/A₄=C₂	72	4+	C18.6S4	432,253
Dic₉.₂A₄	The non-split extension by Dic₉ of A₄ acting through Inn(Dic₉)	144	4+	Dic9.2A4	432,262
Dic₆⋊₅D₉	The semidirect product of Dic₆ and D₉ acting through Inn(Dic₆)	72	4+	Dic6:5D9	432,282
Dic₉.D₆	4^th non-split extension by Dic₉ of D₆ acting via D₆/S₃=C₂	72	4+	Dic9.D6	432,289
S₃×D₃₆	Direct product of S₃ and D₃₆	72	4+	S3xD36	432,291
D₉×D₁₂	Direct product of D₉ and D₁₂	72	4+	D9xD12	432,292
D₁₈⋊D₆	4^th semidirect product of D₁₈ and D₆ acting via D₆/S₃=C₂	36	4+	D18:D6	432,315

Groups of order 436

		d	ρ	Label	ID
C₁₀₉⋊C₄	The semidirect product of C₁₀₉ and C₄ acting faithfully	109	4+	C109:C4	436,3

Groups of order 440

		d	ρ	Label	ID
D₅₅⋊₂C₄	The semidirect product of D₅₅ and C₄ acting via C₄/C₂=C₂	220	4+	D55:2C4	440,19
C₅⋊D₄₄	The semidirect product of C₅ and D₄₄ acting via D₄₄/D₂₂=C₂	220	4+	C5:D44	440,21
C₁₁⋊D₂₀	The semidirect product of C₁₁ and D₂₀ acting via D₂₀/D₁₀=C₂	220	4+	C11:D20	440,22
C₂×D₅×D₁₁	Direct product of C₂, D₅ and D₁₁	110	4+	C2xD5xD11	440,47

Groups of order 444

		d	ρ	Label	ID
S₃×D₃₇	Direct product of S₃ and D₃₇	111	4+	S3xD37	444,11

Groups of order 448

		d	ρ	Label	ID
D₅₆.C₄	4^th non-split extension by D₅₆ of C₄ acting via C₄/C₂=C₂	112	4+	D56.C4	448,52
C₂₈.₃D₈	3^rd non-split extension by C₂₈ of D₈ acting via D₈/C₄=C₂²	112	4+	C28.3D8	448,73
C₇⋊D₃₂	The semidirect product of C₇ and D₃₂ acting via D₃₂/D₁₆=C₂	224	4+	C7:D32	448,76
C₇⋊SD₆₄	The semidirect product of C₇ and SD₆₄ acting via SD₆₄/Q₃₂=C₂	224	4+	C7:SD64	448,78
D₄⋊₄D₂₈	3^rd semidirect product of D₄ and D₂₈ acting via D₂₈/D₁₄=C₂	56	4+	D4:4D28	448,356
C₈.₂₁D₂₈	7^th non-split extension by C₈ of D₂₈ acting via D₂₈/D₁₄=C₂	112	4+	C8.21D28	448,431
C₁₆⋊D₁₄	1^st semidirect product of C₁₆ and D₁₄ acting via D₁₄/C₇=C₂²	112	4+	C16:D14	448,442
D₇×D₁₆	Direct product of D₇ and D₁₆	112	4+	D7xD16	448,444
D₁₁₂⋊C₂	6^th semidirect product of D₁₁₂ and C₂ acting faithfully	112	4+	D112:C2	448,448
Q₃₂⋊₃D₇	The semidirect product of Q₃₂ and D₇ acting through Inn(Q₃₂)	224	4+	Q32:3D7	448,453
D₄.₄D₂₈	4^th non-split extension by D₄ of D₂₈ acting via D₂₈/C₂₈=C₂	112	4+	D4.4D28	448,676
Q₁₆⋊D₁₄	2^nd semidirect product of Q₁₆ and D₁₄ acting via D₁₄/C₁₄=C₂	112	4+	Q16:D14	448,727
D₄.₁₂D₂₈	2^nd non-split extension by D₄ of D₂₈ acting through Inn(D₄)	112	4+	D4.12D28	448,1205
D₈⋊₁₅D₁₄	4^th semidirect product of D₈ and D₁₄ acting through Inn(D₈)	112	4+	D8:15D14	448,1222

Groups of order 452

		d	ρ	Label	ID
C₁₁₃⋊C₄	The semidirect product of C₁₁₃ and C₄ acting faithfully	113	4+	C113:C4	452,3

Groups of order 456

		d	ρ	Label	ID
D₅₇⋊C₄	The semidirect product of D₅₇ and C₄ acting via C₄/C₂=C₂	228	4+	D57:C4	456,14
C₃⋊D₇₆	The semidirect product of C₃ and D₇₆ acting via D₇₆/D₃₈=C₂	228	4+	C3:D76	456,16
C₁₉⋊D₁₂	The semidirect product of C₁₉ and D₁₂ acting via D₁₂/D₆=C₂	228	4+	C19:D12	456,17
C₂×S₃×D₁₉	Direct product of C₂, S₃ and D₁₉	114	4+	C2xS3xD19	456,47

Groups of order 460

		d	ρ	Label	ID
D₅×D₂₃	Direct product of D₅ and D₂₃	115	4+	D5xD23	460,7

Groups of order 464

		d	ρ	Label	ID
D₄⋊D₂₉	The semidirect product of D₄ and D₂₉ acting via D₂₉/C₂₉=C₂	232	4+	D4:D29	464,15
Q₈⋊D₂₉	The semidirect product of Q₈ and D₂₉ acting via D₂₉/C₂₉=C₂	232	4+	Q8:D29	464,17
D₂₉.D₄	The non-split extension by D₂₉ of D₄ acting via D₄/C₂²=C₂	116	4+	D29.D4	464,34
D₄×D₂₉	Direct product of D₄ and D₂₉	116	4+	D4xD29	464,39
Q₈⋊₂D₂₉	The semidirect product of Q₈ and D₂₉ acting through Inn(Q₈)	232	4+	Q8:2D29	464,42

Groups of order 468

		d	ρ	Label	ID
D₉×D₁₃	Direct product of D₉ and D₁₃	117	4+	D9xD13	468,11
(C₃×C₃₉)⋊C₄	1^st semidirect product of C₃×C₃₉ and C₄ acting faithfully	78	4+	(C3xC39):C4	468,41
S₃×D₃₉	Direct product of S₃ and D₃₉	78	4+	S3xD39	468,45

Groups of order 476

		d	ρ	Label	ID
D₇×D₁₇	Direct product of D₇ and D₁₇	119	4+	D7xD17	476,7

Groups of order 480

		d	ρ	Label	ID
C₃⋊D₈₀	The semidirect product of C₃ and D₈₀ acting via D₈₀/D₄₀=C₂	240	4+	C3:D80	480,14
C₅⋊D₄₈	The semidirect product of C₅ and D₄₈ acting via D₄₈/D₂₄=C₂	240	4+	C5:D48	480,15
C₂₄.D₁₀	9^th non-split extension by C₂₄ of D₁₀ acting via D₁₀/C₅=C₂²	240	4+	C24.D10	480,19
Dic₁₂⋊D₅	1^st semidirect product of Dic₁₂ and D₅ acting via D₅/C₅=C₂	240	4+	Dic12:D5	480,21
C₆₀.₂₉D₄	29^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4+	C60.29D4	480,36
M₄(2)⋊D₁₅	3^rd semidirect product of M₄(2) and D₁₅ acting via D₁₅/C₁₅=C₂	120	4+	M4(2):D15	480,183
C₁₅⋊₇D₁₆	1^st semidirect product of C₁₅ and D₁₆ acting via D₁₆/D₈=C₂	240	4+	C15:7D16	480,186
C₈.₆D₃₀	3^rd non-split extension by C₈ of D₃₀ acting via D₃₀/D₁₅=C₂	240	4+	C8.6D30	480,188
D₅×D₂₄	Direct product of D₅ and D₂₄	120	4+	D5xD24	480,324
C₂₄⋊D₁₀	1^st semidirect product of C₂₄ and D₁₀ acting via D₁₀/C₅=C₂²	120	4+	C24:D10	480,325
S₃×D₄₀	Direct product of S₃ and D₄₀	120	4+	S3xD40	480,328
C₄₀⋊₁D₆	1^st semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4+	C40:1D6	480,329
D₁₂₀⋊C₂	12^nd semidirect product of D₁₂₀ and C₂ acting faithfully	240	4+	D120:C2	480,347
D₁₂₀⋊₅C₂	5^th semidirect product of D₁₂₀ and C₂ acting faithfully	240	4+	D120:5C2	480,351
D₂₀⋊₁₉D₆	2^nd semidirect product of D₂₀ and D₆ acting via D₆/C₆=C₂	120	4+	D20:19D6	480,377
C₆₀.₃₈D₄	38^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4+	C60.38D4	480,381
C₈⋊D₃₀	1^st semidirect product of C₈ and D₃₀ acting via D₃₀/C₁₅=C₂²	120	4+	C8:D30	480,873
D₈×D₁₅	Direct product of D₈ and D₁₅	120	4+	D8xD15	480,875
Q₈⋊₃D₃₀	2^nd semidirect product of Q₈ and D₃₀ acting via D₃₀/D₁₅=C₂	120	4+	Q8:3D30	480,879
D₁₂₀⋊₈C₂	8^th semidirect product of D₁₂₀ and C₂ acting faithfully	240	4+	D120:8C2	480,884
D₄⋊D₃₀	2^nd semidirect product of D₄ and D₃₀ acting via D₃₀/C₃₀=C₂	120	4+	D4:D30	480,914
Q₈.A₅	The non-split extension by Q₈ of A₅ acting through Inn(Q₈)	48	4+	Q8.A5	480,959
Dic₅.₇S₄	2^nd non-split extension by Dic₅ of S₄ acting through Inn(Dic₅)	80	4+	Dic5.7S4	480,969
GL₂(𝔽₃)⋊D₅	1^st semidirect product of GL₂(𝔽₃) and D₅ acting via D₅/C₅=C₂	80	4+	GL(2,3):D5	480,970
C₂₀.₃S₄	3^rd non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	80	4+	C20.3S4	480,1032
Dic₁₀.A₄	The non-split extension by Dic₁₀ of A₄ acting through Inn(Dic₁₀)	120	4+	Dic10.A4	480,1041
D₂₀⋊₂₉D₆	3^rd semidirect product of D₂₀ and D₆ acting through Inn(D₂₀)	120	4+	D20:29D6	480,1095
D₄⋊₈D₃₀	4^th semidirect product of D₄ and D₃₀ acting through Inn(D₄)	120	4+	D4:8D30	480,1176

Groups of order 484

		d	ρ	Label	ID
C₁₁²⋊C₄	The semidirect product of C₁₁² and C₄ acting faithfully	22	4+	C11^2:C4	484,8
D₁₁²	Direct product of D₁₁ and D₁₁	22	4+	D11^2	484,9

Groups of order 488

		d	ρ	Label	ID
C₂×C₆₁⋊C₄	Direct product of C₂ and C₆₁⋊C₄	122	4+	C2xC61:C4	488,12

Groups of order 492

		d	ρ	Label	ID
S₃×D₄₁	Direct product of S₃ and D₄₁	123	4+	S3xD41	492,7

Groups of order 496

		d	ρ	Label	ID
D₄⋊D₃₁	The semidirect product of D₄ and D₃₁ acting via D₃₁/C₃₁=C₂	248	4+	D4:D31	496,14
Q₈⋊D₃₁	The semidirect product of Q₈ and D₃₁ acting via D₃₁/C₃₁=C₂	248	4+	Q8:D31	496,16
D₄×D₃₁	Direct product of D₄ and D₃₁	124	4+	D4xD31	496,31
Q₈⋊₂D₃₁	The semidirect product of Q₈ and D₃₁ acting through Inn(Q₈)	248	4+	Q8:2D31	496,34

Groups of order 500

		d	ρ	Label	ID
C₁₂₅⋊C₄	The semidirect product of C₁₂₅ and C₄ acting faithfully	125	4+	C125:C4	500,3
C₂₅⋊₂F₅	2^nd semidirect product of C₂₅ and F₅ acting via F₅/C₅=C₄	50	4+	C25:2F5	500,24
D₅×D₂₅	Direct product of D₅ and D₂₅	50	4+	D5xD25	500,26

Symplectic of dimension 4 (ρ=4-)

Groups of order 32

		d	ρ	Label	ID
C₄.₁₀D₄	2^nd non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	16	4-	C4.10D4	32,8
C₈.C₂²	The non-split extension by C₈ of C₂² acting faithfully	16	4-	C8.C2^2	32,44
2_-¹⁺⁴	Gamma matrices = Extraspecial group; = D₄ ○Q₈	16	4-	ES-(2,2)	32,50

Groups of order 40

		d	ρ	Label	ID
C₅⋊C₈	The semidirect product of C₅ and C₈ acting via C₈/C₂=C₄	40	4-	C5:C8	40,3

Groups of order 48

		d	ρ	Label	ID
D₄.S₃	The non-split extension by D₄ of S₃ acting via S₃/C₃=C₂	24	4-	D4.S3	48,16
C₃⋊Q₁₆	The semidirect product of C₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	48	4-	C3:Q16	48,18
D₄⋊₂S₃	The semidirect product of D₄ and S₃ acting through Inn(D₄)	24	4-	D4:2S3	48,39
S₃×Q₈	Direct product of S₃ and Q₈	24	4-	S3xQ8	48,40

Groups of order 64

		d	ρ	Label	ID
C₄².₃C₄	3^rd non-split extension by C₄² of C₄ acting faithfully	16	4-	C4^2.3C4	64,37
C₈.₁₇D₄	4^th non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	32	4-	C8.17D4	64,43
D₄.₁₀D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	16	4-	D4.10D4	64,137
D₄.₅D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	32	4-	D4.5D4	64,154
Q₃₂⋊C₂	2^nd semidirect product of Q₃₂ and C₂ acting faithfully	32	4-	Q32:C2	64,191
Q₈○D₈	Central product of Q₈ and D₈	32	4-	Q8oD8	64,259

Groups of order 72

		d	ρ	Label	ID
C₃²⋊₂C₈	The semidirect product of C₃² and C₈ acting via C₈/C₂=C₄	24	4-	C3^2:2C8	72,19
S₃×Dic₃	Direct product of S₃ and Dic₃	24	4-	S3xDic3	72,20
D₆⋊S₃	1^st semidirect product of D₆ and S₃ acting via S₃/C₃=C₂	24	4-	D6:S3	72,22
C₃²⋊₂Q₈	The semidirect product of C₃² and Q₈ acting via Q₈/C₂=C₂²	24	4-	C3^2:2Q8	72,24

Groups of order 80

		d	ρ	Label	ID
D₄.D₅	The non-split extension by D₄ of D₅ acting via D₅/C₅=C₂	40	4-	D4.D5	80,16
C₅⋊Q₁₆	The semidirect product of C₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	80	4-	C5:Q16	80,18
C₂².F₅	The non-split extension by C₂² of F₅ acting via F₅/D₅=C₂	40	4-	C2^2.F5	80,33
D₄⋊₂D₅	The semidirect product of D₄ and D₅ acting through Inn(D₄)	40	4-	D4:2D5	80,40
Q₈×D₅	Direct product of Q₈ and D₅	40	4-	Q8xD5	80,41

Groups of order 96

		d	ρ	Label	ID
C₁₂.₄₇D₄	4^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48	4-	C12.47D4	96,31
D₈.S₃	The non-split extension by D₈ of S₃ acting via S₃/C₃=C₂	48	4-	D8.S3	96,34
C₃⋊Q₃₂	The semidirect product of C₃ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	96	4-	C3:Q32	96,36
C₈.D₆	1^st non-split extension by C₈ of D₆ acting via D₆/C₃=C₂²	48	4-	C8.D6	96,116
D₈⋊₃S₃	The semidirect product of D₈ and S₃ acting through Inn(D₈)	48	4-	D8:3S3	96,119
D₄.D₆	4^th non-split extension by D₄ of D₆ acting via D₆/S₃=C₂	48	4-	D4.D6	96,122
S₃×Q₁₆	Direct product of S₃ and Q₁₆	48	4-	S3xQ16	96,124
Q₈.₁₄D₆	4^th non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4-	Q8.14D6	96,158
Q₈.D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/C₂=S₃	16	4-	Q8.D6	96,190
C₄.S₄	2^nd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	32	4-	C4.S4	96,191
D₄.A₄	The non-split extension by D₄ of A₄ acting through Inn(D₄)	16	4-	D4.A4	96,202
Q₈○D₁₂	Central product of Q₈ and D₁₂	48	4-	Q8oD12	96,217

Groups of order 104

		d	ρ	Label	ID
C₁₃⋊C₈	The semidirect product of C₁₃ and C₈ acting via C₈/C₂=C₄	104	4-	C13:C8	104,3

Groups of order 112

		d	ρ	Label	ID
D₄.D₇	The non-split extension by D₄ of D₇ acting via D₇/C₇=C₂	56	4-	D4.D7	112,15
C₇⋊Q₁₆	The semidirect product of C₇ and Q₁₆ acting via Q₁₆/Q₈=C₂	112	4-	C7:Q16	112,17
D₄⋊₂D₇	The semidirect product of D₄ and D₇ acting through Inn(D₄)	56	4-	D4:2D7	112,32
Q₈×D₇	Direct product of Q₈ and D₇	56	4-	Q8xD7	112,33

Groups of order 120

		d	ρ	Label	ID
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
C₁₅⋊D₄	1^st semidirect product of C₁₅ and D₄ acting via D₄/C₂=C₂²	60	4-	C15:D4	120,11
C₁₅⋊Q₈	The semidirect product of C₁₅ and Q₈ acting via Q₈/C₂=C₂²	120	4-	C15:Q8	120,14

Groups of order 128

		d	ρ	Label	ID
C₈.₂₅D₈	2^nd non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	32	4-	C8.25D8	128,90
C₄².₄D₄	4^th non-split extension by C₄² of D₄ acting faithfully	16	4-	C4^2.4D4	128,137
(C₂×Q₈).D₄	6^th non-split extension by C₂×Q₈ of D₄ acting faithfully	32	4-	(C2xQ8).D4	128,143
C₁₆.₁₈D₄	4^th non-split extension by C₁₆ of D₄ acting via D₄/C₂²=C₂	64	4-	C16.18D4	128,152
D₈.₁₂D₄	4^th non-split extension by D₈ of D₄ acting via D₄/C₂²=C₂	64	4-	D8.12D4	128,927
Q₈≀C₂	Wreath product of Q₈ by C₂	16	4-	Q8wrC2	128,937
C₈.₅D₈	5^th non-split extension by C₈ of D₈ acting via D₈/C₄=C₂²	32	4-	C8.5D8	128,946
D₄.₄D₈	4^th non-split extension by D₄ of D₈ acting via D₈/C₈=C₂	64	4-	D4.4D8	128,954
Q₆₄⋊C₂	2^nd semidirect product of Q₆₄ and C₂ acting faithfully	64	4-	Q64:C2	128,996
D₈○Q₁₆	Central product of D₈ and Q₁₆	32	4-	D8oQ16	128,2025
Q₈○D₁₆	Central product of Q₈ and D₁₆	64	4-	Q8oD16	128,2149

Groups of order 136

		d	ρ	Label	ID
C₁₇⋊₂C₈	The semidirect product of C₁₇ and C₈ acting via C₈/C₂=C₄	136	4-	C17:2C8	136,3

Groups of order 144

		d	ρ	Label	ID
D₄.D₉	The non-split extension by D₄ of D₉ acting via D₉/C₉=C₂	72	4-	D4.D9	144,15
C₉⋊Q₁₆	The semidirect product of C₉ and Q₁₆ acting via Q₁₆/Q₈=C₂	144	4-	C9:Q16	144,17
Q₈.D₉	The non-split extension by Q₈ of D₉ acting via D₉/C₃=S₃	144	4-	Q8.D9	144,31
D₄⋊₂D₉	The semidirect product of D₄ and D₉ acting through Inn(D₄)	72	4-	D4:2D9	144,42
Q₈×D₉	Direct product of Q₈ and D₉	72	4-	Q8xD9	144,43
D₁₂.S₃	1^st non-split extension by D₁₂ of S₃ acting via S₃/C₃=C₂	48	4-	D12.S3	144,59
C₃²⋊₃Q₁₆	2^nd semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4-	C3^2:3Q16	144,62
C₃²⋊₂SD₁₆	The semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₂=D₄	24	4-	C3^2:2SD16	144,118
C₃²⋊Q₁₆	The semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₂=D₄	48	4-	C3^2:Q16	144,119
C₆.₅S₄	5^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	48	4-	C6.5S4	144,124
S₃×SL₂(𝔽₃)	Direct product of S₃ and SL₂(𝔽₃); = SL₂(ℤ/6ℤ)	24	4-	S3xSL(2,3)	144,128
C₆².C₄	2^nd non-split extension by C₆² of C₄ acting faithfully	24	4-	C6^2.C4	144,135
S₃×Dic₆	Direct product of S₃ and Dic₆	48	4-	S3xDic6	144,137
D₁₂⋊₅S₃	The semidirect product of D₁₂ and S₃ acting through Inn(D₁₂)	48	4-	D12:5S3	144,138
D₆.₄D₆	4^th non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	24	4-	D6.4D6	144,148

Groups of order 160

		d	ρ	Label	ID
C₄.₁₂D₂₀	4^th non-split extension by C₄ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4-	C4.12D20	160,31
D₈.D₅	The non-split extension by D₈ of D₅ acting via D₅/C₅=C₂	80	4-	D8.D5	160,34
C₅⋊Q₃₂	The semidirect product of C₅ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	160	4-	C5:Q32	160,36
Dic₅.D₄	1^st non-split extension by Dic₅ of D₄ acting via D₄/C₂=C₂²	80	4-	Dic5.D4	160,80
C₈.D₁₀	1^st non-split extension by C₈ of D₁₀ acting via D₁₀/C₅=C₂²	80	4-	C8.D10	160,130
D₈⋊₃D₅	The semidirect product of D₈ and D₅ acting through Inn(D₈)	80	4-	D8:3D5	160,133
SD₁₆⋊D₅	2^nd semidirect product of SD₁₆ and D₅ acting via D₅/C₅=C₂	80	4-	SD16:D5	160,136
D₅×Q₁₆	Direct product of D₅ and Q₁₆	80	4-	D5xQ16	160,138
D₄.₉D₁₀	4^th non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	80	4-	D4.9D10	160,172
2_-¹⁺⁴⋊C₅	The semidirect product of 2_-¹⁺⁴ and C₅ acting faithfully	32	4-	ES-(2,2):C5	160,199
D₄.₁₀D₁₀	The non-split extension by D₄ of D₁₀ acting through Inn(D₄)	80	4-	D4.10D10	160,225

Groups of order 168

		d	ρ	Label	ID
Dic₃×D₇	Direct product of Dic₃ and D₇	84	4-	Dic3xD7	168,12
S₃×Dic₇	Direct product of S₃ and Dic₇	84	4-	S3xDic7	168,13
C₂₁⋊D₄	1^st semidirect product of C₂₁ and D₄ acting via D₄/C₂=C₂²	84	4-	C21:D4	168,15
C₂₁⋊Q₈	The semidirect product of C₂₁ and Q₈ acting via Q₈/C₂=C₂²	168	4-	C21:Q8	168,18

Groups of order 176

		d	ρ	Label	ID
D₄.D₁₁	The non-split extension by D₄ of D₁₁ acting via D₁₁/C₁₁=C₂	88	4-	D4.D11	176,15
C₁₁⋊Q₁₆	The semidirect product of C₁₁ and Q₁₆ acting via Q₁₆/Q₈=C₂	176	4-	C11:Q16	176,17
D₄⋊₂D₁₁	The semidirect product of D₄ and D₁₁ acting through Inn(D₄)	88	4-	D4:2D11	176,32
Q₈×D₁₁	Direct product of Q₈ and D₁₁	88	4-	Q8xD11	176,33

Groups of order 192

		d	ρ	Label	ID
C₂₄.₈D₄	8^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	96	4-	C24.8D4	192,55
C₁₂.₄D₈	4^th non-split extension by C₁₂ of D₈ acting via D₈/C₄=C₂²	96	4-	C12.4D8	192,76
D₁₆.S₃	The non-split extension by D₁₆ of S₃ acting via S₃/C₃=C₂	96	4-	D16.S3	192,79
C₃⋊Q₆₄	The semidirect product of C₃ and Q₆₄ acting via Q₆₄/Q₃₂=C₂	192	4-	C3:Q64	192,81
Q₈.₁₄D₁₂	4^th non-split extension by Q₈ of D₁₂ acting via D₁₂/D₆=C₂	48	4-	Q8.14D12	192,385
C₂₄.₁₈D₄	18^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	96	4-	C24.18D4	192,455
C₁₆.D₆	1^st non-split extension by C₁₆ of D₆ acting via D₆/C₃=C₂²	96	4-	C16.D6	192,468
D₁₆⋊₃S₃	The semidirect product of D₁₆ and S₃ acting through Inn(D₁₆)	96	4-	D16:3S3	192,471
SD₃₂⋊S₃	2^nd semidirect product of SD₃₂ and S₃ acting via S₃/C₃=C₂	96	4-	SD32:S3	192,474
S₃×Q₃₂	Direct product of S₃ and Q₃₂	96	4-	S3xQ32	192,476
Q₈.₁₀D₁₂	5^th non-split extension by Q₈ of D₁₂ acting via D₁₂/C₁₂=C₂	96	4-	Q8.10D12	192,702
D₈.₉D₆	4^th non-split extension by D₈ of D₆ acting via D₆/C₆=C₂	96	4-	D8.9D6	192,754
C₈.S₄	2^nd non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	64	4-	C8.S4	192,962
D₄.S₄	2^nd non-split extension by D₄ of S₄ acting via S₄/A₄=C₂	32	4-	D4.S4	192,989
D₈.A₄	The non-split extension by D₈ of A₄ acting through Inn(D₈)	32	4-	D8.A4	192,1019
D₄.₁₃D₁₂	3^rd non-split extension by D₄ of D₁₂ acting through Inn(D₄)	96	4-	D4.13D12	192,1312
D₈.₁₀D₆	The non-split extension by D₈ of D₆ acting through Inn(D₈)	96	4-	D8.10D6	192,1330
D₄.₅S₄	2^nd non-split extension by D₄ of S₄ acting through Inn(D₄)	32	4-	D4.5S4	192,1486

Groups of order 200

		d	ρ	Label	ID
C₂₅⋊C₈	The semidirect product of C₂₅ and C₈ acting via C₈/C₂=C₄	200	4-	C25:C8	200,3
C₅²⋊₅C₈	4^th semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4-	C5^2:5C8	200,21
D₅×Dic₅	Direct product of D₅ and Dic₅	40	4-	D5xDic5	200,22
C₅²⋊₂D₄	1^st semidirect product of C₅² and D₄ acting via D₄/C₂=C₂²	40	4-	C5^2:2D4	200,24
C₅²⋊₂Q₈	The semidirect product of C₅² and Q₈ acting via Q₈/C₂=C₂²	40	4-	C5^2:2Q8	200,26

Groups of order 208

		d	ρ	Label	ID
D₄.D₁₃	The non-split extension by D₄ of D₁₃ acting via D₁₃/C₁₃=C₂	104	4-	D4.D13	208,16
C₁₃⋊Q₁₆	The semidirect product of C₁₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	208	4-	C13:Q16	208,18
C₁₃⋊M₄(2)	The semidirect product of C₁₃ and M₄(2) acting via M₄(2)/C₂²=C₄	104	4-	C13:M4(2)	208,33
D₄⋊₂D₁₃	The semidirect product of D₄ and D₁₃ acting through Inn(D₄)	104	4-	D4:2D13	208,40
Q₈×D₁₃	Direct product of Q₈ and D₁₃	104	4-	Q8xD13	208,41

Groups of order 216

		d	ρ	Label	ID
C₉⋊Dic₆	The semidirect product of C₉ and Dic₆ acting via Dic₆/Dic₃=C₂	72	4-	C9:Dic6	216,26
Dic₃×D₉	Direct product of Dic₃ and D₉	72	4-	Dic3xD9	216,27
S₃×Dic₉	Direct product of S₃ and Dic₉	72	4-	S3xDic9	216,30
D₆⋊D₉	1^st semidirect product of D₆ and D₉ acting via D₉/C₉=C₂	72	4-	D6:D9	216,31

Groups of order 224

		d	ρ	Label	ID
C₄.₁₂D₂₈	4^th non-split extension by C₄ of D₂₈ acting via D₂₈/D₁₄=C₂	112	4-	C4.12D28	224,30
D₈.D₇	The non-split extension by D₈ of D₇ acting via D₇/C₇=C₂	112	4-	D8.D7	224,33
C₇⋊Q₃₂	The semidirect product of C₇ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	224	4-	C7:Q32	224,35
C₈.D₁₄	1^st non-split extension by C₈ of D₁₄ acting via D₁₄/C₇=C₂²	112	4-	C8.D14	224,104
D₈⋊₃D₇	The semidirect product of D₈ and D₇ acting through Inn(D₈)	112	4-	D8:3D7	224,107
SD₁₆⋊D₇	2^nd semidirect product of SD₁₆ and D₇ acting via D₇/C₇=C₂	112	4-	SD16:D7	224,110
D₇×Q₁₆	Direct product of D₇ and Q₁₆	112	4-	D7xQ16	224,112
D₄.₉D₁₄	4^th non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	112	4-	D4.9D14	224,146
D₄.₁₀D₁₄	The non-split extension by D₄ of D₁₄ acting through Inn(D₄)	112	4-	D4.10D14	224,186

Groups of order 232

		d	ρ	Label	ID
C₂₉⋊C₈	The semidirect product of C₂₉ and C₈ acting via C₈/C₂=C₄	232	4-	C29:C8	232,3

Groups of order 240

		d	ρ	Label	ID
C₆.D₂₀	2^nd non-split extension by C₆ of D₂₀ acting via D₂₀/D₁₀=C₂	120	4-	C6.D20	240,18
D₁₂.D₅	1^st non-split extension by D₁₂ of D₅ acting via D₅/C₅=C₂	120	4-	D12.D5	240,20
C₃⋊Dic₂₀	The semidirect product of C₃ and Dic₂₀ acting via Dic₂₀/Dic₁₀=C₂	240	4-	C3:Dic20	240,23
C₅⋊Dic₁₂	The semidirect product of C₅ and Dic₁₂ acting via Dic₁₂/Dic₆=C₂	240	4-	C5:Dic12	240,24
D₄.D₁₅	The non-split extension by D₄ of D₁₅ acting via D₁₅/C₁₅=C₂	120	4-	D4.D15	240,77
C₁₅⋊₇Q₁₆	1^st semidirect product of C₁₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	240	4-	C15:7Q16	240,79
CSU₂(𝔽₅)	Conformal special unitary group on 𝔽₅²; = C₂ .₂ S₅	48	4-	CSU(2,5)	240,89
C₂.S₅	2^nd central stem extension by C₂ of S₅	40	4-	C2.S5	240,90
Q₈.D₁₅	The non-split extension by Q₈ of D₁₅ acting via D₁₅/C₅=S₃	80	4-	Q8.D15	240,105
D₅×SL₂(𝔽₃)	Direct product of D₅ and SL₂(𝔽₃)	40	4-	D5xSL(2,3)	240,109
D₅×Dic₆	Direct product of D₅ and Dic₆	120	4-	D5xDic6	240,125
D₂₀⋊₅S₃	The semidirect product of D₂₀ and S₃ acting through Inn(D₂₀)	120	4-	D20:5S3	240,126
S₃×Dic₁₀	Direct product of S₃ and Dic₁₀	120	4-	S3xDic10	240,128
D₁₂⋊₅D₅	The semidirect product of D₁₂ and D₅ acting through Inn(D₁₂)	120	4-	D12:5D5	240,133
C₃₀.C₂³	17^th non-split extension by C₃₀ of C₂³ acting via C₂³/C₂=C₂²	120	4-	C30.C2^3	240,141
D₄⋊₂D₁₅	The semidirect product of D₄ and D₁₅ acting through Inn(D₄)	120	4-	D4:2D15	240,180
Q₈×D₁₅	Direct product of Q₈ and D₁₅	120	4-	Q8xD15	240,181

Groups of order 264

		d	ρ	Label	ID
Dic₃×D₁₁	Direct product of Dic₃ and D₁₁	132	4-	Dic3xD11	264,5
S₃×Dic₁₁	Direct product of S₃ and Dic₁₁	132	4-	S3xDic11	264,6
C₃₃⋊D₄	1^st semidirect product of C₃₃ and D₄ acting via D₄/C₂=C₂²	132	4-	C33:D4	264,8
C₃₃⋊Q₈	The semidirect product of C₃₃ and Q₈ acting via Q₈/C₂=C₂²	264	4-	C33:Q8	264,11

Groups of order 272

		d	ρ	Label	ID
D₄.D₁₇	The non-split extension by D₄ of D₁₇ acting via D₁₇/C₁₇=C₂	136	4-	D4.D17	272,16
C₁₇⋊Q₁₆	The semidirect product of C₁₇ and Q₁₆ acting via Q₁₆/Q₈=C₂	272	4-	C17:Q16	272,18
C₁₇⋊M₄(2)	The semidirect product of C₁₇ and M₄(2) acting via M₄(2)/C₂²=C₄	136	4-	C17:M4(2)	272,34
D₄⋊₂D₁₇	The semidirect product of D₄ and D₁₇ acting through Inn(D₄)	136	4-	D4:2D17	272,41
Q₈×D₁₇	Direct product of Q₈ and D₁₇	136	4-	Q8xD17	272,42

Groups of order 280

		d	ρ	Label	ID
D₇×Dic₅	Direct product of D₇ and Dic₅	140	4-	D7xDic5	280,7
D₅×Dic₇	Direct product of D₅ and Dic₇	140	4-	D5xDic7	280,8
C₃₅⋊D₄	1^st semidirect product of C₃₅ and D₄ acting via D₄/C₂=C₂²	140	4-	C35:D4	280,10
C₃₅⋊Q₈	The semidirect product of C₃₅ and Q₈ acting via Q₈/C₂=C₂²	280	4-	C35:Q8	280,13

Groups of order 288

		d	ρ	Label	ID
C₄.D₃₆	3^rd non-split extension by C₄ of D₃₆ acting via D₃₆/D₁₈=C₂	144	4-	C4.D36	288,30
D₈.D₉	The non-split extension by D₈ of D₉ acting via D₉/C₉=C₂	144	4-	D8.D9	288,34
C₉⋊Q₃₂	The semidirect product of C₉ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	288	4-	C9:Q32	288,36
C₈.D₁₈	1^st non-split extension by C₈ of D₁₈ acting via D₁₈/C₉=C₂²	144	4-	C8.D18	288,119
D₈⋊₃D₉	The semidirect product of D₈ and D₉ acting through Inn(D₈)	144	4-	D8:3D9	288,122
SD₁₆⋊D₉	2^nd semidirect product of SD₁₆ and D₉ acting via D₉/C₉=C₂	144	4-	SD16:D9	288,125
Q₁₆×D₉	Direct product of Q₁₆ and D₉	144	4-	Q16xD9	288,127
D₄.D₁₈	3^rd non-split extension by D₄ of D₁₈ acting via D₁₈/C₁₈=C₂	144	4-	D4.D18	288,159
C₃²⋊₃SD₃₂	2^nd semidirect product of C₃² and SD₃₂ acting via SD₃₂/C₈=C₂²	96	4-	C3^2:3SD32	288,196
C₃²⋊₃Q₃₂	2^nd semidirect product of C₃² and Q₃₂ acting via Q₃₂/C₈=C₂²	96	4-	C3^2:3Q32	288,199
C₁₂.₇₁D₁₂	2^nd non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48	4-	C12.71D12	288,209
C₁₂.₃S₄	3^rd non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	144	4-	C12.3S4	288,338
D₄.₁₀D₁₈	The non-split extension by D₄ of D₁₈ acting through Inn(D₄)	144	4-	D4.10D18	288,364
Dic₃≀C₂	Wreath product of Dic₃ by C₂	24	4-	Dic3wrC2	288,389
C₃⋊Dic₃.D₄	9^th non-split extension by C₃⋊Dic₃ of D₄ acting via D₄/C₂=C₂²	48	4-	C3:Dic3.D4	288,428
S₃×Dic₁₂	Direct product of S₃ and Dic₁₂	96	4-	S3xDic12	288,447
C₂₄.₃D₆	3^rd non-split extension by C₂₄ of D₆ acting via D₆/C₃=C₂²	96	4-	C24.3D6	288,448
D₂₄⋊₇S₃	The semidirect product of D₂₄ and S₃ acting through Inn(D₂₄)	96	4-	D24:7S3	288,455
D₁₂.₂₉D₆	4^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4-	D12.29D6	288,479
S₃×CSU₂(𝔽₃)	Direct product of S₃ and CSU₂(𝔽₃)	48	4-	S3xCSU(2,3)	288,848
D₆.S₄	1^st non-split extension by D₆ of S₄ acting via S₄/A₄=C₂	48	4-	D6.S4	288,849
C₆².₁₅D₄	15^th non-split extension by C₆² of D₄ acting faithfully	48	4-	C6^2.15D4	288,887
C₁₂.₆S₄	6^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	96	4-	C12.6S4	288,913
D₁₂.A₄	The non-split extension by D₁₂ of A₄ acting through Inn(D₁₂)	48	4-	D12.A4	288,926
D₁₂.₃₄D₆	The non-split extension by D₁₂ of D₆ acting through Inn(D₁₂)	48	4-	D12.34D6	288,946

Groups of order 296

		d	ρ	Label	ID
C₃₇⋊C₈	The semidirect product of C₃₇ and C₈ acting via C₈/C₂=C₄	296	4-	C37:C8	296,3

Groups of order 304

		d	ρ	Label	ID
D₄.D₁₉	The non-split extension by D₄ of D₁₉ acting via D₁₉/C₁₉=C₂	152	4-	D4.D19	304,15
C₁₉⋊Q₁₆	The semidirect product of C₁₉ and Q₁₆ acting via Q₁₆/Q₈=C₂	304	4-	C19:Q16	304,17
D₄⋊₂D₁₉	The semidirect product of D₄ and D₁₉ acting through Inn(D₄)	152	4-	D4:2D19	304,32
Q₈×D₁₉	Direct product of Q₈ and D₁₉	152	4-	Q8xD19	304,33

Groups of order 312

		d	ρ	Label	ID
Dic₃×D₁₃	Direct product of Dic₃ and D₁₃	156	4-	Dic3xD13	312,15
S₃×Dic₁₃	Direct product of S₃ and Dic₁₃	156	4-	S3xDic13	312,16
C₃₉⋊D₄	1^st semidirect product of C₃₉ and D₄ acting via D₄/C₂=C₂²	156	4-	C39:D4	312,18
C₃₉⋊Q₈	The semidirect product of C₃₉ and Q₈ acting via Q₈/C₂=C₂²	312	4-	C39:Q8	312,21

Groups of order 320

		d	ρ	Label	ID
C₄₀.₈D₄	8^th non-split extension by C₄₀ of D₄ acting via D₄/C₂=C₂²	160	4-	C40.8D4	320,54
C₂₀.₄D₈	4^th non-split extension by C₂₀ of D₈ acting via D₈/C₄=C₂²	160	4-	C20.4D8	320,75
D₁₆.D₅	The non-split extension by D₁₆ of D₅ acting via D₅/C₅=C₂	160	4-	D16.D5	320,78
C₅⋊Q₆₄	The semidirect product of C₅ and Q₆₄ acting via Q₆₄/Q₃₂=C₂	320	4-	C5:Q64	320,80
C₄².F₅	1^st non-split extension by C₄² of F₅ acting via F₅/C₅=C₄	80	4-	C4^2.F5	320,193
D₄.₉D₂₀	4^th non-split extension by D₄ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4-	D4.9D20	320,453
C₈.₂₀D₂₀	6^th non-split extension by C₈ of D₂₀ acting via D₂₀/D₁₀=C₂	160	4-	C8.20D20	320,523
C₁₆.D₁₀	1^st non-split extension by C₁₆ of D₁₀ acting via D₁₀/C₅=C₂²	160	4-	C16.D10	320,536
D₁₆⋊₃D₅	The semidirect product of D₁₆ and D₅ acting through Inn(D₁₆)	160	4-	D16:3D5	320,539
SD₃₂⋊D₅	2^nd semidirect product of SD₃₂ and D₅ acting via D₅/C₅=C₂	160	4-	SD32:D5	320,542
D₅×Q₃₂	Direct product of D₅ and Q₃₂	160	4-	D5xQ32	320,544
D₄.₅D₂₀	5^th non-split extension by D₄ of D₂₀ acting via D₂₀/C₂₀=C₂	160	4-	D4.5D20	320,770
C₄₀.₃₁C₂³	24^th non-split extension by C₄₀ of C₂³ acting via C₂³/C₂=C₂²	160	4-	C40.31C2^3	320,822
D₄.₁₃D₂₀	3^rd non-split extension by D₄ of D₂₀ acting through Inn(D₄)	160	4-	D4.13D20	320,1425
D₂₀.₄₇D₄	3^rd non-split extension by D₂₀ of D₄ acting through Inn(D₂₀)	160	4-	D20.47D4	320,1443
2_-¹⁺⁴.D₅	The non-split extension by 2_-¹⁺⁴ of D₅ acting faithfully	64	4-	ES-(2,2).D5	320,1581

Groups of order 328

		d	ρ	Label	ID
C₄₁⋊₂C₈	The semidirect product of C₄₁ and C₈ acting via C₈/C₂=C₄	328	4-	C41:2C8	328,3

Groups of order 336

		d	ρ	Label	ID
C₆.D₂₈	2^nd non-split extension by C₆ of D₂₈ acting via D₂₈/D₁₄=C₂	168	4-	C6.D28	336,34
D₁₂.D₇	1^st non-split extension by D₁₂ of D₇ acting via D₇/C₇=C₂	168	4-	D12.D7	336,36
C₃⋊Dic₂₈	The semidirect product of C₃ and Dic₂₈ acting via Dic₂₈/Dic₁₄=C₂	336	4-	C3:Dic28	336,39
C₇⋊Dic₁₂	The semidirect product of C₇ and Dic₁₂ acting via Dic₁₂/Dic₆=C₂	336	4-	C7:Dic12	336,40
D₄.D₂₁	The non-split extension by D₄ of D₂₁ acting via D₂₁/C₂₁=C₂	168	4-	D4.D21	336,102
C₂₁⋊₇Q₁₆	1^st semidirect product of C₂₁ and Q₁₆ acting via Q₁₆/Q₈=C₂	336	4-	C21:7Q16	336,104
Q₈.D₂₁	The non-split extension by Q₈ of D₂₁ acting via D₂₁/C₇=S₃	112	4-	Q8.D21	336,118
D₇×SL₂(𝔽₃)	Direct product of D₇ and SL₂(𝔽₃)	56	4-	D7xSL(2,3)	336,132
D₇×Dic₆	Direct product of D₇ and Dic₆	168	4-	D7xDic6	336,137
D₂₈⋊₅S₃	The semidirect product of D₂₈ and S₃ acting through Inn(D₂₈)	168	4-	D28:5S3	336,138
S₃×Dic₁₄	Direct product of S₃ and Dic₁₄	168	4-	S3xDic14	336,140
D₁₂⋊₅D₇	The semidirect product of D₁₂ and D₇ acting through Inn(D₁₂)	168	4-	D12:5D7	336,145
C₄₂.C₂³	17^th non-split extension by C₄₂ of C₂³ acting via C₂³/C₂=C₂²	168	4-	C42.C2^3	336,153
D₄⋊₂D₂₁	The semidirect product of D₄ and D₂₁ acting through Inn(D₄)	168	4-	D4:2D21	336,199
Q₈×D₂₁	Direct product of Q₈ and D₂₁	168	4-	Q8xD21	336,200

Groups of order 352

		d	ρ	Label	ID
C₄₄.₄₇D₄	4^th non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	176	4-	C44.47D4	352,30
D₈.D₁₁	The non-split extension by D₈ of D₁₁ acting via D₁₁/C₁₁=C₂	176	4-	D8.D11	352,33
C₁₁⋊Q₃₂	The semidirect product of C₁₁ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	352	4-	C11:Q32	352,35
C₈.D₂₂	1^st non-split extension by C₈ of D₂₂ acting via D₂₂/C₁₁=C₂²	176	4-	C8.D22	352,104
D₈⋊₃D₁₁	The semidirect product of D₈ and D₁₁ acting through Inn(D₈)	176	4-	D8:3D11	352,107
D₄.D₂₂	4^th non-split extension by D₄ of D₂₂ acting via D₂₂/D₁₁=C₂	176	4-	D4.D22	352,110
Q₁₆×D₁₁	Direct product of Q₁₆ and D₁₁	176	4-	Q16xD11	352,112
D₄.₉D₂₂	4^th non-split extension by D₄ of D₂₂ acting via D₂₂/C₂₂=C₂	176	4-	D4.9D22	352,146
D₄.₁₀D₂₂	The non-split extension by D₄ of D₂₂ acting through Inn(D₄)	176	4-	D4.10D22	352,185

Groups of order 360

		d	ρ	Label	ID
C₄₅⋊Q₈	The semidirect product of C₄₅ and Q₈ acting via Q₈/C₂=C₂²	360	4-	C45:Q8	360,7
D₉×Dic₅	Direct product of D₉ and Dic₅	180	4-	D9xDic5	360,8
D₅×Dic₉	Direct product of D₅ and Dic₉	180	4-	D5xDic9	360,11
C₄₅⋊D₄	2^nd semidirect product of C₄₅ and D₄ acting via D₄/C₂=C₂²	180	4-	C45:D4	360,12
(C₃×C₆).F₅	The non-split extension by C₃×C₆ of F₅ acting via F₅/C₅=C₄	120	4-	(C3xC6).F5	360,57
Dic₃×D₁₅	Direct product of Dic₃ and D₁₅	120	4-	Dic3xD15	360,77
S₃×Dic₁₅	Direct product of S₃ and Dic₁₅	120	4-	S3xDic15	360,78
D₆⋊D₁₅	1^st semidirect product of D₆ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4-	D6:D15	360,80
C₃⋊Dic₃₀	The semidirect product of C₃ and Dic₃₀ acting via Dic₃₀/Dic₁₅=C₂	120	4-	C3:Dic30	360,83

Groups of order 368

		d	ρ	Label	ID
D₄.D₂₃	The non-split extension by D₄ of D₂₃ acting via D₂₃/C₂₃=C₂	184	4-	D4.D23	368,15
C₂₃⋊Q₁₆	The semidirect product of C₂₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	368	4-	C23:Q16	368,17
D₄⋊₂D₂₃	The semidirect product of D₄ and D₂₃ acting through Inn(D₄)	184	4-	D4:2D23	368,32
Q₈×D₂₃	Direct product of Q₈ and D₂₃	184	4-	Q8xD23	368,33

Groups of order 392

		d	ρ	Label	ID
C₇²⋊₂C₈	The semidirect product of C₇² and C₈ acting via C₈/C₂=C₄	56	4-	C7^2:2C8	392,17
D₇×Dic₇	Direct product of D₇ and Dic₇	56	4-	D7xDic7	392,18
C₇²⋊₂D₄	1^st semidirect product of C₇² and D₄ acting via D₄/C₂=C₂²	56	4-	C7^2:2D4	392,20
C₇²⋊₂Q₈	The semidirect product of C₇² and Q₈ acting via Q₈/C₂=C₂²	56	4-	C7^2:2Q8	392,22

Groups of order 400

		d	ρ	Label	ID
D₄.D₂₅	The non-split extension by D₄ of D₂₅ acting via D₂₅/C₂₅=C₂	200	4-	D4.D25	400,15
C₂₅⋊Q₁₆	The semidirect product of C₂₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	400	4-	C25:Q16	400,17
C₂₅⋊M₄(2)	The semidirect product of C₂₅ and M₄(2) acting via M₄(2)/C₂²=C₄	200	4-	C25:M4(2)	400,33
D₄⋊₂D₂₅	The semidirect product of D₄ and D₂₅ acting through Inn(D₄)	200	4-	D4:2D25	400,40
Q₈×D₂₅	Direct product of Q₈ and D₂₅	200	4-	Q8xD25	400,41
C₅²⋊₃SD₁₆	2^nd semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₄=C₂²	80	4-	C5^2:3SD16	400,67
C₅²⋊₃Q₁₆	2^nd semidirect product of C₅² and Q₁₆ acting via Q₁₆/C₄=C₂²	80	4-	C5^2:3Q16	400,70
C₅²⋊SD₁₆	The semidirect product of C₅² and SD₁₆ acting via SD₁₆/C₂=D₄	40	4-	C5^2:SD16	400,132
C₅²⋊Q₁₆	The semidirect product of C₅² and Q₁₆ acting via Q₁₆/C₂=D₄	80	4-	C5^2:Q16	400,133
C₅²⋊₁₄M₄(2)	4^th semidirect product of C₅² and M₄(2) acting via M₄(2)/C₂²=C₄	40	4-	C5^2:14M4(2)	400,161
D₅×Dic₁₀	Direct product of D₅ and Dic₁₀	80	4-	D5xDic10	400,163
D₂₀⋊₅D₅	The semidirect product of D₂₀ and D₅ acting through Inn(D₂₀)	80	4-	D20:5D5	400,164
D₁₀.₄D₁₀	4^th non-split extension by D₁₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4-	D10.4D10	400,174

Groups of order 408

		d	ρ	Label	ID
Dic₃×D₁₇	Direct product of Dic₃ and D₁₇	204	4-	Dic3xD17	408,7
S₃×Dic₁₇	Direct product of S₃ and Dic₁₇	204	4-	S3xDic17	408,8
C₅₁⋊D₄	1^st semidirect product of C₅₁ and D₄ acting via D₄/C₂=C₂²	204	4-	C51:D4	408,10
C₅₁⋊Q₈	The semidirect product of C₅₁ and Q₈ acting via Q₈/C₂=C₂²	408	4-	C51:Q8	408,13

Groups of order 416

		d	ρ	Label	ID
C₄.₁₂D₅₂	4^th non-split extension by C₄ of D₅₂ acting via D₅₂/D₂₆=C₂	208	4-	C4.12D52	416,31
D₈.D₁₃	The non-split extension by D₈ of D₁₃ acting via D₁₃/C₁₃=C₂	208	4-	D8.D13	416,34
C₁₃⋊Q₃₂	The semidirect product of C₁₃ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	416	4-	C13:Q32	416,36
Dic₁₃.D₄	1^st non-split extension by Dic₁₃ of D₄ acting via D₄/C₂=C₂²	208	4-	Dic13.D4	416,80
C₈.D₂₆	1^st non-split extension by C₈ of D₂₆ acting via D₂₆/C₁₃=C₂²	208	4-	C8.D26	416,130
D₈⋊₃D₁₃	The semidirect product of D₈ and D₁₃ acting through Inn(D₈)	208	4-	D8:3D13	416,133
D₄.D₂₆	4^th non-split extension by D₄ of D₂₆ acting via D₂₆/D₁₃=C₂	208	4-	D4.D26	416,136
Q₁₆×D₁₃	Direct product of Q₁₆ and D₁₃	208	4-	Q16xD13	416,138
D₄.₉D₂₆	4^th non-split extension by D₄ of D₂₆ acting via D₂₆/C₂₆=C₂	208	4-	D4.9D26	416,172
D₄.₁₀D₂₆	The non-split extension by D₄ of D₂₆ acting through Inn(D₄)	208	4-	D4.10D26	416,224

Groups of order 424

		d	ρ	Label	ID
C₅₃⋊C₈	The semidirect product of C₅₃ and C₈ acting via C₈/C₂=C₄	424	4-	C53:C8	424,3

Groups of order 432

		d	ρ	Label	ID
D₄.D₂₇	The non-split extension by D₄ of D₂₇ acting via D₂₇/C₂₇=C₂	216	4-	D4.D27	432,15
C₂₇⋊Q₁₆	The semidirect product of C₂₇ and Q₁₆ acting via Q₁₆/Q₈=C₂	432	4-	C27:Q16	432,17
Q₈.D₂₇	The non-split extension by Q₈ of D₂₇ acting via D₂₇/C₉=S₃	432	4-	Q8.D27	432,37
D₄⋊₂D₂₇	The semidirect product of D₄ and D₂₇ acting through Inn(D₄)	216	4-	D4:2D27	432,48
Q₈×D₂₇	Direct product of Q₈ and D₂₇	216	4-	Q8xD27	432,49
D₃₆.S₃	1^st non-split extension by D₃₆ of S₃ acting via S₃/C₃=C₂	144	4-	D36.S3	432,62
C₃⋊Dic₃₆	The semidirect product of C₃ and Dic₃₆ acting via Dic₃₆/Dic₁₈=C₂	144	4-	C3:Dic36	432,65
C₃₆.D₆	12^nd non-split extension by C₃₆ of D₆ acting via D₆/C₃=C₂²	144	4-	C36.D6	432,71
C₉⋊Dic₁₂	The semidirect product of C₉ and Dic₁₂ acting via Dic₁₂/Dic₆=C₂	144	4-	C9:Dic12	432,75
C₁₈.₅S₄	5^th non-split extension by C₁₈ of S₄ acting via S₄/A₄=C₂	144	4-	C18.5S4	432,252
D₉×SL₂(𝔽₃)	Direct product of D₉ and SL₂(𝔽₃)	72	4-	D9xSL(2,3)	432,264
D₉×Dic₆	Direct product of D₉ and Dic₆	144	4-	D9xDic6	432,280
S₃×Dic₁₈	Direct product of S₃ and Dic₁₈	144	4-	S3xDic18	432,284
D₁₂⋊₅D₉	The semidirect product of D₁₂ and D₉ acting through Inn(D₁₂)	144	4-	D12:5D9	432,285
D₃₆⋊₅S₃	The semidirect product of D₃₆ and S₃ acting through Inn(D₃₆)	144	4-	D36:5S3	432,288
D₁₈.₄D₆	4^th non-split extension by D₁₈ of D₆ acting via D₆/S₃=C₂	72	4-	D18.4D6	432,310

Groups of order 440

		d	ρ	Label	ID
Dic₅×D₁₁	Direct product of Dic₅ and D₁₁	220	4-	Dic5xD11	440,17
D₅×Dic₁₁	Direct product of D₅ and Dic₁₁	220	4-	D5xDic11	440,18
C₅₅⋊D₄	1^st semidirect product of C₅₅ and D₄ acting via D₄/C₂=C₂²	220	4-	C55:D4	440,20
C₅₅⋊Q₈	The semidirect product of C₅₅ and Q₈ acting via Q₈/C₂=C₂²	440	4-	C55:Q8	440,23

Groups of order 448

		d	ρ	Label	ID
C₅₆.₈D₄	8^th non-split extension by C₅₆ of D₄ acting via D₄/C₂=C₂²	224	4-	C56.8D4	448,53
C₂₈.₄D₈	4^th non-split extension by C₂₈ of D₈ acting via D₈/C₄=C₂²	224	4-	C28.4D8	448,74
D₁₆.D₇	The non-split extension by D₁₆ of D₇ acting via D₇/C₇=C₂	224	4-	D16.D7	448,77
C₇⋊Q₆₄	The semidirect product of C₇ and Q₆₄ acting via Q₆₄/Q₃₂=C₂	448	4-	C7:Q64	448,79
D₄.₉D₂₈	4^th non-split extension by D₄ of D₂₈ acting via D₂₈/D₁₄=C₂	112	4-	D4.9D28	448,360
C₈.₂₀D₂₈	6^th non-split extension by C₈ of D₂₈ acting via D₂₈/D₁₄=C₂	224	4-	C8.20D28	448,430
C₁₆.D₁₄	1^st non-split extension by C₁₆ of D₁₄ acting via D₁₄/C₇=C₂²	224	4-	C16.D14	448,443
D₁₆⋊₃D₇	The semidirect product of D₁₆ and D₇ acting through Inn(D₁₆)	224	4-	D16:3D7	448,446
SD₃₂⋊D₇	2^nd semidirect product of SD₃₂ and D₇ acting via D₇/C₇=C₂	224	4-	SD32:D7	448,449
D₇×Q₃₂	Direct product of D₇ and Q₃₂	224	4-	D7xQ32	448,451
D₄.₅D₂₈	5^th non-split extension by D₄ of D₂₈ acting via D₂₈/C₂₈=C₂	224	4-	D4.5D28	448,677
C₅₆.₃₁C₂³	24^th non-split extension by C₅₆ of C₂³ acting via C₂³/C₂=C₂²	224	4-	C56.31C2^3	448,729
D₄.₁₃D₂₈	3^rd non-split extension by D₄ of D₂₈ acting through Inn(D₄)	224	4-	D4.13D28	448,1206
D₈.₁₀D₁₄	The non-split extension by D₈ of D₁₄ acting through Inn(D₈)	224	4-	D8.10D14	448,1224

Groups of order 456

		d	ρ	Label	ID
Dic₃×D₁₉	Direct product of Dic₃ and D₁₉	228	4-	Dic3xD19	456,12
S₃×Dic₁₉	Direct product of S₃ and Dic₁₉	228	4-	S3xDic19	456,13
C₅₇⋊D₄	1^st semidirect product of C₅₇ and D₄ acting via D₄/C₂=C₂²	228	4-	C57:D4	456,15
C₅₇⋊Q₈	The semidirect product of C₅₇ and Q₈ acting via Q₈/C₂=C₂²	456	4-	C57:Q8	456,18

Groups of order 464

		d	ρ	Label	ID
D₄.D₂₉	The non-split extension by D₄ of D₂₉ acting via D₂₉/C₂₉=C₂	232	4-	D4.D29	464,16
C₂₉⋊Q₁₆	The semidirect product of C₂₉ and Q₁₆ acting via Q₁₆/Q₈=C₂	464	4-	C29:Q16	464,18
C₂₉⋊M₄(2)	The semidirect product of C₂₉ and M₄(2) acting via M₄(2)/C₂²=C₄	232	4-	C29:M4(2)	464,33
D₄⋊₂D₂₉	The semidirect product of D₄ and D₂₉ acting through Inn(D₄)	232	4-	D4:2D29	464,40
Q₈×D₂₉	Direct product of Q₈ and D₂₉	232	4-	Q8xD29	464,41

Groups of order 480

		d	ρ	Label	ID
D₄₀.S₃	1^st non-split extension by D₄₀ of S₃ acting via S₃/C₃=C₂	240	4-	D40.S3	480,18
D₂₄.D₅	1^st non-split extension by D₂₄ of D₅ acting via D₅/C₅=C₂	240	4-	D24.D5	480,20
C₃⋊Dic₄₀	The semidirect product of C₃ and Dic₄₀ acting via Dic₄₀/Dic₂₀=C₂	480	4-	C3:Dic40	480,23
C₅⋊Dic₂₄	The semidirect product of C₅ and Dic₂₄ acting via Dic₂₄/Dic₁₂=C₂	480	4-	C5:Dic24	480,24
C₆₀.₃₁D₄	31^st non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	240	4-	C60.31D4	480,39
C₄.D₆₀	4^th non-split extension by C₄ of D₆₀ acting via D₆₀/D₃₀=C₂	240	4-	C4.D60	480,184
D₈.D₁₅	The non-split extension by D₈ of D₁₅ acting via D₁₅/C₁₅=C₂	240	4-	D8.D15	480,187
C₁₅⋊₇Q₃₂	1^st semidirect product of C₁₅ and Q₃₂ acting via Q₃₂/Q₁₆=C₂	480	4-	C15:7Q32	480,189
D₅×Dic₁₂	Direct product of D₅ and Dic₁₂	240	4-	D5xDic12	480,335
Dic₆₀⋊C₂	14^th semidirect product of Dic₆₀ and C₂ acting faithfully	240	4-	Dic60:C2	480,336
S₃×Dic₂₀	Direct product of S₃ and Dic₂₀	240	4-	S3xDic20	480,338
D₂₄⋊₇D₅	The semidirect product of D₂₄ and D₅ acting through Inn(D₂₄)	240	4-	D24:7D5	480,346
D₄₀⋊₇S₃	The semidirect product of D₄₀ and S₃ acting through Inn(D₄₀)	240	4-	D40:7S3	480,349
C₄₀.₂D₆	2^nd non-split extension by C₄₀ of D₆ acting via D₆/C₃=C₂²	240	4-	C40.2D6	480,350
C₆₀.₆₃D₄	63^rd non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	240	4-	C60.63D4	480,389
D₁₂.₃₃D₁₀	4^th non-split extension by D₁₂ of D₁₀ acting via D₁₀/C₁₀=C₂	240	4-	D12.33D10	480,398
C₈.D₃₀	1^st non-split extension by C₈ of D₃₀ acting via D₃₀/C₁₅=C₂²	240	4-	C8.D30	480,874
D₈⋊₃D₁₅	The semidirect product of D₈ and D₁₅ acting through Inn(D₈)	240	4-	D8:3D15	480,877
SD₁₆⋊D₁₅	2^nd semidirect product of SD₁₆ and D₁₅ acting via D₁₅/C₁₅=C₂	240	4-	SD16:D15	480,880
Q₁₆×D₁₅	Direct product of Q₁₆ and D₁₅	240	4-	Q16xD15	480,882
D₄.₉D₃₀	4^th non-split extension by D₄ of D₃₀ acting via D₃₀/C₃₀=C₂	240	4-	D4.9D30	480,916
C₂².S₅	The non-split extension by C₂² of S₅ acting via S₅/A₅=C₂	48	4-	C2^2.S5	480,953
D₄.A₅	The non-split extension by D₄ of A₅ acting through Inn(D₄)	48	4-	D4.A5	480,957
D₅×CSU₂(𝔽₃)	Direct product of D₅ and CSU₂(𝔽₃)	80	4-	D5xCSU(2,3)	480,971
D₁₀.₁S₄	1^st non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	80	4-	D10.1S4	480,972
C₂₀.₂S₄	2^nd non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	160	4-	C20.2S4	480,1030
D₂₀.A₄	The non-split extension by D₂₀ of A₄ acting through Inn(D₂₀)	80	4-	D20.A4	480,1043
D₂₀.₃₉D₆	The non-split extension by D₂₀ of D₆ acting through Inn(D₂₀)	240	4-	D20.39D6	480,1077
D₄.₁₀D₃₀	The non-split extension by D₄ of D₃₀ acting through Inn(D₄)	240	4-	D4.10D30	480,1177

