Metacyclic groups

A metacyclic group is an extension of a cyclic group by a cyclic group. All metacyclic groups are supersoluble and in particular monomial. See also metabelian groups.

Groups of order 1

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

Groups of order 2

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

Groups of order 3

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

Groups of order 4

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

Groups of order 5

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

Groups of order 6

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

Groups of order 7

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

Groups of order 8

		d	ρ	Label	ID
C₈	Cyclic group	8	1	C8	8,1
D₄	Dihedral group; = He₂ = AΣL₁(F₄) = 2₊¹⁺² = square symmetries	4	2+	D4	8,3
Q₈	Quaternion group; = C₄ .C₂ = Dic₂ = 2_-¹⁺²	8	2-	Q8	8,4
C₂xC₄	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
D₆	Dihedral group; = C₂xS₃ = hexagon symmetries	6	2+	D6	12,4
Dic₃	Dicyclic group; = C₃ :C₄	12	2-	Dic3	12,1
C₂xC₆	Abelian group of type [2,6]	12		C2xC6	12,5

Groups of order 13

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

Groups of order 14

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

Groups of order 15

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

Groups of order 16

		d	ρ	Label	ID
C₁₆	Cyclic group	16	1	C16	16,1
D₈	Dihedral group	8	2+	D8	16,7
Q₁₆	Generalised quaternion group; = C₈ .C₂ = Dic₄	16	2-	Q16	16,9
SD₁₆	Semidihedral group; = Q₈ :C₂ = QD₁₆	8	2	SD16	16,8
M₄(2)	Modular maximal-cyclic group; = C₈ :₃ C₂	8	2	M4(2)	16,6
C₄:C₄	The semidirect product of C₄ and C₄ acting via C₄/C₂=C₂	16		C4:C4	16,4
C₄²	Abelian group of type [4,4]	16		C4^2	16,2
C₂xC₈	Abelian group of type [2,8]	16		C2xC8	16,5

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
C₃xC₆	Abelian group of type [3,6]	18		C3xC6	18,5
C₃xS₃	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; = C₂xD₅	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
C₂xC₁₀	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
D₁₂	Dihedral group	12	2+	D12	24,6
Dic₆	Dicyclic group; = C₃ :Q₈	24	2-	Dic6	24,4
C₃:C₈	The semidirect product of C₃ and C₈ acting via C₈/C₄=C₂	24	2	C3:C8	24,1
C₂xC₁₂	Abelian group of type [2,12]	24		C2xC12	24,9
C₄xS₃	Direct product of C₄ and S₃	12	2	C4xS3	24,5
C₃xD₄	Direct product of C₃ and D₄	12	2	C3xD4	24,10
C₃xQ₈	Direct product of C₃ and Q₈	24	2	C3xQ8	24,11
C₂xDic₃	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
3_-¹⁺²	Extraspecial group	9	3	ES-(3,1)	27,4
C₃xC₉	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; = C₂xD₇	14	2+	D14	28,3
Dic₇	Dicyclic group; = C₇ :C₄	28	2-	Dic7	28,1
C₂xC₁₄	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
C₅xS₃	Direct product of C₅ and S₃	15	2	C5xS3	30,1
C₃xD₅	Direct product of C₃ and D₅	15	2	C3xD5	30,2

Groups of order 31

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

Groups of order 32

		d	ρ	Label	ID
C₃₂	Cyclic group	32	1	C32	32,1
D₁₆	Dihedral group	16	2+	D16	32,18
Q₃₂	Generalised quaternion group; = C₁₆ .C₂ = Dic₈	32	2-	Q32	32,20
SD₃₂	Semidihedral group; = C₁₆ :₂ C₂ = QD₃₂	16	2	SD32	32,19
M₅(2)	Modular maximal-cyclic group; = C₁₆ :₃ C₂	16	2	M5(2)	32,17
C₄:C₈	The semidirect product of C₄ and C₈ acting via C₈/C₄=C₂	32		C4:C8	32,12
C₈:C₄	3^rd semidirect product of C₈ and C₄ acting via C₄/C₂=C₂	32		C8:C4	32,4
C₈.C₄	1^st non-split extension by C₈ of C₄ acting via C₄/C₂=C₂	16	2	C8.C4	32,15
C₂.D₈	2^nd central extension by C₂ of D₈	32		C2.D8	32,14
C₄.Q₈	1^st non-split extension by C₄ of Q₈ acting via Q₈/C₄=C₂	32		C4.Q8	32,13
C₄xC₈	Abelian group of type [4,8]	32		C4xC8	32,3
C₂xC₁₆	Abelian group of type [2,16]	32		C2xC16	32,16

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; = C₂xD₉	18	2+	D18	36,4
Dic₉	Dicyclic group; = C₉ :C₄	36	2-	Dic9	36,1
C₆²	Abelian group of type [6,6]	36		C6^2	36,14
C₂xC₁₈	Abelian group of type [2,18]	36		C2xC18	36,5
C₃xC₁₂	Abelian group of type [3,12]	36		C3xC12	36,8
S₃xC₆	Direct product of C₆ and S₃	12	2	S3xC6	36,12
C₃xDic₃	Direct product of C₃ and Dic₃	12	2	C3xDic3	36,6

Groups of order 37

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

Groups of order 38

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

Groups of order 39

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

Groups of order 40

		d	ρ	Label	ID
C₄₀	Cyclic group	40	1	C40	40,2
D₂₀	Dihedral group	20	2+	D20	40,6
Dic₁₀	Dicyclic group; = C₅ :Q₈	40	2-	Dic10	40,4
C₅: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
C₂xC₂₀	Abelian group of type [2,20]	40		C2xC20	40,9
C₂xF₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	10	4+	C2xF5	40,12
C₄xD₅	Direct product of C₄ and D₅	20	2	C4xD5	40,5
C₅xD₄	Direct product of C₅ and D₄	20	2	C5xD4	40,10
C₅xQ₈	Direct product of C₅ and Q₈	40	2	C5xQ8	40,11
C₂xDic₅	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
S₃xC₇	Direct product of C₇ and S₃	21	2	S3xC7	42,3
C₃xD₇	Direct product of C₃ and D₇	21	2	C3xD7	42,4
C₂xC₇: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; = C₂xD₁₁	22	2+	D22	44,3
Dic₁₁	Dicyclic group; = C₁₁ :C₄	44	2-	Dic11	44,1
C₂xC₂₂	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
C₃xC₁₅	Abelian group of type [3,15]	45		C3xC15	45,2

Groups of order 46

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

Groups of order 47

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

Groups of order 48

		d	ρ	Label	ID
C₄₈	Cyclic group	48	1	C48	48,2
D₂₄	Dihedral group	24	2+	D24	48,7
Dic₁₂	Dicyclic group; = C₃ :₁ Q₁₆	48	2-	Dic12	48,8
C₈:S₃	3^rd semidirect product of C₈ and S₃ acting via S₃/C₃=C₂	24	2	C8:S3	48,5
C₂₄:C₂	2^nd semidirect product of C₂₄ and C₂ acting faithfully	24	2	C24:C2	48,6
C₃:C₁₆	The semidirect product of C₃ and C₁₆ acting via C₁₆/C₈=C₂	48	2	C3:C16	48,1
C₄:Dic₃	The semidirect product of C₄ and Dic₃ acting via Dic₃/C₆=C₂	48		C4:Dic3	48,13
C₄.Dic₃	The non-split extension by C₄ of Dic₃ acting via Dic₃/C₆=C₂	24	2	C4.Dic3	48,10
C₄xC₁₂	Abelian group of type [4,12]	48		C4xC12	48,20
C₂xC₂₄	Abelian group of type [2,24]	48		C2xC24	48,23
S₃xC₈	Direct product of C₈ and S₃	24	2	S3xC8	48,4
C₃xD₈	Direct product of C₃ and D₈	24	2	C3xD8	48,25
C₃xSD₁₆	Direct product of C₃ and SD₁₆	24	2	C3xSD16	48,26
C₃xM₄(2)	Direct product of C₃ and M₄(2)	24	2	C3xM4(2)	48,24
C₃xQ₁₆	Direct product of C₃ and Q₁₆	48	2	C3xQ16	48,27
C₄xDic₃	Direct product of C₄ and Dic₃	48		C4xDic3	48,11
C₂xC₃:C₈	Direct product of C₂ and C₃:C₈	48		C2xC3:C8	48,9
C₃xC₄:C₄	Direct product of C₃ and C₄:C₄	48		C3xC4:C4	48,22

Groups of order 49

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

Groups of order 50

		d	ρ	Label	ID
C₅₀	Cyclic group	50	1	C50	50,2
D₂₅	Dihedral group	25	2+	D25	50,1
C₅xC₁₀	Abelian group of type [5,10]	50		C5xC10	50,5
C₅xD₅	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; = C₂xD₁₃	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
C₂xC₂₆	Abelian group of type [2,26]	52		C2xC26	52,5

Groups of order 53

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

Groups of order 54

		d	ρ	Label	ID
C₅₄	Cyclic group	54	1	C54	54,2
D₂₇	Dihedral group	27	2+	D27	54,1
C₉:C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	9	6+	C9:C6	54,6
C₃xC₁₈	Abelian group of type [3,18]	54		C3xC18	54,9
S₃xC₉	Direct product of C₉ and S₃	18	2	S3xC9	54,4
C₃xD₉	Direct product of C₃ and D₉	18	2	C3xD9	54,3
C₂x3_-¹⁺²	Direct product of C₂ and 3_-¹⁺²	18	3	C2xES-(3,1)	54,11

