A-groups

An A-group is a group all of whose Sylow subgroups are abelian. See also Z-groups.

Groups of order 1

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

Groups of order 2

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

Groups of order 3

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

Groups of order 4

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

Groups of order 5

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

Groups of order 6

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

Groups of order 7

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

Groups of order 8

		d	ρ	Label	ID
C₈	Cyclic group	8	1	C8	8,1
C₂³	Elementary abelian group of type [2,2,2]	8		C2^3	8,5
C₂×C₄	Abelian group of type [2,4]	8		C2xC4	8,2

Groups of order 9

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

Groups of order 10

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

Groups of order 11

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

Groups of order 12

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

Groups of order 13

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

Groups of order 14

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

Groups of order 15

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

Groups of order 16

		d	ρ	Label	ID
C₁₆	Cyclic group	16	1	C16	16,1
C₄²	Abelian group of type [4,4]	16		C4^2	16,2
C₂⁴	Elementary abelian group of type [2,2,2,2]	16		C2^4	16,14
C₂×C₈	Abelian group of type [2,8]	16		C2xC8	16,5
C₂²×C₄	Abelian group of type [2,2,4]	16		C2^2xC4	16,10

Groups of order 17

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

Groups of order 18

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

Groups of order 19

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

Groups of order 20

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

Groups of order 21

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

Groups of order 22

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

Groups of order 23

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

Groups of order 24

		d	ρ	Label	ID
C₂₄	Cyclic group	24	1	C24	24,2
C₃⋊C₈	The semidirect product of C₃ and C₈ acting via C₈/C₄=C₂	24	2	C3:C8	24,1
C₂×C₁₂	Abelian group of type [2,12]	24		C2xC12	24,9
C₂²×C₆	Abelian group of type [2,2,6]	24		C2^2xC6	24,15
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	6	3+	C2xA4	24,13
C₄×S₃	Direct product of C₄ and S₃	12	2	C4xS3	24,5
C₂²×S₃	Direct product of C₂² and S₃	12		C2^2xS3	24,14
C₂×Dic₃	Direct product of C₂ and Dic₃	24		C2xDic3	24,7

Groups of order 25

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

Groups of order 26

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

Groups of order 27

		d	ρ	Label	ID
C₂₇	Cyclic group	27	1	C27	27,1
C₃³	Elementary abelian group of type [3,3,3]	27		C3^3	27,5
C₃×C₉	Abelian group of type [3,9]	27		C3xC9	27,2

Groups of order 28

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

Groups of order 29

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

Groups of order 30

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

Groups of order 31

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

Groups of order 32

		d	ρ	Label	ID
C₃₂	Cyclic group	32	1	C32	32,1
C₂⁵	Elementary abelian group of type [2,2,2,2,2]	32		C2^5	32,51
C₄×C₈	Abelian group of type [4,8]	32		C4xC8	32,3
C₂×C₁₆	Abelian group of type [2,16]	32		C2xC16	32,16
C₂×C₄²	Abelian group of type [2,4,4]	32		C2xC4^2	32,21
C₂²×C₈	Abelian group of type [2,2,8]	32		C2^2xC8	32,36
C₂³×C₄	Abelian group of type [2,2,2,4]	32		C2^3xC4	32,45

Groups of order 33

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

Groups of order 34

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

Groups of order 35

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

Groups of order 36

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

Groups of order 37

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

Groups of order 38

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

Groups of order 39

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

Groups of order 40

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

Groups of order 41

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

Groups of order 42

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

Groups of order 43

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

Groups of order 44

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

Groups of order 45

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

Groups of order 46

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

Groups of order 47

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

Groups of order 48

		d	ρ	Label	ID
C₄₈	Cyclic group	48	1	C48	48,2
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	12	3	C4^2:C3	48,3
C₂²⋊A₄	The semidirect product of C₂² and A₄ acting via A₄/C₂²=C₃	12		C2^2:A4	48,50
C₃⋊C₁₆	The semidirect product of C₃ and C₁₆ acting via C₁₆/C₈=C₂	48	2	C3:C16	48,1
C₄×C₁₂	Abelian group of type [4,12]	48		C4xC12	48,20
C₂×C₂₄	Abelian group of type [2,24]	48		C2xC24	48,23
C₂³×C₆	Abelian group of type [2,2,2,6]	48		C2^3xC6	48,52
C₂²×C₁₂	Abelian group of type [2,2,12]	48		C2^2xC12	48,44
C₄×A₄	Direct product of C₄ and A₄	12	3	C4xA4	48,31
C₂²×A₄	Direct product of C₂² and A₄	12		C2^2xA4	48,49
S₃×C₈	Direct product of C₈ and S₃	24	2	S3xC8	48,4
S₃×C₂³	Direct product of C₂³ and S₃	24		S3xC2^3	48,51
C₄×Dic₃	Direct product of C₄ and Dic₃	48		C4xDic3	48,11
C₂²×Dic₃	Direct product of C₂² and Dic₃	48		C2^2xDic3	48,42
S₃×C₂×C₄	Direct product of C₂×C₄ and S₃	24		S3xC2xC4	48,35
C₂×C₃⋊C₈	Direct product of C₂ and C₃⋊C₈	48		C2xC3:C8	48,9

Groups of order 49

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

Groups of order 50

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

Groups of order 51

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

Groups of order 52

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

Groups of order 53

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

Groups of order 54

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

Groups of order 55

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

Groups of order 56

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

Groups of order 57

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

Groups of order 58

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

Groups of order 59

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

Groups of order 60

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

Groups of order 61

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

Groups of order 62

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

Groups of order 63

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

Groups of order 64

		d	ρ	Label	ID
C₆₄	Cyclic group	64	1	C64	64,1
C₈²	Abelian group of type [8,8]	64		C8^2	64,2
C₄³	Abelian group of type [4,4,4]	64		C4^3	64,55
C₂⁶	Elementary abelian group of type [2,2,2,2,2,2]	64		C2^6	64,267
C₄×C₁₆	Abelian group of type [4,16]	64		C4xC16	64,26
C₂×C₃₂	Abelian group of type [2,32]	64		C2xC32	64,50
C₂³×C₈	Abelian group of type [2,2,2,8]	64		C2^3xC8	64,246
C₂⁴×C₄	Abelian group of type [2,2,2,2,4]	64		C2^4xC4	64,260
C₂²×C₁₆	Abelian group of type [2,2,16]	64		C2^2xC16	64,183
C₂²×C₄²	Abelian group of type [2,2,4,4]	64		C2^2xC4^2	64,192
C₂×C₄×C₈	Abelian group of type [2,4,8]	64		C2xC4xC8	64,83

Groups of order 65

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

Groups of order 66

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

Groups of order 67

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

Groups of order 68

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

Groups of order 69

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

Groups of order 70

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

Groups of order 71

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

Groups of order 72

		d	ρ	Label	ID
C₇₂	Cyclic group	72	1	C72	72,2
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	9	8+	F9	72,39
C₃²⋊₂C₈	The semidirect product of C₃² and C₈ acting via C₈/C₂=C₄	24	4-	C3^2:2C8	72,19
C₉⋊C₈	The semidirect product of C₉ and C₈ acting via C₈/C₄=C₂	72	2	C9:C8	72,1
C₃²⋊₄C₈	2^nd semidirect product of C₃² and C₈ acting via C₈/C₄=C₂	72		C3^2:4C8	72,13
C₆.D₆	2^nd non-split extension by C₆ of D₆ acting via D₆/S₃=C₂	12	4+	C6.D6	72,21
C₂×C₃₆	Abelian group of type [2,36]	72		C2xC36	72,9
C₃×C₂₄	Abelian group of type [3,24]	72		C3xC24	72,14
C₆×C₁₂	Abelian group of type [6,12]	72		C6xC12	72,36
C₂×C₆²	Abelian group of type [2,6,6]	72		C2xC6^2	72,50
C₂²×C₁₈	Abelian group of type [2,2,18]	72		C2^2xC18	72,18
S₃×A₄	Direct product of S₃ and A₄	12	6+	S3xA4	72,44
C₆×A₄	Direct product of C₆ and A₄	18	3	C6xA4	72,47
S₃×C₁₂	Direct product of C₁₂ and S₃	24	2	S3xC12	72,27
S₃×Dic₃	Direct product of S₃ and Dic₃	24	4-	S3xDic3	72,20
C₆×Dic₃	Direct product of C₆ and Dic₃	24		C6xDic3	72,29
C₄×D₉	Direct product of C₄ and D₉	36	2	C4xD9	72,5
C₂²×D₉	Direct product of C₂² and D₉	36		C2^2xD9	72,17
C₂×Dic₉	Direct product of C₂ and Dic₉	72		C2xDic9	72,7
C₂×S₃²	Direct product of C₂, S₃ and S₃	12	4+	C2xS3^2	72,46
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	12	4+	C2xC3^2:C4	72,45
C₂×C₃.A₄	Direct product of C₂ and C₃.A₄	18	3	C2xC3.A4	72,16
C₃×C₃⋊C₈	Direct product of C₃ and C₃⋊C₈	24	2	C3xC3:C8	72,12
S₃×C₂×C₆	Direct product of C₂×C₆ and S₃	24		S3xC2xC6	72,48
C₄×C₃⋊S₃	Direct product of C₄ and C₃⋊S₃	36		C4xC3:S3	72,32
C₂²×C₃⋊S₃	Direct product of C₂² and C₃⋊S₃	36		C2^2xC3:S3	72,49
C₂×C₃⋊Dic₃	Direct product of C₂ and C₃⋊Dic₃	72		C2xC3:Dic3	72,34

Groups of order 73

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

Groups of order 74

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

Groups of order 75

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

Groups of order 76

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

Groups of order 77

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

Groups of order 78

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

Groups of order 79

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

Groups of order 80

		d	ρ	Label	ID
C₈₀	Cyclic group	80	1	C80	80,2
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	10	5+	C2^4:C5	80,49
D₅⋊C₈	The semidirect product of D₅ and C₈ acting via C₈/C₄=C₂	40	4	D5:C8	80,28
C₅⋊C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5:C16	80,3
C₅⋊₂C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₈=C₂	80	2	C5:2C16	80,1
C₄×C₂₀	Abelian group of type [4,20]	80		C4xC20	80,20
C₂×C₄₀	Abelian group of type [2,40]	80		C2xC40	80,23
C₂²×C₂₀	Abelian group of type [2,2,20]	80		C2^2xC20	80,45
C₂³×C₁₀	Abelian group of type [2,2,2,10]	80		C2^3xC10	80,52
C₄×F₅	Direct product of C₄ and F₅	20	4	C4xF5	80,30
C₂²×F₅	Direct product of C₂² and F₅	20		C2^2xF5	80,50
C₈×D₅	Direct product of C₈ and D₅	40	2	C8xD5	80,4
C₂³×D₅	Direct product of C₂³ and D₅	40		C2^3xD5	80,51
C₄×Dic₅	Direct product of C₄ and Dic₅	80		C4xDic5	80,11
C₂²×Dic₅	Direct product of C₂² and Dic₅	80		C2^2xDic5	80,43
C₂×C₄×D₅	Direct product of C₂×C₄ and D₅	40		C2xC4xD5	80,36
C₂×C₅⋊C₈	Direct product of C₂ and C₅⋊C₈	80		C2xC5:C8	80,32
C₂×C₅⋊₂C₈	Direct product of C₂ and C₅⋊₂C₈	80		C2xC5:2C8	80,9

Groups of order 81

		d	ρ	Label	ID
C₈₁	Cyclic group	81	1	C81	81,1
C₉²	Abelian group of type [9,9]	81		C9^2	81,2
C₃⁴	Elementary abelian group of type [3,3,3,3]	81		C3^4	81,15
C₃×C₂₇	Abelian group of type [3,27]	81		C3xC27	81,5
C₃²×C₉	Abelian group of type [3,3,9]	81		C3^2xC9	81,11

Groups of order 82

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

Groups of order 83

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

Groups of order 84

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

Groups of order 85

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

Groups of order 86

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

Groups of order 87

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

Groups of order 88

		d	ρ	Label	ID
C₈₈	Cyclic group	88	1	C88	88,2
C₁₁⋊C₈	The semidirect product of C₁₁ and C₈ acting via C₈/C₄=C₂	88	2	C11:C8	88,1
C₂×C₄₄	Abelian group of type [2,44]	88		C2xC44	88,8
C₂²×C₂₂	Abelian group of type [2,2,22]	88		C2^2xC22	88,12
C₄×D₁₁	Direct product of C₄ and D₁₁	44	2	C4xD11	88,4
C₂²×D₁₁	Direct product of C₂² and D₁₁	44		C2^2xD11	88,11
C₂×Dic₁₁	Direct product of C₂ and Dic₁₁	88		C2xDic11	88,6

Groups of order 89

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

Groups of order 90

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

Groups of order 91

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

Groups of order 92

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

Groups of order 93

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

Groups of order 94

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

Groups of order 95

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

Groups of order 96

		d	ρ	Label	ID
C₉₆	Cyclic group	96	1	C96	96,2
C₃⋊C₃₂	The semidirect product of C₃ and C₃₂ acting via C₃₂/C₁₆=C₂	96	2	C3:C32	96,1
C₄×C₂₄	Abelian group of type [4,24]	96		C4xC24	96,46
C₂×C₄₈	Abelian group of type [2,48]	96		C2xC48	96,59
C₂⁴×C₆	Abelian group of type [2,2,2,2,6]	96		C2^4xC6	96,231
C₂²×C₂₄	Abelian group of type [2,2,24]	96		C2^2xC24	96,176
C₂³×C₁₂	Abelian group of type [2,2,2,12]	96		C2^3xC12	96,220
C₂×C₄×C₁₂	Abelian group of type [2,4,12]	96		C2xC4xC12	96,161
C₈×A₄	Direct product of C₈ and A₄	24	3	C8xA4	96,73
C₂³×A₄	Direct product of C₂³ and A₄	24		C2^3xA4	96,228
S₃×C₁₆	Direct product of C₁₆ and S₃	48	2	S3xC16	96,4
S₃×C₄²	Direct product of C₄² and S₃	48		S3xC4^2	96,78
S₃×C₂⁴	Direct product of C₂⁴ and S₃	48		S3xC2^4	96,230
C₈×Dic₃	Direct product of C₈ and Dic₃	96		C8xDic3	96,20
C₂³×Dic₃	Direct product of C₂³ and Dic₃	96		C2^3xDic3	96,218
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	12	3	C2xC4^2:C3	96,68
C₂×C₂²⋊A₄	Direct product of C₂ and C₂²⋊A₄	12		C2xC2^2:A4	96,229
C₂×C₄×A₄	Direct product of C₂×C₄ and A₄	24		C2xC4xA4	96,196
S₃×C₂×C₈	Direct product of C₂×C₈ and S₃	48		S3xC2xC8	96,106
S₃×C₂²×C₄	Direct product of C₂²×C₄ and S₃	48		S3xC2^2xC4	96,206
C₄×C₃⋊C₈	Direct product of C₄ and C₃⋊C₈	96		C4xC3:C8	96,9
C₂×C₃⋊C₁₆	Direct product of C₂ and C₃⋊C₁₆	96		C2xC3:C16	96,18
C₂²×C₃⋊C₈	Direct product of C₂² and C₃⋊C₈	96		C2^2xC3:C8	96,127
C₂×C₄×Dic₃	Direct product of C₂×C₄ and Dic₃	96		C2xC4xDic3	96,129

Groups of order 97

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

Groups of order 98

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

Groups of order 99

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

Groups of order 100

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

Groups of order 101

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

Groups of order 102

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

Groups of order 103

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

Groups of order 104

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

Groups of order 105

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

Groups of order 106

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

Groups of order 107

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

Groups of order 108

		d	ρ	Label	ID
C₁₀₈	Cyclic group	108	1	C108	108,2
D₅₄	Dihedral group; = C₂×D₂₇	54	2+	D54	108,4
Dic₂₇	Dicyclic group; = C₂₇ ⋊C₄	108	2-	Dic27	108,1
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	12	4	C3^3:C4	108,37
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	12	4	C3^2:4D6	108,40
C₉⋊Dic₃	The semidirect product of C₉ and Dic₃ acting via Dic₃/C₆=C₂	108		C9:Dic3	108,10
C₃³⋊₅C₄	3^rd semidirect product of C₃³ and C₄ acting via C₄/C₂=C₂	108		C3^3:5C4	108,34
C₉.A₄	The central extension by C₉ of A₄	54	3	C9.A4	108,3
C₂×C₅₄	Abelian group of type [2,54]	108		C2xC54	108,5
C₃×C₃₆	Abelian group of type [3,36]	108		C3xC36	108,12
C₆×C₁₈	Abelian group of type [6,18]	108		C6xC18	108,29
C₃×C₆²	Abelian group of type [3,6,6]	108		C3xC6^2	108,45
C₃²×C₁₂	Abelian group of type [3,3,12]	108		C3^2xC12	108,35
S₃×D₉	Direct product of S₃ and D₉	18	4+	S3xD9	108,16
C₉×A₄	Direct product of C₉ and A₄	36	3	C9xA4	108,18
C₆×D₉	Direct product of C₆ and D₉	36	2	C6xD9	108,23
S₃×C₁₈	Direct product of C₁₈ and S₃	36	2	S3xC18	108,24
C₃²×A₄	Direct product of C₃² and A₄	36		C3^2xA4	108,41
C₃×Dic₉	Direct product of C₃ and Dic₉	36	2	C3xDic9	108,6
C₉×Dic₃	Direct product of C₉ and Dic₃	36	2	C9xDic3	108,7
C₃²×Dic₃	Direct product of C₃² and Dic₃	36		C3^2xDic3	108,32
C₃×S₃²	Direct product of C₃, S₃ and S₃	12	4	C3xS3^2	108,38
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	12	4	C3xC3^2:C4	108,36
S₃×C₃⋊S₃	Direct product of S₃ and C₃⋊S₃	18		S3xC3:S3	108,39
S₃×C₃×C₆	Direct product of C₃×C₆ and S₃	36		S3xC3xC6	108,42
C₆×C₃⋊S₃	Direct product of C₆ and C₃⋊S₃	36		C6xC3:S3	108,43
C₃×C₃⋊Dic₃	Direct product of C₃ and C₃⋊Dic₃	36		C3xC3:Dic3	108,33
C₂×C₉⋊S₃	Direct product of C₂ and C₉⋊S₃	54		C2xC9:S3	108,27
C₃×C₃.A₄	Direct product of C₃ and C₃.A₄	54		C3xC3.A4	108,20
C₂×C₃³⋊C₂	Direct product of C₂ and C₃³⋊C₂	54		C2xC3^3:C2	108,44

Groups of order 109

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

Groups of order 110

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

Groups of order 111

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

Groups of order 112

		d	ρ	Label	ID
C₁₁₂	Cyclic group	112	1	C112	112,2
C₇⋊C₁₆	The semidirect product of C₇ and C₁₆ acting via C₁₆/C₈=C₂	112	2	C7:C16	112,1
C₄×C₂₈	Abelian group of type [4,28]	112		C4xC28	112,19
C₂×C₅₆	Abelian group of type [2,56]	112		C2xC56	112,22
C₂²×C₂₈	Abelian group of type [2,2,28]	112		C2^2xC28	112,37
C₂³×C₁₄	Abelian group of type [2,2,2,14]	112		C2^3xC14	112,43
C₂×F₈	Direct product of C₂ and F₈	14	7+	C2xF8	112,41
C₈×D₇	Direct product of C₈ and D₇	56	2	C8xD7	112,3
C₂³×D₇	Direct product of C₂³ and D₇	56		C2^3xD7	112,42
C₄×Dic₇	Direct product of C₄ and Dic₇	112		C4xDic7	112,10
C₂²×Dic₇	Direct product of C₂² and Dic₇	112		C2^2xDic7	112,35
C₂×C₄×D₇	Direct product of C₂×C₄ and D₇	56		C2xC4xD7	112,28
C₂×C₇⋊C₈	Direct product of C₂ and C₇⋊C₈	112		C2xC7:C8	112,8