Groups of order 488

		d	ρ	Label	ID
C₆₁⋊C₈	The semidirect product of C₆₁ and C₈ acting via C₈/C₂=C₄	488	4-	C61:C8	488,3

Groups of order 496

		d	ρ	Label	ID
D₄.D₃₁	The non-split extension by D₄ of D₃₁ acting via D₃₁/C₃₁=C₂	248	4-	D4.D31	496,15
C₃₁⋊Q₁₆	The semidirect product of C₃₁ and Q₁₆ acting via Q₁₆/Q₈=C₂	496	4-	C31:Q16	496,17
D₄⋊₂D₃₁	The semidirect product of D₄ and D₃₁ acting through Inn(D₄)	248	4-	D4:2D31	496,32
Q₈×D₃₁	Direct product of Q₈ and D₃₁	248	4-	Q8xD31	496,33

Complex of dimension 4 (ρ=4)

Groups of order 60

		d	ρ	Label	ID
C₃×F₅	Direct product of C₃ and F₅	15	4	C3xF5	60,6
C₃⋊F₅	The semidirect product of C₃ and F₅ acting via F₅/D₅=C₂	15	4	C3:F5	60,7

Groups of order 64

		d	ρ	Label	ID
C₄.₉C₄²	1^st central stem extension by C₄ of C₄²	16	4	C4.9C4^2	64,18
C₄.₁₀C₄²	2^nd central stem extension by C₄ of C₄²	16	4	C4.10C4^2	64,19
M₄(2)⋊₄C₄	4^th semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	16	4	M4(2):4C4	64,25
C₁₆⋊C₄	2^nd semidirect product of C₁₆ and C₄ acting faithfully	16	4	C16:C4	64,28
C₂³.C₈	The non-split extension by C₂³ of C₈ acting via C₈/C₂=C₄	16	4	C2^3.C8	64,30
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	16	4	C2^3.D4	64,33
C₄²⋊₃C₄	3^rd semidirect product of C₄² and C₄ acting faithfully	16	4	C4^2:3C4	64,35
C₄².C₄	2^nd non-split extension by C₄² of C₄ acting faithfully	16	4	C4^2.C4	64,36
D₈⋊₂C₄	2^nd semidirect product of D₈ and C₄ acting via C₄/C₂=C₂	16	4	D8:2C4	64,41
C₈.Q₈	The non-split extension by C₈ of Q₈ acting via Q₈/C₂=C₂²	16	4	C8.Q8	64,46
C₂³.C₂³	2^nd non-split extension by C₂³ of C₂³ acting via C₂³/C₂=C₂²	16	4	C2^3.C2^3	64,91
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
C₄²⋊C₂²	1^st semidirect product of C₄² and C₂² acting faithfully	16	4	C4^2:C2^2	64,102
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
C₈.₂₆D₄	13^rd non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	16	4	C8.26D4	64,125
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
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	16	4	C2^3.7D4	64,139
D₄.₃D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	16	4	D4.3D4	64,152
Q₈○M₄(2)	Central product of Q₈ and M₄(2)	16	4	Q8oM4(2)	64,249
D₈⋊C₂²	4^th semidirect product of D₈ and C₂² acting via C₂²/C₂=C₂	16	4	D8:C2^2	64,256
D₄○SD₁₆	Central product of D₄ and SD₁₆	16	4	D4oSD16	64,258
C₂.C₂⁵	6^th central stem extension by C₂ of C₂⁵	16	4	C2.C2^5	64,266

Groups of order 80

		d	ρ	Label	ID
C₅⋊C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5:C16	80,3
D₅⋊C₈	The semidirect product of D₅ and C₈ acting via C₈/C₄=C₂	40	4	D5:C8	80,28
C₄.F₅	The non-split extension by C₄ of F₅ acting via F₅/D₅=C₂	40	4	C4.F5	80,29
C₄×F₅	Direct product of C₄ and F₅	20	4	C4xF5	80,30
C₄⋊F₅	The semidirect product of C₄ and F₅ acting via F₅/D₅=C₂	20	4	C4:F5	80,31

Groups of order 96

		d	ρ	Label	ID
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	24	4	C2^3.6D6	96,13
C₁₂.₅₃D₄	10^th non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	48	4	C12.53D4	96,29
D₁₂⋊C₄	4^th semidirect product of D₁₂ and C₄ acting via C₄/C₂=C₂	24	4	D12:C4	96,32
C₁₂.D₄	8^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	24	4	C12.D4	96,40
C₂³.₇D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	24	4	C2^3.7D6	96,41
C₁₂.₁₀D₄	10^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	C12.10D4	96,43
Q₈⋊₃Dic₃	2^nd semidirect product of Q₈ and Dic₃ acting via Dic₃/C₆=C₂	24	4	Q8:3Dic3	96,44
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	24	4	C3xC2^3:C4	96,49
C₃×C₄.D₄	Direct product of C₃ and C₄.D₄	24	4	C3xC4.D4	96,50
C₃×C₄.₁₀D₄	Direct product of C₃ and C₄.₁₀D₄	48	4	C3xC4.10D4	96,51
S₃×M₄(2)	Direct product of S₃ and M₄(2)	24	4	S3xM4(2)	96,113
D₁₂.C₄	The non-split extension by D₁₂ of C₄ acting via C₄/C₂=C₂	48	4	D12.C4	96,114
D₈⋊S₃	2^nd semidirect product of D₈ and S₃ acting via S₃/C₃=C₂	24	4	D8:S3	96,118
S₃×SD₁₆	Direct product of S₃ and SD₁₆	24	4	S3xSD16	96,120
Q₈.₇D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/S₃=C₂	48	4	Q8.7D6	96,123
Q₁₆⋊S₃	2^nd semidirect product of Q₁₆ and S₃ acting via S₃/C₃=C₂	48	4	Q16:S3	96,125
D₁₂⋊₆C₂²	4^th semidirect product of D₁₂ and C₂² acting via C₂²/C₂=C₂	24	4	D12:6C2^2	96,139
Q₈.₁₁D₆	1^st non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4	Q8.11D6	96,149
D₄.Dic₃	The non-split extension by D₄ of Dic₃ acting through Inn(D₄)	48	4	D4.Dic3	96,155
Q₈.₁₃D₆	3^rd non-split extension by Q₈ of D₆ acting via D₆/C₆=C₂	48	4	Q8.13D6	96,157
C₃×C₈⋊C₂²	Direct product of C₃ and C₈⋊C₂²	24	4	C3xC8:C2^2	96,183
C₃×C₈.C₂²	Direct product of C₃ and C₈.C₂²	48	4	C3xC8.C2^2	96,184
D₄⋊₆D₆	2^nd semidirect product of D₄ and D₆ acting through Inn(D₄)	24	4	D4:6D6	96,211
Q₈.₁₅D₆	1^st non-split extension by Q₈ of D₆ acting through Inn(Q₈)	48	4	Q8.15D6	96,214
S₃×C₄○D₄	Direct product of S₃ and C₄○D₄	24	4	S3xC4oD4	96,215
C₃×2₊¹⁺⁴	Direct product of C₃ and 2₊¹⁺⁴	24	4	C3xES+(2,2)	96,224
C₃×2_-¹⁺⁴	Direct product of C₃ and 2_-¹⁺⁴	48	4	C3xES-(2,2)	96,225

Groups of order 100

		d	ρ	Label	ID
C₅×F₅	Direct product of C₅ and F₅	20	4	C5xF5	100,9
D₅.D₅	The non-split extension by D₅ of D₅ acting via D₅/C₅=C₂	20	4	D5.D5	100,10

Groups of order 108

		d	ρ	Label	ID
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	12	4	C3xC3^2:C4	108,36
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	12	4	C3^3:C4	108,37
C₃×S₃²	Direct product of C₃, S₃ and S₃	12	4	C3xS3^2	108,38
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	12	4	C3^2:4D6	108,40

Groups of order 120

		d	ρ	Label	ID
C₃×C₅⋊C₈	Direct product of C₃ and C₅⋊C₈	120	4	C3xC5:C8	120,6
C₁₅⋊C₈	1^st semidirect product of C₁₅ and C₈ acting via C₈/C₂=C₄	120	4	C15:C8	120,7
C₆×F₅	Direct product of C₆ and F₅	30	4	C6xF5	120,40
C₂×C₃⋊F₅	Direct product of C₂ and C₃⋊F₅	30	4	C2xC3:F5	120,41

Groups of order 128

		d	ρ	Label	ID
C₂⁴.C₈	2^nd non-split extension by C₂⁴ of C₈ acting via C₈/C₂=C₄	16	4	C2^4.C8	128,52
C₂³.₁M₄(2)	1^st non-split extension by C₂³ of M₄(2) acting via M₄(2)/C₄=C₄	32	4	C2^3.1M4(2)	128,53
C₄².C₈	1^st non-split extension by C₄² of C₈ acting via C₈/C₂=C₄	16	4	C4^2.C8	128,59
C₂²⋊C₄.C₈	The non-split extension by C₂²⋊C₄ of C₈ acting via C₈/C₂=C₄	32	4	C2^2:C4.C8	128,60
C₈.₃₂D₈	9^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	16	4	C8.32D8	128,68
C₈.₂₉D₈	6^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	16	4	C8.29D8	128,91
C₈.₁Q₁₆	1^st non-split extension by C₈ of Q₁₆ acting via Q₁₆/C₄=C₂²	32	4	C8.1Q16	128,98
C₁₆.C₈	1^st non-split extension by C₁₆ of C₈ acting via C₈/C₂=C₄	32	4	C16.C8	128,101
M₄(2).C₈	2^nd non-split extension by M₄(2) of C₈ acting via C₈/C₄=C₂	32	4	M4(2).C8	128,110
C₂³.₉D₈	2^nd non-split extension by C₂³ of D₈ acting via D₈/C₄=C₂²	32	4	C2^3.9D8	128,116
C₈.₁₃C₄²	7^th non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	32	4	C8.13C4^2	128,117
M₅(2).C₄	2^nd non-split extension by M₅(2) of C₄ acting via C₄/C₂=C₂	32	4	M5(2).C4	128,120
C₈.₄C₄²	4^th non-split extension by C₈ of C₄² acting via C₄²/C₂²=C₂²	32	4	C8.4C4^2	128,121
C₂³.₂C₄²	2^nd non-split extension by C₂³ of C₄² acting via C₄²/C₄=C₄	32	4	C2^3.2C4^2	128,123
C₂³.₃C₄²	3^rd non-split extension by C₂³ of C₄² acting via C₄²/C₄=C₄	32	4	C2^3.3C4^2	128,124
(C₂²×C₈)⋊C₄	4^th semidirect product of C₂²×C₈ and C₄ acting faithfully	32	4	(C2^2xC8):C4	128,127
C₃₂⋊C₄	2^nd semidirect product of C₃₂ and C₄ acting faithfully	32	4	C32:C4	128,130
C₂³.C₁₆	The non-split extension by C₂³ of C₁₆ acting via C₁₆/C₄=C₄	32	4	C2^3.C16	128,132
C₄².₂D₄	2^nd non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.2D4	128,135
C₄².₃D₄	3^rd non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.3D4	128,136
(C₄×C₈)⋊₆C₄	6^th semidirect product of C₄×C₈ and C₄ acting faithfully	16	4	(C4xC8):6C4	128,141
(C₄×C₈).C₄	6^th non-split extension by C₄×C₈ of C₄ acting faithfully	16	4	(C4xC8).C4	128,142
(C₄×C₈)⋊C₄	3^rd semidirect product of C₄×C₈ and C₄ acting faithfully	32	4	(C4xC8):C4	128,146
D₁₆⋊₃C₄	2^nd semidirect product of D₁₆ and C₄ acting via C₄/C₂=C₂	32	4	D16:3C4	128,150
C₈.Q₁₆	2^nd non-split extension by C₈ of Q₁₆ acting via Q₁₆/C₄=C₂²	32	4	C8.Q16	128,158
C₈.₁₆C₄²	10^th non-split extension by C₈ of C₄² acting via C₄²/C₂×C₄=C₂	32	4	C8.16C4^2	128,479
C₂³.₅C₄²	5^th non-split extension by C₂³ of C₄² acting via C₄²/C₄=C₄	32	4	C2^3.5C4^2	128,489
2₊¹⁺⁴.₂C₄	The non-split extension by 2₊¹⁺⁴ of C₄ acting via C₄/C₂=C₂	32	4	ES+(2,2).2C4	128,523
2₊¹⁺⁴⋊₄C₄	3^rd semidirect product of 2₊¹⁺⁴ and C₄ acting via C₄/C₂=C₂	32	4	ES+(2,2):4C4	128,526
(C₂×D₄).₂₄Q₈	5^th non-split extension by C₂×D₄ of Q₈ acting via Q₈/C₄=C₂	32	4	(C2xD4).24Q8	128,544
(C₂×C₈).₁₀₃D₄	71^st non-split extension by C₂×C₈ of D₄ acting via D₄/C₂=C₂²	32	4	(C2xC8).103D4	128,545
C₈○D₄⋊C₄	1^st semidirect product of C₈○D₄ and C₄ acting via C₄/C₂=C₂	32	4	C8oD4:C4	128,546
(C₂×C₄²)⋊C₄	8^th semidirect product of C₂×C₄² and C₄ acting faithfully	16	4	(C2xC4^2):C4	128,559
C₈.(C₄⋊C₄)	4^th non-split extension by C₈ of C₄⋊C₄ acting via C₄⋊C₄/C₂²=C₂²	32	4	C8.(C4:C4)	128,565
C₈⋊C₄⋊₁₇C₄	12^nd semidirect product of C₈⋊C₄ and C₄ acting via C₄/C₂=C₂	16	4	C8:C4:17C4	128,573
M₄(2).₄₀D₄	4^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	4	M4(2).40D4	128,590
M₄(2).₄₁D₄	5^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	16	4	M4(2).41D4	128,593
(C₂×D₄).Q₈	9^th non-split extension by C₂×D₄ of Q₈ acting via Q₈/C₂=C₂²	32	4	(C2xD4).Q8	128,600
M₄(2).₄₄D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	4	M4(2).44D4	128,613
M₄(2)⋊₁₉D₄	6^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	16	4	M4(2):19D4	128,616
(C₂×C₈)⋊D₄	3^rd semidirect product of C₂×C₈ and D₄ acting faithfully	16	4	(C2xC8):D4	128,623
C₄².₄₂₆D₄	59^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	16	4	C4^2.426D4	128,638
C₄².₄₂₇D₄	60^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	16	4	C4^2.427D4	128,664
M₄(2).₂₇D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32	4	M4(2).27D4	128,685
M₄(2).₃₀D₄	11^st non-split extension by M₄(2) of D₄ acting via D₄/C₄=C₂	32	4	M4(2).30D4	128,708
C₄²⋊₂D₄	2^nd semidirect product of C₄² and D₄ acting faithfully	16	4	C4^2:2D4	128,742
(C₂×C₈).₂D₄	2^nd non-split extension by C₂×C₈ of D₄ acting faithfully	32	4	(C2xC8).2D4	128,749
C₄².₈D₄	8^th non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.8D4	128,763
C₄².₁₃₁D₄	113^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	16	4	C4^2.131D4	128,782
C₂²⋊C₄.₇D₄	5^th non-split extension by C₂²⋊C₄ of D₄ acting via D₄/C₂=C₂²	32	4	C2^2:C4.7D4	128,785
C₄².₉D₄	9^th non-split extension by C₄² of D₄ acting faithfully	32	4	C4^2.9D4	128,812
C₂⁴.₁₁Q₈	10^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	16	4	C2^4.11Q8	128,823
C₄².₁₀D₄	10^th non-split extension by C₄² of D₄ acting faithfully	32	4	C4^2.10D4	128,830
C₄².₃₂Q₈	32^nd non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	16	4	C4^2.32Q8	128,834
C₂²⋊C₄.Q₈	1^st non-split extension by C₂²⋊C₄ of Q₈ acting via Q₈/C₂=C₂²	32	4	C2^2:C4.Q8	128,835
C₈.₂₃C₄²	4^th central extension by C₈ of C₄²	32	4	C8.23C4^2	128,842
M₅(2).₁₉C₂²	6^th non-split extension by M₅(2) of C₂² acting via C₂²/C₂=C₂	32	4	M5(2).19C2^2	128,847
M₅(2)⋊₁₂C₂²	8^th semidirect product of M₅(2) and C₂² acting via C₂²/C₂=C₂	32	4	M5(2):12C2^2	128,849
C₄○C₂≀C₄	Central product of C₄ and C₂≀C₄	16	4	C4oC2wrC4	128,852
C₄⋊Q₈⋊₂₉C₄	24^th semidirect product of C₄⋊Q₈ and C₄ acting via C₄/C₂=C₂	16	4	C4:Q8:29C4	128,858
(C₂×D₄).₁₃₅D₄	97^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂=C₂²	16	4	(C2xD4).135D4	128,864
C₂³.₂₀SD₁₆	10^th non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₄=C₂²	32	4	C2^3.20SD16	128,875
C₂³.₁₃D₈	6^th non-split extension by C₂³ of D₈ acting via D₈/C₄=C₂²	32	4	C2^3.13D8	128,877
C₂³.₂₁SD₁₆	11^st non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₄=C₂²	32	4	C2^3.21SD16	128,880
M₄(2).₁C₈	1^st non-split extension by M₄(2) of C₈ acting via C₈/C₄=C₂	32	4	M4(2).1C8	128,885
M₅(2)⋊₃C₄	3^rd semidirect product of M₅(2) and C₄ acting via C₄/C₂=C₂	32	4	M5(2):3C4	128,887
M₅(2).₁C₄	1^st non-split extension by M₅(2) of C₄ acting via C₄/C₂=C₂	32	4	M5(2).1C4	128,893
C₈.₅M₄(2)	5^th non-split extension by C₈ of M₄(2) acting via M₄(2)/C₄=C₂²	16	4	C8.5M4(2)	128,897
C₈.₁₉M₄(2)	7^th non-split extension by C₈ of M₄(2) acting via M₄(2)/C₂×C₄=C₂	32	4	C8.19M4(2)	128,898
D₈.C₈	The non-split extension by D₈ of C₈ acting via C₈/C₄=C₂	32	4	D8.C8	128,903
D₁₆⋊₅C₄	4^th semidirect product of D₁₆ and C₄ acting via C₄/C₂=C₂	32	4	D16:5C4	128,911
Q₁₆.D₄	2^nd non-split extension by Q₁₆ of D₄ acting via D₄/C₂=C₂²	32	4	Q16.D4	128,925
D₈.₃D₄	3^rd non-split extension by D₈ of D₄ acting via D₄/C₂=C₂²	32	4	D8.3D4	128,926
C₄²⋊₄D₄	4^th semidirect product of C₄² and D₄ acting faithfully	16	4	C4^2:4D4	128,929
C₄².₁₃D₄	13^rd non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.13D4	128,930
C₄².₁₇D₄	17^th non-split extension by C₄² of D₄ acting faithfully	16	4	C4^2.17D4	128,936
C₈.₃D₈	3^rd non-split extension by C₈ of D₈ acting via D₈/C₄=C₂²	32	4	C8.3D8	128,944
D₄.₅D₈	5^th non-split extension by D₄ of D₈ acting via D₈/C₈=C₂	32	4	D4.5D8	128,955
D₈⋊₃Q₈	3^rd semidirect product of D₈ and Q₈ acting via Q₈/C₄=C₂	16	4	D8:3Q8	128,962
D₈.₂Q₈	2^nd non-split extension by D₈ of Q₈ acting via Q₈/C₄=C₂	32	4	D8.2Q8	128,963
2_-¹⁺⁴⋊₅C₄	4^th semidirect product of 2_-¹⁺⁴ and C₄ acting via C₄/C₂=C₂	16	4	ES-(2,2):5C4	128,1633
M₄(2).₂₉C₂³	11^st non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	32	4	M4(2).29C2^3	128,1648
C₄².₂₈₃C₂³	144^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	32	4	C4^2.283C2^3	128,1687
M₄(2).₅₁D₄	1^st non-split extension by M₄(2) of D₄ acting through Inn(M₄(2))	16	4	M4(2).51D4	128,1688
M₄(2)○D₈	Central product of M₄(2) and D₈	32	4	M4(2)oD8	128,1689
C₄².₃₁₃C₂³	174^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	16	4	C4^2.313C2^3	128,1750
C₂³.₇C₂⁴	7^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	16	4	C2^3.7C2^4	128,1757
M₄(2).₁₀C₂³	10^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂=C₂²	32	4	M4(2).10C2^3	128,1799
D₈○SD₁₆	Central product of D₈ and SD₁₆	32	4	D8oSD16	128,2022
D₈⋊₆D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	16	4	D8:6D4	128,2023
Q₈○M₅(2)	Central product of Q₈ and M₅(2)	32	4	Q8oM5(2)	128,2139
D₁₆⋊C₂²	4^th semidirect product of D₁₆ and C₂² acting via C₂²/C₂=C₂	32	4	D16:C2^2	128,2146
D₄○SD₃₂	Central product of D₄ and SD₃₂	32	4	D4oSD32	128,2148
C₄.₂₂C₂⁵	4^th central extension by C₄ of C₂⁵	32	4	C4.22C2^5	128,2305
C₈.C₂⁴	6^th non-split extension by C₈ of C₂⁴ acting via C₂⁴/C₂²=C₂²	32	4	C8.C2^4	128,2316

Groups of order 140

		d	ρ	Label	ID
C₇×F₅	Direct product of C₇ and F₅	35	4	C7xF5	140,5
C₇⋊F₅	The semidirect product of C₇ and F₅ acting via F₅/D₅=C₂	35	4	C7:F5	140,6

Groups of order 144

		d	ρ	Label	ID
C₃²⋊₂C₁₆	The semidirect product of C₃² and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^2:2C16	144,51
S₃×C₃⋊C₈	Direct product of S₃ and C₃⋊C₈	48	4	S3xC3:C8	144,52
C₁₂.₂₉D₆	3^rd non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.29D6	144,53
D₆.Dic₃	The non-split extension by D₆ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D6.Dic3	144,54
C₁₂.₃₁D₆	5^th non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.31D6	144,55
C₃²⋊₂D₈	1^st semidirect product of C₃² and D₈ acting via D₈/C₄=C₂²	48	4	C3^2:2D8	144,56
Dic₆⋊S₃	2^nd semidirect product of Dic₆ and S₃ acting via S₃/C₃=C₂	48	4	Dic6:S3	144,58
C₃²⋊₂Q₁₆	1^st semidirect product of C₃² and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3^2:2Q16	144,61
C₃×D₄⋊S₃	Direct product of C₃ and D₄⋊S₃	24	4	C3xD4:S3	144,80
C₃×D₄.S₃	Direct product of C₃ and D₄.S₃	24	4	C3xD4.S3	144,81
C₃×Q₈⋊₂S₃	Direct product of C₃ and Q₈⋊₂S₃	48	4	C3xQ8:2S3	144,82
C₃×C₃⋊Q₁₆	Direct product of C₃ and C₃⋊Q₁₆	48	4	C3xC3:Q16	144,83
C₃⋊S₃.Q₈	The non-split extension by C₃⋊S₃ of Q₈ acting via Q₈/C₂=C₂²	24	4	C3:S3.Q8	144,116
C₃²⋊D₈	The semidirect product of C₃² and D₈ acting via D₈/C₂=D₄	24	4	C3^2:D8	144,117
C₃⋊S₃⋊₃C₈	2^nd semidirect product of C₃⋊S₃ and C₈ acting via C₈/C₄=C₂	24	4	C3:S3:3C8	144,130
C₃²⋊M₄(2)	The semidirect product of C₃² and M₄(2) acting via M₄(2)/C₄=C₄	24	4	C3^2:M4(2)	144,131
C₄×C₃²⋊C₄	Direct product of C₄ and C₃²⋊C₄	24	4	C4xC3^2:C4	144,132
C₄⋊(C₃²⋊C₄)	The semidirect product of C₄ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	24	4	C4:(C3^2:C4)	144,133
D₁₂⋊S₃	3^rd semidirect product of D₁₂ and S₃ acting via S₃/C₃=C₂	24	4	D12:S3	144,139
Dic₃.D₆	2^nd non-split extension by Dic₃ of D₆ acting via D₆/S₃=C₂	24	4	Dic3.D6	144,140
D₆.D₆	1^st non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	24	4	D6.D6	144,141
C₄×S₃²	Direct product of C₄, S₃ and S₃	24	4	C4xS3^2	144,143
D₆⋊D₆	2^nd semidirect product of D₆ and D₆ acting via D₆/S₃=C₂	24	4	D6:D6	144,145
D₆.₃D₆	3^rd non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	24	4	D6.3D6	144,147
S₃×C₃⋊D₄	Direct product of S₃ and C₃⋊D₄	24	4	S3xC3:D4	144,153
C₃×S₃×D₄	Direct product of C₃, S₃ and D₄	24	4	C3xS3xD4	144,162
C₃×D₄⋊₂S₃	Direct product of C₃ and D₄⋊₂S₃	24	4	C3xD4:2S3	144,163
C₃×S₃×Q₈	Direct product of C₃, S₃ and Q₈	48	4	C3xS3xQ8	144,164
C₃×Q₈⋊₃S₃	Direct product of C₃ and Q₈⋊₃S₃	48	4	C3xQ8:3S3	144,165

Groups of order 156

		d	ρ	Label	ID
C₃×C₁₃⋊C₄	Direct product of C₃ and C₁₃⋊C₄	39	4	C3xC13:C4	156,9
C₃₉⋊C₄	1^st semidirect product of C₃₉ and C₄ acting faithfully	39	4	C39:C4	156,10

Groups of order 160

		d	ρ	Label	ID
C₅⋊C₃₂	The semidirect product of C₅ and C₃₂ acting via C₃₂/C₈=C₄	160	4	C5:C32	160,3
C₂³.₁D₁₀	1^st non-split extension by C₂³ of D₁₀ acting via D₁₀/C₅=C₂²	40	4	C2^3.1D10	160,13
C₂₀.₅₃D₄	10^th non-split extension by C₂₀ of D₄ acting via D₄/C₂²=C₂	80	4	C20.53D4	160,29
D₂₀⋊₇C₄	4^th semidirect product of D₂₀ and C₄ acting via C₄/C₂=C₂	40	4	D20:7C4	160,32
C₂₀.D₄	8^th non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	40	4	C20.D4	160,40
C₂³⋊Dic₅	The semidirect product of C₂³ and Dic₅ acting via Dic₅/C₅=C₄	40	4	C2^3:Dic5	160,41
C₂₀.₁₀D₄	10^th non-split extension by C₂₀ of D₄ acting via D₄/C₂=C₂²	80	4	C20.10D4	160,43
D₄⋊₂Dic₅	2^nd semidirect product of D₄ and Dic₅ acting via Dic₅/C₁₀=C₂	40	4	D4:2Dic5	160,44
C₅×C₂³⋊C₄	Direct product of C₅ and C₂³⋊C₄	40	4	C5xC2^3:C4	160,49
C₅×C₄.D₄	Direct product of C₅ and C₄.D₄	40	4	C5xC4.D4	160,50
C₅×C₄.₁₀D₄	Direct product of C₅ and C₄.₁₀D₄	80	4	C5xC4.10D4	160,51
D₅⋊C₁₆	The semidirect product of D₅ and C₁₆ acting via C₁₆/C₈=C₂	80	4	D5:C16	160,64
C₈.F₅	3^rd non-split extension by C₈ of F₅ acting via F₅/D₅=C₂	80	4	C8.F5	160,65
C₈×F₅	Direct product of C₈ and F₅	40	4	C8xF5	160,66
C₈⋊F₅	3^rd semidirect product of C₈ and F₅ acting via F₅/D₅=C₂	40	4	C8:F5	160,67
C₄₀⋊C₄	2^nd semidirect product of C₄₀ and C₄ acting faithfully	40	4	C40:C4	160,68
D₅.D₈	The non-split extension by D₅ of D₈ acting via D₈/C₈=C₂	40	4	D5.D8	160,69
C₄₀.C₄	2^nd non-split extension by C₄₀ of C₄ acting faithfully	80	4	C40.C4	160,70
D₁₀.Q₈	2^nd non-split extension by D₁₀ of Q₈ acting via Q₈/C₄=C₂	80	4	D10.Q8	160,71
C₂₀.C₈	1^st non-split extension by C₂₀ of C₈ acting via C₈/C₂=C₄	80	4	C20.C8	160,73
C₂³⋊F₅	The semidirect product of C₂³ and F₅ acting via F₅/C₅=C₄	40	4	C2^3:F5	160,86
C₂³.F₅	The non-split extension by C₂³ of F₅ acting via F₅/C₅=C₄	40	4	C2^3.F5	160,88
D₅×M₄(2)	Direct product of D₅ and M₄(2)	40	4	D5xM4(2)	160,127
D₂₀.₂C₄	The non-split extension by D₂₀ of C₄ acting via C₄/C₂=C₂	80	4	D20.2C4	160,128
D₈⋊D₅	2^nd semidirect product of D₈ and D₅ acting via D₅/C₅=C₂	40	4	D8:D5	160,132
D₅×SD₁₆	Direct product of D₅ and SD₁₆	40	4	D5xSD16	160,134
SD₁₆⋊₃D₅	The semidirect product of SD₁₆ and D₅ acting through Inn(SD₁₆)	80	4	SD16:3D5	160,137
Q₁₆⋊D₅	2^nd semidirect product of Q₁₆ and D₅ acting via D₅/C₅=C₂	80	4	Q16:D5	160,139
D₄.D₁₀	1^st non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D4.D10	160,153
C₂₀.C₂³	15^th non-split extension by C₂₀ of C₂³ acting via C₂³/C₂=C₂²	80	4	C20.C2^3	160,163
D₄.Dic₅	The non-split extension by D₄ of Dic₅ acting through Inn(D₄)	80	4	D4.Dic5	160,169
D₄.₈D₁₀	3^rd non-split extension by D₄ of D₁₀ acting via D₁₀/C₁₀=C₂	80	4	D4.8D10	160,171
C₅×C₈⋊C₂²	Direct product of C₅ and C₈⋊C₂²	40	4	C5xC8:C2^2	160,197
C₅×C₈.C₂²	Direct product of C₅ and C₈.C₂²	80	4	C5xC8.C2^2	160,198
D₅⋊M₄(2)	The semidirect product of D₅ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	40	4	D5:M4(2)	160,202
D₁₀.C₂³	11^st non-split extension by D₁₀ of C₂³ acting via C₂³/C₂²=C₂	40	4	D10.C2^3	160,205
D₄⋊₆D₁₀	2^nd semidirect product of D₄ and D₁₀ acting through Inn(D₄)	40	4	D4:6D10	160,219
Q₈.₁₀D₁₀	1^st non-split extension by Q₈ of D₁₀ acting through Inn(Q₈)	80	4	Q8.10D10	160,222
D₅×C₄○D₄	Direct product of D₅ and C₄○D₄	40	4	D5xC4oD4	160,223
C₅×2₊¹⁺⁴	Direct product of C₅ and 2₊¹⁺⁴	40	4	C5xES+(2,2)	160,232
C₅×2_-¹⁺⁴	Direct product of C₅ and 2_-¹⁺⁴	80	4	C5xES-(2,2)	160,233

Groups of order 180

		d	ρ	Label	ID
C₉×F₅	Direct product of C₉ and F₅	45	4	C9xF5	180,5
C₉⋊F₅	The semidirect product of C₉ and F₅ acting via F₅/D₅=C₂	45	4	C9:F5	180,6
C₃×C₃⋊F₅	Direct product of C₃ and C₃⋊F₅	30	4	C3xC3:F5	180,21
C₅×C₃²⋊C₄	Direct product of C₅ and C₃²⋊C₄	30	4	C5xC3^2:C4	180,23
C₃²⋊Dic₅	The semidirect product of C₃² and Dic₅ acting via Dic₅/C₅=C₄	30	4	C3^2:Dic5	180,24
C₃×S₃×D₅	Direct product of C₃, S₃ and D₅	30	4	C3xS3xD5	180,26
C₅×S₃²	Direct product of C₅, S₃ and S₃	30	4	C5xS3^2	180,28
D₁₅⋊S₃	The semidirect product of D₁₅ and S₃ acting via S₃/C₃=C₂	30	4	D15:S3	180,30

Groups of order 192

		d	ρ	Label	ID
C₂³.SL₂(𝔽₃)	1^st non-split extension by C₂³ of SL₂(𝔽₃) acting via SL₂(𝔽₃)/C₂=A₄	16	4	C2^3.SL(2,3)	192,4
C₁₂.₁₅C₄²	8^th non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48	4	C12.15C4^2	192,25
C₈.Dic₆	1^st non-split extension by C₈ of Dic₆ acting via Dic₆/C₆=C₂²	48	4	C8.Dic6	192,46
D₂₄⋊₈C₄	8^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:8C4	192,47
C₂₄.₇Q₈	7^th non-split extension by C₂₄ of Q₈ acting via Q₈/C₂=C₂²	96	4	C24.7Q8	192,52
C₂₄.₆Q₈	6^th non-split extension by C₂₄ of Q₈ acting via Q₈/C₂=C₂²	48	4	C24.6Q8	192,53
Dic₁₂.C₄	3^rd non-split extension by Dic₁₂ of C₄ acting via C₄/C₂=C₂	96	4	Dic12.C4	192,56
C₂₄.₉₇D₄	20^th non-split extension by C₂₄ of D₄ acting via D₄/C₂²=C₂	48	4	C24.97D4	192,70
C₄₈⋊C₄	2^nd semidirect product of C₄₈ and C₄ acting faithfully	48	4	C48:C4	192,71
C₂₄.Q₈	1^st non-split extension by C₂₄ of Q₈ acting via Q₈/C₂=C₂²	48	4	C24.Q8	192,72
C₈.₂₅D₁₂	11^st non-split extension by C₈ of D₁₂ acting via D₁₂/D₆=C₂	48	4	C8.25D12	192,73
Dic₆.C₈	2^nd non-split extension by Dic₆ of C₈ acting via C₈/C₄=C₂	96	4	Dic6.C8	192,74
D₂₄⋊₂C₄	2^nd semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:2C4	192,77
C₄²⋊₃Dic₃	1^st semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2:3Dic3	192,90
(C₂×C₁₂).Q₈	8^th non-split extension by C₂×C₁₂ of Q₈ acting via Q₈/C₂=C₂²	48	4	(C2xC12).Q8	192,92
C₂⁴⋊₅Dic₃	1^st semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₃=C₄	24	4	C2^4:5Dic3	192,95
(C₂²×C₁₂)⋊C₄	2^nd semidirect product of C₂²×C₁₂ and C₄ acting faithfully	48	4	(C2^2xC12):C4	192,98
C₄²⋊₄Dic₃	2^nd semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2:4Dic3	192,100
C₄².Dic₃	2^nd non-split extension by C₄² of Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2.Dic3	192,101
C₄²⋊₅Dic₃	3^rd semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	24	4	C4^2:5Dic3	192,104
C₄².₃Dic₃	3^rd non-split extension by C₄² of Dic₃ acting via Dic₃/C₃=C₄	48	4	C4^2.3Dic3	192,107
C₂₄.D₄	52^nd non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.D4	192,112
(C₂×C₂₄)⋊C₄	1^st semidirect product of C₂×C₂₄ and C₄ acting faithfully	48	4	(C2xC24):C4	192,115
C₁₂.₂₀C₄²	13^rd non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48	4	C12.20C4^2	192,116
M₄(2)⋊₄Dic₃	4^th semidirect product of M₄(2) and Dic₃ acting via Dic₃/C₆=C₂	48	4	M4(2):4Dic3	192,118
C₁₂.₂₁C₄²	14^th non-split extension by C₁₂ of C₄² acting via C₄²/C₂×C₄=C₂	48	4	C12.21C4^2	192,119
C₂₄.₉₉D₄	22^nd non-split extension by C₂₄ of D₄ acting via D₄/C₂²=C₂	96	4	C24.99D4	192,120
D₈.Dic₃	2^nd non-split extension by D₈ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D8.Dic3	192,122
Q₁₆.Dic₃	2^nd non-split extension by Q₁₆ of Dic₃ acting via Dic₃/C₆=C₂	96	4	Q16.Dic3	192,124
D₈⋊₂Dic₃	2^nd semidirect product of D₈ and Dic₃ acting via Dic₃/C₆=C₂	48	4	D8:2Dic3	192,125
C₂₄.₄₁D₄	41^st non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	96	4	C24.41D4	192,126
C₃×C₄.₉C₄²	Direct product of C₃ and C₄.₉C₄²	48	4	C3xC4.9C4^2	192,143
C₃×C₄.₁₀C₄²	Direct product of C₃ and C₄.₁₀C₄²	48	4	C3xC4.10C4^2	192,144
C₃×M₄(2)⋊₄C₄	Direct product of C₃ and M₄(2)⋊₄C₄	48	4	C3xM4(2):4C4	192,150
C₃×C₁₆⋊C₄	Direct product of C₃ and C₁₆⋊C₄	48	4	C3xC16:C4	192,153
C₃×C₂³.C₈	Direct product of C₃ and C₂³.C₈	48	4	C3xC2^3.C8	192,155
C₃×C₂≀C₄	Direct product of C₃ and C₂≀C₄	24	4	C3xC2wrC4	192,157
C₃×C₂³.D₄	Direct product of C₃ and C₂³.D₄	48	4	C3xC2^3.D4	192,158
C₃×C₄²⋊C₄	Direct product of C₃ and C₄²⋊C₄	24	4	C3xC4^2:C4	192,159
C₃×C₄²⋊₃C₄	Direct product of C₃ and C₄²⋊₃C₄	48	4	C3xC4^2:3C4	192,160
C₃×C₄².C₄	Direct product of C₃ and C₄².C₄	48	4	C3xC4^2.C4	192,161
C₃×C₄².₃C₄	Direct product of C₃ and C₄².₃C₄	48	4	C3xC4^2.3C4	192,162
C₃×D₈⋊₂C₄	Direct product of C₃ and D₈⋊₂C₄	48	4	C3xD8:2C4	192,166
C₃×M₅(2)⋊C₂	Direct product of C₃ and M₅(2)⋊C₂	48	4	C3xM5(2):C2	192,167
C₃×C₈.₁₇D₄	Direct product of C₃ and C₈.₁₇D₄	96	4	C3xC8.17D4	192,168
C₃×C₈.Q₈	Direct product of C₃ and C₈.Q₈	48	4	C3xC8.Q8	192,171
2₊¹⁺⁴.C₆	1^st non-split extension by 2₊¹⁺⁴ of C₆ acting faithfully	16	4	ES+(2,2).C6	192,202
D₂₄⋊₄C₄	4^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:4C4	192,276
S₃×C₄≀C₂	Direct product of S₃ and C₄≀C₂	24	4	S3xC4wrC2	192,379
C₄²⋊₃D₆	1^st semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:3D6	192,380
M₄(2).₂₂D₆	5^th non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	4	M4(2).22D6	192,382
C₄².₁₉₆D₆	16^th non-split extension by C₄² of D₆ acting via D₆/S₃=C₂	48	4	C4^2.196D6	192,383
C₄²⋊₅D₆	3^rd semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:5D6	192,384
D₄.₁₀D₁₂	5^th non-split extension by D₄ of D₁₂ acting via D₁₂/D₆=C₂	48	4	D4.10D12	192,386
S₃×C₈.C₄	Direct product of S₃ and C₈.C₄	48	4	S3xC8.C4	192,451
M₄(2).₂₅D₆	8^th non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	4	M4(2).25D6	192,452
D₂₄⋊₁₀C₄	10^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:10C4	192,453
D₂₄⋊₇C₄	7^th semidirect product of D₂₄ and C₄ acting via C₄/C₂=C₂	48	4	D24:7C4	192,454
C₂₄.₄₂D₄	42^nd non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.42D4	192,457
S₃×M₅(2)	Direct product of S₃ and M₅(2)	48	4	S3xM5(2)	192,465
C₁₆.₁₂D₆	9^th non-split extension by C₁₆ of D₆ acting via D₆/S₃=C₂	96	4	C16.12D6	192,466
D₈⋊D₆	2^nd semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	4	D8:D6	192,470
S₃×SD₃₂	Direct product of S₃ and SD₃₂	48	4	S3xSD32	192,472
D₆.₂D₈	2^nd non-split extension by D₆ of D₈ acting via D₈/C₈=C₂	96	4	D6.2D8	192,475
Q₃₂⋊S₃	2^nd semidirect product of Q₃₂ and S₃ acting via S₃/C₃=C₂	96	4	Q32:S3	192,477
C₄²⋊₆D₆	4^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:6D6	192,564
(C₂×D₁₂)⋊₁₃C₄	9^th semidirect product of C₂×D₁₂ and C₄ acting via C₄/C₂=C₂	48	4	(C2xD12):13C4	192,565
C₂⁴⋊₆D₆	1^st semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	24	4	C2^4:6D6	192,591
C₂²⋊C₄⋊D₆	4^th semidirect product of C₂²⋊C₄ and D₆ acting via D₆/C₃=C₂²	48	4	C2^2:C4:D6	192,612
C₄²⋊₇D₆	5^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	48	4	C4^2:7D6	192,620
D₁₂.₁₄D₄	14^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	D12.14D4	192,621
C₄²⋊₈D₆	6^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	24	4	C4^2:8D6	192,636
D₁₂.₁₅D₄	15^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	4	D12.15D4	192,654
C₂³.₈Dic₆	6^th non-split extension by C₂³ of Dic₆ acting via Dic₆/C₆=C₂²	48	4	C2^3.8Dic6	192,683
C₂³.₉Dic₆	7^th non-split extension by C₂³ of Dic₆ acting via Dic₆/C₆=C₂²	48	4	C2^3.9Dic6	192,684
M₄(2).₃₁D₆	4^th non-split extension by M₄(2) of D₆ acting via D₆/C₆=C₂	48	4	M4(2).31D6	192,691
M₄(2)⋊₂₄D₆	8^th semidirect product of M₄(2) and D₆ acting via D₆/C₆=C₂	48	4	M4(2):24D6	192,698
C₂₄.₇₈C₂³	24^th non-split extension by C₂₄ of C₂³ acting via C₂³/C₂²=C₂	96	4	C24.78C2^3	192,699
Q₈.₈D₁₂	3^rd non-split extension by Q₈ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4	Q8.8D12	192,700
C₂₄.₁₀₀D₄	23^rd non-split extension by C₂₄ of D₄ acting via D₄/C₂²=C₂	48	4	C24.100D4	192,703
C₂₄.₅₄D₄	54^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.54D4	192,704
D₈.D₆	1^st non-split extension by D₈ of D₆ acting via D₆/C₆=C₂	48	4	D8.D6	192,706
C₂₄.₂₃D₄	23^rd non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.23D4	192,719
C₂₄.₄₄D₄	44^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	48	4	C24.44D4	192,736
C₂₄.₂₇C₂³	20^th non-split extension by C₂₄ of C₂³ acting via C₂³/C₂=C₂²	96	4	C24.27C2^3	192,738
C₂₄.₂₉D₄	29^th non-split extension by C₂₄ of D₄ acting via D₄/C₂=C₂²	96	4	C24.29D4	192,751
Q₁₆.D₆	3^rd non-split extension by Q₁₆ of D₆ acting via D₆/C₆=C₂	96	4	Q16.D6	192,753
D₈⋊₅Dic₃	The semidirect product of D₈ and Dic₃ acting through Inn(D₈)	48	4	D8:5Dic3	192,755
D₈⋊₄Dic₃	4^th semidirect product of D₈ and Dic₃ acting via Dic₃/C₆=C₂	48	4	D8:4Dic3	192,756
(C₆×D₄)⋊₉C₄	5^th semidirect product of C₆×D₄ and C₄ acting via C₄/C₂=C₂	48	4	(C6xD4):9C4	192,795
(C₆×D₄).₁₆C₄	10^th non-split extension by C₆×D₄ of C₄ acting via C₄/C₂=C₂	48	4	(C6xD4).16C4	192,796
(C₆×D₄)⋊₁₀C₄	6^th semidirect product of C₆×D₄ and C₄ acting via C₄/C₂=C₂	48	4	(C6xD4):10C4	192,799
C₃×C₂³.C₂³	Direct product of C₃ and C₂³.C₂³	48	4	C3xC2^3.C2^3	192,843
C₃×M₄(2).₈C₂²	Direct product of C₃ and M₄(2).₈C₂²	48	4	C3xM4(2).8C2^2	192,846
C₃×C₄²⋊C₂²	Direct product of C₃ and C₄²⋊C₂²	48	4	C3xC4^2:C2^2	192,854
C₃×M₄(2).C₄	Direct product of C₃ and M₄(2).C₄	48	4	C3xM4(2).C4	192,863
C₃×C₈.₂₆D₄	Direct product of C₃ and C₈.₂₆D₄	48	4	C3xC8.26D4	192,877
C₃×D₄⋊₄D₄	Direct product of C₃ and D₄⋊₄D₄	24	4	C3xD4:4D4	192,886
C₃×D₄.₈D₄	Direct product of C₃ and D₄.₈D₄	48	4	C3xD4.8D4	192,887
C₃×D₄.₉D₄	Direct product of C₃ and D₄.₉D₄	48	4	C3xD4.9D4	192,888
C₃×D₄.₁₀D₄	Direct product of C₃ and D₄.₁₀D₄	48	4	C3xD4.10D4	192,889
C₃×C₂≀C₂²	Direct product of C₃ and C₂≀C₂²	24	4	C3xC2wrC2^2	192,890
C₃×C₂³.₇D₄	Direct product of C₃ and C₂³.₇D₄	48	4	C3xC2^3.7D4	192,891
C₃×D₄.₃D₄	Direct product of C₃ and D₄.₃D₄	48	4	C3xD4.3D4	192,904
C₃×D₄.₄D₄	Direct product of C₃ and D₄.₄D₄	48	4	C3xD4.4D4	192,905
C₃×D₄.₅D₄	Direct product of C₃ and D₄.₅D₄	96	4	C3xD4.5D4	192,906
C₃×C₁₆⋊C₂²	Direct product of C₃ and C₁₆⋊C₂²	48	4	C3xC16:C2^2	192,942
C₃×Q₃₂⋊C₂	Direct product of C₃ and Q₃₂⋊C₂	96	4	C3xQ32:C2	192,943
C₈.₅S₄	5^th non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4	C8.5S4	192,964
C₈.₄S₄	4^th non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4	C8.4S4	192,965
U₂(𝔽₃)⋊C₂	6^th semidirect product of U₂(𝔽₃) and C₂ acting faithfully	32	4	U(2,3):C2	192,982
Q₈.₄S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	48	4	Q8.4S4	192,987
D₄.₃S₄	3^rd non-split extension by D₄ of S₄ acting via S₄/A₄=C₂	32	4	D4.3S4	192,990
M₄(2).A₄	The non-split extension by M₄(2) of A₄ acting through Inn(M₄(2))	32	4	M4(2).A4	192,1013
SD₁₆.A₄	The non-split extension by SD₁₆ of A₄ acting through Inn(SD₁₆)	32	4	SD16.A4	192,1018
M₄(2)⋊₂₆D₆	2^nd semidirect product of M₄(2) and D₆ acting through Inn(M₄(2))	48	4	M4(2):26D6	192,1304
C₂₄.₉C₂³	2^nd non-split extension by C₂₄ of C₂³ acting via C₂³/C₂=C₂²	48	4	C24.9C2^3	192,1307
S₃×C₈○D₄	Direct product of S₃ and C₈○D₄	48	4	S3xC8oD4	192,1308
M₄(2)⋊₂₈D₆	4^th semidirect product of M₄(2) and D₆ acting through Inn(M₄(2))	48	4	M4(2):28D6	192,1309
D₄.₁₁D₁₂	1^st non-split extension by D₄ of D₁₂ acting through Inn(D₄)	48	4	D4.11D12	192,1310
D₈⋊₁₃D₆	2^nd semidirect product of D₈ and D₆ acting through Inn(D₈)	48	4	D8:13D6	192,1316
SD₁₆⋊₁₃D₆	2^nd semidirect product of SD₁₆ and D₆ acting through Inn(SD₁₆)	48	4	SD16:13D6	192,1321
D₁₂.₃₀D₄	13^rd non-split extension by D₁₂ of D₄ acting via D₄/C₄=C₂	96	4	D12.30D4	192,1325
S₃×C₄○D₈	Direct product of S₃ and C₄○D₈	48	4	S3xC4oD8	192,1326
SD₁₆⋊D₆	3^rd semidirect product of SD₁₆ and D₆ acting via D₆/C₆=C₂	48	4	SD16:D6	192,1327
D₈⋊₁₁D₆	5^th semidirect product of D₈ and D₆ acting via D₆/C₆=C₂	48	4	D8:11D6	192,1329
C₁₂.₇₆C₂⁴	23^rd non-split extension by C₁₂ of C₂⁴ acting via C₂⁴/C₂³=C₂	48	4	C12.76C2^4	192,1378
C₁₂.C₂⁴	35^th non-split extension by C₁₂ of C₂⁴ acting via C₂⁴/C₂²=C₂²	48	4	C12.C2^4	192,1381
C₃×Q₈○M₄(2)	Direct product of C₃ and Q₈○M₄(2)	48	4	C3xQ8oM4(2)	192,1457
C₃×D₈⋊C₂²	Direct product of C₃ and D₈⋊C₂²	48	4	C3xD8:C2^2	192,1464
C₃×D₄○D₈	Direct product of C₃ and D₄○D₈	48	4	C3xD4oD8	192,1465
C₃×D₄○SD₁₆	Direct product of C₃ and D₄○SD₁₆	48	4	C3xD4oSD16	192,1466
C₃×Q₈○D₈	Direct product of C₃ and Q₈○D₈	96	4	C3xQ8oD8	192,1467
GL₂(𝔽₃)⋊C₂²	3^rd semidirect product of GL₂(𝔽₃) and C₂² acting via C₂²/C₂=C₂	32	4	GL(2,3):C2^2	192,1482
Q₈.₆S₄	1^st non-split extension by Q₈ of S₄ acting through Inn(Q₈)	32	4	Q8.6S4	192,1483
D₄.₄S₄	1^st non-split extension by D₄ of S₄ acting through Inn(D₄)	16	4	D4.4S4	192,1485
C₂³.S₄	4^th non-split extension by C₂³ of S₄ acting faithfully	16	4	C2^3.S4	192,1491
Q₈.S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	16	4	Q8.S4	192,1492
2_-¹⁺⁴⋊₃C₆	2^nd semidirect product of 2_-¹⁺⁴ and C₆ acting via C₆/C₂=C₃	32	4	ES-(2,2):3C6	192,1504
2₊¹⁺⁴.₃C₆	The non-split extension by 2₊¹⁺⁴ of C₆ acting via C₆/C₂=C₃	16	4	ES+(2,2).3C6	192,1509
C₆.C₂⁵	14^th non-split extension by C₆ of C₂⁵ acting via C₂⁵/C₂⁴=C₂	48	4	C6.C2^5	192,1523
C₃×C₂.C₂⁵	Direct product of C₃ and C₂.C₂⁵	48	4	C3xC2.C2^5	192,1536

Groups of order 200

		d	ρ	Label	ID
C₅×C₅⋊C₈	Direct product of C₅ and C₅⋊C₈	40	4	C5xC5:C8	200,18
C₅²⋊₃C₈	2^nd semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4	C5^2:3C8	200,19
C₁₀×F₅	Direct product of C₁₀ and F₅	40	4	C10xF5	200,45
C₂×D₅.D₅	Direct product of C₂ and D₅.D₅	40	4	C2xD5.D5	200,46

Groups of order 204

		d	ρ	Label	ID
C₃×C₁₇⋊C₄	Direct product of C₃ and C₁₇⋊C₄	51	4	C3xC17:C4	204,5
C₅₁⋊C₄	1^st semidirect product of C₅₁ and C₄ acting faithfully	51	4	C51:C4	204,6

Groups of order 208

		d	ρ	Label	ID
C₁₃⋊C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₄=C₄	208	4	C13:C16	208,3
D₁₃⋊C₈	The semidirect product of D₁₃ and C₈ acting via C₈/C₄=C₂	104	4	D13:C8	208,28
C₅₂.C₄	1^st non-split extension by C₅₂ of C₄ acting faithfully	104	4	C52.C4	208,29
C₄×C₁₃⋊C₄	Direct product of C₄ and C₁₃⋊C₄	52	4	C4xC13:C4	208,30
C₅₂⋊C₄	1^st semidirect product of C₅₂ and C₄ acting faithfully	52	4	C52:C4	208,31

Groups of order 216

		d	ρ	Label	ID
C₃×C₃²⋊₂C₈	Direct product of C₃ and C₃²⋊₂C₈	24	4	C3xC3^2:2C8	216,117
C₃³⋊₄C₈	2^nd semidirect product of C₃³ and C₈ acting via C₈/C₂=C₄	24	4	C3^3:4C8	216,118
C₃×S₃×Dic₃	Direct product of C₃, S₃ and Dic₃	24	4	C3xS3xDic3	216,119
C₃×C₆.D₆	Direct product of C₃ and C₆.D₆	24	4	C3xC6.D6	216,120
C₃×D₆⋊S₃	Direct product of C₃ and D₆⋊S₃	24	4	C3xD6:S3	216,121
C₃×C₃⋊D₁₂	Direct product of C₃ and C₃⋊D₁₂	24	4	C3xC3:D12	216,122
C₃×C₃²⋊₂Q₈	Direct product of C₃ and C₃²⋊₂Q₈	24	4	C3xC3^2:2Q8	216,123
C₃³⋊₉(C₂×C₄)	6^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	24	4	C3^3:9(C2xC4)	216,131
C₃³⋊₉D₄	6^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	24	4	C3^3:9D4	216,132
C₃³⋊₅Q₈	3^rd semidirect product of C₃³ and Q₈ acting via Q₈/C₂=C₂²	24	4	C3^3:5Q8	216,133
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	12	4	C3xS3wrC2	216,157
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	12	4	C3^3:D4	216,158
C₆×C₃²⋊C₄	Direct product of C₆ and C₃²⋊C₄	24	4	C6xC3^2:C4	216,168
C₂×C₃³⋊C₄	Direct product of C₂ and C₃³⋊C₄	24	4	C2xC3^3:C4	216,169
S₃²×C₆	Direct product of C₆, S₃ and S₃	24	4	S3^2xC6	216,170
C₂×C₃²⋊₄D₆	Direct product of C₂ and C₃²⋊₄D₆	24	4	C2xC3^2:4D6	216,172

Groups of order 220

		d	ρ	Label	ID
C₁₁×F₅	Direct product of C₁₁ and F₅	55	4	C11xF5	220,9
C₁₁⋊F₅	The semidirect product of C₁₁ and F₅ acting via F₅/D₅=C₂	55	4	C11:F5	220,10

Groups of order 224

		d	ρ	Label	ID
C₂³.₁D₁₄	1^st non-split extension by C₂³ of D₁₄ acting via D₁₄/C₇=C₂²	56	4	C2^3.1D14	224,12
C₂₈.₅₃D₄	10^th non-split extension by C₂₈ of D₄ acting via D₄/C₂²=C₂	112	4	C28.53D4	224,28
D₂₈⋊₄C₄	4^th semidirect product of D₂₈ and C₄ acting via C₄/C₂=C₂	56	4	D28:4C4	224,31
C₂₈.D₄	8^th non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	56	4	C28.D4	224,39
C₂³⋊Dic₇	The semidirect product of C₂³ and Dic₇ acting via Dic₇/C₇=C₄	56	4	C2^3:Dic7	224,40
C₂₈.₁₀D₄	10^th non-split extension by C₂₈ of D₄ acting via D₄/C₂=C₂²	112	4	C28.10D4	224,42
D₄⋊₂Dic₇	2^nd semidirect product of D₄ and Dic₇ acting via Dic₇/C₁₄=C₂	56	4	D4:2Dic7	224,43
C₇×C₂³⋊C₄	Direct product of C₇ and C₂³⋊C₄	56	4	C7xC2^3:C4	224,48
C₇×C₄.D₄	Direct product of C₇ and C₄.D₄	56	4	C7xC4.D4	224,49
C₇×C₄.₁₀D₄	Direct product of C₇ and C₄.₁₀D₄	112	4	C7xC4.10D4	224,50
D₇×M₄(2)	Direct product of D₇ and M₄(2)	56	4	D7xM4(2)	224,101
D₂₈.C₄	The non-split extension by D₂₈ of C₄ acting via C₄/C₂=C₂	112	4	D28.C4	224,102
D₈⋊D₇	2^nd semidirect product of D₈ and D₇ acting via D₇/C₇=C₂	56	4	D8:D7	224,106
D₇×SD₁₆	Direct product of D₇ and SD₁₆	56	4	D7xSD16	224,108
SD₁₆⋊₃D₇	The semidirect product of SD₁₆ and D₇ acting through Inn(SD₁₆)	112	4	SD16:3D7	224,111
Q₁₆⋊D₇	2^nd semidirect product of Q₁₆ and D₇ acting via D₇/C₇=C₂	112	4	Q16:D7	224,113
D₄.D₁₄	1^st non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	56	4	D4.D14	224,127
C₂₈.C₂³	15^th non-split extension by C₂₈ of C₂³ acting via C₂³/C₂=C₂²	112	4	C28.C2^3	224,137
Q₈.Dic₇	The non-split extension by Q₈ of Dic₇ acting through Inn(Q₈)	112	4	Q8.Dic7	224,143
D₄.₈D₁₄	3^rd non-split extension by D₄ of D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D4.8D14	224,145
C₇×C₈⋊C₂²	Direct product of C₇ and C₈⋊C₂²	56	4	C7xC8:C2^2	224,171
C₇×C₈.C₂²	Direct product of C₇ and C₈.C₂²	112	4	C7xC8.C2^2	224,172
D₄⋊₆D₁₄	2^nd semidirect product of D₄ and D₁₄ acting through Inn(D₄)	56	4	D4:6D14	224,180
Q₈.₁₀D₁₄	1^st non-split extension by Q₈ of D₁₄ acting through Inn(Q₈)	112	4	Q8.10D14	224,183
D₇×C₄○D₄	Direct product of D₇ and C₄○D₄	56	4	D7xC4oD4	224,184
C₇×2₊¹⁺⁴	Direct product of C₇ and 2₊¹⁺⁴	56	4	C7xES+(2,2)	224,193
C₇×2_-¹⁺⁴	Direct product of C₇ and 2_-¹⁺⁴	112	4	C7xES-(2,2)	224,194