Groups of order 55

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

Groups of order 56

		d	ρ	Label	ID
C₅₆	Cyclic group	56	1	C56	56,2
D₂₈	Dihedral group	28	2+	D28	56,5
Dic₁₄	Dicyclic group; = C₇ :Q₈	56	2-	Dic14	56,3
C₇:C₈	The semidirect product of C₇ and C₈ acting via C₈/C₄=C₂	56	2	C7:C8	56,1
C₂xC₂₈	Abelian group of type [2,28]	56		C2xC28	56,8
C₄xD₇	Direct product of C₄ and D₇	28	2	C4xD7	56,4
C₇xD₄	Direct product of C₇ and D₄	28	2	C7xD4	56,9
C₇xQ₈	Direct product of C₇ and Q₈	56	2	C7xQ8	56,10
C₂xDic₇	Direct product of C₂ and Dic₇	56		C2xDic7	56,6

Groups of order 57

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

Groups of order 58

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

Groups of order 59

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

Groups of order 60

		d	ρ	Label	ID
C₆₀	Cyclic group	60	1	C60	60,4
D₃₀	Dihedral group; = C₂xD₁₅	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
C₂xC₃₀	Abelian group of type [2,30]	60		C2xC30	60,13
C₃xF₅	Direct product of C₃ and F₅	15	4	C3xF5	60,6
C₆xD₅	Direct product of C₆ and D₅	30	2	C6xD5	60,10
S₃xC₁₀	Direct product of C₁₀ and S₃	30	2	S3xC10	60,11
C₅xDic₃	Direct product of C₅ and Dic₃	60	2	C5xDic3	60,1
C₃xDic₅	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
C₃xC₂₁	Abelian group of type [3,21]	63		C3xC21	63,4
C₃xC₇:C₃	Direct product of C₃ and C₇:C₃	21	3	C3xC7:C3	63,3

Groups of order 64

		d	ρ	Label	ID
C₆₄	Cyclic group	64	1	C64	64,1
D₃₂	Dihedral group	32	2+	D32	64,52
Q₆₄	Generalised quaternion group; = C₃₂ .C₂ = Dic₁₆	64	2-	Q64	64,54
SD₆₄	Semidihedral group; = C₃₂ :₂ C₂ = QD₆₄	32	2	SD64	64,53
M₆(2)	Modular maximal-cyclic group; = C₃₂ :₃ C₂	32	2	M6(2)	64,51
C₁₆:C₄	2^nd semidirect product of C₁₆ and C₄ acting faithfully	16	4	C16:C4	64,28
C₄:C₁₆	The semidirect product of C₄ and C₁₆ acting via C₁₆/C₈=C₂	64		C4:C16	64,44
C₈:C₈	3^rd semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:C8	64,3
C₈:₂C₈	2^nd semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:2C8	64,15
C₈:₁C₈	1^st semidirect product of C₈ and C₈ acting via C₈/C₄=C₂	64		C8:1C8	64,16
C₁₆:₅C₄	3^rd semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:5C4	64,27
C₁₆:₃C₄	1^st semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:3C4	64,47
C₁₆:₄C₄	2^nd semidirect product of C₁₆ and C₄ acting via C₄/C₂=C₂	64		C16:4C4	64,48
C₈.Q₈	The non-split extension by C₈ of Q₈ acting via Q₈/C₂=C₂²	16	4	C8.Q8	64,46
C₈.C₈	1^st non-split extension by C₈ of C₈ acting via C₈/C₄=C₂	16	2	C8.C8	64,45
C₈.₄Q₈	3^rd non-split extension by C₈ of Q₈ acting via Q₈/C₄=C₂	32	2	C8.4Q8	64,49
C₈²	Abelian group of type [8,8]	64		C8^2	64,2
C₄xC₁₆	Abelian group of type [4,16]	64		C4xC16	64,26
C₂xC₃₂	Abelian group of type [2,32]	64		C2xC32	64,50

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
S₃xC₁₁	Direct product of C₁₁ and S₃	33	2	S3xC11	66,1
C₃xD₁₁	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; = C₂xD₁₇	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
C₂xC₃₄	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
C₇xD₅	Direct product of C₇ and D₅	35	2	C7xD5	70,1
C₅xD₇	Direct product of C₅ and D₇	35	2	C5xD7	70,2

Groups of order 71

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

Groups of order 72

		d	ρ	Label	ID
C₇₂	Cyclic group	72	1	C72	72,2
D₃₆	Dihedral group	36	2+	D36	72,6
Dic₁₈	Dicyclic group; = C₉ :Q₈	72	2-	Dic18	72,4
C₉:C₈	The semidirect product of C₉ and C₈ acting via C₈/C₄=C₂	72	2	C9:C8	72,1
C₂xC₃₆	Abelian group of type [2,36]	72		C2xC36	72,9
C₃xC₂₄	Abelian group of type [3,24]	72		C3xC24	72,14
C₆xC₁₂	Abelian group of type [6,12]	72		C6xC12	72,36
S₃xC₁₂	Direct product of C₁₂ and S₃	24	2	S3xC12	72,27
C₃xD₁₂	Direct product of C₃ and D₁₂	24	2	C3xD12	72,28
C₃xDic₆	Direct product of C₃ and Dic₆	24	2	C3xDic6	72,26
C₆xDic₃	Direct product of C₆ and Dic₃	24		C6xDic3	72,29
C₄xD₉	Direct product of C₄ and D₉	36	2	C4xD9	72,5
D₄xC₉	Direct product of C₉ and D₄	36	2	D4xC9	72,10
D₄xC₃²	Direct product of C₃² and D₄	36		D4xC3^2	72,37
Q₈xC₉	Direct product of C₉ and Q₈	72	2	Q8xC9	72,11
C₂xDic₉	Direct product of C₂ and Dic₉	72		C2xDic9	72,7
Q₈xC₃²	Direct product of C₃² and Q₈	72		Q8xC3^2	72,38
C₃xC₃:C₈	Direct product of C₃ and C₃:C₈	24	2	C3xC3:C8	72,12

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
C₅xC₁₅	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; = C₂xD₁₉	38	2+	D38	76,3
Dic₁₉	Dicyclic group; = C₁₉ :C₄	76	2-	Dic19	76,1
C₂xC₃₈	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
S₃xC₁₃	Direct product of C₁₃ and S₃	39	2	S3xC13	78,3
C₃xD₁₃	Direct product of C₃ and D₁₃	39	2	C3xD13	78,4
C₂xC₁₃:C₃	Direct product of C₂ and C₁₃:C₃	26	3	C2xC13:C3	78,2

Groups of order 79

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

Groups of order 80

		d	ρ	Label	ID
C₈₀	Cyclic group	80	1	C80	80,2
D₄₀	Dihedral group	40	2+	D40	80,7
Dic₂₀	Dicyclic group; = C₅ :₁ Q₁₆	80	2-	Dic20	80,8
C₄:F₅	The semidirect product of C₄ and F₅ acting via F₅/D₅=C₂	20	4	C4:F5	80,31
D₅:C₈	The semidirect product of D₅ and C₈ acting via C₈/C₄=C₂	40	4	D5:C8	80,28
C₈:D₅	3^rd semidirect product of C₈ and D₅ acting via D₅/C₅=C₂	40	2	C8:D5	80,5
C₄₀:C₂	2^nd semidirect product of C₄₀ and C₂ acting faithfully	40	2	C40:C2	80,6
C₅:C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₄=C₄	80	4	C5:C16	80,3
C₅:₂C₁₆	The semidirect product of C₅ and C₁₆ acting via C₁₆/C₈=C₂	80	2	C5:2C16	80,1
C₄:Dic₅	The semidirect product of C₄ and Dic₅ acting via Dic₅/C₁₀=C₂	80		C4:Dic5	80,13
C₄.F₅	The non-split extension by C₄ of F₅ acting via F₅/D₅=C₂	40	4	C4.F5	80,29
C₄.Dic₅	The non-split extension by C₄ of Dic₅ acting via Dic₅/C₁₀=C₂	40	2	C4.Dic5	80,10
C₄xC₂₀	Abelian group of type [4,20]	80		C4xC20	80,20
C₂xC₄₀	Abelian group of type [2,40]	80		C2xC40	80,23
C₄xF₅	Direct product of C₄ and F₅	20	4	C4xF5	80,30
C₈xD₅	Direct product of C₈ and D₅	40	2	C8xD5	80,4
C₅xD₈	Direct product of C₅ and D₈	40	2	C5xD8	80,25
C₅xSD₁₆	Direct product of C₅ and SD₁₆	40	2	C5xSD16	80,26
C₅xM₄(2)	Direct product of C₅ and M₄(2)	40	2	C5xM4(2)	80,24
C₅xQ₁₆	Direct product of C₅ and Q₁₆	80	2	C5xQ16	80,27
C₄xDic₅	Direct product of C₄ and Dic₅	80		C4xDic5	80,11
C₂xC₅:C₈	Direct product of C₂ and C₅:C₈	80		C2xC5:C8	80,32
C₅xC₄:C₄	Direct product of C₅ and C₄:C₄	80		C5xC4:C4	80,22
C₂xC₅:₂C₈	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
C₂₇:C₃	The semidirect product of C₂₇ and C₃ acting faithfully	27	3	C27:C3	81,6
C₉:C₉	The semidirect product of C₉ and C₉ acting via C₉/C₃=C₃	81		C9:C9	81,4
C₉²	Abelian group of type [9,9]	81		C9^2	81,2
C₃xC₂₇	Abelian group of type [3,27]	81		C3xC27	81,5