Groups of order 113

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

Groups of order 114

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

Groups of order 115

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

Groups of order 116

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

Groups of order 117

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

Groups of order 118

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

Groups of order 119

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

Groups of order 120

		d	ρ	Label	ID
C₁₂₀	Cyclic group	120	1	C120	120,4
C₁₅⋊₃C₈	1^st semidirect product of C₁₅ and C₈ acting via C₈/C₄=C₂	120	2	C15:3C8	120,3
C₁₅⋊C₈	1^st semidirect product of C₁₅ and C₈ acting via C₈/C₂=C₄	120	4	C15:C8	120,7
D₃₀.C₂	The non-split extension by D₃₀ of C₂ acting faithfully	60	4+	D30.C2	120,10
C₂×C₆₀	Abelian group of type [2,60]	120		C2xC60	120,31
C₂²×C₃₀	Abelian group of type [2,2,30]	120		C2^2xC30	120,47
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	15	8+	S3xF5	120,36
D₅×A₄	Direct product of D₅ and A₄	20	6+	D5xA4	120,39
C₆×F₅	Direct product of C₆ and F₅	30	4	C6xF5	120,40
C₁₀×A₄	Direct product of C₁₀ and A₄	30	3	C10xA4	120,43
S₃×C₂₀	Direct product of C₂₀ and S₃	60	2	S3xC20	120,22
D₅×C₁₂	Direct product of C₁₂ and D₅	60	2	D5xC12	120,17
C₄×D₁₅	Direct product of C₄ and D₁₅	60	2	C4xD15	120,27
D₅×Dic₃	Direct product of D₅ and Dic₃	60	4-	D5xDic3	120,8
S₃×Dic₅	Direct product of S₃ and Dic₅	60	4-	S3xDic5	120,9
C₂²×D₁₅	Direct product of C₂² and D₁₅	60		C2^2xD15	120,46
C₆×Dic₅	Direct product of C₆ and Dic₅	120		C6xDic5	120,19
C₁₀×Dic₃	Direct product of C₁₀ and Dic₃	120		C10xDic3	120,24
C₂×Dic₁₅	Direct product of C₂ and Dic₁₅	120		C2xDic15	120,29
C₂×S₃×D₅	Direct product of C₂, S₃ and D₅	30	4+	C2xS3xD5	120,42
C₂×C₃⋊F₅	Direct product of C₂ and C₃⋊F₅	30	4	C2xC3:F5	120,41
D₅×C₂×C₆	Direct product of C₂×C₆ and D₅	60		D5xC2xC6	120,44
S₃×C₂×C₁₀	Direct product of C₂×C₁₀ and S₃	60		S3xC2xC10	120,45
C₅×C₃⋊C₈	Direct product of C₅ and C₃⋊C₈	120	2	C5xC3:C8	120,1
C₃×C₅⋊C₈	Direct product of C₃ and C₅⋊C₈	120	4	C3xC5:C8	120,6
C₃×C₅⋊₂C₈	Direct product of C₃ and C₅⋊₂C₈	120	2	C3xC5:2C8	120,2

Groups of order 121

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

Groups of order 122

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

Groups of order 123

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

Groups of order 124

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

Groups of order 125

		d	ρ	Label	ID
C₁₂₅	Cyclic group	125	1	C125	125,1
C₅³	Elementary abelian group of type [5,5,5]	125		C5^3	125,5
C₅×C₂₅	Abelian group of type [5,25]	125		C5xC25	125,2

Groups of order 126

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

Groups of order 127

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

Groups of order 128

		d	ρ	Label	ID
C₁₂₈	Cyclic group	128	1	C128	128,1
C₂⁷	Elementary abelian group of type [2,2,2,2,2,2,2]	128		C2^7	128,2328
C₈×C₁₆	Abelian group of type [8,16]	128		C8xC16	128,42
C₄×C₃₂	Abelian group of type [4,32]	128		C4xC32	128,128
C₂×C₆₄	Abelian group of type [2,64]	128		C2xC64	128,159
C₂×C₈²	Abelian group of type [2,8,8]	128		C2xC8^2	128,179
C₄²×C₈	Abelian group of type [4,4,8]	128		C4^2xC8	128,456
C₂×C₄³	Abelian group of type [2,4,4,4]	128		C2xC4^3	128,997
C₂⁴×C₈	Abelian group of type [2,2,2,2,8]	128		C2^4xC8	128,2301
C₂⁵×C₄	Abelian group of type [2,2,2,2,2,4]	128		C2^5xC4	128,2319
C₂²×C₃₂	Abelian group of type [2,2,32]	128		C2^2xC32	128,988
C₂³×C₁₆	Abelian group of type [2,2,2,16]	128		C2^3xC16	128,2136
C₂³×C₄²	Abelian group of type [2,2,2,4,4]	128		C2^3xC4^2	128,2150
C₂×C₄×C₁₆	Abelian group of type [2,4,16]	128		C2xC4xC16	128,837
C₂²×C₄×C₈	Abelian group of type [2,2,4,8]	128		C2^2xC4xC8	128,1601

Groups of order 129

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

Groups of order 130

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

Groups of order 131

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

Groups of order 132

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

Groups of order 133

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

Groups of order 134

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

Groups of order 135

		d	ρ	Label	ID
C₁₃₅	Cyclic group	135	1	C135	135,1
C₃×C₄₅	Abelian group of type [3,45]	135		C3xC45	135,2
C₃²×C₁₅	Abelian group of type [3,3,15]	135		C3^2xC15	135,5

Groups of order 136

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

Groups of order 137

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

Groups of order 138

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

Groups of order 139

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

Groups of order 140

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

Groups of order 141

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

Groups of order 142

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

Groups of order 143

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

Groups of order 144

		d	ρ	Label	ID
C₁₄₄	Cyclic group	144	1	C144	144,2
C₄²⋊C₉	The semidirect product of C₄² and C₉ acting via C₉/C₃=C₃	36	3	C4^2:C9	144,3
C₂⁴⋊C₉	2^nd semidirect product of C₂⁴ and C₉ acting via C₉/C₃=C₃	36		C2^4:C9	144,111
C₃²⋊₂C₁₆	The semidirect product of C₃² and C₁₆ acting via C₁₆/C₄=C₄	48	4	C3^2:2C16	144,51
C₉⋊C₁₆	The semidirect product of C₉ and C₁₆ acting via C₁₆/C₈=C₂	144	2	C9:C16	144,1
C₃⋊S₃⋊₃C₈	2^nd semidirect product of C₃⋊S₃ and C₈ acting via C₈/C₄=C₂	24	4	C3:S3:3C8	144,130
C₁₂.₂₉D₆	3^rd non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	24	4	C12.29D6	144,53
C₂.F₉	The central extension by C₂ of F₉	48	8-	C2.F9	144,114
C₂₄.S₃	9^th non-split extension by C₂₄ of S₃ acting via S₃/C₃=C₂	144		C24.S3	144,29
C₁₂²	Abelian group of type [12,12]	144		C12^2	144,101
C₄×C₃₆	Abelian group of type [4,36]	144		C4xC36	144,20
C₂×C₇₂	Abelian group of type [2,72]	144		C2xC72	144,23
C₃×C₄₈	Abelian group of type [3,48]	144		C3xC48	144,30
C₆×C₂₄	Abelian group of type [6,24]	144		C6xC24	144,104
C₂²×C₃₆	Abelian group of type [2,2,36]	144		C2^2xC36	144,47
C₂³×C₁₈	Abelian group of type [2,2,2,18]	144		C2^3xC18	144,113
C₂²×C₆²	Abelian group of type [2,2,6,6]	144		C2^2xC6^2	144,197
C₂×C₆×C₁₂	Abelian group of type [2,6,12]	144		C2xC6xC12	144,178
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	12	9+	A4^2	144,184
C₂×F₉	Direct product of C₂ and F₉	18	8+	C2xF9	144,185
C₁₂×A₄	Direct product of C₁₂ and A₄	36	3	C12xA4	144,155
Dic₃×A₄	Direct product of Dic₃ and A₄	36	6-	Dic3xA4	144,129
S₃×C₂₄	Direct product of C₂₄ and S₃	48	2	S3xC24	144,69
Dic₃²	Direct product of Dic₃ and Dic₃	48		Dic3^2	144,63
Dic₃×C₁₂	Direct product of C₁₂ and Dic₃	48		Dic3xC12	144,76
C₈×D₉	Direct product of C₈ and D₉	72	2	C8xD9	144,5
C₂³×D₉	Direct product of C₂³ and D₉	72		C2^3xD9	144,112
C₄×Dic₉	Direct product of C₄ and Dic₉	144		C4xDic9	144,11
C₂²×Dic₉	Direct product of C₂² and Dic₉	144		C2^2xDic9	144,45
C₂×S₃×A₄	Direct product of C₂, S₃ and A₄	18	6+	C2xS3xA4	144,190
C₄×S₃²	Direct product of C₄, S₃ and S₃	24	4	C4xS3^2	144,143
C₂²×S₃²	Direct product of C₂², S₃ and S₃	24		C2^2xS3^2	144,192
C₄×C₃²⋊C₄	Direct product of C₄ and C₃²⋊C₄	24	4	C4xC3^2:C4	144,132
C₂×C₆.D₆	Direct product of C₂ and C₆.D₆	24		C2xC6.D6	144,149
C₂²×C₃²⋊C₄	Direct product of C₂² and C₃²⋊C₄	24		C2^2xC3^2:C4	144,191
A₄×C₂×C₆	Direct product of C₂×C₆ and A₄	36		A4xC2xC6	144,193
C₄×C₃.A₄	Direct product of C₄ and C₃.A₄	36	3	C4xC3.A4	144,34
C₃×C₄²⋊C₃	Direct product of C₃ and C₄²⋊C₃	36	3	C3xC4^2:C3	144,68
C₃×C₂²⋊A₄	Direct product of C₃ and C₂²⋊A₄	36		C3xC2^2:A4	144,194
C₂²×C₃.A₄	Direct product of C₂² and C₃.A₄	36		C2^2xC3.A4	144,110
C₆×C₃⋊C₈	Direct product of C₆ and C₃⋊C₈	48		C6xC3:C8	144,74
S₃×C₃⋊C₈	Direct product of S₃ and C₃⋊C₈	48	4	S3xC3:C8	144,52
C₃×C₃⋊C₁₆	Direct product of C₃ and C₃⋊C₁₆	48	2	C3xC3:C16	144,28
S₃×C₂×C₁₂	Direct product of C₂×C₁₂ and S₃	48		S3xC2xC12	144,159
S₃×C₂²×C₆	Direct product of C₂²×C₆ and S₃	48		S3xC2^2xC6	144,195
C₂×S₃×Dic₃	Direct product of C₂, S₃ and Dic₃	48		C2xS3xDic3	144,146
Dic₃×C₂×C₆	Direct product of C₂×C₆ and Dic₃	48		Dic3xC2xC6	144,166
C₂×C₃²⋊₂C₈	Direct product of C₂ and C₃²⋊₂C₈	48		C2xC3^2:2C8	144,134
C₂×C₄×D₉	Direct product of C₂×C₄ and D₉	72		C2xC4xD9	144,38
C₈×C₃⋊S₃	Direct product of C₈ and C₃⋊S₃	72		C8xC3:S3	144,85
C₂³×C₃⋊S₃	Direct product of C₂³ and C₃⋊S₃	72		C2^3xC3:S3	144,196
C₂×C₉⋊C₈	Direct product of C₂ and C₉⋊C₈	144		C2xC9:C8	144,9
C₄×C₃⋊Dic₃	Direct product of C₄ and C₃⋊Dic₃	144		C4xC3:Dic3	144,92
C₂×C₃²⋊₄C₈	Direct product of C₂ and C₃²⋊₄C₈	144		C2xC3^2:4C8	144,90
C₂²×C₃⋊Dic₃	Direct product of C₂² and C₃⋊Dic₃	144		C2^2xC3:Dic3	144,176
C₂×C₄×C₃⋊S₃	Direct product of C₂×C₄ and C₃⋊S₃	72		C2xC4xC3:S3	144,169

Groups of order 145

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

Groups of order 146

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

Groups of order 147

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

Groups of order 148

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

Groups of order 149

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

Groups of order 150

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

Groups of order 151

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

Groups of order 152

		d	ρ	Label	ID
C₁₅₂	Cyclic group	152	1	C152	152,2
C₁₉⋊C₈	The semidirect product of C₁₉ and C₈ acting via C₈/C₄=C₂	152	2	C19:C8	152,1
C₂×C₇₆	Abelian group of type [2,76]	152		C2xC76	152,8
C₂²×C₃₈	Abelian group of type [2,2,38]	152		C2^2xC38	152,12
C₄×D₁₉	Direct product of C₄ and D₁₉	76	2	C4xD19	152,4
C₂²×D₁₉	Direct product of C₂² and D₁₉	76		C2^2xD19	152,11
C₂×Dic₁₉	Direct product of C₂ and Dic₁₉	152		C2xDic19	152,6

Groups of order 153

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

Groups of order 154

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

Groups of order 155

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

Groups of order 156

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

Groups of order 157

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

Groups of order 158

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

Groups of order 159

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

Groups of order 160

		d	ρ	Label	ID
C₁₆₀	Cyclic group	160	1	C160	160,2
D₅⋊C₁₆	The semidirect product of D₅ and C₁₆ acting via C₁₆/C₈=C₂	80	4	D5:C16	160,64
C₅⋊C₃₂	The semidirect product of C₅ and C₃₂ acting via C₃₂/C₈=C₄	160	4	C5:C32	160,3
C₅⋊₂C₃₂	The semidirect product of C₅ and C₃₂ acting via C₃₂/C₁₆=C₂	160	2	C5:2C32	160,1
C₄×C₄₀	Abelian group of type [4,40]	160		C4xC40	160,46
C₂×C₈₀	Abelian group of type [2,80]	160		C2xC80	160,59
C₂²×C₄₀	Abelian group of type [2,2,40]	160		C2^2xC40	160,190
C₂³×C₂₀	Abelian group of type [2,2,2,20]	160		C2^3xC20	160,228
C₂⁴×C₁₀	Abelian group of type [2,2,2,2,10]	160		C2^4xC10	160,238
C₂×C₄×C₂₀	Abelian group of type [2,4,20]	160		C2xC4xC20	160,175
C₈×F₅	Direct product of C₈ and F₅	40	4	C8xF5	160,66
C₂³×F₅	Direct product of C₂³ and F₅	40		C2^3xF5	160,236
D₅×C₁₆	Direct product of C₁₆ and D₅	80	2	D5xC16	160,4
D₅×C₄²	Direct product of C₄² and D₅	80		D5xC4^2	160,92
D₅×C₂⁴	Direct product of C₂⁴ and D₅	80		D5xC2^4	160,237
C₈×Dic₅	Direct product of C₈ and Dic₅	160		C8xDic5	160,20
C₂³×Dic₅	Direct product of C₂³ and Dic₅	160		C2^3xDic5	160,226
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	10	5+	C2xC2^4:C5	160,235
C₂×C₄×F₅	Direct product of C₂×C₄ and F₅	40		C2xC4xF5	160,203
D₅×C₂×C₈	Direct product of C₂×C₈ and D₅	80		D5xC2xC8	160,120
C₂×D₅⋊C₈	Direct product of C₂ and D₅⋊C₈	80		C2xD5:C8	160,200
D₅×C₂²×C₄	Direct product of C₂²×C₄ and D₅	80		D5xC2^2xC4	160,214
C₄×C₅⋊C₈	Direct product of C₄ and C₅⋊C₈	160		C4xC5:C8	160,75
C₂×C₅⋊C₁₆	Direct product of C₂ and C₅⋊C₁₆	160		C2xC5:C16	160,72
C₄×C₅⋊₂C₈	Direct product of C₄ and C₅⋊₂C₈	160		C4xC5:2C8	160,9
C₂²×C₅⋊C₈	Direct product of C₂² and C₅⋊C₈	160		C2^2xC5:C8	160,210
C₂×C₄×Dic₅	Direct product of C₂×C₄ and Dic₅	160		C2xC4xDic5	160,143
C₂×C₅⋊₂C₁₆	Direct product of C₂ and C₅⋊₂C₁₆	160		C2xC5:2C16	160,18
C₂²×C₅⋊₂C₈	Direct product of C₂² and C₅⋊₂C₈	160		C2^2xC5:2C8	160,141

Groups of order 161

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

Groups of order 162

		d	ρ	Label	ID
C₁₆₂	Cyclic group	162	1	C162	162,2
D₈₁	Dihedral group	81	2+	D81	162,1
C₉⋊D₉	The semidirect product of C₉ and D₉ acting via D₉/C₉=C₂	81		C9:D9	162,16
C₂₇⋊S₃	The semidirect product of C₂₇ and S₃ acting via S₃/C₃=C₂	81		C27:S3	162,18
C₃⁴⋊C₂	4^th semidirect product of C₃⁴ and C₂ acting faithfully	81		C3^4:C2	162,54
C₃²⋊₄D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₉=C₂	81		C3^2:4D9	162,45
C₉×C₁₈	Abelian group of type [9,18]	162		C9xC18	162,23
C₃×C₅₄	Abelian group of type [3,54]	162		C3xC54	162,26
C₃³×C₆	Abelian group of type [3,3,3,6]	162		C3^3xC6	162,55
C₃²×C₁₈	Abelian group of type [3,3,18]	162		C3^2xC18	162,47
C₉×D₉	Direct product of C₉ and D₉	18	2	C9xD9	162,3
S₃×C₂₇	Direct product of C₂₇ and S₃	54	2	S3xC27	162,8
C₃×D₂₇	Direct product of C₃ and D₂₇	54	2	C3xD27	162,7
S₃×C₃³	Direct product of C₃³ and S₃	54		S3xC3^3	162,51
C₃²×D₉	Direct product of C₃² and D₉	54		C3^2xD9	162,32
C₃²×C₃⋊S₃	Direct product of C₃² and C₃⋊S₃	18		C3^2xC3:S3	162,52
S₃×C₃×C₉	Direct product of C₃×C₉ and S₃	54		S3xC3xC9	162,33
C₃×C₉⋊S₃	Direct product of C₃ and C₉⋊S₃	54		C3xC9:S3	162,38
C₉×C₃⋊S₃	Direct product of C₉ and C₃⋊S₃	54		C9xC3:S3	162,39
C₃×C₃³⋊C₂	Direct product of C₃ and C₃³⋊C₂	54		C3xC3^3:C2	162,53

Groups of order 163

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

Groups of order 164

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

Groups of order 165

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

Groups of order 166

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

Groups of order 167

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

Groups of order 168

		d	ρ	Label	ID
C₁₆₈	Cyclic group	168	1	C168	168,6
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	8	7+	AGammaL(1,8)	168,43
D₇⋊A₄	The semidirect product of D₇ and A₄ acting via A₄/C₂²=C₃	28	6+	D7:A4	168,49
C₇⋊C₂₄	The semidirect product of C₇ and C₂₄ acting via C₂₄/C₄=C₆	56	6	C7:C24	168,1
D₂₁⋊C₄	The semidirect product of D₂₁ and C₄ acting via C₄/C₂=C₂	84	4+	D21:C4	168,14
C₂₁⋊C₈	1^st semidirect product of C₂₁ and C₈ acting via C₈/C₄=C₂	168	2	C21:C8	168,5
C₂×C₈₄	Abelian group of type [2,84]	168		C2xC84	168,39
C₂²×C₄₂	Abelian group of type [2,2,42]	168		C2^2xC42	168,57
C₃×F₈	Direct product of C₃ and F₈	24	7	C3xF8	168,44
A₄×D₇	Direct product of A₄ and D₇	28	6+	A4xD7	168,48
C₄×F₇	Direct product of C₄ and F₇	28	6	C4xF7	168,8
C₂²×F₇	Direct product of C₂² and F₇	28		C2^2xF7	168,47
A₄×C₁₄	Direct product of C₁₄ and A₄	42	3	A4xC14	168,52
S₃×C₂₈	Direct product of C₂₈ and S₃	84	2	S3xC28	168,30
C₁₂×D₇	Direct product of C₁₂ and D₇	84	2	C12xD7	168,25
C₄×D₂₁	Direct product of C₄ and D₂₁	84	2	C4xD21	168,35
Dic₃×D₇	Direct product of Dic₃ and D₇	84	4-	Dic3xD7	168,12
S₃×Dic₇	Direct product of S₃ and Dic₇	84	4-	S3xDic7	168,13
C₂²×D₂₁	Direct product of C₂² and D₂₁	84		C2^2xD21	168,56
C₆×Dic₇	Direct product of C₆ and Dic₇	168		C6xDic7	168,27
Dic₃×C₁₄	Direct product of C₁₄ and Dic₃	168		Dic3xC14	168,32
C₂×Dic₂₁	Direct product of C₂ and Dic₂₁	168		C2xDic21	168,37
C₂×C₇⋊A₄	Direct product of C₂ and C₇⋊A₄	42	3	C2xC7:A4	168,53
C₂×S₃×D₇	Direct product of C₂, S₃ and D₇	42	4+	C2xS3xD7	168,50
C₈×C₇⋊C₃	Direct product of C₈ and C₇⋊C₃	56	3	C8xC7:C3	168,2
C₂×C₇⋊C₁₂	Direct product of C₂ and C₇⋊C₁₂	56		C2xC7:C12	168,10
C₂³×C₇⋊C₃	Direct product of C₂³ and C₇⋊C₃	56		C2^3xC7:C3	168,51
C₂×C₆×D₇	Direct product of C₂×C₆ and D₇	84		C2xC6xD7	168,54
S₃×C₂×C₁₄	Direct product of C₂×C₁₄ and S₃	84		S3xC2xC14	168,55
C₇×C₃⋊C₈	Direct product of C₇ and C₃⋊C₈	168	2	C7xC3:C8	168,3
C₃×C₇⋊C₈	Direct product of C₃ and C₇⋊C₈	168	2	C3xC7:C8	168,4
C₂×C₄×C₇⋊C₃	Direct product of C₂×C₄ and C₇⋊C₃	56		C2xC4xC7:C3	168,19