Groups of order 240

		d	ρ	Label	ID
C₃×C₅⋊C₁₆	Direct product of C₃ and C₅⋊C₁₆	240	4	C3xC5:C16	240,5
C₁₅⋊C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₄=C₄	240	4	C15:C16	240,6
D₅×C₃⋊C₈	Direct product of D₅ and C₃⋊C₈	120	4	D5xC3:C8	240,7
S₃×C₅⋊₂C₈	Direct product of S₃ and C₅⋊₂C₈	120	4	S3xC5:2C8	240,8
D₁₅⋊₂C₈	The semidirect product of D₁₅ and C₈ acting via C₈/C₄=C₂	120	4	D15:2C8	240,9
C₂₀.₃₂D₆	11^st non-split extension by C₂₀ of D₆ acting via D₆/S₃=C₂	120	4	C20.32D6	240,10
D₆.Dic₅	The non-split extension by D₆ of Dic₅ acting via Dic₅/C₁₀=C₂	120	4	D6.Dic5	240,11
D₃₀.₅C₄	3^rd non-split extension by D₃₀ of C₄ acting via C₄/C₂=C₂	120	4	D30.5C4	240,12
C₁₅⋊D₈	1^st semidirect product of C₁₅ and D₈ acting via D₈/C₄=C₂²	120	4	C15:D8	240,13
C₃₀.D₄	4^th non-split extension by C₃₀ of D₄ acting via D₄/C₂=C₂²	120	4	C30.D4	240,16
C₂₀.D₆	4^th non-split extension by C₂₀ of D₆ acting via D₆/C₃=C₂²	120	4	C20.D6	240,17
C₁₅⋊Q₁₆	1^st semidirect product of C₁₅ and Q₁₆ acting via Q₁₆/C₄=C₂²	240	4	C15:Q16	240,22
C₃×D₄⋊D₅	Direct product of C₃ and D₄⋊D₅	120	4	C3xD4:D5	240,44
C₃×D₄.D₅	Direct product of C₃ and D₄.D₅	120	4	C3xD4.D5	240,45
C₃×Q₈⋊D₅	Direct product of C₃ and Q₈⋊D₅	120	4	C3xQ8:D5	240,46
C₃×C₅⋊Q₁₆	Direct product of C₃ and C₅⋊Q₁₆	240	4	C3xC5:Q16	240,47
C₅×D₄⋊S₃	Direct product of C₅ and D₄⋊S₃	120	4	C5xD4:S3	240,60
C₅×D₄.S₃	Direct product of C₅ and D₄.S₃	120	4	C5xD4.S3	240,61
C₅×Q₈⋊₂S₃	Direct product of C₅ and Q₈⋊₂S₃	120	4	C5xQ8:2S3	240,62
C₅×C₃⋊Q₁₆	Direct product of C₅ and C₃⋊Q₁₆	240	4	C5xC3:Q16	240,63
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	12	4	A5:C4	240,91
C₃×D₅⋊C₈	Direct product of C₃ and D₅⋊C₈	120	4	C3xD5:C8	240,111
C₃×C₄.F₅	Direct product of C₃ and C₄.F₅	120	4	C3xC4.F5	240,112
C₁₂×F₅	Direct product of C₁₂ and F₅	60	4	C12xF5	240,113
C₃×C₄⋊F₅	Direct product of C₃ and C₄⋊F₅	60	4	C3xC4:F5	240,114
C₃×C₂².F₅	Direct product of C₃ and C₂².F₅	120	4	C3xC2^2.F5	240,116
C₃×C₂²⋊F₅	Direct product of C₃ and C₂²⋊F₅	60	4	C3xC2^2:F5	240,117
C₆₀.C₄	3^rd non-split extension by C₆₀ of C₄ acting faithfully	120	4	C60.C4	240,118
C₁₂.F₅	1^st non-split extension by C₁₂ of F₅ acting via F₅/D₅=C₂	120	4	C12.F5	240,119
C₄×C₃⋊F₅	Direct product of C₄ and C₃⋊F₅	60	4	C4xC3:F5	240,120
C₆₀⋊C₄	1^st semidirect product of C₆₀ and C₄ acting faithfully	60	4	C60:C4	240,121
C₁₅⋊₈M₄(2)	1^st semidirect product of C₁₅ and M₄(2) acting via M₄(2)/C₂²=C₄	120	4	C15:8M4(2)	240,123
D₁₀.D₆	6^th non-split extension by D₁₀ of D₆ acting via D₆/C₆=C₂	60	4	D10.D6	240,124
D₂₀⋊S₃	3^rd semidirect product of D₂₀ and S₃ acting via S₃/C₃=C₂	120	4	D20:S3	240,127
D₁₂⋊D₅	3^rd semidirect product of D₁₂ and D₅ acting via D₅/C₅=C₂	120	4	D12:D5	240,129
D₁₅⋊Q₈	The semidirect product of D₁₅ and Q₈ acting via Q₈/C₄=C₂	120	4	D15:Q8	240,131
D₆.D₁₀	3^rd non-split extension by D₆ of D₁₀ acting via D₁₀/C₁₀=C₂	120	4	D6.D10	240,132
C₄×S₃×D₅	Direct product of C₄, S₃ and D₅	60	4	C4xS3xD5	240,135
C₂₀⋊D₆	2^nd semidirect product of C₂₀ and D₆ acting via D₆/C₃=C₂²	60	4	C20:D6	240,138
Dic₅.D₆	5^th non-split extension by Dic₅ of D₆ acting via D₆/S₃=C₂	120	4	Dic5.D6	240,140
Dic₃.D₁₀	6^th non-split extension by Dic₃ of D₁₀ acting via D₁₀/D₅=C₂	120	4	Dic3.D10	240,143
D₅×C₃⋊D₄	Direct product of D₅ and C₃⋊D₄	60	4	D5xC3:D4	240,149
S₃×C₅⋊D₄	Direct product of S₃ and C₅⋊D₄	60	4	S3xC5:D4	240,150
C₃×D₄×D₅	Direct product of C₃, D₄ and D₅	60	4	C3xD4xD5	240,159
C₃×D₄⋊₂D₅	Direct product of C₃ and D₄⋊₂D₅	120	4	C3xD4:2D5	240,160
C₃×Q₈×D₅	Direct product of C₃, Q₈ and D₅	120	4	C3xQ8xD5	240,161
C₃×Q₈⋊₂D₅	Direct product of C₃ and Q₈⋊₂D₅	120	4	C3xQ8:2D5	240,162
C₅×S₃×D₄	Direct product of C₅, S₃ and D₄	60	4	C5xS3xD4	240,169
C₅×D₄⋊₂S₃	Direct product of C₅ and D₄⋊₂S₃	120	4	C5xD4:2S3	240,170
C₅×S₃×Q₈	Direct product of C₅, S₃ and Q₈	120	4	C5xS3xQ8	240,171
C₅×Q₈⋊₃S₃	Direct product of C₅ and Q₈⋊₃S₃	120	4	C5xQ8:3S3	240,172

Groups of order 252

		d	ρ	Label	ID
C₇×C₃²⋊C₄	Direct product of C₇ and C₃²⋊C₄	42	4	C7xC3^2:C4	252,31
C₃²⋊Dic₇	The semidirect product of C₃² and Dic₇ acting via Dic₇/C₇=C₄	42	4	C3^2:Dic7	252,32
C₃×S₃×D₇	Direct product of C₃, S₃ and D₇	42	4	C3xS3xD7	252,33
S₃²×C₇	Direct product of C₇, S₃ and S₃	42	4	S3^2xC7	252,35
D₂₁⋊S₃	The semidirect product of D₂₁ and S₃ acting via S₃/C₃=C₂	42	4	D21:S3	252,37

Groups of order 260

		d	ρ	Label	ID
C₅×C₁₃⋊C₄	Direct product of C₅ and C₁₃⋊C₄	65	4	C5xC13:C4	260,5
C₆₅⋊C₄	3^rd semidirect product of C₆₅ and C₄ acting faithfully	65	4	C65:C4	260,6
C₁₃×F₅	Direct product of C₁₃ and F₅	65	4	C13xF5	260,7
C₁₃⋊₃F₅	The semidirect product of C₁₃ and F₅ acting via F₅/D₅=C₂	65	4	C13:3F5	260,8

Groups of order 272

		d	ρ	Label	ID
C₁₇⋊₃C₁₆	The semidirect product of C₁₇ and C₁₆ acting via C₁₆/C₄=C₄	272	4	C17:3C16	272,3
C₆₈.C₄	3^rd non-split extension by C₆₈ of C₄ acting faithfully	136	4	C68.C4	272,29
D₃₄.₄C₄	3^rd non-split extension by D₃₄ of C₄ acting via C₄/C₂=C₂	136	4	D34.4C4	272,30
C₄×C₁₇⋊C₄	Direct product of C₄ and C₁₇⋊C₄	68	4	C4xC17:C4	272,31
C₆₈⋊C₄	1^st semidirect product of C₆₈ and C₄ acting faithfully	68	4	C68:C4	272,32

Groups of order 280

		d	ρ	Label	ID
C₇×C₅⋊C₈	Direct product of C₇ and C₅⋊C₈	280	4	C7xC5:C8	280,5
C₃₅⋊C₈	1^st semidirect product of C₃₅ and C₈ acting via C₈/C₂=C₄	280	4	C35:C8	280,6
C₁₄×F₅	Direct product of C₁₄ and F₅	70	4	C14xF5	280,34
C₂×C₇⋊F₅	Direct product of C₂ and C₇⋊F₅	70	4	C2xC7:F5	280,35

Groups of order 288

		d	ρ	Label	ID
C₂².D₃₆	1^st non-split extension by C₂² of D₃₆ acting via D₃₆/D₁₈=C₂	72	4	C2^2.D36	288,13
C₃₆.₅₃D₄	9^th non-split extension by C₃₆ of D₄ acting via D₄/C₂²=C₂	144	4	C36.53D4	288,29
Dic₁₈⋊C₄	4^th semidirect product of Dic₁₈ and C₄ acting via C₄/C₂=C₂	72	4	Dic18:C4	288,32
C₃₆.D₄	7^th non-split extension by C₃₆ of D₄ acting via D₄/C₂=C₂²	72	4	C36.D4	288,39
C₂³⋊₂Dic₉	The semidirect product of C₂³ and Dic₉ acting via Dic₉/C₉=C₄	72	4	C2^3:2Dic9	288,41
C₃₆.₉D₄	9^th non-split extension by C₃₆ of D₄ acting via D₄/C₂=C₂²	144	4	C36.9D4	288,42
Q₈⋊₃Dic₉	2^nd semidirect product of Q₈ and Dic₉ acting via Dic₉/C₁₈=C₂	72	4	Q8:3Dic9	288,44
C₉×C₂³⋊C₄	Direct product of C₉ and C₂³⋊C₄	72	4	C9xC2^3:C4	288,49
C₉×C₄.D₄	Direct product of C₉ and C₄.D₄	72	4	C9xC4.D4	288,50
C₉×C₄.₁₀D₄	Direct product of C₉ and C₄.₁₀D₄	144	4	C9xC4.10D4	288,51
C₁₂.₉S₄	9^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	4	C12.9S4	288,70
M₄(2)×D₉	Direct product of M₄(2) and D₉	72	4	M4(2)xD9	288,116
D₃₆.C₄	The non-split extension by D₃₆ of C₄ acting via C₄/C₂=C₂	144	4	D36.C4	288,117
D₈⋊D₉	2^nd semidirect product of D₈ and D₉ acting via D₉/C₉=C₂	72	4	D8:D9	288,121
SD₁₆×D₉	Direct product of SD₁₆ and D₉	72	4	SD16xD9	288,123
SD₁₆⋊₃D₉	The semidirect product of SD₁₆ and D₉ acting through Inn(SD₁₆)	144	4	SD16:3D9	288,126
Q₁₆⋊D₉	2^nd semidirect product of Q₁₆ and D₉ acting via D₉/C₉=C₂	144	4	Q16:D9	288,128
D₃₆⋊₆C₂²	4^th semidirect product of D₃₆ and C₂² acting via C₂²/C₂=C₂	72	4	D36:6C2^2	288,143
C₃₆.C₂³	16^th non-split extension by C₃₆ of C₂³ acting via C₂³/C₂=C₂²	144	4	C36.C2^3	288,153
D₄.Dic₉	The non-split extension by D₄ of Dic₉ acting through Inn(D₄)	144	4	D4.Dic9	288,158
D₄.₉D₁₈	4^th non-split extension by D₄ of D₁₈ acting via D₁₈/C₁₈=C₂	144	4	D4.9D18	288,161
C₉×C₈⋊C₂²	Direct product of C₉ and C₈⋊C₂²	72	4	C9xC8:C2^2	288,186
C₉×C₈.C₂²	Direct product of C₉ and C₈.C₂²	144	4	C9xC8.C2^2	288,187
C₃²⋊₂C₃₂	The semidirect product of C₃² and C₃₂ acting via C₃₂/C₈=C₄	96	4	C3^2:2C32	288,188
S₃×C₃⋊C₁₆	Direct product of S₃ and C₃⋊C₁₆	96	4	S3xC3:C16	288,189
C₂₄.₆₀D₆	13^rd non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.60D6	288,190
C₂₄.₆₁D₆	14^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	96	4	C24.61D6	288,191
C₂₄.₆₂D₆	15^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.62D6	288,192
C₃²⋊₂D₁₆	1^st semidirect product of C₃² and D₁₆ acting via D₁₆/C₈=C₂²	96	4	C3^2:2D16	288,193
D₂₄.S₃	2^nd non-split extension by D₂₄ of S₃ acting via S₃/C₃=C₂	96	4	D24.S3	288,195
C₃²⋊₂Q₃₂	1^st semidirect product of C₃² and Q₃₂ acting via Q₃₂/C₈=C₂²	96	4	C3^2:2Q32	288,198
C₁₂.D₁₂	13^rd non-split extension by C₁₂ of D₁₂ acting via D₁₂/C₆=C₂²	48	4	C12.D12	288,206
C₁₂.₁₄D₁₂	14^th non-split extension by C₁₂ of D₁₂ acting via D₁₂/C₆=C₂²	48	4	C12.14D12	288,208
D₁₂⋊₄Dic₃	4^th semidirect product of D₁₂ and Dic₃ acting via Dic₃/C₆=C₂	24	4	D12:4Dic3	288,216
D₁₂⋊₂Dic₃	2^nd semidirect product of D₁₂ and Dic₃ acting via Dic₃/C₆=C₂	48	4	D12:2Dic3	288,217
C₁₂.₈₀D₁₂	11^st non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48	4	C12.80D12	288,218
C₁₂.₈₂D₁₂	13^rd non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	48	4	C12.82D12	288,225
C₆².₅Q₈	2^nd non-split extension by C₆² of Q₈ acting via Q₈/C₂=C₂²	48	4	C6^2.5Q8	288,226
C₆².₃₁D₄	15^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	24	4	C6^2.31D4	288,228
C₆².₃₂D₄	16^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	24	4	C6^2.32D4	288,229
C₃×C₂³.₆D₆	Direct product of C₃ and C₂³.₆D₆	24	4	C3xC2^3.6D6	288,240
C₃×C₁₂.₅₃D₄	Direct product of C₃ and C₁₂.₅₃D₄	48	4	C3xC12.53D4	288,256
C₃×C₁₂.₄₆D₄	Direct product of C₃ and C₁₂.₄₆D₄	48	4	C3xC12.46D4	288,257
C₃×C₁₂.₄₇D₄	Direct product of C₃ and C₁₂.₄₇D₄	48	4	C3xC12.47D4	288,258
C₃×D₁₂⋊C₄	Direct product of C₃ and D₁₂⋊C₄	48	4	C3xD12:C4	288,259
C₃×C₃⋊D₁₆	Direct product of C₃ and C₃⋊D₁₆	48	4	C3xC3:D16	288,260
C₃×D₈.S₃	Direct product of C₃ and D₈.S₃	48	4	C3xD8.S3	288,261
C₃×C₈.₆D₆	Direct product of C₃ and C₈.₆D₆	96	4	C3xC8.6D6	288,262
C₃×C₃⋊Q₃₂	Direct product of C₃ and C₃⋊Q₃₂	96	4	C3xC3:Q32	288,263
C₃×C₁₂.D₄	Direct product of C₃ and C₁₂.D₄	24	4	C3xC12.D4	288,267
C₃×C₂³.₇D₆	Direct product of C₃ and C₂³.₇D₆	24	4	C3xC2^3.7D6	288,268
C₃×C₁₂.₁₀D₄	Direct product of C₃ and C₁₂.₁₀D₄	48	4	C3xC12.10D4	288,270
C₃×Q₈⋊₃Dic₃	Direct product of C₃ and Q₈⋊₃Dic₃	48	4	C3xQ8:3Dic3	288,271
Q₈.D₁₈	2^nd non-split extension by Q₈ of D₁₈ acting via D₁₈/C₆=S₃	144	4	Q8.D18	288,337
C₁₂.₁₁S₄	11^st non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	144	4	C12.11S4	288,339
2₊¹⁺⁴⋊C₉	1^st semidirect product of 2₊¹⁺⁴ and C₉ acting via C₉/C₃=C₃	72	4	ES+(2,2):C9	288,348
2_-¹⁺⁴⋊C₉	The semidirect product of 2_-¹⁺⁴ and C₉ acting via C₉/C₃=C₃	144	4	ES-(2,2):C9	288,349
2₊¹⁺⁴⋊₂C₉	2^nd semidirect product of 2₊¹⁺⁴ and C₉ acting via C₉/C₃=C₃	72	4	ES+(2,2):2C9	288,351
D₄⋊₆D₁₈	2^nd semidirect product of D₄ and D₁₈ acting through Inn(D₄)	72	4	D4:6D18	288,358
Q₈.₁₅D₁₈	1^st non-split extension by Q₈ of D₁₈ acting through Inn(Q₈)	144	4	Q8.15D18	288,361
C₄○D₄×D₉	Direct product of C₄○D₄ and D₉	72	4	C4oD4xD9	288,362
C₉×2₊¹⁺⁴	Direct product of C₉ and 2₊¹⁺⁴	72	4	C9xES+(2,2)	288,371
C₉×2_-¹⁺⁴	Direct product of C₉ and 2_-¹⁺⁴	144	4	C9xES-(2,2)	288,372
S₃²⋊C₈	The semidirect product of S₃² and C₈ acting via C₈/C₄=C₂	24	4	S3^2:C8	288,374
C₄.S₃≀C₂	1^st non-split extension by C₄ of S₃≀C₂ acting via S₃≀C₂/S₃²=C₂	24	4	C4.S3wrC2	288,375
(C₃×C₁₂).D₄	2^nd non-split extension by C₃×C₁₂ of D₄ acting faithfully	48	4	(C3xC12).D4	288,376
C₃⋊S₃.₂D₈	1^st non-split extension by C₃⋊S₃ of D₈ acting via D₈/C₄=C₂²	24	4	C3:S3.2D8	288,377
C₃⋊S₃.₂Q₁₆	1^st non-split extension by C₃⋊S₃ of Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3:S3.2Q16	288,378
C₃²⋊C₄≀C₂	The semidirect product of C₃² and C₄≀C₂ acting via C₄≀C₂/C₄=D₄	48	4	C3^2:C4wrC2	288,379
C₃²⋊C₄⋊C₈	2^nd semidirect product of C₃²⋊C₄ and C₈ acting via C₈/C₄=C₂	48	4	C3^2:C4:C8	288,380
C₄.₁₉S₃≀C₂	4^th central extension by C₄ of S₃≀C₂	48	4	C4.19S3wrC2	288,381
C₃⋊U₂(𝔽₃)	The semidirect product of C₃ and U₂(𝔽₃) acting via U₂(𝔽₃)/C₄.A₄=C₂	72	4	C3:U(2,3)	288,404
SL₂(𝔽₃).Dic₃	The non-split extension by SL₂(𝔽₃) of Dic₃ acting through Inn(SL₂(𝔽₃))	96	4	SL(2,3).Dic3	288,410
C₃⋊S₃⋊₃C₁₆	2^nd semidirect product of C₃⋊S₃ and C₁₆ acting via C₁₆/C₈=C₂	48	4	C3:S3:3C16	288,412
C₃²⋊₃M₅(2)	The semidirect product of C₃² and M₅(2) acting via M₅(2)/C₈=C₄	48	4	C3^2:3M5(2)	288,413
C₈×C₃²⋊C₄	Direct product of C₈ and C₃²⋊C₄	48	4	C8xC3^2:C4	288,414
(C₃×C₂₄)⋊C₄	2^nd semidirect product of C₃×C₂₄ and C₄ acting faithfully	48	4	(C3xC24):C4	288,415
C₈⋊(C₃²⋊C₄)	2^nd semidirect product of C₈ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	48	4	C8:(C3^2:C4)	288,416
C₃⋊S₃.₄D₈	The non-split extension by C₃⋊S₃ of D₈ acting via D₈/C₈=C₂	48	4	C3:S3.4D8	288,417
(C₃×C₂₄).C₄	4^th non-split extension by C₃×C₂₄ of C₄ acting faithfully	48	4	(C3xC24).C4	288,418
C₈.(C₃²⋊C₄)	1^st non-split extension by C₈ of C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	48	4	C8.(C3^2:C4)	288,419
C₆².₄C₈	2^nd non-split extension by C₆² of C₈ acting via C₈/C₂=C₄	48	4	C6^2.4C8	288,421
(C₂×C₆²)⋊C₄	4^th semidirect product of C₂×C₆² and C₄ acting faithfully	24	4	(C2xC6^2):C4	288,434
(C₂×C₆²).C₄	5^th non-split extension by C₂×C₆² of C₄ acting faithfully	24	4	(C2xC6^2).C4	288,436
S₃²×C₈	Direct product of C₈, S₃ and S₃	48	4	S3^2xC8	288,437
S₃×C₈⋊S₃	Direct product of S₃ and C₈⋊S₃	48	4	S3xC8:S3	288,438
C₂₄⋊D₆	14^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:D6	288,439
S₃×C₂₄⋊C₂	Direct product of S₃ and C₂₄⋊C₂	48	4	S3xC24:C2	288,440
D₂₄⋊S₃	2^nd semidirect product of D₂₄ and S₃ acting via S₃/C₃=C₂	48	4	D24:S3	288,443
C₂₄⋊₉D₆	9^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:9D6	288,444
C₂₄⋊₄D₆	4^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:4D6	288,445
C₂₄⋊₆D₆	6^th semidirect product of C₂₄ and D₆ acting via D₆/C₃=C₂²	48	4	C24:6D6	288,446
Dic₁₂⋊S₃	2^nd semidirect product of Dic₁₂ and S₃ acting via S₃/C₃=C₂	48	4	Dic12:S3	288,449
C₂₄.₂₃D₆	23^rd non-split extension by C₂₄ of D₆ acting via D₆/C₃=C₂²	48	4	C24.23D6	288,450
C₂₄.₆₃D₆	16^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.63D6	288,451
C₂₄.₆₄D₆	17^th non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.64D6	288,452
C₂₄.D₆	46^th non-split extension by C₂₄ of D₆ acting via D₆/C₃=C₂²	48	4	C24.D6	288,453
D₆.₁D₁₂	1^st non-split extension by D₆ of D₁₂ acting via D₁₂/C₁₂=C₂	48	4	D6.1D12	288,454
D₁₂.₂D₆	2^nd non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	4	D12.2D6	288,457
D₂₄⋊₅S₃	5^th semidirect product of D₂₄ and S₃ acting via S₃/C₃=C₂	48	4	D24:5S3	288,458
D₁₂.₄D₆	4^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	4	D12.4D6	288,459
S₃×C₄.Dic₃	Direct product of S₃ and C₄.Dic₃	48	4	S3xC4.Dic3	288,461
D₁₂.₂Dic₃	The non-split extension by D₁₂ of Dic₃ acting through Inn(D₁₂)	48	4	D12.2Dic3	288,462
D₁₂.Dic₃	The non-split extension by D₁₂ of Dic₃ acting via Dic₃/C₆=C₂	48	4	D12.Dic3	288,463
C₃⋊C₈.₂₂D₆	11^st non-split extension by C₃⋊C₈ of D₆ acting via D₆/S₃=C₂	48	4	C3:C8.22D6	288,465
C₃⋊C₈⋊₂₀D₆	9^th semidirect product of C₃⋊C₈ and D₆ acting via D₆/S₃=C₂	24	4	C3:C8:20D6	288,466
D₁₂.₃₀D₆	5^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.30D6	288,470
D₁₂⋊₂₀D₆	4^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	48	4	D12:20D6	288,471
D₁₂.₃₂D₆	7^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.32D6	288,475
D₁₂.₂₇D₆	2^nd non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.27D6	288,477
D₁₂.₂₈D₆	3^rd non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.28D6	288,478
Dic₆.₂₉D₆	3^rd non-split extension by Dic₆ of D₆ acting via D₆/C₆=C₂	48	4	Dic6.29D6	288,481
C₃×S₃×M₄(2)	Direct product of C₃, S₃ and M₄(2)	48	4	C3xS3xM4(2)	288,677
C₃×D₁₂.C₄	Direct product of C₃ and D₁₂.C₄	48	4	C3xD12.C4	288,678
C₃×C₈⋊D₆	Direct product of C₃ and C₈⋊D₆	48	4	C3xC8:D6	288,679
C₃×C₈.D₆	Direct product of C₃ and C₈.D₆	48	4	C3xC8.D6	288,680
C₃×S₃×D₈	Direct product of C₃, S₃ and D₈	48	4	C3xS3xD8	288,681
C₃×D₈⋊S₃	Direct product of C₃ and D₈⋊S₃	48	4	C3xD8:S3	288,682
C₃×D₈⋊₃S₃	Direct product of C₃ and D₈⋊₃S₃	48	4	C3xD8:3S3	288,683
C₃×S₃×SD₁₆	Direct product of C₃, S₃ and SD₁₆	48	4	C3xS3xSD16	288,684
C₃×Q₈⋊₃D₆	Direct product of C₃ and Q₈⋊₃D₆	48	4	C3xQ8:3D6	288,685
C₃×D₄.D₆	Direct product of C₃ and D₄.D₆	48	4	C3xD4.D6	288,686
C₃×Q₈.₇D₆	Direct product of C₃ and Q₈.₇D₆	48	4	C3xQ8.7D6	288,687
C₃×S₃×Q₁₆	Direct product of C₃, S₃ and Q₁₆	96	4	C3xS3xQ16	288,688
C₃×Q₁₆⋊S₃	Direct product of C₃ and Q₁₆⋊S₃	96	4	C3xQ16:S3	288,689
C₃×D₂₄⋊C₂	Direct product of C₃ and D₂₄⋊C₂	96	4	C3xD24:C2	288,690
C₃×D₁₂⋊₆C₂²	Direct product of C₃ and D₁₂⋊₆C₂²	24	4	C3xD12:6C2^2	288,703
C₃×Q₈.₁₁D₆	Direct product of C₃ and Q₈.₁₁D₆	48	4	C3xQ8.11D6	288,713
C₃×D₄.Dic₃	Direct product of C₃ and D₄.Dic₃	48	4	C3xD4.Dic3	288,719
C₃×D₄⋊D₆	Direct product of C₃ and D₄⋊D₆	48	4	C3xD4:D6	288,720
C₃×Q₈.₁₃D₆	Direct product of C₃ and Q₈.₁₃D₆	48	4	C3xQ8.13D6	288,721
C₃×Q₈.₁₄D₆	Direct product of C₃ and Q₈.₁₄D₆	48	4	C3xQ8.14D6	288,722
CSU₂(𝔽₃)⋊S₃	1^st semidirect product of CSU₂(𝔽₃) and S₃ acting via S₃/C₃=C₂	96	4	CSU(2,3):S3	288,844
Dic₃.₄S₄	1^st non-split extension by Dic₃ of S₄ acting through Inn(Dic₃)	48	4	Dic3.4S4	288,845
D₆.₂S₄	2^nd non-split extension by D₆ of S₄ acting via S₄/A₄=C₂	48	4	D6.2S4	288,850
S₃×GL₂(𝔽₃)	Direct product of S₃ and GL₂(𝔽₃); = GL₂(ℤ/6ℤ)	24	4	S3xGL(2,3)	288,851
S₃²⋊Q₈	The semidirect product of S₃² and Q₈ acting via Q₈/C₄=C₂	24	4	S3^2:Q8	288,868
C₃²⋊D₈⋊₅C₂	The semidirect product of C₃²⋊D₈ and C₂ acting through Inn(C₃²⋊D₈)	48	4	C3^2:D8:5C2	288,871
C₃²⋊D₈⋊C₂	3^rd semidirect product of C₃²⋊D₈ and C₂ acting faithfully	24	4	C3^2:D8:C2	288,872
C₃²⋊Q₁₆⋊C₂	1^st semidirect product of C₃²⋊Q₁₆ and C₂ acting faithfully	48	4	C3^2:Q16:C2	288,874
C₄×S₃≀C₂	Direct product of C₄ and S₃≀C₂	24	4	C4xS3wrC2	288,877
S₃²⋊D₄	The semidirect product of S₃² and D₄ acting via D₄/C₄=C₂	24	4	S3^2:D4	288,878
C₆².₉D₄	9^th non-split extension by C₆² of D₄ acting faithfully	24	4	C6^2.9D4	288,881
C₆².₁₂D₄	12^nd non-split extension by C₆² of D₄ acting faithfully	24	4	C6^2.12D4	288,884
C₃×Q₈.D₆	Direct product of C₃ and Q₈.D₆	48	4	C3xQ8.D6	288,901
C₃×C₄.S₄	Direct product of C₃ and C₄.S₄	96	4	C3xC4.S4	288,902
C₃×C₄.₃S₄	Direct product of C₃ and C₄.₃S₄	48	4	C3xC4.3S4	288,904
SL₂(𝔽₃).D₆	2^nd non-split extension by SL₂(𝔽₃) of D₆ acting via D₆/C₆=C₂	48	4	SL(2,3).D6	288,912
C₁₂.₁₄S₄	14^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	48	4	C12.14S4	288,914
SL₂(𝔽₃).₁₁D₆	1^st non-split extension by SL₂(𝔽₃) of D₆ acting through Inn(SL₂(𝔽₃))	48	4	SL(2,3).11D6	288,923
S₃×C₄.A₄	Direct product of S₃ and C₄.A₄	48	4	S3xC4.A4	288,925
C₃⋊S₃⋊M₄(2)	2^nd semidirect product of C₃⋊S₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	24	4	C3:S3:M4(2)	288,931
(C₆×C₁₂)⋊₅C₄	5^th semidirect product of C₆×C₁₂ and C₄ acting faithfully	24	4	(C6xC12):5C4	288,934
D₁₂.₃₃D₆	8^th non-split extension by D₁₂ of D₆ acting via D₆/C₆=C₂	48	4	D12.33D6	288,945
S₃×C₄○D₁₂	Direct product of S₃ and C₄○D₁₂	48	4	S3xC4oD12	288,953
D₁₂⋊₂₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	24	4	D12:23D6	288,954
D₁₂⋊₂₄D₆	8^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	48	4	D12:24D6	288,955
C₃²⋊2₊¹⁺⁴	The semidirect product of C₃² and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂³=C₂²	24	4	C3^2:ES+(2,2)	288,978
C₃×Q₈.A₄	Direct product of C₃ and Q₈.A₄	72	4	C3xQ8.A4	288,984
C₃×D₄.A₄	Direct product of C₃ and D₄.A₄	48	4	C3xD4.A4	288,985
C₃×C₂³⋊A₄	Direct product of C₃ and C₂³⋊A₄	24	4	C3xC2^3:A4	288,987
C₃×D₄⋊₆D₆	Direct product of C₃ and D₄⋊₆D₆	24	4	C3xD4:6D6	288,994
C₃×Q₈.₁₅D₆	Direct product of C₃ and Q₈.₁₅D₆	48	4	C3xQ8.15D6	288,997
C₃×S₃×C₄○D₄	Direct product of C₃, S₃ and C₄○D₄	48	4	C3xS3xC4oD4	288,998
C₃×D₄○D₁₂	Direct product of C₃ and D₄○D₁₂	48	4	C3xD4oD12	288,999
C₃×Q₈○D₁₂	Direct product of C₃ and Q₈○D₁₂	48	4	C3xQ8oD12	288,1000

Groups of order 300

		d	ρ	Label	ID
C₃×C₂₅⋊C₄	Direct product of C₃ and C₂₅⋊C₄	75	4	C3xC25:C4	300,5
C₇₅⋊C₄	1^st semidirect product of C₇₅ and C₄ acting faithfully	75	4	C75:C4	300,6
C₁₅×F₅	Direct product of C₁₅ and F₅	60	4	C15xF5	300,28
C₃×D₅.D₅	Direct product of C₃ and D₅.D₅	60	4	C3xD5.D5	300,29
C₃×C₅²⋊C₄	Direct product of C₃ and C₅²⋊C₄	30	4	C3xC5^2:C4	300,31
C₅×C₃⋊F₅	Direct product of C₅ and C₃⋊F₅	60	4	C5xC3:F5	300,32
D₅.D₁₅	The non-split extension by D₅ of D₁₅ acting via D₁₅/C₁₅=C₂	60	4	D5.D15	300,33
C₁₅⋊₂F₅	2^nd semidirect product of C₁₅ and F₅ acting via F₅/C₅=C₄	30	4	C15:2F5	300,35
C₃×D₅²	Direct product of C₃, D₅ and D₅	30	4	C3xD5^2	300,36
C₅×S₃×D₅	Direct product of C₅, S₃ and D₅	30	4	C5xS3xD5	300,37
D₁₅⋊D₅	The semidirect product of D₁₅ and D₅ acting via D₅/C₅=C₂	30	4	D15:D5	300,40

Groups of order 312

		d	ρ	Label	ID
C₃×C₁₃⋊C₈	Direct product of C₃ and C₁₃⋊C₈	312	4	C3xC13:C8	312,13
C₃₉⋊C₈	1^st semidirect product of C₃₉ and C₈ acting via C₈/C₂=C₄	312	4	C39:C8	312,14
C₆×C₁₃⋊C₄	Direct product of C₆ and C₁₃⋊C₄	78	4	C6xC13:C4	312,52
C₂×C₃₉⋊C₄	Direct product of C₂ and C₃₉⋊C₄	78	4	C2xC39:C4	312,53

Groups of order 320

		d	ρ	Label	ID
C₅⋊C₆₄	The semidirect product of C₅ and C₆₄ acting via C₆₄/C₁₆=C₄	320	4	C5:C64	320,3
C₂₀.₄₅C₄²	8^th non-split extension by C₂₀ of C₄² acting via C₄²/C₂×C₄=C₂	80	4	C20.45C4^2	320,24
C₈.Dic₁₀	1^st non-split extension by C₈ of Dic₁₀ acting via Dic₁₀/C₁₀=C₂²	80	4	C8.Dic10	320,45
D₄₀⋊₁₄C₄	8^th semidirect product of D₄₀ and C₄ acting via C₄/C₂=C₂	80	4	D40:14C4	320,46
C₄₀.₇Q₈	7^th non-split extension by C₄₀ of Q₈ acting via Q₈/C₂=C₂²	160	4	C40.7Q8	320,51
C₄₀.₆Q₈	6^th non-split extension by C₄₀ of Q₈ acting via Q₈/C₂=C₂²	80	4	C40.6Q8	320,52
D₄₀.₅C₄	3^rd non-split extension by D₄₀ of C₄ acting via C₄/C₂=C₂	160	4	D40.5C4	320,55
C₄₀.₉Q₈	9^th non-split extension by C₄₀ of Q₈ acting via Q₈/C₂=C₂²	80	4	C40.9Q8	320,69
C₈₀⋊C₄	6^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:C4	320,70
C₄₀.Q₈	1^st non-split extension by C₄₀ of Q₈ acting via Q₈/C₂=C₂²	80	4	C40.Q8	320,71
C₈.₂₅D₂₀	11^st non-split extension by C₈ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4	C8.25D20	320,72
D₂₀.₄C₈	2^nd non-split extension by D₂₀ of C₈ acting via C₈/C₄=C₂	160	4	D20.4C8	320,73
D₄₀⋊₈C₄	2^nd semidirect product of D₄₀ and C₄ acting via C₄/C₂=C₂	80	4	D40:8C4	320,76
C₄²⋊₁Dic₅	1^st semidirect product of C₄² and Dic₅ acting via Dic₅/C₅=C₄	80	4	C4^2:1Dic5	320,89
C₂₀.₆₀(C₄⋊C₄)	7^th non-split extension by C₂₀ of C₄⋊C₄ acting via C₄⋊C₄/C₂×C₄=C₂	80	4	C20.60(C4:C4)	320,91
C₂⁴⋊₂Dic₅	1^st semidirect product of C₂⁴ and Dic₅ acting via Dic₅/C₅=C₄	40	4	C2^4:2Dic5	320,94
(C₂²×C₂₀)⋊C₄	2^nd semidirect product of C₂²×C₂₀ and C₄ acting faithfully	80	4	(C2^2xC20):C4	320,97
C₄²⋊Dic₅	2^nd semidirect product of C₄² and Dic₅ acting via Dic₅/C₅=C₄	80	4	C4^2:Dic5	320,99
C₄².Dic₅	2^nd non-split extension by C₄² of Dic₅ acting via Dic₅/C₅=C₄	80	4	C4^2.Dic5	320,100
C₄²⋊₃Dic₅	3^rd semidirect product of C₄² and Dic₅ acting via Dic₅/C₅=C₄	40	4	C4^2:3Dic5	320,103
C₄².₃Dic₅	3^rd non-split extension by C₄² of Dic₅ acting via Dic₅/C₅=C₄	80	4	C4^2.3Dic5	320,106
C₄₀.D₄	48^th non-split extension by C₄₀ of D₄ acting via D₄/C₂=C₂²	80	4	C40.D4	320,111
(C₂×C₄₀)⋊C₄	11^st semidirect product of C₂×C₄₀ and C₄ acting faithfully	80	4	(C2xC40):C4	320,114
C₂³.₉D₂₀	2^nd non-split extension by C₂³ of D₂₀ acting via D₂₀/C₁₀=C₂²	80	4	C2^3.9D20	320,115
M₄(2)⋊₄Dic₅	4^th semidirect product of M₄(2) and Dic₅ acting via Dic₅/C₁₀=C₂	80	4	M4(2):4Dic5	320,117
C₂₀.₅₁C₄²	14^th non-split extension by C₂₀ of C₄² acting via C₄²/C₂×C₄=C₂	80	4	C20.51C4^2	320,118
C₄₀.₉₂D₄	15^th non-split extension by C₄₀ of D₄ acting via D₄/C₂²=C₂	160	4	C40.92D4	320,119
D₈.Dic₅	2^nd non-split extension by D₈ of Dic₅ acting via Dic₅/C₁₀=C₂	80	4	D8.Dic5	320,121
Q₁₆.Dic₅	2^nd non-split extension by Q₁₆ of Dic₅ acting via Dic₅/C₁₀=C₂	160	4	Q16.Dic5	320,123
D₈⋊₂Dic₅	2^nd semidirect product of D₈ and Dic₅ acting via Dic₅/C₁₀=C₂	80	4	D8:2Dic5	320,124
C₂₀.₅₈D₈	12^nd non-split extension by C₂₀ of D₈ acting via D₈/D₄=C₂	160	4	C20.58D8	320,125
C₅×C₄.₉C₄²	Direct product of C₅ and C₄.₉C₄²	80	4	C5xC4.9C4^2	320,142
C₅×C₄.₁₀C₄²	Direct product of C₅ and C₄.₁₀C₄²	80	4	C5xC4.10C4^2	320,143
C₅×M₄(2)⋊₄C₄	Direct product of C₅ and M₄(2)⋊₄C₄	80	4	C5xM4(2):4C4	320,149
C₅×C₁₆⋊C₄	Direct product of C₅ and C₁₆⋊C₄	80	4	C5xC16:C4	320,152
C₅×C₂³.C₈	Direct product of C₅ and C₂³.C₈	80	4	C5xC2^3.C8	320,154
C₅×C₂≀C₄	Direct product of C₅ and C₂≀C₄	40	4	C5xC2wrC4	320,156
C₅×C₂³.D₄	Direct product of C₅ and C₂³.D₄	80	4	C5xC2^3.D4	320,157
C₅×C₄²⋊C₄	Direct product of C₅ and C₄²⋊C₄	40	4	C5xC4^2:C4	320,158
C₅×C₄²⋊₃C₄	Direct product of C₅ and C₄²⋊₃C₄	80	4	C5xC4^2:3C4	320,159
C₅×C₄².C₄	Direct product of C₅ and C₄².C₄	80	4	C5xC4^2.C4	320,160
C₅×C₄².₃C₄	Direct product of C₅ and C₄².₃C₄	80	4	C5xC4^2.3C4	320,161
C₅×D₈⋊₂C₄	Direct product of C₅ and D₈⋊₂C₄	80	4	C5xD8:2C4	320,165
C₅×M₅(2)⋊C₂	Direct product of C₅ and M₅(2)⋊C₂	80	4	C5xM5(2):C2	320,166
C₅×C₈.₁₇D₄	Direct product of C₅ and C₈.₁₇D₄	160	4	C5xC8.17D4	320,167
C₅×C₈.Q₈	Direct product of C₅ and C₈.Q₈	80	4	C5xC8.Q8	320,170
D₅⋊C₃₂	The semidirect product of D₅ and C₃₂ acting via C₃₂/C₁₆=C₂	160	4	D5:C32	320,179
C₈₀.C₄	5^th non-split extension by C₈₀ of C₄ acting faithfully	160	4	C80.C4	320,180
C₁₆×F₅	Direct product of C₁₆ and F₅	80	4	C16xF5	320,181
C₁₆⋊₇F₅	3^rd semidirect product of C₁₆ and F₅ acting via F₅/D₅=C₂	80	4	C16:7F5	320,182
C₁₆⋊F₅	3^rd semidirect product of C₁₆ and F₅ acting via F₅/C₅=C₄	80	4	C16:F5	320,183
C₁₆⋊₄F₅	4^th semidirect product of C₁₆ and F₅ acting via F₅/C₅=C₄	80	4	C16:4F5	320,184
C₈₀⋊₄C₄	4^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:4C4	320,185
C₈₀⋊₅C₄	5^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:5C4	320,186
C₈₀⋊₂C₄	2^nd semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:2C4	320,187
C₈₀⋊₃C₄	3^rd semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:3C4	320,188
C₁₆.F₅	1^st non-split extension by C₁₆ of F₅ acting via F₅/D₅=C₂	160	4	C16.F5	320,189
C₈₀.₂C₄	2^nd non-split extension by C₈₀ of C₄ acting faithfully	160	4	C80.2C4	320,190
C₄²⋊₂F₅	2^nd semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	80	4	C4^2:2F5	320,192
C₄².₂F₅	2^nd non-split extension by C₄² of F₅ acting via F₅/C₅=C₄	80	4	C4^2.2F5	320,194
C₄².₃F₅	3^rd non-split extension by C₄² of F₅ acting via F₅/C₅=C₄	80	4	C4^2.3F5	320,198
C₄².₉F₅	6^th non-split extension by C₄² of F₅ acting via F₅/D₅=C₂	80	4	C4^2.9F5	320,199
C₄²⋊₆F₅	3^rd semidirect product of C₄² and F₅ acting via F₅/D₅=C₂	40	4	C4^2:6F5	320,200
C₄²⋊₃F₅	3^rd semidirect product of C₄² and F₅ acting via F₅/C₅=C₄	80	4	C4^2:3F5	320,201
C₅⋊M₆(2)	The semidirect product of C₅ and M₆(2) acting via M₆(2)/C₂×C₈=C₄	160	4	C5:M6(2)	320,215
C₄₀.₁C₈	1^st non-split extension by C₄₀ of C₈ acting via C₈/C₂=C₄	80	4	C40.1C8	320,227
C₂₀.₂₃C₄²	16^th non-split extension by C₂₀ of C₄² acting via C₄²/C₄=C₄	80	4	C20.23C4^2	320,228
C₂₀.₁₀M₄(2)	4^th non-split extension by C₂₀ of M₄(2) acting via M₄(2)/C₄=C₄	80	4	C20.10M4(2)	320,229
(C₂×C₈)⋊F₅	1^st semidirect product of C₂×C₈ and F₅ acting via F₅/C₅=C₄	80	4	(C2xC8):F5	320,232
C₂₀.₂₄C₄²	17^th non-split extension by C₂₀ of C₄² acting via C₄²/C₄=C₄	80	4	C20.24C4^2	320,233
C₂₀.₂₅C₄²	18^th non-split extension by C₂₀ of C₄² acting via C₄²/C₄=C₄	80	4	C20.25C4^2	320,235
C₂₀.₂₉M₄(2)	4^th non-split extension by C₂₀ of M₄(2) acting via M₄(2)/C₂²=C₄	80	4	C20.29M4(2)	320,250
(C₂²×C₄)⋊F₅	1^st semidirect product of C₂²×C₄ and F₅ acting via F₅/C₅=C₄	80	4	(C2^2xC4):F5	320,254
C₂⁴⋊₂F₅	1^st semidirect product of C₂⁴ and F₅ acting via F₅/C₅=C₄	40	4	C2^4:2F5	320,272
D₄₀⋊₁₀C₄	4^th semidirect product of D₄₀ and C₄ acting via C₄/C₂=C₂	80	4	D40:10C4	320,344
D₅×C₄≀C₂	Direct product of D₅ and C₄≀C₂	40	4	D5xC4wrC2	320,447
C₄²⋊D₁₀	1^st semidirect product of C₄² and D₁₀ acting via D₁₀/C₅=C₂²	80	4	C4^2:D10	320,448
M₄(2).₂₂D₁₀	5^th non-split extension by M₄(2) of D₁₀ acting via D₁₀/D₅=C₂	80	4	M4(2).22D10	320,450
C₄².₁₉₆D₁₀	16^th non-split extension by C₄² of D₁₀ acting via D₁₀/D₅=C₂	80	4	C4^2.196D10	320,451
M₄(2)⋊D₁₀	4^th semidirect product of M₄(2) and D₁₀ acting via D₁₀/C₅=C₂²	80	4	M4(2):D10	320,452
D₄.₁₀D₂₀	5^th non-split extension by D₄ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4	D4.10D20	320,454
D₅×C₈.C₄	Direct product of D₅ and C₈.C₄	80	4	D5xC8.C4	320,519
M₄(2).₂₅D₁₀	8^th non-split extension by M₄(2) of D₁₀ acting via D₁₀/D₅=C₂	80	4	M4(2).25D10	320,520
D₄₀⋊₁₆C₄	10^th semidirect product of D₄₀ and C₄ acting via C₄/C₂=C₂	80	4	D40:16C4	320,521
D₄₀⋊₁₃C₄	7^th semidirect product of D₄₀ and C₄ acting via C₄/C₂=C₂	80	4	D40:13C4	320,522
C₈.₂₄D₂₀	10^th non-split extension by C₈ of D₂₀ acting via D₂₀/D₁₀=C₂	80	4	C8.24D20	320,525
D₅×M₅(2)	Direct product of D₅ and M₅(2)	80	4	D5xM5(2)	320,533
D₂₀.₅C₈	3^rd non-split extension by D₂₀ of C₈ acting via C₈/C₄=C₂	160	4	D20.5C8	320,534
D₁₆⋊D₅	2^nd semidirect product of D₁₆ and D₅ acting via D₅/C₅=C₂	80	4	D16:D5	320,538
D₅×SD₃₂	Direct product of D₅ and SD₃₂	80	4	D5xSD32	320,540
SD₃₂⋊₃D₅	The semidirect product of SD₃₂ and D₅ acting through Inn(SD₃₂)	160	4	SD32:3D5	320,543
Q₃₂⋊D₅	2^nd semidirect product of Q₃₂ and D₅ acting via D₅/C₅=C₂	160	4	Q32:D5	320,545
C₄²⋊₄D₁₀	4^th semidirect product of C₄² and D₁₀ acting via D₁₀/C₅=C₂²	80	4	C4^2:4D10	320,632
(C₂×D₂₀)⋊₂₅C₄	10^th semidirect product of C₂×D₂₀ and C₄ acting via C₄/C₂=C₂	80	4	(C2xD20):25C4	320,633
C₂⁴⋊₂D₁₀	1^st semidirect product of C₂⁴ and D₁₀ acting via D₁₀/C₅=C₂²	40	4	C2^4:2D10	320,659
C₂²⋊C₄⋊D₁₀	4^th semidirect product of C₂²⋊C₄ and D₁₀ acting via D₁₀/C₅=C₂²	80	4	C2^2:C4:D10	320,680
C₄²⋊₅D₁₀	5^th semidirect product of C₄² and D₁₀ acting via D₁₀/C₅=C₂²	80	4	C4^2:5D10	320,688
D₂₀.₁₄D₄	14^th non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	4	D20.14D4	320,689
D₂₀⋊₅D₄	5^th semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	40	4	D20:5D4	320,704
D₂₀.₁₅D₄	15^th non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	4	D20.15D4	320,722
C₂³.Dic₁₀	6^th non-split extension by C₂³ of Dic₁₀ acting via Dic₁₀/C₁₀=C₂²	80	4	C2^3.Dic10	320,751
M₄(2).Dic₅	1^st non-split extension by M₄(2) of Dic₅ acting via Dic₅/C₁₀=C₂	80	4	M4(2).Dic5	320,752
M₄(2).₃₁D₁₀	4^th non-split extension by M₄(2) of D₁₀ acting via D₁₀/C₁₀=C₂	80	4	M4(2).31D10	320,759
C₂³.₂₀D₂₀	13^rd non-split extension by C₂³ of D₂₀ acting via D₂₀/C₁₀=C₂²	80	4	C2^3.20D20	320,766
C₄₀.₇₀C₂³	16^th non-split extension by C₄₀ of C₂³ acting via C₂³/C₂²=C₂	160	4	C40.70C2^3	320,767
D₄.₃D₂₀	3^rd non-split extension by D₄ of D₂₀ acting via D₂₀/C₂₀=C₂	80	4	D4.3D20	320,768
C₄₀.₉₃D₄	16^th non-split extension by C₄₀ of D₄ acting via D₄/C₂²=C₂	80	4	C40.93D4	320,771
C₄₀.₅₀D₄	50^th non-split extension by C₄₀ of D₄ acting via D₄/C₂=C₂²	80	4	C40.50D4	320,772
D₈.D₁₀	1^st non-split extension by D₈ of D₁₀ acting via D₁₀/C₁₀=C₂	80	4	D8.D10	320,774
C₄₀.₂₃D₄	23^rd non-split extension by C₄₀ of D₄ acting via D₄/C₂=C₂²	80	4	C40.23D4	320,787
C₄₀.₄₄D₄	44^th non-split extension by C₄₀ of D₄ acting via D₄/C₂=C₂²	80	4	C40.44D4	320,804
Q₁₆.D₁₀	1^st non-split extension by Q₁₆ of D₁₀ acting via D₁₀/C₁₀=C₂	160	4	Q16.D10	320,806
C₄₀.₂₉D₄	29^th non-split extension by C₄₀ of D₄ acting via D₄/C₂=C₂²	160	4	C40.29D4	320,819
C₄₀.₃₀C₂³	23^rd non-split extension by C₄₀ of C₂³ acting via C₂³/C₂=C₂²	160	4	C40.30C2^3	320,821
D₈⋊₅Dic₅	The semidirect product of D₈ and Dic₅ acting through Inn(D₈)	80	4	D8:5Dic5	320,823
D₈⋊₄Dic₅	4^th semidirect product of D₈ and Dic₅ acting via Dic₅/C₁₀=C₂	80	4	D8:4Dic5	320,824
(D₄×C₁₀)⋊₂₁C₄	5^th semidirect product of D₄×C₁₀ and C₄ acting via C₄/C₂=C₂	80	4	(D4xC10):21C4	320,863
(D₄×C₁₀).₂₉C₄	10^th non-split extension by D₄×C₁₀ of C₄ acting via C₄/C₂=C₂	80	4	(D4xC10).29C4	320,864
(D₄×C₁₀)⋊₂₂C₄	6^th semidirect product of D₄×C₁₀ and C₄ acting via C₄/C₂=C₂	80	4	(D4xC10):22C4	320,867
C₅×C₂³.C₂³	Direct product of C₅ and C₂³.C₂³	80	4	C5xC2^3.C2^3	320,911
C₅×M₄(2).₈C₂²	Direct product of C₅ and M₄(2).₈C₂²	80	4	C5xM4(2).8C2^2	320,914
C₅×C₄²⋊C₂²	Direct product of C₅ and C₄²⋊C₂²	80	4	C5xC4^2:C2^2	320,922
C₅×M₄(2).C₄	Direct product of C₅ and M₄(2).C₄	80	4	C5xM4(2).C4	320,931
C₅×C₈.₂₆D₄	Direct product of C₅ and C₈.₂₆D₄	80	4	C5xC8.26D4	320,945
C₅×D₄⋊₄D₄	Direct product of C₅ and D₄⋊₄D₄	40	4	C5xD4:4D4	320,954
C₅×D₄.₈D₄	Direct product of C₅ and D₄.₈D₄	80	4	C5xD4.8D4	320,955
C₅×D₄.₉D₄	Direct product of C₅ and D₄.₉D₄	80	4	C5xD4.9D4	320,956
C₅×D₄.₁₀D₄	Direct product of C₅ and D₄.₁₀D₄	80	4	C5xD4.10D4	320,957
C₅×C₂≀C₂²	Direct product of C₅ and C₂≀C₂²	40	4	C5xC2wrC2^2	320,958
C₅×C₂³.₇D₄	Direct product of C₅ and C₂³.₇D₄	80	4	C5xC2^3.7D4	320,959
C₅×D₄.₃D₄	Direct product of C₅ and D₄.₃D₄	80	4	C5xD4.3D4	320,972
C₅×D₄.₄D₄	Direct product of C₅ and D₄.₄D₄	80	4	C5xD4.4D4	320,973
C₅×D₄.₅D₄	Direct product of C₅ and D₄.₅D₄	160	4	C5xD4.5D4	320,974
C₅×C₁₆⋊C₂²	Direct product of C₅ and C₁₆⋊C₂²	80	4	C5xC16:C2^2	320,1010
C₅×Q₃₂⋊C₂	Direct product of C₅ and Q₃₂⋊C₂	160	4	C5xQ32:C2	320,1011
D₅⋊M₅(2)	The semidirect product of D₅ and M₅(2) acting via M₅(2)/C₂×C₈=C₂	80	4	D5:M5(2)	320,1053
C₂₀.₁₂C₄²	5^th non-split extension by C₂₀ of C₄² acting via C₄²/C₄=C₄	80	4	C20.12C4^2	320,1056
(C₂×C₈)⋊₆F₅	4^th semidirect product of C₂×C₈ and F₅ acting via F₅/D₅=C₂	80	4	(C2xC8):6F5	320,1059
(C₈×D₅).C₄	6^th non-split extension by C₈×D₅ of C₄ acting via C₄/C₂=C₂	80	4	(C8xD5).C4	320,1062
C₂³⋊F₅⋊₅C₂	The semidirect product of C₂³⋊F₅ and C₂ acting through Inn(C₂³⋊F₅)	80	4	C2^3:F5:5C2	320,1083
(C₄×D₅).D₄	54^th non-split extension by C₄×D₅ of D₄ acting via D₄/C₂=C₂²	80	4	(C4xD5).D4	320,1099
C₄₀.₄₇C₂³	40^th non-split extension by C₄₀ of C₂³ acting via C₂³/C₂=C₂²	80	4	C40.47C2^3	320,1417
C₄₀.₉C₂³	2^nd non-split extension by C₄₀ of C₂³ acting via C₂³/C₂=C₂²	80	4	C40.9C2^3	320,1420
D₅×C₈○D₄	Direct product of D₅ and C₈○D₄	80	4	D5xC8oD4	320,1421
C₂₀.₇₂C₂⁴	19^th non-split extension by C₂₀ of C₂⁴ acting via C₂⁴/C₂³=C₂	80	4	C20.72C2^4	320,1422
D₄.₁₁D₂₀	1^st non-split extension by D₄ of D₂₀ acting through Inn(D₄)	80	4	D4.11D20	320,1423
D₈⋊₁₃D₁₀	2^nd semidirect product of D₈ and D₁₀ acting through Inn(D₈)	80	4	D8:13D10	320,1429
D₂₀.₂₉D₄	12^nd non-split extension by D₂₀ of D₄ acting via D₄/C₄=C₂	80	4	D20.29D4	320,1434
D₂₀.₃₀D₄	13^rd non-split extension by D₂₀ of D₄ acting via D₄/C₄=C₂	160	4	D20.30D4	320,1438
D₅×C₄○D₈	Direct product of D₅ and C₄○D₈	80	4	D5xC4oD8	320,1439
Q₁₆⋊D₁₀	4^th semidirect product of Q₁₆ and D₁₀ acting via D₁₀/C₁₀=C₂	80	4	Q16:D10	320,1440
D₈⋊₁₁D₁₀	5^th semidirect product of D₈ and D₁₀ acting via D₁₀/C₁₀=C₂	80	4	D8:11D10	320,1442
C₂₀.₇₆C₂⁴	23^rd non-split extension by C₂₀ of C₂⁴ acting via C₂⁴/C₂³=C₂	80	4	C20.76C2^4	320,1491
C₂₀.C₂⁴	35^th non-split extension by C₂₀ of C₂⁴ acting via C₂⁴/C₂²=C₂²	80	4	C20.C2^4	320,1494
C₅×Q₈○M₄(2)	Direct product of C₅ and Q₈○M₄(2)	80	4	C5xQ8oM4(2)	320,1570
C₅×D₈⋊C₂²	Direct product of C₅ and D₈⋊C₂²	80	4	C5xD8:C2^2	320,1577
C₅×D₄○D₈	Direct product of C₅ and D₄○D₈	80	4	C5xD4oD8	320,1578
C₅×D₄○SD₁₆	Direct product of C₅ and D₄○SD₁₆	80	4	C5xD4oSD16	320,1579
C₅×Q₈○D₈	Direct product of C₅ and Q₈○D₈	160	4	C5xQ8oD8	320,1580
2_-¹⁺⁴⋊D₅	The semidirect product of 2_-¹⁺⁴ and D₅ acting faithfully	32	4	ES-(2,2):D5	320,1582
2_-¹⁺⁴.C₁₀	The non-split extension by 2_-¹⁺⁴ of C₁₀ acting via C₁₀/C₂=C₅	64	4	ES-(2,2).C10	320,1586
C₁₀.C₂⁵	14^th non-split extension by C₁₀ of C₂⁵ acting via C₂⁵/C₂⁴=C₂	80	4	C10.C2^5	320,1621
C₅×C₂.C₂⁵	Direct product of C₅ and C₂.C₂⁵	80	4	C5xC2.C2^5	320,1634

Groups of order 324

		d	ρ	Label	ID
C₉×C₃²⋊C₄	Direct product of C₉ and C₃²⋊C₄	36	4	C9xC3^2:C4	324,109
C₃²⋊₃Dic₉	The semidirect product of C₃² and Dic₉ acting via Dic₉/C₉=C₄	36	4	C3^2:3Dic9	324,112
C₃×S₃×D₉	Direct product of C₃, S₃ and D₉	36	4	C3xS3xD9	324,114
S₃²×C₉	Direct product of C₉, S₃ and S₃	36	4	S3^2xC9	324,115
C₃²⋊₅D₁₈	2^nd semidirect product of C₃² and D₁₈ acting via D₁₈/C₉=C₂²	36	4	C3^2:5D18	324,123
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	9	4	C3^3:A4	324,160
C₃×C₃³⋊C₄	Direct product of C₃ and C₃³⋊C₄; = AΣL₁(𝔽₈₁)	12	4	C3xC3^3:C4	324,162
C₃×C₃²⋊₄D₆	Direct product of C₃ and C₃²⋊₄D₆	12	4	C3xC3^2:4D6	324,167

Groups of order 336

		d	ρ	Label	ID
D₇×C₃⋊C₈	Direct product of D₇ and C₃⋊C₈	168	4	D7xC3:C8	336,23
S₃×C₇⋊C₈	Direct product of S₃ and C₇⋊C₈	168	4	S3xC7:C8	336,24
D₂₁⋊C₈	The semidirect product of D₂₁ and C₈ acting via C₈/C₄=C₂	168	4	D21:C8	336,25
C₂₈.₃₂D₆	11^st non-split extension by C₂₈ of D₆ acting via D₆/S₃=C₂	168	4	C28.32D6	336,26
D₆.Dic₇	The non-split extension by D₆ of Dic₇ acting via Dic₇/C₁₄=C₂	168	4	D6.Dic7	336,27
D₄₂.C₄	3^rd non-split extension by D₄₂ of C₄ acting via C₄/C₂=C₂	168	4	D42.C4	336,28
C₂₁⋊D₈	1^st semidirect product of C₂₁ and D₈ acting via D₈/C₄=C₂²	168	4	C21:D8	336,29
C₂₈.D₆	3^rd non-split extension by C₂₈ of D₆ acting via D₆/C₃=C₂²	168	4	C28.D6	336,32
C₄₂.D₄	5^th non-split extension by C₄₂ of D₄ acting via D₄/C₂=C₂²	168	4	C42.D4	336,33
C₂₁⋊Q₁₆	1^st semidirect product of C₂₁ and Q₁₆ acting via Q₁₆/C₄=C₂²	336	4	C21:Q16	336,38
C₃×D₄⋊D₇	Direct product of C₃ and D₄⋊D₇	168	4	C3xD4:D7	336,69
C₃×D₄.D₇	Direct product of C₃ and D₄.D₇	168	4	C3xD4.D7	336,70
C₃×Q₈⋊D₇	Direct product of C₃ and Q₈⋊D₇	168	4	C3xQ8:D7	336,71
C₃×C₇⋊Q₁₆	Direct product of C₃ and C₇⋊Q₁₆	336	4	C3xC7:Q16	336,72
C₇×D₄⋊S₃	Direct product of C₇ and D₄⋊S₃	168	4	C7xD4:S3	336,85
C₇×D₄.S₃	Direct product of C₇ and D₄.S₃	168	4	C7xD4.S3	336,86
C₇×Q₈⋊₂S₃	Direct product of C₇ and Q₈⋊₂S₃	168	4	C7xQ8:2S3	336,87
C₇×C₃⋊Q₁₆	Direct product of C₇ and C₃⋊Q₁₆	336	4	C7xC3:Q16	336,88
SL₂(𝔽₇)	Special linear group on 𝔽₇²; = C₂ .GL₃(𝔽₂)	16	4	SL(2,7)	336,114
D₂₈⋊S₃	3^rd semidirect product of D₂₈ and S₃ acting via S₃/C₃=C₂	168	4	D28:S3	336,139
D₁₂⋊D₇	3^rd semidirect product of D₁₂ and D₇ acting via D₇/C₇=C₂	168	4	D12:D7	336,141
D₂₁⋊Q₈	The semidirect product of D₂₁ and Q₈ acting via Q₈/C₄=C₂	168	4	D21:Q8	336,143
D₆.D₁₄	3^rd non-split extension by D₆ of D₁₄ acting via D₁₄/C₁₄=C₂	168	4	D6.D14	336,144
C₄×S₃×D₇	Direct product of C₄, S₃ and D₇	84	4	C4xS3xD7	336,147
C₂₈⋊D₆	2^nd semidirect product of C₂₈ and D₆ acting via D₆/C₃=C₂²	84	4	C28:D6	336,150
Dic₇.D₆	5^th non-split extension by Dic₇ of D₆ acting via D₆/S₃=C₂	168	4	Dic7.D6	336,152
Dic₃.D₁₄	6^th non-split extension by Dic₃ of D₁₄ acting via D₁₄/D₇=C₂	168	4	Dic3.D14	336,155
D₇×C₃⋊D₄	Direct product of D₇ and C₃⋊D₄	84	4	D7xC3:D4	336,161
S₃×C₇⋊D₄	Direct product of S₃ and C₇⋊D₄	84	4	S3xC7:D4	336,162
C₃×D₄×D₇	Direct product of C₃, D₄ and D₇	84	4	C3xD4xD7	336,178
C₃×D₄⋊₂D₇	Direct product of C₃ and D₄⋊₂D₇	168	4	C3xD4:2D7	336,179
C₃×Q₈×D₇	Direct product of C₃, Q₈ and D₇	168	4	C3xQ8xD7	336,180
C₃×Q₈⋊₂D₇	Direct product of C₃ and Q₈⋊₂D₇	168	4	C3xQ8:2D7	336,181
S₃×C₇×D₄	Direct product of C₇, S₃ and D₄	84	4	S3xC7xD4	336,188
C₇×D₄⋊₂S₃	Direct product of C₇ and D₄⋊₂S₃	168	4	C7xD4:2S3	336,189
S₃×C₇×Q₈	Direct product of C₇, S₃ and Q₈	168	4	S3xC7xQ8	336,190
C₇×Q₈⋊₃S₃	Direct product of C₇ and Q₈⋊₃S₃	168	4	C7xQ8:3S3	336,191

Groups of order 340

		d	ρ	Label	ID
C₅×C₁₇⋊C₄	Direct product of C₅ and C₁₇⋊C₄	85	4	C5xC17:C4	340,5
C₈₅⋊C₄	3^rd semidirect product of C₈₅ and C₄ acting faithfully	85	4	C85:C4	340,6
C₁₇×F₅	Direct product of C₁₇ and F₅	85	4	C17xF5	340,7
C₁₇⋊₃F₅	The semidirect product of C₁₇ and F₅ acting via F₅/D₅=C₂	85	4	C17:3F5	340,8