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; = C₂xD₂₁	42	2+	D42	84,14
Dic₂₁	Dicyclic group; = C₃ :Dic₇	84	2-	Dic21	84,5
C₇:C₁₂	The semidirect product of C₇ and C₁₂ acting via C₁₂/C₂=C₆	28	6-	C7:C12	84,1
C₂xC₄₂	Abelian group of type [2,42]	84		C2xC42	84,15
C₂xF₇	Direct product of C₂ and F₇; = Aut(D₁₄) = Hol(C₁₄)	14	6+	C2xF7	84,7
C₆xD₇	Direct product of C₆ and D₇	42	2	C6xD7	84,12
S₃xC₁₄	Direct product of C₁₄ and S₃	42	2	S3xC14	84,13
C₇xDic₃	Direct product of C₇ and Dic₃	84	2	C7xDic3	84,3
C₃xDic₇	Direct product of C₃ and Dic₇	84	2	C3xDic7	84,4
C₄xC₇:C₃	Direct product of C₄ and C₇:C₃	28	3	C4xC7:C3	84,2
C₂²xC₇:C₃	Direct product of C₂² and C₇:C₃	28		C2^2xC7:C3	84,9

Groups of order 85

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

Groups of order 86

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

Groups of order 87

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

Groups of order 88

		d	ρ	Label	ID
C₈₈	Cyclic group	88	1	C88	88,2
D₄₄	Dihedral group	44	2+	D44	88,5
Dic₂₂	Dicyclic group; = C₁₁ :Q₈	88	2-	Dic22	88,3
C₁₁:C₈	The semidirect product of C₁₁ and C₈ acting via C₈/C₄=C₂	88	2	C11:C8	88,1
C₂xC₄₄	Abelian group of type [2,44]	88		C2xC44	88,8
C₄xD₁₁	Direct product of C₄ and D₁₁	44	2	C4xD11	88,4
D₄xC₁₁	Direct product of C₁₁ and D₄	44	2	D4xC11	88,9
Q₈xC₁₁	Direct product of C₁₁ and Q₈	88	2	Q8xC11	88,10
C₂xDic₁₁	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
C₃xC₃₀	Abelian group of type [3,30]	90		C3xC30	90,10
S₃xC₁₅	Direct product of C₁₅ and S₃	30	2	S3xC15	90,6
C₃xD₁₅	Direct product of C₃ and D₁₅	30	2	C3xD15	90,7
C₅xD₉	Direct product of C₅ and D₉	45	2	C5xD9	90,1
C₉xD₅	Direct product of C₉ and D₅	45	2	C9xD5	90,2
C₃²xD₅	Direct product of C₃² and D₅	45		C3^2xD5	90,5

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; = C₂xD₂₃	46	2+	D46	92,3
Dic₂₃	Dicyclic group; = C₂₃ :C₄	92	2-	Dic23	92,1
C₂xC₄₆	Abelian group of type [2,46]	92		C2xC46	92,4

Groups of order 93

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

Groups of order 94

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

Groups of order 95

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

Groups of order 96

		d	ρ	Label	ID
C₉₆	Cyclic group	96	1	C96	96,2
D₄₈	Dihedral group	48	2+	D48	96,6
Dic₂₄	Dicyclic group; = C₃ :₁ Q₃₂	96	2-	Dic24	96,8
C₄₈:C₂	2^nd semidirect product of C₄₈ and C₂ acting faithfully	48	2	C48:C2	96,7
C₃:C₃₂	The semidirect product of C₃ and C₃₂ acting via C₃₂/C₁₆=C₂	96	2	C3:C32	96,1
C₁₂:C₈	1^st semidirect product of C₁₂ and C₈ acting via C₈/C₄=C₂	96		C12:C8	96,11
C₂₄:C₄	5^th semidirect product of C₂₄ and C₄ acting via C₄/C₂=C₂	96		C24:C4	96,22
C₂₄:₁C₄	1^st semidirect product of C₂₄ and C₄ acting via C₄/C₂=C₂	96		C24:1C4	96,25
C₈:Dic₃	2^nd semidirect product of C₈ and Dic₃ acting via Dic₃/C₆=C₂	96		C8:Dic3	96,24
D₆.C₈	The non-split extension by D₆ of C₈ acting via C₈/C₄=C₂	48	2	D6.C8	96,5
C₁₂.C₈	1^st non-split extension by C₁₂ of C₈ acting via C₈/C₄=C₂	48	2	C12.C8	96,19
C₂₄.C₄	1^st non-split extension by C₂₄ of C₄ acting via C₄/C₂=C₂	48	2	C24.C4	96,26
C₄xC₂₄	Abelian group of type [4,24]	96		C4xC24	96,46
C₂xC₄₈	Abelian group of type [2,48]	96		C2xC48	96,59
S₃xC₁₆	Direct product of C₁₆ and S₃	48	2	S3xC16	96,4
C₃xD₁₆	Direct product of C₃ and D₁₆	48	2	C3xD16	96,61
C₃xSD₃₂	Direct product of C₃ and SD₃₂	48	2	C3xSD32	96,62
C₃xM₅(2)	Direct product of C₃ and M₅(2)	48	2	C3xM5(2)	96,60
C₃xQ₃₂	Direct product of C₃ and Q₃₂	96	2	C3xQ32	96,63
C₈xDic₃	Direct product of C₈ and Dic₃	96		C8xDic3	96,20
C₃xC₈.C₄	Direct product of C₃ and C₈.C₄	48	2	C3xC8.C4	96,58
C₄xC₃:C₈	Direct product of C₄ and C₃:C₈	96		C4xC3:C8	96,9
C₃xC₄:C₈	Direct product of C₃ and C₄:C₈	96		C3xC4:C8	96,55
C₂xC₃:C₁₆	Direct product of C₂ and C₃:C₁₆	96		C2xC3:C16	96,18
C₃xC₈:C₄	Direct product of C₃ and C₈:C₄	96		C3xC8:C4	96,47
C₃xC₂.D₈	Direct product of C₃ and C₂.D₈	96		C3xC2.D8	96,57
C₃xC₄.Q₈	Direct product of C₃ and C₄.Q₈	96		C3xC4.Q8	96,56

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
C₇xC₁₄	Abelian group of type [7,14]	98		C7xC14	98,5
C₇xD₇	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
C₃xC₃₃	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; = C₂xD₂₅	50	2+	D50	100,4
Dic₂₅	Dicyclic group; = C₂₅ :₂ C₄	100	2-	Dic25	100,1
C₂₅:C₄	The semidirect product of C₂₅ and C₄ acting faithfully	25	4+	C25:C4	100,3
C₁₀²	Abelian group of type [10,10]	100		C10^2	100,16
C₂xC₅₀	Abelian group of type [2,50]	100		C2xC50	100,5
C₅xC₂₀	Abelian group of type [5,20]	100		C5xC20	100,8
C₅xF₅	Direct product of C₅ and F₅	20	4	C5xF5	100,9
D₅xC₁₀	Direct product of C₁₀ and D₅	20	2	D5xC10	100,14
C₅xDic₅	Direct product of C₅ and Dic₅	20	2	C5xDic5	100,6

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
S₃xC₁₇	Direct product of C₁₇ and S₃	51	2	S3xC17	102,1
C₃xD₁₇	Direct product of C₃ and D₁₇	51	2	C3xD17	102,2

Groups of order 103

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

Groups of order 104

		d	ρ	Label	ID
C₁₀₄	Cyclic group	104	1	C104	104,2
D₅₂	Dihedral group	52	2+	D52	104,6
Dic₂₆	Dicyclic group; = C₁₃ :Q₈	104	2-	Dic26	104,4
C₁₃: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
C₂xC₅₂	Abelian group of type [2,52]	104		C2xC52	104,9
C₄xD₁₃	Direct product of C₄ and D₁₃	52	2	C4xD13	104,5
D₄xC₁₃	Direct product of C₁₃ and D₄	52	2	D4xC13	104,10
Q₈xC₁₃	Direct product of C₁₃ and Q₈	104	2	Q8xC13	104,11
C₂xDic₁₃	Direct product of C₂ and Dic₁₃	104		C2xDic13	104,7
C₂xC₁₃: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
C₅xC₇: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; = C₂xD₂₇	54	2+	D54	108,4
Dic₂₇	Dicyclic group; = C₂₇ :C₄	108	2-	Dic27	108,1
C₉:C₁₂	The semidirect product of C₉ and C₁₂ acting via C₁₂/C₂=C₆	36	6-	C9:C12	108,9
C₂xC₅₄	Abelian group of type [2,54]	108		C2xC54	108,5
C₃xC₃₆	Abelian group of type [3,36]	108		C3xC36	108,12
C₆xC₁₈	Abelian group of type [6,18]	108		C6xC18	108,29
C₆xD₉	Direct product of C₆ and D₉	36	2	C6xD9	108,23
S₃xC₁₈	Direct product of C₁₈ and S₃	36	2	S3xC18	108,24
C₃xDic₉	Direct product of C₃ and Dic₉	36	2	C3xDic9	108,6
C₉xDic₃	Direct product of C₉ and Dic₃	36	2	C9xDic3	108,7
C₄x3_-¹⁺²	Direct product of C₄ and 3_-¹⁺²	36	3	C4xES-(3,1)	108,14
C₂²x3_-¹⁺²	Direct product of C₂² and 3_-¹⁺²	36		C2^2xES-(3,1)	108,31
C₂xC₉:C₆	Direct product of C₂ and C₉:C₆; = Aut(D₁₈) = Hol(C₁₈)	18	6+	C2xC9:C6	108,26