Groups of order 169

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

Groups of order 170

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

Groups of order 171

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

Groups of order 172

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

Groups of order 173

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

Groups of order 174

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

Groups of order 175

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

Groups of order 176

		d	ρ	Label	ID
C₁₇₆	Cyclic group	176	1	C176	176,2
C₁₁⋊C₁₆	The semidirect product of C₁₁ and C₁₆ acting via C₁₆/C₈=C₂	176	2	C11:C16	176,1
C₄×C₄₄	Abelian group of type [4,44]	176		C4xC44	176,19
C₂×C₈₈	Abelian group of type [2,88]	176		C2xC88	176,22
C₂²×C₄₄	Abelian group of type [2,2,44]	176		C2^2xC44	176,37
C₂³×C₂₂	Abelian group of type [2,2,2,22]	176		C2^3xC22	176,42
C₈×D₁₁	Direct product of C₈ and D₁₁	88	2	C8xD11	176,3
C₂³×D₁₁	Direct product of C₂³ and D₁₁	88		C2^3xD11	176,41
C₄×Dic₁₁	Direct product of C₄ and Dic₁₁	176		C4xDic11	176,10
C₂²×Dic₁₁	Direct product of C₂² and Dic₁₁	176		C2^2xDic11	176,35
C₂×C₄×D₁₁	Direct product of C₂×C₄ and D₁₁	88		C2xC4xD11	176,28
C₂×C₁₁⋊C₈	Direct product of C₂ and C₁₁⋊C₈	176		C2xC11:C8	176,8

Groups of order 177

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

Groups of order 178

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

Groups of order 179

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

Groups of order 180

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

Groups of order 181

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

Groups of order 182

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

Groups of order 183

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

Groups of order 184

		d	ρ	Label	ID
C₁₈₄	Cyclic group	184	1	C184	184,2
C₂₃⋊C₈	The semidirect product of C₂₃ and C₈ acting via C₈/C₄=C₂	184	2	C23:C8	184,1
C₂×C₉₂	Abelian group of type [2,92]	184		C2xC92	184,8
C₂²×C₄₆	Abelian group of type [2,2,46]	184		C2^2xC46	184,12
C₄×D₂₃	Direct product of C₄ and D₂₃	92	2	C4xD23	184,4
C₂²×D₂₃	Direct product of C₂² and D₂₃	92		C2^2xD23	184,11
C₂×Dic₂₃	Direct product of C₂ and Dic₂₃	184		C2xDic23	184,6

Groups of order 185

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

Groups of order 186

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

Groups of order 187

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

Groups of order 188

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

Groups of order 189

		d	ρ	Label	ID
C₁₈₉	Cyclic group	189	1	C189	189,2
C₇⋊C₂₇	The semidirect product of C₇ and C₂₇ acting via C₂₇/C₉=C₃	189	3	C7:C27	189,1
C₃×C₆₃	Abelian group of type [3,63]	189		C3xC63	189,9
C₃²×C₂₁	Abelian group of type [3,3,21]	189		C3^2xC21	189,13
C₉×C₇⋊C₃	Direct product of C₉ and C₇⋊C₃	63	3	C9xC7:C3	189,3
C₃²×C₇⋊C₃	Direct product of C₃² and C₇⋊C₃	63		C3^2xC7:C3	189,12
C₃×C₇⋊C₉	Direct product of C₃ and C₇⋊C₉	189		C3xC7:C9	189,6

Groups of order 190

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

Groups of order 191

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

Groups of order 192

		d	ρ	Label	ID
C₁₉₂	Cyclic group	192	1	C192	192,2
C₈²⋊C₃	The semidirect product of C₈² and C₃ acting faithfully	24	3	C8^2:C3	192,3
C₂⁶⋊C₃	3^rd semidirect product of C₂⁶ and C₃ acting faithfully	24		C2^6:C3	192,1541
C₄²⋊₂A₄	The semidirect product of C₄² and A₄ acting via A₄/C₂²=C₃	24		C4^2:2A4	192,1020
C₃⋊C₆₄	The semidirect product of C₃ and C₆₄ acting via C₆₄/C₃₂=C₂	192	2	C3:C64	192,1
C₈×C₂₄	Abelian group of type [8,24]	192		C8xC24	192,127
C₄×C₄₈	Abelian group of type [4,48]	192		C4xC48	192,151
C₂×C₉₆	Abelian group of type [2,96]	192		C2xC96	192,175
C₂⁵×C₆	Abelian group of type [2,2,2,2,2,6]	192		C2^5xC6	192,1543
C₄²×C₁₂	Abelian group of type [4,4,12]	192		C4^2xC12	192,807
C₂²×C₄₈	Abelian group of type [2,2,48]	192		C2^2xC48	192,935
C₂³×C₂₄	Abelian group of type [2,2,2,24]	192		C2^3xC24	192,1454
C₂⁴×C₁₂	Abelian group of type [2,2,2,2,12]	192		C2^4xC12	192,1530
C₂×C₄×C₂₄	Abelian group of type [2,4,24]	192		C2xC4xC24	192,835
C₂²×C₄×C₁₂	Abelian group of type [2,2,4,12]	192		C2^2xC4xC12	192,1400
A₄×C₁₆	Direct product of C₁₆ and A₄	48	3	A4xC16	192,203
A₄×C₄²	Direct product of C₄² and A₄	48		A4xC4^2	192,993
A₄×C₂⁴	Direct product of C₂⁴ and A₄	48		A4xC2^4	192,1539
S₃×C₃₂	Direct product of C₃₂ and S₃	96	2	S3xC32	192,5
S₃×C₂⁵	Direct product of C₂⁵ and S₃	96		S3xC2^5	192,1542
Dic₃×C₁₆	Direct product of C₁₆ and Dic₃	192		Dic3xC16	192,59
Dic₃×C₄²	Direct product of C₄² and Dic₃	192		Dic3xC4^2	192,489
Dic₃×C₂⁴	Direct product of C₂⁴ and Dic₃	192		Dic3xC2^4	192,1528
C₄×C₄²⋊C₃	Direct product of C₄ and C₄²⋊C₃	12	3	C4xC4^2:C3	192,188
C₂²×C₂²⋊A₄	Direct product of C₂² and C₂²⋊A₄	12		C2^2xC2^2:A4	192,1540
C₄×C₂²⋊A₄	Direct product of C₄ and C₂²⋊A₄	24		C4xC2^2:A4	192,1505
C₂²×C₄²⋊C₃	Direct product of C₂² and C₄²⋊C₃	24		C2^2xC4^2:C3	192,992
A₄×C₂×C₈	Direct product of C₂×C₈ and A₄	48		A4xC2xC8	192,1010
A₄×C₂²×C₄	Direct product of C₂²×C₄ and A₄	48		A4xC2^2xC4	192,1496
S₃×C₄×C₈	Direct product of C₄×C₈ and S₃	96		S3xC4xC8	192,243
S₃×C₂×C₁₆	Direct product of C₂×C₁₆ and S₃	96		S3xC2xC16	192,458
S₃×C₂×C₄²	Direct product of C₂×C₄² and S₃	96		S3xC2xC4^2	192,1030
S₃×C₂²×C₈	Direct product of C₂²×C₈ and S₃	96		S3xC2^2xC8	192,1295
S₃×C₂³×C₄	Direct product of C₂³×C₄ and S₃	96		S3xC2^3xC4	192,1511
C₈×C₃⋊C₈	Direct product of C₈ and C₃⋊C₈	192		C8xC3:C8	192,12
C₄×C₃⋊C₁₆	Direct product of C₄ and C₃⋊C₁₆	192		C4xC3:C16	192,19
C₂×C₃⋊C₃₂	Direct product of C₂ and C₃⋊C₃₂	192		C2xC3:C32	192,57
C₂³×C₃⋊C₈	Direct product of C₂³ and C₃⋊C₈	192		C2^3xC3:C8	192,1339
Dic₃×C₂×C₈	Direct product of C₂×C₈ and Dic₃	192		Dic3xC2xC8	192,657
C₂²×C₃⋊C₁₆	Direct product of C₂² and C₃⋊C₁₆	192		C2^2xC3:C16	192,655
Dic₃×C₂²×C₄	Direct product of C₂²×C₄ and Dic₃	192		Dic3xC2^2xC4	192,1341
C₂×C₄×C₃⋊C₈	Direct product of C₂×C₄ and C₃⋊C₈	192		C2xC4xC3:C8	192,479

Groups of order 193

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

Groups of order 194

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

Groups of order 195

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

Groups of order 196

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

Groups of order 197

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

Groups of order 198

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

Groups of order 199

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

Groups of order 200

		d	ρ	Label	ID
C₂₀₀	Cyclic group	200	1	C200	200,2
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	10	8+	D5:F5	200,42
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	10	8+	C5^2:C8	200,40
Dic₅⋊₂D₅	The semidirect product of Dic₅ and D₅ acting through Inn(Dic₅)	20	4+	Dic5:2D5	200,23
C₅²⋊₃C₈	2^nd semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4	C5^2:3C8	200,19
C₅²⋊₅C₈	4^th semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	40	4-	C5^2:5C8	200,21
C₂₅⋊C₈	The semidirect product of C₂₅ and C₈ acting via C₈/C₂=C₄	200	4-	C25:C8	200,3
C₂₅⋊₂C₈	The semidirect product of C₂₅ and C₈ acting via C₈/C₄=C₂	200	2	C25:2C8	200,1
C₅²⋊₇C₈	2^nd semidirect product of C₅² and C₈ acting via C₈/C₄=C₂	200		C5^2:7C8	200,16
C₅²⋊₄C₈	3^rd semidirect product of C₅² and C₈ acting via C₈/C₂=C₄	200		C5^2:4C8	200,20
C₅×C₄₀	Abelian group of type [5,40]	200		C5xC40	200,17
C₂×C₁₀₀	Abelian group of type [2,100]	200		C2xC100	200,9
C₁₀×C₂₀	Abelian group of type [10,20]	200		C10xC20	200,37
C₂²×C₅₀	Abelian group of type [2,2,50]	200		C2^2xC50	200,14
C₂×C₁₀²	Abelian group of type [2,10,10]	200		C2xC10^2	200,52
D₅×F₅	Direct product of D₅ and F₅	20	8+	D5xF5	200,41
D₅×C₂₀	Direct product of C₂₀ and D₅	40	2	D5xC20	200,28
C₁₀×F₅	Direct product of C₁₀ and F₅	40	4	C10xF5	200,45
D₅×Dic₅	Direct product of D₅ and Dic₅	40	4-	D5xDic5	200,22
C₁₀×Dic₅	Direct product of C₁₀ and Dic₅	40		C10xDic5	200,30
C₄×D₂₅	Direct product of C₄ and D₂₅	100	2	C4xD25	200,5
C₂²×D₂₅	Direct product of C₂² and D₂₅	100		C2^2xD25	200,13
C₂×Dic₂₅	Direct product of C₂ and Dic₂₅	200		C2xDic25	200,7
C₂×D₅²	Direct product of C₂, D₅ and D₅	20	4+	C2xD5^2	200,49
C₂×C₅²⋊C₄	Direct product of C₂ and C₅²⋊C₄	20	4+	C2xC5^2:C4	200,48
C₅×C₅⋊C₈	Direct product of C₅ and C₅⋊C₈	40	4	C5xC5:C8	200,18
D₅×C₂×C₁₀	Direct product of C₂×C₁₀ and D₅	40		D5xC2xC10	200,50
C₅×C₅⋊₂C₈	Direct product of C₅ and C₅⋊₂C₈	40	2	C5xC5:2C8	200,15
C₂×D₅.D₅	Direct product of C₂ and D₅.D₅	40	4	C2xD5.D5	200,46
C₂×C₂₅⋊C₄	Direct product of C₂ and C₂₅⋊C₄	50	4+	C2xC25:C4	200,12
C₂×C₅⋊F₅	Direct product of C₂ and C₅⋊F₅	50		C2xC5:F5	200,47
C₄×C₅⋊D₅	Direct product of C₄ and C₅⋊D₅	100		C4xC5:D5	200,33
C₂²×C₅⋊D₅	Direct product of C₂² and C₅⋊D₅	100		C2^2xC5:D5	200,51
C₂×C₅²⋊₆C₄	Direct product of C₂ and C₅²⋊₆C₄	200		C2xC5^2:6C4	200,35

Groups of order 201

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

Groups of order 202

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

Groups of order 203

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

Groups of order 204

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

Groups of order 205

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

Groups of order 206

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

Groups of order 207

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

Groups of order 208

		d	ρ	Label	ID
C₂₀₈	Cyclic group	208	1	C208	208,2
D₁₃⋊C₈	The semidirect product of D₁₃ and C₈ acting via C₈/C₄=C₂	104	4	D13:C8	208,28
C₁₃⋊C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₄=C₄	208	4	C13:C16	208,3
C₁₃⋊₂C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	2	C13:2C16	208,1
C₄×C₅₂	Abelian group of type [4,52]	208		C4xC52	208,20
C₂×C₁₀₄	Abelian group of type [2,104]	208		C2xC104	208,23
C₂²×C₅₂	Abelian group of type [2,2,52]	208		C2^2xC52	208,45
C₂³×C₂₆	Abelian group of type [2,2,2,26]	208		C2^3xC26	208,51
C₈×D₁₃	Direct product of C₈ and D₁₃	104	2	C8xD13	208,4
C₂³×D₁₃	Direct product of C₂³ and D₁₃	104		C2^3xD13	208,50
C₄×Dic₁₃	Direct product of C₄ and Dic₁₃	208		C4xDic13	208,11
C₂²×Dic₁₃	Direct product of C₂² and Dic₁₃	208		C2^2xDic13	208,43
C₄×C₁₃⋊C₄	Direct product of C₄ and C₁₃⋊C₄	52	4	C4xC13:C4	208,30
C₂²×C₁₃⋊C₄	Direct product of C₂² and C₁₃⋊C₄	52		C2^2xC13:C4	208,49
C₂×C₄×D₁₃	Direct product of C₂×C₄ and D₁₃	104		C2xC4xD13	208,36
C₂×C₁₃⋊C₈	Direct product of C₂ and C₁₃⋊C₈	208		C2xC13:C8	208,32
C₂×C₁₃⋊₂C₈	Direct product of C₂ and C₁₃⋊₂C₈	208		C2xC13:2C8	208,9

Groups of order 209

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

Groups of order 210

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

Groups of order 211

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

Groups of order 212

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

Groups of order 213

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

Groups of order 214

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

Groups of order 215

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

Groups of order 216

		d	ρ	Label	ID
C₂₁₆	Cyclic group	216	1	C216	216,2
C₃⋊F₉	The semidirect product of C₃ and F₉ acting via F₉/C₃²⋊C₄=C₂	24	8	C3:F9	216,155
C₃³⋊₄C₈	2^nd semidirect product of C₃³ and C₈ acting via C₈/C₂=C₄	24	4	C3^3:4C8	216,118
C₂₇⋊C₈	The semidirect product of C₂₇ and C₈ acting via C₈/C₄=C₂	216	2	C27:C8	216,1
C₃³⋊₇C₈	3^rd semidirect product of C₃³ and C₈ acting via C₈/C₄=C₂	216		C3^3:7C8	216,84
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⋊₈(C₂×C₄)	5^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	36		C3^3:8(C2xC4)	216,126
C₁₈.D₆	3^rd non-split extension by C₁₈ of D₆ acting via D₆/S₃=C₂	36	4+	C18.D6	216,28
C₃₆.S₃	6^th non-split extension by C₃₆ of S₃ acting via S₃/C₃=C₂	216		C36.S3	216,16
C₆³	Abelian group of type [6,6,6]	216		C6^3	216,177
C₃×C₇₂	Abelian group of type [3,72]	216		C3xC72	216,18
C₆×C₃₆	Abelian group of type [6,36]	216		C6xC36	216,73
C₂×C₁₀₈	Abelian group of type [2,108]	216		C2xC108	216,9
C₂²×C₅₄	Abelian group of type [2,2,54]	216		C2^2xC54	216,24
C₃²×C₂₄	Abelian group of type [3,3,24]	216		C3^2xC24	216,85
C₂×C₆×C₁₈	Abelian group of type [2,6,18]	216		C2xC6xC18	216,114
C₃×C₆×C₁₂	Abelian group of type [3,6,12]	216		C3xC6xC12	216,150
C₃×F₉	Direct product of C₃ and F₉	24	8	C3xF9	216,154
A₄×D₉	Direct product of A₄ and D₉	36	6+	A4xD9	216,97
A₄×C₁₈	Direct product of C₁₈ and A₄	54	3	A4xC18	216,103
S₃×C₃₆	Direct product of C₃₆ and S₃	72	2	S3xC36	216,47
C₁₂×D₉	Direct product of C₁₂ and D₉	72	2	C12xD9	216,45
S₃×C₆²	Direct product of C₆² and S₃	72		S3xC6^2	216,174
Dic₃×D₉	Direct product of Dic₃ and D₉	72	4-	Dic3xD9	216,27
S₃×Dic₉	Direct product of S₃ and Dic₉	72	4-	S3xDic9	216,30
C₆×Dic₉	Direct product of C₆ and Dic₉	72		C6xDic9	216,55
Dic₃×C₁₈	Direct product of C₁₈ and Dic₃	72		Dic3xC18	216,56
C₄×D₂₇	Direct product of C₄ and D₂₇	108	2	C4xD27	216,5
C₂²×D₂₇	Direct product of C₂² and D₂₇	108		C2^2xD27	216,23
C₂×Dic₂₇	Direct product of C₂ and Dic₂₇	216		C2xDic27	216,7
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	12	8+	S3^3	216,162
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	12	8+	S3xC3^2:C4	216,156
S₃²×C₆	Direct product of C₆, S₃ and S₃	24	4	S3^2xC6	216,170
C₃×S₃×A₄	Direct product of C₃, S₃ and A₄	24	6	C3xS3xA4	216,166
C₆×C₃²⋊C₄	Direct product of C₆ and C₃²⋊C₄	24	4	C6xC3^2:C4	216,168
C₃×S₃×Dic₃	Direct product of C₃, S₃ and Dic₃	24	4	C3xS3xDic3	216,119
C₂×C₃³⋊C₄	Direct product of C₂ and C₃³⋊C₄	24	4	C2xC3^3:C4	216,169
C₃×C₆.D₆	Direct product of C₃ and C₆.D₆	24	4	C3xC6.D6	216,120
C₃×C₃²⋊₂C₈	Direct product of C₃ and C₃²⋊₂C₈	24	4	C3xC3^2:2C8	216,117
C₂×C₃²⋊₄D₆	Direct product of C₂ and C₃²⋊₄D₆	24	4	C2xC3^2:4D6	216,172
C₂×S₃×D₉	Direct product of C₂, S₃ and D₉	36	4+	C2xS3xD9	216,101
A₄×C₃⋊S₃	Direct product of A₄ and C₃⋊S₃	36		A4xC3:S3	216,167
S₃×C₃.A₄	Direct product of S₃ and C₃.A₄	36	6	S3xC3.A4	216,98
A₄×C₃×C₆	Direct product of C₃×C₆ and A₄	54		A4xC3xC6	216,173
C₂×C₉.A₄	Direct product of C₂ and C₉.A₄	54	3	C2xC9.A4	216,22
C₆×C₃.A₄	Direct product of C₆ and C₃.A₄	54		C6xC3.A4	216,105
C₃×C₉⋊C₈	Direct product of C₃ and C₉⋊C₈	72	2	C3xC9:C8	216,12
C₉×C₃⋊C₈	Direct product of C₉ and C₃⋊C₈	72	2	C9xC3:C8	216,13
C₂×C₆×D₉	Direct product of C₂×C₆ and D₉	72		C2xC6xD9	216,108
S₃×C₂×C₁₈	Direct product of C₂×C₁₈ and S₃	72		S3xC2xC18	216,109
S₃×C₃×C₁₂	Direct product of C₃×C₁₂ and S₃	72		S3xC3xC12	216,136
C₁₂×C₃⋊S₃	Direct product of C₁₂ and C₃⋊S₃	72		C12xC3:S3	216,141
C₃²×C₃⋊C₈	Direct product of C₃² and C₃⋊C₈	72		C3^2xC3:C8	216,82
Dic₃×C₃×C₆	Direct product of C₃×C₆ and Dic₃	72		Dic3xC3xC6	216,138
S₃×C₃⋊Dic₃	Direct product of S₃ and C₃⋊Dic₃	72		S3xC3:Dic3	216,124
Dic₃×C₃⋊S₃	Direct product of Dic₃ and C₃⋊S₃	72		Dic3xC3:S3	216,125
C₆×C₃⋊Dic₃	Direct product of C₆ and C₃⋊Dic₃	72		C6xC3:Dic3	216,143
C₃×C₃²⋊₄C₈	Direct product of C₃ and C₃²⋊₄C₈	72		C3xC3^2:4C8	216,83
C₄×C₉⋊S₃	Direct product of C₄ and C₉⋊S₃	108		C4xC9:S3	216,64
C₂²×C₉⋊S₃	Direct product of C₂² and C₉⋊S₃	108		C2^2xC9:S3	216,112
C₄×C₃³⋊C₂	Direct product of C₄ and C₃³⋊C₂	108		C4xC3^3:C2	216,146
C₂²×C₃³⋊C₂	Direct product of C₂² and C₃³⋊C₂	108		C2^2xC3^3:C2	216,176
C₂×C₉⋊Dic₃	Direct product of C₂ and C₉⋊Dic₃	216		C2xC9:Dic3	216,69
C₂×C₃³⋊₅C₄	Direct product of C₂ and C₃³⋊₅C₄	216		C2xC3^3:5C4	216,148
C₂×S₃×C₃⋊S₃	Direct product of C₂, S₃ and C₃⋊S₃	36		C2xS3xC3:S3	216,171
C₂×C₆×C₃⋊S₃	Direct product of C₂×C₆ and C₃⋊S₃	72		C2xC6xC3:S3	216,175