Groups of order 348

		d	ρ	Label	ID
C₃×C₂₉⋊C₄	Direct product of C₃ and C₂₉⋊C₄	87	4	C3xC29:C4	348,5
C₈₇⋊C₄	1^st semidirect product of C₈₇ and C₄ acting faithfully	87	4	C87:C4	348,6

Groups of order 352

		d	ρ	Label	ID
C₂².₂D₄₄	1^st non-split extension by C₂² of D₄₄ acting via D₄₄/D₂₂=C₂	88	4	C2^2.2D44	352,12
C₄₄.₅₃D₄	10^th non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	176	4	C44.53D4	352,28
D₄₄⋊₄C₄	4^th semidirect product of D₄₄ and C₄ acting via C₄/C₂=C₂	88	4	D44:4C4	352,31
C₄₄.D₄	8^th non-split extension by C₄₄ of D₄ acting via D₄/C₂=C₂²	88	4	C44.D4	352,39
C₂³⋊Dic₁₁	The semidirect product of C₂³ and Dic₁₁ acting via Dic₁₁/C₁₁=C₄	88	4	C2^3:Dic11	352,40
C₄₄.₁₀D₄	10^th non-split extension by C₄₄ of D₄ acting via D₄/C₂=C₂²	176	4	C44.10D4	352,42
C₄₄.₅₆D₄	13^rd non-split extension by C₄₄ of D₄ acting via D₄/C₂²=C₂	88	4	C44.56D4	352,43
C₁₁×C₂³⋊C₄	Direct product of C₁₁ and C₂³⋊C₄	88	4	C11xC2^3:C4	352,48
C₁₁×C₄.D₄	Direct product of C₁₁ and C₄.D₄	88	4	C11xC4.D4	352,49
C₁₁×C₄.₁₀D₄	Direct product of C₁₁ and C₄.₁₀D₄	176	4	C11xC4.10D4	352,50
M₄(2)×D₁₁	Direct product of M₄(2) and D₁₁	88	4	M4(2)xD11	352,101
D₄₄.C₄	The non-split extension by D₄₄ of C₄ acting via C₄/C₂=C₂	176	4	D44.C4	352,102
D₄⋊D₂₂	2^nd semidirect product of D₄ and D₂₂ acting via D₂₂/D₁₁=C₂	88	4	D4:D22	352,106
SD₁₆×D₁₁	Direct product of SD₁₆ and D₁₁	88	4	SD16xD11	352,108
Q₈.D₂₂	2^nd non-split extension by Q₈ of D₂₂ acting via D₂₂/D₁₁=C₂	176	4	Q8.D22	352,111
Q₁₆⋊D₁₁	2^nd semidirect product of Q₁₆ and D₁₁ acting via D₁₁/C₁₁=C₂	176	4	Q16:D11	352,113
D₄₄⋊₆C₂²	4^th semidirect product of D₄₄ and C₂² acting via C₂²/C₂=C₂	88	4	D44:6C2^2	352,127
C₄₄.C₂³	15^th non-split extension by C₄₄ of C₂³ acting via C₂³/C₂=C₂²	176	4	C44.C2^3	352,137
Q₈.Dic₁₁	The non-split extension by Q₈ of Dic₁₁ acting through Inn(Q₈)	176	4	Q8.Dic11	352,143
D₄.₈D₂₂	3^rd non-split extension by D₄ of D₂₂ acting via D₂₂/C₂₂=C₂	176	4	D4.8D22	352,145
C₁₁×C₈⋊C₂²	Direct product of C₁₁ and C₈⋊C₂²	88	4	C11xC8:C2^2	352,171
C₁₁×C₈.C₂²	Direct product of C₁₁ and C₈.C₂²	176	4	C11xC8.C2^2	352,172
D₄⋊₆D₂₂	2^nd semidirect product of D₄ and D₂₂ acting through Inn(D₄)	88	4	D4:6D22	352,179
Q₈.₁₀D₂₂	1^st non-split extension by Q₈ of D₂₂ acting through Inn(Q₈)	176	4	Q8.10D22	352,182
C₄○D₄×D₁₁	Direct product of C₄○D₄ and D₁₁	88	4	C4oD4xD11	352,183
C₁₁×2₊¹⁺⁴	Direct product of C₁₁ and 2₊¹⁺⁴	88	4	C11xES+(2,2)	352,192
C₁₁×2_-¹⁺⁴	Direct product of C₁₁ and 2_-¹⁺⁴	176	4	C11xES-(2,2)	352,193

Groups of order 360

		d	ρ	Label	ID
C₉×C₅⋊C₈	Direct product of C₉ and C₅⋊C₈	360	4	C9xC5:C8	360,5
C₄₅⋊C₈	1^st semidirect product of C₄₅ and C₈ acting via C₈/C₂=C₄	360	4	C45:C8	360,6
C₁₈×F₅	Direct product of C₁₈ and F₅	90	4	C18xF5	360,43
C₂×C₉⋊F₅	Direct product of C₂ and C₉⋊F₅	90	4	C2xC9:F5	360,44
C₃×C₁₅⋊C₈	Direct product of C₃ and C₁₅⋊C₈	120	4	C3xC15:C8	360,53
C₅×C₃²⋊₂C₈	Direct product of C₅ and C₃²⋊₂C₈	120	4	C5xC3^2:2C8	360,55
(C₃×C₁₅)⋊₉C₈	6^th semidirect product of C₃×C₁₅ and C₈ acting via C₈/C₂=C₄	120	4	(C3xC15):9C8	360,56
C₃×D₅×Dic₃	Direct product of C₃, D₅ and Dic₃	60	4	C3xD5xDic3	360,58
C₃×S₃×Dic₅	Direct product of C₃, S₃ and Dic₅	120	4	C3xS3xDic5	360,59
C₃×D₃₀.C₂	Direct product of C₃ and D₃₀.C₂	120	4	C3xD30.C2	360,60
C₃×C₁₅⋊D₄	Direct product of C₃ and C₁₅⋊D₄	60	4	C3xC15:D4	360,61
C₃×C₃⋊D₂₀	Direct product of C₃ and C₃⋊D₂₀	60	4	C3xC3:D20	360,62
C₃×C₅⋊D₁₂	Direct product of C₃ and C₅⋊D₁₂	120	4	C3xC5:D12	360,63
C₃×C₁₅⋊Q₈	Direct product of C₃ and C₁₅⋊Q₈	120	4	C3xC15:Q8	360,64
C₅×S₃×Dic₃	Direct product of C₅, S₃ and Dic₃	120	4	C5xS3xDic3	360,72
C₅×C₆.D₆	Direct product of C₅ and C₆.D₆	60	4	C5xC6.D6	360,73
C₅×D₆⋊S₃	Direct product of C₅ and D₆⋊S₃	120	4	C5xD6:S3	360,74
C₅×C₃⋊D₁₂	Direct product of C₅ and C₃⋊D₁₂	60	4	C5xC3:D12	360,75
C₅×C₃²⋊₂Q₈	Direct product of C₅ and C₃²⋊₂Q₈	120	4	C5xC3^2:2Q8	360,76
D₃₀.S₃	The non-split extension by D₃₀ of S₃ acting via S₃/C₃=C₂	120	4	D30.S3	360,84
Dic₁₅⋊S₃	3^rd semidirect product of Dic₁₅ and S₃ acting via S₃/C₃=C₂	60	4	Dic15:S3	360,85
D₃₀⋊S₃	3^rd semidirect product of D₃₀ and S₃ acting via S₃/C₃=C₂	60	4	D30:S3	360,86
C₃²⋊₃D₂₀	2^nd semidirect product of C₃² and D₂₀ acting via D₂₀/C₁₀=C₂²	120	4	C3^2:3D20	360,87
C₃²⋊₃Dic₁₀	2^nd semidirect product of C₃² and Dic₁₀ acting via Dic₁₀/C₁₀=C₂²	120	4	C3^2:3Dic10	360,88
C₃×S₅	Direct product of C₃ and S₅	15	4	C3xS5	360,119
C₅×S₃≀C₂	Direct product of C₅ and S₃≀C₂	30	4	C5xS3wrC2	360,132
S₃²⋊D₅	The semidirect product of S₃² and D₅ acting via D₅/C₅=C₂	30	4	S3^2:D5	360,133
C₆×C₃⋊F₅	Direct product of C₆ and C₃⋊F₅	60	4	C6xC3:F5	360,146
C₁₀×C₃²⋊C₄	Direct product of C₁₀ and C₃²⋊C₄	60	4	C10xC3^2:C4	360,148
C₂×C₃²⋊Dic₅	Direct product of C₂ and C₃²⋊Dic₅	60	4	C2xC3^2:Dic5	360,149
S₃×C₆×D₅	Direct product of C₆, S₃ and D₅	60	4	S3xC6xD5	360,151
S₃²×C₁₀	Direct product of C₁₀, S₃ and S₃	60	4	S3^2xC10	360,153
C₂×D₁₅⋊S₃	Direct product of C₂ and D₁₅⋊S₃	60	4	C2xD15:S3	360,155

Groups of order 364

		d	ρ	Label	ID
C₇×C₁₃⋊C₄	Direct product of C₇ and C₁₃⋊C₄	91	4	C7xC13:C4	364,5
C₉₁⋊C₄	1^st semidirect product of C₉₁ and C₄ acting faithfully	91	4	C91:C4	364,6

Groups of order 380

		d	ρ	Label	ID
C₁₉×F₅	Direct product of C₁₉ and F₅	95	4	C19xF5	380,5
C₁₉⋊F₅	The semidirect product of C₁₉ and F₅ acting via F₅/D₅=C₂	95	4	C19:F5	380,6

Groups of order 396

		d	ρ	Label	ID
C₁₁×C₃²⋊C₄	Direct product of C₁₁ and C₃²⋊C₄	66	4	C11xC3^2:C4	396,17
C₃²⋊Dic₁₁	The semidirect product of C₃² and Dic₁₁ acting via Dic₁₁/C₁₁=C₄	66	4	C3^2:Dic11	396,18
C₃×S₃×D₁₁	Direct product of C₃, S₃ and D₁₁	66	4	C3xS3xD11	396,19
S₃²×C₁₁	Direct product of C₁₁, S₃ and S₃	66	4	S3^2xC11	396,21
D₃₃⋊S₃	The semidirect product of D₃₃ and S₃ acting via S₃/C₃=C₂	66	4	D33:S3	396,23

Groups of order 400

		d	ρ	Label	ID
C₂₅⋊C₁₆	The semidirect product of C₂₅ and C₁₆ acting via C₁₆/C₄=C₄	400	4	C25:C16	400,3
D₂₅⋊C₈	The semidirect product of D₂₅ and C₈ acting via C₈/C₄=C₂	200	4	D25:C8	400,28
C₁₀₀.C₄	1^st non-split extension by C₁₀₀ of C₄ acting faithfully	200	4	C100.C4	400,29
C₄×C₂₅⋊C₄	Direct product of C₄ and C₂₅⋊C₄	100	4	C4xC25:C4	400,30
C₁₀₀⋊C₄	1^st semidirect product of C₁₀₀ and C₄ acting faithfully	100	4	C100:C4	400,31
C₅×C₅⋊C₁₆	Direct product of C₅ and C₅⋊C₁₆	80	4	C5xC5:C16	400,56
C₅²⋊₃C₁₆	2^nd semidirect product of C₅² and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5^2:3C16	400,57
C₅²⋊₅C₁₆	4^th semidirect product of C₅² and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5^2:5C16	400,59
D₅×C₅⋊₂C₈	Direct product of D₅ and C₅⋊₂C₈	80	4	D5xC5:2C8	400,60
C₂₀.₂₉D₁₀	3^rd non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.29D10	400,61
C₂₀.₃₀D₁₀	4^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	80	4	C20.30D10	400,62
C₂₀.₃₁D₁₀	5^th non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.31D10	400,63
C₅²⋊₂D₈	1^st semidirect product of C₅² and D₈ acting via D₈/C₄=C₂²	80	4	C5^2:2D8	400,64
D₂₀.D₅	2^nd non-split extension by D₂₀ of D₅ acting via D₅/C₅=C₂	80	4	D20.D5	400,66
C₅²⋊₂Q₁₆	1^st semidirect product of C₅² and Q₁₆ acting via Q₁₆/C₄=C₂²	80	4	C5^2:2Q16	400,69
C₅×D₄⋊D₅	Direct product of C₅ and D₄⋊D₅	40	4	C5xD4:D5	400,87
C₅×D₄.D₅	Direct product of C₅ and D₄.D₅	40	4	C5xD4.D5	400,88
C₅×Q₈⋊D₅	Direct product of C₅ and Q₈⋊D₅	80	4	C5xQ8:D5	400,89
C₅×C₅⋊Q₁₆	Direct product of C₅ and C₅⋊Q₁₆	80	4	C5xC5:Q16	400,90
C₂.D₅≀C₂	2^nd central extension by C₂ of D₅≀C₂	20	4	C2.D5wrC2	400,130
C₅²⋊D₈	The semidirect product of C₅² and D₈ acting via D₈/C₂=D₄	40	4	C5^2:D8	400,131
C₅×D₅⋊C₈	Direct product of C₅ and D₅⋊C₈	80	4	C5xD5:C8	400,135
C₅×C₄.F₅	Direct product of C₅ and C₄.F₅	80	4	C5xC4.F5	400,136
C₂₀×F₅	Direct product of C₂₀ and F₅	80	4	C20xF5	400,137
C₅×C₄⋊F₅	Direct product of C₅ and C₄⋊F₅	80	4	C5xC4:F5	400,138
C₅×C₂².F₅	Direct product of C₅ and C₂².F₅	40	4	C5xC2^2.F5	400,140
C₅×C₂²⋊F₅	Direct product of C₅ and C₂²⋊F₅	40	4	C5xC2^2:F5	400,141
C₂₀.₁₄F₅	3^rd non-split extension by C₂₀ of F₅ acting via F₅/D₅=C₂	80	4	C20.14F5	400,142
C₂₀.₁₂F₅	1^st non-split extension by C₂₀ of F₅ acting via F₅/D₅=C₂	80	4	C20.12F5	400,143
C₄×D₅.D₅	Direct product of C₄ and D₅.D₅	80	4	C4xD5.D5	400,144
C₂₀⋊₅F₅	1^st semidirect product of C₂₀ and F₅ acting via F₅/D₅=C₂	80	4	C20:5F5	400,145
C₁₀².C₄	4^th non-split extension by C₁₀² of C₄ acting faithfully	40	4	C10^2.C4	400,147
D₁₀.D₁₀	5^th non-split extension by D₁₀ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D10.D10	400,148
C₂₀.₁₁F₅	11^st non-split extension by C₂₀ of F₅ acting via F₅/C₅=C₄	40	4	C20.11F5	400,156
C₅²⋊₈M₄(2)	4^th semidirect product of C₅² and M₄(2) acting via M₄(2)/C₄=C₄	40	4	C5^2:8M4(2)	400,157
C₄×C₅²⋊C₄	Direct product of C₄ and C₅²⋊C₄	40	4	C4xC5^2:C4	400,158
C₂₀⋊₂F₅	2^nd semidirect product of C₂₀ and F₅ acting via F₅/C₅=C₄	40	4	C20:2F5	400,159
D₂₀⋊D₅	3^rd semidirect product of D₂₀ and D₅ acting via D₅/C₅=C₂	40	4	D20:D5	400,165
Dic₁₀⋊D₅	4^th semidirect product of Dic₁₀ and D₅ acting via D₅/C₅=C₂	40	4	Dic10:D5	400,166
D₁₀.₉D₁₀	1^st non-split extension by D₁₀ of D₁₀ acting via D₁₀/C₁₀=C₂	40	4	D10.9D10	400,167
C₄×D₅²	Direct product of C₄, D₅ and D₅	40	4	C4xD5^2	400,169
C₂₀⋊D₁₀	2^nd semidirect product of C₂₀ and D₁₀ acting via D₁₀/C₅=C₂²	40	4	C20:D10	400,171
Dic₅.D₁₀	3^rd non-split extension by Dic₅ of D₁₀ acting via D₁₀/D₅=C₂	40	4	Dic5.D10	400,173
D₅×C₅⋊D₄	Direct product of D₅ and C₅⋊D₄	40	4	D5xC5:D4	400,179
C₅×D₄×D₅	Direct product of C₅, D₄ and D₅	40	4	C5xD4xD5	400,185
C₅×D₄⋊₂D₅	Direct product of C₅ and D₄⋊₂D₅	40	4	C5xD4:2D5	400,186
C₅×Q₈×D₅	Direct product of C₅, Q₈ and D₅	80	4	C5xQ8xD5	400,187
C₅×Q₈⋊₂D₅	Direct product of C₅ and Q₈⋊₂D₅	80	4	C5xQ8:2D5	400,188

Groups of order 408

		d	ρ	Label	ID
C₃×C₁₇⋊₂C₈	Direct product of C₃ and C₁₇⋊₂C₈	408	4	C3xC17:2C8	408,5
C₅₁⋊₃C₈	1^st semidirect product of C₅₁ and C₈ acting via C₈/C₂=C₄	408	4	C51:3C8	408,6
C₆×C₁₇⋊C₄	Direct product of C₆ and C₁₇⋊C₄	102	4	C6xC17:C4	408,39
C₂×C₅₁⋊C₄	Direct product of C₂ and C₅₁⋊C₄	102	4	C2xC51:C4	408,40

Groups of order 416

		d	ρ	Label	ID
C₁₃⋊C₃₂	The semidirect product of C₁₃ and C₃₂ acting via C₃₂/C₈=C₄	416	4	C13:C32	416,3
C₂².₂D₅₂	1^st non-split extension by C₂² of D₅₂ acting via D₅₂/D₂₆=C₂	104	4	C2^2.2D52	416,13
C₅₂.₅₃D₄	10^th non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	208	4	C52.53D4	416,29
D₅₂⋊₇C₄	4^th semidirect product of D₅₂ and C₄ acting via C₄/C₂=C₂	104	4	D52:7C4	416,32
C₅₂.D₄	8^th non-split extension by C₅₂ of D₄ acting via D₄/C₂=C₂²	104	4	C52.D4	416,40
C₂³⋊Dic₁₃	The semidirect product of C₂³ and Dic₁₃ acting via Dic₁₃/C₁₃=C₄	104	4	C2^3:Dic13	416,41
C₅₂.₁₀D₄	10^th non-split extension by C₅₂ of D₄ acting via D₄/C₂=C₂²	208	4	C52.10D4	416,43
C₅₂.₅₆D₄	13^rd non-split extension by C₅₂ of D₄ acting via D₄/C₂²=C₂	104	4	C52.56D4	416,44
C₁₃×C₂³⋊C₄	Direct product of C₁₃ and C₂³⋊C₄	104	4	C13xC2^3:C4	416,49
C₁₃×C₄.D₄	Direct product of C₁₃ and C₄.D₄	104	4	C13xC4.D4	416,50
C₁₃×C₄.₁₀D₄	Direct product of C₁₃ and C₄.₁₀D₄	208	4	C13xC4.10D4	416,51
D₁₃⋊C₁₆	The semidirect product of D₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	4	D13:C16	416,64
D₂₆.C₈	3^rd non-split extension by D₂₆ of C₈ acting via C₈/C₄=C₂	208	4	D26.C8	416,65
C₈×C₁₃⋊C₄	Direct product of C₈ and C₁₃⋊C₄	104	4	C8xC13:C4	416,66
C₁₀₄⋊C₄	4^th semidirect product of C₁₀₄ and C₄ acting faithfully	104	4	C104:C4	416,67
D₂₆.₈D₄	4^th non-split extension by D₂₆ of D₄ acting via D₄/C₄=C₂	104	4	D26.8D4	416,68
D₁₃.D₈	The non-split extension by D₁₃ of D₈ acting via D₈/C₈=C₂	104	4	D13.D8	416,69
C₁₀₄.C₄	2^nd non-split extension by C₁₀₄ of C₄ acting faithfully	208	4	C104.C4	416,70
C₁₀₄.₁C₄	1^st non-split extension by C₁₀₄ of C₄ acting faithfully	208	4	C104.1C4	416,71
C₅₂.C₈	1^st non-split extension by C₅₂ of C₈ acting via C₈/C₂=C₄	208	4	C52.C8	416,73
D₂₆.₄D₄	4^th non-split extension by D₂₆ of D₄ acting via D₄/C₂=C₂²	104	4	D26.4D4	416,86
Dic₁₃.₄D₄	4^th non-split extension by Dic₁₃ of D₄ acting via D₄/C₂=C₂²	104	4	Dic13.4D4	416,88
M₄(2)×D₁₃	Direct product of M₄(2) and D₁₃	104	4	M4(2)xD13	416,127
D₅₂.₂C₄	The non-split extension by D₅₂ of C₄ acting via C₄/C₂=C₂	208	4	D52.2C4	416,128
D₈⋊D₁₃	2^nd semidirect product of D₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	4	D8:D13	416,132
SD₁₆×D₁₃	Direct product of SD₁₆ and D₁₃	104	4	SD16xD13	416,134
D₂₆.₆D₄	2^nd non-split extension by D₂₆ of D₄ acting via D₄/C₄=C₂	208	4	D26.6D4	416,137
Q₁₆⋊D₁₃	2^nd semidirect product of Q₁₆ and D₁₃ acting via D₁₃/C₁₃=C₂	208	4	Q16:D13	416,139
D₅₂⋊₆C₂²	4^th semidirect product of D₅₂ and C₂² acting via C₂²/C₂=C₂	104	4	D52:6C2^2	416,153
Q₈.D₂₆	1^st non-split extension by Q₈ of D₂₆ acting via D₂₆/C₂₆=C₂	208	4	Q8.D26	416,163
D₄.Dic₁₃	The non-split extension by D₄ of Dic₁₃ acting through Inn(D₄)	208	4	D4.Dic13	416,169
C₅₂.C₂³	18^th non-split extension by C₅₂ of C₂³ acting via C₂³/C₂=C₂²	208	4	C52.C2^3	416,171
C₁₃×C₈⋊C₂²	Direct product of C₁₃ and C₈⋊C₂²	104	4	C13xC8:C2^2	416,197
C₁₃×C₈.C₂²	Direct product of C₁₃ and C₈.C₂²	208	4	C13xC8.C2^2	416,198
D₁₃⋊M₄(2)	The semidirect product of D₁₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	104	4	D13:M4(2)	416,201
D₂₆.C₂³	11^st non-split extension by D₂₆ of C₂³ acting via C₂³/C₂²=C₂	104	4	D26.C2^3	416,204
D₄⋊₆D₂₆	2^nd semidirect product of D₄ and D₂₆ acting through Inn(D₄)	104	4	D4:6D26	416,218
Q₈.₁₀D₂₆	1^st non-split extension by Q₈ of D₂₆ acting through Inn(Q₈)	208	4	Q8.10D26	416,221
C₄○D₄×D₁₃	Direct product of C₄○D₄ and D₁₃	104	4	C4oD4xD13	416,222
C₁₃×2₊¹⁺⁴	Direct product of C₁₃ and 2₊¹⁺⁴	104	4	C13xES+(2,2)	416,231
C₁₃×2_-¹⁺⁴	Direct product of C₁₃ and 2_-¹⁺⁴	208	4	C13xES-(2,2)	416,232

Groups of order 420

		d	ρ	Label	ID
F₅×C₂₁	Direct product of C₂₁ and F₅	105	4	F5xC21	420,20
C₃×C₇⋊F₅	Direct product of C₃ and C₇⋊F₅	105	4	C3xC7:F5	420,21
C₇×C₃⋊F₅	Direct product of C₇ and C₃⋊F₅	105	4	C7xC3:F5	420,22
C₅⋊Dic₂₁	The semidirect product of C₅ and Dic₂₁ acting via Dic₂₁/C₂₁=C₄	105	4	C5:Dic21	420,23
C₃×D₅×D₇	Direct product of C₃, D₅ and D₇	105	4	C3xD5xD7	420,24
C₅×S₃×D₇	Direct product of C₅, S₃ and D₇	105	4	C5xS3xD7	420,25
S₃×C₇×D₅	Direct product of C₇, S₃ and D₅	105	4	S3xC7xD5	420,27
D₁₅⋊D₇	The semidirect product of D₁₅ and D₇ acting via D₇/C₇=C₂	105	4	D15:D7	420,30

Groups of order 432

		d	ρ	Label	ID
D₉×C₃⋊C₈	Direct product of D₉ and C₃⋊C₈	144	4	D9xC3:C8	432,58
C₃₆.₃₈D₆	9^th non-split extension by C₃₆ of D₆ acting via D₆/S₃=C₂	72	4	C36.38D6	432,59
C₃₆.₃₉D₆	10^th non-split extension by C₃₆ of D₆ acting via D₆/S₃=C₂	144	4	C36.39D6	432,60
C₃₆.₄₀D₆	11^st non-split extension by C₃₆ of D₆ acting via D₆/S₃=C₂	72	4	C36.40D6	432,61
S₃×C₉⋊C₈	Direct product of S₃ and C₉⋊C₈	144	4	S3xC9:C8	432,66
D₆.Dic₉	The non-split extension by D₆ of Dic₉ acting via Dic₉/C₁₈=C₂	144	4	D6.Dic9	432,67
D₃₆⋊S₃	2^nd semidirect product of D₃₆ and S₃ acting via S₃/C₃=C₂	144	4	D36:S3	432,68
D₁₂.D₉	2^nd non-split extension by D₁₂ of D₉ acting via D₉/C₉=C₂	144	4	D12.D9	432,70
Dic₆⋊D₉	2^nd semidirect product of Dic₆ and D₉ acting via D₉/C₉=C₂	144	4	Dic6:D9	432,72
C₁₂.D₁₈	16^th non-split extension by C₁₂ of D₁₈ acting via D₁₈/C₉=C₂²	144	4	C12.D18	432,74
C₃×D₄.D₉	Direct product of C₃ and D₄.D₉	72	4	C3xD4.D9	432,148
C₃×D₄⋊D₉	Direct product of C₃ and D₄⋊D₉	72	4	C3xD4:D9	432,149
C₉×D₄⋊S₃	Direct product of C₉ and D₄⋊S₃	72	4	C9xD4:S3	432,150
C₉×D₄.S₃	Direct product of C₉ and D₄.S₃	72	4	C9xD4.S3	432,151
C₃×C₉⋊Q₁₆	Direct product of C₃ and C₉⋊Q₁₆	144	4	C3xC9:Q16	432,156
C₃×Q₈⋊₂D₉	Direct product of C₃ and Q₈⋊₂D₉	144	4	C3xQ8:2D9	432,157
C₉×Q₈⋊₂S₃	Direct product of C₉ and Q₈⋊₂S₃	144	4	C9xQ8:2S3	432,158
C₉×C₃⋊Q₁₆	Direct product of C₉ and C₃⋊Q₁₆	144	4	C9xC3:Q16	432,159
C₃×Q₈.D₉	Direct product of C₃ and Q₈.D₉	144	4	C3xQ8.D9	432,244
C₃×Q₈⋊D₉	Direct product of C₃ and Q₈⋊D₉	144	4	C3xQ8:D9	432,246
Q₈⋊C₉⋊₃S₃	The semidirect product of Q₈⋊C₉ and S₃ acting through Inn(Q₈⋊C₉)	144	4	Q8:C9:3S3	432,267
S₃×Q₈⋊C₉	Direct product of S₃ and Q₈⋊C₉	144	4	S3xQ8:C9	432,268
D₁₈.D₆	1^st non-split extension by D₁₈ of D₆ acting via D₆/S₃=C₂	72	4	D18.D6	432,281
Dic₁₈⋊S₃	3^rd semidirect product of Dic₁₈ and S₃ acting via S₃/C₃=C₂	72	4	Dic18:S3	432,283
D₁₂⋊D₉	3^rd semidirect product of D₁₂ and D₉ acting via D₉/C₉=C₂	72	4	D12:D9	432,286
D₆.D₁₈	1^st non-split extension by D₆ of D₁₈ acting via D₁₈/C₁₈=C₂	72	4	D6.D18	432,287
C₄×S₃×D₉	Direct product of C₄, S₃ and D₉	72	4	C4xS3xD9	432,290
C₃₆⋊D₆	2^nd semidirect product of C₃₆ and D₆ acting via D₆/C₃=C₂²	72	4	C36:D6	432,293
D₁₈.₃D₆	3^rd non-split extension by D₁₈ of D₆ acting via D₆/S₃=C₂	72	4	D18.3D6	432,305
Dic₃.D₁₈	5^th non-split extension by Dic₃ of D₁₈ acting via D₁₈/D₉=C₂	72	4	Dic3.D18	432,309
S₃×C₉⋊D₄	Direct product of S₃ and C₉⋊D₄	72	4	S3xC9:D4	432,313
D₉×C₃⋊D₄	Direct product of D₉ and C₃⋊D₄	72	4	D9xC3:D4	432,314
C₃×D₄×D₉	Direct product of C₃, D₄ and D₉	72	4	C3xD4xD9	432,356
C₃×D₄⋊₂D₉	Direct product of C₃ and D₄⋊₂D₉	72	4	C3xD4:2D9	432,357
S₃×D₄×C₉	Direct product of C₉, S₃ and D₄	72	4	S3xD4xC9	432,358
C₉×D₄⋊₂S₃	Direct product of C₉ and D₄⋊₂S₃	72	4	C9xD4:2S3	432,359
C₃×Q₈×D₉	Direct product of C₃, Q₈ and D₉	144	4	C3xQ8xD9	432,364
C₃×Q₈⋊₃D₉	Direct product of C₃ and Q₈⋊₃D₉	144	4	C3xQ8:3D9	432,365
S₃×Q₈×C₉	Direct product of C₉, S₃ and Q₈	144	4	S3xQ8xC9	432,366
C₉×Q₈⋊₃S₃	Direct product of C₉ and Q₈⋊₃S₃	144	4	C9xQ8:3S3	432,367
C₃×C₃²⋊₂C₁₆	Direct product of C₃ and C₃²⋊₂C₁₆	48	4	C3xC3^2:2C16	432,412
C₃³⋊₄C₁₆	2^nd semidirect product of C₃³ and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^3:4C16	432,413
C₃×S₃×C₃⋊C₈	Direct product of C₃, S₃ and C₃⋊C₈	48	4	C3xS3xC3:C8	432,414
C₃×C₁₂.₂₉D₆	Direct product of C₃ and C₁₂.₂₉D₆	48	4	C3xC12.29D6	432,415
C₃×D₆.Dic₃	Direct product of C₃ and D₆.Dic₃	48	4	C3xD6.Dic3	432,416
C₃×C₁₂.₃₁D₆	Direct product of C₃ and C₁₂.₃₁D₆	48	4	C3xC12.31D6	432,417
C₃×C₃²⋊₂D₈	Direct product of C₃ and C₃²⋊₂D₈	48	4	C3xC3^2:2D8	432,418
C₃×C₃⋊D₂₄	Direct product of C₃ and C₃⋊D₂₄	48	4	C3xC3:D24	432,419
C₃×Dic₆⋊S₃	Direct product of C₃ and Dic₆⋊S₃	48	4	C3xDic6:S3	432,420
C₃×D₁₂.S₃	Direct product of C₃ and D₁₂.S₃	48	4	C3xD12.S3	432,421
C₃×C₃²⋊₅SD₁₆	Direct product of C₃ and C₃²⋊₅SD₁₆	48	4	C3xC3^2:5SD16	432,422
C₃×C₃²⋊₂Q₁₆	Direct product of C₃ and C₃²⋊₂Q₁₆	48	4	C3xC3^2:2Q16	432,423
C₃×C₃²⋊₃Q₁₆	Direct product of C₃ and C₃²⋊₃Q₁₆	48	4	C3xC3^2:3Q16	432,424
C₁₂.₉₃S₃²	13^rd non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	4	C12.93S3^2	432,455
C₃³⋊₁₀M₄(2)	6^th semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₄=C₂²	48	4	C3^3:10M4(2)	432,456
C₃³⋊₉D₈	6^th semidirect product of C₃³ and D₈ acting via D₈/C₄=C₂²	48	4	C3^3:9D8	432,457
C₃³⋊₁₈SD₁₆	10^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₄=C₂²	48	4	C3^3:18SD16	432,458
C₃³⋊₉Q₁₆	6^th semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₄=C₂²	48	4	C3^3:9Q16	432,459
C₃×S₃²⋊C₄	Direct product of C₃ and S₃²⋊C₄	24	4	C3xS3^2:C4	432,574
C₃×C₃⋊S₃.Q₈	Direct product of C₃ and C₃⋊S₃.Q₈	48	4	C3xC3:S3.Q8	432,575
C₃×C₃²⋊D₈	Direct product of C₃ and C₃²⋊D₈	24	4	C3xC3^2:D8	432,576
C₃×C₃²⋊₂SD₁₆	Direct product of C₃ and C₃²⋊₂SD₁₆	24	4	C3xC3^2:2SD16	432,577
C₃×C₃²⋊Q₁₆	Direct product of C₃ and C₃²⋊Q₁₆	48	4	C3xC3^2:Q16	432,578
C₃⋊S₃.₂D₁₂	1^st non-split extension by C₃⋊S₃ of D₁₂ acting via D₁₂/C₆=C₂²	24	4	C3:S3.2D12	432,579
S₃²⋊Dic₃	The semidirect product of S₃² and Dic₃ acting via Dic₃/C₆=C₂	24	4	S3^2:Dic3	432,580
C₃³⋊C₄⋊C₄	2^nd semidirect product of C₃³⋊C₄ and C₄ acting via C₄/C₂=C₂	48	4	C3^3:C4:C4	432,581
C₃³⋊D₈	2^nd semidirect product of C₃³ and D₈ acting via D₈/C₂=D₄	24	4	C3^3:D8	432,582
C₃³⋊₆SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	4	C3^3:6SD16	432,583
C₃³⋊₇SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	4	C3^3:7SD16	432,584
C₃³⋊Q₁₆	2^nd semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₂=D₄	48	4	C3^3:Q16	432,585
C₃×C₆.₅S₄	Direct product of C₃ and C₆.₅S₄	48	4	C3xC6.5S4	432,616
C₃×C₆.₆S₄	Direct product of C₃ and C₆.₆S₄	48	4	C3xC6.6S4	432,617
C₃×Dic₃.A₄	Direct product of C₃ and Dic₃.A₄	48	4	C3xDic3.A4	432,622
C₃×S₃×SL₂(𝔽₃)	Direct product of C₃, S₃ and SL₂(𝔽₃)	48	4	C3xS3xSL(2,3)	432,623
C₃×C₃⋊S₃⋊₃C₈	Direct product of C₃ and C₃⋊S₃⋊₃C₈	48	4	C3xC3:S3:3C8	432,628
C₃×C₃²⋊M₄(2)	Direct product of C₃ and C₃²⋊M₄(2)	48	4	C3xC3^2:M4(2)	432,629
C₁₂×C₃²⋊C₄	Direct product of C₁₂ and C₃²⋊C₄	48	4	C12xC3^2:C4	432,630
C₃×C₄⋊(C₃²⋊C₄)	Direct product of C₃ and C₄⋊(C₃²⋊C₄)	48	4	C3xC4:(C3^2:C4)	432,631
C₃×C₆².C₄	Direct product of C₃ and C₆².C₄	24	4	C3xC6^2.C4	432,633
C₃×C₆²⋊C₄	Direct product of C₃ and C₆²⋊C₄	24	4	C3xC6^2:C4	432,634
C₃³⋊₇(C₂×C₈)	2^nd semidirect product of C₃³ and C₂×C₈ acting via C₂×C₈/C₄=C₄	48	4	C3^3:7(C2xC8)	432,635
C₃³⋊₄M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₄=C₄	48	4	C3^3:4M4(2)	432,636
C₄×C₃³⋊C₄	Direct product of C₄ and C₃³⋊C₄	48	4	C4xC3^3:C4	432,637
C₃³⋊₉(C₄⋊C₄)	2^nd semidirect product of C₃³ and C₄⋊C₄ acting via C₄⋊C₄/C₄=C₄	48	4	C3^3:9(C4:C4)	432,638
C₃³⋊₁₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂²=C₄	24	4	C3^3:12M4(2)	432,640
C₆²⋊₁₁Dic₃	1^st semidirect product of C₆² and Dic₃ acting via Dic₃/C₃=C₄	24	4	C6^2:11Dic3	432,641
C₃×S₃×Dic₆	Direct product of C₃, S₃ and Dic₆	48	4	C3xS3xDic6	432,642
C₃×D₁₂⋊₅S₃	Direct product of C₃ and D₁₂⋊₅S₃	48	4	C3xD12:5S3	432,643
C₃×D₁₂⋊S₃	Direct product of C₃ and D₁₂⋊S₃	48	4	C3xD12:S3	432,644
C₃×Dic₃.D₆	Direct product of C₃ and Dic₃.D₆	48	4	C3xDic3.D6	432,645
C₃×D₆.D₆	Direct product of C₃ and D₆.D₆	48	4	C3xD6.D6	432,646
C₃×D₆.₆D₆	Direct product of C₃ and D₆.₆D₆	48	4	C3xD6.6D6	432,647
S₃²×C₁₂	Direct product of C₁₂, S₃ and S₃	48	4	S3^2xC12	432,648
C₃×S₃×D₁₂	Direct product of C₃, S₃ and D₁₂	48	4	C3xS3xD12	432,649
C₃×D₆⋊D₆	Direct product of C₃ and D₆⋊D₆	48	4	C3xD6:D6	432,650
C₃×D₆.₃D₆	Direct product of C₃ and D₆.₃D₆	24	4	C3xD6.3D6	432,652
C₃×D₆.₄D₆	Direct product of C₃ and D₆.₄D₆	24	4	C3xD6.4D6	432,653
C₃×S₃×C₃⋊D₄	Direct product of C₃, S₃ and C₃⋊D₄	24	4	C3xS3xC3:D4	432,658
C₃×Dic₃⋊D₆	Direct product of C₃ and Dic₃⋊D₆	24	4	C3xDic3:D6	432,659
C₃⋊S₃⋊₄Dic₆	The semidirect product of C₃⋊S₃ and Dic₆ acting via Dic₆/C₁₂=C₂	48	4	C3:S3:4Dic6	432,687
C₁₂⋊S₃⋊₁₂S₃	6^th semidirect product of C₁₂⋊S₃ and S₃ acting via S₃/C₃=C₂	48	4	C12:S3:12S3	432,688
C₁₂.₉₅S₃²	15^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	4	C12.95S3^2	432,689
C₄×C₃²⋊₄D₆	Direct product of C₄ and C₃²⋊₄D₆	48	4	C4xC3^2:4D6	432,690
C₁₂⋊₃S₃²	3^rd semidirect product of C₁₂ and S₃² acting via S₃²/C₃²=C₂²	48	4	C12:3S3^2	432,691
C₆².₉₆D₆	44^th non-split extension by C₆² of D₆ acting via D₆/C₃=C₂²	24	4	C6^2.96D6	432,693
C₆²⋊₂₄D₆	5^th semidirect product of C₆² and D₆ acting via D₆/C₃=C₂²	24	4	C6^2:24D6	432,696
C₆×S₃≀C₂	Direct product of C₆ and S₃≀C₂	24	4	C6xS3wrC2	432,754
C₂×C₃³⋊D₄	Direct product of C₂ and C₃³⋊D₄	24	4	C2xC3^3:D4	432,755

Groups of order 440

		d	ρ	Label	ID
C₁₁×C₅⋊C₈	Direct product of C₁₁ and C₅⋊C₈	440	4	C11xC5:C8	440,15
C₅₅⋊C₈	1^st semidirect product of C₅₅ and C₈ acting via C₈/C₂=C₄	440	4	C55:C8	440,16
F₅×C₂₂	Direct product of C₂₂ and F₅	110	4	F5xC22	440,45
C₂×C₁₁⋊F₅	Direct product of C₂ and C₁₁⋊F₅	110	4	C2xC11:F5	440,46

Groups of order 444

		d	ρ	Label	ID
C₃×C₃₇⋊C₄	Direct product of C₃ and C₃₇⋊C₄	111	4	C3xC37:C4	444,9
C₃₇⋊Dic₃	The semidirect product of C₃₇ and Dic₃ acting via Dic₃/C₃=C₄	111	4	C37:Dic3	444,10

Groups of order 448

		d	ρ	Label	ID
C₂₈.₁₅C₄²	8^th non-split extension by C₂₈ of C₄² acting via C₄²/C₂×C₄=C₂	112	4	C28.15C4^2	448,23
C₅₆.Q₈	5^th non-split extension by C₅₆ of Q₈ acting via Q₈/C₂=C₂²	112	4	C56.Q8	448,44
D₅₆⋊₈C₄	8^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:8C4	448,45
C₈.₇Dic₁₄	4^th non-split extension by C₈ of Dic₁₄ acting via Dic₁₄/Dic₇=C₂	224	4	C8.7Dic14	448,50
C₈.Dic₁₄	2^nd non-split extension by C₈ of Dic₁₄ acting via Dic₁₄/C₁₄=C₂²	112	4	C8.Dic14	448,51
Dic₂₈.C₄	3^rd non-split extension by Dic₂₈ of C₄ acting via C₄/C₂=C₂	224	4	Dic28.C4	448,54
C₅₆.₉Q₈	9^th non-split extension by C₅₆ of Q₈ acting via Q₈/C₂=C₂²	112	4	C56.9Q8	448,68
C₁₁₂⋊C₄	2^nd semidirect product of C₁₁₂ and C₄ acting faithfully	112	4	C112:C4	448,69
C₁₆⋊Dic₇	1^st semidirect product of C₁₆ and Dic₇ acting via Dic₇/C₇=C₄	112	4	C16:Dic7	448,70
M₅(2)⋊D₇	3^rd semidirect product of M₅(2) and D₇ acting via D₇/C₇=C₂	112	4	M5(2):D7	448,71
Dic₁₄.C₈	2^nd non-split extension by Dic₁₄ of C₈ acting via C₈/C₄=C₂	224	4	Dic14.C8	448,72
D₅₆⋊₂C₄	2^nd semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:2C4	448,75
C₄²⋊Dic₇	1^st semidirect product of C₄² and Dic₇ acting via Dic₇/C₇=C₄	112	4	C4^2:Dic7	448,88
(C₂×C₂₈).Q₈	8^th non-split extension by C₂×C₂₈ of Q₈ acting via Q₈/C₂=C₂²	112	4	(C2xC28).Q8	448,90
C₂⁴⋊Dic₇	1^st semidirect product of C₂⁴ and Dic₇ acting via Dic₇/C₇=C₄	56	4	C2^4:Dic7	448,93
(C₂²×C₂₈)⋊C₄	2^nd semidirect product of C₂²×C₂₈ and C₄ acting faithfully	112	4	(C2^2xC28):C4	448,96
C₄²⋊₂Dic₇	2^nd semidirect product of C₄² and Dic₇ acting via Dic₇/C₇=C₄	112	4	C4^2:2Dic7	448,98
C₄².Dic₇	2^nd non-split extension by C₄² of Dic₇ acting via Dic₇/C₇=C₄	112	4	C4^2.Dic7	448,99
C₄²⋊₃Dic₇	3^rd semidirect product of C₄² and Dic₇ acting via Dic₇/C₇=C₄	56	4	C4^2:3Dic7	448,102
C₄².₃Dic₇	3^rd non-split extension by C₄² of Dic₇ acting via Dic₇/C₇=C₄	112	4	C4^2.3Dic7	448,105
C₅₆.D₄	48^th non-split extension by C₅₆ of D₄ acting via D₄/C₂=C₂²	112	4	C56.D4	448,110
(C₂×C₅₆)⋊C₄	1^st semidirect product of C₂×C₅₆ and C₄ acting faithfully	112	4	(C2xC56):C4	448,113
C₂³.₉D₂₈	2^nd non-split extension by C₂³ of D₂₈ acting via D₂₈/C₁₄=C₂²	112	4	C2^3.9D28	448,114
M₄(2)⋊₄Dic₇	4^th semidirect product of M₄(2) and Dic₇ acting via Dic₇/C₁₄=C₂	112	4	M4(2):4Dic7	448,116
C₂₈.₂₁C₄²	14^th non-split extension by C₂₈ of C₄² acting via C₄²/C₂×C₄=C₂	112	4	C28.21C4^2	448,117
C₅₆.₉₂D₄	15^th non-split extension by C₅₆ of D₄ acting via D₄/C₂²=C₂	224	4	C56.92D4	448,118
D₈.Dic₇	2^nd non-split extension by D₈ of Dic₇ acting via Dic₇/C₁₄=C₂	112	4	D8.Dic7	448,120
Q₁₆.Dic₇	2^nd non-split extension by Q₁₆ of Dic₇ acting via Dic₇/C₁₄=C₂	224	4	Q16.Dic7	448,122
D₈⋊₂Dic₇	2^nd semidirect product of D₈ and Dic₇ acting via Dic₇/C₁₄=C₂	112	4	D8:2Dic7	448,123
C₂₈.₅₈D₈	12^nd non-split extension by C₂₈ of D₈ acting via D₈/D₄=C₂	224	4	C28.58D8	448,124
C₇×C₄.₉C₄²	Direct product of C₇ and C₄.₉C₄²	112	4	C7xC4.9C4^2	448,141
C₇×C₄.₁₀C₄²	Direct product of C₇ and C₄.₁₀C₄²	112	4	C7xC4.10C4^2	448,142
C₇×M₄(2)⋊₄C₄	Direct product of C₇ and M₄(2)⋊₄C₄	112	4	C7xM4(2):4C4	448,148
C₇×C₁₆⋊C₄	Direct product of C₇ and C₁₆⋊C₄	112	4	C7xC16:C4	448,151
C₇×C₂³.C₈	Direct product of C₇ and C₂³.C₈	112	4	C7xC2^3.C8	448,153
C₇×C₂≀C₄	Direct product of C₇ and C₂≀C₄	56	4	C7xC2wrC4	448,155
C₇×C₂³.D₄	Direct product of C₇ and C₂³.D₄	112	4	C7xC2^3.D4	448,156
C₇×C₄²⋊C₄	Direct product of C₇ and C₄²⋊C₄	56	4	C7xC4^2:C4	448,157
C₇×C₄²⋊₃C₄	Direct product of C₇ and C₄²⋊₃C₄	112	4	C7xC4^2:3C4	448,158
C₇×C₄².C₄	Direct product of C₇ and C₄².C₄	112	4	C7xC4^2.C4	448,159
C₇×C₄².₃C₄	Direct product of C₇ and C₄².₃C₄	112	4	C7xC4^2.3C4	448,160
C₇×D₈⋊₂C₄	Direct product of C₇ and D₈⋊₂C₄	112	4	C7xD8:2C4	448,164
C₇×M₅(2)⋊C₂	Direct product of C₇ and M₅(2)⋊C₂	112	4	C7xM5(2):C2	448,165
C₇×C₈.₁₇D₄	Direct product of C₇ and C₈.₁₇D₄	224	4	C7xC8.17D4	448,166
C₇×C₈.Q₈	Direct product of C₇ and C₈.Q₈	112	4	C7xC8.Q8	448,169
D₅₆⋊₄C₄	4^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:4C4	448,251
D₇×C₄≀C₂	Direct product of D₇ and C₄≀C₂	56	4	D7xC4wrC2	448,354
C₄²⋊D₁₄	1^st semidirect product of C₄² and D₁₄ acting via D₁₄/C₇=C₂²	112	4	C4^2:D14	448,355
M₄(2).₂₂D₁₄	5^th non-split extension by M₄(2) of D₁₄ acting via D₁₄/D₇=C₂	112	4	M4(2).22D14	448,357
C₄².₁₉₆D₁₄	16^th non-split extension by C₄² of D₁₄ acting via D₁₄/D₇=C₂	112	4	C4^2.196D14	448,358
M₄(2)⋊D₁₄	4^th semidirect product of M₄(2) and D₁₄ acting via D₁₄/C₇=C₂²	112	4	M4(2):D14	448,359
D₄.₁₀D₂₈	5^th non-split extension by D₄ of D₂₈ acting via D₂₈/D₁₄=C₂	112	4	D4.10D28	448,361
D₇×C₈.C₄	Direct product of D₇ and C₈.C₄	112	4	D7xC8.C4	448,426
M₄(2).₂₅D₁₄	8^th non-split extension by M₄(2) of D₁₄ acting via D₁₄/D₇=C₂	112	4	M4(2).25D14	448,427
D₅₆⋊₁₀C₄	10^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:10C4	448,428
D₅₆⋊₇C₄	7^th semidirect product of D₅₆ and C₄ acting via C₄/C₂=C₂	112	4	D56:7C4	448,429
C₈.₂₄D₂₈	10^th non-split extension by C₈ of D₂₈ acting via D₂₈/D₁₄=C₂	112	4	C8.24D28	448,432
D₇×M₅(2)	Direct product of D₇ and M₅(2)	112	4	D7xM5(2)	448,440
C₁₆.₁₂D₁₄	9^th non-split extension by C₁₆ of D₁₄ acting via D₁₄/D₇=C₂	224	4	C16.12D14	448,441
D₈⋊D₁₄	2^nd semidirect product of D₈ and D₁₄ acting via D₁₄/D₇=C₂	112	4	D8:D14	448,445
D₇×SD₃₂	Direct product of D₇ and SD₃₂	112	4	D7xSD32	448,447
SD₃₂⋊₃D₇	The semidirect product of SD₃₂ and D₇ acting through Inn(SD₃₂)	224	4	SD32:3D7	448,450
Q₃₂⋊D₇	2^nd semidirect product of Q₃₂ and D₇ acting via D₇/C₇=C₂	224	4	Q32:D7	448,452
C₄²⋊₄D₁₄	4^th semidirect product of C₄² and D₁₄ acting via D₁₄/C₇=C₂²	112	4	C4^2:4D14	448,539
(C₂×D₂₈)⋊₁₃C₄	9^th semidirect product of C₂×D₂₈ and C₄ acting via C₄/C₂=C₂	112	4	(C2xD28):13C4	448,540
C₂⁴⋊D₁₄	1^st semidirect product of C₂⁴ and D₁₄ acting via D₁₄/C₇=C₂²	56	4	C2^4:D14	448,566
C₂²⋊C₄⋊D₁₄	4^th semidirect product of C₂²⋊C₄ and D₁₄ acting via D₁₄/C₇=C₂²	112	4	C2^2:C4:D14	448,587
C₄²⋊₅D₁₄	5^th semidirect product of C₄² and D₁₄ acting via D₁₄/C₇=C₂²	112	4	C4^2:5D14	448,595
D₂₈.₁₄D₄	14^th non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	4	D28.14D4	448,596
D₂₈⋊₅D₄	5^th semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	56	4	D28:5D4	448,611
D₂₈.₁₅D₄	15^th non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	4	D28.15D4	448,629
C₂³.Dic₁₄	6^th non-split extension by C₂³ of Dic₁₄ acting via Dic₁₄/C₁₄=C₂²	112	4	C2^3.Dic14	448,658
M₄(2).Dic₇	1^st non-split extension by M₄(2) of Dic₇ acting via Dic₇/C₁₄=C₂	112	4	M4(2).Dic7	448,659
M₄(2).₃₁D₁₄	4^th non-split extension by M₄(2) of D₁₄ acting via D₁₄/C₁₄=C₂	112	4	M4(2).31D14	448,666
C₂³.₂₀D₂₈	13^rd non-split extension by C₂³ of D₂₈ acting via D₂₈/C₁₄=C₂²	112	4	C2^3.20D28	448,673
C₅₆.₇₀C₂³	16^th non-split extension by C₅₆ of C₂³ acting via C₂³/C₂²=C₂	224	4	C56.70C2^3	448,674
D₄.₃D₂₈	3^rd non-split extension by D₄ of D₂₈ acting via D₂₈/C₂₈=C₂	112	4	D4.3D28	448,675
C₅₆.₉₃D₄	16^th non-split extension by C₅₆ of D₄ acting via D₄/C₂²=C₂	112	4	C56.93D4	448,678
C₅₆.₅₀D₄	50^th non-split extension by C₅₆ of D₄ acting via D₄/C₂=C₂²	112	4	C56.50D4	448,679
D₈.D₁₄	1^st non-split extension by D₈ of D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D8.D14	448,681
C₅₆.₂₃D₄	23^rd non-split extension by C₅₆ of D₄ acting via D₄/C₂=C₂²	112	4	C56.23D4	448,694
C₅₆.₄₄D₄	44^th non-split extension by C₅₆ of D₄ acting via D₄/C₂=C₂²	112	4	C56.44D4	448,711
Q₁₆.D₁₄	1^st non-split extension by Q₁₆ of D₁₄ acting via D₁₄/C₁₄=C₂	224	4	Q16.D14	448,713
C₅₆.₂₉D₄	29^th non-split extension by C₅₆ of D₄ acting via D₄/C₂=C₂²	224	4	C56.29D4	448,726
C₅₆.₃₀C₂³	23^rd non-split extension by C₅₆ of C₂³ acting via C₂³/C₂=C₂²	224	4	C56.30C2^3	448,728
D₈⋊₅Dic₇	The semidirect product of D₈ and Dic₇ acting through Inn(D₈)	112	4	D8:5Dic7	448,730
D₈⋊₄Dic₇	4^th semidirect product of D₈ and Dic₇ acting via Dic₇/C₁₄=C₂	112	4	D8:4Dic7	448,731
(D₄×C₁₄)⋊₉C₄	5^th semidirect product of D₄×C₁₄ and C₄ acting via C₄/C₂=C₂	112	4	(D4xC14):9C4	448,770
(D₄×C₁₄).₁₆C₄	10^th non-split extension by D₄×C₁₄ of C₄ acting via C₄/C₂=C₂	112	4	(D4xC14).16C4	448,771
(D₄×C₁₄)⋊₁₀C₄	6^th semidirect product of D₄×C₁₄ and C₄ acting via C₄/C₂=C₂	112	4	(D4xC14):10C4	448,774
C₇×C₂³.C₂³	Direct product of C₇ and C₂³.C₂³	112	4	C7xC2^3.C2^3	448,818
C₇×M₄(2).₈C₂²	Direct product of C₇ and M₄(2).₈C₂²	112	4	C7xM4(2).8C2^2	448,821
C₇×C₄²⋊C₂²	Direct product of C₇ and C₄²⋊C₂²	112	4	C7xC4^2:C2^2	448,829
C₇×M₄(2).C₄	Direct product of C₇ and M₄(2).C₄	112	4	C7xM4(2).C4	448,838
C₇×C₈.₂₆D₄	Direct product of C₇ and C₈.₂₆D₄	112	4	C7xC8.26D4	448,852
C₇×D₄⋊₄D₄	Direct product of C₇ and D₄⋊₄D₄	56	4	C7xD4:4D4	448,861
C₇×D₄.₈D₄	Direct product of C₇ and D₄.₈D₄	112	4	C7xD4.8D4	448,862
C₇×D₄.₉D₄	Direct product of C₇ and D₄.₉D₄	112	4	C7xD4.9D4	448,863
C₇×D₄.₁₀D₄	Direct product of C₇ and D₄.₁₀D₄	112	4	C7xD4.10D4	448,864
C₇×C₂≀C₂²	Direct product of C₇ and C₂≀C₂²	56	4	C7xC2wrC2^2	448,865
C₇×C₂³.₇D₄	Direct product of C₇ and C₂³.₇D₄	112	4	C7xC2^3.7D4	448,866
C₇×D₄.₃D₄	Direct product of C₇ and D₄.₃D₄	112	4	C7xD4.3D4	448,879
C₇×D₄.₄D₄	Direct product of C₇ and D₄.₄D₄	112	4	C7xD4.4D4	448,880
C₇×D₄.₅D₄	Direct product of C₇ and D₄.₅D₄	224	4	C7xD4.5D4	448,881
C₇×C₁₆⋊C₂²	Direct product of C₇ and C₁₆⋊C₂²	112	4	C7xC16:C2^2	448,917
C₇×Q₃₂⋊C₂	Direct product of C₇ and Q₃₂⋊C₂	224	4	C7xQ32:C2	448,918
C₂₈.₇₀C₂⁴	17^th non-split extension by C₂₈ of C₂⁴ acting via C₂⁴/C₂³=C₂	112	4	C28.70C2^4	448,1198
C₅₆.₉C₂³	2^nd non-split extension by C₅₆ of C₂³ acting via C₂³/C₂=C₂²	112	4	C56.9C2^3	448,1201
D₇×C₈○D₄	Direct product of D₇ and C₈○D₄	112	4	D7xC8oD4	448,1202
C₅₆.₄₉C₂³	42^nd non-split extension by C₅₆ of C₂³ acting via C₂³/C₂=C₂²	112	4	C56.49C2^3	448,1203
D₄.₁₁D₂₈	1^st non-split extension by D₄ of D₂₈ acting through Inn(D₄)	112	4	D4.11D28	448,1204
D₈⋊₁₃D₁₄	2^nd semidirect product of D₈ and D₁₄ acting through Inn(D₈)	112	4	D8:13D14	448,1210
D₂₈.₂₉D₄	12^nd non-split extension by D₂₈ of D₄ acting via D₄/C₄=C₂	112	4	D28.29D4	448,1215
D₂₈.₃₀D₄	13^rd non-split extension by D₂₈ of D₄ acting via D₄/C₄=C₂	224	4	D28.30D4	448,1219
D₇×C₄○D₈	Direct product of D₇ and C₄○D₈	112	4	D7xC4oD8	448,1220
D₈⋊₁₀D₁₄	4^th semidirect product of D₈ and D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D8:10D14	448,1221
D₈⋊₁₁D₁₄	5^th semidirect product of D₈ and D₁₄ acting via D₁₄/C₁₄=C₂	112	4	D8:11D14	448,1223
C₂₈.₇₆C₂⁴	23^rd non-split extension by C₂₈ of C₂⁴ acting via C₂⁴/C₂³=C₂	112	4	C28.76C2^4	448,1272
C₂₈.C₂⁴	35^th non-split extension by C₂₈ of C₂⁴ acting via C₂⁴/C₂²=C₂²	112	4	C28.C2^4	448,1275
C₇×Q₈○M₄(2)	Direct product of C₇ and Q₈○M₄(2)	112	4	C7xQ8oM4(2)	448,1351
C₇×D₈⋊C₂²	Direct product of C₇ and D₈⋊C₂²	112	4	C7xD8:C2^2	448,1358
C₇×D₄○D₈	Direct product of C₇ and D₄○D₈	112	4	C7xD4oD8	448,1359
C₇×D₄○SD₁₆	Direct product of C₇ and D₄○SD₁₆	112	4	C7xD4oSD16	448,1360
C₇×Q₈○D₈	Direct product of C₇ and Q₈○D₈	224	4	C7xQ8oD8	448,1361
C₁₄.C₂⁵	14^th non-split extension by C₁₄ of C₂⁵ acting via C₂⁵/C₂⁴=C₂	112	4	C14.C2^5	448,1378
C₇×C₂.C₂⁵	Direct product of C₇ and C₂.C₂⁵	112	4	C7xC2.C2^5	448,1391

Groups of order 460

		d	ρ	Label	ID
F₅×C₂₃	Direct product of C₂₃ and F₅	115	4	F5xC23	460,5
C₂₃⋊F₅	The semidirect product of C₂₃ and F₅ acting via F₅/D₅=C₂	115	4	C23:F5	460,6

Groups of order 464

		d	ρ	Label	ID
C₂₉⋊C₁₆	The semidirect product of C₂₉ and C₁₆ acting via C₁₆/C₄=C₄	464	4	C29:C16	464,3
D₂₉⋊C₈	The semidirect product of D₂₉ and C₈ acting via C₈/C₄=C₂	232	4	D29:C8	464,28
C₁₁₆.C₄	1^st non-split extension by C₁₁₆ of C₄ acting faithfully	232	4	C116.C4	464,29
C₄×C₂₉⋊C₄	Direct product of C₄ and C₂₉⋊C₄	116	4	C4xC29:C4	464,30
C₁₁₆⋊C₄	1^st semidirect product of C₁₁₆ and C₄ acting faithfully	116	4	C116:C4	464,31

Groups of order 468

		d	ρ	Label	ID
C₉×C₁₃⋊C₄	Direct product of C₉ and C₁₃⋊C₄	117	4	C9xC13:C4	468,9
C₁₃⋊Dic₉	The semidirect product of C₁₃ and Dic₉ acting via Dic₉/C₉=C₄	117	4	C13:Dic9	468,10
C₃×C₃₉⋊C₄	Direct product of C₃ and C₃₉⋊C₄	78	4	C3xC39:C4	468,37
C₁₃×C₃²⋊C₄	Direct product of C₁₃ and C₃²⋊C₄	78	4	C13xC3^2:C4	468,39
C₃²⋊Dic₁₃	The semidirect product of C₃² and Dic₁₃ acting via Dic₁₃/C₁₃=C₄	78	4	C3^2:Dic13	468,40
C₃×S₃×D₁₃	Direct product of C₃, S₃ and D₁₃	78	4	C3xS3xD13	468,42
S₃²×C₁₃	Direct product of C₁₃, S₃ and S₃	78	4	S3^2xC13	468,44
D₃₉⋊S₃	The semidirect product of D₃₉ and S₃ acting via S₃/C₃=C₂	78	4	D39:S3	468,46

Groups of order 476

		d	ρ	Label	ID
C₇×C₁₇⋊C₄	Direct product of C₇ and C₁₇⋊C₄	119	4	C7xC17:C4	476,5
C₁₇⋊Dic₇	The semidirect product of C₁₇ and Dic₇ acting via Dic₇/C₇=C₄	119	4	C17:Dic7	476,6