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
D₅xC₁₁	Direct product of C₁₁ and D₅	55	2	D5xC11	110,3
C₅xD₁₁	Direct product of C₅ and D₁₁	55	2	C5xD11	110,4
C₂xC₁₁:C₅	Direct product of C₂ and C₁₁:C₅	22	5	C2xC11:C5	110,2

Groups of order 111

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

Groups of order 112

		d	ρ	Label	ID
C₁₁₂	Cyclic group	112	1	C112	112,2
D₅₆	Dihedral group	56	2+	D56	112,6
Dic₂₈	Dicyclic group; = C₇ :₁ Q₁₆	112	2-	Dic28	112,7
C₈:D₇	3^rd semidirect product of C₈ and D₇ acting via D₇/C₇=C₂	56	2	C8:D7	112,4
C₅₆:C₂	2^nd semidirect product of C₅₆ and C₂ acting faithfully	56	2	C56:C2	112,5
C₇:C₁₆	The semidirect product of C₇ and C₁₆ acting via C₁₆/C₈=C₂	112	2	C7:C16	112,1
C₄:Dic₇	The semidirect product of C₄ and Dic₇ acting via Dic₇/C₁₄=C₂	112		C4:Dic7	112,12
C₄.Dic₇	The non-split extension by C₄ of Dic₇ acting via Dic₇/C₁₄=C₂	56	2	C4.Dic7	112,9
C₄xC₂₈	Abelian group of type [4,28]	112		C4xC28	112,19
C₂xC₅₆	Abelian group of type [2,56]	112		C2xC56	112,22
C₈xD₇	Direct product of C₈ and D₇	56	2	C8xD7	112,3
C₇xD₈	Direct product of C₇ and D₈	56	2	C7xD8	112,24
C₇xSD₁₆	Direct product of C₇ and SD₁₆	56	2	C7xSD16	112,25
C₇xM₄(2)	Direct product of C₇ and M₄(2)	56	2	C7xM4(2)	112,23
C₇xQ₁₆	Direct product of C₇ and Q₁₆	112	2	C7xQ16	112,26
C₄xDic₇	Direct product of C₄ and Dic₇	112		C4xDic7	112,10
C₂xC₇:C₈	Direct product of C₂ and C₇:C₈	112		C2xC7:C8	112,8
C₇xC₄:C₄	Direct product of C₇ and C₄:C₄	112		C7xC4:C4	112,21

Groups of order 113

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

Groups of order 114

		d	ρ	Label	ID
C₁₁₄	Cyclic group	114	1	C114	114,6
D₅₇	Dihedral group	57	2+	D57	114,5
C₁₉:C₆	The semidirect product of C₁₉ and C₆ acting faithfully	19	6+	C19:C6	114,1
S₃xC₁₉	Direct product of C₁₉ and S₃	57	2	S3xC19	114,3
C₃xD₁₉	Direct product of C₃ and D₁₉	57	2	C3xD19	114,4
C₂xC₁₉: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; = C₂xD₂₉	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
C₂xC₅₈	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
C₃xC₃₉	Abelian group of type [3,39]	117		C3xC39	117,4
C₃xC₁₃:C₃	Direct product of C₃ and C₁₃:C₃	39	3	C3xC13:C3	117,3

Groups of order 118

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

Groups of order 119

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

Groups of order 120

		d	ρ	Label	ID
C₁₂₀	Cyclic group	120	1	C120	120,4
D₆₀	Dihedral group	60	2+	D60	120,28
Dic₃₀	Dicyclic group; = C₁₅ :₂ Q₈	120	2-	Dic30	120,26
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
C₂xC₆₀	Abelian group of type [2,60]	120		C2xC60	120,31
C₆xF₅	Direct product of C₆ and F₅	30	4	C6xF5	120,40
S₃xC₂₀	Direct product of C₂₀ and S₃	60	2	S3xC20	120,22
D₅xC₁₂	Direct product of C₁₂ and D₅	60	2	D5xC12	120,17
C₃xD₂₀	Direct product of C₃ and D₂₀	60	2	C3xD20	120,18
C₅xD₁₂	Direct product of C₅ and D₁₂	60	2	C5xD12	120,23
C₄xD₁₅	Direct product of C₄ and D₁₅	60	2	C4xD15	120,27
D₄xC₁₅	Direct product of C₁₅ and D₄	60	2	D4xC15	120,32
Q₈xC₁₅	Direct product of C₁₅ and Q₈	120	2	Q8xC15	120,33
C₆xDic₅	Direct product of C₆ and Dic₅	120		C6xDic5	120,19
C₅xDic₆	Direct product of C₅ and Dic₆	120	2	C5xDic6	120,21
C₃xDic₁₀	Direct product of C₃ and Dic₁₀	120	2	C3xDic10	120,16
C₁₀xDic₃	Direct product of C₁₀ and Dic₃	120		C10xDic3	120,24
C₂xDic₁₅	Direct product of C₂ and Dic₁₅	120		C2xDic15	120,29
C₂xC₃:F₅	Direct product of C₂ and C₃:F₅	30	4	C2xC3:F5	120,41
C₅xC₃:C₈	Direct product of C₅ and C₃:C₈	120	2	C5xC3:C8	120,1
C₃xC₅:C₈	Direct product of C₃ and C₅:C₈	120	4	C3xC5:C8	120,6
C₃xC₅:₂C₈	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; = C₂xD₃₁	62	2+	D62	124,3
Dic₃₁	Dicyclic group; = C₃₁ :C₄	124	2-	Dic31	124,1
C₂xC₆₂	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
5_-¹⁺²	Extraspecial group	25	5	ES-(5,1)	125,4
C₅xC₂₅	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
C₃xC₄₂	Abelian group of type [3,42]	126		C3xC42	126,16
C₃xF₇	Direct product of C₃ and F₇	21	6	C3xF7	126,7
S₃xC₂₁	Direct product of C₂₁ and S₃	42	2	S3xC21	126,12
C₃xD₂₁	Direct product of C₃ and D₂₁	42	2	C3xD21	126,13
C₇xD₉	Direct product of C₇ and D₉	63	2	C7xD9	126,3
C₉xD₇	Direct product of C₉ and D₇	63	2	C9xD7	126,4
C₃²xD₇	Direct product of C₃² and D₇	63		C3^2xD7	126,11
S₃xC₇:C₃	Direct product of S₃ and C₇:C₃	21	6	S3xC7:C3	126,8
C₆xC₇:C₃	Direct product of C₆ and C₇:C₃	42	3	C6xC7:C3	126,10
C₂xC₇:C₉	Direct product of C₂ and C₇:C₉	126	3	C2xC7:C9	126,2

Groups of order 127

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

Groups of order 128

		d	ρ	Label	ID
C₁₂₈	Cyclic group	128	1	C128	128,1
D₆₄	Dihedral group	64	2+	D64	128,161
Q₁₂₈	Generalised quaternion group; = C₆₄ .C₂ = Dic₃₂	128	2-	Q128	128,163
SD₁₂₈	Semidihedral group; = C₆₄ :₂ C₂ = QD₁₂₈	64	2	SD128	128,162
M₇(2)	Modular maximal-cyclic group; = C₆₄ :₃ C₂	64	2	M7(2)	128,160
C₃₂:C₄	2^nd semidirect product of C₃₂ and C₄ acting faithfully	32	4	C32:C4	128,130
C₄:C₃₂	The semidirect product of C₄ and C₃₂ acting via C₃₂/C₁₆=C₂	128		C4:C32	128,153
C₁₆:₅C₈	3^rd semidirect product of C₁₆ and C₈ acting via C₈/C₄=C₂	128		C16:5C8	128,43
C₈:C₁₆	3^rd semidirect product of C₈ and C₁₆ acting via C₁₆/C₈=C₂	128		C8:C16	128,44
C₁₆:C₈	2^nd semidirect product of C₁₆ and C₈ acting via C₈/C₂=C₄	128		C16:C8	128,45
C₈:₂C₁₆	2^nd semidirect product of C₈ and C₁₆ acting via C₁₆/C₈=C₂	128		C8:2C16	128,99
C₁₆:₁C₈	1^st semidirect product of C₁₆ and C₈ acting via C₈/C₂=C₄	128		C16:1C8	128,100
C₁₆:₃C₈	1^st semidirect product of C₁₆ and C₈ acting via C₈/C₄=C₂	128		C16:3C8	128,103
C₁₆:₄C₈	2^nd semidirect product of C₁₆ and C₈ acting via C₈/C₄=C₂	128		C16:4C8	128,104
C₃₂:₅C₄	3^rd semidirect product of C₃₂ and C₄ acting via C₄/C₂=C₂	128		C32:5C4	128,129
C₃₂:₃C₄	1^st semidirect product of C₃₂ and C₄ acting via C₄/C₂=C₂	128		C32:3C4	128,155
C₃₂:₄C₄	2^nd semidirect product of C₃₂ and C₄ acting via C₄/C₂=C₂	128		C32:4C4	128,156
C₁₆.C₈	1^st non-split extension by C₁₆ of C₈ acting via C₈/C₂=C₄	32	4	C16.C8	128,101
C₁₆.₃C₈	1^st non-split extension by C₁₆ of C₈ acting via C₈/C₄=C₂	32	2	C16.3C8	128,105
C₈.C₁₆	1^st non-split extension by C₈ of C₁₆ acting via C₁₆/C₈=C₂	32	2	C8.C16	128,154
C₈.Q₁₆	2^nd non-split extension by C₈ of Q₁₆ acting via Q₁₆/C₄=C₂²	32	4	C8.Q16	128,158
C₃₂.C₄	1^st non-split extension by C₃₂ of C₄ acting via C₄/C₂=C₂	64	2	C32.C4	128,157
C₈.₃₆D₈	3^rd central extension by C₈ of D₈	128		C8.36D8	128,102
C₈xC₁₆	Abelian group of type [8,16]	128		C8xC16	128,42
C₄xC₃₂	Abelian group of type [4,32]	128		C4xC32	128,128
C₂xC₆₄	Abelian group of type [2,64]	128		C2xC64	128,159