Groups of order 217

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

Groups of order 218

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

Groups of order 219

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

Groups of order 220

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

Groups of order 221

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

Groups of order 222

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

Groups of order 223

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

Groups of order 224

		d	ρ	Label	ID
C₂₂₄	Cyclic group	224	1	C224	224,2
C₇⋊C₃₂	The semidirect product of C₇ and C₃₂ acting via C₃₂/C₁₆=C₂	224	2	C7:C32	224,1
C₄×C₅₆	Abelian group of type [4,56]	224		C4xC56	224,45
C₂×C₁₁₂	Abelian group of type [2,112]	224		C2xC112	224,58
C₂²×C₅₆	Abelian group of type [2,2,56]	224		C2^2xC56	224,164
C₂³×C₂₈	Abelian group of type [2,2,2,28]	224		C2^3xC28	224,189
C₂⁴×C₁₄	Abelian group of type [2,2,2,2,14]	224		C2^4xC14	224,197
C₂×C₄×C₂₈	Abelian group of type [2,4,28]	224		C2xC4xC28	224,149
C₄×F₈	Direct product of C₄ and F₈	28	7	C4xF8	224,173
C₂²×F₈	Direct product of C₂² and F₈	28		C2^2xF8	224,195
D₇×C₁₆	Direct product of C₁₆ and D₇	112	2	D7xC16	224,3
D₇×C₄²	Direct product of C₄² and D₇	112		D7xC4^2	224,66
D₇×C₂⁴	Direct product of C₂⁴ and D₇	112		D7xC2^4	224,196
C₈×Dic₇	Direct product of C₈ and Dic₇	224		C8xDic7	224,19
C₂³×Dic₇	Direct product of C₂³ and Dic₇	224		C2^3xDic7	224,187
D₇×C₂×C₈	Direct product of C₂×C₈ and D₇	112		D7xC2xC8	224,94
D₇×C₂²×C₄	Direct product of C₂²×C₄ and D₇	112		D7xC2^2xC4	224,175
C₄×C₇⋊C₈	Direct product of C₄ and C₇⋊C₈	224		C4xC7:C8	224,8
C₂×C₇⋊C₁₆	Direct product of C₂ and C₇⋊C₁₆	224		C2xC7:C16	224,17
C₂²×C₇⋊C₈	Direct product of C₂² and C₇⋊C₈	224		C2^2xC7:C8	224,115
C₂×C₄×Dic₇	Direct product of C₂×C₄ and Dic₇	224		C2xC4xDic7	224,117

Groups of order 225

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

Groups of order 226

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

Groups of order 227

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

Groups of order 228

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

Groups of order 229

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

Groups of order 230

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

Groups of order 231

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

Groups of order 232

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

Groups of order 233

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

Groups of order 234

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

Groups of order 235

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

Groups of order 236

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

Groups of order 237

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

Groups of order 238

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

Groups of order 239

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

Groups of order 240

		d	ρ	Label	ID
C₂₄₀	Cyclic group	240	1	C240	240,4
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	16	15+	F16	240,191
D₁₅⋊C₈	The semidirect product of D₁₅ and C₈ acting via C₈/C₂=C₄	120	8+	D15:C8	240,99
D₁₅⋊₂C₈	The semidirect product of D₁₅ and C₈ acting via C₈/C₄=C₂	120	4	D15:2C8	240,9
C₁₅⋊₃C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₈=C₂	240	2	C15:3C16	240,3
C₁₅⋊C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₄=C₄	240	4	C15:C16	240,6
C₆₀.C₄	3^rd non-split extension by C₆₀ of C₄ acting faithfully	120	4	C60.C4	240,118
C₄×C₆₀	Abelian group of type [4,60]	240		C4xC60	240,81
C₂×C₁₂₀	Abelian group of type [2,120]	240		C2xC120	240,84
C₂²×C₆₀	Abelian group of type [2,2,60]	240		C2^2xC60	240,185
C₂³×C₃₀	Abelian group of type [2,2,2,30]	240		C2^3xC30	240,208
C₄×A₅	Direct product of C₄ and A₅	20	3	C4xA5	240,92
A₄×F₅	Direct product of A₄ and F₅	20	12+	A4xF5	240,193
C₂²×A₅	Direct product of C₂² and A₅	20		C2^2xA5	240,190
A₄×C₂₀	Direct product of C₂₀ and A₄	60	3	A4xC20	240,152
C₁₂×F₅	Direct product of C₁₂ and F₅	60	4	C12xF5	240,113
Dic₃×F₅	Direct product of Dic₃ and F₅	60	8-	Dic3xF5	240,95
A₄×Dic₅	Direct product of A₄ and Dic₅	60	6-	A4xDic5	240,110
S₃×C₄₀	Direct product of C₄₀ and S₃	120	2	S3xC40	240,49
D₅×C₂₄	Direct product of C₂₄ and D₅	120	2	D5xC24	240,33
C₈×D₁₅	Direct product of C₈ and D₁₅	120	2	C8xD15	240,65
C₂³×D₁₅	Direct product of C₂³ and D₁₅	120		C2^3xD15	240,207
C₁₂×Dic₅	Direct product of C₁₂ and Dic₅	240		C12xDic5	240,40
Dic₃×C₂₀	Direct product of C₂₀ and Dic₃	240		Dic3xC20	240,56
C₄×Dic₁₅	Direct product of C₄ and Dic₁₅	240		C4xDic15	240,72
Dic₃×Dic₅	Direct product of Dic₃ and Dic₅	240		Dic3xDic5	240,25
C₂²×Dic₁₅	Direct product of C₂² and Dic₁₅	240		C2^2xDic15	240,183
C₂×D₅×A₄	Direct product of C₂, D₅ and A₄	30	6+	C2xD5xA4	240,198
C₂×S₃×F₅	Direct product of C₂, S₃ and F₅; = Aut(D₃₀) = Hol(C₃₀)	30	8+	C2xS3xF5	240,195
C₃×C₂⁴⋊C₅	Direct product of C₃ and C₂⁴⋊C₅	30	5	C3xC2^4:C5	240,199
C₄×S₃×D₅	Direct product of C₄, S₃ and D₅	60	4	C4xS3xD5	240,135
C₄×C₃⋊F₅	Direct product of C₄ and C₃⋊F₅	60	4	C4xC3:F5	240,120
C₂×C₆×F₅	Direct product of C₂×C₆ and F₅	60		C2xC6xF5	240,200
A₄×C₂×C₁₀	Direct product of C₂×C₁₀ and A₄	60		A4xC2xC10	240,203
C₅×C₄²⋊C₃	Direct product of C₅ and C₄²⋊C₃	60	3	C5xC4^2:C3	240,32
C₂²×S₃×D₅	Direct product of C₂², S₃ and D₅	60		C2^2xS3xD5	240,202
C₂²×C₃⋊F₅	Direct product of C₂² and C₃⋊F₅	60		C2^2xC3:F5	240,201
C₅×C₂²⋊A₄	Direct product of C₅ and C₂²⋊A₄	60		C5xC2^2:A4	240,204
S₃×C₅⋊C₈	Direct product of S₃ and C₅⋊C₈	120	8-	S3xC5:C8	240,98
D₅×C₃⋊C₈	Direct product of D₅ and C₃⋊C₈	120	4	D5xC3:C8	240,7
S₃×C₂×C₂₀	Direct product of C₂×C₂₀ and S₃	120		S3xC2xC20	240,166
D₅×C₂×C₁₂	Direct product of C₂×C₁₂ and D₅	120		D5xC2xC12	240,156
C₂×C₄×D₁₅	Direct product of C₂×C₄ and D₁₅	120		C2xC4xD15	240,176
S₃×C₅⋊₂C₈	Direct product of S₃ and C₅⋊₂C₈	120	4	S3xC5:2C8	240,8
C₃×D₅⋊C₈	Direct product of C₃ and D₅⋊C₈	120	4	C3xD5:C8	240,111
C₂×D₅×Dic₃	Direct product of C₂, D₅ and Dic₃	120		C2xD5xDic3	240,139
C₂×S₃×Dic₅	Direct product of C₂, S₃ and Dic₅	120		C2xS3xDic5	240,142
D₅×C₂²×C₆	Direct product of C₂²×C₆ and D₅	120		D5xC2^2xC6	240,205
S₃×C₂²×C₁₀	Direct product of C₂²×C₁₀ and S₃	120		S3xC2^2xC10	240,206
C₂×D₃₀.C₂	Direct product of C₂ and D₃₀.C₂	120		C2xD30.C2	240,144
C₆×C₅⋊C₈	Direct product of C₆ and C₅⋊C₈	240		C6xC5:C8	240,115
C₅×C₃⋊C₁₆	Direct product of C₅ and C₃⋊C₁₆	240	2	C5xC3:C16	240,1
C₃×C₅⋊C₁₆	Direct product of C₃ and C₅⋊C₁₆	240	4	C3xC5:C16	240,5
C₁₀×C₃⋊C₈	Direct product of C₁₀ and C₃⋊C₈	240		C10xC3:C8	240,54
C₆×C₅⋊₂C₈	Direct product of C₆ and C₅⋊₂C₈	240		C6xC5:2C8	240,38
C₂×C₁₅⋊C₈	Direct product of C₂ and C₁₅⋊C₈	240		C2xC15:C8	240,122
C₂×C₆×Dic₅	Direct product of C₂×C₆ and Dic₅	240		C2xC6xDic5	240,163
C₃×C₅⋊₂C₁₆	Direct product of C₃ and C₅⋊₂C₁₆	240	2	C3xC5:2C16	240,2
C₂×C₁₅⋊₃C₈	Direct product of C₂ and C₁₅⋊₃C₈	240		C2xC15:3C8	240,70
Dic₃×C₂×C₁₀	Direct product of C₂×C₁₀ and Dic₃	240		Dic3xC2xC10	240,173

Groups of order 241

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

Groups of order 242

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

Groups of order 243

		d	ρ	Label	ID
C₂₄₃	Cyclic group	243	1	C243	243,1
C₃⁵	Elementary abelian group of type [3,3,3,3,3]	243		C3^5	243,67
C₉×C₂₇	Abelian group of type [9,27]	243		C9xC27	243,10
C₃×C₈₁	Abelian group of type [3,81]	243		C3xC81	243,23
C₃×C₉²	Abelian group of type [3,9,9]	243		C3xC9^2	243,31
C₃³×C₉	Abelian group of type [3,3,3,9]	243		C3^3xC9	243,61
C₃²×C₂₇	Abelian group of type [3,3,27]	243		C3^2xC27	243,48

Groups of order 244

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

Groups of order 245

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

Groups of order 246

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

Groups of order 247

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

Groups of order 248

		d	ρ	Label	ID
C₂₄₈	Cyclic group	248	1	C248	248,2
C₃₁⋊C₈	The semidirect product of C₃₁ and C₈ acting via C₈/C₄=C₂	248	2	C31:C8	248,1
C₂×C₁₂₄	Abelian group of type [2,124]	248		C2xC124	248,8
C₂²×C₆₂	Abelian group of type [2,2,62]	248		C2^2xC62	248,12
C₄×D₃₁	Direct product of C₄ and D₃₁	124	2	C4xD31	248,4
C₂²×D₃₁	Direct product of C₂² and D₃₁	124		C2^2xD31	248,11
C₂×Dic₃₁	Direct product of C₂ and Dic₃₁	248		C2xDic31	248,6

Groups of order 249

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

Groups of order 250

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

Groups of order 251

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

Groups of order 252

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

Groups of order 253

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

Groups of order 254

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

Groups of order 255

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

Groups of order 257

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

Groups of order 258

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

Groups of order 259

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

Groups of order 260

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

Groups of order 261

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

Groups of order 262

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

Groups of order 263

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

Groups of order 264

		d	ρ	Label	ID
C₂₆₄	Cyclic group	264	1	C264	264,4
D₃₃⋊C₄	The semidirect product of D₃₃ and C₄ acting via C₄/C₂=C₂	132	4+	D33:C4	264,7
C₃₃⋊C₈	1^st semidirect product of C₃₃ and C₈ acting via C₈/C₄=C₂	264	2	C33:C8	264,3
C₂×C₁₃₂	Abelian group of type [2,132]	264		C2xC132	264,28
C₂²×C₆₆	Abelian group of type [2,2,66]	264		C2^2xC66	264,39
A₄×D₁₁	Direct product of A₄ and D₁₁	44	6+	A4xD11	264,33
A₄×C₂₂	Direct product of C₂₂ and A₄	66	3	A4xC22	264,35
S₃×C₄₄	Direct product of C₄₄ and S₃	132	2	S3xC44	264,19
C₄×D₃₃	Direct product of C₄ and D₃₃	132	2	C4xD33	264,24
C₁₂×D₁₁	Direct product of C₁₂ and D₁₁	132	2	C12xD11	264,14
Dic₃×D₁₁	Direct product of Dic₃ and D₁₁	132	4-	Dic3xD11	264,5
S₃×Dic₁₁	Direct product of S₃ and Dic₁₁	132	4-	S3xDic11	264,6
C₂²×D₃₃	Direct product of C₂² and D₃₃	132		C2^2xD33	264,38
C₆×Dic₁₁	Direct product of C₆ and Dic₁₁	264		C6xDic11	264,16
Dic₃×C₂₂	Direct product of C₂₂ and Dic₃	264		Dic3xC22	264,21
C₂×Dic₃₃	Direct product of C₂ and Dic₃₃	264		C2xDic33	264,26
C₂×S₃×D₁₁	Direct product of C₂, S₃ and D₁₁	66	4+	C2xS3xD11	264,34
S₃×C₂×C₂₂	Direct product of C₂×C₂₂ and S₃	132		S3xC2xC22	264,37
C₂×C₆×D₁₁	Direct product of C₂×C₆ and D₁₁	132		C2xC6xD11	264,36
C₁₁×C₃⋊C₈	Direct product of C₁₁ and C₃⋊C₈	264	2	C11xC3:C8	264,1
C₃×C₁₁⋊C₈	Direct product of C₃ and C₁₁⋊C₈	264	2	C3xC11:C8	264,2

Groups of order 265

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

Groups of order 266

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

Groups of order 267

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

Groups of order 268

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

Groups of order 269

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

Groups of order 270

		d	ρ	Label	ID
C₂₇₀	Cyclic group	270	1	C270	270,4
D₁₃₅	Dihedral group	135	2+	D135	270,3
C₃⋊D₄₅	The semidirect product of C₃ and D₄₅ acting via D₄₅/C₄₅=C₂	135		C3:D45	270,18
C₃³⋊D₅	3^rd semidirect product of C₃³ and D₅ acting via D₅/C₅=C₂	135		C3^3:D5	270,29
C₃×C₉₀	Abelian group of type [3,90]	270		C3xC90	270,20
C₃²×C₃₀	Abelian group of type [3,3,30]	270		C3^2xC30	270,30
S₃×C₄₅	Direct product of C₄₅ and S₃	90	2	S3xC45	270,9
C₁₅×D₉	Direct product of C₁₅ and D₉	90	2	C15xD9	270,8
C₃×D₄₅	Direct product of C₃ and D₄₅	90	2	C3xD45	270,12
C₉×D₁₅	Direct product of C₉ and D₁₅	90	2	C9xD15	270,13
C₃²×D₁₅	Direct product of C₃² and D₁₅	90		C3^2xD15	270,25
C₅×D₂₇	Direct product of C₅ and D₂₇	135	2	C5xD27	270,1
D₅×C₂₇	Direct product of C₂₇ and D₅	135	2	D5xC27	270,2
D₅×C₃³	Direct product of C₃³ and D₅	135		D5xC3^3	270,23
S₃×C₃×C₁₅	Direct product of C₃×C₁₅ and S₃	90		S3xC3xC15	270,24
C₁₅×C₃⋊S₃	Direct product of C₁₅ and C₃⋊S₃	90		C15xC3:S3	270,26
C₃×C₃⋊D₁₅	Direct product of C₃ and C₃⋊D₁₅	90		C3xC3:D15	270,27
D₅×C₃×C₉	Direct product of C₃×C₉ and D₅	135		D5xC3xC9	270,5
C₅×C₉⋊S₃	Direct product of C₅ and C₉⋊S₃	135		C5xC9:S3	270,16
C₅×C₃³⋊C₂	Direct product of C₅ and C₃³⋊C₂	135		C5xC3^3:C2	270,28

Groups of order 271

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

Groups of order 272

		d	ρ	Label	ID
C₂₇₂	Cyclic group	272	1	C272	272,2
F₁₇	Frobenius group; = C₁₇ ⋊C₁₆ = AGL₁(𝔽₁₇) = Aut(D₁₇) = Hol(C₁₇)	17	16+	F17	272,50
C₁₇⋊₄C₁₆	The semidirect product of C₁₇ and C₁₆ acting via C₁₆/C₈=C₂	272	2	C17:4C16	272,1
C₁₇⋊₃C₁₆	The semidirect product of C₁₇ and C₁₆ acting via C₁₆/C₄=C₄	272	4	C17:3C16	272,3
C₆₈.C₄	3^rd non-split extension by C₆₈ of C₄ acting faithfully	136	4	C68.C4	272,29
C₃₄.C₈	The non-split extension by C₃₄ of C₈ acting faithfully	272	8-	C34.C8	272,28
C₄×C₆₈	Abelian group of type [4,68]	272		C4xC68	272,20
C₂×C₁₃₆	Abelian group of type [2,136]	272		C2xC136	272,23
C₂²×C₆₈	Abelian group of type [2,2,68]	272		C2^2xC68	272,46
C₂³×C₃₄	Abelian group of type [2,2,2,34]	272		C2^3xC34	272,54
C₈×D₁₇	Direct product of C₈ and D₁₇	136	2	C8xD17	272,4
C₂³×D₁₇	Direct product of C₂³ and D₁₇	136		C2^3xD17	272,53
C₄×Dic₁₇	Direct product of C₄ and Dic₁₇	272		C4xDic17	272,11
C₂²×Dic₁₇	Direct product of C₂² and Dic₁₇	272		C2^2xDic17	272,44
C₂×C₁₇⋊C₈	Direct product of C₂ and C₁₇⋊C₈	34	8+	C2xC17:C8	272,51
C₄×C₁₇⋊C₄	Direct product of C₄ and C₁₇⋊C₄	68	4	C4xC17:C4	272,31
C₂²×C₁₇⋊C₄	Direct product of C₂² and C₁₇⋊C₄	68		C2^2xC17:C4	272,52
C₂×C₄×D₁₇	Direct product of C₂×C₄ and D₁₇	136		C2xC4xD17	272,37
C₂×C₁₇⋊₃C₈	Direct product of C₂ and C₁₇⋊₃C₈	272		C2xC17:3C8	272,9
C₂×C₁₇⋊₂C₈	Direct product of C₂ and C₁₇⋊₂C₈	272		C2xC17:2C8	272,33