Groups of order 480

		d	ρ	Label	ID
C₃×C₅⋊C₃₂	Direct product of C₃ and C₅⋊C₃₂	480	4	C3xC5:C32	480,5
C₁₅⋊C₃₂	1^st semidirect product of C₁₅ and C₃₂ acting via C₃₂/C₈=C₄	480	4	C15:C32	480,6
D₅×C₃⋊C₁₆	Direct product of D₅ and C₃⋊C₁₆	240	4	D5xC3:C16	480,7
S₃×C₅⋊₂C₁₆	Direct product of S₃ and C₅⋊₂C₁₆	240	4	S3xC5:2C16	480,8
D₁₅⋊₂C₁₆	The semidirect product of D₁₅ and C₁₆ acting via C₁₆/C₈=C₂	240	4	D15:2C16	480,9
C₄₀.₅₁D₆	12^nd non-split extension by C₄₀ of D₆ acting via D₆/S₃=C₂	240	4	C40.51D6	480,10
C₄₀.₅₂D₆	13^rd non-split extension by C₄₀ of D₆ acting via D₆/S₃=C₂	240	4	C40.52D6	480,11
D₃₀.₅C₈	3^rd non-split extension by D₃₀ of C₈ acting via C₈/C₄=C₂	240	4	D30.5C8	480,12
C₁₅⋊D₁₆	1^st semidirect product of C₁₅ and D₁₆ acting via D₁₆/C₈=C₂²	240	4	C15:D16	480,13
C₄₀.D₆	6^th non-split extension by C₄₀ of D₆ acting via D₆/C₃=C₂²	240	4	C40.D6	480,16
C₁₅⋊SD₃₂	2^nd semidirect product of C₁₅ and SD₃₂ acting via SD₃₂/C₈=C₂²	240	4	C15:SD32	480,17
C₁₅⋊Q₃₂	1^st semidirect product of C₁₅ and Q₃₂ acting via Q₃₂/C₈=C₂²	480	4	C15:Q32	480,22
C₆₀.₂₈D₄	28^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.28D4	480,34
C₂₀.₅D₁₂	5^th non-split extension by C₂₀ of D₁₂ acting via D₁₂/C₆=C₂²	120	4	C20.5D12	480,35
C₁₂.₆D₂₀	6^th non-split extension by C₁₂ of D₂₀ acting via D₂₀/C₁₀=C₂²	240	4	C12.6D20	480,37
C₆₀.₅₄D₄	54^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	240	4	C60.54D4	480,38
C₆₀.₉₆D₄	96^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.96D4	480,52
C₆₀.₉₇D₄	97^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.97D4	480,53
C₆₀.₉₈D₄	98^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.98D4	480,54
C₆₀.₉₉D₄	99^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.99D4	480,55
D₆₀⋊₁₃C₄	7^th semidirect product of D₆₀ and C₄ acting via C₄/C₂=C₂	120	4	D60:13C4	480,56
D₆₀⋊₁₆C₄	10^th semidirect product of D₆₀ and C₄ acting via C₄/C₂=C₂	120	4	D60:16C4	480,57
C₆₀.₁₀₅D₄	105^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	240	4	C60.105D4	480,67
C₆₀.D₄	106^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	240	4	C60.D4	480,68
C₁₂.₅₉D₂₀	13^rd non-split extension by C₁₂ of D₂₀ acting via D₂₀/D₁₀=C₂	240	4	C12.59D20	480,69
(C₂×C₆).D₂₀	2^nd non-split extension by C₂×C₆ of D₂₀ acting via D₂₀/C₁₀=C₂²	120	4	(C2xC6).D20	480,71
C₁₅⋊₈(C₂³⋊C₄)	2^nd semidirect product of C₁₅ and C₂³⋊C₄ acting via C₂³⋊C₄/C₂³=C₂²	120	4	C15:8(C2^3:C4)	480,72
C₁₅⋊₉(C₂³⋊C₄)	3^rd semidirect product of C₁₅ and C₂³⋊C₄ acting via C₂³⋊C₄/C₂³=C₂²	120	4	C15:9(C2^3:C4)	480,73
C₃×C₂³.₁D₁₀	Direct product of C₃ and C₂³.₁D₁₀	120	4	C3xC2^3.1D10	480,84
C₃×C₂₀.₅₃D₄	Direct product of C₃ and C₂₀.₅₃D₄	240	4	C3xC20.53D4	480,100
C₃×C₂₀.₄₆D₄	Direct product of C₃ and C₂₀.₄₆D₄	120	4	C3xC20.46D4	480,101
C₃×C₄.₁₂D₂₀	Direct product of C₃ and C₄.₁₂D₂₀	240	4	C3xC4.12D20	480,102
C₃×D₂₀⋊₇C₄	Direct product of C₃ and D₂₀⋊₇C₄	120	4	C3xD20:7C4	480,103
C₃×C₅⋊D₁₆	Direct product of C₃ and C₅⋊D₁₆	240	4	C3xC5:D16	480,104
C₃×D₈.D₅	Direct product of C₃ and D₈.D₅	240	4	C3xD8.D5	480,105
C₃×C₅⋊SD₃₂	Direct product of C₃ and C₅⋊SD₃₂	240	4	C3xC5:SD32	480,106
C₃×C₅⋊Q₃₂	Direct product of C₃ and C₅⋊Q₃₂	480	4	C3xC5:Q32	480,107
C₃×C₂₀.D₄	Direct product of C₃ and C₂₀.D₄	120	4	C3xC20.D4	480,111
C₃×C₂³⋊Dic₅	Direct product of C₃ and C₂³⋊Dic₅	120	4	C3xC2^3:Dic5	480,112
C₃×C₂₀.₁₀D₄	Direct product of C₃ and C₂₀.₁₀D₄	240	4	C3xC20.10D4	480,114
C₃×D₄⋊₂Dic₅	Direct product of C₃ and D₄⋊₂Dic₅	120	4	C3xD4:2Dic5	480,115
C₅×C₂³.₆D₆	Direct product of C₅ and C₂³.₆D₆	120	4	C5xC2^3.6D6	480,125
C₅×C₁₂.₅₃D₄	Direct product of C₅ and C₁₂.₅₃D₄	240	4	C5xC12.53D4	480,141
C₅×C₁₂.₄₆D₄	Direct product of C₅ and C₁₂.₄₆D₄	120	4	C5xC12.46D4	480,142
C₅×C₁₂.₄₇D₄	Direct product of C₅ and C₁₂.₄₇D₄	240	4	C5xC12.47D4	480,143
C₅×D₁₂⋊C₄	Direct product of C₅ and D₁₂⋊C₄	120	4	C5xD12:C4	480,144
C₅×C₃⋊D₁₆	Direct product of C₅ and C₃⋊D₁₆	240	4	C5xC3:D16	480,145
C₅×D₈.S₃	Direct product of C₅ and D₈.S₃	240	4	C5xD8.S3	480,146
C₅×C₈.₆D₆	Direct product of C₅ and C₈.₆D₆	240	4	C5xC8.6D6	480,147
C₅×C₃⋊Q₃₂	Direct product of C₅ and C₃⋊Q₃₂	480	4	C5xC3:Q32	480,148
C₅×C₁₂.D₄	Direct product of C₅ and C₁₂.D₄	120	4	C5xC12.D4	480,152
C₅×C₂³.₇D₆	Direct product of C₅ and C₂³.₇D₆	120	4	C5xC2^3.7D6	480,153
C₅×C₁₂.₁₀D₄	Direct product of C₅ and C₁₂.₁₀D₄	240	4	C5xC12.10D4	480,155
C₅×Q₈⋊₃Dic₃	Direct product of C₅ and Q₈⋊₃Dic₃	120	4	C5xQ8:3Dic3	480,156
C₂³.₆D₃₀	1^st non-split extension by C₂³ of D₃₀ acting via D₃₀/C₁₅=C₂²	120	4	C2^3.6D30	480,166
C₆₀.₂₁₀D₄	10^th non-split extension by C₆₀ of D₄ acting via D₄/C₂²=C₂	240	4	C60.210D4	480,182
D₆₀⋊₁₀C₄	4^th semidirect product of D₆₀ and C₄ acting via C₄/C₂=C₂	120	4	D60:10C4	480,185
C₆₀.₈D₄	8^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.8D4	480,193
C₂³.₇D₃₀	2^nd non-split extension by C₂³ of D₃₀ acting via D₃₀/C₁₅=C₂²	120	4	C2^3.7D30	480,194
C₆₀.₁₀D₄	10^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	240	4	C60.10D4	480,196
Q₈⋊₃Dic₁₅	2^nd semidirect product of Q₈ and Dic₁₅ acting via Dic₁₅/C₃₀=C₂	120	4	Q8:3Dic15	480,197
C₁₅×C₂³⋊C₄	Direct product of C₁₅ and C₂³⋊C₄	120	4	C15xC2^3:C4	480,202
C₁₅×C₄.D₄	Direct product of C₁₅ and C₄.D₄	120	4	C15xC4.D4	480,203
C₁₅×C₄.₁₀D₄	Direct product of C₁₅ and C₄.₁₀D₄	240	4	C15xC4.10D4	480,204
A₅⋊C₈	The semidirect product of A₅ and C₈ acting via C₈/C₄=C₂	40	4	A5:C8	480,217
GL₂(𝔽₅)	General linear group on 𝔽₅²; = SL₂(𝔽₅)⋊₁ C₄ = Aut(C₅²)	24	4	GL(2,5)	480,218
C₅⋊₂U₂(𝔽₃)	The semidirect product of C₅ and U₂(𝔽₃) acting via U₂(𝔽₃)/C₄.A₄=C₂	120	4	C5:2U(2,3)	480,261
SL₂(𝔽₃).Dic₅	The non-split extension by SL₂(𝔽₃) of Dic₅ acting through Inn(SL₂(𝔽₃))	160	4	SL(2,3).Dic5	480,267
C₃×D₅⋊C₁₆	Direct product of C₃ and D₅⋊C₁₆	240	4	C3xD5:C16	480,269
C₃×C₈.F₅	Direct product of C₃ and C₈.F₅	240	4	C3xC8.F5	480,270
F₅×C₂₄	Direct product of C₂₄ and F₅	120	4	F5xC24	480,271
C₃×C₈⋊F₅	Direct product of C₃ and C₈⋊F₅	120	4	C3xC8:F5	480,272
C₃×C₄₀⋊C₄	Direct product of C₃ and C₄₀⋊C₄	120	4	C3xC40:C4	480,273
C₃×D₅.D₈	Direct product of C₃ and D₅.D₈	120	4	C3xD5.D8	480,274
C₃×C₄₀.C₄	Direct product of C₃ and C₄₀.C₄	240	4	C3xC40.C4	480,275
C₃×D₁₀.Q₈	Direct product of C₃ and D₁₀.Q₈	240	4	C3xD10.Q8	480,276
C₃×C₂₀.C₈	Direct product of C₃ and C₂₀.C₈	240	4	C3xC20.C8	480,278
C₃×D₁₀.D₄	Direct product of C₃ and D₁₀.D₄	120	4	C3xD10.D4	480,279
C₃×Dic₅.D₄	Direct product of C₃ and Dic₅.D₄	240	4	C3xDic5.D4	480,285
C₃×C₂³⋊F₅	Direct product of C₃ and C₂³⋊F₅	120	4	C3xC2^3:F5	480,291
C₃×C₂³.F₅	Direct product of C₃ and C₂³.F₅	120	4	C3xC2^3.F5	480,293
C₂₄.F₅	5^th non-split extension by C₂₄ of F₅ acting via F₅/D₅=C₂	240	4	C24.F5	480,294
C₁₂₀.C₄	6^th non-split extension by C₁₂₀ of C₄ acting faithfully	240	4	C120.C4	480,295
C₈×C₃⋊F₅	Direct product of C₈ and C₃⋊F₅	120	4	C8xC3:F5	480,296
C₂₄⋊F₅	5^th semidirect product of C₂₄ and F₅ acting via F₅/D₅=C₂	120	4	C24:F5	480,297
C₁₂₀⋊C₄	2^nd semidirect product of C₁₂₀ and C₄ acting faithfully	120	4	C120:C4	480,298
D₅.D₂₄	The non-split extension by D₅ of D₂₄ acting via D₂₄/C₂₄=C₂	120	4	D5.D24	480,299
C₄₀.Dic₃	2^nd non-split extension by C₄₀ of Dic₃ acting via Dic₃/C₃=C₄	240	4	C40.Dic3	480,300
C₂₄.₁F₅	1^st non-split extension by C₂₄ of F₅ acting via F₅/D₅=C₂	240	4	C24.1F5	480,301
C₆₀.C₈	1^st non-split extension by C₆₀ of C₈ acting via C₈/C₂=C₄	240	4	C60.C8	480,303
(C₂×C₆₀)⋊C₄	2^nd semidirect product of C₂×C₆₀ and C₄ acting faithfully	120	4	(C2xC60):C4	480,304
(C₂×C₆₀).C₄	2^nd non-split extension by C₂×C₆₀ of C₄ acting faithfully	240	4	(C2xC60).C4	480,310
C₃⋊(C₂³⋊F₅)	The semidirect product of C₃ and C₂³⋊F₅ acting via C₂³⋊F₅/C₂×C₅⋊D₄=C₂	120	4	C3:(C2^3:F5)	480,316
C₅⋊(C₁₂.D₄)	The semidirect product of C₅ and C₁₂.D₄ acting via C₁₂.D₄/C₂²×C₆=C₄	120	4	C5:(C12.D4)	480,318
S₃×C₈×D₅	Direct product of C₈, S₃ and D₅	120	4	S3xC8xD5	480,319
D₅×C₈⋊S₃	Direct product of D₅ and C₈⋊S₃	120	4	D5xC8:S3	480,320
S₃×C₈⋊D₅	Direct product of S₃ and C₈⋊D₅	120	4	S3xC8:D5	480,321
C₄₀⋊D₆	17^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:D6	480,322
D₅×C₂₄⋊C₂	Direct product of D₅ and C₂₄⋊C₂	120	4	D5xC24:C2	480,323
D₂₄⋊D₅	2^nd semidirect product of D₂₄ and D₅ acting via D₅/C₅=C₂	120	4	D24:D5	480,326
S₃×C₄₀⋊C₂	Direct product of S₃ and C₄₀⋊C₂	120	4	S3xC40:C2	480,327
D₄₀⋊S₃	2^nd semidirect product of D₄₀ and S₃ acting via S₃/C₃=C₂	120	4	D40:S3	480,330
C₄₀⋊₁₄D₆	14^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:14D6	480,331
C₄₀⋊₅D₆	5^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:5D6	480,332
D₂₄⋊₆D₅	6^th semidirect product of D₂₄ and D₅ acting via D₅/C₅=C₂	120	4	D24:6D5	480,333
C₄₀⋊₈D₆	8^th semidirect product of C₄₀ and D₆ acting via D₆/C₃=C₂²	120	4	C40:8D6	480,334
C₂₄.₂D₁₀	2^nd non-split extension by C₂₄ of D₁₀ acting via D₁₀/C₅=C₂²	240	4	C24.2D10	480,337
Dic₂₀⋊S₃	2^nd semidirect product of Dic₂₀ and S₃ acting via S₃/C₃=C₂	240	4	Dic20:S3	480,339
Dic₁₀.D₆	1^st non-split extension by Dic₁₀ of D₆ acting via D₆/C₃=C₂²	240	4	Dic10.D6	480,340
C₄₀.₅₄D₆	15^th non-split extension by C₄₀ of D₆ acting via D₆/S₃=C₂	240	4	C40.54D6	480,341
C₄₀.₃₄D₆	34^th non-split extension by C₄₀ of D₆ acting via D₆/C₃=C₂²	240	4	C40.34D6	480,342
C₄₀.₅₅D₆	16^th non-split extension by C₄₀ of D₆ acting via D₆/S₃=C₂	240	4	C40.55D6	480,343
C₄₀.₃₅D₆	35^th non-split extension by C₄₀ of D₆ acting via D₆/C₃=C₂²	240	4	C40.35D6	480,344
C₄₀.₃₁D₆	31^st non-split extension by C₄₀ of D₆ acting via D₆/C₃=C₂²	240	4	C40.31D6	480,345
D₆.₁D₂₀	1^st non-split extension by D₆ of D₂₀ acting via D₂₀/C₂₀=C₂	240	4	D6.1D20	480,348
Dic₆.D₁₀	2^nd non-split extension by Dic₆ of D₁₀ acting via D₁₀/C₅=C₂²	240	4	Dic6.D10	480,352
D₄₀⋊₅S₃	5^th semidirect product of D₄₀ and S₃ acting via S₃/C₃=C₂	240	4	D40:5S3	480,353
D₃₀.₃D₄	3^rd non-split extension by D₃₀ of D₄ acting via D₄/C₂=C₂²	240	4	D30.3D4	480,354
D₂₄⋊₅D₅	5^th semidirect product of D₂₄ and D₅ acting via D₅/C₅=C₂	240	4	D24:5D5	480,355
D₃₀.₄D₄	4^th non-split extension by D₃₀ of D₄ acting via D₄/C₂=C₂²	240	4	D30.4D4	480,356
D₅×C₄.Dic₃	Direct product of D₅ and C₄.Dic₃	120	4	D5xC4.Dic3	480,358
D₂₀.₃Dic₃	The non-split extension by D₂₀ of Dic₃ acting through Inn(D₂₀)	240	4	D20.3Dic3	480,359
D₂₀.₂Dic₃	The non-split extension by D₂₀ of Dic₃ acting via Dic₃/C₆=C₂	240	4	D20.2Dic3	480,360
D₁₂.₂Dic₅	The non-split extension by D₁₂ of Dic₅ acting through Inn(D₁₂)	240	4	D12.2Dic5	480,362
S₃×C₄.Dic₅	Direct product of S₃ and C₄.Dic₅	120	4	S3xC4.Dic5	480,363
D₁₂.Dic₅	The non-split extension by D₁₂ of Dic₅ acting via Dic₅/C₁₀=C₂	240	4	D12.Dic5	480,364
D₆₀.₅C₄	3^rd non-split extension by D₆₀ of C₄ acting via C₄/C₂=C₂	240	4	D60.5C4	480,366
D₆₀.₄C₄	2^nd non-split extension by D₆₀ of C₄ acting via C₄/C₂=C₂	240	4	D60.4C4	480,367
D₁₅⋊₄M₄(2)	The semidirect product of D₁₅ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	120	4	D15:4M4(2)	480,368
D₂₀.₃₄D₆	5^th non-split extension by D₂₀ of D₆ acting via D₆/C₆=C₂	240	4	D20.34D6	480,373
C₆₀.₃₆D₄	36^th non-split extension by C₆₀ of D₄ acting via D₄/C₂=C₂²	120	4	C60.36D4	480,374
D₂₀⋊₂₁D₆	4^th semidirect product of D₂₀ and D₆ acting via D₆/C₆=C₂	120	4	D20:21D6	480,375
C₂₀.₆₀D₁₂	14^th non-split extension by C₂₀ of D₁₂ acting via D₁₂/D₆=C₂	240	4	C20.60D12	480,379
D₆₀⋊₃₆C₂²	17^th semidirect product of D₆₀ and C₂² acting via C₂²/C₂=C₂	120	4	D60:36C2^2	480,380
D₂₀.₃₇D₆	8^th non-split extension by D₂₀ of D₆ acting via D₆/C₆=C₂	240	4	D20.37D6	480,383
D₁₂.₃₇D₁₀	8^th non-split extension by D₁₂ of D₁₀ acting via D₁₀/C₁₀=C₂	240	4	D12.37D10	480,385
D₂₀.₃₁D₆	2^nd non-split extension by D₂₀ of D₆ acting via D₆/C₆=C₂	240	4	D20.31D6	480,387
D₆₀⋊₃₀C₂²	11^st semidirect product of D₆₀ and C₂² acting via C₂²/C₂=C₂	120	4	D60:30C2^2	480,388
C₁₂.D₂₀	17^th non-split extension by C₁₂ of D₂₀ acting via D₂₀/C₁₀=C₂²	240	4	C12.D20	480,391
C₂₀.D₁₂	18^th non-split extension by C₂₀ of D₁₂ acting via D₁₂/C₆=C₂²	240	4	C20.D12	480,397
C₃×D₅×M₄(2)	Direct product of C₃, D₅ and M₄(2)	120	4	C3xD5xM4(2)	480,699
C₃×D₂₀.₂C₄	Direct product of C₃ and D₂₀.₂C₄	240	4	C3xD20.2C4	480,700
C₃×C₈⋊D₁₀	Direct product of C₃ and C₈⋊D₁₀	120	4	C3xC8:D10	480,701
C₃×C₈.D₁₀	Direct product of C₃ and C₈.D₁₀	240	4	C3xC8.D10	480,702
C₃×D₅×D₈	Direct product of C₃, D₅ and D₈	120	4	C3xD5xD8	480,703
C₃×D₈⋊D₅	Direct product of C₃ and D₈⋊D₅	120	4	C3xD8:D5	480,704
C₃×D₈⋊₃D₅	Direct product of C₃ and D₈⋊₃D₅	240	4	C3xD8:3D5	480,705
C₃×D₅×SD₁₆	Direct product of C₃, D₅ and SD₁₆	120	4	C3xD5xSD16	480,706
C₃×D₄₀⋊C₂	Direct product of C₃ and D₄₀⋊C₂	120	4	C3xD40:C2	480,707
C₃×SD₁₆⋊D₅	Direct product of C₃ and SD₁₆⋊D₅	240	4	C3xSD16:D5	480,708
C₃×SD₁₆⋊₃D₅	Direct product of C₃ and SD₁₆⋊₃D₅	240	4	C3xSD16:3D5	480,709
C₃×D₅×Q₁₆	Direct product of C₃, D₅ and Q₁₆	240	4	C3xD5xQ16	480,710
C₃×Q₁₆⋊D₅	Direct product of C₃ and Q₁₆⋊D₅	240	4	C3xQ16:D5	480,711
C₃×Q₈.D₁₀	Direct product of C₃ and Q₈.D₁₀	240	4	C3xQ8.D10	480,712
C₃×D₄.D₁₀	Direct product of C₃ and D₄.D₁₀	120	4	C3xD4.D10	480,725
C₃×C₂₀.C₂³	Direct product of C₃ and C₂₀.C₂³	240	4	C3xC20.C2^3	480,735
C₃×D₄.Dic₅	Direct product of C₃ and D₄.Dic₅	240	4	C3xD4.Dic5	480,741
C₃×D₄⋊D₁₀	Direct product of C₃ and D₄⋊D₁₀	120	4	C3xD4:D10	480,742
C₃×D₄.₈D₁₀	Direct product of C₃ and D₄.₈D₁₀	240	4	C3xD4.8D10	480,743
C₃×D₄.₉D₁₀	Direct product of C₃ and D₄.₉D₁₀	240	4	C3xD4.9D10	480,744
C₅×S₃×M₄(2)	Direct product of C₅, S₃ and M₄(2)	120	4	C5xS3xM4(2)	480,785
C₅×D₁₂.C₄	Direct product of C₅ and D₁₂.C₄	240	4	C5xD12.C4	480,786
C₅×C₈⋊D₆	Direct product of C₅ and C₈⋊D₆	120	4	C5xC8:D6	480,787
C₅×C₈.D₆	Direct product of C₅ and C₈.D₆	240	4	C5xC8.D6	480,788
C₅×S₃×D₈	Direct product of C₅, S₃ and D₈	120	4	C5xS3xD8	480,789
C₅×D₈⋊S₃	Direct product of C₅ and D₈⋊S₃	120	4	C5xD8:S3	480,790
C₅×D₈⋊₃S₃	Direct product of C₅ and D₈⋊₃S₃	240	4	C5xD8:3S3	480,791
C₅×S₃×SD₁₆	Direct product of C₅, S₃ and SD₁₆	120	4	C5xS3xSD16	480,792
C₅×Q₈⋊₃D₆	Direct product of C₅ and Q₈⋊₃D₆	120	4	C5xQ8:3D6	480,793
C₅×D₄.D₆	Direct product of C₅ and D₄.D₆	240	4	C5xD4.D6	480,794
C₅×Q₈.₇D₆	Direct product of C₅ and Q₈.₇D₆	240	4	C5xQ8.7D6	480,795
C₅×S₃×Q₁₆	Direct product of C₅, S₃ and Q₁₆	240	4	C5xS3xQ16	480,796
C₅×Q₁₆⋊S₃	Direct product of C₅ and Q₁₆⋊S₃	240	4	C5xQ16:S3	480,797
C₅×D₂₄⋊C₂	Direct product of C₅ and D₂₄⋊C₂	240	4	C5xD24:C2	480,798
C₅×D₁₂⋊₆C₂²	Direct product of C₅ and D₁₂⋊₆C₂²	120	4	C5xD12:6C2^2	480,811
C₅×Q₈.₁₁D₆	Direct product of C₅ and Q₈.₁₁D₆	240	4	C5xQ8.11D6	480,821
C₅×D₄.Dic₃	Direct product of C₅ and D₄.Dic₃	240	4	C5xD4.Dic3	480,827
C₅×D₄⋊D₆	Direct product of C₅ and D₄⋊D₆	120	4	C5xD4:D6	480,828
C₅×Q₈.₁₃D₆	Direct product of C₅ and Q₈.₁₃D₆	240	4	C5xQ8.13D6	480,829
C₅×Q₈.₁₄D₆	Direct product of C₅ and Q₈.₁₄D₆	240	4	C5xQ8.14D6	480,830
M₄(2)×D₁₅	Direct product of M₄(2) and D₁₅	120	4	M4(2)xD15	480,871
D₆₀.₃C₄	1^st non-split extension by D₆₀ of C₄ acting via C₄/C₂=C₂	240	4	D60.3C4	480,872
D₈⋊D₁₅	2^nd semidirect product of D₈ and D₁₅ acting via D₁₅/C₁₅=C₂	120	4	D8:D15	480,876
SD₁₆×D₁₅	Direct product of SD₁₆ and D₁₅	120	4	SD16xD15	480,878
D₄.₅D₃₀	5^th non-split extension by D₄ of D₃₀ acting via D₃₀/D₁₅=C₂	240	4	D4.5D30	480,881
Q₁₆⋊D₁₅	2^nd semidirect product of Q₁₆ and D₁₅ acting via D₁₅/C₁₅=C₂	240	4	Q16:D15	480,883
D₄.D₃₀	1^st non-split extension by D₄ of D₃₀ acting via D₃₀/C₃₀=C₂	120	4	D4.D30	480,897
Q₈.₁₁D₃₀	1^st non-split extension by Q₈ of D₃₀ acting via D₃₀/C₃₀=C₂	240	4	Q8.11D30	480,907
D₄.Dic₁₅	The non-split extension by D₄ of Dic₁₅ acting through Inn(D₄)	240	4	D4.Dic15	480,913
D₄.₈D₃₀	3^rd non-split extension by D₄ of D₃₀ acting via D₃₀/C₃₀=C₂	240	4	D4.8D30	480,915
C₁₅×C₈⋊C₂²	Direct product of C₁₅ and C₈⋊C₂²	120	4	C15xC8:C2^2	480,941
C₁₅×C₈.C₂²	Direct product of C₁₅ and C₈.C₂²	240	4	C15xC8.C2^2	480,942
C₄×S₅	Direct product of C₄ and S₅; = CO₃(𝔽₅)	20	4	C4xS5	480,943
C₄.₆S₅	3^rd central extension by C₄ of S₅	48	4	C4.6S5	480,946
C₄.S₅	2^nd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	48	4	C4.S5	480,947
C₄.₃S₅	3^rd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	40	4	C4.3S5	480,948
CSU₂(𝔽₃)⋊D₅	1^st semidirect product of CSU₂(𝔽₃) and D₅ acting via D₅/C₅=C₂	160	4	CSU(2,3):D5	480,967
Dic₅.₆S₄	1^st non-split extension by Dic₅ of S₄ acting through Inn(Dic₅)	80	4	Dic5.6S4	480,968
D₁₀.₂S₄	2^nd non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	80	4	D10.2S4	480,973
D₅×GL₂(𝔽₃)	Direct product of D₅ and GL₂(𝔽₃)	40	4	D5xGL(2,3)	480,974
C₅×Q₈.D₆	Direct product of C₅ and Q₈.D₆	80	4	C5xQ8.D6	480,1018
C₅×C₄.S₄	Direct product of C₅ and C₄.S₄	160	4	C5xC4.S4	480,1019
C₅×C₄.₃S₄	Direct product of C₅ and C₄.₃S₄	80	4	C5xC4.3S4	480,1021
Q₈.D₃₀	2^nd non-split extension by Q₈ of D₃₀ acting via D₃₀/C₁₀=S₃	80	4	Q8.D30	480,1029
C₂₀.₆S₄	6^th non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	80	4	C20.6S4	480,1031
SL₂(𝔽₃).₁₁D₁₀	1^st non-split extension by SL₂(𝔽₃) of D₁₀ acting through Inn(SL₂(𝔽₃))	80	4	SL(2,3).11D10	480,1040
D₅×C₄.A₄	Direct product of D₅ and C₄.A₄	80	4	D5xC4.A4	480,1042
C₃×2_-¹⁺⁴⋊C₅	Direct product of C₃ and 2_-¹⁺⁴⋊C₅	96	4	C3xES-(2,2):C5	480,1046
C₃×D₅⋊M₄(2)	Direct product of C₃ and D₅⋊M₄(2)	120	4	C3xD5:M4(2)	480,1049
C₃×D₁₀.C₂³	Direct product of C₃ and D₁₀.C₂³	120	4	C3xD10.C2^3	480,1052
C₆₀.₅₉(C₂×C₄)	13^rd non-split extension by C₆₀ of C₂×C₄ acting via C₂×C₄/C₂=C₄	120	4	C60.59(C2xC4)	480,1062
(C₂×C₁₂)⋊₆F₅	4^th semidirect product of C₂×C₁₂ and F₅ acting via F₅/D₅=C₂	120	4	(C2xC12):6F5	480,1065
D₂₀.₃₈D₆	9^th non-split extension by D₂₀ of D₆ acting via D₆/C₆=C₂	240	4	D20.38D6	480,1076
C₃₀.C₂⁴	8^th non-split extension by C₃₀ of C₂⁴ acting via C₂⁴/C₂²=C₂²	240	4	C30.C2^4	480,1080
D₅×C₄○D₁₂	Direct product of D₅ and C₄○D₁₂	120	4	D5xC4oD12	480,1090
S₃×C₄○D₂₀	Direct product of S₃ and C₄○D₂₀	120	4	S3xC4oD20	480,1091
D₂₀⋊₂₄D₆	7^th semidirect product of D₂₀ and D₆ acting via D₆/C₆=C₂	120	4	D20:24D6	480,1092
D₂₀⋊₂₅D₆	8^th semidirect product of D₂₀ and D₆ acting via D₆/C₆=C₂	120	4	D20:25D6	480,1093
D₂₀⋊₂₆D₆	9^th semidirect product of D₂₀ and D₆ acting via D₆/C₆=C₂	120	4	D20:26D6	480,1094
C₁₅⋊2₊¹⁺⁴	The semidirect product of C₁₅ and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂³=C₂²	120	4	C15:ES+(2,2)	480,1125
C₅×Q₈.A₄	Direct product of C₅ and Q₈.A₄	120	4	C5xQ8.A4	480,1131
C₅×D₄.A₄	Direct product of C₅ and D₄.A₄	80	4	C5xD4.A4	480,1132
C₅×C₂³⋊A₄	Direct product of C₅ and C₂³⋊A₄	40	4	C5xC2^3:A4	480,1134
C₃×D₄⋊₆D₁₀	Direct product of C₃ and D₄⋊₆D₁₀	120	4	C3xD4:6D10	480,1141
C₃×Q₈.₁₀D₁₀	Direct product of C₃ and Q₈.₁₀D₁₀	240	4	C3xQ8.10D10	480,1144
C₃×D₅×C₄○D₄	Direct product of C₃, D₅ and C₄○D₄	120	4	C3xD5xC4oD4	480,1145
C₃×D₄⋊₈D₁₀	Direct product of C₃ and D₄⋊₈D₁₀	120	4	C3xD4:8D10	480,1146
C₃×D₄.₁₀D₁₀	Direct product of C₃ and D₄.₁₀D₁₀	240	4	C3xD4.10D10	480,1147
C₅×D₄⋊₆D₆	Direct product of C₅ and D₄⋊₆D₆	120	4	C5xD4:6D6	480,1156
C₅×Q₈.₁₅D₆	Direct product of C₅ and Q₈.₁₅D₆	240	4	C5xQ8.15D6	480,1159
C₅×S₃×C₄○D₄	Direct product of C₅, S₃ and C₄○D₄	120	4	C5xS3xC4oD4	480,1160
C₅×D₄○D₁₂	Direct product of C₅ and D₄○D₁₂	120	4	C5xD4oD12	480,1161
C₅×Q₈○D₁₂	Direct product of C₅ and Q₈○D₁₂	240	4	C5xQ8oD12	480,1162
D₄⋊₆D₃₀	2^nd semidirect product of D₄ and D₃₀ acting through Inn(D₄)	120	4	D4:6D30	480,1171
Q₈.₁₅D₃₀	1^st non-split extension by Q₈ of D₃₀ acting through Inn(Q₈)	240	4	Q8.15D30	480,1174
C₄○D₄×D₁₅	Direct product of C₄○D₄ and D₁₅	120	4	C4oD4xD15	480,1175
C₁₅×2₊¹⁺⁴	Direct product of C₁₅ and 2₊¹⁺⁴	120	4	C15xES+(2,2)	480,1184
C₁₅×2_-¹⁺⁴	Direct product of C₁₅ and 2_-¹⁺⁴	240	4	C15xES-(2,2)	480,1185

Groups of order 492

		d	ρ	Label	ID
C₃×C₄₁⋊C₄	Direct product of C₃ and C₄₁⋊C₄	123	4	C3xC41:C4	492,5
C₄₁⋊Dic₃	The semidirect product of C₄₁ and Dic₃ acting via Dic₃/C₃=C₄	123	4	C41:Dic3	492,6

Groups of order 500

		d	ρ	Label	ID
F₅×C₂₅	Direct product of C₂₅ and F₅	100	4	F5xC25	500,15
C₅×C₂₅⋊C₄	Direct product of C₅ and C₂₅⋊C₄	100	4	C5xC25:C4	500,16
D₅.D₂₅	The non-split extension by D₅ of D₂₅ acting via D₂₅/C₂₅=C₂	100	4	D5.D25	500,19
D₂₅.D₅	The non-split extension by D₂₅ of D₅ acting via D₅/C₅=C₂	100	4	D25.D5	500,20
C₅×D₅.D₅	Direct product of C₅ and D₅.D₅	20	4	C5xD5.D5	500,42
C₅×C₅²⋊C₄	Direct product of C₅ and C₅²⋊C₄	20	4	C5xC5^2:C4	500,44
C₅³⋊₆C₄	6^th semidirect product of C₅³ and C₄ acting faithfully	20	4	C5^3:6C4	500,46
C₅×D₅²	Direct product of C₅, D₅ and D₅	20	4	C5xD5^2	500,50
C₅²⋊₅D₁₀	2^nd semidirect product of C₅² and D₁₀ acting via D₁₀/C₅=C₂²	20	4	C5^2:5D10	500,52

Orthogonal of dimension 5 (ρ=5+)

Groups of order 80

		d	ρ	Label	ID
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	10	5+	C2^4:C5	80,49

Groups of order 160

		d	ρ	Label	ID
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	10	5+	C2^4:D5	160,234
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	10	5+	C2xC2^4:C5	160,235

Groups of order 320

		d	ρ	Label	ID
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	10	5+	C2^4:F5	320,1635
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	10	5+	C2xC2^4:D5	320,1636

Groups of order 360

		d	ρ	Label	ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	6	5+	A6	360,118

Complex of dimension 5 (ρ=5)

Groups of order 55

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

Groups of order 110

		d	ρ	Label	ID
C₂×C₁₁⋊C₅	Direct product of C₂ and C₁₁⋊C₅	22	5	C2xC11:C5	110,2

Groups of order 125

		d	ρ	Label	ID
He₅	Heisenberg group; = C₅² ⋊C₅ = 5₊¹⁺²	25	5	He5	125,3
5_-¹⁺²	Extraspecial group	25	5	ES-(5,1)	125,4

Groups of order 155

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

Groups of order 165

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

Groups of order 205

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

Groups of order 220

		d	ρ	Label	ID
C₄×C₁₁⋊C₅	Direct product of C₄ and C₁₁⋊C₅	44	5	C4xC11:C5	220,2

Groups of order 240

		d	ρ	Label	ID
C₃×C₂⁴⋊C₅	Direct product of C₃ and C₂⁴⋊C₅	30	5	C3xC2^4:C5	240,199

Groups of order 250

		d	ρ	Label	ID
He₅⋊C₂	2^nd semidirect product of He₅ and C₂ acting faithfully	25	5	He5:C2	250,8
C₂×He₅	Direct product of C₂ and He₅	50	5	C2xHe5	250,10
C₂×5_-¹⁺²	Direct product of C₂ and 5_-¹⁺²	50	5	C2xES-(5,1)	250,11

Groups of order 275

		d	ρ	Label	ID
C₁₁⋊C₂₅	The semidirect product of C₁₁ and C₂₅ acting via C₂₅/C₅=C₅	275	5	C11:C25	275,1
C₅×C₁₁⋊C₅	Direct product of C₅ and C₁₁⋊C₅	55	5	C5xC11:C5	275,3

Groups of order 305

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

Groups of order 310

		d	ρ	Label	ID
C₂×C₃₁⋊C₅	Direct product of C₂ and C₃₁⋊C₅	62	5	C2xC31:C5	310,2

Groups of order 320

		d	ρ	Label	ID
C₂⁵.D₅	The non-split extension by C₂⁵ of D₅ acting faithfully	20	5	C2^5.D5	320,1583
C₄×C₂⁴⋊C₅	Direct product of C₄ and C₂⁴⋊C₅	20	5	C4xC2^4:C5	320,1584

Groups of order 330

		d	ρ	Label	ID
C₆×C₁₁⋊C₅	Direct product of C₆ and C₁₁⋊C₅	66	5	C6xC11:C5	330,4

Groups of order 355

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

Groups of order 375

		d	ρ	Label	ID
He₅⋊C₃	The semidirect product of He₅ and C₃ acting faithfully	75	5	He5:C3	375,2
C₃×He₅	Direct product of C₃ and He₅	75	5	C3xHe5	375,4
C₃×5_-¹⁺²	Direct product of C₃ and 5_-¹⁺²	75	5	C3xES-(5,1)	375,5

Groups of order 385

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

Groups of order 400

		d	ρ	Label	ID
C₂⁴⋊C₂₅	The semidirect product of C₂⁴ and C₂₅ acting via C₂₅/C₅=C₅	50	5	C2^4:C25	400,52
C₅×C₂⁴⋊C₅	Direct product of C₅ and C₂⁴⋊C₅	50	5	C5xC2^4:C5	400,213

Groups of order 405

		d	ρ	Label	ID
C₃⁴⋊C₅	The semidirect product of C₃⁴ and C₅ acting faithfully	15	5	C3^4:C5	405,15

Groups of order 410

		d	ρ	Label	ID
C₂×C₄₁⋊C₅	Direct product of C₂ and C₄₁⋊C₅	82	5	C2xC41:C5	410,2

Groups of order 440

		d	ρ	Label	ID
C₈×C₁₁⋊C₅	Direct product of C₈ and C₁₁⋊C₅	88	5	C8xC11:C5	440,2

Groups of order 465

		d	ρ	Label	ID
C₃×C₃₁⋊C₅	Direct product of C₃ and C₃₁⋊C₅	93	5	C3xC31:C5	465,2

Groups of order 480

		d	ρ	Label	ID
C₃×C₂⁴⋊D₅	Direct product of C₃ and C₂⁴⋊D₅	30	5	C3xC2^4:D5	480,1194
C₆×C₂⁴⋊C₅	Direct product of C₆ and C₂⁴⋊C₅	30	5	C6xC2^4:C5	480,1204

Groups of order 495

		d	ρ	Label	ID
C₉×C₁₁⋊C₅	Direct product of C₉ and C₁₁⋊C₅	99	5	C9xC11:C5	495,1

Groups of order 500

		d	ρ	Label	ID
He₅⋊₆C₄	2^nd semidirect product of He₅ and C₄ acting via C₄/C₂=C₂	100	5	He5:6C4	500,11
C₄×He₅	Direct product of C₄ and He₅	100	5	C4xHe5	500,13
C₄×5_-¹⁺²	Direct product of C₄ and 5_-¹⁺²	100	5	C4xES-(5,1)	500,14
He₅⋊₄C₄	4^th semidirect product of He₅ and C₄ acting faithfully; = Aut(5_-¹⁺²)	25	5	He5:4C4	500,25
C₂×He₅⋊C₂	Direct product of C₂ and He₅⋊C₂	50	5	C2xHe5:C2	500,33

Orthogonal of dimension 6 (ρ=6+)

Groups of order 42

		d	ρ	Label	ID
F₇	Frobenius group; = C₇ ⋊C₆ = AGL₁(𝔽₇) = Aut(D₇) = Hol(C₇)	7	6+	F7	42,1

Groups of order 54

		d	ρ	Label	ID
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	9	6+	C3^2:C6	54,5
C₉⋊C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	9	6+	C9:C6	54,6

Groups of order 72

		d	ρ	Label	ID
C₃.S₄	The non-split extension by C₃ of S₄ acting via S₄/A₄=C₂	18	6+	C3.S4	72,15
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	12	6+	C3:S4	72,43
S₃×A₄	Direct product of S₃ and A₄	12	6+	S3xA4	72,44

Groups of order 78

		d	ρ	Label	ID
C₁₃⋊C₆	The semidirect product of C₁₃ and C₆ acting faithfully	13	6+	C13:C6	78,1

Groups of order 84

		d	ρ	Label	ID
C₂×F₇	Direct product of C₂ and F₇; = Aut(D₁₄) = Hol(C₁₄)	14	6+	C2xF7	84,7

Groups of order 96

		d	ρ	Label	ID
C₂³.₃A₄	1^st non-split extension by C₂³ of A₄ acting via A₄/C₂²=C₃	12	6+	C2^3.3A4	96,3
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	8	6+	C2^4:C6	96,70
C₂³.A₄	2^nd non-split extension by C₂³ of A₄ acting faithfully	12	6+	C2^3.A4	96,72
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	12	6+	C4:S4	96,187
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
D₄×A₄	Direct product of D₄ and A₄	12	6+	D4xA4	96,197
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	8	6+	C2^2:S4	96,227

Groups of order 108

		d	ρ	Label	ID
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	9	6+	C3^2:D6	108,17
C₂×C₃²⋊C₆	Direct product of C₂ and C₃²⋊C₆	18	6+	C2xC3^2:C6	108,25
C₂×C₉⋊C₆	Direct product of C₂ and C₉⋊C₆; = Aut(D₁₈) = Hol(C₁₈)	18	6+	C2xC9:C6	108,26

Groups of order 114

		d	ρ	Label	ID
C₁₉⋊C₆	The semidirect product of C₁₉ and C₆ acting faithfully	19	6+	C19:C6	114,1

Groups of order 120

		d	ρ	Label	ID
C₅⋊S₄	The semidirect product of C₅ and S₄ acting via S₄/A₄=C₂	20	6+	C5:S4	120,38
D₅×A₄	Direct product of D₅ and A₄	20	6+	D5xA4	120,39

Groups of order 126

		d	ρ	Label	ID
C₃⋊F₇	The semidirect product of C₃ and F₇ acting via F₇/C₇⋊C₃=C₂	21	6+	C3:F7	126,9

Groups of order 144

		d	ρ	Label	ID
C₂×C₃.S₄	Direct product of C₂ and C₃.S₄	18	6+	C2xC3.S4	144,109
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	12	6+	S3xS4	144,183
C₂×C₃⋊S₄	Direct product of C₂ and C₃⋊S₄	18	6+	C2xC3:S4	144,189
C₂×S₃×A₄	Direct product of C₂, S₃ and A₄	18	6+	C2xS3xA4	144,190

Groups of order 150

		d	ρ	Label	ID
C₅²⋊C₆	The semidirect product of C₅² and C₆ acting faithfully	15	6+	C5^2:C6	150,6

Groups of order 156

		d	ρ	Label	ID
C₂×C₁₃⋊C₆	Direct product of C₂ and C₁₃⋊C₆	26	6+	C2xC13:C6	156,8

Groups of order 162

		d	ρ	Label	ID
C₂₇⋊C₆	The semidirect product of C₂₇ and C₆ acting faithfully	27	6+	C27:C6	162,9
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	9	6+	C3^3:C6	162,11
He₃.S₃	1^st non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.S3	162,13
He₃.₂S₃	2^nd non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.2S3	162,15
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	9	6+	C3^3:S3	162,19
He₃.₃S₃	3^rd non-split extension by He₃ of S₃ acting faithfully	27	6+	He3.3S3	162,20
He₃⋊S₃	3^rd semidirect product of He₃ and S₃ acting faithfully	27	6+	He3:S3	162,21
3_-¹⁺².S₃	The non-split extension by 3_-¹⁺² of S₃ acting faithfully	27	6+	ES-(3,1).S3	162,22
He₃.₄S₃	The non-split extension by He₃ of S₃ acting via S₃/C₃=C₂	27	6+	He3.4S3	162,43

Groups of order 168

		d	ρ	Label	ID
C₄⋊F₇	The semidirect product of C₄ and F₇ acting via F₇/C₇⋊C₃=C₂	28	6+	C4:F7	168,9
C₇⋊S₄	The semidirect product of C₇ and S₄ acting via S₄/A₄=C₂	28	6+	C7:S4	168,46
A₄×D₇	Direct product of A₄ and D₇	28	6+	A4xD7	168,48
D₇⋊A₄	The semidirect product of D₇ and A₄ acting via A₄/C₂²=C₃	28	6+	D7:A4	168,49

Groups of order 186

		d	ρ	Label	ID
C₃₁⋊C₆	The semidirect product of C₃₁ and C₆ acting faithfully	31	6+	C31:C6	186,1

Groups of order 192

		d	ρ	Label	ID
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	24	6+	C2^3.8S4	192,181
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	12	6+	C2^4:C12	192,191
C₂³⋊₂D₄⋊C₃	The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully	12	6+	C2^3:2D4:C3	192,194
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	12	6+	C2^4.2A4	192,197
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	8	6+	C2^4:D6	192,955
C₄²⋊D₆	The semidirect product of C₄² and D₆ acting faithfully	12	6+	C4^2:D6	192,956
A₄⋊D₈	The semidirect product of A₄ and D₈ acting via D₈/C₈=C₂	24	6+	A4:D8	192,961
D₄⋊S₄	The semidirect product of D₄ and S₄ acting via S₄/A₄=C₂	24	6+	D4:S4	192,974
C₂×C₂⁴⋊C₆	Direct product of C₂ and C₂⁴⋊C₆	12	6+	C2xC2^4:C6	192,1000
C₂×C₂³.A₄	Direct product of C₂ and C₂³.A₄	12	6+	C2xC2^3.A4	192,1002
A₄×D₈	Direct product of A₄ and D₈	24	6+	A4xD8	192,1014
D₄×S₄	Direct product of D₄ and S₄	12	6+	D4xS4	192,1472
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	12	6+	C2^4:4Dic3	192,1495
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	12	6+	C2xC2^2:S4	192,1538

Groups of order 210

		d	ρ	Label	ID
C₅⋊F₇	The semidirect product of C₅ and F₇ acting via F₇/C₇⋊C₃=C₂	35	6+	C5:F7	210,3

Groups of order 216

		d	ρ	Label	ID
C₉.S₄	The non-split extension by C₉ of S₄ acting via S₄/A₄=C₂	54	6+	C9.S4	216,21
He₃⋊₂D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₂=C₂²	36	6+	He3:2D4	216,35
He₃⋊₄D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₄=C₂	36	6+	He3:4D4	216,51
D₃₆⋊C₃	The semidirect product of D₃₆ and C₃ acting faithfully	36	6+	D36:C3	216,54
He₃⋊C₈	The semidirect product of He₃ and C₈ acting faithfully	27	6+	He3:C8	216,86
He₃⋊D₄	The semidirect product of He₃ and D₄ acting faithfully	18	6+	He3:D4	216,87
C₃².S₄	The non-split extension by C₃² of S₄ acting via S₄/C₂²=S₃	18	6+	C3^2.S4	216,90
C₆²⋊S₃	4^th semidirect product of C₆² and S₃ acting faithfully	18	6+	C6^2:S3	216,92
C₉⋊S₄	The semidirect product of C₉ and S₄ acting via S₄/A₄=C₂	36	6+	C9:S4	216,93
D₉⋊A₄	The semidirect product of D₉ and A₄ acting via A₄/C₂²=C₃	36	6+	D9:A4	216,96
A₄×D₉	Direct product of A₄ and D₉	36	6+	A4xD9	216,97
C₆²⋊C₆	3^rd semidirect product of C₆² and C₆ acting faithfully	18	6+	C6^2:C6	216,99
C₂×C₃²⋊D₆	Direct product of C₂ and C₃²⋊D₆	18	6+	C2xC3^2:D6	216,102

Groups of order 222

		d	ρ	Label	ID
C₃₇⋊C₆	The semidirect product of C₃₇ and C₆ acting faithfully	37	6+	C37:C6	222,1

Groups of order 228

		d	ρ	Label	ID
C₂×C₁₉⋊C₆	Direct product of C₂ and C₁₉⋊C₆	38	6+	C2xC19:C6	228,7

Groups of order 234

		d	ρ	Label	ID
D₃₉⋊C₃	The semidirect product of D₃₉ and C₃ acting faithfully	39	6+	D39:C3	234,9

Groups of order 240

		d	ρ	Label	ID
D₅×S₄	Direct product of D₅ and S₄	20	6+	D5xS4	240,194
C₂×C₅⋊S₄	Direct product of C₂ and C₅⋊S₄	30	6+	C2xC5:S4	240,197
C₂×D₅×A₄	Direct product of C₂, D₅ and A₄	30	6+	C2xD5xA4	240,198

Groups of order 252

		d	ρ	Label	ID
C₂×C₃⋊F₇	Direct product of C₂ and C₃⋊F₇	42	6+	C2xC3:F7	252,30

Groups of order 258

		d	ρ	Label	ID
C₄₃⋊C₆	The semidirect product of C₄₃ and C₆ acting faithfully	43	6+	C43:C6	258,1

Groups of order 264

		d	ρ	Label	ID
C₁₁⋊S₄	The semidirect product of C₁₁ and S₄ acting via S₄/A₄=C₂	44	6+	C11:S4	264,32
A₄×D₁₁	Direct product of A₄ and D₁₁	44	6+	A4xD11	264,33

Groups of order 270

		d	ρ	Label	ID
He₃⋊D₅	1^st semidirect product of He₃ and D₅ acting via D₅/C₅=C₂	45	6+	He3:D5	270,14
D₄₅⋊C₃	The semidirect product of D₄₅ and C₃ acting faithfully	45	6+	D45:C3	270,15

Groups of order 288

		d	ρ	Label	ID
C₄²⋊D₉	The semidirect product of C₄² and D₉ acting via D₉/C₃=S₃	36	6+	C4^2:D9	288,67
C₂²⋊D₃₆	The semidirect product of C₂² and D₃₆ acting via D₃₆/C₁₂=S₃	36	6+	C2^2:D36	288,334
(C₄×C₁₂)⋊S₃	1^st semidirect product of C₄×C₁₂ and S₃ acting faithfully	36	6+	(C4xC12):S3	288,401
(C₄×C₁₂)⋊C₆	3^rd semidirect product of C₄×C₁₂ and C₆ acting faithfully	36	6+	(C4xC12):C6	288,405
A₄⋊D₁₂	The semidirect product of A₄ and D₁₂ acting via D₁₂/D₆=C₂	36	6+	A4:D12	288,858
C₁₂⋊S₄	1^st semidirect product of C₁₂ and S₄ acting via S₄/A₄=C₂	36	6+	C12:S4	288,909
A₄×D₁₂	Direct product of A₄ and D₁₂	36	6+	A4xD12	288,920
A₄≀C₂	Wreath product of A₄ by C₂	8	6+	A4wrC2	288,1025
C₂×S₃×S₄	Direct product of C₂, S₃ and S₄; = Aut(S₃×SL₂(𝔽₃))	18	6+	C2xS3xS4	288,1028

Groups of order 294

		d	ρ	Label	ID
C₄₉⋊C₆	The semidirect product of C₄₉ and C₆ acting faithfully	49	6+	C49:C6	294,1
C₇⋊₅F₇	The semidirect product of C₇ and F₇ acting via F₇/C₇⋊C₃=C₂	21	6+	C7:5F7	294,10
C₇²⋊C₆	7^th semidirect product of C₇² and C₆ acting faithfully	21	6+	C7^2:C6	294,14

Groups of order 300

		d	ρ	Label	ID
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	15	6+	C5^2:D6	300,25
C₂×C₅²⋊C₆	Direct product of C₂ and C₅²⋊C₆	30	6+	C2xC5^2:C6	300,27

Groups of order 312

		d	ρ	Label	ID
D₅₂⋊C₃	The semidirect product of D₅₂ and C₃ acting faithfully	52	6+	D52:C3	312,10
C₁₃⋊S₄	The semidirect product of C₁₃ and S₄ acting via S₄/A₄=C₂	52	6+	C13:S4	312,48
A₄×D₁₃	Direct product of A₄ and D₁₃	52	6+	A4xD13	312,50
D₁₃⋊A₄	The semidirect product of D₁₃ and A₄ acting via A₄/C₂²=C₃	52	6+	D13:A4	312,51

Groups of order 324

		d	ρ	Label	ID
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	9	6+	He3:D6	324,39
He₃.D₆	1^st non-split extension by He₃ of D₆ acting faithfully	27	6+	He3.D6	324,40
He₃.₂D₆	2^nd non-split extension by He₃ of D₆ acting faithfully	27	6+	He3.2D6	324,41
C₂×C₂₇⋊C₆	Direct product of C₂ and C₂₇⋊C₆	54	6+	C2xC27:C6	324,67
C₂×C₃³⋊C₆	Direct product of C₂ and C₃³⋊C₆	18	6+	C2xC3^3:C6	324,69
C₂×He₃.S₃	Direct product of C₂ and He₃.S₃	54	6+	C2xHe3.S3	324,71
C₂×He₃.₂S₃	Direct product of C₂ and He₃.₂S₃	54	6+	C2xHe3.2S3	324,73
C₂×C₃³⋊S₃	Direct product of C₂ and C₃³⋊S₃	18	6+	C2xC3^3:S3	324,77
C₂×He₃.₃S₃	Direct product of C₂ and He₃.₃S₃	54	6+	C2xHe3.3S3	324,78
C₂×He₃⋊S₃	Direct product of C₂ and He₃⋊S₃	54	6+	C2xHe3:S3	324,79
C₂×3_-¹⁺².S₃	Direct product of C₂ and 3_-¹⁺².S₃	54	6+	C2xES-(3,1).S3	324,80
He₃.₆D₆	The non-split extension by He₃ of D₆ acting via D₆/C₃=C₂²	27	6+	He3.6D6	324,125
C₂×He₃.₄S₃	Direct product of C₂ and He₃.₄S₃	54	6+	C2xHe3.4S3	324,147

Groups of order 336

		d	ρ	Label	ID
D₅₆⋊C₃	The semidirect product of D₅₆ and C₃ acting faithfully	56	6+	D56:C3	336,10
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	8	6+	PGL(2,7)	336,208
D₇×S₄	Direct product of D₇ and S₄	28	6+	D7xS4	336,212
C₂×C₇⋊S₄	Direct product of C₂ and C₇⋊S₄	42	6+	C2xC7:S4	336,215
C₂×A₄×D₇	Direct product of C₂, A₄ and D₇	42	6+	C2xA4xD7	336,217
C₂×D₇⋊A₄	Direct product of C₂ and D₇⋊A₄	42	6+	C2xD7:A4	336,218

Groups of order 342

		d	ρ	Label	ID
D₅₇⋊C₃	The semidirect product of D₅₇ and C₃ acting faithfully	57	6+	D57:C3	342,11

Groups of order 360

		d	ρ	Label	ID
C₂²⋊D₄₅	The semidirect product of C₂² and D₄₅ acting via D₄₅/C₁₅=S₃	90	6+	C2^2:D45	360,41
S₃×A₅	Direct product of S₃ and A₅	15	6+	S3xA5	360,121
A₄⋊D₁₅	The semidirect product of A₄ and D₁₅ acting via D₁₅/C₁₅=C₂	60	6+	A4:D15	360,141
A₄×D₁₅	Direct product of A₄ and D₁₅	60	6+	A4xD15	360,144

Groups of order 366

		d	ρ	Label	ID
C₆₁⋊C₆	The semidirect product of C₆₁ and C₆ acting faithfully	61	6+	C61:C6	366,1

Groups of order 372

		d	ρ	Label	ID
C₂×C₃₁⋊C₆	Direct product of C₂ and C₃₁⋊C₆	62	6+	C2xC31:C6	372,7

Groups of order 378

		d	ρ	Label	ID
C₉⋊F₇	1^st semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:F7	378,18
C₉⋊₂F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:2F7	378,19
C₉⋊₅F₇	The semidirect product of C₉ and F₇ acting via F₇/C₇⋊C₃=C₂	63	6+	C9:5F7	378,20
C₃²⋊F₇	The semidirect product of C₃² and F₇ acting via F₇/C₇=C₆	63	6+	C3^2:F7	378,22
He₃⋊D₇	1^st semidirect product of He₃ and D₇ acting via D₇/C₇=C₂	63	6+	He3:D7	378,38
D₆₃⋊C₃	1^st semidirect product of D₆₃ and C₃ acting faithfully	63	6+	D63:C3	378,39

Groups of order 390

		d	ρ	Label	ID
D₆₅⋊C₃	The semidirect product of D₆₅ and C₃ acting faithfully	65	6+	D65:C3	390,3

Groups of order 402

		d	ρ	Label	ID
C₆₇⋊C₆	The semidirect product of C₆₇ and C₆ acting faithfully	67	6+	C67:C6	402,1

Groups of order 408

		d	ρ	Label	ID
C₁₇⋊S₄	The semidirect product of C₁₇ and S₄ acting via S₄/A₄=C₂	68	6+	C17:S4	408,37
A₄×D₁₇	Direct product of A₄ and D₁₇	68	6+	A4xD17	408,38

Groups of order 420

		d	ρ	Label	ID
C₂×C₅⋊F₇	Direct product of C₂ and C₅⋊F₇	70	6+	C2xC5:F7	420,19

Groups of order 432

		d	ρ	Label	ID
He₃⋊₂D₈	1^st semidirect product of He₃ and D₈ acting via D₈/C₄=C₂²	72	6+	He3:2D8	432,79
He₃⋊₄D₈	1^st semidirect product of He₃ and D₈ acting via D₈/C₈=C₂	72	6+	He3:4D8	432,118
D₇₂⋊C₃	The semidirect product of D₇₂ and C₃ acting faithfully	72	6+	D72:C3	432,123
C₂×C₉.S₄	Direct product of C₂ and C₉.S₄	54	6+	C2xC9.S4	432,224
He₃⋊D₈	The semidirect product of He₃ and D₈ acting via D₈/C₂=D₄	72	6+	He3:D8	432,235
C₁₂.₈₆S₃²	6^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	36	6+	C12.86S3^2	432,302
He₃⋊SD₁₆	The semidirect product of He₃ and SD₁₆ acting faithfully	27	6+	He3:SD16	432,520
D₉×S₄	Direct product of D₉ and S₄	36	6+	D9xS4	432,521
C₆²⋊₅D₆	5^th semidirect product of C₆² and D₆ acting faithfully	18	6+	C6^2:5D6	432,523
C₂×He₃⋊C₈	Direct product of C₂ and He₃⋊C₈	54	6+	C2xHe3:C8	432,529
C₂×He₃⋊D₄	Direct product of C₂ and He₃⋊D₄	36	6+	C2xHe3:D4	432,530
C₂×C₃².S₄	Direct product of C₂ and C₃².S₄	18	6+	C2xC3^2.S4	432,533
C₂×C₆²⋊S₃	Direct product of C₂ and C₆²⋊S₃	18	6+	C2xC6^2:S3	432,535
C₂×C₉⋊S₄	Direct product of C₂ and C₉⋊S₄	54	6+	C2xC9:S4	432,536
C₂×D₉⋊A₄	Direct product of C₂ and D₉⋊A₄	54	6+	C2xD9:A4	432,539
C₂×A₄×D₉	Direct product of C₂, A₄ and D₉	54	6+	C2xA4xD9	432,540
C₂×C₆²⋊C₆	Direct product of C₂ and C₆²⋊C₆	18	6+	C2xC6^2:C6	432,542

Groups of order 438

		d	ρ	Label	ID
C₇₃⋊C₆	The semidirect product of C₇₃ and C₆ acting faithfully	73	6+	C73:C6	438,1

Groups of order 444

		d	ρ	Label	ID
C₂×C₃₇⋊C₆	Direct product of C₂ and C₃₇⋊C₆	74	6+	C2xC37:C6	444,8

Groups of order 450

		d	ρ	Label	ID
C₅²⋊D₉	The semidirect product of C₅² and D₉ acting via D₉/C₃=S₃	45	6+	C5^2:D9	450,11
C₅²⋊(C₃⋊S₃)	The semidirect product of C₅² and C₃⋊S₃ acting via C₃⋊S₃/C₃=S₃	45	6+	C5^2:(C3:S3)	450,21
C₅⋊D₁₅⋊C₃	The semidirect product of C₅⋊D₁₅ and C₃ acting faithfully	45	6+	C5:D15:C3	450,24

Groups of order 456

		d	ρ	Label	ID
D₇₆⋊C₃	The semidirect product of D₇₆ and C₃ acting faithfully	76	6+	D76:C3	456,9
C₁₉⋊S₄	The semidirect product of C₁₉ and S₄ acting via S₄/A₄=C₂	76	6+	C19:S4	456,43
A₄×D₁₉	Direct product of A₄ and D₁₉	76	6+	A4xD19	456,45
D₁₉⋊A₄	The semidirect product of D₁₉ and A₄ acting via A₄/C₂²=C₃	76	6+	D19:A4	456,46