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
D₅xC₁₃	Direct product of C₁₃ and D₅	65	2	D5xC13	130,1
C₅xD₁₃	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; = C₂xD₃₃	66	2+	D66	132,9
Dic₃₃	Dicyclic group; = C₃₃ :₁ C₄	132	2-	Dic33	132,3
C₂xC₆₆	Abelian group of type [2,66]	132		C2xC66	132,10
S₃xC₂₂	Direct product of C₂₂ and S₃	66	2	S3xC22	132,8
C₆xD₁₁	Direct product of C₆ and D₁₁	66	2	C6xD11	132,7
C₁₁xDic₃	Direct product of C₁₁ and Dic₃	132	2	C11xDic3	132,1
C₃xDic₁₁	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
C₃xC₄₅	Abelian group of type [3,45]	135		C3xC45	135,2
C₅x3_-¹⁺²	Direct product of C₅ and 3_-¹⁺²	45	3	C5xES-(3,1)	135,4

Groups of order 136

		d	ρ	Label	ID
C₁₃₆	Cyclic group	136	1	C136	136,2
D₆₈	Dihedral group	68	2+	D68	136,6
Dic₃₄	Dicyclic group; = C₁₇ :Q₈	136	2-	Dic34	136,4
C₁₇:C₈	The semidirect product of C₁₇ and C₈ acting faithfully	17	8+	C17:C8	136,12
C₁₇:₃C₈	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
C₂xC₆₈	Abelian group of type [2,68]	136		C2xC68	136,9
C₄xD₁₇	Direct product of C₄ and D₁₇	68	2	C4xD17	136,5
D₄xC₁₇	Direct product of C₁₇ and D₄	68	2	D4xC17	136,10
Q₈xC₁₇	Direct product of C₁₇ and Q₈	136	2	Q8xC17	136,11
C₂xDic₁₇	Direct product of C₂ and Dic₁₇	136		C2xDic17	136,7
C₂xC₁₇: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
S₃xC₂₃	Direct product of C₂₃ and S₃	69	2	S3xC23	138,1
C₃xD₂₃	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; = C₂xD₃₅	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
C₂xC₇₀	Abelian group of type [2,70]	140		C2xC70	140,11
C₇xF₅	Direct product of C₇ and F₅	35	4	C7xF5	140,5
C₁₀xD₇	Direct product of C₁₀ and D₇	70	2	C10xD7	140,8
D₅xC₁₄	Direct product of C₁₄ and D₅	70	2	D5xC14	140,9
C₇xDic₅	Direct product of C₇ and Dic₅	140	2	C7xDic5	140,1
C₅xDic₇	Direct product of C₅ and Dic₇	140	2	C5xDic7	140,2

Groups of order 141

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

Groups of order 142

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

Groups of order 143

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

Groups of order 144

		d	ρ	Label	ID
C₁₄₄	Cyclic group	144	1	C144	144,2
D₇₂	Dihedral group	72	2+	D72	144,8
Dic₃₆	Dicyclic group; = C₉ :₁ Q₁₆	144	2-	Dic36	144,4
C₈:D₉	3^rd semidirect product of C₈ and D₉ acting via D₉/C₉=C₂	72	2	C8:D9	144,6
C₇₂:C₂	2^nd semidirect product of C₇₂ and C₂ acting faithfully	72	2	C72:C2	144,7
C₉:C₁₆	The semidirect product of C₉ and C₁₆ acting via C₁₆/C₈=C₂	144	2	C9:C16	144,1
C₄:Dic₉	The semidirect product of C₄ and Dic₉ acting via Dic₉/C₁₈=C₂	144		C4:Dic9	144,13
C₄.Dic₉	The non-split extension by C₄ of Dic₉ acting via Dic₉/C₁₈=C₂	72	2	C4.Dic9	144,10
C₁₂²	Abelian group of type [12,12]	144		C12^2	144,101
C₄xC₃₆	Abelian group of type [4,36]	144		C4xC36	144,20
C₂xC₇₂	Abelian group of type [2,72]	144		C2xC72	144,23
C₃xC₄₈	Abelian group of type [3,48]	144		C3xC48	144,30
C₆xC₂₄	Abelian group of type [6,24]	144		C6xC24	144,104
S₃xC₂₄	Direct product of C₂₄ and S₃	48	2	S3xC24	144,69
C₃xD₂₄	Direct product of C₃ and D₂₄	48	2	C3xD24	144,72
C₃xDic₁₂	Direct product of C₃ and Dic₁₂	48	2	C3xDic12	144,73
Dic₃xC₁₂	Direct product of C₁₂ and Dic₃	48		Dic3xC12	144,76
C₈xD₉	Direct product of C₈ and D₉	72	2	C8xD9	144,5
C₉xD₈	Direct product of C₉ and D₈	72	2	C9xD8	144,25
C₉xSD₁₆	Direct product of C₉ and SD₁₆	72	2	C9xSD16	144,26
C₃²xD₈	Direct product of C₃² and D₈	72		C3^2xD8	144,106
C₉xM₄(2)	Direct product of C₉ and M₄(2)	72	2	C9xM4(2)	144,24
C₃²xSD₁₆	Direct product of C₃² and SD₁₆	72		C3^2xSD16	144,107
C₃²xM₄(2)	Direct product of C₃² and M₄(2)	72		C3^2xM4(2)	144,105
C₉xQ₁₆	Direct product of C₉ and Q₁₆	144	2	C9xQ16	144,27
C₄xDic₉	Direct product of C₄ and Dic₉	144		C4xDic9	144,11
C₃²xQ₁₆	Direct product of C₃² and Q₁₆	144		C3^2xQ16	144,108
C₃xC₄.Dic₃	Direct product of C₃ and C₄.Dic₃	24	2	C3xC4.Dic3	144,75
C₆xC₃:C₈	Direct product of C₆ and C₃:C₈	48		C6xC3:C8	144,74
C₃xC₃:C₁₆	Direct product of C₃ and C₃:C₁₆	48	2	C3xC3:C16	144,28
C₃xC₈:S₃	Direct product of C₃ and C₈:S₃	48	2	C3xC8:S3	144,70
C₃xC₂₄:C₂	Direct product of C₃ and C₂₄:C₂	48	2	C3xC24:C2	144,71
C₃xC₄:Dic₃	Direct product of C₃ and C₄:Dic₃	48		C3xC4:Dic3	144,78
C₂xC₉:C₈	Direct product of C₂ and C₉:C₈	144		C2xC9:C8	144,9
C₉xC₄:C₄	Direct product of C₉ and C₄:C₄	144		C9xC4:C4	144,22
C₃²xC₄:C₄	Direct product of C₃² and C₄:C₄	144		C3^2xC4:C4	144,103

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
C₄₉:C₃	The semidirect product of C₄₉ and C₃ acting faithfully	49	3	C49:C3	147,1
C₇xC₂₁	Abelian group of type [7,21]	147		C7xC21	147,6
C₇xC₇: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; = C₂xD₃₇	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
C₂xC₇₄	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
C₅xC₃₀	Abelian group of type [5,30]	150		C5xC30	150,13
D₅xC₁₅	Direct product of C₁₅ and D₅	30	2	D5xC15	150,8
C₅xD₁₅	Direct product of C₅ and D₁₅	30	2	C5xD15	150,11
S₃xC₂₅	Direct product of C₂₅ and S₃	75	2	S3xC25	150,1
C₃xD₂₅	Direct product of C₃ and D₂₅	75	2	C3xD25	150,2
S₃xC₅²	Direct product of C₅² and S₃	75		S3xC5^2	150,10

Groups of order 151

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

Groups of order 152

		d	ρ	Label	ID
C₁₅₂	Cyclic group	152	1	C152	152,2
D₇₆	Dihedral group	76	2+	D76	152,5
Dic₃₈	Dicyclic group; = C₁₉ :Q₈	152	2-	Dic38	152,3
C₁₉:C₈	The semidirect product of C₁₉ and C₈ acting via C₈/C₄=C₂	152	2	C19:C8	152,1
C₂xC₇₆	Abelian group of type [2,76]	152		C2xC76	152,8
C₄xD₁₉	Direct product of C₄ and D₁₉	76	2	C4xD19	152,4
D₄xC₁₉	Direct product of C₁₉ and D₄	76	2	D4xC19	152,9
Q₈xC₁₉	Direct product of C₁₉ and Q₈	152	2	Q8xC19	152,10
C₂xDic₁₉	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
C₃xC₅₁	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
C₁₁xD₇	Direct product of C₁₁ and D₇	77	2	C11xD7	154,1
C₇xD₁₁	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; = C₂xD₃₉	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
C₂₆.C₆	The non-split extension by C₂₆ of C₆ acting faithfully	52	6-	C26.C6	156,1
C₂xC₇₈	Abelian group of type [2,78]	156		C2xC78	156,18
S₃xC₂₆	Direct product of C₂₆ and S₃	78	2	S3xC26	156,16
C₆xD₁₃	Direct product of C₆ and D₁₃	78	2	C6xD13	156,15
Dic₃xC₁₃	Direct product of C₁₃ and Dic₃	156	2	Dic3xC13	156,3
C₃xDic₁₃	Direct product of C₃ and Dic₁₃	156	2	C3xDic13	156,4
C₂xC₁₃:C₆	Direct product of C₂ and C₁₃:C₆	26	6+	C2xC13:C6	156,8
C₃xC₁₃:C₄	Direct product of C₃ and C₁₃:C₄	39	4	C3xC13:C4	156,9
C₄xC₁₃:C₃	Direct product of C₄ and C₁₃:C₃	52	3	C4xC13:C3	156,2
C₂²xC₁₃:C₃	Direct product of C₂² and C₁₃:C₃	52		C2^2xC13:C3	156,12