Groups of order 273

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

Groups of order 274

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

Groups of order 275

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

Groups of order 276

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

Groups of order 277

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

Groups of order 278

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

Groups of order 279

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

Groups of order 280

		d	ρ	Label	ID
C₂₈₀	Cyclic group	280	1	C280	280,4
C₃₅⋊₃C₈	1^st semidirect product of C₃₅ and C₈ acting via C₈/C₄=C₂	280	2	C35:3C8	280,3
C₃₅⋊C₈	1^st semidirect product of C₃₅ and C₈ acting via C₈/C₂=C₄	280	4	C35:C8	280,6
D₇₀.C₂	The non-split extension by D₇₀ of C₂ acting faithfully	140	4+	D70.C2	280,9
C₂×C₁₄₀	Abelian group of type [2,140]	280		C2xC140	280,29
C₂²×C₇₀	Abelian group of type [2,2,70]	280		C2^2xC70	280,40
D₇×F₅	Direct product of D₇ and F₅	35	8+	D7xF5	280,32
C₅×F₈	Direct product of C₅ and F₈	40	7	C5xF8	280,33
C₁₄×F₅	Direct product of C₁₄ and F₅	70	4	C14xF5	280,34
D₇×C₂₀	Direct product of C₂₀ and D₇	140	2	D7xC20	280,15
D₅×C₂₈	Direct product of C₂₈ and D₅	140	2	D5xC28	280,20
C₄×D₃₅	Direct product of C₄ and D₃₅	140	2	C4xD35	280,25
D₇×Dic₅	Direct product of D₇ and Dic₅	140	4-	D7xDic5	280,7
D₅×Dic₇	Direct product of D₅ and Dic₇	140	4-	D5xDic7	280,8
C₂²×D₃₅	Direct product of C₂² and D₃₅	140		C2^2xD35	280,39
C₁₀×Dic₇	Direct product of C₁₀ and Dic₇	280		C10xDic7	280,17
C₁₄×Dic₅	Direct product of C₁₄ and Dic₅	280		C14xDic5	280,22
C₂×Dic₃₅	Direct product of C₂ and Dic₃₅	280		C2xDic35	280,27
C₂×D₅×D₇	Direct product of C₂, D₅ and D₇	70	4+	C2xD5xD7	280,36
C₂×C₇⋊F₅	Direct product of C₂ and C₇⋊F₅	70	4	C2xC7:F5	280,35
D₇×C₂×C₁₀	Direct product of C₂×C₁₀ and D₇	140		D7xC2xC10	280,37
D₅×C₂×C₁₄	Direct product of C₂×C₁₄ and D₅	140		D5xC2xC14	280,38
C₅×C₇⋊C₈	Direct product of C₅ and C₇⋊C₈	280	2	C5xC7:C8	280,2
C₇×C₅⋊C₈	Direct product of C₇ and C₅⋊C₈	280	4	C7xC5:C8	280,5
C₇×C₅⋊₂C₈	Direct product of C₇ and C₅⋊₂C₈	280	2	C7xC5:2C8	280,1

Groups of order 281

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

Groups of order 282

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

Groups of order 283

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

Groups of order 284

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

Groups of order 285

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

Groups of order 286

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

Groups of order 287

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

Groups of order 288

		d	ρ	Label	ID
C₂₈₈	Cyclic group	288	1	C288	288,2
C₃²⋊C₃₂	The semidirect product of C₃² and C₃₂ acting via C₃₂/C₄=C₈	96	8	C3^2:C32	288,373
C₃²⋊₂C₃₂	The semidirect product of C₃² and C₃₂ acting via C₃₂/C₈=C₄	96	4	C3^2:2C32	288,188
C₉⋊C₃₂	The semidirect product of C₉ and C₃₂ acting via C₃₂/C₁₆=C₂	288	2	C9:C32	288,1
C₃⋊S₃⋊₃C₁₆	2^nd semidirect product of C₃⋊S₃ and C₁₆ acting via C₁₆/C₈=C₂	48	4	C3:S3:3C16	288,412
C₄.₃F₉	2^nd central extension by C₄ of F₉	48	8	C4.3F9	288,861
C₂₄.₆₀D₆	13^rd non-split extension by C₂₄ of D₆ acting via D₆/S₃=C₂	48	4	C24.60D6	288,190
C₄₈.S₃	9^th non-split extension by C₄₈ of S₃ acting via S₃/C₃=C₂	288		C48.S3	288,65
C₆.(S₃×C₈)	3^rd non-split extension by C₆ of S₃×C₈ acting via S₃×C₈/C₃⋊C₈=C₂	96		C6.(S3xC8)	288,201
C₄×C₇₂	Abelian group of type [4,72]	288		C4xC72	288,46
C₃×C₉₆	Abelian group of type [3,96]	288		C3xC96	288,66
C₆×C₄₈	Abelian group of type [6,48]	288		C6xC48	288,327
C₂×C₁₄₄	Abelian group of type [2,144]	288		C2xC144	288,59
C₁₂×C₂₄	Abelian group of type [12,24]	288		C12xC24	288,314
C₂²×C₇₂	Abelian group of type [2,2,72]	288		C2^2xC72	288,179
C₂³×C₃₆	Abelian group of type [2,2,2,36]	288		C2^3xC36	288,367
C₂×C₁₂²	Abelian group of type [2,12,12]	288		C2xC12^2	288,811
C₂⁴×C₁₈	Abelian group of type [2,2,2,2,18]	288		C2^4xC18	288,840
C₂³×C₆²	Abelian group of type [2,2,2,6,6]	288		C2^3xC6^2	288,1045
C₂×C₄×C₃₆	Abelian group of type [2,4,36]	288		C2xC4xC36	288,164
C₂×C₆×C₂₄	Abelian group of type [2,6,24]	288		C2xC6xC24	288,826
C₂²×C₆×C₁₂	Abelian group of type [2,2,6,12]	288		C2^2xC6xC12	288,1018
C₄×F₉	Direct product of C₄ and F₉	36	8	C4xF9	288,863
C₂²×F₉	Direct product of C₂² and F₉	36		C2^2xF9	288,1030
A₄×C₂₄	Direct product of C₂₄ and A₄	72	3	A4xC24	288,637
S₃×C₄₈	Direct product of C₄₈ and S₃	96	2	S3xC48	288,231
Dic₃×C₂₄	Direct product of C₂₄ and Dic₃	96		Dic3xC24	288,247
C₁₆×D₉	Direct product of C₁₆ and D₉	144	2	C16xD9	288,4
C₄²×D₉	Direct product of C₄² and D₉	144		C4^2xD9	288,81
C₂⁴×D₉	Direct product of C₂⁴ and D₉	144		C2^4xD9	288,839
C₈×Dic₉	Direct product of C₈ and Dic₉	288		C8xDic9	288,21
C₂³×Dic₉	Direct product of C₂³ and Dic₉	288		C2^3xDic9	288,365
C₂×A₄²	Direct product of C₂, A₄ and A₄	18	9+	C2xA4^2	288,1029
C₄×S₃×A₄	Direct product of C₄, S₃ and A₄	36	6	C4xS3xA4	288,919
C₂×C₄²⋊C₉	Direct product of C₂ and C₄²⋊C₉	36	3	C2xC4^2:C9	288,71
S₃×C₄²⋊C₃	Direct product of S₃ and C₄²⋊C₃	36	6	S3xC4^2:C3	288,407
C₆×C₄²⋊C₃	Direct product of C₆ and C₄²⋊C₃	36	3	C6xC4^2:C3	288,632
C₂²×S₃×A₄	Direct product of C₂², S₃ and A₄	36		C2^2xS3xA4	288,1037
S₃×C₂²⋊A₄	Direct product of S₃ and C₂²⋊A₄	36		S3xC2^2:A4	288,1038
C₆×C₂²⋊A₄	Direct product of C₆ and C₂²⋊A₄	36		C6xC2^2:A4	288,1042
C₂×C₂⁴⋊C₉	Direct product of C₂ and C₂⁴⋊C₉	36		C2xC2^4:C9	288,838
S₃²×C₈	Direct product of C₈, S₃ and S₃	48	4	S3^2xC8	288,437
S₃²×C₂³	Direct product of C₂³, S₃ and S₃	48		S3^2xC2^3	288,1040
C₈×C₃²⋊C₄	Direct product of C₈ and C₃²⋊C₄	48	4	C8xC3^2:C4	288,414
C₄×C₆.D₆	Direct product of C₄ and C₆.D₆	48		C4xC6.D6	288,530
C₂³×C₃²⋊C₄	Direct product of C₂³ and C₃²⋊C₄	48		C2^3xC3^2:C4	288,1039
C₂²×C₆.D₆	Direct product of C₂² and C₆.D₆	48		C2^2xC6.D6	288,972
C₂×C₁₂.₂₉D₆	Direct product of C₂ and C₁₂.₂₉D₆	48		C2xC12.29D6	288,464
A₄×C₃⋊C₈	Direct product of A₄ and C₃⋊C₈	72	6	A4xC3:C8	288,408
A₄×C₂×C₁₂	Direct product of C₂×C₁₂ and A₄	72		A4xC2xC12	288,979
C₈×C₃.A₄	Direct product of C₈ and C₃.A₄	72	3	C8xC3.A4	288,76
A₄×C₂²×C₆	Direct product of C₂²×C₆ and A₄	72		A4xC2^2xC6	288,1041
C₂×Dic₃×A₄	Direct product of C₂, Dic₃ and A₄	72		C2xDic3xA4	288,927
C₂³×C₃.A₄	Direct product of C₂³ and C₃.A₄	72		C2^3xC3.A4	288,837
C₃×C₃⋊C₃₂	Direct product of C₃ and C₃⋊C₃₂	96	2	C3xC3:C32	288,64
C₁₂×C₃⋊C₈	Direct product of C₁₂ and C₃⋊C₈	96		C12xC3:C8	288,236
C₆×C₃⋊C₁₆	Direct product of C₆ and C₃⋊C₁₆	96		C6xC3:C16	288,245
S₃×C₃⋊C₁₆	Direct product of S₃ and C₃⋊C₁₆	96	4	S3xC3:C16	288,189
S₃×C₄×C₁₂	Direct product of C₄×C₁₂ and S₃	96		S3xC4xC12	288,642
S₃×C₂×C₂₄	Direct product of C₂×C₂₄ and S₃	96		S3xC2xC24	288,670
C₂×Dic₃²	Direct product of C₂, Dic₃ and Dic₃	96		C2xDic3^2	288,602
S₃×C₂³×C₆	Direct product of C₂³×C₆ and S₃	96		S3xC2^3xC6	288,1043
Dic₃×C₃⋊C₈	Direct product of Dic₃ and C₃⋊C₈	96		Dic3xC3:C8	288,200
C₄×S₃×Dic₃	Direct product of C₄, S₃ and Dic₃	96		C4xS3xDic3	288,523
C₂×C₂.F₉	Direct product of C₂ and C₂.F₉	96		C2xC2.F9	288,865
S₃×C₂²×C₁₂	Direct product of C₂²×C₁₂ and S₃	96		S3xC2^2xC12	288,989
Dic₃×C₂×C₁₂	Direct product of C₂×C₁₂ and Dic₃	96		Dic3xC2xC12	288,693
C₄×C₃²⋊₂C₈	Direct product of C₄ and C₃²⋊₂C₈	96		C4xC3^2:2C8	288,423
C₂²×S₃×Dic₃	Direct product of C₂², S₃ and Dic₃	96		C2^2xS3xDic3	288,969
Dic₃×C₂²×C₆	Direct product of C₂²×C₆ and Dic₃	96		Dic3xC2^2xC6	288,1001
C₂×C₃²⋊₂C₁₆	Direct product of C₂ and C₃²⋊₂C₁₆	96		C2xC3^2:2C16	288,420
C₂²×C₃²⋊₂C₈	Direct product of C₂² and C₃²⋊₂C₈	96		C2^2xC3^2:2C8	288,939
C₂×C₈×D₉	Direct product of C₂×C₈ and D₉	144		C2xC8xD9	288,110
C₁₆×C₃⋊S₃	Direct product of C₁₆ and C₃⋊S₃	144		C16xC3:S3	288,272
C₂²×C₄×D₉	Direct product of C₂²×C₄ and D₉	144		C2^2xC4xD9	288,353
C₄²×C₃⋊S₃	Direct product of C₄² and C₃⋊S₃	144		C4^2xC3:S3	288,728
C₂⁴×C₃⋊S₃	Direct product of C₂⁴ and C₃⋊S₃	144		C2^4xC3:S3	288,1044
C₄×C₉⋊C₈	Direct product of C₄ and C₉⋊C₈	288		C4xC9:C8	288,9
C₂×C₉⋊C₁₆	Direct product of C₂ and C₉⋊C₁₆	288		C2xC9:C16	288,18
C₂²×C₉⋊C₈	Direct product of C₂² and C₉⋊C₈	288		C2^2xC9:C8	288,130
C₂×C₄×Dic₉	Direct product of C₂×C₄ and Dic₉	288		C2xC4xDic9	288,132
C₈×C₃⋊Dic₃	Direct product of C₈ and C₃⋊Dic₃	288		C8xC3:Dic3	288,288
C₂×C₂₄.S₃	Direct product of C₂ and C₂₄.S₃	288		C2xC24.S3	288,286
C₄×C₃²⋊₄C₈	Direct product of C₄ and C₃²⋊₄C₈	288		C4xC3^2:4C8	288,277
C₂³×C₃⋊Dic₃	Direct product of C₂³ and C₃⋊Dic₃	288		C2^3xC3:Dic3	288,1016
C₂²×C₃²⋊₄C₈	Direct product of C₂² and C₃²⋊₄C₈	288		C2^2xC3^2:4C8	288,777
S₃²×C₂×C₄	Direct product of C₂×C₄, S₃ and S₃	48		S3^2xC2xC4	288,950
C₂×C₄×C₃²⋊C₄	Direct product of C₂×C₄ and C₃²⋊C₄	48		C2xC4xC3^2:C4	288,932
C₂×C₃⋊S₃⋊₃C₈	Direct product of C₂ and C₃⋊S₃⋊₃C₈	48		C2xC3:S3:3C8	288,929
C₂×C₄×C₃.A₄	Direct product of C₂×C₄ and C₃.A₄	72		C2xC4xC3.A4	288,343
C₂×S₃×C₃⋊C₈	Direct product of C₂, S₃ and C₃⋊C₈	96		C2xS3xC3:C8	288,460
C₂×C₆×C₃⋊C₈	Direct product of C₂×C₆ and C₃⋊C₈	96		C2xC6xC3:C8	288,691
C₂×C₈×C₃⋊S₃	Direct product of C₂×C₈ and C₃⋊S₃	144		C2xC8xC3:S3	288,756
C₂²×C₄×C₃⋊S₃	Direct product of C₂²×C₄ and C₃⋊S₃	144		C2^2xC4xC3:S3	288,1004
C₂×C₄×C₃⋊Dic₃	Direct product of C₂×C₄ and C₃⋊Dic₃	288		C2xC4xC3:Dic3	288,779

Groups of order 289

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

Groups of order 290

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

Groups of order 291

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

Groups of order 292

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

Groups of order 293

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

Groups of order 294

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

Groups of order 295

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

Groups of order 296

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

Groups of order 297

		d	ρ	Label	ID
C₂₉₇	Cyclic group	297	1	C297	297,1
C₃×C₉₉	Abelian group of type [3,99]	297		C3xC99	297,2
C₃²×C₃₃	Abelian group of type [3,3,33]	297		C3^2xC33	297,5

Groups of order 298

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

Groups of order 299

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

Groups of order 300

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

Groups of order 301

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

Groups of order 302

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

Groups of order 303

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

Groups of order 304

		d	ρ	Label	ID
C₃₀₄	Cyclic group	304	1	C304	304,2
C₁₉⋊C₁₆	The semidirect product of C₁₉ and C₁₆ acting via C₁₆/C₈=C₂	304	2	C19:C16	304,1
C₄×C₇₆	Abelian group of type [4,76]	304		C4xC76	304,19
C₂×C₁₅₂	Abelian group of type [2,152]	304		C2xC152	304,22
C₂²×C₇₆	Abelian group of type [2,2,76]	304		C2^2xC76	304,37
C₂³×C₃₈	Abelian group of type [2,2,2,38]	304		C2^3xC38	304,42
C₈×D₁₉	Direct product of C₈ and D₁₉	152	2	C8xD19	304,3
C₂³×D₁₉	Direct product of C₂³ and D₁₉	152		C2^3xD19	304,41
C₄×Dic₁₉	Direct product of C₄ and Dic₁₉	304		C4xDic19	304,10
C₂²×Dic₁₉	Direct product of C₂² and Dic₁₉	304		C2^2xDic19	304,35
C₂×C₄×D₁₉	Direct product of C₂×C₄ and D₁₉	152		C2xC4xD19	304,28
C₂×C₁₉⋊C₈	Direct product of C₂ and C₁₉⋊C₈	304		C2xC19:C8	304,8

Groups of order 305

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

Groups of order 306

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

Groups of order 307

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

Groups of order 308

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

Groups of order 309

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

Groups of order 310

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

Groups of order 311

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

Groups of order 312

		d	ρ	Label	ID
C₃₁₂	Cyclic group	312	1	C312	312,6
D₁₃⋊A₄	The semidirect product of D₁₃ and A₄ acting via A₄/C₂²=C₃	52	6+	D13:A4	312,51
C₁₃⋊C₂₄	The semidirect product of C₁₃ and C₂₄ acting via C₂₄/C₂=C₁₂	104	12-	C13:C24	312,7
C₁₃⋊₂C₂₄	The semidirect product of C₁₃ and C₂₄ acting via C₂₄/C₄=C₆	104	6	C13:2C24	312,1
C₃₉⋊₃C₈	1^st semidirect product of C₃₉ and C₈ acting via C₈/C₄=C₂	312	2	C39:3C8	312,5
C₃₉⋊C₈	1^st semidirect product of C₃₉ and C₈ acting via C₈/C₂=C₄	312	4	C39:C8	312,14
D₇₈.C₂	The non-split extension by D₇₈ of C₂ acting faithfully	156	4+	D78.C2	312,17
C₂×C₁₅₆	Abelian group of type [2,156]	312		C2xC156	312,42
C₂²×C₇₈	Abelian group of type [2,2,78]	312		C2^2xC78	312,61
C₂×F₁₃	Direct product of C₂ and F₁₃; = Aut(D₂₆) = Hol(C₂₆)	26	12+	C2xF13	312,45
A₄×D₁₃	Direct product of A₄ and D₁₃	52	6+	A4xD13	312,50
A₄×C₂₆	Direct product of C₂₆ and A₄	78	3	A4xC26	312,56
S₃×C₅₂	Direct product of C₅₂ and S₃	156	2	S3xC52	312,33
C₄×D₃₉	Direct product of C₄ and D₃₉	156	2	C4xD39	312,38
C₁₂×D₁₃	Direct product of C₁₂ and D₁₃	156	2	C12xD13	312,28
Dic₃×D₁₃	Direct product of Dic₃ and D₁₃	156	4-	Dic3xD13	312,15
S₃×Dic₁₃	Direct product of S₃ and Dic₁₃	156	4-	S3xDic13	312,16
C₂²×D₃₉	Direct product of C₂² and D₃₉	156		C2^2xD39	312,60
C₆×Dic₁₃	Direct product of C₆ and Dic₁₃	312		C6xDic13	312,30
Dic₃×C₂₆	Direct product of C₂₆ and Dic₃	312		Dic3xC26	312,35
C₂×Dic₃₉	Direct product of C₂ and Dic₃₉	312		C2xDic39	312,40
S₃×C₁₃⋊C₄	Direct product of S₃ and C₁₃⋊C₄	39	8+	S3xC13:C4	312,46
C₄×C₁₃⋊C₆	Direct product of C₄ and C₁₃⋊C₆	52	6	C4xC13:C6	312,9
C₂²×C₁₃⋊C₆	Direct product of C₂² and C₁₃⋊C₆	52		C2^2xC13:C6	312,49
C₆×C₁₃⋊C₄	Direct product of C₆ and C₁₃⋊C₄	78	4	C6xC13:C4	312,52
C₂×C₁₃⋊A₄	Direct product of C₂ and C₁₃⋊A₄	78	3	C2xC13:A4	312,57
C₂×S₃×D₁₃	Direct product of C₂, S₃ and D₁₃	78	4+	C2xS3xD13	312,54
C₂×C₃₉⋊C₄	Direct product of C₂ and C₃₉⋊C₄	78	4	C2xC39:C4	312,53
C₈×C₁₃⋊C₃	Direct product of C₈ and C₁₃⋊C₃	104	3	C8xC13:C3	312,2
C₂×C₂₆.C₆	Direct product of C₂ and C₂₆.C₆	104		C2xC26.C6	312,11
C₂³×C₁₃⋊C₃	Direct product of C₂³ and C₁₃⋊C₃	104		C2^3xC13:C3	312,55
S₃×C₂×C₂₆	Direct product of C₂×C₂₆ and S₃	156		S3xC2xC26	312,59
C₂×C₆×D₁₃	Direct product of C₂×C₆ and D₁₃	156		C2xC6xD13	312,58
C₁₃×C₃⋊C₈	Direct product of C₁₃ and C₃⋊C₈	312	2	C13xC3:C8	312,3
C₃×C₁₃⋊C₈	Direct product of C₃ and C₁₃⋊C₈	312	4	C3xC13:C8	312,13
C₃×C₁₃⋊₂C₈	Direct product of C₃ and C₁₃⋊₂C₈	312	2	C3xC13:2C8	312,4
C₂×C₄×C₁₃⋊C₃	Direct product of C₂×C₄ and C₁₃⋊C₃	104		C2xC4xC13:C3	312,22