Groups of order 462

		d	ρ	Label	ID
C₁₁⋊F₇	The semidirect product of C₁₁ and F₇ acting via F₇/C₇⋊C₃=C₂	77	6+	C11:F7	462,3

Groups of order 468

		d	ρ	Label	ID
C₂×D₃₉⋊C₃	Direct product of C₂ and D₃₉⋊C₃	78	6+	C2xD39:C3	468,35

Groups of order 474

		d	ρ	Label	ID
C₇₉⋊C₆	The semidirect product of C₇₉ and C₆ acting faithfully	79	6+	C79:C6	474,1

Groups of order 480

		d	ρ	Label	ID
C₄²⋊D₁₅	The semidirect product of C₄² and D₁₅ acting via D₁₅/C₅=S₃	60	6+	C4^2:D15	480,258
C₂₀⋊₄D₄⋊C₃	The semidirect product of C₂₀⋊₄D₄ and C₃ acting faithfully	60	6+	C20:4D4:C3	480,262
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	20	6+	C2^2:S5	480,951
D₄×A₅	Direct product of D₄ and A₅	20	6+	D4xA5	480,956
A₄⋊D₂₀	The semidirect product of A₄ and D₂₀ acting via D₂₀/D₁₀=C₂	60	6+	A4:D20	480,981
C₂₀⋊S₄	1^st semidirect product of C₂₀ and S₄ acting via S₄/A₄=C₂	60	6+	C20:S4	480,1026
A₄×D₂₀	Direct product of A₄ and D₂₀	60	6+	A4xD20	480,1037
C₂×D₅×S₄	Direct product of C₂, D₅ and S₄	30	6+	C2xD5xS4	480,1193

Groups of order 486

		d	ρ	Label	ID
He₃.D₉	1^st non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.D9	486,27
He₃.₂D₉	2^nd non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.2D9	486,29
C₈₁⋊C₆	The semidirect product of C₈₁ and C₆ acting faithfully	81	6+	C81:C6	486,34
C₉²⋊C₆	1^st semidirect product of C₉² and C₆ acting faithfully	27	6+	C9^2:C6	486,35
C₉²⋊S₃	1^st semidirect product of C₉² and S₃ acting faithfully	27	6+	C9^2:S3	486,36
C₉²⋊₂C₆	2^nd semidirect product of C₉² and C₆ acting faithfully	27	6+	C9^2:2C6	486,37
C₉².S₃	2^nd non-split extension by C₉² of S₃ acting faithfully	27	6+	C9^2.S3	486,38
C₃³.D₉	3^rd non-split extension by C₃³ of D₉ acting via D₉/C₃=S₃	27	6+	C3^3.D9	486,55
He₃.₃D₉	3^rd non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.3D9	486,58
He₃.₄D₉	4^th non-split extension by He₃ of D₉ acting via D₉/C₃=S₃	81	6+	He3.4D9	486,59
He₃.₅D₉	The non-split extension by He₃ of D₉ acting via D₉/C₉=C₂	81	6+	He3.5D9	486,163
C₃≀C₃.S₃	The non-split extension by C₃≀C₃ of S₃ acting via S₃/C₃=C₂	27	6+	C3wrC3.S3	486,175
C₃≀C₃⋊S₃	2^nd semidirect product of C₃≀C₃ and S₃ acting via S₃/C₃=C₂	27	6+	C3wrC3:S3	486,189

Symplectic of dimension 6 (ρ=6-)

Groups of order 84

		d	ρ	Label	ID
C₇⋊C₁₂	The semidirect product of C₇ and C₁₂ acting via C₁₂/C₂=C₆	28	6-	C7:C12	84,1

Groups of order 96

		d	ρ	Label	ID
A₄⋊Q₈	The semidirect product of A₄ and Q₈ acting via Q₈/C₄=C₂	24	6-	A4:Q8	96,185
Q₈×A₄	Direct product of Q₈ and A₄	24	6-	Q8xA4	96,199
Q₈⋊A₄	1^st semidirect product of Q₈ and A₄ acting via A₄/C₂²=C₃	24	6-	Q8:A4	96,203

Groups of order 108

		d	ρ	Label	ID
C₃²⋊C₁₂	The semidirect product of C₃² and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C3^2:C12	108,8
C₉⋊C₁₂	The semidirect product of C₉ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C9:C12	108,9

Groups of order 144

		d	ρ	Label	ID
C₆.S₄	3^rd non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	36	6-	C6.S4	144,33
C₆.₇S₄	7^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	36	6-	C6.7S4	144,126
Dic₃×A₄	Direct product of Dic₃ and A₄	36	6-	Dic3xA4	144,129

Groups of order 156

		d	ρ	Label	ID
C₂₆.C₆	The non-split extension by C₂₆ of C₆ acting faithfully	52	6-	C26.C6	156,1

Groups of order 168

		d	ρ	Label	ID
C₄.F₇	The non-split extension by C₄ of F₇ acting via F₇/C₇⋊C₃=C₂	56	6-	C4.F7	168,7

Groups of order 192

		d	ρ	Label	ID
C₄²⋊₂C₁₂	2^nd semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	24	6-	C4^2:2C12	192,193
(C₂²×C₄).A₄	4^th non-split extension by C₂²×C₄ of A₄ acting faithfully	24	6-	(C2^2xC4).A4	192,196
A₄⋊Q₁₆	The semidirect product of A₄ and Q₁₆ acting via Q₁₆/C₈=C₂	48	6-	A4:Q16	192,957
A₄⋊₂Q₁₆	The semidirect product of A₄ and Q₁₆ acting via Q₁₆/Q₈=C₂	48	6-	A4:2Q16	192,975
A₄×Q₁₆	Direct product of A₄ and Q₁₆	48	6-	A4xQ16	192,1016
Q₈×S₄	Direct product of Q₈ and S₄	24	6-	Q8xS4	192,1477
Q₈.₁S₄	1^st non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	48	6-	Q8.1S4	192,1489

Groups of order 216

		d	ρ	Label	ID
He₃⋊₂Q₈	The semidirect product of He₃ and Q₈ acting via Q₈/C₂=C₂²	72	6-	He3:2Q8	216,33
He₃⋊(C₂×C₄)	2^nd semidirect product of He₃ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	36	6-	He3:(C2xC4)	216,36
He₃⋊₃Q₈	1^st semidirect product of He₃ and Q₈ acting via Q₈/C₄=C₂	72	6-	He3:3Q8	216,49
C₃₆.C₆	1^st non-split extension by C₃₆ of C₆ acting faithfully	72	6-	C36.C6	216,52

Groups of order 228

		d	ρ	Label	ID
C₁₉⋊C₁₂	The semidirect product of C₁₉ and C₁₂ acting via C₁₂/C₂=C₆	76	6-	C19:C12	228,1

Groups of order 240

		d	ρ	Label	ID
A₄⋊Dic₅	The semidirect product of A₄ and Dic₅ acting via Dic₅/C₁₀=C₂	60	6-	A4:Dic5	240,107
A₄×Dic₅	Direct product of A₄ and Dic₅	60	6-	A4xDic5	240,110

Groups of order 252

		d	ρ	Label	ID
C₆.F₇	The non-split extension by C₆ of F₇ acting via F₇/C₇⋊C₃=C₂	84	6-	C6.F7	252,18

Groups of order 288

		d	ρ	Label	ID
C₁₂.₁S₄	1^st non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	6-	C12.1S4	288,332
Dic₃.S₄	3^rd non-split extension by Dic₃ of S₄ acting via S₄/A₄=C₂	72	6-	Dic3.S4	288,852
Dic₃×S₄	Direct product of Dic₃ and S₄	36	6-	Dic3xS4	288,853
A₄×SL₂(𝔽₃)	Direct product of A₄ and SL₂(𝔽₃)	24	6-	A4xSL(2,3)	288,859
A₄⋊Dic₆	The semidirect product of A₄ and Dic₆ acting via Dic₆/C₁₂=C₂	72	6-	A4:Dic6	288,907
A₄×Dic₆	Direct product of A₄ and Dic₆	72	6-	A4xDic6	288,918

Groups of order 300

		d	ρ	Label	ID
C₅²⋊₂C₁₂	The semidirect product of C₅² and C₁₂ acting via C₁₂/C₂=C₆	60	6-	C5^2:2C12	300,14

Groups of order 312

		d	ρ	Label	ID
Dic₂₆⋊C₃	The semidirect product of Dic₂₆ and C₃ acting faithfully	104	6-	Dic26:C3	312,8

Groups of order 324

		d	ρ	Label	ID
C₂₇⋊C₁₂	The semidirect product of C₂₇ and C₁₂ acting via C₁₂/C₂=C₆	108	6-	C27:C12	324,12
C₃³⋊C₁₂	1^st semidirect product of C₃³ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C3^3:C12	324,14
He₃.Dic₃	1^st non-split extension by He₃ of Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3.Dic3	324,16
He₃.₂Dic₃	2^nd non-split extension by He₃ of Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3.2Dic3	324,18
C₃³⋊Dic₃	2^nd semidirect product of C₃³ and Dic₃ acting via Dic₃/C₂=S₃	36	6-	C3^3:Dic3	324,22
He₃.₃Dic₃	3^rd non-split extension by He₃ of Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3.3Dic3	324,23
He₃⋊Dic₃	3^rd semidirect product of He₃ and Dic₃ acting via Dic₃/C₂=S₃	108	6-	He3:Dic3	324,24
3_-¹⁺².Dic₃	The non-split extension by 3_-¹⁺² of Dic₃ acting via Dic₃/C₂=S₃	108	6-	ES-(3,1).Dic3	324,25
He₃.₄Dic₃	The non-split extension by He₃ of Dic₃ acting via Dic₃/C₆=C₂	108	6-	He3.4Dic3	324,101

Groups of order 336

		d	ρ	Label	ID
C₈.F₇	The non-split extension by C₈ of F₇ acting via F₇/C₇⋊C₃=C₂	112	6-	C8.F7	336,11
A₄⋊Dic₇	The semidirect product of A₄ and Dic₇ acting via Dic₇/C₁₄=C₂	84	6-	A4:Dic7	336,120
A₄×Dic₇	Direct product of A₄ and Dic₇	84	6-	A4xDic7	336,133
Dic₇⋊A₄	The semidirect product of Dic₇ and A₄ acting via A₄/C₂²=C₃	84	6-	Dic7:A4	336,136

Groups of order 372

		d	ρ	Label	ID
C₃₁⋊C₁₂	The semidirect product of C₃₁ and C₁₂ acting via C₁₂/C₂=C₆	124	6-	C31:C12	372,1

Groups of order 420

		d	ρ	Label	ID
C₃₅⋊₃C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting via C₁₂/C₂=C₆	140	6-	C35:3C12	420,3

Groups of order 432

		d	ρ	Label	ID
C₁₈.S₄	3^rd non-split extension by C₁₈ of S₄ acting via S₄/A₄=C₂	108	6-	C18.S4	432,39
He₃⋊₂Q₁₆	1^st semidirect product of He₃ and Q₁₆ acting via Q₁₆/C₄=C₂²	144	6-	He3:2Q16	432,80
He₃⋊₄Q₁₆	1^st semidirect product of He₃ and Q₁₆ acting via Q₁₆/C₈=C₂	144	6-	He3:4Q16	432,114
C₇₂.C₆	1^st non-split extension by C₇₂ of C₆ acting faithfully	144	6-	C72.C6	432,119
He₃⋊Q₁₆	The semidirect product of He₃ and Q₁₆ acting via Q₁₆/C₂=D₄	144	6-	He3:Q16	432,236
C₆.S₃≀C₂	4^th non-split extension by C₆ of S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	72	6-	C6.S3wrC2	432,237
C₆².Dic₃	8^th non-split extension by C₆² of Dic₃ acting via Dic₃/C₂=S₃	36	6-	C6^2.Dic3	432,249
C₆²⋊₅Dic₃	4^th semidirect product of C₆² and Dic₃ acting via Dic₃/C₂=S₃	36	6-	C6^2:5Dic3	432,251
A₄⋊Dic₉	The semidirect product of A₄ and Dic₉ acting via Dic₉/C₁₈=C₂	108	6-	A4:Dic9	432,254
Dic₉⋊A₄	The semidirect product of Dic₉ and A₄ acting via A₄/C₂²=C₃	108	6-	Dic9:A4	432,265
A₄×Dic₉	Direct product of A₄ and Dic₉	108	6-	A4xDic9	432,266
C₆²⋊₄C₁₂	3^rd semidirect product of C₆² and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C6^2:4C12	432,272
C₁₂.₈₅S₃²	5^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	72	6-	C12.85S3^2	432,298

Groups of order 444

		d	ρ	Label	ID
C₇₄.C₆	The non-split extension by C₇₄ of C₆ acting faithfully	148	6-	C74.C6	444,1

Groups of order 456

		d	ρ	Label	ID
Dic₃₈⋊C₃	The semidirect product of Dic₃₈ and C₃ acting faithfully	152	6-	Dic38:C3	456,7

Groups of order 468

		d	ρ	Label	ID
C₃₉⋊₃C₁₂	1^st semidirect product of C₃₉ and C₁₂ acting via C₁₂/C₂=C₆	156	6-	C39:3C12	468,21

Groups of order 480

		d	ρ	Label	ID
Q₈×A₅	Direct product of Q₈ and A₅	40	6-	Q8xA5	480,958
A₄⋊Dic₁₀	The semidirect product of A₄ and Dic₁₀ acting via Dic₁₀/Dic₅=C₂	120	6-	A4:Dic10	480,975
Dic₅×S₄	Direct product of Dic₅ and S₄	60	6-	Dic5xS4	480,976
C₂₀.₁S₄	1^st non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	120	6-	C20.1S4	480,1024
A₄×Dic₁₀	Direct product of A₄ and Dic₁₀	120	6-	A4xDic10	480,1035

Complex of dimension 6 (ρ=6)

Groups of order 96

		d	ρ	Label	ID
C₄²⋊C₆	1^st semidirect product of C₄² and C₆ acting faithfully	16	6	C4^2:C6	96,71

Groups of order 126

		d	ρ	Label	ID
C₇⋊C₁₈	The semidirect product of C₇ and C₁₈ acting via C₁₈/C₃=C₆	63	6	C7:C18	126,1
C₃×F₇	Direct product of C₃ and F₇	21	6	C3xF7	126,7
S₃×C₇⋊C₃	Direct product of S₃ and C₇⋊C₃	21	6	S3xC7:C3	126,8

Groups of order 162

		d	ρ	Label	ID
C₃²⋊C₁₈	The semidirect product of C₃² and C₁₈ acting via C₁₈/C₃=C₆	18	6	C3^2:C18	162,4
C₉⋊C₁₈	The semidirect product of C₉ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C9:C18	162,6
C₃²⋊₂D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	18	6	C3^2:2D9	162,17
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	18	6	C3xC3^2:C6	162,34
S₃×He₃	Direct product of S₃ and He₃	18	6	S3xHe3	162,35
C₃×C₉⋊C₆	Direct product of C₃ and C₉⋊C₆	18	6	C3xC9:C6	162,36
S₃×3_-¹⁺²	Direct product of S₃ and 3_-¹⁺²	18	6	S3xES-(3,1)	162,37
He₃⋊₅S₃	2^nd semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	18	6	He3:5S3	162,46

Groups of order 168

		d	ρ	Label	ID
C₇⋊C₂₄	The semidirect product of C₇ and C₂₄ acting via C₂₄/C₄=C₆	56	6	C7:C24	168,1
C₄×F₇	Direct product of C₄ and F₇	28	6	C4xF7	168,8
Dic₇⋊C₆	The semidirect product of Dic₇ and C₆ acting faithfully	28	6	Dic7:C6	168,11
D₄×C₇⋊C₃	Direct product of D₄ and C₇⋊C₃	28	6	D4xC7:C3	168,20
Q₈×C₇⋊C₃	Direct product of Q₈ and C₇⋊C₃	56	6	Q8xC7:C3	168,21
C₁₄.A₄	The non-split extension by C₁₄ of A₄ acting via A₄/C₂²=C₃	56	6	C14.A4	168,23

Groups of order 192

		d	ρ	Label	ID
C₂³.₇S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	24	6	C2^3.7S4	192,180
C₄²⋊₄C₄⋊C₃	The semidirect product of C₄²⋊₄C₄ and C₃ acting faithfully	24	6	C4^2:4C4:C3	192,190
C₄²⋊C₁₂	1^st semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	24	6	C4^2:C12	192,192
C₂⁴.A₄	1^st non-split extension by C₂⁴ of A₄ acting faithfully	24	6	C2^4.A4	192,195
C₂⁴.₃A₄	3^rd non-split extension by C₂⁴ of A₄ acting faithfully	24	6	C2^4.3A4	192,198
C₂³.₁₉(C₂×A₄)	12^nd non-split extension by C₂³ of C₂×A₄ acting via C₂×A₄/C₂³=C₃	24	6	C2^3.19(C2xA4)	192,199
C₈⋊S₄	3^rd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	24	6	C8:S4	192,959
C₈⋊₂S₄	2^nd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	24	6	C8:2S4	192,960
A₄⋊M₄(2)	The semidirect product of A₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	24	6	A4:M4(2)	192,968
A₄⋊SD₁₆	The semidirect product of A₄ and SD₁₆ acting via SD₁₆/D₄=C₂	24	6	A4:SD16	192,973
Q₈⋊₃S₄	The semidirect product of Q₈ and S₄ acting via S₄/A₄=C₂	24	6	Q8:3S4	192,976
C₂×C₄²⋊C₆	Direct product of C₂ and C₄²⋊C₆	24	6	C2xC4^2:C6	192,1001
A₄×M₄(2)	Direct product of A₄ and M₄(2)	24	6	A4xM4(2)	192,1011
A₄×SD₁₆	Direct product of A₄ and SD₁₆	24	6	A4xSD16	192,1015
C₂⁴.₁₀D₆	9^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	24	6	C2^4.10D6	192,1471
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	24	6	D4:2S4	192,1473
Q₈⋊₄S₄	The semidirect product of Q₈ and S₄ acting through Inn(Q₈)	24	6	Q8:4S4	192,1478
Q₈⋊S₄	1^st semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃	24	6	Q8:S4	192,1490
A₄×C₄○D₄	Direct product of A₄ and C₄○D₄	24	6	A4xC4oD4	192,1501
C₄○D₄⋊A₄	1^st semidirect product of C₄○D₄ and A₄ acting via A₄/C₂²=C₃	24	6	C4oD4:A4	192,1507

Groups of order 210

		d	ρ	Label	ID
C₅×F₇	Direct product of C₅ and F₇	35	6	C5xF7	210,1
D₅×C₇⋊C₃	Direct product of D₅ and C₇⋊C₃	35	6	D5xC7:C3	210,2

Groups of order 216

		d	ρ	Label	ID
He₃⋊₃C₈	1^st semidirect product of He₃ and C₈ acting via C₈/C₄=C₂	72	6	He3:3C8	216,14
C₉⋊C₂₄	The semidirect product of C₉ and C₂₄ acting via C₂₄/C₄=C₆	72	6	C9:C24	216,15
C₆.S₃²	2^nd non-split extension by C₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	36	6	C6.S3^2	216,34
He₃⋊₃D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₂=C₂²	36	6	He3:3D4	216,37
C₁₈.A₄	The non-split extension by C₁₈ of A₄ acting via A₄/C₂²=C₃	72	6	C18.A4	216,39
Q₈⋊3_-¹⁺²	The semidirect product of Q₈ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	72	6	Q8:ES-(3,1)	216,41
Q₈⋊He₃	The semidirect product of Q₈ and He₃ acting via He₃/C₃²=C₃	72	6	Q8:He3	216,42
C₄×C₃²⋊C₆	Direct product of C₄ and C₃²⋊C₆	36	6	C4xC3^2:C6	216,50
C₄×C₉⋊C₆	Direct product of C₄ and C₉⋊C₆	36	6	C4xC9:C6	216,53
He₃⋊₆D₄	1^st semidirect product of He₃ and D₄ acting via D₄/C₂²=C₂	36	6	He3:6D4	216,60
Dic₉⋊C₆	The semidirect product of Dic₉ and C₆ acting faithfully	36	6	Dic9:C6	216,62
He₃⋊₄Q₈	2^nd semidirect product of He₃ and Q₈ acting via Q₈/C₄=C₂	72	6	He3:4Q8	216,66
He₃⋊₅D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₄=C₂	36	6	He3:5D4	216,68
He₃⋊₇D₄	2^nd semidirect product of He₃ and D₄ acting via D₄/C₂²=C₂	36	6	He3:7D4	216,72
D₄×He₃	Direct product of D₄ and He₃	36	6	D4xHe3	216,77
D₄×3_-¹⁺²	Direct product of D₄ and 3_-¹⁺²	36	6	D4xES-(3,1)	216,78
Q₈×He₃	Direct product of Q₈ and He₃	72	6	Q8xHe3	216,80
Q₈×3_-¹⁺²	Direct product of Q₈ and 3_-¹⁺²	72	6	Q8xES-(3,1)	216,81
C₃×C₃.S₄	Direct product of C₃ and C₃.S₄	36	6	C3xC3.S4	216,91
S₃×C₃.A₄	Direct product of S₃ and C₃.A₄	36	6	S3xC3.A4	216,98
C₃×C₃⋊S₄	Direct product of C₃ and C₃⋊S₄	24	6	C3xC3:S4	216,164
C₃×S₃×A₄	Direct product of C₃, S₃ and A₄	24	6	C3xS3xA4	216,166

Groups of order 234

		d	ρ	Label	ID
C₁₃⋊C₁₈	The semidirect product of C₁₃ and C₁₈ acting via C₁₈/C₃=C₆	117	6	C13:C18	234,1
C₃×C₁₃⋊C₆	Direct product of C₃ and C₁₃⋊C₆	39	6	C3xC13:C6	234,7
S₃×C₁₃⋊C₃	Direct product of S₃ and C₁₃⋊C₃	39	6	S3xC13:C3	234,8

Groups of order 252

		d	ρ	Label	ID
C₇⋊C₃₆	The semidirect product of C₇ and C₃₆ acting via C₃₆/C₆=C₆	252	6	C7:C36	252,1
C₂×C₇⋊C₁₈	Direct product of C₂ and C₇⋊C₁₈	126	6	C2xC7:C18	252,7
C₃×C₇⋊C₁₂	Direct product of C₃ and C₇⋊C₁₂	84	6	C3xC7:C12	252,16
Dic₃×C₇⋊C₃	Direct product of Dic₃ and C₇⋊C₃	84	6	Dic3xC7:C3	252,17
C₆×F₇	Direct product of C₆ and F₇	42	6	C6xF7	252,28
C₂×S₃×C₇⋊C₃	Direct product of C₂, S₃ and C₇⋊C₃	42	6	C2xS3xC7:C3	252,29

Groups of order 270

		d	ρ	Label	ID
D₅×He₃	Direct product of D₅ and He₃	45	6	D5xHe3	270,6
D₅×3_-¹⁺²	Direct product of D₅ and 3_-¹⁺²	45	6	D5xES-(3,1)	270,7
C₅×C₃²⋊C₆	Direct product of C₅ and C₃²⋊C₆	45	6	C5xC3^2:C6	270,10
C₅×C₉⋊C₆	Direct product of C₅ and C₉⋊C₆	45	6	C5xC9:C6	270,11
C₃²⋊D₁₅	2^nd semidirect product of C₃² and D₁₅ acting via D₁₅/C₅=S₃	45	6	C3^2:D15	270,19

Groups of order 288

		d	ρ	Label	ID
C₂.(C₄²⋊C₉)	The central stem extension by C₂ of C₄²⋊C₉	36	6	C2.(C4^2:C9)	288,3
C₁₂.S₄	8^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	6	C12.S4	288,68
C₂⁴⋊C₁₈	1^st semidirect product of C₂⁴ and C₁₈ acting via C₁₈/C₃=C₆	36	6	C2^4:C18	288,73
C₄²⋊C₁₈	1^st semidirect product of C₄² and C₁₈ acting via C₁₈/C₃=C₆	72	6	C4^2:C18	288,74
C₄²⋊₂C₁₈	2^nd semidirect product of C₄² and C₁₈ acting via C₁₈/C₃=C₆	36	6	C4^2:2C18	288,75
C₃×C₂³.₃A₄	Direct product of C₃ and C₂³.₃A₄	36	6	C3xC2^3.3A4	288,230
C₄×C₃.S₄	Direct product of C₄ and C₃.S₄	36	6	C4xC3.S4	288,333
C₂³.D₁₈	5^th non-split extension by C₂³ of D₁₈ acting via D₁₈/C₆=S₃	36	6	C2^3.D18	288,342
D₄×C₃.A₄	Direct product of D₄ and C₃.A₄	36	6	D4xC3.A4	288,344
Q₈×C₃.A₄	Direct product of Q₈ and C₃.A₄	72	6	Q8xC3.A4	288,346
C₂²⋊(Q₈⋊C₉)	The semidirect product of C₂² and Q₈⋊C₉ acting via Q₈⋊C₉/C₃×Q₈=C₃	72	6	C2^2:(Q8:C9)	288,350
C₁₂.₁₂S₄	12^nd non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	6	C12.12S4	288,402
C₄²⋊C₃⋊S₃	1^st semidirect product of C₄²⋊C₃ and S₃ acting via S₃/C₃=C₂	48	6	C4^2:C3:S3	288,406
S₃×C₄²⋊C₃	Direct product of S₃ and C₄²⋊C₃	36	6	S3xC4^2:C3	288,407
A₄×C₃⋊C₈	Direct product of A₄ and C₃⋊C₈	72	6	A4xC3:C8	288,408
(C₂²×S₃)⋊A₄	The semidirect product of C₂²×S₃ and A₄ acting faithfully	24	6	(C2^2xS3):A4	288,411
C₃×C₂⁴⋊C₆	Direct product of C₃ and C₂⁴⋊C₆	24	6	C3xC2^4:C6	288,634
C₃×C₄²⋊C₆	Direct product of C₃ and C₄²⋊C₆	48	6	C3xC4^2:C6	288,635
C₃×C₂³.A₄	Direct product of C₃ and C₂³.A₄	36	6	C3xC2^3.A4	288,636
C₂⁴⋊D₉	3^rd semidirect product of C₂⁴ and D₉ acting via D₉/C₃=S₃	36	6	C2^4:D9	288,836
Dic₃⋊₂S₄	The semidirect product of Dic₃ and S₄ acting through Inn(Dic₃)	36	6	Dic3:2S4	288,854
Dic₃⋊S₄	The semidirect product of Dic₃ and S₄ acting via S₄/A₄=C₂	36	6	Dic3:S4	288,855
S₃×A₄⋊C₄	Direct product of S₃ and A₄⋊C₄	36	6	S3xA4:C4	288,856
D₆⋊S₄	1^st semidirect product of D₆ and S₄ acting via S₄/A₄=C₂	36	6	D6:S4	288,857
C₃×A₄⋊Q₈	Direct product of C₃ and A₄⋊Q₈	72	6	C3xA4:Q8	288,896
C₃×C₄⋊S₄	Direct product of C₃ and C₄⋊S₄	36	6	C3xC4:S4	288,898
C₃×A₄⋊D₄	Direct product of C₃ and A₄⋊D₄	36	6	C3xA4:D4	288,906
C₄×C₃⋊S₄	Direct product of C₄ and C₃⋊S₄	36	6	C4xC3:S4	288,908
(C₂×C₆)⋊₄S₄	2^nd semidirect product of C₂×C₆ and S₄ acting via S₄/A₄=C₂	36	6	(C2xC6):4S4	288,917
C₄×S₃×A₄	Direct product of C₄, S₃ and A₄	36	6	C4xS3xA4	288,919
A₄×C₃⋊D₄	Direct product of A₄ and C₃⋊D₄	36	6	A4xC3:D4	288,928
C₃×D₄×A₄	Direct product of C₃, D₄ and A₄	36	6	C3xD4xA4	288,980
C₃×Q₈×A₄	Direct product of C₃, Q₈ and A₄	72	6	C3xQ8xA4	288,982
C₃×Q₈⋊A₄	Direct product of C₃ and Q₈⋊A₄	72	6	C3xQ8:A4	288,986
C₃×C₂²⋊S₄	Direct product of C₃ and C₂²⋊S₄	24	6	C3xC2^2:S4	288,1035
(C₂×C₆)⋊S₄	2^nd semidirect product of C₂×C₆ and S₄ acting via S₄/C₂²=S₃	24	6	(C2xC6):S4	288,1036

Groups of order 294

		d	ρ	Label	ID
C₇×F₇	Direct product of C₇ and F₇	42	6	C7xF7	294,8
D₇×C₇⋊C₃	Direct product of D₇ and C₇⋊C₃	42	6	D7xC7:C3	294,9
C₇⋊₃F₇	1^st semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	42	6	C7:3F7	294,11
C₇⋊₄F₇	2^nd semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	14	6	C7:4F7	294,12

Groups of order 312

		d	ρ	Label	ID
C₁₃⋊₂C₂₄	The semidirect product of C₁₃ and C₂₄ acting via C₂₄/C₄=C₆	104	6	C13:2C24	312,1
C₄×C₁₃⋊C₆	Direct product of C₄ and C₁₃⋊C₆	52	6	C4xC13:C6	312,9
D₂₆⋊C₆	2^nd semidirect product of D₂₆ and C₆ acting faithfully	52	6	D26:C6	312,12
D₄×C₁₃⋊C₃	Direct product of D₄ and C₁₃⋊C₃	52	6	D4xC13:C3	312,23
Q₈×C₁₃⋊C₃	Direct product of Q₈ and C₁₃⋊C₃	104	6	Q8xC13:C3	312,24
C₂₆.A₄	The non-split extension by C₂₆ of A₄ acting via A₄/C₂²=C₃	104	6	C26.A4	312,26

Groups of order 324

		d	ρ	Label	ID
C₃²⋊C₃₆	The semidirect product of C₃² and C₃₆ acting via C₃₆/C₆=C₆	36	6	C3^2:C36	324,7
C₉⋊C₃₆	The semidirect product of C₉ and C₃₆ acting via C₃₆/C₆=C₆	36	6	C9:C36	324,9
C₃²⋊₂Dic₉	2^nd semidirect product of C₃² and Dic₉ acting via Dic₉/C₆=S₃	36	6	C3^2:2Dic9	324,20
C₂×C₃²⋊C₁₈	Direct product of C₂ and C₃²⋊C₁₈	36	6	C2xC3^2:C18	324,62
C₂×C₉⋊C₁₈	Direct product of C₂ and C₉⋊C₁₈	36	6	C2xC9:C18	324,64
C₂×C₃²⋊₂D₉	Direct product of C₂ and C₃²⋊₂D₉	36	6	C2xC3^2:2D9	324,75
C₃×C₃²⋊C₁₂	Direct product of C₃ and C₃²⋊C₁₂	36	6	C3xC3^2:C12	324,92
Dic₃×He₃	Direct product of Dic₃ and He₃	36	6	Dic3xHe3	324,93
C₃×C₉⋊C₁₂	Direct product of C₃ and C₉⋊C₁₂	36	6	C3xC9:C12	324,94
Dic₃×3_-¹⁺²	Direct product of Dic₃ and 3_-¹⁺²	36	6	Dic3xES-(3,1)	324,95
He₃⋊₆Dic₃	2^nd semidirect product of He₃ and Dic₃ acting via Dic₃/C₆=C₂	36	6	He3:6Dic3	324,104
He₃⋊₄Dic₃	The semidirect product of He₃ and Dic₃ acting via Dic₃/C₃=C₄	18	6	He3:4Dic3	324,113
C₃×C₃²⋊D₆	Direct product of C₃ and C₃²⋊D₆	18	6	C3xC3^2:D6	324,117
S₃×He₃⋊C₂	Direct product of S₃ and He₃⋊C₂	18	6	S3xHe3:C2	324,122
C₆×C₃²⋊C₆	Direct product of C₆ and C₃²⋊C₆	36	6	C6xC3^2:C6	324,138
C₂×S₃×He₃	Direct product of C₂, S₃ and He₃	36	6	C2xS3xHe3	324,139
C₆×C₉⋊C₆	Direct product of C₆ and C₉⋊C₆	36	6	C6xC9:C6	324,140
C₂×S₃×3_-¹⁺²	Direct product of C₂, S₃ and 3_-¹⁺²	36	6	C2xS3xES-(3,1)	324,141
C₂×He₃⋊₅S₃	Direct product of C₂ and He₃⋊₅S₃	36	6	C2xHe3:5S3	324,150

Groups of order 336

		d	ρ	Label	ID
C₇⋊C₄₈	The semidirect product of C₇ and C₄₈ acting via C₄₈/C₈=C₆	112	6	C7:C48	336,1
C₈×F₇	Direct product of C₈ and F₇	56	6	C8xF7	336,7
C₈⋊F₇	3^rd semidirect product of C₈ and F₇ acting via F₇/C₇⋊C₃=C₂	56	6	C8:F7	336,8
C₅₆⋊C₆	2^nd semidirect product of C₅₆ and C₆ acting faithfully	56	6	C56:C6	336,9
C₂₈.C₁₂	1^st non-split extension by C₂₈ of C₁₂ acting via C₁₂/C₂=C₆	56	6	C28.C12	336,13
M₄(2)×C₇⋊C₃	Direct product of M₄(2) and C₇⋊C₃	56	6	M4(2)xC7:C3	336,52
D₈×C₇⋊C₃	Direct product of D₈ and C₇⋊C₃	56	6	D8xC7:C3	336,53
SD₁₆×C₇⋊C₃	Direct product of SD₁₆ and C₇⋊C₃	56	6	SD16xC7:C3	336,54
Q₁₆×C₇⋊C₃	Direct product of Q₁₆ and C₇⋊C₃	112	6	Q16xC7:C3	336,55
D₂₈⋊₆C₆	2^nd semidirect product of D₂₈ and C₆ acting via C₆/C₂=C₃	56	6	D28:6C6	336,124
C₄○D₄×C₇⋊C₃	Direct product of C₄○D₄ and C₇⋊C₃	56	6	C4oD4xC7:C3	336,167
C₂₈.A₄	The non-split extension by C₂₈ of A₄ acting via A₄/C₂²=C₃	112	6	C28.A4	336,173

Groups of order 342

		d	ρ	Label	ID
C₅₇.C₆	The non-split extension by C₅₇ of C₆ acting faithfully	171	6	C57.C6	342,1
C₃×C₁₉⋊C₆	Direct product of C₃ and C₁₉⋊C₆	57	6	C3xC19:C6	342,9
S₃×C₁₉⋊C₃	Direct product of S₃ and C₁₉⋊C₃	57	6	S3xC19:C3	342,10

Groups of order 360

		d	ρ	Label	ID
C₅×C₃.S₄	Direct product of C₅ and C₃.S₄	90	6	C5xC3.S4	360,40
D₅×C₃.A₄	Direct product of D₅ and C₃.A₄	90	6	D5xC3.A4	360,42
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	15	6	GammaL(2,4)	360,120
C₃×C₅⋊S₄	Direct product of C₃ and C₅⋊S₄	60	6	C3xC5:S4	360,139
C₅×C₃⋊S₄	Direct product of C₅ and C₃⋊S₄	60	6	C5xC3:S4	360,140
C₃×D₅×A₄	Direct product of C₃, D₅ and A₄	60	6	C3xD5xA4	360,142
C₅×S₃×A₄	Direct product of C₅, S₃ and A₄	60	6	C5xS3xA4	360,143

Groups of order 378

		d	ρ	Label	ID
C₇⋊C₅₄	The semidirect product of C₇ and C₅₄ acting via C₅₄/C₉=C₆	189	6	C7:C54	378,1
C₉×F₇	Direct product of C₉ and F₇	63	6	C9xF7	378,7
C₉⋊₃F₇	1^st semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:3F7	378,8
C₉⋊₄F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:4F7	378,9
C₃².F₇	The non-split extension by C₃² of F₇ acting via F₇/D₇=C₃	63	6	C3^2.F7	378,11
D₇⋊He₃	The semidirect product of D₇ and He₃ acting via He₃/C₃²=C₃	63	6	D7:He3	378,12
C₆₃⋊C₆	5^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:C6	378,13
C₆₃⋊₆C₆	6^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:6C6	378,14
D₉×C₇⋊C₃	Direct product of D₉ and C₇⋊C₃	63	6	D9xC7:C3	378,15
S₃×C₇⋊C₉	Direct product of S₃ and C₇⋊C₉	126	6	S3xC7:C9	378,16
C₇⋊He₃⋊C₂	3^rd semidirect product of C₇⋊He₃ and C₂ acting faithfully	63	6	C7:He3:C2	378,17
D₂₁⋊C₉	The semidirect product of D₂₁ and C₉ acting via C₉/C₃=C₃	126	6	D21:C9	378,21
D₇×He₃	Direct product of D₇ and He₃	63	6	D7xHe3	378,30
D₇×3_-¹⁺²	Direct product of D₇ and 3_-¹⁺²	63	6	D7xES-(3,1)	378,31
C₇×C₃²⋊C₆	Direct product of C₇ and C₃²⋊C₆	63	6	C7xC3^2:C6	378,34
C₇×C₉⋊C₆	Direct product of C₇ and C₉⋊C₆	63	6	C7xC9:C6	378,35
C₃²⋊D₂₁	2^nd semidirect product of C₃² and D₂₁ acting via D₂₁/C₇=S₃	63	6	C3^2:D21	378,43
C₃×S₃×C₇⋊C₃	Direct product of C₃, S₃ and C₇⋊C₃	42	6	C3xS3xC7:C3	378,48
C₃×C₃⋊F₇	Direct product of C₃ and C₃⋊F₇	42	6	C3xC3:F7	378,49

Groups of order 390

		d	ρ	Label	ID
C₅×C₁₃⋊C₆	Direct product of C₅ and C₁₃⋊C₆	65	6	C5xC13:C6	390,1
D₅×C₁₃⋊C₃	Direct product of D₅ and C₁₃⋊C₃	65	6	D5xC13:C3	390,2

Groups of order 420

		d	ρ	Label	ID
C₅×C₇⋊C₁₂	Direct product of C₅ and C₇⋊C₁₂	140	6	C5xC7:C12	420,1
Dic₅×C₇⋊C₃	Direct product of Dic₅ and C₇⋊C₃	140	6	Dic5xC7:C3	420,2
C₁₀×F₇	Direct product of C₁₀ and F₇	70	6	C10xF7	420,17
C₂×D₅×C₇⋊C₃	Direct product of C₂, D₅ and C₇⋊C₃	70	6	C2xD5xC7:C3	420,18

Groups of order 432

		d	ρ	Label	ID
He₃⋊₃C₁₆	1^st semidirect product of He₃ and C₁₆ acting via C₁₆/C₈=C₂	144	6	He3:3C16	432,30
C₉⋊C₄₈	The semidirect product of C₉ and C₄₈ acting via C₄₈/C₈=C₆	144	6	C9:C48	432,31
C₃²⋊C₆⋊C₈	The semidirect product of C₃²⋊C₆ and C₈ acting via C₈/C₄=C₂	72	6	C3^2:C6:C8	432,76
He₃⋊M₄(2)	1^st semidirect product of He₃ and M₄(2) acting via M₄(2)/C₄=C₂²	72	6	He3:M4(2)	432,77
He₃⋊₃SD₁₆	1^st semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₄=C₂²	72	6	He3:3SD16	432,78
C₁₂.₈₉S₃²	9^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	72	6	C12.89S3^2	432,81
He₃⋊₃M₄(2)	2^nd semidirect product of He₃ and M₄(2) acting via M₄(2)/C₄=C₂²	72	6	He3:3M4(2)	432,82
C₈×C₃²⋊C₆	Direct product of C₈ and C₃²⋊C₆	72	6	C8xC3^2:C6	432,115
He₃⋊₅M₄(2)	1^st semidirect product of He₃ and M₄(2) acting via M₄(2)/C₈=C₂	72	6	He3:5M4(2)	432,116
He₃⋊₆SD₁₆	1^st semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₈=C₂	72	6	He3:6SD16	432,117
C₈×C₉⋊C₆	Direct product of C₈ and C₉⋊C₆	72	6	C8xC9:C6	432,120
C₇₂⋊C₆	4^th semidirect product of C₇₂ and C₆ acting faithfully	72	6	C72:C6	432,121
C₇₂⋊₂C₆	2^nd semidirect product of C₇₂ and C₆ acting faithfully	72	6	C72:2C6	432,122
He₃⋊₇M₄(2)	1^st semidirect product of He₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	72	6	He3:7M4(2)	432,137
C₃₆.C₁₂	1^st non-split extension by C₃₆ of C₁₂ acting via C₁₂/C₂=C₆	72	6	C36.C12	432,143
He₃⋊₆M₄(2)	2^nd semidirect product of He₃ and M₄(2) acting via M₄(2)/C₈=C₂	72	6	He3:6M4(2)	432,174
He₃⋊₇SD₁₆	2^nd semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₈=C₂	72	6	He3:7SD16	432,175
He₃⋊₅D₈	2^nd semidirect product of He₃ and D₈ acting via D₈/C₈=C₂	72	6	He3:5D8	432,176
He₃⋊₅Q₁₆	2^nd semidirect product of He₃ and Q₁₆ acting via Q₁₆/C₈=C₂	144	6	He3:5Q16	432,177
He₃⋊₈M₄(2)	2^nd semidirect product of He₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	72	6	He3:8M4(2)	432,185
He₃⋊₇D₈	2^nd semidirect product of He₃ and D₈ acting via D₈/D₄=C₂	72	6	He3:7D8	432,192
He₃⋊₉SD₁₆	2^nd semidirect product of He₃ and SD₁₆ acting via SD₁₆/D₄=C₂	72	6	He3:9SD16	432,193
He₃⋊₁₁SD₁₆	2^nd semidirect product of He₃ and SD₁₆ acting via SD₁₆/Q₈=C₂	72	6	He3:11SD16	432,196
He₃⋊₇Q₁₆	2^nd semidirect product of He₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	144	6	He3:7Q16	432,197
M₄(2)×He₃	Direct product of M₄(2) and He₃	72	6	M4(2)xHe3	432,213
M₄(2)×3_-¹⁺²	Direct product of M₄(2) and 3_-¹⁺²	72	6	M4(2)xES-(3,1)	432,214
D₈×He₃	Direct product of D₈ and He₃	72	6	D8xHe3	432,216
D₈×3_-¹⁺²	Direct product of D₈ and 3_-¹⁺²	72	6	D8xES-(3,1)	432,217
SD₁₆×He₃	Direct product of SD₁₆ and He₃	72	6	SD16xHe3	432,219
SD₁₆×3_-¹⁺²	Direct product of SD₁₆ and 3_-¹⁺²	72	6	SD16xES-(3,1)	432,220
Q₁₆×He₃	Direct product of Q₁₆ and He₃	144	6	Q16xHe3	432,222
Q₁₆×3_-¹⁺²	Direct product of Q₁₆ and 3_-¹⁺²	144	6	Q16xES-(3,1)	432,223
He₃⋊C₁₆	The semidirect product of He₃ and C₁₆ acting via C₁₆/C₂=C₈	144	6	He3:C16	432,233
He₃⋊₂SD₁₆	The semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₂=D₄	72	6	He3:2SD16	432,234
C₃²⋊D₆⋊C₄	The semidirect product of C₃²⋊D₆ and C₄ acting via C₄/C₂=C₂	36	6	C3^2:D6:C4	432,238
C₃×C₆.S₄	Direct product of C₃ and C₆.S₄	36	6	C3xC6.S4	432,250
C₃²⋊₂CSU₂(𝔽₃)	2^nd semidirect product of C₃² and CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/Q₈=S₃	144	6	C3^2:2CSU(2,3)	432,257
C₃²⋊₃GL₂(𝔽₃)	2^nd semidirect product of C₃² and GL₂(𝔽₃) acting via GL₂(𝔽₃)/Q₈=S₃	72	6	C3^2:3GL(2,3)	432,258
Dic₃×C₃.A₄	Direct product of Dic₃ and C₃.A₄	36	6	Dic3xC3.A4	432,271
He₃⋊₁M₄(2)	The semidirect product of He₃ and M₄(2) acting via M₄(2)/C₄=C₄	72	6	He3:1M4(2)	432,274
C₄⋊(He₃⋊C₄)	The semidirect product of C₄ and He₃⋊C₄ acting via He₃⋊C₄/He₃⋊C₂=C₂	72	6	C4:(He3:C4)	432,276
He₃⋊₄M₄(2)	The semidirect product of He₃ and M₄(2) acting via M₄(2)/C₂²=C₄	72	6	He3:4M4(2)	432,278
C₂²⋊(He₃⋊C₄)	The semidirect product of C₂² and He₃⋊C₄ acting via He₃⋊C₄/He₃⋊C₂=C₂	36	6	C2^2:(He3:C4)	432,279
C₁₂.₈₄S₃²	4^th non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	72	6	C12.84S3^2	432,296
C₁₂.₉₁S₃²	11^st non-split extension by C₁₂ of S₃² acting via S₃²/C₃⋊S₃=C₂	72	6	C12.91S3^2	432,297
C₄×C₃²⋊D₆	Direct product of C₄ and C₃²⋊D₆	36	6	C4xC3^2:D6	432,300
C₆².₉D₆	9^th non-split extension by C₆² of D₆ acting faithfully	72	6	C6^2.9D6	432,319
C₆²⋊₂D₆	2^nd semidirect product of C₆² and D₆ acting faithfully	36	6	C6^2:2D6	432,324
C₃₆.A₄	The non-split extension by C₃₆ of A₄ acting via A₄/C₂²=C₃	144	6	C36.A4	432,330
Q₈⋊C₉⋊₄C₆	3^rd semidirect product of Q₈⋊C₉ and C₆ acting via C₆/C₂=C₃	72	6	Q8:C9:4C6	432,338
C₄○D₄⋊He₃	The semidirect product of C₄○D₄ and He₃ acting via He₃/C₃²=C₃	72	6	C4oD4:He3	432,339
C₆².₃₆D₆	19^th non-split extension by C₆² of D₆ acting via D₆/C₂=S₃	72	6	C6^2.36D6	432,351
D₃₆⋊₆C₆	2^nd semidirect product of D₃₆ and C₆ acting via C₆/C₂=C₃	72	6	D36:6C6	432,355
C₆².₄₇D₆	30^th non-split extension by C₆² of D₆ acting via D₆/C₂=S₃	72	6	C6^2.47D6	432,387
D₄×He₃⋊C₂	Direct product of D₄ and He₃⋊C₂	36	6	D4xHe3:C2	432,390
C₆².₁₆D₆	16^th non-split extension by C₆² of D₆ acting faithfully	72	6	C6^2.16D6	432,391
Q₈×He₃⋊C₂	Direct product of Q₈ and He₃⋊C₂	72	6	Q8xHe3:C2	432,394
He₃⋊₅D₄⋊C₂	6^th semidirect product of He₃⋊₅D₄ and C₂ acting faithfully	72	6	He3:5D4:C2	432,395
C₄○D₄×He₃	Direct product of C₄○D₄ and He₃	72	6	C4oD4xHe3	432,410
C₄○D₄×3_-¹⁺²	Direct product of C₄○D₄ and 3_-¹⁺²	72	6	C4oD4xES-(3,1)	432,411
C₆×C₃.S₄	Direct product of C₆ and C₃.S₄	36	6	C6xC3.S4	432,534
C₂×S₃×C₃.A₄	Direct product of C₂, S₃ and C₃.A₄	36	6	C2xS3xC3.A4	432,541
C₃×C₆.₇S₄	Direct product of C₃ and C₆.₇S₄	36	6	C3xC6.7S4	432,618
C₃×Dic₃×A₄	Direct product of C₃, Dic₃ and A₄	36	6	C3xDic3xA4	432,624
C₃×S₃×S₄	Direct product of C₃, S₃ and S₄	24	6	C3xS3xS4	432,745
C₆×C₃⋊S₄	Direct product of C₆ and C₃⋊S₄	36	6	C6xC3:S4	432,761
S₃×C₆×A₄	Direct product of C₆, S₃ and A₄	36	6	S3xC6xA4	432,763

Groups of order 450

		d	ρ	Label	ID
C₅²⋊C₁₈	The semidirect product of C₅² and C₁₈ acting via C₁₈/C₃=C₆	45	6	C5^2:C18	450,12
C₃×C₅²⋊C₆	Direct product of C₃ and C₅²⋊C₆	45	6	C3xC5^2:C6	450,22
S₃×C₅²⋊C₃	Direct product of S₃ and C₅²⋊C₃	45	6	S3xC5^2:C3	450,23

Groups of order 456

		d	ρ	Label	ID
C₁₉⋊C₂₄	The semidirect product of C₁₉ and C₂₄ acting via C₂₄/C₄=C₆	152	6	C19:C24	456,1
C₄×C₁₉⋊C₆	Direct product of C₄ and C₁₉⋊C₆	76	6	C4xC19:C6	456,8
D₃₈⋊C₆	2^nd semidirect product of D₃₈ and C₆ acting faithfully	76	6	D38:C6	456,11
D₄×C₁₉⋊C₃	Direct product of D₄ and C₁₉⋊C₃	76	6	D4xC19:C3	456,20
Q₈×C₁₉⋊C₃	Direct product of Q₈ and C₁₉⋊C₃	152	6	Q8xC19:C3	456,21
C₃₈.A₄	The non-split extension by C₃₈ of A₄ acting via A₄/C₂²=C₃	152	6	C38.A4	456,23

Groups of order 462

		d	ρ	Label	ID
C₇⋊C₃×D₁₁	Direct product of C₇⋊C₃ and D₁₁	77	6	C7:C3xD11	462,1
C₁₁×F₇	Direct product of C₁₁ and F₇	77	6	C11xF7	462,2

Groups of order 468

		d	ρ	Label	ID
C₁₃⋊₂C₃₆	The semidirect product of C₁₃ and C₃₆ acting via C₃₆/C₆=C₆	468	6	C13:2C36	468,1
C₂×C₁₃⋊C₁₈	Direct product of C₂ and C₁₃⋊C₁₈	234	6	C2xC13:C18	468,8
C₃×C₂₆.C₆	Direct product of C₃ and C₂₆.C₆	156	6	C3xC26.C6	468,19
Dic₃×C₁₃⋊C₃	Direct product of Dic₃ and C₁₃⋊C₃	156	6	Dic3xC13:C3	468,20
C₆×C₁₃⋊C₆	Direct product of C₆ and C₁₃⋊C₆	78	6	C6xC13:C6	468,33
C₂×S₃×C₁₃⋊C₃	Direct product of C₂, S₃ and C₁₃⋊C₃	78	6	C2xS3xC13:C3	468,34

Groups of order 480

		d	ρ	Label	ID
C₅×C₂³.₃A₄	Direct product of C₅ and C₂³.₃A₄	60	6	C5xC2^3.3A4	480,74
C₂₀.S₄	4^th non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	120	6	C20.S4	480,259
(C₄×C₂₀)⋊C₆	1^st semidirect product of C₄×C₂₀ and C₆ acting faithfully	80	6	(C4xC20):C6	480,263
D₅×C₄²⋊C₃	Direct product of D₅ and C₄²⋊C₃	60	6	D5xC4^2:C3	480,264
A₄×C₅⋊₂C₈	Direct product of A₄ and C₅⋊₂C₈	120	6	A4xC5:2C8	480,265
(C₂²×D₅)⋊A₄	The semidirect product of C₂²×D₅ and A₄ acting faithfully	40	6	(C2^2xD5):A4	480,268
C₅×C₂⁴⋊C₆	Direct product of C₅ and C₂⁴⋊C₆	40	6	C5xC2^4:C6	480,656
C₅×C₄²⋊C₆	Direct product of C₅ and C₄²⋊C₆	80	6	C5xC4^2:C6	480,657
C₅×C₂³.A₄	Direct product of C₅ and C₂³.A₄	60	6	C5xC2^3.A4	480,658
C₄⋊S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	20	6	C4:S5	480,944
A₅⋊Q₈	The semidirect product of A₅ and Q₈ acting via Q₈/C₄=C₂	24	6	A5:Q8	480,945
Dic₅⋊₂S₄	The semidirect product of Dic₅ and S₄ acting through Inn(Dic₅)	60	6	Dic5:2S4	480,977
Dic₅⋊S₄	The semidirect product of Dic₅ and S₄ acting via S₄/A₄=C₂	60	6	Dic5:S4	480,978
D₅×A₄⋊C₄	Direct product of D₅ and A₄⋊C₄	60	6	D5xA4:C4	480,979
D₁₀⋊S₄	1^st semidirect product of D₁₀ and S₄ acting via S₄/A₄=C₂	60	6	D10:S4	480,980
C₅×A₄⋊Q₈	Direct product of C₅ and A₄⋊Q₈	120	6	C5xA4:Q8	480,1013
C₅×C₄⋊S₄	Direct product of C₅ and C₄⋊S₄	60	6	C5xC4:S4	480,1015
C₅×A₄⋊D₄	Direct product of C₅ and A₄⋊D₄	60	6	C5xA4:D4	480,1023
C₄×C₅⋊S₄	Direct product of C₄ and C₅⋊S₄	60	6	C4xC5:S4	480,1025
C₂⁴⋊₂D₁₅	1^st semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₅=S₃	60	6	C2^4:2D15	480,1034
C₄×D₅×A₄	Direct product of C₄, D₅ and A₄	60	6	C4xD5xA4	480,1036
A₄×C₅⋊D₄	Direct product of A₄ and C₅⋊D₄	60	6	A4xC5:D4	480,1045
C₅×D₄×A₄	Direct product of C₅, D₄ and A₄	60	6	C5xD4xA4	480,1127
C₅×Q₈×A₄	Direct product of C₅, Q₈ and A₄	120	6	C5xQ8xA4	480,1129
C₅×Q₈⋊A₄	Direct product of C₅ and Q₈⋊A₄	120	6	C5xQ8:A4	480,1133
C₅×C₂²⋊S₄	Direct product of C₅ and C₂²⋊S₄	40	6	C5xC2^2:S4	480,1200
C₂⁴⋊₄D₁₅	3^rd semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₅=S₃	40	6	C2^4:4D15	480,1201

Groups of order 486

		d	ρ	Label	ID
C₃.C₃≀S₃	1^st non-split extension by C₃ of C₃≀S₃ acting via C₃≀S₃/C₃≀C₃=C₂	54	6	C3.C3wrS3	486,4
C₃²⋊C₉.S₃	1^st non-split extension by C₃²⋊C₉ of S₃ acting faithfully	18	6	C3^2:C9.S3	486,5
C₃²⋊C₉⋊C₆	1^st semidirect product of C₃²⋊C₉ and C₆ acting faithfully	18	6	C3^2:C9:C6	486,6
C₃²⋊C₉⋊S₃	1^st semidirect product of C₃²⋊C₉ and S₃ acting faithfully	18	6	C3^2:C9:S3	486,7
C₃.₃C₃≀S₃	3^rd non-split extension by C₃ of C₃≀S₃ acting via C₃≀S₃/C₃≀C₃=C₂	54	6	C3.3C3wrS3	486,8
(C₃×He₃).C₆	2^nd non-split extension by C₃×He₃ of C₆ acting faithfully	54	6	(C3xHe3).C6	486,9
C₃²⋊C₉.C₆	2^nd non-split extension by C₃²⋊C₉ of C₆ acting faithfully	54	6	C3^2:C9.C6	486,10
C₃³.(C₃×S₃)	8^th non-split extension by C₃³ of C₃×S₃ acting faithfully	54	6	C3^3.(C3xS3)	486,11
C₃²⋊₂D₉.C₃	3^rd non-split extension by C₃²⋊₂D₉ of C₃ acting faithfully	54	6	C3^2:2D9.C3	486,12
C₂₇⋊₃C₁₈	The semidirect product of C₂₇ and C₁₈ acting via C₁₈/C₃=C₆	54	6	C27:3C18	486,15
C₃²⋊C₅₄	The semidirect product of C₃² and C₅₄ acting via C₅₄/C₉=C₆	54	6	C3^2:C54	486,16
C₃³⋊₁C₁₈	1^st semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C3^3:1C18	486,18
C₃³⋊₁D₉	1^st semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	18	6	C3^3:1D9	486,19
(C₃×C₉)⋊C₁₈	2^nd semidirect product of C₃×C₉ and C₁₈ acting via C₁₈/C₃=C₆	54	6	(C3xC9):C18	486,20
(C₃×C₉)⋊D₉	2^nd semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	54	6	(C3xC9):D9	486,21
C₉⋊S₃⋊₃C₉	3^rd semidirect product of C₉⋊S₃ and C₉ acting via C₉/C₃=C₃	54	6	C9:S3:3C9	486,22
(C₃×C₉)⋊₃D₉	3^rd semidirect product of C₃×C₉ and D₉ acting via D₉/C₃=S₃	54	6	(C3xC9):3D9	486,23
C₉⋊C₅₄	The semidirect product of C₉ and C₅₄ acting via C₅₄/C₉=C₆	54	6	C9:C54	486,30
C₃²⋊₂D₂₇	2^nd semidirect product of C₃² and D₂₇ acting via D₂₇/C₉=S₃	54	6	C3^2:2D27	486,51
C₉×C₃²⋊C₆	Direct product of C₉ and C₃²⋊C₆	54	6	C9xC3^2:C6	486,98
D₉×He₃	Direct product of D₉ and He₃	54	6	D9xHe3	486,99
C₉×C₉⋊C₆	Direct product of C₉ and C₉⋊C₆	54	6	C9xC9:C6	486,100
D₉×3_-¹⁺²	Direct product of D₉ and 3_-¹⁺²	54	6	D9xES-(3,1)	486,101
C₃⁴⋊C₆	1^st semidirect product of C₃⁴ and C₆ acting faithfully	18	6	C3^4:C6	486,102
C₃⁴.C₆	4^th non-split extension by C₃⁴ of C₆ acting faithfully	18	6	C3^4.C6	486,104
D₉⋊He₃	The semidirect product of D₉ and He₃ acting via He₃/C₃²=C₃	54	6	D9:He3	486,106
C₉⋊He₃⋊C₂	3^rd semidirect product of C₉⋊He₃ and C₂ acting faithfully	54	6	C9:He3:C2	486,107
D₉⋊3_-¹⁺²	The semidirect product of D₉ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	54	6	D9:ES-(3,1)	486,108
C₉²⋊₇C₆	7^th semidirect product of C₉² and C₆ acting faithfully	54	6	C9^2:7C6	486,109
C₉²⋊₈C₆	8^th semidirect product of C₉² and C₆ acting faithfully	18	6	C9^2:8C6	486,110
C₃×C₂₇⋊C₆	Direct product of C₃ and C₂₇⋊C₆	54	6	C3xC27:C6	486,113
S₃×C₂₇⋊C₃	Direct product of S₃ and C₂₇⋊C₃	54	6	S3xC27:C3	486,114
C₃×C₃³⋊C₆	Direct product of C₃ and C₃³⋊C₆	18	6	C3xC3^3:C6	486,116
S₃×C₃≀C₃	Direct product of S₃ and C₃≀C₃	18	6	S3xC3wrC3	486,117
C₃×He₃.S₃	Direct product of C₃ and He₃.S₃	54	6	C3xHe3.S3	486,119
S₃×He₃.C₃	Direct product of S₃ and He₃.C₃	54	6	S3xHe3.C3	486,120
C₃×He₃.₂S₃	Direct product of C₃ and He₃.₂S₃	54	6	C3xHe3.2S3	486,122
S₃×He₃⋊C₃	Direct product of S₃ and He₃⋊C₃	54	6	S3xHe3:C3	486,123
S₃×C₃.He₃	Direct product of S₃ and C₃.He₃	54	6	S3xC3.He3	486,124
C₉²⋊₃S₃	3^rd semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:3S3	486,139
C₉²⋊₄S₃	4^th semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:4S3	486,140
C₃⁴⋊₃S₃	3^rd semidirect product of C₃⁴ and S₃ acting faithfully	18	6	C3^4:3S3	486,145
C₃⁴.₇S₃	7^th non-split extension by C₃⁴ of S₃ acting faithfully	18	6	C3^4.7S3	486,147
(C₃²×C₉)⋊S₃	14^th semidirect product of C₃²×C₉ and S₃ acting faithfully	54	6	(C3^2xC9):S3	486,149
(C₃²×C₉)⋊₈S₃	8^th semidirect product of C₃²×C₉ and S₃ acting faithfully	54	6	(C3^2xC9):8S3	486,150
C₉⋊C₉⋊₂S₃	2^nd semidirect product of C₉⋊C₉ and S₃ acting faithfully	54	6	C9:C9:2S3	486,152
C₉²⋊₆S₃	6^th semidirect product of C₉² and S₃ acting faithfully	18	6	C9^2:6S3	486,153
C₉²⋊₅S₃	5^th semidirect product of C₉² and S₃ acting faithfully	54	6	C9^2:5S3	486,156
C₃×C₃³⋊S₃	Direct product of C₃ and C₃³⋊S₃	18	6	C3xC3^3:S3	486,165
C₃⁴⋊₅S₃	5^th semidirect product of C₃⁴ and S₃ acting faithfully	18	6	C3^4:5S3	486,166
C₃×He₃.₃S₃	Direct product of C₃ and He₃.₃S₃	54	6	C3xHe3.3S3	486,168
He₃.C₃⋊S₃	5^th semidirect product of He₃.C₃ and S₃ acting via S₃/C₃=C₂	54	6	He3.C3:S3	486,169
C₃×He₃⋊S₃	Direct product of C₃ and He₃⋊S₃	54	6	C3xHe3:S3	486,171
He₃⋊C₃⋊₂S₃	1^st semidirect product of He₃⋊C₃ and S₃ acting via S₃/C₃=C₂	54	6	He3:C3:2S3	486,172
C₃×3_-¹⁺².S₃	Direct product of C₃ and 3_-¹⁺².S₃	54	6	C3xES-(3,1).S3	486,174
He₃⋊₄D₉	2^nd semidirect product of He₃ and D₉ acting via D₉/C₉=C₂	54	6	He3:4D9	486,182
S₃×C₉○He₃	Direct product of S₃ and C₉○He₃	54	6	S3xC9oHe3	486,226
C₃×He₃.₄S₃	Direct product of C₃ and He₃.₄S₃	54	6	C3xHe3.4S3	486,234
C₉○He₃⋊₄S₃	2^nd semidirect product of C₉○He₃ and S₃ acting via S₃/C₃=C₂	54	6	C9oHe3:4S3	486,246