Groups of order 157

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

Groups of order 158

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

Groups of order 159

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

Groups of order 160

		d	ρ	Label	ID
C₁₆₀	Cyclic group	160	1	C160	160,2
D₈₀	Dihedral group	80	2+	D80	160,6
Dic₄₀	Dicyclic group; = C₅ :₁ Q₃₂	160	2-	Dic40	160,8
C₈:F₅	3^rd semidirect product of C₈ and F₅ acting via F₅/D₅=C₂	40	4	C8:F5	160,67
C₄₀:C₄	2^nd semidirect product of C₄₀ and C₄ acting faithfully	40	4	C40:C4	160,68
D₅:C₁₆	The semidirect product of D₅ and C₁₆ acting via C₁₆/C₈=C₂	80	4	D5:C16	160,64
C₈₀:C₂	5^th semidirect product of C₈₀ and C₂ acting faithfully	80	2	C80:C2	160,5
C₁₆:D₅	2^nd semidirect product of C₁₆ and D₅ acting via D₅/C₅=C₂	80	2	C16:D5	160,7
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
C₂₀:₃C₈	1^st semidirect product of C₂₀ and C₈ acting via C₈/C₄=C₂	160		C20:3C8	160,11
C₄₀:₈C₄	4^th semidirect product of C₄₀ and C₄ acting via C₄/C₂=C₂	160		C40:8C4	160,22
C₄₀:₆C₄	2^nd semidirect product of C₄₀ and C₄ acting via C₄/C₂=C₂	160		C40:6C4	160,24
C₄₀:₅C₄	1^st semidirect product of C₄₀ and C₄ acting via C₄/C₂=C₂	160		C40:5C4	160,25
C₂₀:C₈	1^st semidirect product of C₂₀ and C₈ acting via C₈/C₂=C₄	160		C20:C8	160,76
D₅.D₈	The non-split extension by D₅ of D₈ acting via D₈/C₈=C₂	40	4	D5.D8	160,69
C₈.F₅	3^rd non-split extension by C₈ of F₅ acting via F₅/D₅=C₂	80	4	C8.F5	160,65
C₂₀.₄C₈	1^st non-split extension by C₂₀ of C₈ acting via C₈/C₄=C₂	80	2	C20.4C8	160,19
C₄₀.₆C₄	1^st non-split extension by C₄₀ of C₄ acting via C₄/C₂=C₂	80	2	C40.6C4	160,26
C₄₀.C₄	2^nd non-split extension by C₄₀ of C₄ acting faithfully	80	4	C40.C4	160,70
C₂₀.C₈	1^st non-split extension by C₂₀ of C₈ acting via C₈/C₂=C₄	80	4	C20.C8	160,73
D₁₀.Q₈	2^nd non-split extension by D₁₀ of Q₈ acting via Q₈/C₄=C₂	80	4	D10.Q8	160,71
C₄xC₄₀	Abelian group of type [4,40]	160		C4xC40	160,46
C₂xC₈₀	Abelian group of type [2,80]	160		C2xC80	160,59
C₈xF₅	Direct product of C₈ and F₅	40	4	C8xF5	160,66
D₅xC₁₆	Direct product of C₁₆ and D₅	80	2	D5xC16	160,4
C₅xD₁₆	Direct product of C₅ and D₁₆	80	2	C5xD16	160,61
C₅xSD₃₂	Direct product of C₅ and SD₃₂	80	2	C5xSD32	160,62
C₅xM₅(2)	Direct product of C₅ and M₅(2)	80	2	C5xM5(2)	160,60
C₅xQ₃₂	Direct product of C₅ and Q₃₂	160	2	C5xQ32	160,63
C₈xDic₅	Direct product of C₈ and Dic₅	160		C8xDic5	160,20
C₅xC₈.C₄	Direct product of C₅ and C₈.C₄	80	2	C5xC8.C4	160,58
C₄xC₅:C₈	Direct product of C₄ and C₅:C₈	160		C4xC5:C8	160,75
C₅xC₄:C₈	Direct product of C₅ and C₄:C₈	160		C5xC4:C8	160,55
C₂xC₅:C₁₆	Direct product of C₂ and C₅:C₁₆	160		C2xC5:C16	160,72
C₅xC₈:C₄	Direct product of C₅ and C₈:C₄	160		C5xC8:C4	160,47
C₄xC₅:₂C₈	Direct product of C₄ and C₅:₂C₈	160		C4xC5:2C8	160,9
C₂xC₅:₂C₁₆	Direct product of C₂ and C₅:₂C₁₆	160		C2xC5:2C16	160,18
C₅xC₂.D₈	Direct product of C₅ and C₂.D₈	160		C5xC2.D8	160,57
C₅xC₄.Q₈	Direct product of C₅ and C₄.Q₈	160		C5xC4.Q8	160,56

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:C₁₈	The semidirect product of C₉ and C₁₈ acting via C₁₈/C₃=C₆	18	6	C9:C18	162,6
C₂₇:C₆	The semidirect product of C₂₇ and C₆ acting faithfully	27	6+	C27:C6	162,9
C₉xC₁₈	Abelian group of type [9,18]	162		C9xC18	162,23
C₃xC₅₄	Abelian group of type [3,54]	162		C3xC54	162,26
C₉xD₉	Direct product of C₉ and D₉	18	2	C9xD9	162,3
S₃xC₂₇	Direct product of C₂₇ and S₃	54	2	S3xC27	162,8
C₃xD₂₇	Direct product of C₃ and D₂₇	54	2	C3xD27	162,7
C₂xC₂₇:C₃	Direct product of C₂ and C₂₇:C₃	54	3	C2xC27:C3	162,27
C₂xC₉:C₉	Direct product of C₂ and C₉:C₉	162		C2xC9:C9	162,25

Groups of order 163

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

Groups of order 164

		d	ρ	Label	ID
C₁₆₄	Cyclic group	164	1	C164	164,2
D₈₂	Dihedral group; = C₂xD₄₁	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
C₂xC₈₂	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
C₃xC₁₁:C₅	Direct product of C₃ and C₁₁:C₅	33	5	C3xC11:C5	165,1

Groups of order 166

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

Groups of order 167

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

Groups of order 168

		d	ρ	Label	ID
C₁₆₈	Cyclic group	168	1	C168	168,6
D₈₄	Dihedral group	84	2+	D84	168,36
Dic₄₂	Dicyclic group; = C₂₁ :₂ Q₈	168	2-	Dic42	168,34
C₄:F₇	The semidirect product of C₄ and F₇ acting via F₇/C₇:C₃=C₂	28	6+	C4:F7	168,9
C₇:C₂₄	The semidirect product of C₇ and C₂₄ acting via C₂₄/C₄=C₆	56	6	C7:C24	168,1
C₂₁:C₈	1^st semidirect product of C₂₁ and C₈ acting via C₈/C₄=C₂	168	2	C21:C8	168,5
C₄.F₇	The non-split extension by C₄ of F₇ acting via F₇/C₇:C₃=C₂	56	6-	C4.F7	168,7
C₂xC₈₄	Abelian group of type [2,84]	168		C2xC84	168,39
C₄xF₇	Direct product of C₄ and F₇	28	6	C4xF7	168,8
S₃xC₂₈	Direct product of C₂₈ and S₃	84	2	S3xC28	168,30
C₁₂xD₇	Direct product of C₁₂ and D₇	84	2	C12xD7	168,25
C₃xD₂₈	Direct product of C₃ and D₂₈	84	2	C3xD28	168,26
C₇xD₁₂	Direct product of C₇ and D₁₂	84	2	C7xD12	168,31
C₄xD₂₁	Direct product of C₄ and D₂₁	84	2	C4xD21	168,35
D₄xC₂₁	Direct product of C₂₁ and D₄	84	2	D4xC21	168,40
Q₈xC₂₁	Direct product of C₂₁ and Q₈	168	2	Q8xC21	168,41
C₆xDic₇	Direct product of C₆ and Dic₇	168		C6xDic7	168,27
C₇xDic₆	Direct product of C₇ and Dic₆	168	2	C7xDic6	168,29
C₃xDic₁₄	Direct product of C₃ and Dic₁₄	168	2	C3xDic14	168,24
Dic₃xC₁₄	Direct product of C₁₄ and Dic₃	168		Dic3xC14	168,32
C₂xDic₂₁	Direct product of C₂ and Dic₂₁	168		C2xDic21	168,37
D₄xC₇:C₃	Direct product of D₄ and C₇:C₃	28	6	D4xC7:C3	168,20
C₈xC₇:C₃	Direct product of C₈ and C₇:C₃	56	3	C8xC7:C3	168,2
Q₈xC₇:C₃	Direct product of Q₈ and C₇:C₃	56	6	Q8xC7:C3	168,21
C₂xC₇:C₁₂	Direct product of C₂ and C₇:C₁₂	56		C2xC7:C12	168,10
C₇xC₃:C₈	Direct product of C₇ and C₃:C₈	168	2	C7xC3:C8	168,3
C₃xC₇:C₈	Direct product of C₃ and C₇:C₈	168	2	C3xC7:C8	168,4
C₂xC₄xC₇:C₃	Direct product of C₂xC₄ 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
D₅xC₁₇	Direct product of C₁₇ and D₅	85	2	D5xC17	170,1
C₅xD₁₇	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
C₃xC₅₇	Abelian group of type [3,57]	171		C3xC57	171,5
C₃xC₁₉: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; = C₂xD₄₃	86	2+	D86	172,3
Dic₄₃	Dicyclic group; = C₄₃ :C₄	172	2-	Dic43	172,1
C₂xC₈₆	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
S₃xC₂₉	Direct product of C₂₉ and S₃	87	2	S3xC29	174,1
C₃xD₂₉	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
C₅xC₃₅	Abelian group of type [5,35]	175		C5xC35	175,2