Groups of order 313

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

Groups of order 314

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

Groups of order 315

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

Groups of order 316

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

Groups of order 317

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

Groups of order 318

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

Groups of order 319

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

Groups of order 320

		d	ρ	Label	ID
C₃₂₀	Cyclic group	320	1	C320	320,2
D₅⋊C₃₂	The semidirect product of D₅ and C₃₂ acting via C₃₂/C₁₆=C₂	160	4	D5:C32	320,179
C₅⋊C₆₄	The semidirect product of C₅ and C₆₄ acting via C₆₄/C₁₆=C₄	320	4	C5:C64	320,3
C₅⋊₂C₆₄	The semidirect product of C₅ and C₆₄ acting via C₆₄/C₃₂=C₂	320	2	C5:2C64	320,1
Dic₅⋊C₁₆	2^nd semidirect product of Dic₅ and C₁₆ acting via C₁₆/C₈=C₂	320		Dic5:C16	320,223
C₈×C₄₀	Abelian group of type [8,40]	320		C8xC40	320,126
C₄×C₈₀	Abelian group of type [4,80]	320		C4xC80	320,150
C₂×C₁₆₀	Abelian group of type [2,160]	320		C2xC160	320,174
C₄²×C₂₀	Abelian group of type [4,4,20]	320		C4^2xC20	320,875
C₂²×C₈₀	Abelian group of type [2,2,80]	320		C2^2xC80	320,1003
C₂³×C₄₀	Abelian group of type [2,2,2,40]	320		C2^3xC40	320,1567
C₂⁴×C₂₀	Abelian group of type [2,2,2,2,20]	320		C2^4xC20	320,1628
C₂⁵×C₁₀	Abelian group of type [2,2,2,2,2,10]	320		C2^5xC10	320,1640
C₂×C₄×C₄₀	Abelian group of type [2,4,40]	320		C2xC4xC40	320,903
C₂²×C₄×C₂₀	Abelian group of type [2,2,4,20]	320		C2^2xC4xC20	320,1513
C₁₆×F₅	Direct product of C₁₆ and F₅	80	4	C16xF5	320,181
C₄²×F₅	Direct product of C₄² and F₅	80		C4^2xF5	320,1023
C₂⁴×F₅	Direct product of C₂⁴ and F₅	80		C2^4xF5	320,1638
D₅×C₃₂	Direct product of C₃₂ and D₅	160	2	D5xC32	320,4
D₅×C₂⁵	Direct product of C₂⁵ and D₅	160		D5xC2^5	320,1639
C₁₆×Dic₅	Direct product of C₁₆ and Dic₅	320		C16xDic5	320,58
C₄²×Dic₅	Direct product of C₄² and Dic₅	320		C4^2xDic5	320,557
C₂⁴×Dic₅	Direct product of C₂⁴ and Dic₅	320		C2^4xDic5	320,1626
C₄×C₂⁴⋊C₅	Direct product of C₄ and C₂⁴⋊C₅	20	5	C4xC2^4:C5	320,1584
C₂²×C₂⁴⋊C₅	Direct product of C₂² and C₂⁴⋊C₅	20		C2^2xC2^4:C5	320,1637
C₂×C₈×F₅	Direct product of C₂×C₈ and F₅	80		C2xC8xF5	320,1054
C₂²×C₄×F₅	Direct product of C₂²×C₄ and F₅	80		C2^2xC4xF5	320,1590
D₅×C₄×C₈	Direct product of C₄×C₈ and D₅	160		D5xC4xC8	320,311
D₅×C₂×C₁₆	Direct product of C₂×C₁₆ and D₅	160		D5xC2xC16	320,526
C₄×D₅⋊C₈	Direct product of C₄ and D₅⋊C₈	160		C4xD5:C8	320,1013
D₅×C₂×C₄²	Direct product of C₂×C₄² and D₅	160		D5xC2xC4^2	320,1143
D₅×C₂²×C₈	Direct product of C₂²×C₈ and D₅	160		D5xC2^2xC8	320,1408
D₅×C₂³×C₄	Direct product of C₂³×C₄ and D₅	160		D5xC2^3xC4	320,1609
C₂×D₅⋊C₁₆	Direct product of C₂ and D₅⋊C₁₆	160		C2xD5:C16	320,1051
C₂²×D₅⋊C₈	Direct product of C₂² and D₅⋊C₈	160		C2^2xD5:C8	320,1587
C₈×C₅⋊C₈	Direct product of C₈ and C₅⋊C₈	320		C8xC5:C8	320,216
C₄×C₅⋊C₁₆	Direct product of C₄ and C₅⋊C₁₆	320		C4xC5:C16	320,195
C₂×C₅⋊C₃₂	Direct product of C₂ and C₅⋊C₃₂	320		C2xC5:C32	320,214
C₈×C₅⋊₂C₈	Direct product of C₈ and C₅⋊₂C₈	320		C8xC5:2C8	320,11
C₂³×C₅⋊C₈	Direct product of C₂³ and C₅⋊C₈	320		C2^3xC5:C8	320,1605
C₂×C₈×Dic₅	Direct product of C₂×C₈ and Dic₅	320		C2xC8xDic5	320,725
C₄×C₅⋊₂C₁₆	Direct product of C₄ and C₅⋊₂C₁₆	320		C4xC5:2C16	320,18
C₂×C₅⋊₂C₃₂	Direct product of C₂ and C₅⋊₂C₃₂	320		C2xC5:2C32	320,56
C₂²×C₅⋊C₁₆	Direct product of C₂² and C₅⋊C₁₆	320		C2^2xC5:C16	320,1080
C₂³×C₅⋊₂C₈	Direct product of C₂³ and C₅⋊₂C₈	320		C2^3xC5:2C8	320,1452
C₂²×C₄×Dic₅	Direct product of C₂²×C₄ and Dic₅	320		C2^2xC4xDic5	320,1454
C₂²×C₅⋊₂C₁₆	Direct product of C₂² and C₅⋊₂C₁₆	320		C2^2xC5:2C16	320,723
C₂×C₄×C₅⋊C₈	Direct product of C₂×C₄ and C₅⋊C₈	320		C2xC4xC5:C8	320,1084
C₂×C₄×C₅⋊₂C₈	Direct product of C₂×C₄ and C₅⋊₂C₈	320		C2xC4xC5:2C8	320,547

Groups of order 321

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

Groups of order 322

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

Groups of order 323

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

Groups of order 324

		d	ρ	Label	ID
C₃₂₄	Cyclic group	324	1	C324	324,2
D₁₆₂	Dihedral group; = C₂×D₈₁	162	2+	D162	324,4
Dic₈₁	Dicyclic group; = C₈₁ ⋊C₄	324	2-	Dic81	324,1
C₉²⋊C₄	The semidirect product of C₉² and C₄ acting faithfully	18	4+	C9^2:C4	324,35
C₃⁴⋊₄C₄	4^th semidirect product of C₃⁴ and C₄ acting faithfully	18		C3^4:4C4	324,164
C₃⁴⋊C₄	3^rd semidirect product of C₃⁴ and C₄ acting faithfully	36		C3^4:C4	324,163
C₃²⋊₅D₁₈	2^nd semidirect product of C₃² and D₁₈ acting via D₁₈/C₉=C₂²	36	4	C3^2:5D18	324,123
C₃³⋊₁₇D₆	5^th semidirect product of C₃³ and D₆ acting via D₆/C₃=C₂²	36		C3^3:17D6	324,170
C₃²⋊₃Dic₉	The semidirect product of C₃² and Dic₉ acting via Dic₉/C₉=C₄	36	4	C3^2:3Dic9	324,112
C₉⋊Dic₉	The semidirect product of C₉ and Dic₉ acting via Dic₉/C₁₈=C₂	324		C9:Dic9	324,19
C₂₇⋊Dic₃	The semidirect product of C₂₇ and Dic₃ acting via Dic₃/C₆=C₂	324		C27:Dic3	324,21
C₃⁴⋊₈C₄	4^th semidirect product of C₃⁴ and C₄ acting via C₄/C₂=C₂	324		C3^4:8C4	324,158
C₃²⋊₅Dic₉	2^nd semidirect product of C₃² and Dic₉ acting via Dic₉/C₁₈=C₂	324		C3^2:5Dic9	324,103
C₂₇.A₄	The central extension by C₂₇ of A₄	162	3	C27.A4	324,3
C₁₈²	Abelian group of type [18,18]	324		C18^2	324,81
C₉×C₃₆	Abelian group of type [9,36]	324		C9xC36	324,26
C₆×C₅₄	Abelian group of type [6,54]	324		C6xC54	324,84
C₂×C₁₆₂	Abelian group of type [2,162]	324		C2xC162	324,5
C₃×C₁₀₈	Abelian group of type [3,108]	324		C3xC108	324,29
C₃²×C₃₆	Abelian group of type [3,3,36]	324		C3^2xC36	324,105
C₃³×C₁₂	Abelian group of type [3,3,3,12]	324		C3^3xC12	324,159
C₃²×C₆²	Abelian group of type [3,3,6,6]	324		C3^2xC6^2	324,176
C₃×C₆×C₁₈	Abelian group of type [3,6,18]	324		C3xC6xC18	324,151
D₉²	Direct product of D₉ and D₉	18	4+	D9^2	324,36
D₉×C₁₈	Direct product of C₁₈ and D₉	36	2	D9xC18	324,61
C₉×Dic₉	Direct product of C₉ and Dic₉	36	2	C9xDic9	324,6
S₃×D₂₇	Direct product of S₃ and D₂₇	54	4+	S3xD27	324,38
S₃×C₅₄	Direct product of C₅₄ and S₃	108	2	S3xC54	324,66
A₄×C₂₇	Direct product of C₂₇ and A₄	108	3	A4xC27	324,42
C₆×D₂₇	Direct product of C₆ and D₂₇	108	2	C6xD27	324,65
A₄×C₃³	Direct product of C₃³ and A₄	108		A4xC3^3	324,171
C₃×Dic₂₇	Direct product of C₃ and Dic₂₇	108	2	C3xDic27	324,10
Dic₃×C₂₇	Direct product of C₂₇ and Dic₃	108	2	Dic3xC27	324,11
C₃²×Dic₉	Direct product of C₃² and Dic₉	108		C3^2xDic9	324,90
Dic₃×C₃³	Direct product of C₃³ and Dic₃	108		Dic3xC3^3	324,155
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
S₃²×C₉	Direct product of C₉, S₃ and S₃	36	4	S3^2xC9	324,115
C₃×S₃×D₉	Direct product of C₃, S₃ and D₉	36	4	C3xS3xD9	324,114
S₃²×C₃²	Direct product of C₃², S₃ and S₃	36		S3^2xC3^2	324,165
C₉×C₃²⋊C₄	Direct product of C₉ and C₃²⋊C₄	36	4	C9xC3^2:C4	324,109
C₃²×C₃²⋊C₄	Direct product of C₃² and C₃²⋊C₄	36		C3^2xC3^2:C4	324,161
C₃²×C₃⋊Dic₃	Direct product of C₃² and C₃⋊Dic₃	36		C3^2xC3:Dic3	324,156
S₃×C₉⋊S₃	Direct product of S₃ and C₉⋊S₃	54		S3xC9:S3	324,120
D₉×C₃⋊S₃	Direct product of D₉ and C₃⋊S₃	54		D9xC3:S3	324,119
S₃×C₃³⋊C₂	Direct product of S₃ and C₃³⋊C₂	54		S3xC3^3:C2	324,168
A₄×C₃×C₉	Direct product of C₃×C₉ and A₄	108		A4xC3xC9	324,126
D₉×C₃×C₆	Direct product of C₃×C₆ and D₉	108		D9xC3xC6	324,136
C₆×C₉⋊S₃	Direct product of C₆ and C₉⋊S₃	108		C6xC9:S3	324,142
S₃×C₃×C₁₈	Direct product of C₃×C₁₈ and S₃	108		S3xC3xC18	324,137
C₁₈×C₃⋊S₃	Direct product of C₁₈ and C₃⋊S₃	108		C18xC3:S3	324,143
S₃×C₃²×C₆	Direct product of C₃²×C₆ and S₃	108		S3xC3^2xC6	324,172
Dic₃×C₃×C₉	Direct product of C₃×C₉ and Dic₃	108		Dic3xC3xC9	324,91
C₃×C₉⋊Dic₃	Direct product of C₃ and C₉⋊Dic₃	108		C3xC9:Dic3	324,96
C₉×C₃⋊Dic₃	Direct product of C₉ and C₃⋊Dic₃	108		C9xC3:Dic3	324,97
C₆×C₃³⋊C₂	Direct product of C₆ and C₃³⋊C₂	108		C6xC3^3:C2	324,174
C₃×C₃³⋊₅C₄	Direct product of C₃ and C₃³⋊₅C₄	108		C3xC3^3:5C4	324,157
C₂×C₉⋊D₉	Direct product of C₂ and C₉⋊D₉	162		C2xC9:D9	324,74
C₂×C₂₇⋊S₃	Direct product of C₂ and C₂₇⋊S₃	162		C2xC27:S3	324,76
C₃×C₉.A₄	Direct product of C₃ and C₉.A₄	162		C3xC9.A4	324,44
C₉×C₃.A₄	Direct product of C₉ and C₃.A₄	162		C9xC3.A4	324,46
C₂×C₃⁴⋊C₂	Direct product of C₂ and C₃⁴⋊C₂	162		C2xC3^4:C2	324,175
C₃²×C₃.A₄	Direct product of C₃² and C₃.A₄	162		C3^2xC3.A4	324,133
C₂×C₃²⋊₄D₉	Direct product of C₂ and C₃²⋊₄D₉	162		C2xC3^2:4D9	324,149
C₃⋊S₃²	Direct product of C₃⋊S₃ and C₃⋊S₃	18		C3:S3^2	324,169
C₃×S₃×C₃⋊S₃	Direct product of C₃, S₃ and C₃⋊S₃	36		C3xS3xC3:S3	324,166
C₃⋊S₃×C₃×C₆	Direct product of C₃×C₆ and C₃⋊S₃	36		C3:S3xC3xC6	324,173

Groups of order 325

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

Groups of order 326

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

Groups of order 327

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

Groups of order 328

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

Groups of order 329

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

Groups of order 330

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

Groups of order 331

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

Groups of order 332

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

Groups of order 333

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

Groups of order 334

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

Groups of order 335

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

Groups of order 336

		d	ρ	Label	ID
C₃₃₆	Cyclic group	336	1	C336	336,6
Dic₇⋊A₄	The semidirect product of Dic₇ and A₄ acting via A₄/C₂²=C₃	84	6-	Dic7:A4	336,136
C₇⋊C₄₈	The semidirect product of C₇ and C₄₈ acting via C₄₈/C₈=C₆	112	6	C7:C48	336,1
D₂₁⋊C₈	The semidirect product of D₂₁ and C₈ acting via C₈/C₄=C₂	168	4	D21:C8	336,25
C₂₁⋊C₁₆	1^st semidirect product of C₂₁ and C₁₆ acting via C₁₆/C₈=C₂	336	2	C21:C16	336,5
C₄²⋊(C₇⋊C₃)	The semidirect product of C₄² and C₇⋊C₃ acting via C₇⋊C₃/C₇=C₃	84	3	C4^2:(C7:C3)	336,57
C₇⋊(C₂²⋊A₄)	The semidirect product of C₇ and C₂²⋊A₄ acting via C₂²⋊A₄/C₂⁴=C₃	84		C7:(C2^2:A4)	336,224
C₄×C₈₄	Abelian group of type [4,84]	336		C4xC84	336,106
C₂×C₁₆₈	Abelian group of type [2,168]	336		C2xC168	336,109
C₂²×C₈₄	Abelian group of type [2,2,84]	336		C2^2xC84	336,204
C₂³×C₄₂	Abelian group of type [2,2,2,42]	336		C2^3xC42	336,228
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	14	7+	C2xAGammaL(1,8)	336,210
S₃×F₈	Direct product of S₃ and F₈	24	14+	S3xF8	336,211
C₆×F₈	Direct product of C₆ and F₈	42	7	C6xF8	336,213
C₈×F₇	Direct product of C₈ and F₇	56	6	C8xF7	336,7
C₂³×F₇	Direct product of C₂³ and F₇	56		C2^3xF7	336,216
A₄×C₂₈	Direct product of C₂₈ and A₄	84	3	A4xC28	336,168
A₄×Dic₇	Direct product of A₄ and Dic₇	84	6-	A4xDic7	336,133
S₃×C₅₆	Direct product of C₅₆ and S₃	168	2	S3xC56	336,74
D₇×C₂₄	Direct product of C₂₄ and D₇	168	2	D7xC24	336,58
C₈×D₂₁	Direct product of C₈ and D₂₁	168	2	C8xD21	336,90
C₂³×D₂₁	Direct product of C₂³ and D₂₁	168		C2^3xD21	336,227
C₁₂×Dic₇	Direct product of C₁₂ and Dic₇	336		C12xDic7	336,65
Dic₃×C₂₈	Direct product of C₂₈ and Dic₃	336		Dic3xC28	336,81
C₄×Dic₂₁	Direct product of C₄ and Dic₂₁	336		C4xDic21	336,97
Dic₃×Dic₇	Direct product of Dic₃ and Dic₇	336		Dic3xDic7	336,41
C₂²×Dic₂₁	Direct product of C₂² and Dic₂₁	336		C2^2xDic21	336,202
C₂×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
C₂×C₄×F₇	Direct product of C₂×C₄ and F₇	56		C2xC4xF7	336,122
C₄×C₇⋊A₄	Direct product of C₄ and C₇⋊A₄	84	3	C4xC7:A4	336,171
C₄×S₃×D₇	Direct product of C₄, S₃ and D₇	84	4	C4xS3xD7	336,147
A₄×C₂×C₁₄	Direct product of C₂×C₁₄ and A₄	84		A4xC2xC14	336,221
C₇×C₄²⋊C₃	Direct product of C₇ and C₄²⋊C₃	84	3	C7xC4^2:C3	336,56
C₂²×C₇⋊A₄	Direct product of C₂² and C₇⋊A₄	84		C2^2xC7:A4	336,222
C₂²×S₃×D₇	Direct product of C₂², S₃ and D₇	84		C2^2xS3xD7	336,219
C₇×C₂²⋊A₄	Direct product of C₇ and C₂²⋊A₄	84		C7xC2^2:A4	336,223
C₁₆×C₇⋊C₃	Direct product of C₁₆ and C₇⋊C₃	112	3	C16xC7:C3	336,2
C₂×C₇⋊C₂₄	Direct product of C₂ and C₇⋊C₂₄	112		C2xC7:C24	336,12
C₄×C₇⋊C₁₂	Direct product of C₄ and C₇⋊C₁₂	112		C4xC7:C12	336,14
C₄²×C₇⋊C₃	Direct product of C₄² and C₇⋊C₃	112		C4^2xC7:C3	336,48
C₂⁴×C₇⋊C₃	Direct product of C₂⁴ and C₇⋊C₃	112		C2^4xC7:C3	336,220
C₂²×C₇⋊C₁₂	Direct product of C₂² and C₇⋊C₁₂	112		C2^2xC7:C12	336,129
S₃×C₇⋊C₈	Direct product of S₃ and C₇⋊C₈	168	4	S3xC7:C8	336,24
D₇×C₃⋊C₈	Direct product of D₇ and C₃⋊C₈	168	4	D7xC3:C8	336,23
S₃×C₂×C₂₈	Direct product of C₂×C₂₈ and S₃	168		S3xC2xC28	336,185
D₇×C₂×C₁₂	Direct product of C₂×C₁₂ and D₇	168		D7xC2xC12	336,175
C₂×C₄×D₂₁	Direct product of C₂×C₄ and D₂₁	168		C2xC4xD21	336,195
C₂×Dic₃×D₇	Direct product of C₂, Dic₃ and D₇	168		C2xDic3xD7	336,151
C₂×S₃×Dic₇	Direct product of C₂, S₃ and Dic₇	168		C2xS3xDic7	336,154
D₇×C₂²×C₆	Direct product of C₂²×C₆ and D₇	168		D7xC2^2xC6	336,225
C₂×D₂₁⋊C₄	Direct product of C₂ and D₂₁⋊C₄	168		C2xD21:C4	336,156
S₃×C₂²×C₁₄	Direct product of C₂²×C₁₄ and S₃	168		S3xC2^2xC14	336,226
C₆×C₇⋊C₈	Direct product of C₆ and C₇⋊C₈	336		C6xC7:C8	336,63
C₇×C₃⋊C₁₆	Direct product of C₇ and C₃⋊C₁₆	336	2	C7xC3:C16	336,3
C₃×C₇⋊C₁₆	Direct product of C₃ and C₇⋊C₁₆	336	2	C3xC7:C16	336,4
C₁₄×C₃⋊C₈	Direct product of C₁₄ and C₃⋊C₈	336		C14xC3:C8	336,79
C₂×C₂₁⋊C₈	Direct product of C₂ and C₂₁⋊C₈	336		C2xC21:C8	336,95
C₂×C₆×Dic₇	Direct product of C₂×C₆ and Dic₇	336		C2xC6xDic7	336,182
Dic₃×C₂×C₁₄	Direct product of C₂×C₁₄ and Dic₃	336		Dic3xC2xC14	336,192
C₂×C₈×C₇⋊C₃	Direct product of C₂×C₈ and C₇⋊C₃	112		C2xC8xC7:C3	336,51
C₂²×C₄×C₇⋊C₃	Direct product of C₂²×C₄ and C₇⋊C₃	112		C2^2xC4xC7:C3	336,164