Orthogonal of dimension 7 (ρ=7+)

Groups of order 56

		d	ρ	Label	ID
F₈	Frobenius group; = C₂³ ⋊C₇ = AGL₁(𝔽₈)	8	7+	F8	56,11

Groups of order 112

		d	ρ	Label	ID
C₂×F₈	Direct product of C₂ and F₈	14	7+	C2xF8	112,41

Groups of order 168

		d	ρ	Label	ID
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	8	7+	AGammaL(1,8)	168,43

Groups of order 336

		d	ρ	Label	ID
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	14	7+	C2xAGammaL(1,8)	336,210

Groups of order 448

		d	ρ	Label	ID
C₂³⋊F₈	2^nd semidirect product of C₂³ and F₈ acting via F₈/C₂³=C₇	14	7+	C2^3:F8	448,1394

Complex of dimension 7 (ρ=7)

Groups of order 168

		d	ρ	Label	ID
C₃×F₈	Direct product of C₃ and F₈	24	7	C3xF8	168,44

Groups of order 203

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

Groups of order 224

		d	ρ	Label	ID
C₄×F₈	Direct product of C₄ and F₈	28	7	C4xF8	224,173

Groups of order 280

		d	ρ	Label	ID
C₅×F₈	Direct product of C₅ and F₈	40	7	C5xF8	280,33

Groups of order 301

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

Groups of order 336

		d	ρ	Label	ID
C₆×F₈	Direct product of C₆ and F₈	42	7	C6xF8	336,213

Groups of order 343

		d	ρ	Label	ID
He₇	Heisenberg group; = C₇² ⋊C₇ = 7₊¹⁺²	49	7	He7	343,3
7_-¹⁺²	Extraspecial group	49	7	ES-(7,1)	343,4

Groups of order 392

		d	ρ	Label	ID
C₇.F₈	The central extension by C₇ of F₈	98	7	C7.F8	392,11
C₇×F₈	Direct product of C₇ and F₈	56	7	C7xF8	392,39

Groups of order 406

		d	ρ	Label	ID
C₂×C₂₉⋊C₇	Direct product of C₂ and C₂₉⋊C₇	58	7	C2xC29:C7	406,2

Groups of order 448

		d	ρ	Label	ID
C₄³⋊C₇	The semidirect product of C₄³ and C₇ acting faithfully	28	7	C4^3:C7	448,178
C₈×F₈	Direct product of C₈ and F₈	56	7	C8xF8	448,919

Groups of order 497

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

Orthogonal of dimension 8 (ρ=8+)

Groups of order 72

		d	ρ	Label	ID
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	9	8+	F9	72,39
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	9	8+	PSU(3,2)	72,41

Groups of order 120

		d	ρ	Label	ID
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	15	8+	S3xF5	120,36

Groups of order 128

		d	ρ	Label	ID
C₂³.D₈	1^st non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	16	8+	C2^3.D8	128,71
C₂³.SD₁₆	1^st non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	16	8+	C2^3.SD16	128,73
C₄.C₄≀C₂	9^th non-split extension by C₄ of C₄≀C₂ acting via C₄≀C₂/C₄²=C₂	16	8+	C4.C4wrC2	128,87
C₈⋊C₄⋊C₄	1^st semidirect product of C₈⋊C₄ and C₄ acting faithfully	16	8+	C8:C4:C4	128,138
C₈⋊C₄⋊₅C₄	5^th semidirect product of C₈⋊C₄ and C₄ acting faithfully	16	8+	C8:C4:5C4	128,144
C₄○D₄.D₄	3^rd non-split extension by C₄○D₄ of D₄ acting via D₄/C₂=C₂²	16	8+	C4oD4.D4	128,527
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	16	8+	C2^4.C2^3	128,560
C₂⁴.₆(C₂×C₄)	6^th non-split extension by C₂⁴ of C₂×C₄ acting faithfully	16	8+	C2^4.6(C2xC4)	128,561
M₄(2).₄₇D₄	11^st non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	16	8+	M4(2).47D4	128,635
C₄².₅D₄	5^th non-split extension by C₄² of D₄ acting faithfully	16	8+	C4^2.5D4	128,636
(C₂×C₈)⋊₄D₄	4^th semidirect product of C₂×C₈ and D₄ acting faithfully	16	8+	(C2xC8):4D4	128,642
C₄²⋊D₄	1^st semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:D4	128,643
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	16	8+	C2^4.28D4	128,645
M₄(2)⋊₂₁D₄	8^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	16	8+	M4(2):21D4	128,646
M₄(2)⋊₅D₄	5^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	16	8+	M4(2):5D4	128,740
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	16	8+	C2^4:Q8	128,764
M₄(2).₈D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	16	8+	M4(2).8D4	128,780
C₂⁴.Q₈	The non-split extension by C₂⁴ of Q₈ acting faithfully	16	8+	C2^4.Q8	128,801
(C₂×C₈).D₄	5^th non-split extension by C₂×C₈ of D₄ acting faithfully	16	8+	(C2xC8).D4	128,813
C₂⁴.₄C₂³	4^th non-split extension by C₂⁴ of C₂³ acting faithfully	16	8+	C2^4.4C2^3	128,836
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	16	8+	C2^4.36D4	128,853
C₂≀C₄⋊C₂	6^th semidirect product of C₂≀C₄ and C₂ acting faithfully	16	8+	C2wrC4:C2	128,854
C₂⁴.₃₉D₄	39^th non-split extension by C₂⁴ of D₄ acting faithfully	16	8+	C2^4.39D4	128,859
C₄.₄D₄⋊C₄	6^th semidirect product of C₄.₄D₄ and C₄ acting faithfully	16	8+	C4.4D4:C4	128,860
C₄⋊₁D₄.C₄	5^th non-split extension by C₄⋊₁D₄ of C₄ acting faithfully	16	8+	C4:1D4.C4	128,866
D₁₆⋊C₄	The semidirect product of D₁₆ and C₄ acting faithfully; = Aut(D₁₆) = Hol(C₁₆)	16	8+	D16:C4	128,913
D₈⋊D₄	The semidirect product of D₈ and D₄ acting via D₄/C₂=C₂²	16	8+	D8:D4	128,922
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:5D4	128,931
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	16	8+	C4^2:6D4	128,932
C₄².₁₅D₄	15^th non-split extension by C₄² of D₄ acting faithfully	16	8+	C4^2.15D4	128,934
M₅(2).C₂²	8^th non-split extension by M₅(2) of C₂² acting faithfully	16	8+	M5(2).C2^2	128,970
C₂³.C₂⁴	3^rd non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	16	8+	C2^3.C2^4	128,1615
M₄(2).₂₄C₂³	6^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	16	8+	M4(2).24C2^3	128,1620
M₄(2)⋊C₂³	3^rd semidirect product of M₄(2) and C₂³ acting via C₂³/C₂=C₂²	16	8+	M4(2):C2^3	128,1751
C₄².₁₂C₂³	12^nd non-split extension by C₄² of C₂³ acting faithfully	16	8+	C4^2.12C2^3	128,1753
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	16	8+	C2^4:C2^3	128,1758
C₂³.₉C₂⁴	9^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	16	8+	C2^3.9C2^4	128,1759
M₄(2).₃₇D₄	1^st non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	16	8+	M4(2).37D4	128,1800
D₈⋊₁₁D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	16	8+	D8:11D4	128,2020
D₈⋊C₂³	6^th semidirect product of D₈ and C₂³ acting via C₂³/C₂²=C₂	16	8+	D8:C2^3	128,2317
2₊¹⁺⁶	Extraspecial group; = D₄ ○2₊¹⁺⁴	16	8+	ES+(2,3)	128,2326

Groups of order 136

		d	ρ	Label	ID
C₁₇⋊C₈	The semidirect product of C₁₇ and C₈ acting faithfully	17	8+	C17:C8	136,12

Groups of order 144

		d	ρ	Label	ID
C₂.PSU₃(𝔽₂)	The central extension by C₂ of PSU₃(𝔽₂)	24	8+	C2.PSU(3,2)	144,120
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	9	8+	AGammaL(1,9)	144,182
C₂×F₉	Direct product of C₂ and F₉	18	8+	C2xF9	144,185
C₂×PSU₃(𝔽₂)	Direct product of C₂ and PSU₃(𝔽₂)	18	8+	C2xPSU(3,2)	144,187

Groups of order 160

		d	ρ	Label	ID
D₂₀⋊C₄	1^st semidirect product of D₂₀ and C₄ acting faithfully	40	8+	D20:C4	160,82
Q₈⋊₂F₅	2^nd semidirect product of Q₈ and F₅ acting via F₅/D₅=C₂	40	8+	Q8:2F5	160,85
D₄×F₅	Direct product of D₄ and F₅; = Aut(D₂₀) = Hol(C₂₀)	20	8+	D4xF5	160,207
Q₈.F₅	The non-split extension by Q₈ of F₅ acting through Inn(Q₈)	80	8+	Q8.F5	160,208

Groups of order 192

		d	ρ	Label	ID
C₃⋊C₂≀C₄	The semidirect product of C₃ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	24	8+	C3:C2wrC4	192,30
C₂³.₂D₁₂	2^nd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3.2D12	192,33
C₂³.₃D₁₂	3^rd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3.3D12	192,34
(C₂×C₄).D₁₂	3^rd non-split extension by C₂×C₄ of D₁₂ acting via D₁₂/C₃=D₄	48	8+	(C2xC4).D12	192,36
C₂³⋊D₁₂	The semidirect product of C₂³ and D₁₂ acting via D₁₂/C₃=D₄	24	8+	C2^3:D12	192,300
S₃×C₂³⋊C₄	Direct product of S₃ and C₂³⋊C₄	24	8+	S3xC2^3:C4	192,302
S₃×C₄.D₄	Direct product of S₃ and C₄.D₄	24	8+	S3xC4.D4	192,303
D₁₂⋊₁D₄	1^st semidirect product of D₁₂ and D₄ acting via D₄/C₂=C₂²	24	8+	D12:1D4	192,306
D₁₂.₃D₄	3^rd non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8+	D12.3D4	192,308
M₄(2).₂₁D₆	4^th non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	8+	M4(2).21D6	192,310
D₁₂.₅D₄	5^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8+	D12.5D4	192,312
D₁₂.₆D₄	6^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8+	D12.6D4	192,313
D₁₂⋊₁₈D₄	6^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	24	8+	D12:18D4	192,757
M₄(2).D₆	12^nd non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	48	8+	M4(2).D6	192,758
D₁₂.₃₉D₄	9^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48	8+	D12.39D4	192,761
M₄(2).₁₅D₆	15^th non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	48	8+	M4(2).15D6	192,762
2₊¹⁺⁴⋊₆S₃	1^st semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	24	8+	ES+(2,2):6S3	192,800
2₊¹⁺⁴⋊₇S₃	2^nd semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	24	8+	ES+(2,2):7S3	192,803
2_-¹⁺⁴⋊₄S₃	1^st semidirect product of 2_-¹⁺⁴ and S₃ acting via S₃/C₃=C₂	48	8+	ES-(2,2):4S3	192,804
S₃×C₈⋊C₂²	Direct product of S₃ and C₈⋊C₂²; = Aut(D₂₄) = Hol(C₂₄)	24	8+	S3xC8:C2^2	192,1331
D₈⋊₅D₆	5^th semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	8+	D8:5D6	192,1333
D₂₄⋊C₂²	3^rd semidirect product of D₂₄ and C₂² acting faithfully	48	8+	D24:C2^2	192,1336
C₂₄.C₂³	6^th non-split extension by C₂₄ of C₂³ acting faithfully	48	8+	C24.C2^3	192,1337
D₁₂.₃₂C₂³	13^rd non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8+	D12.32C2^3	192,1394
D₁₂.₃₄C₂³	15^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8+	D12.34C2^3	192,1396
S₃×2₊¹⁺⁴	Direct product of S₃ and 2₊¹⁺⁴	24	8+	S3xES+(2,2)	192,1524
D₁₂.₃₉C₂³	20^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8+	D12.39C2^3	192,1527

Groups of order 200

		d	ρ	Label	ID
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	10	8+	C5^2:C8	200,40
D₅×F₅	Direct product of D₅ and F₅	20	8+	D5xF5	200,41
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	10	8+	D5:F5	200,42
C₅²⋊Q₈	The semidirect product of C₅² and Q₈ acting faithfully	10	8+	C5^2:Q8	200,44

Groups of order 216

		d	ρ	Label	ID
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	9	8+	ASL(2,3)	216,153
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	12	8+	S3xC3^2:C4	216,156
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	12	8+	C3^2:2D12	216,159
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	12	8+	S3^3	216,162

Groups of order 240

		d	ρ	Label	ID
D₆⋊F₅	The semidirect product of D₆ and F₅ acting via F₅/D₅=C₂	60	8+	D6:F5	240,96
D₁₅⋊C₈	The semidirect product of D₁₅ and C₈ acting via C₈/C₂=C₄	120	8+	D15:C8	240,99
Dic₃.F₅	The non-split extension by Dic₃ of F₅ acting via F₅/D₅=C₂	120	8+	Dic3.F5	240,101
C₂×S₃×F₅	Direct product of C₂, S₃ and F₅; = Aut(D₃₀) = Hol(C₃₀)	30	8+	C2xS3xF5	240,195

Groups of order 272

		d	ρ	Label	ID
C₂×C₁₇⋊C₈	Direct product of C₂ and C₁₇⋊C₈	34	8+	C2xC17:C8	272,51

Groups of order 280

		d	ρ	Label	ID
D₇×F₅	Direct product of D₇ and F₅	35	8+	D7xF5	280,32

Groups of order 288

		d	ρ	Label	ID
C₃²⋊D₁₆	The semidirect product of C₃² and D₁₆ acting via D₁₆/C₄=D₄	48	8+	C3^2:D16	288,382
C₃²⋊SD₃₂	The semidirect product of C₃² and SD₃₂ acting via SD₃₂/C₄=D₄	48	8+	C3^2:SD32	288,383
C₃⋊S₃.₅D₈	The non-split extension by C₃⋊S₃ of D₈ acting via D₈/D₄=C₂	24	8+	C3:S3.5D8	288,430
C₃²⋊₇C₄≀C₂	The semidirect product of C₃² and C₄≀C₂ acting via C₄≀C₂/Q₈=C₄	48	8+	C3^2:7C4wrC2	288,433
S₃×D₄⋊S₃	Direct product of S₃ and D₄⋊S₃	48	8+	S3xD4:S3	288,572
Dic₆⋊₃D₆	3^rd semidirect product of Dic₆ and D₆ acting via D₆/C₃=C₂²	48	8+	Dic6:3D6	288,573
D₁₂⋊D₆	4^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	24	8+	D12:D6	288,574
Dic₆⋊D₆	4^th semidirect product of Dic₆ and D₆ acting via D₆/C₃=C₂²	24	8+	Dic6:D6	288,578
D₁₂.₇D₆	7^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.7D6	288,582
Dic₆.₂₀D₆	7^th non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8+	Dic6.20D6	288,583
D₁₂⋊₅D₆	5^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	24	8+	D12:5D6	288,585
S₃×Q₈⋊₂S₃	Direct product of S₃ and Q₈⋊₂S₃	48	8+	S3xQ8:2S3	288,586
D₁₂⋊₆D₆	6^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	48	8+	D12:6D6	288,587
D₁₂.₁₀D₆	10^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.10D6	288,589
Dic₆.₁₀D₆	10^th non-split extension by Dic₆ of D₆ acting via D₆/C₃=C₂²	48	8+	Dic6.10D6	288,593
Dic₆.₂₂D₆	9^th non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8+	Dic6.22D6	288,596
D₁₂.₁₃D₆	13^rd non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.13D6	288,597
D₁₂.₁₄D₆	14^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8+	D12.14D6	288,598
C₂.AΓL₁(𝔽₉)	1^st central extension by C₂ of AΓL₁(𝔽₉)	24	8+	C2.AGammaL(1,9)	288,841
C₂²⋊F₉	The semidirect product of C₂² and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8+	C2^2:F9	288,867
C₄.₄S₃≀C₂	4^th non-split extension by C₄ of S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	24	8+	C4.4S3wrC2	288,869
C₃⋊S₃⋊D₈	The semidirect product of C₃⋊S₃ and D₈ acting via D₈/C₄=C₂²	24	8+	C3:S3:D8	288,873
C₃⋊S₃⋊₂SD₁₆	The semidirect product of C₃⋊S₃ and SD₁₆ acting via SD₁₆/C₄=C₂²	24	8+	C3:S3:2SD16	288,875
C₄⋊S₃≀C₂	The semidirect product of C₄ and S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	24	8+	C4:S3wrC2	288,879
C₆²⋊D₄	2^nd semidirect product of C₆² and D₄ acting faithfully	24	8+	C6^2:D4	288,890
C₆²⋊Q₈	1^st semidirect product of C₆² and Q₈ acting faithfully	24	8+	C6^2:Q8	288,895
D₄×C₃²⋊C₄	Direct product of D₄ and C₃²⋊C₄	24	8+	D4xC3^2:C4	288,936
C₁₂⋊S₃.C₄	The non-split extension by C₁₂⋊S₃ of C₄ acting faithfully	48	8+	C12:S3.C4	288,937
S₃²×D₄	Direct product of S₃, S₃ and D₄	24	8+	S3^2xD4	288,958
Dic₆⋊₁₂D₆	6^th semidirect product of Dic₆ and D₆ acting via D₆/S₃=C₂	24	8+	Dic6:12D6	288,960
D₁₂⋊₁₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	24	8+	D12:13D6	288,962
Dic₆.₂₆D₆	13^rd non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8+	Dic6.26D6	288,964
S₃×Q₈⋊₃S₃	Direct product of S₃ and Q₈⋊₃S₃	48	8+	S3xQ8:3S3	288,966
D₁₂⋊₁₆D₆	10^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8+	D12:16D6	288,968
C₂×AΓL₁(𝔽₉)	Direct product of C₂ and AΓL₁(𝔽₉)	18	8+	C2xAGammaL(1,9)	288,1027

Groups of order 312

		d	ρ	Label	ID
S₃×C₁₃⋊C₄	Direct product of S₃ and C₁₃⋊C₄	39	8+	S3xC13:C4	312,46

Groups of order 320

		d	ρ	Label	ID
C₅⋊₃C₂≀C₄	The semidirect product of C₅ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	40	8+	C5:3C2wrC4	320,29
C₂³.₂D₂₀	2^nd non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3.2D20	320,32
C₂³.₃D₂₀	3^rd non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3.3D20	320,33
(C₂×C₄).D₂₀	3^rd non-split extension by C₂×C₄ of D₂₀ acting via D₂₀/C₅=D₄	80	8+	(C2xC4).D20	320,35
C₅⋊C₂≀C₄	The semidirect product of C₅ and C₂≀C₄ acting via C₂≀C₄/C₂²⋊C₄=C₄	40	8+	C5:C2wrC4	320,202
(C₂²×F₅)⋊C₄	The semidirect product of C₂²×F₅ and C₄ acting faithfully	40	8+	(C2^2xF5):C4	320,204
D₅.D₁₆	The non-split extension by D₅ of D₁₆ acting via D₁₆/D₈=C₂	80	8+	D5.D16	320,242
D₄₀.C₄	1^st non-split extension by D₄₀ of C₄ acting faithfully	80	8+	D40.C4	320,244
D₄₀⋊₁C₄	1^st semidirect product of D₄₀ and C₄ acting faithfully	80	8+	D40:1C4	320,245
Q₁₆.F₅	1^st non-split extension by Q₁₆ of F₅ acting via F₅/D₅=C₂	160	8+	Q16.F5	320,247
(C₂×D₄)⋊F₅	2^nd semidirect product of C₂×D₄ and F₅ acting via F₅/C₅=C₄	40	8+	(C2xD4):F5	320,260
(C₂×Q₈)⋊F₅	2^nd semidirect product of C₂×Q₈ and F₅ acting via F₅/C₅=C₄	80	8+	(C2xQ8):F5	320,266
C₂³⋊D₂₀	The semidirect product of C₂³ and D₂₀ acting via D₂₀/C₅=D₄	40	8+	C2^3:D20	320,368
D₅×C₂³⋊C₄	Direct product of D₅ and C₂³⋊C₄	40	8+	D5xC2^3:C4	320,370
D₅×C₄.D₄	Direct product of D₅ and C₄.D₄	40	8+	D5xC4.D4	320,371
D₂₀⋊₁D₄	1^st semidirect product of D₂₀ and D₄ acting via D₄/C₂=C₂²	40	8+	D20:1D4	320,374
D₂₀.₃D₄	3^rd non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	8+	D20.3D4	320,376
M₄(2).₂₁D₁₀	4^th non-split extension by M₄(2) of D₁₀ acting via D₁₀/D₅=C₂	80	8+	M4(2).21D10	320,378
D₂₀.₅D₄	5^th non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	8+	D20.5D4	320,380
D₂₀.₆D₄	6^th non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	8+	D20.6D4	320,381
D₂₀⋊₁₈D₄	6^th semidirect product of D₂₀ and D₄ acting via D₄/C₂²=C₂	40	8+	D20:18D4	320,825
M₄(2).D₁₀	12^nd non-split extension by M₄(2) of D₁₀ acting via D₁₀/C₅=C₂²	80	8+	M4(2).D10	320,826
D₂₀.₃₉D₄	9^th non-split extension by D₂₀ of D₄ acting via D₄/C₂²=C₂	80	8+	D20.39D4	320,829
M₄(2).₁₅D₁₀	15^th non-split extension by M₄(2) of D₁₀ acting via D₁₀/C₅=C₂²	80	8+	M4(2).15D10	320,830
2₊¹⁺⁴⋊D₅	1^st semidirect product of 2₊¹⁺⁴ and D₅ acting via D₅/C₅=C₂	40	8+	ES+(2,2):D5	320,868
2₊¹⁺⁴⋊₂D₅	2^nd semidirect product of 2₊¹⁺⁴ and D₅ acting via D₅/C₅=C₂	40	8+	ES+(2,2):2D5	320,871
2_-¹⁺⁴⋊₂D₅	1^st semidirect product of 2_-¹⁺⁴ and D₅ acting via D₅/C₅=C₂	80	8+	ES-(2,2):2D5	320,872
D₈×F₅	Direct product of D₈ and F₅	40	8+	D8xF5	320,1068
D₄₀⋊C₄	2^nd semidirect product of D₄₀ and C₄ acting faithfully	40	8+	D40:C4	320,1069
Q₁₆⋊₅F₅	The semidirect product of Q₁₆ and F₅ acting through Inn(Q₁₆)	80	8+	Q16:5F5	320,1078
Q₁₆⋊F₅	4^th semidirect product of Q₁₆ and F₅ acting via F₅/D₅=C₂	80	8+	Q16:F5	320,1079
(D₄×C₁₀)⋊C₄	6^th semidirect product of D₄×C₁₀ and C₄ acting faithfully	40	8+	(D4xC10):C4	320,1105
(C₂×D₄)⋊₇F₅	5^th semidirect product of C₂×D₄ and F₅ acting via F₅/D₅=C₂	40	8+	(C2xD4):7F5	320,1108
D₅⋊(C₄.D₄)	The semidirect product of D₅ and C₄.D₄ acting via C₄.D₄/C₂×D₄=C₂	40	8+	D5:(C4.D4)	320,1116
(C₂×Q₈)⋊₆F₅	4^th semidirect product of C₂×Q₈ and F₅ acting via F₅/D₅=C₂	80	8+	(C2xQ8):6F5	320,1122
(C₂×Q₈)⋊₇F₅	5^th semidirect product of C₂×Q₈ and F₅ acting via F₅/D₅=C₂	80	8+	(C2xQ8):7F5	320,1123
D₅×C₈⋊C₂²	Direct product of D₅ and C₈⋊C₂²	40	8+	D5xC8:C2^2	320,1444
D₈⋊₅D₁₀	5^th semidirect product of D₈ and D₁₀ acting via D₁₀/D₅=C₂	80	8+	D8:5D10	320,1446
D₄₀⋊C₂²	3^rd semidirect product of D₄₀ and C₂² acting faithfully	80	8+	D40:C2^2	320,1449
C₄₀.C₂³	6^th non-split extension by C₄₀ of C₂³ acting faithfully	80	8+	C40.C2^3	320,1450
D₂₀.₃₂C₂³	13^rd non-split extension by D₂₀ of C₂³ acting via C₂³/C₂²=C₂	80	8+	D20.32C2^3	320,1507
D₂₀.₃₄C₂³	15^th non-split extension by D₂₀ of C₂³ acting via C₂³/C₂²=C₂	80	8+	D20.34C2^3	320,1509
D₁₀.C₂⁴	15^th non-split extension by D₁₀ of C₂⁴ acting via C₂⁴/C₂³=C₂	40	8+	D10.C2^4	320,1596
Dic₅.₂₀C₂⁴	20^th non-split extension by Dic₅ of C₂⁴ acting via C₂⁴/C₂³=C₂	80	8+	Dic5.20C2^4	320,1598
D₅×2₊¹⁺⁴	Direct product of D₅ and 2₊¹⁺⁴	40	8+	D5xES+(2,2)	320,1622
D₂₀.₃₉C₂³	20^th non-split extension by D₂₀ of C₂³ acting via C₂³/C₂²=C₂	80	8+	D20.39C2^3	320,1625

Groups of order 328

		d	ρ	Label	ID
C₄₁⋊C₈	The semidirect product of C₄₁ and C₈ acting faithfully	41	8+	C41:C8	328,12

Groups of order 360

		d	ρ	Label	ID
D₉×F₅	Direct product of D₉ and F₅	45	8+	D9xF5	360,39
C₃⋊F₅⋊S₃	The semidirect product of C₃⋊F₅ and S₃ acting via S₃/C₃=C₂	30	8+	C3:F5:S3	360,129
D₅×C₃²⋊C₄	Direct product of D₅ and C₃²⋊C₄	30	8+	D5xC3^2:C4	360,130
C₃²⋊F₅⋊C₂	The semidirect product of C₃²⋊F₅ and C₂ acting faithfully	30	8+	C3^2:F5:C2	360,131
C₃²⋊D₂₀	The semidirect product of C₃² and D₂₀ acting via D₂₀/C₅=D₄	30	8+	C3^2:D20	360,134
S₃²×D₅	Direct product of S₃, S₃ and D₅	30	8+	S3^2xD5	360,137

Groups of order 392

		d	ρ	Label	ID
C₇²⋊C₈	The semidirect product of C₇² and C₈ acting faithfully	28	8+	C7^2:C8	392,36
C₇²⋊Q₈	The semidirect product of C₇² and Q₈ acting faithfully	28	8+	C7^2:Q8	392,38

Groups of order 400

		d	ρ	Label	ID
D₅.D₂₀	The non-split extension by D₅ of D₂₀ acting via D₂₀/D₁₀=C₂	40	8+	D5.D20	400,118
Dic₅.₄F₅	The non-split extension by Dic₅ of F₅ acting through Inn(Dic₅)	40	8+	Dic5.4F5	400,121
Dic₅.F₅	1^st non-split extension by Dic₅ of F₅ acting via F₅/D₅=C₂	40	8+	Dic5.F5	400,123
C₅²⋊₃C₄²	2^nd semidirect product of C₅² and C₄² acting via C₄²/C₂=C₂×C₄	20	8+	C5^2:3C4^2	400,124
D₁₀⋊F₅	2^nd semidirect product of D₁₀ and F₅ acting via F₅/D₅=C₂	20	8+	D10:F5	400,125
Dic₅⋊F₅	3^rd semidirect product of Dic₅ and F₅ acting via F₅/D₅=C₂	20	8+	Dic5:F5	400,126
(C₅×C₁₀).Q₈	The non-split extension by C₅×C₁₀ of Q₈ acting faithfully	20	8+	(C5xC10).Q8	400,134
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	10	8+	C5^2:M4(2)	400,206
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	10	8+	D5wrC2:C2	400,207
C₂×C₅²⋊C₈	Direct product of C₂ and C₅²⋊C₈	20	8+	C2xC5^2:C8	400,208
C₂×D₅×F₅	Direct product of C₂, D₅ and F₅	40	8+	C2xD5xF5	400,209
C₂×D₅⋊F₅	Direct product of C₂ and D₅⋊F₅	20	8+	C2xD5:F5	400,210
C₂×C₅²⋊Q₈	Direct product of C₂ and C₅²⋊Q₈	20	8+	C2xC5^2:Q8	400,212

Groups of order 408

		d	ρ	Label	ID
S₃×C₁₇⋊C₄	Direct product of S₃ and C₁₇⋊C₄	51	8+	S3xC17:C4	408,35

Groups of order 416

		d	ρ	Label	ID
D₅₂⋊₁C₄	1^st semidirect product of D₅₂ and C₄ acting faithfully	104	8+	D52:1C4	416,82
D₅₂⋊C₄	2^nd semidirect product of D₅₂ and C₄ acting faithfully	104	8+	D52:C4	416,85
D₄×C₁₃⋊C₄	Direct product of D₄ and C₁₃⋊C₄	52	8+	D4xC13:C4	416,206
D₅₂.C₄	The non-split extension by D₅₂ of C₄ acting faithfully	208	8+	D52.C4	416,207

Groups of order 432

		d	ρ	Label	ID
D₆⋊(C₃²⋊C₄)	The semidirect product of D₆ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	24	8+	D6:(C3^2:C4)	432,568
C₃³⋊₅(C₂×C₈)	2^nd semidirect product of C₃³ and C₂×C₈ acting via C₂×C₈/C₂=C₂×C₄	24	8+	C3^3:5(C2xC8)	432,571
C₃³⋊₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	24	8+	C3^3:2M4(2)	432,573
(C₃×C₆).₈D₁₂	1^st non-split extension by C₃×C₆ of D₁₂ acting via D₁₂/C₃=D₄	24	8+	(C3xC6).8D12	432,586
C₃²⋊₂D₂₄	The semidirect product of C₃² and D₂₄ acting via D₂₄/C₆=D₄	24	8+	C3^2:2D24	432,588
C₃³⋊₈SD₁₆	4^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	24	8+	C3^3:8SD16	432,589
S₃×C₆.D₆	Direct product of S₃ and C₆.D₆	24	8+	S3xC6.D6	432,595
S₃×C₃⋊D₁₂	Direct product of S₃ and C₃⋊D₁₂	24	8+	S3xC3:D12	432,598
D₆⋊₄S₃²	1^st semidirect product of D₆ and S₃² acting via S₃²/C₃⋊S₃=C₂	24	8+	D6:4S3^2	432,599
(S₃×C₆)⋊D₆	1^st semidirect product of S₃×C₆ and D₆ acting via D₆/C₃=C₂²	24	8+	(S3xC6):D6	432,601
C₃⋊S₃⋊₄D₁₂	The semidirect product of C₃⋊S₃ and D₁₂ acting via D₁₂/D₆=C₂	24	8+	C3:S3:4D12	432,602
C₃³⋊₆(C₂×Q₈)	3^rd semidirect product of C₃³ and C₂×Q₈ acting via C₂×Q₈/C₂=C₂³	24	8+	C3^3:6(C2xQ8)	432,605
(S₃×C₆).D₆	9^th non-split extension by S₃×C₆ of D₆ acting via D₆/C₃=C₂²	24	8+	(S3xC6).D6	432,606
D₆.₃S₃²	3^rd non-split extension by D₆ of S₃² acting via S₃²/C₃×S₃=C₂	24	8+	D6.3S3^2	432,609
Dic₃.S₃²	4^th non-split extension by Dic₃ of S₃² acting via S₃²/C₃×S₃=C₂	24	8+	Dic3.S3^2	432,612
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	9	8+	AGL(2,3)	432,734
C₂×ASL₂(𝔽₃)	Direct product of C₂ and ASL₂(𝔽₃)	18	8+	C2xASL(2,3)	432,735
S₃×S₃≀C₂	Direct product of S₃ and S₃≀C₂	12	8+	S3xS3wrC2	432,741
C₂×S₃×C₃²⋊C₄	Direct product of C₂, S₃ and C₃²⋊C₄	24	8+	C2xS3xC3^2:C4	432,753
C₂×C₃²⋊₂D₁₂	Direct product of C₂ and C₃²⋊₂D₁₂	24	8+	C2xC3^2:2D12	432,756
C₂×S₃³	Direct product of C₂, S₃, S₃ and S₃	24	8+	C2xS3^3	432,759

Groups of order 440

		d	ρ	Label	ID
F₅×D₁₁	Direct product of F₅ and D₁₁	55	8+	F5xD11	440,43

Groups of order 448

		d	ρ	Label	ID
C₇⋊C₂≀C₄	The semidirect product of C₇ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	56	8+	C7:C2wrC4	448,28
C₂³.₂D₂₈	2^nd non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3.2D28	448,31
C₂³.₃D₂₈	3^rd non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3.3D28	448,32
(C₂×C₄).D₂₈	3^rd non-split extension by C₂×C₄ of D₂₈ acting via D₂₈/C₇=D₄	112	8+	(C2xC4).D28	448,34
C₂³⋊D₂₈	The semidirect product of C₂³ and D₂₈ acting via D₂₈/C₇=D₄	56	8+	C2^3:D28	448,275
D₇×C₂³⋊C₄	Direct product of D₇ and C₂³⋊C₄	56	8+	D7xC2^3:C4	448,277
D₇×C₄.D₄	Direct product of D₇ and C₄.D₄	56	8+	D7xC4.D4	448,278
D₂₈⋊₁D₄	1^st semidirect product of D₂₈ and D₄ acting via D₄/C₂=C₂²	56	8+	D28:1D4	448,281
D₂₈.₃D₄	3^rd non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	8+	D28.3D4	448,283
M₄(2).₂₁D₁₄	4^th non-split extension by M₄(2) of D₁₄ acting via D₁₄/D₇=C₂	112	8+	M4(2).21D14	448,285
D₂₈.₅D₄	5^th non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	8+	D28.5D4	448,287
D₂₈.₆D₄	6^th non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	8+	D28.6D4	448,288
D₂₈⋊₁₈D₄	6^th semidirect product of D₂₈ and D₄ acting via D₄/C₂²=C₂	56	8+	D28:18D4	448,732
M₄(2).D₁₄	12^nd non-split extension by M₄(2) of D₁₄ acting via D₁₄/C₇=C₂²	112	8+	M4(2).D14	448,733
D₂₈.₃₉D₄	9^th non-split extension by D₂₈ of D₄ acting via D₄/C₂²=C₂	112	8+	D28.39D4	448,736
M₄(2).₁₅D₁₄	15^th non-split extension by M₄(2) of D₁₄ acting via D₁₄/C₇=C₂²	112	8+	M4(2).15D14	448,737
2₊¹⁺⁴⋊D₇	1^st semidirect product of 2₊¹⁺⁴ and D₇ acting via D₇/C₇=C₂	56	8+	ES+(2,2):D7	448,775
2₊¹⁺⁴⋊₂D₇	2^nd semidirect product of 2₊¹⁺⁴ and D₇ acting via D₇/C₇=C₂	56	8+	ES+(2,2):2D7	448,778
2_-¹⁺⁴⋊D₇	1^st semidirect product of 2_-¹⁺⁴ and D₇ acting via D₇/C₇=C₂	112	8+	ES-(2,2):D7	448,779
D₇×C₈⋊C₂²	Direct product of D₇ and C₈⋊C₂²	56	8+	D7xC8:C2^2	448,1225
D₈⋊₅D₁₄	5^th semidirect product of D₈ and D₁₄ acting via D₁₄/D₇=C₂	112	8+	D8:5D14	448,1227
D₅₆⋊C₂²	3^rd semidirect product of D₅₆ and C₂² acting faithfully	112	8+	D56:C2^2	448,1230
C₅₆.C₂³	6^th non-split extension by C₅₆ of C₂³ acting faithfully	112	8+	C56.C2^3	448,1231
D₂₈.₃₂C₂³	13^rd non-split extension by D₂₈ of C₂³ acting via C₂³/C₂²=C₂	112	8+	D28.32C2^3	448,1288
D₂₈.₃₄C₂³	15^th non-split extension by D₂₈ of C₂³ acting via C₂³/C₂²=C₂	112	8+	D28.34C2^3	448,1290
D₇×2₊¹⁺⁴	Direct product of D₇ and 2₊¹⁺⁴	56	8+	D7xES+(2,2)	448,1379
D₂₈.₃₉C₂³	20^th non-split extension by D₂₈ of C₂³ acting via C₂³/C₂²=C₂	112	8+	D28.39C2^3	448,1382

Groups of order 480

		d	ρ	Label	ID
D₆₀⋊C₄	1^st semidirect product of D₆₀ and C₄ acting faithfully	120	8+	D60:C4	480,227
D₁₂⋊F₅	1^st semidirect product of D₁₂ and F₅ acting via F₅/D₅=C₂	120	8+	D12:F5	480,228
D₆₀⋊₂C₄	2^nd semidirect product of D₆₀ and C₄ acting faithfully	120	8+	D60:2C4	480,233
D₆₀⋊₅C₄	5^th semidirect product of D₆₀ and C₄ acting faithfully	120	8+	D60:5C4	480,234
D₁₀.₄D₁₂	4^th non-split extension by D₁₀ of D₁₂ acting via D₁₂/C₆=C₂²	120	8+	D10.4D12	480,249
Dic₅.D₁₂	3^rd non-split extension by Dic₅ of D₁₂ acting via D₁₂/C₆=C₂²	120	8+	Dic5.D12	480,250
D₅×D₄⋊S₃	Direct product of D₅ and D₄⋊S₃	120	8+	D5xD4:S3	480,553
Dic₁₀⋊₃D₆	3^rd semidirect product of Dic₁₀ and D₆ acting via D₆/C₃=C₂²	120	8+	Dic10:3D6	480,554
S₃×D₄⋊D₅	Direct product of S₃ and D₄⋊D₅	120	8+	S3xD4:D5	480,555
D₆₀.C₂²	2^nd non-split extension by D₆₀ of C₂² acting faithfully	120	8+	D60.C2^2	480,556
D₁₅⋊D₈	The semidirect product of D₁₅ and D₈ acting via D₈/D₄=C₂	120	8+	D15:D8	480,557
Dic₁₀⋊D₆	4^th semidirect product of Dic₁₀ and D₆ acting via D₆/C₃=C₂²	120	8+	Dic10:D6	480,563
D₂₀.₉D₆	9^th non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	120	8+	D20.9D6	480,567
C₆₀.₁₆C₂³	16^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8+	C60.16C2^3	480,568
C₆₀.₁₉C₂³	19^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8+	C60.19C2^3	480,571
D₁₂.₉D₁₀	9^th non-split extension by D₁₂ of D₁₀ acting via D₁₀/C₅=C₂²	120	8+	D12.9D10	480,572
Dic₆⋊D₁₀	5^th semidirect product of Dic₆ and D₁₀ acting via D₁₀/C₅=C₂²	120	8+	Dic6:D10	480,574
D₁₂⋊₅D₁₀	5^th semidirect product of D₁₂ and D₁₀ acting via D₁₀/C₅=C₂²	120	8+	D12:5D10	480,576
D₅×Q₈⋊₂S₃	Direct product of D₅ and Q₈⋊₂S₃	120	8+	D5xQ8:2S3	480,577
D₂₀⋊D₆	6^th semidirect product of D₂₀ and D₆ acting via D₆/C₃=C₂²	120	8+	D20:D6	480,578
S₃×Q₈⋊D₅	Direct product of S₃ and Q₈⋊D₅	120	8+	S3xQ8:D5	480,579
D₁₂⋊D₁₀	6^th semidirect product of D₁₂ and D₁₀ acting via D₁₀/C₅=C₂²	120	8+	D12:D10	480,580
D₆₀⋊C₂²	6^th semidirect product of D₆₀ and C₂² acting faithfully	120	8+	D60:C2^2	480,582
C₆₀.C₂³	36^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8+	C60.C2^3	480,588
C₆₀.₃₉C₂³	39^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8+	C60.39C2^3	480,591
D₂₀.D₆	15^th non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	240	8+	D20.D6	480,592
Dic₁₀.₂₇D₆	10^th non-split extension by Dic₁₀ of D₆ acting via D₆/S₃=C₂	240	8+	Dic10.27D6	480,595
C₆₀.₄₄C₂³	44^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8+	C60.44C2^3	480,596
D₂₀.₁₆D₆	16^th non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	240	8+	D20.16D6	480,597
D₁₂.D₁₀	16^th non-split extension by D₁₂ of D₁₀ acting via D₁₀/C₅=C₂²	240	8+	D12.D10	480,599
C₅⋊U₂(𝔽₃)	The semidirect product of C₅ and U₂(𝔽₃) acting via U₂(𝔽₃)/SL₂(𝔽₃)=C₄	120	8+	C5:U(2,3)	480,961
SL₂(𝔽₃).F₅	The non-split extension by SL₂(𝔽₃) of F₅ acting through Inn(SL₂(𝔽₃))	160	8+	SL(2,3).F5	480,964
D₆₀.C₄	2^nd non-split extension by D₆₀ of C₄ acting faithfully	240	8+	D60.C4	480,990
Dic₆.F₅	The non-split extension by Dic₆ of F₅ acting via F₅/D₅=C₂	240	8+	Dic6.F5	480,992
F₅×D₁₂	Direct product of F₅ and D₁₂	60	8+	F5xD12	480,995
D₆₀⋊₃C₄	3^rd semidirect product of D₆₀ and C₄ acting faithfully	60	8+	D60:3C4	480,997
D₁₅⋊₂M₄(2)	The semidirect product of D₁₅ and M₄(2) acting via M₄(2)/C₂²=C₄	120	8+	D15:2M4(2)	480,1007
S₃×C₂²⋊F₅	Direct product of S₃ and C₂²⋊F₅	60	8+	S3xC2^2:F5	480,1011
S₃×D₄×D₅	Direct product of S₃, D₄ and D₅	60	8+	S3xD4xD5	480,1097
D₃₀.C₂³	13^rd non-split extension by D₃₀ of C₂³ acting via C₂³/C₂=C₂²	120	8+	D30.C2^3	480,1100
D₂₀⋊₁₄D₆	8^th semidirect product of D₂₀ and D₆ acting via D₆/S₃=C₂	120	8+	D20:14D6	480,1102
D₁₂⋊₁₄D₁₀	8^th semidirect product of D₁₂ and D₁₀ acting via D₁₀/D₅=C₂	120	8+	D12:14D10	480,1103
C₃₀.₃₃C₂⁴	33^rd non-split extension by C₃₀ of C₂⁴ acting via C₂⁴/C₂²=C₂²	240	8+	C30.33C2^4	480,1105
D₅×Q₈⋊₃S₃	Direct product of D₅ and Q₈⋊₃S₃	120	8+	D5xQ8:3S3	480,1108
S₃×Q₈⋊₂D₅	Direct product of S₃ and Q₈⋊₂D₅	120	8+	S3xQ8:2D5	480,1109
D₂₀⋊₁₇D₆	11^st semidirect product of D₂₀ and D₆ acting via D₆/S₃=C₂	120	8+	D20:17D6	480,1111

Symplectic of dimension 8 (ρ=8-)

Groups of order 128

		d	ρ	Label	ID
C₂³.₂D₈	2^nd non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	32	8-	C2^3.2D8	128,72
C₂³.₂SD₁₆	2^nd non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	32	8-	C2^3.2SD16	128,74
C₄².(C₂×C₄)	2^nd non-split extension by C₄² of C₂×C₄ acting faithfully	32	8-	C4^2.(C2xC4)	128,88
(C₂×D₄).D₄	4^th non-split extension by C₂×D₄ of D₄ acting faithfully	32	8-	(C2xD4).D4	128,139
C₈⋊C₄.C₄	3^rd non-split extension by C₈⋊C₄ of C₄ acting faithfully	32	8-	C8:C4.C4	128,145
(C₂²×Q₈)⋊C₄	6^th semidirect product of C₂²×Q₈ and C₄ acting faithfully	32	8-	(C2^2xQ8):C4	128,528
(C₂×Q₈).₂₁₁D₄	19^th non-split extension by C₂×Q₈ of D₄ acting via D₄/C₂²=C₂	32	8-	(C2xQ8).211D4	128,562
M₄(2).₄₆D₄	10^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	8-	M4(2).46D4	128,634
C₄².₆D₄	6^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.6D4	128,637
C₄.(C₄×D₄)	5^th non-split extension by C₄ of C₄×D₄ acting via C₄×D₄/C₄²=C₂	32	8-	C4.(C4xD4)	128,641
C₄².₇D₄	7^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.7D4	128,644
M₄(2).₅₀D₄	14^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	8-	M4(2).50D4	128,647
M₄(2).D₄	3^rd non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32	8-	M4(2).D4	128,741
M₄(2).₉D₄	9^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32	8-	M4(2).9D4	128,781
M₄(2).₁₅D₄	15^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	32	8-	M4(2).15D4	128,802
(C₂×C₈).₆D₄	6^th non-split extension by C₂×C₈ of D₄ acting faithfully	32	8-	(C2xC8).6D4	128,814
C₂³.(C₂×D₄)	6^th non-split extension by C₂³ of C₂×D₄ acting via C₂×D₄/C₂=D₄	32	8-	C2^3.(C2xD4)	128,855
C₄⋊Q₈⋊C₄	5^th semidirect product of C₄⋊Q₈ and C₄ acting faithfully	32	8-	C4:Q8:C4	128,861
C₄⋊Q₈.C₄	5^th non-split extension by C₄⋊Q₈ of C₄ acting faithfully	32	8-	C4:Q8.C4	128,865
(C₂×D₄).₁₃₇D₄	99^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂=C₂²	32	8-	(C2xD4).137D4	128,867
Q₃₂⋊C₄	The semidirect product of Q₃₂ and C₄ acting faithfully	32	8-	Q32:C4	128,912
D₈.D₄	1^st non-split extension by D₈ of D₄ acting via D₄/C₂=C₂²	32	8-	D8.D4	128,923
C₄².₁₄D₄	14^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.14D4	128,933
C₄².₁₆D₄	16^th non-split extension by C₄² of D₄ acting faithfully	32	8-	C4^2.16D4	128,935
C₂³.₁₀SD₁₆	10^th non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	32	8-	C2^3.10SD16	128,971
C₂³.₄C₂⁴	4^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	32	8-	C2^3.4C2^4	128,1616
M₄(2).₂₅C₂³	7^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	32	8-	M4(2).25C2^3	128,1621
M₄(2).C₂³	4^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂=C₂²	32	8-	M4(2).C2^3	128,1752
C₄².₁₃C₂³	13^rd non-split extension by C₄² of C₂³ acting faithfully	32	8-	C4^2.13C2^3	128,1754
C₂³.₁₀C₂⁴	10^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	32	8-	C2^3.10C2^4	128,1760
M₄(2).₃₈D₄	2^nd non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	32	8-	M4(2).38D4	128,1801
D₈.₁₃D₄	5^th non-split extension by D₈ of D₄ acting via D₄/C₂²=C₂	32	8-	D8.13D4	128,2021
C₄.C₂⁵	13^rd non-split extension by C₄ of C₂⁵ acting via C₂⁵/C₂⁴=C₂	32	8-	C4.C2^5	128,2318
2_-¹⁺⁶	Extraspecial group; = D₄ ○2_-¹⁺⁴	32	8-	ES-(2,3)	128,2327

Groups of order 144

		d	ρ	Label	ID
C₂.F₉	The central extension by C₂ of F₉	48	8-	C2.F9	144,114

Groups of order 160

		d	ρ	Label	ID
D₄⋊F₅	2^nd semidirect product of D₄ and F₅ acting via F₅/D₅=C₂	40	8-	D4:F5	160,83
Q₈⋊F₅	1^st semidirect product of Q₈ and F₅ acting via F₅/D₅=C₂	40	8-	Q8:F5	160,84
D₄.F₅	The non-split extension by D₄ of F₅ acting through Inn(D₄)	80	8-	D4.F5	160,206
Q₈×F₅	Direct product of Q₈ and F₅	40	8-	Q8xF5	160,209

Groups of order 192

		d	ρ	Label	ID
(C₂×D₄).D₆	2^nd non-split extension by C₂×D₄ of D₆ acting via D₆/C₃=C₂²	48	8-	(C2xD4).D6	192,31
C₂³.D₁₂	1^st non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	C2^3.D12	192,32
C₂³.₄D₁₂	4^th non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	C2^3.4D12	192,35
(C₂×C₁₂).D₄	16^th non-split extension by C₂×C₁₂ of D₄ acting faithfully	48	8-	(C2xC12).D4	192,37
C₂³⋊C₄⋊₅S₃	The semidirect product of C₂³⋊C₄ and S₃ acting through Inn(C₂³⋊C₄)	48	8-	C2^3:C4:5S3	192,299
C₂³.₅D₁₂	5^th non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	C2^3.5D12	192,301
M₄(2).₁₉D₆	2^nd non-split extension by M₄(2) of D₆ acting via D₆/S₃=C₂	48	8-	M4(2).19D6	192,304
M₄(2)⋊D₆	1^st semidirect product of M₄(2) and D₆ acting via D₆/C₃=C₂²	48	8-	M4(2):D6	192,305
D₁₂.₂D₄	2^nd non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8-	D12.2D4	192,307
S₃×C₄.₁₀D₄	Direct product of S₃ and C₄.₁₀D₄	48	8-	S3xC4.10D4	192,309
D₁₂.₄D₄	4^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	48	8-	D12.4D4	192,311
D₁₂.₇D₄	7^th non-split extension by D₁₂ of D₄ acting via D₄/C₂=C₂²	96	8-	D12.7D4	192,314
M₄(2).₁₃D₆	13^rd non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	48	8-	M4(2).13D6	192,759
D₁₂.₃₈D₄	8^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48	8-	D12.38D4	192,760
M₄(2).₁₆D₆	16^th non-split extension by M₄(2) of D₆ acting via D₆/C₃=C₂²	96	8-	M4(2).16D6	192,763
D₁₂.₄₀D₄	10^th non-split extension by D₁₂ of D₄ acting via D₄/C₂²=C₂	48	8-	D12.40D4	192,764
2₊¹⁺⁴.₄S₃	1^st non-split extension by 2₊¹⁺⁴ of S₃ acting via S₃/C₃=C₂	48	8-	ES+(2,2).4S3	192,801
2₊¹⁺⁴.₅S₃	2^nd non-split extension by 2₊¹⁺⁴ of S₃ acting via S₃/C₃=C₂	48	8-	ES+(2,2).5S3	192,802
2_-¹⁺⁴.₂S₃	The non-split extension by 2_-¹⁺⁴ of S₃ acting via S₃/C₃=C₂	48	8-	ES-(2,2).2S3	192,805
D₈⋊₄D₆	4^th semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	8-	D8:4D6	192,1332
D₈⋊₆D₆	6^th semidirect product of D₈ and D₆ acting via D₆/S₃=C₂	48	8-	D8:6D6	192,1334
S₃×C₈.C₂²	Direct product of S₃ and C₈.C₂²	48	8-	S3xC8.C2^2	192,1335
SD₁₆.D₆	The non-split extension by SD₁₆ of D₆ acting via D₆/S₃=C₂	96	8-	SD16.D6	192,1338
D₁₂.₃₃C₂³	14^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	48	8-	D12.33C2^3	192,1395
D₁₂.₃₅C₂³	16^th non-split extension by D₁₂ of C₂³ acting via C₂³/C₂²=C₂	96	8-	D12.35C2^3	192,1397
D₆.C₂⁴	9^th non-split extension by D₆ of C₂⁴ acting via C₂⁴/C₂³=C₂	48	8-	D6.C2^4	192,1525
S₃×2_-¹⁺⁴	Direct product of S₃ and 2_-¹⁺⁴	48	8-	S3xES-(2,2)	192,1526

Groups of order 240

		d	ρ	Label	ID
Dic₃×F₅	Direct product of Dic₃ and F₅	60	8-	Dic3xF5	240,95
Dic₃⋊F₅	The semidirect product of Dic₃ and F₅ acting via F₅/D₅=C₂	60	8-	Dic3:F5	240,97
S₃×C₅⋊C₈	Direct product of S₃ and C₅⋊C₈	120	8-	S3xC5:C8	240,98
D₆.F₅	The non-split extension by D₆ of F₅ acting via F₅/D₅=C₂	120	8-	D6.F5	240,100

Groups of order 272

		d	ρ	Label	ID
C₃₄.C₈	The non-split extension by C₃₄ of C₈ acting faithfully	272	8-	C34.C8	272,28

Groups of order 288

		d	ρ	Label	ID
C₃²⋊Q₃₂	The semidirect product of C₃² and Q₃₂ acting via Q₃₂/C₄=D₄	96	8-	C3^2:Q32	288,384
C₆².₂Q₈	2^nd non-split extension by C₆² of Q₈ acting faithfully	48	8-	C6^2.2Q8	288,396
C₃²⋊₆C₄≀C₂	The semidirect product of C₃² and C₄≀C₂ acting via C₄≀C₂/D₄=C₄	48	8-	C3^2:6C4wrC2	288,431
C₃⋊S₃.₅Q₁₆	The non-split extension by C₃⋊S₃ of Q₁₆ acting via Q₁₆/Q₈=C₂	48	8-	C3:S3.5Q16	288,432
D₁₂.D₆	5^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.D6	288,575
S₃×D₄.S₃	Direct product of S₃ and D₄.S₃	48	8-	S3xD4.S3	288,576
Dic₆.₁₉D₆	6^th non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8-	Dic6.19D6	288,577
Dic₆.D₆	5^th non-split extension by Dic₆ of D₆ acting via D₆/C₃=C₂²	48	8-	Dic6.D6	288,579
D₁₂⋊₉D₆	3^rd semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:9D6	288,580
D₁₂.₂₂D₆	7^th non-split extension by D₁₂ of D₆ acting via D₆/S₃=C₂	48	8-	D12.22D6	288,581
D₁₂.₈D₆	8^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.8D6	288,584
D₁₂.₉D₆	9^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.9D6	288,588
S₃×C₃⋊Q₁₆	Direct product of S₃ and C₃⋊Q₁₆	96	8-	S3xC3:Q16	288,590
D₁₂.₁₁D₆	11^st non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	96	8-	D12.11D6	288,591
Dic₆.₉D₆	9^th non-split extension by Dic₆ of D₆ acting via D₆/C₃=C₂²	48	8-	Dic6.9D6	288,592
D₁₂.₂₄D₆	9^th non-split extension by D₁₂ of D₆ acting via D₆/S₃=C₂	96	8-	D12.24D6	288,594
D₁₂.₁₂D₆	12^nd non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	96	8-	D12.12D6	288,595
D₁₂.₁₅D₆	15^th non-split extension by D₁₂ of D₆ acting via D₆/C₃=C₂²	48	8-	D12.15D6	288,599
C₂².F₉	The non-split extension by C₂² of F₉ acting via F₉/C₃²⋊C₄=C₂	48	8-	C2^2.F9	288,866
C₃²⋊C₄⋊Q₈	1^st semidirect product of C₃²⋊C₄ and Q₈ acting via Q₈/C₄=C₂	48	8-	C3^2:C4:Q8	288,870
C₃⋊S₃⋊Q₁₆	The semidirect product of C₃⋊S₃ and Q₁₆ acting via Q₁₆/C₄=C₂²	48	8-	C3:S3:Q16	288,876
C₆².₁₃D₄	13^rd non-split extension by C₆² of D₄ acting faithfully	48	8-	C6^2.13D4	288,885
C₆².(C₂×C₄)	The non-split extension by C₆² of C₂×C₄ acting faithfully	48	8-	C6^2.(C2xC4)	288,935
Q₈×C₃²⋊C₄	Direct product of Q₈ and C₃²⋊C₄	48	8-	Q8xC3^2:C4	288,938
Dic₆.₂₄D₆	11^st non-split extension by Dic₆ of D₆ acting via D₆/S₃=C₂	48	8-	Dic6.24D6	288,957
S₃×D₄⋊₂S₃	Direct product of S₃ and D₄⋊₂S₃	48	8-	S3xD4:2S3	288,959
D₁₂⋊₁₂D₆	6^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:12D6	288,961
D₁₂.₂₅D₆	10^th non-split extension by D₁₂ of D₆ acting via D₆/S₃=C₂	48	8-	D12.25D6	288,963
S₃²×Q₈	Direct product of S₃, S₃ and Q₈	48	8-	S3^2xQ8	288,965
D₁₂⋊₁₅D₆	9^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	48	8-	D12:15D6	288,967

Groups of order 320

		d	ρ	Label	ID
(C₂×C₂₀).D₄	2^nd non-split extension by C₂×C₂₀ of D₄ acting faithfully	80	8-	(C2xC20).D4	320,30
C₂³.D₂₀	1^st non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	80	8-	C2^3.D20	320,31
C₂³.₄D₂₀	4^th non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	80	8-	C2^3.4D20	320,34
(C₂×Q₈).D₁₀	2^nd non-split extension by C₂×Q₈ of D₁₀ acting via D₁₀/C₅=C₂²	80	8-	(C2xQ8).D10	320,36
C₂²⋊C₄⋊F₅	2^nd semidirect product of C₂²⋊C₄ and F₅ acting via F₅/C₅=C₄	80	8-	C2^2:C4:F5	320,203
C₂²⋊C₄.F₅	1^st non-split extension by C₂²⋊C₄ of F₅ acting via F₅/D₅=C₂	80	8-	C2^2:C4.F5	320,205
D₁₀.D₈	2^nd non-split extension by D₁₀ of D₈ acting via D₈/C₄=C₂²	80	8-	D10.D8	320,241
D₈.F₅	1^st non-split extension by D₈ of F₅ acting via F₅/D₅=C₂	160	8-	D8.F5	320,243
D₅.Q₃₂	The non-split extension by D₅ of Q₃₂ acting via Q₃₂/Q₁₆=C₂	80	8-	D5.Q32	320,246
Dic₂₀.C₄	1^st non-split extension by Dic₂₀ of C₄ acting faithfully	160	8-	Dic20.C4	320,248
(D₄×C₁₀).C₄	2^nd non-split extension by D₄×C₁₀ of C₄ acting faithfully	80	8-	(D4xC10).C4	320,261
(Q₈×C₁₀).C₄	2^nd non-split extension by Q₈×C₁₀ of C₄ acting faithfully	80	8-	(Q8xC10).C4	320,267
C₂³⋊C₄⋊₅D₅	The semidirect product of C₂³⋊C₄ and D₅ acting through Inn(C₂³⋊C₄)	80	8-	C2^3:C4:5D5	320,367
C₂³.₅D₂₀	5^th non-split extension by C₂³ of D₂₀ acting via D₂₀/C₅=D₄	80	8-	C2^3.5D20	320,369
M₄(2).₁₉D₁₀	2^nd non-split extension by M₄(2) of D₁₀ acting via D₁₀/D₅=C₂	80	8-	M4(2).19D10	320,372
D₂₀.₁D₄	1^st non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	8-	D20.1D4	320,373
D₂₀.₂D₄	2^nd non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	8-	D20.2D4	320,375
D₅×C₄.₁₀D₄	Direct product of D₅ and C₄.₁₀D₄	80	8-	D5xC4.10D4	320,377
D₂₀.₄D₄	4^th non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	80	8-	D20.4D4	320,379
D₂₀.₇D₄	7^th non-split extension by D₂₀ of D₄ acting via D₄/C₂=C₂²	160	8-	D20.7D4	320,382
M₄(2).₁₃D₁₀	13^rd non-split extension by M₄(2) of D₁₀ acting via D₁₀/C₅=C₂²	80	8-	M4(2).13D10	320,827
D₂₀.₃₈D₄	8^th non-split extension by D₂₀ of D₄ acting via D₄/C₂²=C₂	80	8-	D20.38D4	320,828
M₄(2).₁₆D₁₀	16^th non-split extension by M₄(2) of D₁₀ acting via D₁₀/C₅=C₂²	160	8-	M4(2).16D10	320,831
D₂₀.₄₀D₄	10^th non-split extension by D₂₀ of D₄ acting via D₄/C₂²=C₂	80	8-	D20.40D4	320,832
2₊¹⁺⁴.D₅	1^st non-split extension by 2₊¹⁺⁴ of D₅ acting via D₅/C₅=C₂	80	8-	ES+(2,2).D5	320,869
2₊¹⁺⁴.₂D₅	2^nd non-split extension by 2₊¹⁺⁴ of D₅ acting via D₅/C₅=C₂	80	8-	ES+(2,2).2D5	320,870
2_-¹⁺⁴.₂D₅	The non-split extension by 2_-¹⁺⁴ of D₅ acting via D₅/C₅=C₂	80	8-	ES-(2,2).2D5	320,873
D₈⋊₅F₅	The semidirect product of D₈ and F₅ acting through Inn(D₈)	80	8-	D8:5F5	320,1070
D₈⋊F₅	4^th semidirect product of D₈ and F₅ acting via F₅/D₅=C₂	80	8-	D8:F5	320,1071
Q₁₆×F₅	Direct product of Q₁₆ and F₅	80	8-	Q16xF5	320,1076
Dic₂₀⋊C₄	3^rd semidirect product of Dic₂₀ and C₄ acting faithfully	80	8-	Dic20:C4	320,1077
(C₂×D₄)⋊₆F₅	4^th semidirect product of C₂×D₄ and F₅ acting via F₅/D₅=C₂	80	8-	(C2xD4):6F5	320,1107
(C₂×D₄)⋊₈F₅	6^th semidirect product of C₂×D₄ and F₅ acting via F₅/D₅=C₂	80	8-	(C2xD4):8F5	320,1109
(C₂×D₄).₉F₅	6^th non-split extension by C₂×D₄ of F₅ acting via F₅/D₅=C₂	80	8-	(C2xD4).9F5	320,1115
(C₂×Q₈)⋊₄F₅	2^nd semidirect product of C₂×Q₈ and F₅ acting via F₅/D₅=C₂	80	8-	(C2xQ8):4F5	320,1120
(C₂×Q₈).₇F₅	4^th non-split extension by C₂×Q₈ of F₅ acting via F₅/D₅=C₂	80	8-	(C2xQ8).7F5	320,1127
SD₁₆⋊D₁₀	2^nd semidirect product of SD₁₆ and D₁₀ acting via D₁₀/D₅=C₂	80	8-	SD16:D10	320,1445
D₈⋊₆D₁₀	6^th semidirect product of D₈ and D₁₀ acting via D₁₀/D₅=C₂	80	8-	D8:6D10	320,1447
D₅×C₈.C₂²	Direct product of D₅ and C₈.C₂²	80	8-	D5xC8.C2^2	320,1448
D₂₀.₄₄D₄	14^th non-split extension by D₂₀ of D₄ acting via D₄/C₂²=C₂	160	8-	D20.44D4	320,1451
D₂₀.₃₃C₂³	14^th non-split extension by D₂₀ of C₂³ acting via C₂³/C₂²=C₂	80	8-	D20.33C2^3	320,1508
D₂₀.₃₅C₂³	16^th non-split extension by D₂₀ of C₂³ acting via C₂³/C₂²=C₂	160	8-	D20.35C2^3	320,1510
Dic₅.C₂⁴	18^th non-split extension by Dic₅ of C₂⁴ acting via C₂⁴/C₂³=C₂	80	8-	Dic5.C2^4	320,1594
D₅.2_-¹⁺⁴	The non-split extension by D₅ of 2_-¹⁺⁴ acting via 2_-¹⁺⁴/C₂×Q₈=C₂	80	8-	D5.ES-(2,2)	320,1600
D₂₀.₃₇C₂³	18^th non-split extension by D₂₀ of C₂³ acting via C₂³/C₂²=C₂	80	8-	D20.37C2^3	320,1623
D₅×2_-¹⁺⁴	Direct product of D₅ and 2_-¹⁺⁴	80	8-	D5xES-(2,2)	320,1624