Groups of order 176

		d	ρ	Label	ID
C₁₇₆	Cyclic group	176	1	C176	176,2
D₈₈	Dihedral group	88	2+	D88	176,6
Dic₄₄	Dicyclic group; = C₁₁ :₁ Q₁₆	176	2-	Dic44	176,7
C₈₈:C₂	4^th semidirect product of C₈₈ and C₂ acting faithfully	88	2	C88:C2	176,4
C₈:D₁₁	2^nd semidirect product of C₈ and D₁₁ acting via D₁₁/C₁₁=C₂	88	2	C8:D11	176,5
C₁₁:C₁₆	The semidirect product of C₁₁ and C₁₆ acting via C₁₆/C₈=C₂	176	2	C11:C16	176,1
C₄₄:C₄	1^st semidirect product of C₄₄ and C₄ acting via C₄/C₂=C₂	176		C44:C4	176,12
C₄₄.C₄	1^st non-split extension by C₄₄ of C₄ acting via C₄/C₂=C₂	88	2	C44.C4	176,9
C₄xC₄₄	Abelian group of type [4,44]	176		C4xC44	176,19
C₂xC₈₈	Abelian group of type [2,88]	176		C2xC88	176,22
C₈xD₁₁	Direct product of C₈ and D₁₁	88	2	C8xD11	176,3
C₁₁xD₈	Direct product of C₁₁ and D₈	88	2	C11xD8	176,24
C₁₁xSD₁₆	Direct product of C₁₁ and SD₁₆	88	2	C11xSD16	176,25
C₁₁xM₄(2)	Direct product of C₁₁ and M₄(2)	88	2	C11xM4(2)	176,23
C₁₁xQ₁₆	Direct product of C₁₁ and Q₁₆	176	2	C11xQ16	176,26
C₄xDic₁₁	Direct product of C₄ and Dic₁₁	176		C4xDic11	176,10
C₂xC₁₁:C₈	Direct product of C₂ and C₁₁:C₈	176		C2xC11:C8	176,8
C₁₁xC₄:C₄	Direct product of C₁₁ and C₄:C₄	176		C11xC4:C4	176,21

Groups of order 177

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

Groups of order 178

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

Groups of order 179

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

Groups of order 180

		d	ρ	Label	ID
C₁₈₀	Cyclic group	180	1	C180	180,4
D₉₀	Dihedral group; = C₂xD₄₅	90	2+	D90	180,11
Dic₄₅	Dicyclic group; = C₉ :Dic₅	180	2-	Dic45	180,3
C₉:F₅	The semidirect product of C₉ and F₅ acting via F₅/D₅=C₂	45	4	C9:F5	180,6
C₂xC₉₀	Abelian group of type [2,90]	180		C2xC90	180,12
C₃xC₆₀	Abelian group of type [3,60]	180		C3xC60	180,18
C₆xC₃₀	Abelian group of type [6,30]	180		C6xC30	180,37
C₉xF₅	Direct product of C₉ and F₅	45	4	C9xF5	180,5
C₃²xF₅	Direct product of C₃² and F₅	45		C3^2xF5	180,20
S₃xC₃₀	Direct product of C₃₀ and S₃	60	2	S3xC30	180,33
C₆xD₁₅	Direct product of C₆ and D₁₅	60	2	C6xD15	180,34
Dic₃xC₁₅	Direct product of C₁₅ and Dic₃	60	2	Dic3xC15	180,14
C₃xDic₁₅	Direct product of C₃ and Dic₁₅	60	2	C3xDic15	180,15
D₅xC₁₈	Direct product of C₁₈ and D₅	90	2	D5xC18	180,9
C₁₀xD₉	Direct product of C₁₀ and D₉	90	2	C10xD9	180,10
C₅xDic₉	Direct product of C₅ and Dic₉	180	2	C5xDic9	180,1
C₉xDic₅	Direct product of C₉ and Dic₅	180	2	C9xDic5	180,2
C₃²xDic₅	Direct product of C₃² and Dic₅	180		C3^2xDic5	180,13
C₃xC₃:F₅	Direct product of C₃ and C₃:F₅	30	4	C3xC3:F5	180,21
D₅xC₃xC₆	Direct product of C₃xC₆ and D₅	90		D5xC3xC6	180,32

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
C₁₃xD₇	Direct product of C₁₃ and D₇	91	2	C13xD7	182,1
C₇xD₁₃	Direct product of C₇ and D₁₃	91	2	C7xD13	182,2

Groups of order 183

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

Groups of order 184

		d	ρ	Label	ID
C₁₈₄	Cyclic group	184	1	C184	184,2
D₉₂	Dihedral group	92	2+	D92	184,5
Dic₄₆	Dicyclic group; = C₂₃ :Q₈	184	2-	Dic46	184,3
C₂₃:C₈	The semidirect product of C₂₃ and C₈ acting via C₈/C₄=C₂	184	2	C23:C8	184,1
C₂xC₉₂	Abelian group of type [2,92]	184		C2xC92	184,8
C₄xD₂₃	Direct product of C₄ and D₂₃	92	2	C4xD23	184,4
D₄xC₂₃	Direct product of C₂₃ and D₄	92	2	D4xC23	184,9
Q₈xC₂₃	Direct product of C₂₃ and Q₈	184	2	Q8xC23	184,10
C₂xDic₂₃	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
S₃xC₃₁	Direct product of C₃₁ and S₃	93	2	S3xC31	186,3
C₃xD₃₁	Direct product of C₃ and D₃₁	93	2	C3xD31	186,4
C₂xC₃₁: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; = C₂xD₄₇	94	2+	D94	188,3
Dic₄₇	Dicyclic group; = C₄₇ :C₄	188	2-	Dic47	188,1
C₂xC₉₄	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
C₆₃:C₃	2^nd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:C3	189,4
C₆₃:₃C₃	3^rd semidirect product of C₆₃ and C₃ acting faithfully	63	3	C63:3C3	189,5
C₇:C₂₇	The semidirect product of C₇ and C₂₇ acting via C₂₇/C₉=C₃	189	3	C7:C27	189,1
C₃xC₆₃	Abelian group of type [3,63]	189		C3xC63	189,9
C₇x3_-¹⁺²	Direct product of C₇ and 3_-¹⁺²	63	3	C7xES-(3,1)	189,11
C₉xC₇:C₃	Direct product of C₉ and C₇:C₃	63	3	C9xC7:C3	189,3
C₃xC₇: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
D₅xC₁₉	Direct product of C₁₉ and D₅	95	2	D5xC19	190,1
C₅xD₁₉	Direct product of C₅ and D₁₉	95	2	C5xD19	190,2