Groups of order 337

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

Groups of order 338

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

Groups of order 339

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

Groups of order 340

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

Groups of order 341

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

Groups of order 342

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

Groups of order 343

		d	ρ	Label	ID
C₃₄₃	Cyclic group	343	1	C343	343,1
C₇³	Elementary abelian group of type [7,7,7]	343		C7^3	343,5
C₇×C₄₉	Abelian group of type [7,49]	343		C7xC49	343,2

Groups of order 344

		d	ρ	Label	ID
C₃₄₄	Cyclic group	344	1	C344	344,2
C₄₃⋊C₈	The semidirect product of C₄₃ and C₈ acting via C₈/C₄=C₂	344	2	C43:C8	344,1
C₂×C₁₇₂	Abelian group of type [2,172]	344		C2xC172	344,8
C₂²×C₈₆	Abelian group of type [2,2,86]	344		C2^2xC86	344,12
C₄×D₄₃	Direct product of C₄ and D₄₃	172	2	C4xD43	344,4
C₂²×D₄₃	Direct product of C₂² and D₄₃	172		C2^2xD43	344,11
C₂×Dic₄₃	Direct product of C₂ and Dic₄₃	344		C2xDic43	344,6

Groups of order 345

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

Groups of order 346

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

Groups of order 347

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

Groups of order 348

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

Groups of order 349

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

Groups of order 350

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

Groups of order 351

		d	ρ	Label	ID
C₃₅₁	Cyclic group	351	1	C351	351,2
C₃³⋊C₁₃	The semidirect product of C₃³ and C₁₃ acting faithfully	27	13	C3^3:C13	351,12
C₁₃⋊C₂₇	The semidirect product of C₁₃ and C₂₇ acting via C₂₇/C₉=C₃	351	3	C13:C27	351,1
C₃×C₁₁₇	Abelian group of type [3,117]	351		C3xC117	351,9
C₃²×C₃₉	Abelian group of type [3,3,39]	351		C3^2xC39	351,14
C₉×C₁₃⋊C₃	Direct product of C₉ and C₁₃⋊C₃	117	3	C9xC13:C3	351,3
C₃²×C₁₃⋊C₃	Direct product of C₃² and C₁₃⋊C₃	117		C3^2xC13:C3	351,13
C₃×C₁₃⋊C₉	Direct product of C₃ and C₁₃⋊C₉	351		C3xC13:C9	351,6

Groups of order 352

		d	ρ	Label	ID
C₃₅₂	Cyclic group	352	1	C352	352,2
C₁₁⋊C₃₂	The semidirect product of C₁₁ and C₃₂ acting via C₃₂/C₁₆=C₂	352	2	C11:C32	352,1
C₄×C₈₈	Abelian group of type [4,88]	352		C4xC88	352,45
C₂×C₁₇₆	Abelian group of type [2,176]	352		C2xC176	352,58
C₂²×C₈₈	Abelian group of type [2,2,88]	352		C2^2xC88	352,164
C₂³×C₄₄	Abelian group of type [2,2,2,44]	352		C2^3xC44	352,188
C₂⁴×C₂₂	Abelian group of type [2,2,2,2,22]	352		C2^4xC22	352,195
C₂×C₄×C₄₄	Abelian group of type [2,4,44]	352		C2xC4xC44	352,149
C₁₆×D₁₁	Direct product of C₁₆ and D₁₁	176	2	C16xD11	352,3
C₄²×D₁₁	Direct product of C₄² and D₁₁	176		C4^2xD11	352,66
C₂⁴×D₁₁	Direct product of C₂⁴ and D₁₁	176		C2^4xD11	352,194
C₈×Dic₁₁	Direct product of C₈ and Dic₁₁	352		C8xDic11	352,19
C₂³×Dic₁₁	Direct product of C₂³ and Dic₁₁	352		C2^3xDic11	352,186
C₂×C₈×D₁₁	Direct product of C₂×C₈ and D₁₁	176		C2xC8xD11	352,94
C₂²×C₄×D₁₁	Direct product of C₂²×C₄ and D₁₁	176		C2^2xC4xD11	352,174
C₄×C₁₁⋊C₈	Direct product of C₄ and C₁₁⋊C₈	352		C4xC11:C8	352,8
C₂×C₁₁⋊C₁₆	Direct product of C₂ and C₁₁⋊C₁₆	352		C2xC11:C16	352,17
C₂²×C₁₁⋊C₈	Direct product of C₂² and C₁₁⋊C₈	352		C2^2xC11:C8	352,115
C₂×C₄×Dic₁₁	Direct product of C₂×C₄ and Dic₁₁	352		C2xC4xDic11	352,117

Groups of order 353

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

Groups of order 354

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

Groups of order 355

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

Groups of order 356

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

Groups of order 357

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

Groups of order 358

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

Groups of order 359

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

Groups of order 360

		d	ρ	Label	ID
C₃₆₀	Cyclic group	360	1	C360	360,4
C₅⋊F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃⋊S₃=C₄	45	8	C5:F9	360,125
C₅⋊₂F₉	The semidirect product of C₅ and F₉ acting via F₉/C₃²⋊C₄=C₂	45	8	C5:2F9	360,124
Dic₁₅⋊S₃	3^rd semidirect product of Dic₁₅ and S₃ acting via S₃/C₃=C₂	60	4	Dic15:S3	360,85
C₄₅⋊₃C₈	1^st semidirect product of C₄₅ and C₈ acting via C₈/C₄=C₂	360	2	C45:3C8	360,3
C₄₅⋊C₈	1^st semidirect product of C₄₅ and C₈ acting via C₈/C₂=C₄	360	4	C45:C8	360,6
C₃⋊F₅⋊S₃	The semidirect product of C₃⋊F₅ and S₃ acting via S₃/C₃=C₂	30	8+	C3:F5:S3	360,129
C₃²⋊F₅⋊C₂	The semidirect product of C₃²⋊F₅ and C₂ acting faithfully	30	8+	C3^2:F5:C2	360,131
(C₃×C₁₅)⋊₉C₈	6^th semidirect product of C₃×C₁₅ and C₈ acting via C₈/C₂=C₄	120	4	(C3xC15):9C8	360,56
C₆.D₃₀	3^rd non-split extension by C₆ of D₃₀ acting via D₃₀/D₁₅=C₂	60	4+	C6.D30	360,79
D₃₀.S₃	The non-split extension by D₃₀ of S₃ acting via S₃/C₃=C₂	120	4	D30.S3	360,84
D₉₀.C₂	The non-split extension by D₉₀ of C₂ acting faithfully	180	4+	D90.C2	360,9
C₃₀.D₆	11^st non-split extension by C₃₀ of D₆ acting via D₆/C₃=C₂²	180		C30.D6	360,67
C₆₀.S₃	6^th non-split extension by C₆₀ of S₃ acting via S₃/C₃=C₂	360		C60.S3	360,37
C₃₀.Dic₃	3^rd non-split extension by C₃₀ of Dic₃ acting via Dic₃/C₃=C₄	360		C30.Dic3	360,54
(C₃×C₆).F₅	The non-split extension by C₃×C₆ of F₅ acting via F₅/C₅=C₄	120	4-	(C3xC6).F5	360,57
C₆×C₆₀	Abelian group of type [6,60]	360		C6xC60	360,115
C₂×C₁₈₀	Abelian group of type [2,180]	360		C2xC180	360,30
C₃×C₁₂₀	Abelian group of type [3,120]	360		C3xC120	360,38
C₂²×C₉₀	Abelian group of type [2,2,90]	360		C2^2xC90	360,50
C₂×C₆×C₃₀	Abelian group of type [2,6,30]	360		C2xC6xC30	360,162
S₃×A₅	Direct product of S₃ and A₅	15	6+	S3xA5	360,121
C₆×A₅	Direct product of C₆ and A₅	30	3	C6xA5	360,122
D₉×F₅	Direct product of D₉ and F₅	45	8+	D9xF5	360,39
C₅×F₉	Direct product of C₅ and F₉	45	8	C5xF9	360,123
A₄×D₁₅	Direct product of A₄ and D₁₅	60	6+	A4xD15	360,144
A₄×C₃₀	Direct product of C₃₀ and A₄	90	3	A4xC30	360,156
C₁₈×F₅	Direct product of C₁₈ and F₅	90	4	C18xF5	360,43
S₃×C₆₀	Direct product of C₆₀ and S₃	120	2	S3xC60	360,96
C₁₂×D₁₅	Direct product of C₁₂ and D₁₅	120	2	C12xD15	360,101
Dic₃×D₁₅	Direct product of Dic₃ and D₁₅	120	4-	Dic3xD15	360,77
S₃×Dic₁₅	Direct product of S₃ and Dic₁₅	120	4-	S3xDic15	360,78
Dic₃×C₃₀	Direct product of C₃₀ and Dic₃	120		Dic3xC30	360,98
C₆×Dic₁₅	Direct product of C₆ and Dic₁₅	120		C6xDic15	360,103
D₅×C₃₆	Direct product of C₃₆ and D₅	180	2	D5xC36	360,16
D₉×C₂₀	Direct product of C₂₀ and D₉	180	2	D9xC20	360,21
C₄×D₄₅	Direct product of C₄ and D₄₅	180	2	C4xD45	360,26
D₉×Dic₅	Direct product of D₉ and Dic₅	180	4-	D9xDic5	360,8
D₅×Dic₉	Direct product of D₅ and Dic₉	180	4-	D5xDic9	360,11
D₅×C₆²	Direct product of C₆² and D₅	180		D5xC6^2	360,157
C₂²×D₄₅	Direct product of C₂² and D₄₅	180		C2^2xD45	360,49
C₁₈×Dic₅	Direct product of C₁₈ and Dic₅	360		C18xDic5	360,18
C₁₀×Dic₉	Direct product of C₁₀ and Dic₉	360		C10xDic9	360,23
C₂×Dic₄₅	Direct product of C₂ and Dic₄₅	360		C2xDic45	360,28
S₃²×D₅	Direct product of S₃, S₃ and D₅	30	8+	S3^2xD5	360,137
S₃×C₃⋊F₅	Direct product of S₃ and C₃⋊F₅	30	8	S3xC3:F5	360,128
C₃×S₃×F₅	Direct product of C₃, S₃ and F₅	30	8	C3xS3xF5	360,126
D₅×C₃²⋊C₄	Direct product of D₅ and C₃²⋊C₄	30	8+	D5xC3^2:C4	360,130
C₃⋊S₃×F₅	Direct product of C₃⋊S₃ and F₅	45		C3:S3xF5	360,127
C₅×S₃×A₄	Direct product of C₅, S₃ and A₄	60	6	C5xS3xA4	360,143
C₃×D₅×A₄	Direct product of C₃, D₅ and A₄	60	6	C3xD5xA4	360,142
S₃×C₆×D₅	Direct product of C₆, S₃ and D₅	60	4	S3xC6xD5	360,151
C₆×C₃⋊F₅	Direct product of C₆ and C₃⋊F₅	60	4	C6xC3:F5	360,146
S₃²×C₁₀	Direct product of C₁₀, S₃ and S₃	60	4	S3^2xC10	360,153
C₂×S₃×D₁₅	Direct product of C₂, S₃ and D₁₅	60	4+	C2xS3xD15	360,154
C₃×D₅×Dic₃	Direct product of C₃, D₅ and Dic₃	60	4	C3xD5xDic3	360,58
C₂×C₃²⋊F₅	Direct product of C₂ and C₃²⋊F₅	60	4+	C2xC3^2:F5	360,150
C₂×D₁₅⋊S₃	Direct product of C₂ and D₁₅⋊S₃	60	4	C2xD15:S3	360,155
C₁₀×C₃²⋊C₄	Direct product of C₁₀ and C₃²⋊C₄	60	4	C10xC3^2:C4	360,148
C₅×C₆.D₆	Direct product of C₅ and C₆.D₆	60	4	C5xC6.D6	360,73
C₂×C₃²⋊Dic₅	Direct product of C₂ and C₃²⋊Dic₅	60	4	C2xC3^2:Dic5	360,149
C₂×D₅×D₉	Direct product of C₂, D₅ and D₉	90	4+	C2xD5xD9	360,45
C₂×C₉⋊F₅	Direct product of C₂ and C₉⋊F₅	90	4	C2xC9:F5	360,44
C₃×C₆×F₅	Direct product of C₃×C₆ and F₅	90		C3xC6xF5	360,145
D₅×C₃.A₄	Direct product of D₅ and C₃.A₄	90	6	D5xC3.A4	360,42
C₁₀×C₃.A₄	Direct product of C₁₀ and C₃.A₄	90	3	C10xC3.A4	360,46
C₂×C₃²⋊₃F₅	Direct product of C₂ and C₃²⋊₃F₅	90		C2xC3^2:3F5	360,147
C₁₅×C₃⋊C₈	Direct product of C₁₅ and C₃⋊C₈	120	2	C15xC3:C8	360,34
S₃×C₂×C₃₀	Direct product of C₂×C₃₀ and S₃	120		S3xC2xC30	360,158
C₂×C₆×D₁₅	Direct product of C₂×C₆ and D₁₅	120		C2xC6xD15	360,159
C₃×C₁₅⋊C₈	Direct product of C₃ and C₁₅⋊C₈	120	4	C3xC15:C8	360,53
C₃×S₃×Dic₅	Direct product of C₃, S₃ and Dic₅	120	4	C3xS3xDic5	360,59
C₅×S₃×Dic₃	Direct product of C₅, S₃ and Dic₃	120	4	C5xS3xDic3	360,72
C₃×C₁₅⋊₃C₈	Direct product of C₃ and C₁₅⋊₃C₈	120	2	C3xC15:3C8	360,35
C₃×D₃₀.C₂	Direct product of C₃ and D₃₀.C₂	120	4	C3xD30.C2	360,60
C₅×C₃²⋊₂C₈	Direct product of C₅ and C₃²⋊₂C₈	120	4	C5xC3^2:2C8	360,55
D₅×C₂×C₁₈	Direct product of C₂×C₁₈ and D₅	180		D5xC2xC18	360,47
D₉×C₂×C₁₀	Direct product of C₂×C₁₀ and D₉	180		D9xC2xC10	360,48
D₅×C₃×C₁₂	Direct product of C₃×C₁₂ and D₅	180		D5xC3xC12	360,91
C₃⋊S₃×C₂₀	Direct product of C₂₀ and C₃⋊S₃	180		C3:S3xC20	360,106
C₄×C₃⋊D₁₅	Direct product of C₄ and C₃⋊D₁₅	180		C4xC3:D15	360,111
D₅×C₃⋊Dic₃	Direct product of D₅ and C₃⋊Dic₃	180		D5xC3:Dic3	360,65
C₃⋊S₃×Dic₅	Direct product of C₃⋊S₃ and Dic₅	180		C3:S3xDic5	360,66
C₂²×C₃⋊D₁₅	Direct product of C₂² and C₃⋊D₁₅	180		C2^2xC3:D15	360,161
C₅×C₉⋊C₈	Direct product of C₅ and C₉⋊C₈	360	2	C5xC9:C8	360,1
C₉×C₅⋊C₈	Direct product of C₉ and C₅⋊C₈	360	4	C9xC5:C8	360,5
C₉×C₅⋊₂C₈	Direct product of C₉ and C₅⋊₂C₈	360	2	C9xC5:2C8	360,2
C₃²×C₅⋊C₈	Direct product of C₃² and C₅⋊C₈	360		C3^2xC5:C8	360,52
C₃×C₆×Dic₅	Direct product of C₃×C₆ and Dic₅	360		C3xC6xDic5	360,93
C₁₀×C₃⋊Dic₃	Direct product of C₁₀ and C₃⋊Dic₃	360		C10xC3:Dic3	360,108
C₂×C₃⋊Dic₁₅	Direct product of C₂ and C₃⋊Dic₁₅	360		C2xC3:Dic15	360,113
C₃²×C₅⋊₂C₈	Direct product of C₃² and C₅⋊₂C₈	360		C3^2xC5:2C8	360,33
C₅×C₃²⋊₄C₈	Direct product of C₅ and C₃²⋊₄C₈	360		C5xC3^2:4C8	360,36
C₂×D₅×C₃⋊S₃	Direct product of C₂, D₅ and C₃⋊S₃	90		C2xD5xC3:S3	360,152
C₃⋊S₃×C₂×C₁₀	Direct product of C₂×C₁₀ and C₃⋊S₃	180		C3:S3xC2xC10	360,160

Groups of order 361

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

Groups of order 362

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

Groups of order 363

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

Groups of order 364

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

Groups of order 365

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

Groups of order 366

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

Groups of order 367

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

Groups of order 368

		d	ρ	Label	ID
C₃₆₈	Cyclic group	368	1	C368	368,2
C₂₃⋊C₁₆	The semidirect product of C₂₃ and C₁₆ acting via C₁₆/C₈=C₂	368	2	C23:C16	368,1
C₄×C₉₂	Abelian group of type [4,92]	368		C4xC92	368,19
C₂×C₁₈₄	Abelian group of type [2,184]	368		C2xC184	368,22
C₂²×C₉₂	Abelian group of type [2,2,92]	368		C2^2xC92	368,37
C₂³×C₄₆	Abelian group of type [2,2,2,46]	368		C2^3xC46	368,42
C₈×D₂₃	Direct product of C₈ and D₂₃	184	2	C8xD23	368,3
C₂³×D₂₃	Direct product of C₂³ and D₂₃	184		C2^3xD23	368,41
C₄×Dic₂₃	Direct product of C₄ and Dic₂₃	368		C4xDic23	368,10
C₂²×Dic₂₃	Direct product of C₂² and Dic₂₃	368		C2^2xDic23	368,35
C₂×C₄×D₂₃	Direct product of C₂×C₄ and D₂₃	184		C2xC4xD23	368,28
C₂×C₂₃⋊C₈	Direct product of C₂ and C₂₃⋊C₈	368		C2xC23:C8	368,8

Groups of order 369

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

Groups of order 370

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

Groups of order 371

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

Groups of order 372

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

Groups of order 373

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

Groups of order 374

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

Groups of order 375

		d	ρ	Label	ID
C₃₇₅	Cyclic group	375	1	C375	375,1
C₅×C₇₅	Abelian group of type [5,75]	375		C5xC75	375,3
C₅²×C₁₅	Abelian group of type [5,5,15]	375		C5^2xC15	375,7
C₅×C₅²⋊C₃	Direct product of C₅ and C₅²⋊C₃; = AΣL₁(𝔽₁₂₅)	15	3	C5xC5^2:C3	375,6

Groups of order 376

		d	ρ	Label	ID
C₃₇₆	Cyclic group	376	1	C376	376,2
C₄₇⋊C₈	The semidirect product of C₄₇ and C₈ acting via C₈/C₄=C₂	376	2	C47:C8	376,1
C₂×C₁₈₈	Abelian group of type [2,188]	376		C2xC188	376,8
C₂²×C₉₄	Abelian group of type [2,2,94]	376		C2^2xC94	376,12
C₄×D₄₇	Direct product of C₄ and D₄₇	188	2	C4xD47	376,4
C₂²×D₄₇	Direct product of C₂² and D₄₇	188		C2^2xD47	376,11
C₂×Dic₄₇	Direct product of C₂ and Dic₄₇	376		C2xDic47	376,6