Groups of order 400

		d	ρ	Label	ID
C₅²⋊C₁₆	The semidirect product of C₅² and C₁₆ acting via C₁₆/C₂=C₈	80	8-	C5^2:C16	400,116
Dic₅×F₅	Direct product of Dic₅ and F₅	80	8-	Dic5xF5	400,117
D₅.Dic₁₀	The non-split extension by D₅ of Dic₁₀ acting via Dic₁₀/Dic₅=C₂	80	8-	D5.Dic10	400,119
D₅×C₅⋊C₈	Direct product of D₅ and C₅⋊C₈	80	8-	D5xC5:C8	400,120
D₁₀.F₅	1^st non-split extension by D₁₀ of F₅ acting via F₅/D₅=C₂	80	8-	D10.F5	400,122
D₁₀.₂F₅	2^nd non-split extension by D₁₀ of F₅ acting via F₅/D₅=C₂	80	8-	D10.2F5	400,127
C₅²⋊₄M₄(2)	3^rd semidirect product of C₅² and M₄(2) acting via M₄(2)/C₂=C₂×C₄	80	8-	C5^2:4M4(2)	400,128

Groups of order 416

		d	ρ	Label	ID
Dic₂₆⋊C₄	1^st semidirect product of Dic₂₆ and C₄ acting faithfully	104	8-	Dic26:C4	416,83
D₁₃.Q₁₆	The non-split extension by D₁₃ of Q₁₆ acting via Q₁₆/Q₈=C₂	104	8-	D13.Q16	416,84
Dic₂₆.C₄	The non-split extension by Dic₂₆ of C₄ acting faithfully	208	8-	Dic26.C4	416,205
Q₈×C₁₃⋊C₄	Direct product of Q₈ and C₁₃⋊C₄	104	8-	Q8xC13:C4	416,208

Groups of order 432

		d	ρ	Label	ID
Dic₃×C₃²⋊C₄	Direct product of Dic₃ and C₃²⋊C₄	48	8-	Dic3xC3^2:C4	432,567
C₃³⋊(C₄⋊C₄)	The semidirect product of C₃³ and C₄⋊C₄ acting via C₄⋊C₄/C₂=C₂×C₄	48	8-	C3^3:(C4:C4)	432,569
S₃×C₃²⋊₂C₈	Direct product of S₃ and C₃²⋊₂C₈	48	8-	S3xC3^2:2C8	432,570
C₃³⋊M₄(2)	1^st semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	48	8-	C3^3:M4(2)	432,572
(C₃×C₆).₉D₁₂	2^nd non-split extension by C₃×C₆ of D₁₂ acting via D₁₂/C₃=D₄	48	8-	(C3xC6).9D12	432,587
C₃³⋊₃Q₁₆	3^rd semidirect product of C₃³ and Q₁₆ acting via Q₁₆/C₂=D₄	48	8-	C3^3:3Q16	432,590
S₃²×Dic₃	Direct product of S₃, S₃ and Dic₃	48	8-	S3^2xDic3	432,594
Dic₃⋊₆S₃²	2^nd semidirect product of Dic₃ and S₃² acting through Inn(Dic₃)	48	8-	Dic3:6S3^2	432,596
S₃×D₆⋊S₃	Direct product of S₃ and D₆⋊S₃	48	8-	S3xD6:S3	432,597
D₆⋊S₃²	3^rd semidirect product of D₆ and S₃² acting via S₃²/C₃×S₃=C₂	48	8-	D6:S3^2	432,600
S₃×C₃²⋊₂Q₈	Direct product of S₃ and C₃²⋊₂Q₈	48	8-	S3xC3^2:2Q8	432,603
C₃³⋊₅(C₂×Q₈)	2^nd semidirect product of C₃³ and C₂×Q₈ acting via C₂×Q₈/C₂=C₂³	48	8-	C3^3:5(C2xQ8)	432,604
D₆.S₃²	2^nd non-split extension by D₆ of S₃² acting via S₃²/C₃×S₃=C₂	48	8-	D6.S3^2	432,607
D₆.₄S₃²	1^st non-split extension by D₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	8-	D6.4S3^2	432,608
D₆⋊S₃⋊S₃	5^th semidirect product of D₆⋊S₃ and S₃ acting via S₃/C₃=C₂	48	8-	D6:S3:S3	432,610
D₆.₆S₃²	3^rd non-split extension by D₆ of S₃² acting via S₃²/C₃⋊S₃=C₂	48	8-	D6.6S3^2	432,611

Groups of order 448

		d	ρ	Label	ID
(C₂×C₂₈).D₄	2^nd non-split extension by C₂×C₂₈ of D₄ acting faithfully	112	8-	(C2xC28).D4	448,29
C₂³.D₂₈	1^st non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	112	8-	C2^3.D28	448,30
C₂³.₄D₂₈	4^th non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	112	8-	C2^3.4D28	448,33
(C₂×Q₈).D₁₄	2^nd non-split extension by C₂×Q₈ of D₁₄ acting via D₁₄/C₇=C₂²	112	8-	(C2xQ8).D14	448,35
C₂³⋊C₄⋊₅D₇	The semidirect product of C₂³⋊C₄ and D₇ acting through Inn(C₂³⋊C₄)	112	8-	C2^3:C4:5D7	448,274
C₂³.₅D₂₈	5^th non-split extension by C₂³ of D₂₈ acting via D₂₈/C₇=D₄	112	8-	C2^3.5D28	448,276
M₄(2).₁₉D₁₄	2^nd non-split extension by M₄(2) of D₁₄ acting via D₁₄/D₇=C₂	112	8-	M4(2).19D14	448,279
D₂₈.₁D₄	1^st non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	8-	D28.1D4	448,280
D₂₈.₂D₄	2^nd non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	8-	D28.2D4	448,282
D₇×C₄.₁₀D₄	Direct product of D₇ and C₄.₁₀D₄	112	8-	D7xC4.10D4	448,284
D₂₈.₄D₄	4^th non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	112	8-	D28.4D4	448,286
D₂₈.₇D₄	7^th non-split extension by D₂₈ of D₄ acting via D₄/C₂=C₂²	224	8-	D28.7D4	448,289
M₄(2).₁₃D₁₄	13^rd non-split extension by M₄(2) of D₁₄ acting via D₁₄/C₇=C₂²	112	8-	M4(2).13D14	448,734
D₂₈.₃₈D₄	8^th non-split extension by D₂₈ of D₄ acting via D₄/C₂²=C₂	112	8-	D28.38D4	448,735
M₄(2).₁₆D₁₄	16^th non-split extension by M₄(2) of D₁₄ acting via D₁₄/C₇=C₂²	224	8-	M4(2).16D14	448,738
D₂₈.₄₀D₄	10^th non-split extension by D₂₈ of D₄ acting via D₄/C₂²=C₂	112	8-	D28.40D4	448,739
2₊¹⁺⁴.D₇	1^st non-split extension by 2₊¹⁺⁴ of D₇ acting via D₇/C₇=C₂	112	8-	ES+(2,2).D7	448,776
2₊¹⁺⁴.₂D₇	2^nd non-split extension by 2₊¹⁺⁴ of D₇ acting via D₇/C₇=C₂	112	8-	ES+(2,2).2D7	448,777
2_-¹⁺⁴.D₇	The non-split extension by 2_-¹⁺⁴ of D₇ acting via D₇/C₇=C₂	112	8-	ES-(2,2).D7	448,780
SD₁₆⋊D₁₄	2^nd semidirect product of SD₁₆ and D₁₄ acting via D₁₄/D₇=C₂	112	8-	SD16:D14	448,1226
D₈⋊₆D₁₄	6^th semidirect product of D₈ and D₁₄ acting via D₁₄/D₇=C₂	112	8-	D8:6D14	448,1228
D₇×C₈.C₂²	Direct product of D₇ and C₈.C₂²	112	8-	D7xC8.C2^2	448,1229
D₂₈.₄₄D₄	14^th non-split extension by D₂₈ of D₄ acting via D₄/C₂²=C₂	224	8-	D28.44D4	448,1232
D₂₈.₃₃C₂³	14^th non-split extension by D₂₈ of C₂³ acting via C₂³/C₂²=C₂	112	8-	D28.33C2^3	448,1289
D₂₈.₃₅C₂³	16^th non-split extension by D₂₈ of C₂³ acting via C₂³/C₂²=C₂	224	8-	D28.35C2^3	448,1291
D₁₄.C₂⁴	9^th non-split extension by D₁₄ of C₂⁴ acting via C₂⁴/C₂³=C₂	112	8-	D14.C2^4	448,1380
D₇×2_-¹⁺⁴	Direct product of D₇ and 2_-¹⁺⁴	112	8-	D7xES-(2,2)	448,1381

Groups of order 480

		d	ρ	Label	ID
Dic₆⋊F₅	3^rd semidirect product of Dic₆ and F₅ acting via F₅/D₅=C₂	120	8-	Dic6:F5	480,229
Dic₃₀⋊C₄	4^th semidirect product of Dic₃₀ and C₄ acting faithfully	120	8-	Dic30:C4	480,230
D₁₂⋊₄F₅	4^th semidirect product of D₁₂ and F₅ acting via F₅/D₅=C₂	120	8-	D12:4F5	480,231
D₁₂⋊₂F₅	2^nd semidirect product of D₁₂ and F₅ acting via F₅/D₅=C₂	120	8-	D12:2F5	480,232
D₁₀.D₁₂	3^rd non-split extension by D₁₀ of D₁₂ acting via D₁₂/C₆=C₂²	120	8-	D10.D12	480,248
Dic₅.₄D₁₂	4^th non-split extension by Dic₅ of D₁₂ acting via D₁₂/C₆=C₂²	240	8-	Dic5.4D12	480,251
D₃₀.₈D₄	8^th non-split extension by D₃₀ of D₄ acting via D₄/C₂=C₂²	120	8-	D30.8D4	480,558
D₅×D₄.S₃	Direct product of D₅ and D₄.S₃	120	8-	D5xD4.S3	480,559
C₆₀.₈C₂³	8^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8-	C60.8C2^3	480,560
S₃×D₄.D₅	Direct product of S₃ and D₄.D₅	120	8-	S3xD4.D5	480,561
C₆₀.₁₀C₂³	10^th non-split extension by C₆₀ of C₂³ acting faithfully	240	8-	C60.10C2^3	480,562
D₃₀.₉D₄	9^th non-split extension by D₃₀ of D₄ acting via D₄/C₂=C₂²	240	8-	D30.9D4	480,564
D₁₂⋊₁₀D₁₀	4^th semidirect product of D₁₂ and D₁₀ acting via D₁₀/D₅=C₂	120	8-	D12:10D10	480,565
D₁₂.₂₄D₁₀	7^th non-split extension by D₁₂ of D₁₀ acting via D₁₀/D₅=C₂	240	8-	D12.24D10	480,566
D₂₀.₂₄D₆	7^th non-split extension by D₂₀ of D₆ acting via D₆/S₃=C₂	240	8-	D20.24D6	480,569
D₂₀⋊₁₀D₆	4^th semidirect product of D₂₀ and D₆ acting via D₆/S₃=C₂	120	8-	D20:10D6	480,570
D₂₀.₁₀D₆	10^th non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	240	8-	D20.10D6	480,573
D₃₀.₁₁D₄	11^st non-split extension by D₃₀ of D₄ acting via D₄/C₂=C₂²	240	8-	D30.11D4	480,575
D₁₅⋊SD₁₆	The semidirect product of D₁₅ and SD₁₆ acting via SD₁₆/Q₈=C₂	120	8-	D15:SD16	480,581
D₅×C₃⋊Q₁₆	Direct product of D₅ and C₃⋊Q₁₆	240	8-	D5xC3:Q16	480,583
D₂₀.₁₃D₆	13^rd non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	240	8-	D20.13D6	480,584
S₃×C₅⋊Q₁₆	Direct product of S₃ and C₅⋊Q₁₆	240	8-	S3xC5:Q16	480,585
Dic₁₀.₂₆D₆	9^th non-split extension by Dic₁₀ of D₆ acting via D₆/S₃=C₂	240	8-	Dic10.26D6	480,586
D₁₅⋊Q₁₆	The semidirect product of D₁₅ and Q₁₆ acting via Q₁₆/Q₈=C₂	240	8-	D15:Q16	480,587
D₁₂.₂₇D₁₀	10^th non-split extension by D₁₂ of D₁₀ acting via D₁₀/D₅=C₂	240	8-	D12.27D10	480,589
D₂₀.₁₄D₆	14^th non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	240	8-	D20.14D6	480,590
D₂₀.₂₇D₆	10^th non-split extension by D₂₀ of D₆ acting via D₆/S₃=C₂	240	8-	D20.27D6	480,593
D₂₀.₂₈D₆	11^st non-split extension by D₂₀ of D₆ acting via D₆/S₃=C₂	240	8-	D20.28D6	480,594
D₂₀.₁₇D₆	17^th non-split extension by D₂₀ of D₆ acting via D₆/C₃=C₂²	240	8-	D20.17D6	480,598
D₃₀.₄₄D₄	17^th non-split extension by D₃₀ of D₄ acting via D₄/C₂²=C₂	240	8-	D30.44D4	480,600
D₁₀.S₄	3^rd non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	40	8-	D10.S4	480,962
F₅×SL₂(𝔽₃)	Direct product of F₅ and SL₂(𝔽₃)	40	8-	F5xSL(2,3)	480,965
F₅×Dic₆	Direct product of F₅ and Dic₆	120	8-	F5xDic6	480,982
Dic₆⋊₅F₅	5^th semidirect product of Dic₆ and F₅ acting via F₅/D₅=C₂	120	8-	Dic6:5F5	480,984
D₁₂.₂F₅	The non-split extension by D₁₂ of F₅ acting through Inn(D₁₂)	240	8-	D12.2F5	480,987
D₁₂.F₅	The non-split extension by D₁₂ of F₅ acting via F₅/D₅=C₂	240	8-	D12.F5	480,989
C₂²⋊F₅.S₃	The non-split extension by C₂²⋊F₅ of S₃ acting through Inn(C₂²⋊F₅)	120	8-	C2^2:F5.S3	480,999
S₃×C₂².F₅	Direct product of S₃ and C₂².F₅	120	8-	S3xC2^2.F5	480,1004
C₁₅⋊2_-¹⁺⁴	The semidirect product of C₁₅ and 2_-¹⁺⁴ acting via 2_-¹⁺⁴/D₄=C₂²	240	8-	C15:ES-(2,2)	480,1096
D₅×D₄⋊₂S₃	Direct product of D₅ and D₄⋊₂S₃	120	8-	D5xD4:2S3	480,1098
S₃×D₄⋊₂D₅	Direct product of S₃ and D₄⋊₂D₅	120	8-	S3xD4:2D5	480,1099
D₂₀⋊₁₃D₆	7^th semidirect product of D₂₀ and D₆ acting via D₆/S₃=C₂	120	8-	D20:13D6	480,1101
D₂₀.₂₉D₆	12^nd non-split extension by D₂₀ of D₆ acting via D₆/S₃=C₂	240	8-	D20.29D6	480,1104
D₁₂.₂₉D₁₀	12^nd non-split extension by D₁₂ of D₁₀ acting via D₁₀/D₅=C₂	240	8-	D12.29D10	480,1106
S₃×Q₈×D₅	Direct product of S₃, Q₈ and D₅	120	8-	S3xQ8xD5	480,1107
D₂₀⋊₁₆D₆	10^th semidirect product of D₂₀ and D₆ acting via D₆/S₃=C₂	120	8-	D20:16D6	480,1110

Complex of dimension 8 (ρ=8)

Groups of order 216

		d	ρ	Label	ID
C₃×F₉	Direct product of C₃ and F₉	24	8	C3xF9	216,154
C₃⋊F₉	The semidirect product of C₃ and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8	C3:F9	216,155
C₃×PSU₃(𝔽₂)	Direct product of C₃ and PSU₃(𝔽₂)	24	8	C3xPSU(3,2)	216,160
C₃³⋊Q₈	2^nd semidirect product of C₃³ and Q₈ acting faithfully	24	8	C3^3:Q8	216,161

Groups of order 288

		d	ρ	Label	ID
C₃²⋊C₃₂	The semidirect product of C₃² and C₃₂ acting via C₃₂/C₄=C₈	96	8	C3^2:C32	288,373
C₄.₄PSU₃(𝔽₂)	The central extension by C₄ of PSU₃(𝔽₂)	48	8	C4.4PSU(3,2)	288,392
C₄.PSU₃(𝔽₂)	1^st non-split extension by C₄ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C4.PSU(3,2)	288,393
C₄.₂PSU₃(𝔽₂)	2^nd non-split extension by C₄ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C4.2PSU(3,2)	288,394
PSU₃(𝔽₂)⋊C₄	The semidirect product of PSU₃(𝔽₂) and C₄ acting via C₄/C₂=C₂	36	8	PSU(3,2):C4	288,842
F₉⋊C₄	The semidirect product of F₉ and C₄ acting via C₄/C₂=C₂	36	8	F9:C4	288,843
C₄.₃F₉	2^nd central extension by C₄ of F₉	48	8	C4.3F9	288,861
C₄.F₉	The non-split extension by C₄ of F₉ acting via F₉/C₃²⋊C₄=C₂	48	8	C4.F9	288,862
C₄×F₉	Direct product of C₄ and F₉	36	8	C4xF9	288,863
C₄⋊F₉	The semidirect product of C₄ and F₉ acting via F₉/C₃²⋊C₄=C₂	36	8	C4:F9	288,864
C₄.₃PSU₃(𝔽₂)	3^rd non-split extension by C₄ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C4.3PSU(3,2)	288,891
C₄×PSU₃(𝔽₂)	Direct product of C₄ and PSU₃(𝔽₂)	36	8	C4xPSU(3,2)	288,892
C₄⋊PSU₃(𝔽₂)	The semidirect product of C₄ and PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	36	8	C4:PSU(3,2)	288,893

Groups of order 320

		d	ρ	Label	ID
D₂₀.C₈	1^st non-split extension by D₂₀ of C₈ acting via C₈/C₂=C₄	160	8	D20.C8	320,236
M₄(2)⋊F₅	2^nd semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):F5	320,237
M₄(2)⋊₃F₅	3^rd semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):3F5	320,238
M₄(2).F₅	3^rd non-split extension by M₄(2) of F₅ acting via F₅/D₅=C₂	80	8	M4(2).F5	320,239
M₄(2)⋊₄F₅	4^th semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	80	8	M4(2):4F5	320,240
D₄.(C₅⋊C₈)	The non-split extension by D₄ of C₅⋊C₈ acting via C₅⋊C₈/Dic₅=C₂	160	8	D4.(C5:C8)	320,270
Dic₁₀.C₈	2^nd non-split extension by Dic₁₀ of C₈ acting via C₈/C₂=C₄	160	8	Dic10.C8	320,1063
M₄(2)×F₅	Direct product of M₄(2) and F₅	40	8	M4(2)xF5	320,1064
M₄(2)⋊₁F₅	1^st semidirect product of M₄(2) and F₅ acting via F₅/D₅=C₂	40	8	M4(2):1F5	320,1065
M₄(2)⋊₅F₅	The semidirect product of M₄(2) and F₅ acting through Inn(M₄(2))	80	8	M4(2):5F5	320,1066
M₄(2).₁F₅	1^st non-split extension by M₄(2) of F₅ acting via F₅/D₅=C₂	80	8	M4(2).1F5	320,1067
SD₁₆×F₅	Direct product of SD₁₆ and F₅	40	8	SD16xF5	320,1072
SD₁₆⋊F₅	1^st semidirect product of SD₁₆ and F₅ acting via F₅/D₅=C₂	40	8	SD16:F5	320,1073
SD₁₆⋊₃F₅	The semidirect product of SD₁₆ and F₅ acting through Inn(SD₁₆)	80	8	SD16:3F5	320,1074
SD₁₆⋊₂F₅	2^nd semidirect product of SD₁₆ and F₅ acting via F₅/D₅=C₂	80	8	SD16:2F5	320,1075
C₅⋊C₁₆.C₂²	The non-split extension by C₅⋊C₁₆ of C₂² acting via C₂²/C₂=C₂	160	8	C5:C16.C2^2	320,1129
D₅⋊C₄≀C₂	The semidirect product of D₅ and C₄≀C₂ acting via C₄≀C₂/C₄○D₄=C₂	40	8	D5:C4wrC2	320,1130
C₄○D₄⋊F₅	2^nd semidirect product of C₄○D₄ and F₅ acting via F₅/D₅=C₂	40	8	C4oD4:F5	320,1131
C₄○D₂₀⋊C₄	3^rd semidirect product of C₄○D₂₀ and C₄ acting faithfully	80	8	C4oD20:C4	320,1132
D₄⋊F₅⋊C₂	6^th semidirect product of D₄⋊F₅ and C₂ acting faithfully	80	8	D4:F5:C2	320,1133
Dic₅.₂₁C₂⁴	21^st non-split extension by Dic₅ of C₂⁴ acting via C₂⁴/C₂³=C₂	80	8	Dic5.21C2^4	320,1601
Dic₅.₂₂C₂⁴	22^nd non-split extension by Dic₅ of C₂⁴ acting via C₂⁴/C₂³=C₂	80	8	Dic5.22C2^4	320,1602
C₄○D₄×F₅	Direct product of C₄○D₄ and F₅	40	8	C4oD4xF5	320,1603
D₅.2₊¹⁺⁴	The non-split extension by D₅ of 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₄○D₄=C₂	40	8	D5.ES+(2,2)	320,1604

Groups of order 360

		d	ρ	Label	ID
C₅×F₉	Direct product of C₅ and F₉	45	8	C5xF9	360,123
C₅⋊₂F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃²⋊C₄=C₂	45	8	C5:2F9	360,124
C₅⋊F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃⋊S₃=C₄	45	8	C5:F9	360,125
C₃×S₃×F₅	Direct product of C₃, S₃ and F₅	30	8	C3xS3xF5	360,126
S₃×C₃⋊F₅	Direct product of S₃ and C₃⋊F₅	30	8	S3xC3:F5	360,128
C₅×PSU₃(𝔽₂)	Direct product of C₅ and PSU₃(𝔽₂)	45	8	C5xPSU(3,2)	360,135
C₃²⋊Dic₁₀	The semidirect product of C₃² and Dic₁₀ acting via Dic₁₀/C₅=Q₈	45	8	C3^2:Dic10	360,136

Groups of order 408

		d	ρ	Label	ID
C₃×C₁₇⋊C₈	Direct product of C₃ and C₁₇⋊C₈	51	8	C3xC17:C8	408,33
C₅₁⋊C₈	1^st semidirect product of C₅₁ and C₈ acting faithfully	51	8	C51:C8	408,34

Groups of order 432

		d	ρ	Label	ID
C₃×C₂.F₉	Direct product of C₃ and C₂.F₉	48	8	C3xC2.F9	432,565
C₆.F₉	3^rd non-split extension by C₆ of F₉ acting via F₉/C₃²⋊C₄=C₂	48	8	C6.F9	432,566
C₃×C₂.PSU₃(𝔽₂)	Direct product of C₃ and C₂.PSU₃(𝔽₂)	48	8	C3xC2.PSU(3,2)	432,591
C₆.PSU₃(𝔽₂)	1^st non-split extension by C₆ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C6.PSU(3,2)	432,592
C₆.₂PSU₃(𝔽₂)	2^nd non-split extension by C₆ of PSU₃(𝔽₂) acting via PSU₃(𝔽₂)/C₃²⋊C₄=C₂	48	8	C6.2PSU(3,2)	432,593
C₃×AΓL₁(𝔽₉)	Direct product of C₃ and AΓL₁(𝔽₉)	24	8	C3xAGammaL(1,9)	432,737
C₃³⋊SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting faithfully	24	8	C3^3:SD16	432,738
C₆×F₉	Direct product of C₆ and F₉	48	8	C6xF9	432,751
C₂×C₃⋊F₉	Direct product of C₂ and C₃⋊F₉	48	8	C2xC3:F9	432,752
C₆×PSU₃(𝔽₂)	Direct product of C₆ and PSU₃(𝔽₂)	48	8	C6xPSU(3,2)	432,757
C₂×C₃³⋊Q₈	Direct product of C₂ and C₃³⋊Q₈	48	8	C2xC3^3:Q8	432,758

Groups of order 480

		d	ρ	Label	ID
F₅×C₃⋊C₈	Direct product of F₅ and C₃⋊C₈	120	8	F5xC3:C8	480,223
C₃₀.C₄²	2^nd non-split extension by C₃₀ of C₄² acting via C₄²/C₂=C₂×C₄	120	8	C30.C4^2	480,224
C₃₀.₃C₄²	3^rd non-split extension by C₃₀ of C₄² acting via C₄²/C₂=C₂×C₄	120	8	C30.3C4^2	480,225
C₃₀.₄C₄²	4^th non-split extension by C₃₀ of C₄² acting via C₄²/C₂=C₂×C₄	120	8	C30.4C4^2	480,226
Dic₅.Dic₆	3^rd non-split extension by Dic₅ of Dic₆ acting via Dic₆/Dic₃=C₂	120	8	Dic5.Dic6	480,235
Dic₅.₄Dic₆	4^th non-split extension by Dic₅ of Dic₆ acting via Dic₆/Dic₃=C₂	120	8	Dic5.4Dic6	480,236
D₁₀.Dic₆	1^st non-split extension by D₁₀ of Dic₆ acting via Dic₆/Dic₃=C₂	240	8	D10.Dic6	480,237
D₁₀.₂Dic₆	2^nd non-split extension by D₁₀ of Dic₆ acting via Dic₆/Dic₃=C₂	240	8	D10.2Dic6	480,238
S₃×C₅⋊C₁₆	Direct product of S₃ and C₅⋊C₁₆	240	8	S3xC5:C16	480,239
D₁₅⋊C₁₆	The semidirect product of D₁₅ and C₁₆ acting via C₁₆/C₄=C₄	240	8	D15:C16	480,240
C₁₅⋊M₅(2)	1^st semidirect product of C₁₅ and M₅(2) acting via M₅(2)/C₄=C₂×C₄	240	8	C15:M5(2)	480,241
D₃₀.C₈	2^nd non-split extension by D₃₀ of C₈ acting via C₈/C₂=C₄	240	8	D30.C8	480,242
C₃×D₂₀⋊C₄	Direct product of C₃ and D₂₀⋊C₄	120	8	C3xD20:C4	480,287
C₃×D₄⋊F₅	Direct product of C₃ and D₄⋊F₅	120	8	C3xD4:F5	480,288
C₃×Q₈⋊F₅	Direct product of C₃ and Q₈⋊F₅	120	8	C3xQ8:F5	480,289
C₃×Q₈⋊₂F₅	Direct product of C₃ and Q₈⋊₂F₅	120	8	C3xQ8:2F5	480,290
D₂₀⋊Dic₃	1^st semidirect product of D₂₀ and Dic₃ acting via Dic₃/C₃=C₄	120	8	D20:Dic3	480,312
Dic₁₀⋊Dic₃	1^st semidirect product of Dic₁₀ and Dic₃ acting via Dic₃/C₃=C₄	120	8	Dic10:Dic3	480,313
Dic₁₀⋊₂Dic₃	2^nd semidirect product of Dic₁₀ and Dic₃ acting via Dic₃/C₃=C₄	120	8	Dic10:2Dic3	480,314
D₂₀⋊₂Dic₃	2^nd semidirect product of D₂₀ and Dic₃ acting via Dic₃/C₃=C₄	120	8	D20:2Dic3	480,315
C₄⋊F₅⋊₃S₃	The semidirect product of C₄⋊F₅ and S₃ acting through Inn(C₄⋊F₅)	120	8	C4:F5:3S3	480,983
(C₄×S₃)⋊F₅	3^rd semidirect product of C₄×S₃ and F₅ acting via F₅/D₅=C₂	120	8	(C4xS3):F5	480,985
S₃×D₅⋊C₈	Direct product of S₃ and D₅⋊C₈	120	8	S3xD5:C8	480,986
S₃×C₄.F₅	Direct product of S₃ and C₄.F₅	120	8	S3xC4.F5	480,988
D₁₅⋊M₄(2)	The semidirect product of D₁₅ and M₄(2) acting via M₄(2)/C₄=C₄	120	8	D15:M4(2)	480,991
C₅⋊C₈⋊D₆	1^st semidirect product of C₅⋊C₈ and D₆ acting via D₆/C₆=C₂	120	8	C5:C8:D6	480,993
C₄×S₃×F₅	Direct product of C₄, S₃ and F₅	60	8	C4xS3xF5	480,994
S₃×C₄⋊F₅	Direct product of S₃ and C₄⋊F₅	60	8	S3xC4:F5	480,996
C₅⋊C₈.D₆	3^rd non-split extension by C₅⋊C₈ of D₆ acting via D₆/C₆=C₂	240	8	C5:C8.D6	480,1003
D₁₅⋊C₈⋊C₂	5^th semidirect product of D₁₅⋊C₈ and C₂ acting faithfully	240	8	D15:C8:C2	480,1005
F₅×C₃⋊D₄	Direct product of F₅ and C₃⋊D₄	60	8	F5xC3:D4	480,1010
C₃⋊D₄⋊F₅	The semidirect product of C₃⋊D₄ and F₅ acting via F₅/D₅=C₂	60	8	C3:D4:F5	480,1012
C₃×D₄.F₅	Direct product of C₃ and D₄.F₅	240	8	C3xD4.F5	480,1053
C₃×D₄×F₅	Direct product of C₃, D₄ and F₅	60	8	C3xD4xF5	480,1054
C₃×Q₈.F₅	Direct product of C₃ and Q₈.F₅	240	8	C3xQ8.F5	480,1055
C₃×Q₈×F₅	Direct product of C₃, Q₈ and F₅	120	8	C3xQ8xF5	480,1056
Dic₁₀.Dic₃	The non-split extension by Dic₁₀ of Dic₃ acting via Dic₃/C₃=C₄	240	8	Dic10.Dic3	480,1066
D₄×C₃⋊F₅	Direct product of D₄ and C₃⋊F₅	60	8	D4xC3:F5	480,1067
D₂₀.Dic₃	The non-split extension by D₂₀ of Dic₃ acting via Dic₃/C₃=C₄	240	8	D20.Dic3	480,1068
Q₈×C₃⋊F₅	Direct product of Q₈ and C₃⋊F₅	120	8	Q8xC3:F5	480,1069

Orthogonal of dimension 9 (ρ=9+)

Groups of order 144

		d	ρ	Label	ID
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	12	9+	A4^2	144,184

Groups of order 288

		d	ρ	Label	ID
A₄×S₄	Direct product of A₄ and S₄	16	9+	A4xS4	288,1024
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	12	9+	PSO+(4,3)	288,1026
C₂×A₄²	Direct product of C₂, A₄ and A₄	18	9+	C2xA4^2	288,1029

Complex of dimension 9 (ρ=9)

Groups of order 171

		d	ρ	Label	ID
C₁₉⋊C₉	The semidirect product of C₁₉ and C₉ acting faithfully	19	9	C19:C9	171,3

Groups of order 243

		d	ρ	Label	ID
C₂₇⋊C₉	The semidirect product of C₂₇ and C₉ acting faithfully	27	9	C27:C9	243,22
C₃².He₃	4^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.He3	243,28
C₃².₅He₃	5^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.5He3	243,29
C₃².₆He₃	6^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	27	9	C3^2.6He3	243,30
C₃³⋊C₃²	2^nd semidirect product of C₃³ and C₃² acting faithfully	27	9	C3^3:C3^2	243,56
He₃.C₃²	4^th non-split extension by He₃ of C₃² acting via C₃²/C₃=C₃	27	9	He3.C3^2	243,57
He₃⋊C₃²	3^rd semidirect product of He₃ and C₃² acting via C₃²/C₃=C₃	27	9	He3:C3^2	243,58
C₃².C₃³	9^th non-split extension by C₃² of C₃³ acting via C₃³/C₃²=C₃	27	9	C3^2.C3^3	243,59
C₉.₂He₃	2^nd non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	27	9	C9.2He3	243,60
3₊¹⁺⁴	Extraspecial group; = He₃ ○He₃	27	9	ES+(3,2)	243,65
3_-¹⁺⁴	Extraspecial group; = He₃ ○3_-¹⁺²	27	9	ES-(3,2)	243,66

Groups of order 252

		d	ρ	Label	ID
A₄×C₇⋊C₃	Direct product of A₄ and C₇⋊C₃	28	9	A4xC7:C3	252,27

Groups of order 324

		d	ρ	Label	ID
He₃.A₄	The non-split extension by He₃ of A₄ acting via A₄/C₂²=C₃	54	9	He3.A4	324,53
He₃⋊A₄	1^st semidirect product of He₃ and A₄ acting via A₄/C₂²=C₃	54	9	He3:A4	324,54
He₃⋊₂A₄	2^nd semidirect product of He₃ and A₄ acting via A₄/C₂²=C₃	36	9	He3:2A4	324,55
C₆².C₃²	4^th non-split extension by C₆² of C₃² acting faithfully	54	9	C6^2.C3^2	324,56
3_-¹⁺²⋊A₄	1^st semidirect product of 3_-¹⁺² and A₄ acting via A₄/C₂²=C₃	54	9	ES-(3,1):A4	324,57
C₆².₆C₃²	6^th non-split extension by C₆² of C₃² acting faithfully	36	9	C6^2.6C3^2	324,58
He₃.₂A₄	The non-split extension by He₃ of A₄ acting through Inn(He₃)	54	9	He3.2A4	324,129
A₄×He₃	Direct product of A₄ and He₃	36	9	A4xHe3	324,130
A₄×3_-¹⁺²	Direct product of A₄ and 3_-¹⁺²	36	9	A4xES-(3,1)	324,131
C₆².₉C₃²	9^th non-split extension by C₆² of C₃² acting faithfully	54	9	C6^2.9C3^2	324,132

Groups of order 333

		d	ρ	Label	ID
C₃₇⋊C₉	The semidirect product of C₃₇ and C₉ acting faithfully	37	9	C37:C9	333,3

Groups of order 342

		d	ρ	Label	ID
C₂×C₁₉⋊C₉	Direct product of C₂ and C₁₉⋊C₉	38	9	C2xC19:C9	342,8

Groups of order 432

		d	ρ	Label	ID
A₄×C₃.A₄	Direct product of A₄ and C₃.A₄	54	9	A4xC3.A4	432,524
C₃.A₄²	2^nd central extension by C₃ of A₄²	36	9	C3.A4^2	432,525
C₂⁴⋊He₃	The semidirect product of C₂⁴ and He₃ acting via He₃/C₃=C₃²	36	9	C2^4:He3	432,526
C₂⁴⋊3_-¹⁺²	1^st semidirect product of C₂⁴ and 3_-¹⁺² acting via 3_-¹⁺²/C₃=C₃²	54	9	C2^4:ES-(3,1)	432,527
C₂⁴⋊₂3_-¹⁺²	2^nd semidirect product of C₂⁴ and 3_-¹⁺² acting via 3_-¹⁺²/C₃=C₃²	36	9	C2^4:2ES-(3,1)	432,528
C₃×A₄²	Direct product of C₃, A₄ and A₄	36	9	C3xA4^2	432,750

Groups of order 441

		d	ρ	Label	ID
C₇⋊C₃²	Direct product of C₇⋊C₃ and C₇⋊C₃	21	9	C7:C3^2	441,9

Groups of order 468

		d	ρ	Label	ID
A₄×C₁₃⋊C₃	Direct product of A₄ and C₁₃⋊C₃	52	9	A4xC13:C3	468,32

Groups of order 486

		d	ρ	Label	ID
C₂×C₂₇⋊C₉	Direct product of C₂ and C₂₇⋊C₉	54	9	C2xC27:C9	486,82
C₂×C₃².He₃	Direct product of C₂ and C₃².He₃	54	9	C2xC3^2.He3	486,88
C₂×C₃².₅He₃	Direct product of C₂ and C₃².₅He₃	54	9	C2xC3^2.5He3	486,89
C₂×C₃².₆He₃	Direct product of C₂ and C₃².₆He₃	54	9	C2xC3^2.6He3	486,90
C₃≀C₃⋊C₆	2^nd semidirect product of C₃≀C₃ and C₆ acting faithfully	27	9	C3wrC3:C6	486,126
He₃.C₃⋊C₆	3^rd semidirect product of He₃.C₃ and C₆ acting faithfully	27	9	He3.C3:C6	486,128
He₃.(C₃×C₆)	6^th non-split extension by He₃ of C₃×C₆ acting via C₃×C₆/C₃=C₆	27	9	He3.(C3xC6)	486,130
C₃≀C₃.C₆	The non-split extension by C₃≀C₃ of C₆ acting faithfully	27	9	C3wrC3.C6	486,132
C₂×C₃³⋊C₃²	Direct product of C₂ and C₃³⋊C₃²	54	9	C2xC3^3:C3^2	486,215
C₂×He₃.C₃²	Direct product of C₂ and He₃.C₃²	54	9	C2xHe3.C3^2	486,216
C₂×He₃⋊C₃²	Direct product of C₂ and He₃⋊C₃²	54	9	C2xHe3:C3^2	486,217
C₂×C₃².C₃³	Direct product of C₂ and C₃².C₃³	54	9	C2xC3^2.C3^3	486,218
C₂×C₉.₂He₃	Direct product of C₂ and C₉.₂He₃	54	9	C2xC9.2He3	486,219
3₊¹⁺⁴⋊₂C₂	2^nd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	9	ES+(3,2):2C2	486,237
3_-¹⁺⁴⋊₂C₂	2^nd semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	27	9	ES-(3,2):2C2	486,239
3₊¹⁺⁴⋊₃C₂	3^rd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	9	ES+(3,2):3C2	486,249
C₂×3₊¹⁺⁴	Direct product of C₂ and 3₊¹⁺⁴	54	9	C2xES+(3,2)	486,254
C₂×3_-¹⁺⁴	Direct product of C₂ and 3_-¹⁺⁴	54	9	C2xES-(3,2)	486,255

Orthogonal of dimension 10 (ρ=10+)

Groups of order 110

		d	ρ	Label	ID
F₁₁	Frobenius group; = C₁₁ ⋊C₁₀ = AGL₁(𝔽₁₁) = Aut(D₁₁) = Hol(C₁₁)	11	10+	F11	110,1

Groups of order 220

		d	ρ	Label	ID
C₂×F₁₁	Direct product of C₂ and F₁₁; = Aut(D₂₂) = Hol(C₂₂)	22	10+	C2xF11	220,7

Groups of order 250

		d	ρ	Label	ID
C₅²⋊C₁₀	The semidirect product of C₅² and C₁₀ acting faithfully	25	10+	C5^2:C10	250,5
C₂₅⋊C₁₀	The semidirect product of C₂₅ and C₁₀ acting faithfully	25	10+	C25:C10	250,6

Groups of order 310

		d	ρ	Label	ID
C₃₁⋊C₁₀	The semidirect product of C₃₁ and C₁₀ acting faithfully	31	10+	C31:C10	310,1

Groups of order 330

		d	ρ	Label	ID
C₃⋊F₁₁	The semidirect product of C₃ and F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	33	10+	C3:F11	330,3

Groups of order 410

		d	ρ	Label	ID
C₄₁⋊C₁₀	The semidirect product of C₄₁ and C₁₀ acting faithfully	41	10+	C41:C10	410,1

Groups of order 440

		d	ρ	Label	ID
D₄₄⋊C₅	The semidirect product of D₄₄ and C₅ acting faithfully	44	10+	D44:C5	440,9

Groups of order 480

		d	ρ	Label	ID
C₂⁴⋊D₁₅	The semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₃=D₅	30	10+	C2^4:D15	480,1195
S₃×C₂⁴⋊C₅	Direct product of S₃ and C₂⁴⋊C₅	30	10+	S3xC2^4:C5	480,1196

Groups of order 500

		d	ρ	Label	ID
C₅²⋊F₅	3^rd semidirect product of C₅² and F₅ acting faithfully	25	10+	C5^2:F5	500,23
C₅²⋊D₁₀	The semidirect product of C₅² and D₁₀ acting faithfully	25	10+	C5^2:D10	500,27
C₂×C₅²⋊C₁₀	Direct product of C₂ and C₅²⋊C₁₀	50	10+	C2xC5^2:C10	500,30
C₂×C₂₅⋊C₁₀	Direct product of C₂ and C₂₅⋊C₁₀	50	10+	C2xC25:C10	500,31

Symplectic of dimension 10 (ρ=10-)

Groups of order 220

		d	ρ	Label	ID
C₁₁⋊C₂₀	The semidirect product of C₁₁ and C₂₀ acting via C₂₀/C₂=C₁₀	44	10-	C11:C20	220,1

Groups of order 440

		d	ρ	Label	ID
C₄.F₁₁	The non-split extension by C₄ of F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	88	10-	C4.F11	440,7

Groups of order 500

		d	ρ	Label	ID
He₅⋊₅C₄	1^st semidirect product of He₅ and C₄ acting via C₄/C₂=C₂	100	10-	He5:5C4	500,8
C₅₀.C₁₀	The non-split extension by C₅₀ of C₁₀ acting faithfully	100	10-	C50.C10	500,9

Complex of dimension 10 (ρ=10)

Groups of order 330

		d	ρ	Label	ID
C₃×F₁₁	Direct product of C₃ and F₁₁	33	10	C3xF11	330,1
S₃×C₁₁⋊C₅	Direct product of S₃ and C₁₁⋊C₅	33	10	S3xC11:C5	330,2

Groups of order 440

		d	ρ	Label	ID
C₁₁⋊C₄₀	The semidirect product of C₁₁ and C₄₀ acting via C₄₀/C₄=C₁₀	88	10	C11:C40	440,1
C₄×F₁₁	Direct product of C₄ and F₁₁	44	10	C4xF11	440,8
C₂²⋊F₁₁	The semidirect product of C₂² and F₁₁ acting via F₁₁/C₁₁⋊C₅=C₂	44	10	C2^2:F11	440,11
D₄×C₁₁⋊C₅	Direct product of D₄ and C₁₁⋊C₅	44	10	D4xC11:C5	440,13
Q₈×C₁₁⋊C₅	Direct product of Q₈ and C₁₁⋊C₅	88	10	Q8xC11:C5	440,14

Complex of dimension 11 (ρ=11)

Groups of order 253

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

Orthogonal of dimension 12 (ρ=12+)

Groups of order 156

		d	ρ	Label	ID
F₁₃	Frobenius group; = C₁₃ ⋊C₁₂ = AGL₁(𝔽₁₃) = Aut(D₁₃) = Hol(C₁₃)	13	12+	F13	156,7

Groups of order 192

		d	ρ	Label	ID
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	16	12+	C2^4:Dic3	192,184
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	16	12+	C4^2:Dic3	192,185
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	16	12+	C2^4.6A4	192,1008
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	16	12+	C2^4:A4	192,1009
C₄²⋊A₄	The semidirect product of C₄² and A₄ acting faithfully	16	12+	C4^2:A4	192,1023

Groups of order 240

		d	ρ	Label	ID
A₄⋊F₅	The semidirect product of A₄ and F₅ acting via F₅/D₅=C₂	20	12+	A4:F5	240,192
A₄×F₅	Direct product of A₄ and F₅	20	12+	A4xF5	240,193

Groups of order 252

		d	ρ	Label	ID
S₃×F₇	Direct product of S₃ and F₇; = Aut(D₂₁) = Hol(C₂₁)	21	12+	S3xF7	252,26

Groups of order 300

		d	ρ	Label	ID
C₅²⋊Dic₃	The semidirect product of C₅² and Dic₃ acting faithfully	15	12+	C5^2:Dic3	300,23
C₅²⋊C₁₂	The semidirect product of C₅² and C₁₂ acting faithfully	15	12+	C5^2:C12	300,24

Groups of order 312

		d	ρ	Label	ID
C₂×F₁₃	Direct product of C₂ and F₁₃; = Aut(D₂₆) = Hol(C₂₆)	26	12+	C2xF13	312,45

Groups of order 324

		d	ρ	Label	ID
C₃²⋊D₁₈	The semidirect product of C₃² and D₁₈ acting via D₁₈/C₃=D₆	18	12+	C3^2:D18	324,37
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	18	12+	S3xC3^2:C6	324,116
S₃×C₉⋊C₆	Direct product of S₃ and C₉⋊C₆	18	12+	S3xC9:C6	324,118
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	18	12+	He3:5D6	324,121

Groups of order 336

		d	ρ	Label	ID
D₄⋊F₇	The semidirect product of D₄ and F₇ acting via F₇/C₇⋊C₃=C₂	56	12+	D4:F7	336,18
Q₈⋊₂F₇	The semidirect product of Q₈ and F₇ acting via F₇/C₇⋊C₃=C₂	56	12+	Q8:2F7	336,20
D₄×F₇	Direct product of D₄ and F₇; = Aut(D₂₈) = Hol(C₂₈)	28	12+	D4xF7	336,125
Q₈⋊₃F₇	The semidirect product of Q₈ and F₇ acting through Inn(Q₈)	56	12+	Q8:3F7	336,128
Q₈.F₇	The non-split extension by Q₈ of F₇ acting via F₇/D₇=C₃	112	12+	Q8.F7	336,134

Groups of order 420

		d	ρ	Label	ID
D₅×F₇	Direct product of D₅ and F₇	35	12+	D5xF7	420,16

Groups of order 432

		d	ρ	Label	ID
He₃⋊₃D₈	2^nd semidirect product of He₃ and D₈ acting via D₈/C₄=C₂²	72	12+	He3:3D8	432,83
He₃⋊₅SD₁₆	3^rd semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₄=C₂²	72	12+	He3:5SD16	432,85
He₃⋊₆D₈	1^st semidirect product of He₃ and D₈ acting via D₈/D₄=C₂	72	12+	He3:6D8	432,153
D₃₆⋊C₆	1^st semidirect product of D₃₆ and C₆ acting faithfully	72	12+	D36:C6	432,155
He₃⋊₁₀SD₁₆	1^st semidirect product of He₃ and SD₁₆ acting via SD₁₆/Q₈=C₂	72	12+	He3:10SD16	432,161
D₃₆.C₆	1^st non-split extension by D₃₆ of C₆ acting faithfully	72	12+	D36.C6	432,163
C₃².GL₂(𝔽₃)	The non-split extension by C₃² of GL₂(𝔽₃) acting via GL₂(𝔽₃)/Q₈=S₃	72	12+	C3^2.GL(2,3)	432,245
C₃²⋊₂GL₂(𝔽₃)	1^st semidirect product of C₃² and GL₂(𝔽₃) acting via GL₂(𝔽₃)/Q₈=S₃	72	12+	C3^2:2GL(2,3)	432,248
Dic₉.A₄	The non-split extension by Dic₉ of A₄ acting via A₄/C₂²=C₃	144	12+	Dic9.A4	432,261
C₆.(S₃×A₄)	7^th non-split extension by C₆ of S₃×A₄ acting via S₃×A₄/C₃×A₄=C₂	72	12+	C6.(S3xA4)	432,269
C₁₂⋊S₃⋊S₃	3^rd semidirect product of C₁₂⋊S₃ and S₃ acting faithfully	72	12+	C12:S3:S3	432,295
C₃⋊S₃⋊D₁₂	The semidirect product of C₃⋊S₃ and D₁₂ acting via D₁₂/C₄=S₃	36	12+	C3:S3:D12	432,301
C₆²⋊D₆	1^st semidirect product of C₆² and D₆ acting faithfully	36	12+	C6^2:D6	432,323
D₄×C₃²⋊C₆	Direct product of D₄ and C₃²⋊C₆	36	12+	D4xC3^2:C6	432,360
D₄×C₉⋊C₆	Direct product of D₄ and C₉⋊C₆; = Aut(D₃₆) = Hol(C₃₆)	36	12+	D4xC9:C6	432,362
(Q₈×He₃)⋊C₂	4^th semidirect product of Q₈×He₃ and C₂ acting faithfully	72	12+	(Q8xHe3):C2	432,369
D₃₆⋊₃C₆	3^rd semidirect product of D₃₆ and C₆ acting faithfully	72	12+	D36:3C6	432,371
S₃×C₃.S₄	Direct product of S₃ and C₃.S₄	36	12+	S3xC3.S4	432,522
C₆²⋊Dic₃	The semidirect product of C₆² and Dic₃ acting faithfully	24	12+	C6^2:Dic3	432,743
A₄×C₃²⋊C₄	Direct product of A₄ and C₃²⋊C₄	24	12+	A4xC3^2:C4	432,744
S₃×C₃⋊S₄	Direct product of S₃ and C₃⋊S₄	24	12+	S3xC3:S4	432,747
C₆²⋊₁₀D₆	10^th semidirect product of C₆² and D₆ acting faithfully	24	12+	C6^2:10D6	432,748
S₃²×A₄	Direct product of S₃, S₃ and A₄	24	12+	S3^2xA4	432,749

Groups of order 444

		d	ρ	Label	ID
C₃₇⋊C₁₂	The semidirect product of C₃₇ and C₁₂ acting faithfully	37	12+	C37:C12	444,7

Groups of order 468

		d	ρ	Label	ID
S₃×C₁₃⋊C₆	Direct product of S₃ and C₁₃⋊C₆	39	12+	S3xC13:C6	468,31

Groups of order 480

		d	ρ	Label	ID
F₅×S₄	Direct product of F₅ and S₄; = Hol(C₂×C₁₀)	20	12+	F5xS4	480,1189
C₂×A₄⋊F₅	Direct product of C₂ and A₄⋊F₅	30	12+	C2xA4:F5	480,1191
C₂×A₄×F₅	Direct product of C₂, A₄ and F₅	30	12+	C2xA4xF5	480,1192

Symplectic of dimension 12 (ρ=12-)

Groups of order 192

		d	ρ	Label	ID
C₄².A₄	The non-split extension by C₄² of A₄ acting faithfully	48	12-	C4^2.A4	192,1025

Groups of order 312

		d	ρ	Label	ID
C₁₃⋊C₂₄	The semidirect product of C₁₃ and C₂₄ acting via C₂₄/C₂=C₁₂	104	12-	C13:C24	312,7

Groups of order 336

		d	ρ	Label	ID
D₄.F₇	The non-split extension by D₄ of F₇ acting via F₇/C₇⋊C₃=C₂	56	12-	D4.F7	336,19
Q₈.₂F₇	The non-split extension by Q₈ of F₇ acting via F₇/C₇⋊C₃=C₂	112	12-	Q8.2F7	336,21
D₄⋊₂F₇	The semidirect product of D₄ and F₇ acting through Inn(D₄)	56	12-	D4:2F7	336,126
Q₈×F₇	Direct product of Q₈ and F₇	56	12-	Q8xF7	336,127
Q₈⋊F₇	The semidirect product of Q₈ and F₇ acting via F₇/D₇=C₃	56	12-	Q8:F7	336,135

Groups of order 432

		d	ρ	Label	ID
He₃⋊₄SD₁₆	2^nd semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₄=C₂²	72	12-	He3:4SD16	432,84
He₃⋊₃Q₁₆	2^nd semidirect product of He₃ and Q₁₆ acting via Q₁₆/C₄=C₂²	144	12-	He3:3Q16	432,86
He₃⋊₈SD₁₆	1^st semidirect product of He₃ and SD₁₆ acting via SD₁₆/D₄=C₂	72	12-	He3:8SD16	432,152
Dic₁₈⋊C₆	1^st semidirect product of Dic₁₈ and C₆ acting faithfully	72	12-	Dic18:C6	432,154
He₃⋊₆Q₁₆	1^st semidirect product of He₃ and Q₁₆ acting via Q₁₆/Q₈=C₂	144	12-	He3:6Q16	432,160
Dic₁₈.C₆	1^st non-split extension by Dic₁₈ of C₆ acting faithfully	144	12-	Dic18.C6	432,162
C₃².CSU₂(𝔽₃)	The non-split extension by C₃² of CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/Q₈=S₃	144	12-	C3^2.CSU(2,3)	432,243
C₃²⋊CSU₂(𝔽₃)	1^st semidirect product of C₃² and CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/Q₈=S₃	144	12-	C3^2:CSU(2,3)	432,247
D₁₈.A₄	The non-split extension by D₁₈ of A₄ acting via A₄/C₂²=C₃	72	12-	D18.A4	432,263
Q₈⋊He₃⋊C₂	4^th semidirect product of Q₈⋊He₃ and C₂ acting faithfully	72	12-	Q8:He3:C2	432,270
C₃⋊S₃⋊Dic₆	The semidirect product of C₃⋊S₃ and Dic₆ acting via Dic₆/C₄=S₃	72	12-	C3:S3:Dic6	432,294
C₁₂.S₃²	23^rd non-split extension by C₁₂ of S₃² acting via S₃²/C₃²=C₂²	72	12-	C12.S3^2	432,299
C₆².₈D₆	8^th non-split extension by C₆² of D₆ acting faithfully	72	12-	C6^2.8D6	432,318
C₆².₁₃D₆	13^rd non-split extension by C₆² of D₆ acting faithfully	72	12-	C6^2.13D6	432,361
Dic₁₈⋊₂C₆	2^nd semidirect product of Dic₁₈ and C₆ acting faithfully	72	12-	Dic18:2C6	432,363
Q₈×C₃²⋊C₆	Direct product of Q₈ and C₃²⋊C₆	72	12-	Q8xC3^2:C6	432,368
Q₈×C₉⋊C₆	Direct product of Q₈ and C₉⋊C₆	72	12-	Q8xC9:C6	432,370

Groups of order 480

		d	ρ	Label	ID
Dic₅.S₄	5^th non-split extension by Dic₅ of S₄ acting via S₄/A₄=C₂	120	12-	Dic5.S4	480,963
A₄×C₅⋊C₈	Direct product of A₄ and C₅⋊C₈	120	12-	A4xC5:C8	480,966

Complex of dimension 12 (ρ=12)

Groups of order 420

		d	ρ	Label	ID
F₅×C₇⋊C₃	Direct product of F₅ and C₇⋊C₃	35	12	F5xC7:C3	420,14
C₃₅⋊C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting faithfully	35	12	C35:C12	420,15

Groups of order 468

		d	ρ	Label	ID
C₁₃⋊C₃₆	The semidirect product of C₁₃ and C₃₆ acting via C₃₆/C₃=C₁₂	117	12	C13:C36	468,7
C₃×F₁₃	Direct product of C₃ and F₁₃	39	12	C3xF13	468,29
C₃⋊F₁₃	The semidirect product of C₃ and F₁₃ acting via F₁₃/C₁₃⋊C₆=C₂	39	12	C3:F13	468,30

Complex of dimension 13 (ρ=13)

Groups of order 351

		d	ρ	Label	ID
C₃³⋊C₁₃	The semidirect product of C₃³ and C₁₃ acting faithfully	27	13	C3^3:C13	351,12

Orthogonal of dimension 14 (ρ=14+)

Groups of order 336

		d	ρ	Label	ID
S₃×F₈	Direct product of S₃ and F₈	24	14+	S3xF8	336,211

Groups of order 406

		d	ρ	Label	ID
C₂₉⋊C₁₄	The semidirect product of C₂₉ and C₁₄ acting faithfully	29	14+	C29:C14	406,1

Groups of order 448

		d	ρ	Label	ID
D₄×F₈	Direct product of D₄ and F₈	28	14+	D4xF8	448,1363

Symplectic of dimension 14 (ρ=14-)

Groups of order 448

		d	ρ	Label	ID
Q₈×F₈	Direct product of Q₈ and F₈	56	14-	Q8xF8	448,1364

Complex of dimension 14 (ρ=14)

Groups of order 448

		d	ρ	Label	ID
C₂³.F₈	2^nd non-split extension by C₂³ of F₈ acting via F₈/C₂³=C₇	56	14	C2^3.F8	448,179

Orthogonal of dimension 15 (ρ=15+)

Groups of order 240

		d	ρ	Label	ID
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	16	15+	F16	240,191

Groups of order 480

		d	ρ	Label	ID
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	16	15+	F16:C2	480,1188
C₂×F₁₆	Direct product of C₂ and F₁₆	30	15+	C2xF16	480,1190

Complex of dimension 15 (ρ=15)

Groups of order 465

		d	ρ	Label	ID
C₃₁⋊C₁₅	The semidirect product of C₃₁ and C₁₅ acting faithfully	31	15	C31:C15	465,1

Orthogonal of dimension 16 (ρ=16+)

Groups of order 272

		d	ρ	Label	ID
F₁₇	Frobenius group; = C₁₇ ⋊C₁₆ = AGL₁(𝔽₁₇) = Aut(D₁₇) = Hol(C₁₇)	17	16+	F17	272,50

Groups of order 400

		d	ρ	Label	ID
F₅²	Direct product of F₅ and F₅; = Hol(F₅)	20	16+	F5^2	400,205

Groups of order 432

		d	ρ	Label	ID
S₃×F₉	Direct product of S₃ and F₉	24	16+	S3xF9	432,736
C₃³⋊₃SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting faithfully	24	16+	C3^3:3SD16	432,739
F₉⋊S₃	The semidirect product of F₉ and S₃ acting via S₃/C₃=C₂	24	16+	F9:S3	432,740
S₃×PSU₃(𝔽₂)	Direct product of S₃ and PSU₃(𝔽₂)	24	16+	S3xPSU(3,2)	432,742

Orthogonal of dimension 18 (ρ=18+)

Groups of order 342

		d	ρ	Label	ID
F₁₉	Frobenius group; = C₁₉ ⋊C₁₈ = AGL₁(𝔽₁₉) = Aut(D₁₉) = Hol(C₁₉)	19	18+	F19	342,7

Groups of order 486

		d	ρ	Label	ID
C₂₇⋊C₁₈	The semidirect product of C₂₇ and C₁₈ acting faithfully; = Aut(D₂₇) = Hol(C₂₇)	27	18+	C27:C18	486,31
C₉⋊C₉.S₃	2^nd non-split extension by C₉⋊C₉ of S₃ acting faithfully	27	18+	C9:C9.S3	486,39
C₉⋊C₉.₃S₃	3^rd non-split extension by C₉⋊C₉ of S₃ acting faithfully	27	18+	C9:C9.3S3	486,40
C₉⋊C₉⋊S₃	1^st semidirect product of C₉⋊C₉ and S₃ acting faithfully	27	18+	C9:C9:S3	486,41
(C₃×He₃)⋊C₆	8^th semidirect product of C₃×He₃ and C₆ acting faithfully	27	18+	(C3xHe3):C6	486,127
C₉⋊S₃⋊C₃²	2^nd semidirect product of C₉⋊S₃ and C₃² acting faithfully	27	18+	C9:S3:C3^2	486,129
He₃.(C₃×S₃)	5^th non-split extension by He₃ of C₃×S₃ acting via C₃×S₃/C₃=S₃	27	18+	He3.(C3xS3)	486,131
C₃³⋊(C₃×S₃)	4^th semidirect product of C₃³ and C₃×S₃ acting faithfully	27	18+	C3^3:(C3xS3)	486,176
He₃.C₃⋊₂C₆	2^nd semidirect product of He₃.C₃ and C₆ acting faithfully	27	18+	He3.C3:2C6	486,177
He₃⋊(C₃×S₃)	4^th semidirect product of He₃ and C₃×S₃ acting via C₃×S₃/C₃=S₃	27	18+	He3:(C3xS3)	486,178
C₃.He₃⋊C₆	The semidirect product of C₃.He₃ and C₆ acting faithfully	27	18+	C3.He3:C6	486,179
3₊¹⁺⁴⋊C₂	1^st semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	27	18+	ES+(3,2):C2	486,236
3_-¹⁺⁴⋊C₂	1^st semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	27	18+	ES-(3,2):C2	486,238

Orthogonal of dimension 20 (ρ=20+)

Groups of order 500

		d	ρ	Label	ID
C₅²⋊C₂₀	The semidirect product of C₅² and C₂₀ acting faithfully	25	20+	C5^2:C20	500,17
C₂₅⋊C₂₀	The semidirect product of C₂₅ and C₂₀ acting faithfully; = Aut(D₂₅) = Hol(C₂₅)	25	20+	C25:C20	500,18
He₅⋊C₄	2^nd semidirect product of He₅ and C₄ acting faithfully	25	20+	He5:C4	500,21

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