Groups of order 377

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

Groups of order 378

		d	ρ	Label	ID
C₃₇₈	Cyclic group	378	1	C378	378,6
D₁₈₉	Dihedral group	189	2+	D189	378,5
C₉⋊₅F₇	The semidirect product of C₉ and F₇ acting via F₇/C₇⋊C₃=C₂	63	6+	C9:5F7	378,20
C₃²⋊₄F₇	2^nd semidirect product of C₃² and F₇ acting via F₇/C₇⋊C₃=C₂	63		C3^2:4F7	378,51
D₂₁⋊C₉	The semidirect product of D₂₁ and C₉ acting via C₉/C₃=C₃	126	6	D21:C9	378,21
C₇⋊C₅₄	The semidirect product of C₇ and C₅₄ acting via C₅₄/C₉=C₆	189	6	C7:C54	378,1
C₃⋊D₆₃	The semidirect product of C₃ and D₆₃ acting via D₆₃/C₆₃=C₂	189		C3:D63	378,42
C₃³⋊D₇	3^rd semidirect product of C₃³ and D₇ acting via D₇/C₇=C₂	189		C3^3:D7	378,59
C₃×C₁₂₆	Abelian group of type [3,126]	378		C3xC126	378,44
C₃²×C₄₂	Abelian group of type [3,3,42]	378		C3^2xC42	378,60
C₉×F₇	Direct product of C₉ and F₇	63	6	C9xF7	378,7
C₃²×F₇	Direct product of C₃² and F₇	63		C3^2xF7	378,47
S₃×C₆₃	Direct product of C₆₃ and S₃	126	2	S3xC63	378,33
D₉×C₂₁	Direct product of C₂₁ and D₉	126	2	D9xC21	378,32
C₃×D₆₃	Direct product of C₃ and D₆₃	126	2	C3xD63	378,36
C₉×D₂₁	Direct product of C₉ and D₂₁	126	2	C9xD21	378,37
C₃²×D₂₁	Direct product of C₃² and D₂₁	126		C3^2xD21	378,55
C₇×D₂₇	Direct product of C₇ and D₂₇	189	2	C7xD27	378,3
D₇×C₂₇	Direct product of C₂₇ and D₇	189	2	D7xC27	378,4
D₇×C₃³	Direct product of C₃³ and D₇	189		D7xC3^3	378,53
C₃×C₃⋊F₇	Direct product of C₃ and C₃⋊F₇	42	6	C3xC3:F7	378,49
D₉×C₇⋊C₃	Direct product of D₉ and C₇⋊C₃	63	6	D9xC7:C3	378,15
S₃×C₇⋊C₉	Direct product of S₃ and C₇⋊C₉	126	6	S3xC7:C9	378,16
C₁₈×C₇⋊C₃	Direct product of C₁₈ and C₇⋊C₃	126	3	C18xC7:C3	378,23
S₃×C₃×C₂₁	Direct product of C₃×C₂₁ and S₃	126		S3xC3xC21	378,54
C₃⋊S₃×C₂₁	Direct product of C₂₁ and C₃⋊S₃	126		C3:S3xC21	378,56
C₃×C₃⋊D₂₁	Direct product of C₃ and C₃⋊D₂₁	126		C3xC3:D21	378,57
D₇×C₃×C₉	Direct product of C₃×C₉ and D₇	189		D7xC3xC9	378,29
C₃×C₇⋊C₁₈	Direct product of C₃ and C₇⋊C₁₈	189		C3xC7:C18	378,10
C₇×C₉⋊S₃	Direct product of C₇ and C₉⋊S₃	189		C7xC9:S3	378,40
C₇×C₃³⋊C₂	Direct product of C₇ and C₃³⋊C₂	189		C7xC3^3:C2	378,58
C₆×C₇⋊C₉	Direct product of C₆ and C₇⋊C₉	378		C6xC7:C9	378,26
C₂×C₇⋊C₂₇	Direct product of C₂ and C₇⋊C₂₇	378	3	C2xC7:C27	378,2
C₃×S₃×C₇⋊C₃	Direct product of C₃, S₃ and C₇⋊C₃	42	6	C3xS3xC7:C3	378,48
C₃⋊S₃×C₇⋊C₃	Direct product of C₃⋊S₃ and C₇⋊C₃	63		C3:S3xC7:C3	378,50
C₃×C₆×C₇⋊C₃	Direct product of C₃×C₆ and C₇⋊C₃	126		C3xC6xC7:C3	378,52

Groups of order 379

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

Groups of order 380

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

Groups of order 381

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

Groups of order 382

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

Groups of order 383

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

Groups of order 385

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

Groups of order 386

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

Groups of order 387

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

Groups of order 388

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

Groups of order 389

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

Groups of order 390

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

Groups of order 391

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

Groups of order 392

		d	ρ	Label	ID
C₃₉₂	Cyclic group	392	1	C392	392,2
C₇²⋊C₈	The semidirect product of C₇² and C₈ acting faithfully	28	8+	C7^2:C8	392,36
Dic₇⋊₂D₇	The semidirect product of Dic₇ and D₇ acting through Inn(Dic₇)	28	4+	Dic7:2D7	392,19
C₇²⋊₂C₈	The semidirect product of C₇² and C₈ acting via C₈/C₂=C₄	56	4-	C7^2:2C8	392,17
C₄₉⋊C₈	The semidirect product of C₄₉ and C₈ acting via C₈/C₄=C₂	392	2	C49:C8	392,1
C₇²⋊₄C₈	2^nd semidirect product of C₇² and C₈ acting via C₈/C₄=C₂	392		C7^2:4C8	392,15
C₇.F₈	The central extension by C₇ of F₈	98	7	C7.F8	392,11
C₇×C₅₆	Abelian group of type [7,56]	392		C7xC56	392,16
C₂×C₁₉₆	Abelian group of type [2,196]	392		C2xC196	392,8
C₁₄×C₂₈	Abelian group of type [14,28]	392		C14xC28	392,33
C₂²×C₉₈	Abelian group of type [2,2,98]	392		C2^2xC98	392,13
C₂×C₁₄²	Abelian group of type [2,14,14]	392		C2xC14^2	392,44
C₇×F₈	Direct product of C₇ and F₈	56	7	C7xF8	392,39
D₇×C₂₈	Direct product of C₂₈ and D₇	56	2	D7xC28	392,24
D₇×Dic₇	Direct product of D₇ and Dic₇	56	4-	D7xDic7	392,18
C₁₄×Dic₇	Direct product of C₁₄ and Dic₇	56		C14xDic7	392,26
C₄×D₄₉	Direct product of C₄ and D₄₉	196	2	C4xD49	392,4
C₂²×D₄₉	Direct product of C₂² and D₄₉	196		C2^2xD49	392,12
C₂×Dic₄₉	Direct product of C₂ and Dic₄₉	392		C2xDic49	392,6
C₂×D₇²	Direct product of C₂, D₇ and D₇	28	4+	C2xD7^2	392,41
C₂×C₇²⋊C₄	Direct product of C₂ and C₇²⋊C₄	28	4+	C2xC7^2:C4	392,40
C₇×C₇⋊C₈	Direct product of C₇ and C₇⋊C₈	56	2	C7xC7:C8	392,14
D₇×C₂×C₁₄	Direct product of C₂×C₁₄ and D₇	56		D7xC2xC14	392,42
C₄×C₇⋊D₇	Direct product of C₄ and C₇⋊D₇	196		C4xC7:D7	392,29
C₂²×C₇⋊D₇	Direct product of C₂² and C₇⋊D₇	196		C2^2xC7:D7	392,43
C₂×C₇⋊Dic₇	Direct product of C₂ and C₇⋊Dic₇	392		C2xC7:Dic7	392,31

Groups of order 393

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

Groups of order 394

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

Groups of order 395

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

Groups of order 396

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

Groups of order 397

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

Groups of order 398

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

Groups of order 399

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

Groups of order 400

		d	ρ	Label	ID
C₄₀₀	Cyclic group	400	1	C400	400,2
C₅²⋊₃C₄²	2^nd semidirect product of C₅² and C₄² acting via C₄²/C₂=C₂×C₄	20	8+	C5^2:3C4^2	400,124
C₂⁴⋊C₂₅	The semidirect product of C₂⁴ and C₂₅ acting via C₂₅/C₅=C₅	50	5	C2^4:C25	400,52
C₅²⋊C₁₆	The semidirect product of C₅² and C₁₆ acting via C₁₆/C₂=C₈	80	8-	C5^2:C16	400,116
C₅²⋊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
D₂₅⋊C₈	The semidirect product of D₂₅ and C₈ acting via C₈/C₄=C₂	200	4	D25:C8	400,28
C₂₅⋊C₁₆	The semidirect product of C₂₅ and C₁₆ acting via C₁₆/C₄=C₄	400	4	C25:C16	400,3
C₂₅⋊₂C₁₆	The semidirect product of C₂₅ and C₁₆ acting via C₁₆/C₈=C₂	400	2	C25:2C16	400,1
C₅²⋊₇C₁₆	2^nd semidirect product of C₅² and C₁₆ acting via C₁₆/C₈=C₂	400		C5^2:7C16	400,50
C₅²⋊₄C₁₆	3^rd semidirect product of C₅² and C₁₆ acting via C₁₆/C₄=C₄	400		C5^2:4C16	400,58
C₂₀.₁₁F₅	11^st non-split extension by C₂₀ of F₅ acting via F₅/C₅=C₄	40	4	C20.11F5	400,156
C₂₀.₂₉D₁₀	3^rd non-split extension by C₂₀ of D₁₀ acting via D₁₀/D₅=C₂	40	4	C20.29D10	400,61
Dic₅.₄F₅	The non-split extension by Dic₅ of F₅ acting through Inn(Dic₅)	40	8+	Dic5.4F5	400,121
D₁₀.₂F₅	2^nd non-split extension by D₁₀ of F₅ acting via F₅/D₅=C₂	80	8-	D10.2F5	400,127
C₂₀.₁₄F₅	3^rd non-split extension by C₂₀ of F₅ acting via F₅/D₅=C₂	80	4	C20.14F5	400,142
C₂₀.F₅	10^th non-split extension by C₂₀ of F₅ acting via F₅/C₅=C₄	200		C20.F5	400,149
C₂₀²	Abelian group of type [20,20]	400		C20^2	400,108
C₅×C₈₀	Abelian group of type [5,80]	400		C5xC80	400,51
C₄×C₁₀₀	Abelian group of type [4,100]	400		C4xC100	400,20
C₂×C₂₀₀	Abelian group of type [2,200]	400		C2xC200	400,23
C₁₀×C₄₀	Abelian group of type [10,40]	400		C10xC40	400,111
C₂³×C₅₀	Abelian group of type [2,2,2,50]	400		C2^3xC50	400,55
C₂²×C₁₀₀	Abelian group of type [2,2,100]	400		C2^2xC100	400,45
C₂²×C₁₀²	Abelian group of type [2,2,10,10]	400		C2^2xC10^2	400,221
C₂×C₁₀×C₂₀	Abelian group of type [2,10,20]	400		C2xC10xC20	400,201
F₅²	Direct product of F₅ and F₅; = Hol(F₅)	20	16+	F5^2	400,205
D₅×C₄₀	Direct product of C₄₀ and D₅	80	2	D5xC40	400,76
C₂₀×F₅	Direct product of C₂₀ and F₅	80	4	C20xF5	400,137
Dic₅²	Direct product of Dic₅ and Dic₅	80		Dic5^2	400,71
Dic₅×F₅	Direct product of Dic₅ and F₅	80	8-	Dic5xF5	400,117
Dic₅×C₂₀	Direct product of C₂₀ and Dic₅	80		Dic5xC20	400,83
C₈×D₂₅	Direct product of C₈ and D₂₅	200	2	C8xD25	400,5
C₂³×D₂₅	Direct product of C₂³ and D₂₅	200		C2^3xD25	400,54
C₄×Dic₂₅	Direct product of C₄ and Dic₂₅	400		C4xDic25	400,11
C₂²×Dic₂₅	Direct product of C₂² and Dic₂₅	400		C2^2xDic25	400,43
C₂×D₅⋊F₅	Direct product of C₂ and D₅⋊F₅	20	8+	C2xD5:F5	400,210
C₂×C₅²⋊C₈	Direct product of C₂ and C₅²⋊C₈	20	8+	C2xC5^2:C8	400,208
C₄×D₅²	Direct product of C₄, D₅ and D₅	40	4	C4xD5^2	400,169
C₂×D₅×F₅	Direct product of C₂, D₅ and F₅	40	8+	C2xD5xF5	400,209
C₂²×D₅²	Direct product of C₂², D₅ and D₅	40		C2^2xD5^2	400,218
C₄×C₅²⋊C₄	Direct product of C₄ and C₅²⋊C₄	40	4	C4xC5^2:C4	400,158
C₂²×C₅²⋊C₄	Direct product of C₂² and C₅²⋊C₄	40		C2^2xC5^2:C4	400,217
C₂×Dic₅⋊₂D₅	Direct product of C₂ and Dic₅⋊₂D₅	40		C2xDic5:2D5	400,175
C₅×C₂⁴⋊C₅	Direct product of C₅ and C₂⁴⋊C₅	50	5	C5xC2^4:C5	400,213
D₅×C₅⋊C₈	Direct product of D₅ and C₅⋊C₈	80	8-	D5xC5:C8	400,120
C₅×C₅⋊C₁₆	Direct product of C₅ and C₅⋊C₁₆	80	4	C5xC5:C16	400,56
C₁₀×C₅⋊C₈	Direct product of C₁₀ and C₅⋊C₈	80		C10xC5:C8	400,139
D₅×C₂×C₂₀	Direct product of C₂×C₂₀ and D₅	80		D5xC2xC20	400,182
F₅×C₂×C₁₀	Direct product of C₂×C₁₀ and F₅	80		F5xC2xC10	400,214
C₅×D₅⋊C₈	Direct product of C₅ and D₅⋊C₈	80	4	C5xD5:C8	400,135
D₅×C₅⋊₂C₈	Direct product of D₅ and C₅⋊₂C₈	80	4	D5xC5:2C8	400,60
C₂×D₅×Dic₅	Direct product of C₂, D₅ and Dic₅	80		C2xD5xDic5	400,172
C₅×C₅⋊₂C₁₆	Direct product of C₅ and C₅⋊₂C₁₆	80	2	C5xC5:2C16	400,49
C₁₀×C₅⋊₂C₈	Direct product of C₁₀ and C₅⋊₂C₈	80		C10xC5:2C8	400,81
C₄×D₅.D₅	Direct product of C₄ and D₅.D₅	80	4	C4xD5.D5	400,144
Dic₅×C₂×C₁₀	Direct product of C₂×C₁₀ and Dic₅	80		Dic5xC2xC10	400,189
D₅×C₂²×C₁₀	Direct product of C₂²×C₁₀ and D₅	80		D5xC2^2xC10	400,219
C₂×C₅²⋊₃C₈	Direct product of C₂ and C₅²⋊₃C₈	80		C2xC5^2:3C8	400,146
C₂×C₅²⋊₅C₈	Direct product of C₂ and C₅²⋊₅C₈	80		C2xC5^2:5C8	400,160
C₂²×D₅.D₅	Direct product of C₂² and D₅.D₅	80		C2^2xD5.D5	400,215
C₄×C₂₅⋊C₄	Direct product of C₄ and C₂₅⋊C₄	100	4	C4xC25:C4	400,30
C₄×C₅⋊F₅	Direct product of C₄ and C₅⋊F₅	100		C4xC5:F5	400,151
C₂²×C₂₅⋊C₄	Direct product of C₂² and C₂₅⋊C₄	100		C2^2xC25:C4	400,53
C₂²×C₅⋊F₅	Direct product of C₂² and C₅⋊F₅	100		C2^2xC5:F5	400,216
C₈×C₅⋊D₅	Direct product of C₈ and C₅⋊D₅	200		C8xC5:D5	400,92
C₂×C₄×D₂₅	Direct product of C₂×C₄ and D₂₅	200		C2xC4xD25	400,36
C₂³×C₅⋊D₅	Direct product of C₂³ and C₅⋊D₅	200		C2^3xC5:D5	400,220
C₂×C₂₅⋊C₈	Direct product of C₂ and C₂₅⋊C₈	400		C2xC25:C8	400,32
C₂×C₂₅⋊₂C₈	Direct product of C₂ and C₂₅⋊₂C₈	400		C2xC25:2C8	400,9
C₂×C₅²⋊₇C₈	Direct product of C₂ and C₅²⋊₇C₈	400		C2xC5^2:7C8	400,97
C₄×C₅²⋊₆C₄	Direct product of C₄ and C₅²⋊₆C₄	400		C4xC5^2:6C4	400,99
C₂×C₅²⋊₄C₈	Direct product of C₂ and C₅²⋊₄C₈	400		C2xC5^2:4C8	400,153
C₂²×C₅²⋊₆C₄	Direct product of C₂² and C₅²⋊₆C₄	400		C2^2xC5^2:6C4	400,199
C₂×C₄×C₅⋊D₅	Direct product of C₂×C₄ and C₅⋊D₅	200		C2xC4xC5:D5	400,192

Groups of order 401

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

Groups of order 402

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

Groups of order 403

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

Groups of order 404

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

Groups of order 405

		d	ρ	Label	ID
C₄₀₅	Cyclic group	405	1	C405	405,1
C₃⁴⋊C₅	The semidirect product of C₃⁴ and C₅ acting faithfully	15	5	C3^4:C5	405,15
C₉×C₄₅	Abelian group of type [9,45]	405		C9xC45	405,2
C₃×C₁₃₅	Abelian group of type [3,135]	405		C3xC135	405,5
C₃²×C₄₅	Abelian group of type [3,3,45]	405		C3^2xC45	405,11
C₃³×C₁₅	Abelian group of type [3,3,3,15]	405		C3^3xC15	405,16

Groups of order 406

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

Groups of order 407

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

Groups of order 408

		d	ρ	Label	ID
C₄₀₈	Cyclic group	408	1	C408	408,4
C₅₁⋊C₈	1^st semidirect product of C₅₁ and C₈ acting faithfully	51	8	C51:C8	408,34
D₅₁⋊₂C₄	The semidirect product of D₅₁ and C₄ acting via C₄/C₂=C₂	204	4+	D51:2C4	408,9
C₅₁⋊₅C₈	1^st semidirect product of C₅₁ and C₈ acting via C₈/C₄=C₂	408	2	C51:5C8	408,3
C₅₁⋊₃C₈	1^st semidirect product of C₅₁ and C₈ acting via C₈/C₂=C₄	408	4	C51:3C8	408,6
C₂×C₂₀₄	Abelian group of type [2,204]	408		C2xC204	408,30
C₂²×C₁₀₂	Abelian group of type [2,2,102]	408		C2^2xC102	408,46
A₄×D₁₇	Direct product of A₄ and D₁₇	68	6+	A4xD17	408,38
A₄×C₃₄	Direct product of C₃₄ and A₄	102	3	A4xC34	408,42
S₃×C₆₈	Direct product of C₆₈ and S₃	204	2	S3xC68	408,21
C₄×D₅₁	Direct product of C₄ and D₅₁	204	2	C4xD51	408,26
C₁₂×D₁₇	Direct product of C₁₂ and D₁₇	204	2	C12xD17	408,16
Dic₃×D₁₇	Direct product of Dic₃ and D₁₇	204	4-	Dic3xD17	408,7
S₃×Dic₁₇	Direct product of S₃ and Dic₁₇	204	4-	S3xDic17	408,8
C₂²×D₅₁	Direct product of C₂² and D₅₁	204		C2^2xD51	408,45
C₆×Dic₁₇	Direct product of C₆ and Dic₁₇	408		C6xDic17	408,18
Dic₃×C₃₄	Direct product of C₃₄ and Dic₃	408		Dic3xC34	408,23
C₂×Dic₅₁	Direct product of C₂ and Dic₅₁	408		C2xDic51	408,28
C₃×C₁₇⋊C₈	Direct product of C₃ and C₁₇⋊C₈	51	8	C3xC17:C8	408,33
S₃×C₁₇⋊C₄	Direct product of S₃ and C₁₇⋊C₄	51	8+	S3xC17:C4	408,35
C₆×C₁₇⋊C₄	Direct product of C₆ and C₁₇⋊C₄	102	4	C6xC17:C4	408,39
C₂×S₃×D₁₇	Direct product of C₂, S₃ and D₁₇	102	4+	C2xS3xD17	408,41
C₂×C₅₁⋊C₄	Direct product of C₂ and C₅₁⋊C₄	102	4	C2xC51:C4	408,40
S₃×C₂×C₃₄	Direct product of C₂×C₃₄ and S₃	204		S3xC2xC34	408,44
C₂×C₆×D₁₇	Direct product of C₂×C₆ and D₁₇	204		C2xC6xD17	408,43
C₁₇×C₃⋊C₈	Direct product of C₁₇ and C₃⋊C₈	408	2	C17xC3:C8	408,1
C₃×C₁₇⋊₃C₈	Direct product of C₃ and C₁₇⋊₃C₈	408	2	C3xC17:3C8	408,2
C₃×C₁₇⋊₂C₈	Direct product of C₃ and C₁₇⋊₂C₈	408	4	C3xC17:2C8	408,5

Groups of order 409

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

Groups of order 410

		d	ρ	Label	ID
C₄₁₀	Cyclic group	410	1	C410	410,6
D₂₀₅	Dihedral group	205	2+	D205	410,5
C₄₁⋊C₁₀	The semidirect product of C₄₁ and C₁₀ acting faithfully	41	10+	C41:C10	410,1
D₅×C₄₁	Direct product of C₄₁ and D₅