Groups of order 191

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

Groups of order 192

		d	ρ	Label	ID
C₁₉₂	Cyclic group	192	1	C192	192,2
D₉₆	Dihedral group	96	2+	D96	192,7
Dic₄₈	Dicyclic group; = C₃ :₁ Q₆₄	192	2-	Dic48	192,9
C₄₈:C₄	2^nd semidirect product of C₄₈ and C₄ acting faithfully	48	4	C48:C4	192,71
C₉₆:C₂	6^th semidirect product of C₉₆ and C₂ acting faithfully	96	2	C96:C2	192,6
C₃₂:S₃	2^nd semidirect product of C₃₂ and S₃ acting via S₃/C₃=C₂	96	2	C32:S3	192,8
C₃:M₆(2)	The semidirect product of C₃ and M₆(2) acting via M₆(2)/C₂xC₁₆=C₂	96	2	C3:M6(2)	192,58
C₃:C₆₄	The semidirect product of C₃ and C₆₄ acting via C₆₄/C₃₂=C₂	192	2	C3:C64	192,1
C₂₄:C₈	5^th semidirect product of C₂₄ and C₈ acting via C₈/C₄=C₂	192		C24:C8	192,14
C₂₄:₂C₈	2^nd semidirect product of C₂₄ and C₈ acting via C₈/C₄=C₂	192		C24:2C8	192,16
C₂₄:₁C₈	1^st semidirect product of C₂₄ and C₈ acting via C₈/C₄=C₂	192		C24:1C8	192,17
C₄₈:₅C₄	1^st semidirect product of C₄₈ and C₄ acting via C₄/C₂=C₂	192		C48:5C4	192,63
C₄₈:₆C₄	2^nd semidirect product of C₄₈ and C₄ acting via C₄/C₂=C₂	192		C48:6C4	192,64
C₁₂:C₁₆	1^st semidirect product of C₁₂ and C₁₆ acting via C₁₆/C₈=C₂	192		C12:C16	192,21
C₄₈:₁₀C₄	6^th semidirect product of C₄₈ and C₄ acting via C₄/C₂=C₂	192		C48:10C4	192,61
C₂₄.₁C₈	1^st non-split extension by C₂₄ of C₈ acting via C₈/C₄=C₂	48	2	C24.1C8	192,22
C₂₄.Q₈	1^st non-split extension by C₂₄ of Q₈ acting via Q₈/C₂=C₂²	48	4	C24.Q8	192,72
C₄₈.C₄	1^st non-split extension by C₄₈ of C₄ acting via C₄/C₂=C₂	96	2	C48.C4	192,65
C₂₄.C₈	4^th non-split extension by C₂₄ of C₈ acting via C₈/C₄=C₂	192		C24.C8	192,20
C₈xC₂₄	Abelian group of type [8,24]	192		C8xC24	192,127
C₄xC₄₈	Abelian group of type [4,48]	192		C4xC48	192,151
C₂xC₉₆	Abelian group of type [2,96]	192		C2xC96	192,175
S₃xC₃₂	Direct product of C₃₂ and S₃	96	2	S3xC32	192,5
C₃xD₃₂	Direct product of C₃ and D₃₂	96	2	C3xD32	192,177
C₃xSD₆₄	Direct product of C₃ and SD₆₄	96	2	C3xSD64	192,178
C₃xM₆(2)	Direct product of C₃ and M₆(2)	96	2	C3xM6(2)	192,176
C₃xQ₆₄	Direct product of C₃ and Q₆₄	192	2	C3xQ64	192,179
Dic₃xC₁₆	Direct product of C₁₆ and Dic₃	192		Dic3xC16	192,59
C₃xC₁₆:C₄	Direct product of C₃ and C₁₆:C₄	48	4	C3xC16:C4	192,153
C₃xC₈.Q₈	Direct product of C₃ and C₈.Q₈	48	4	C3xC8.Q8	192,171
C₃xC₈.C₈	Direct product of C₃ and C₈.C₈	48	2	C3xC8.C8	192,170
C₃xC₈.₄Q₈	Direct product of C₃ and C₈.₄Q₈	96	2	C3xC8.4Q8	192,174
C₈xC₃:C₈	Direct product of C₈ and C₃:C₈	192		C8xC3:C8	192,12
C₄xC₃:C₁₆	Direct product of C₄ and C₃:C₁₆	192		C4xC3:C16	192,19
C₂xC₃:C₃₂	Direct product of C₂ and C₃:C₃₂	192		C2xC3:C32	192,57
C₃xC₄:C₁₆	Direct product of C₃ and C₄:C₁₆	192		C3xC4:C16	192,169
C₃xC₈:C₈	Direct product of C₃ and C₈:C₈	192		C3xC8:C8	192,128
C₃xC₈:₂C₈	Direct product of C₃ and C₈:₂C₈	192		C3xC8:2C8	192,140
C₃xC₈:₁C₈	Direct product of C₃ and C₈:₁C₈	192		C3xC8:1C8	192,141
C₃xC₁₆:₅C₄	Direct product of C₃ and C₁₆:₅C₄	192		C3xC16:5C4	192,152
C₃xC₁₆:₃C₄	Direct product of C₃ and C₁₆:₃C₄	192		C3xC16:3C4	192,172
C₃xC₁₆:₄C₄	Direct product of C₃ and C₁₆:₄C₄	192		C3xC16:4C4	192,173

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
C₅xC₁₃: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; = C₂xD₄₉	98	2+	D98	196,3
Dic₄₉	Dicyclic group; = C₄₉ :C₄	196	2-	Dic49	196,1
C₁₄²	Abelian group of type [14,14]	196		C14^2	196,12
C₂xC₉₈	Abelian group of type [2,98]	196		C2xC98	196,4
C₇xC₂₈	Abelian group of type [7,28]	196		C7xC28	196,7
D₇xC₁₄	Direct product of C₁₄ and D₇	28	2	D7xC14	196,10
C₇xDic₇	Direct product of C₇ and Dic₇	28	2	C7xDic7	196,5

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
C₃xC₆₆	Abelian group of type [3,66]	198		C3xC66	198,10
S₃xC₃₃	Direct product of C₃₃ and S₃	66	2	S3xC33	198,6
C₃xD₃₃	Direct product of C₃ and D₃₃	66	2	C3xD33	198,7
C₁₁xD₉	Direct product of C₁₁ and D₉	99	2	C11xD9	198,1
C₉xD₁₁	Direct product of C₉ and D₁₁	99	2	C9xD11	198,2
C₃²xD₁₁	Direct product of C₃² and D₁₁	99		C3^2xD11	198,5

Groups of order 199

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

Groups of order 200

		d	ρ	Label	ID
C₂₀₀	Cyclic group	200	1	C200	200,2
D₁₀₀	Dihedral group	100	2+	D100	200,6
Dic₅₀	Dicyclic group; = C₂₅ :Q₈	200	2-	Dic50	200,4
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
C₅xC₄₀	Abelian group of type [5,40]	200		C5xC40	200,17
C₂xC₁₀₀	Abelian group of type [2,100]	200		C2xC100	200,9
C₁₀xC₂₀	Abelian group of type [10,20]	200		C10xC20	200,37
D₅xC₂₀	Direct product of C₂₀ and D₅	40	2	D5xC20	200,28
C₅xD₂₀	Direct product of C₅ and D₂₀	40	2	C5xD20	200,29
C₁₀xF₅	Direct product of C₁₀ and F₅	40	4	C10xF5	200,45
C₅xDic₁₀	Direct product of C₅ and Dic₁₀	40	2	C5xDic10	200,27
C₁₀xDic₅	Direct product of C₁₀ and Dic₅	40		C10xDic5	200,30
C₄xD₂₅	Direct product of C₄ and D₂₅	100	2	C4xD25	200,5
D₄xC₂₅	Direct product of C₂₅ and D₄	100	2	D4xC25	200,10
D₄xC₅²	Direct product of C₅² and D₄	100		D4xC5^2	200,38
Q₈xC₂₅	Direct product of C₂₅ and Q₈	200	2	Q8xC25	200,11
Q₈xC₅²	Direct product of C₅² and Q₈	200		Q8xC5^2	200,39
C₂xDic₂₅	Direct product of C₂ and Dic₂₅	200		C2xDic25	200,7
C₅xC₅:C₈	Direct product of C₅ and C₅:C₈	40	4	C5xC5:C8	200,18
C₅xC₅:₂C₈	Direct product of C₅ and C₅:₂C₈	40	2	C5xC5:2C8	200,15
C₂xC₂₅:C₄	Direct product of C₂ and C₂₅:C₄	50	4+	C2xC25:C4	200,12

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; = C₂xD₅₁	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
C₂xC₁₀₂	Abelian group of type [2,102]	204		C2xC102	204,12
S₃xC₃₄	Direct product of C₃₄ and S₃	102	2	S3xC34	204,10
C₆xD₁₇	Direct product of C₆ and D₁₇	102	2	C6xD17	204,9
Dic₃xC₁₇	Direct product of C₁₇ and Dic₃	204	2	Dic3xC17	204,1
C₃xDic₁₇	Direct product of C₃ and Dic₁₇	204	2	C3xDic17	204,2
C₃xC₁₇: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
C₃xC₆₉	Abelian group of type [3,69]	207		C3xC69	207,2

Groups of order 208

		d	ρ	Label	ID
C₂₀₈	Cyclic group	208	1	C208	208,2
D₁₀₄	Dihedral group	104	2+	D104	208,7
Dic₅₂	Dicyclic group; = C₁₃ :₁ Q₁₆	208	2-	Dic52	208,8
C₅₂:C₄	1^st semidirect product of C₅₂ and C₄ acting faithfully	52	4	C52:C4	208,31
D₁₃:C₈	The semidirect product of D₁₃ and C₈ acting via C₈/C₄=C₂	104	4	D13:C8	208,28
C₈:D₁₃	3^rd semidirect product of C₈ and D₁₃ acting via D₁₃/C₁₃=C₂	104	2	C8:D13	208,5
C₁₀₄:C₂	2^nd semidirect product of C₁₀₄ and C₂ acting faithfully	104	2	C104:C2	208,6
C₁₃:C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₄=C₄	208	4	C13:C16	208,3
C₅₂:₃C₄	1^st semidirect product of C₅₂ and C₄ acting via C₄/C₂=C₂	208		C52:3C4	208,13
C₁₃:₂C₁₆	The semidirect product of C₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	2	C13:2C16	208,1
C₅₂.₄C₄	1^st non-split extension by C₅₂ of C₄ acting via C₄/C₂=C₂	104	2	C52.4C4	208,10
C₅₂.C₄	1^st non-split extension by C₅₂ of C₄ acting faithfully	104	4	C52.C4	208,29
C₄xC₅₂	Abelian group of type [4,52]	208		C4xC52	208,20
C₂xC₁₀₄	Abelian group of type [2,104]	208		C2xC104	208,23
C₈xD₁₃	Direct product of C₈ and D₁₃	104	2	C8xD13	208,4
C₁₃xD₈	Direct product of C₁₃ and D₈	104	2	C13xD8	208,25
C₁₃xSD₁₆	Direct product of C₁₃ and SD₁₆	104	2	C13xSD16	208,26
C₁₃xM₄(2)	Direct product of C₁₃ and M₄(2)	104	2	C13xM4(2)	208,24
C₁₃xQ₁₆	Direct product of C₁₃ and Q₁₆	208	2	C13xQ16	208,27
C₄xDic₁₃	Direct product of C₄ and Dic₁₃	208		C4xDic13	208,11
C₄xC₁₃:C₄	Direct product of C₄ and C₁₃:C₄	52	4	C4xC13:C4	208,30
C₂xC₁₃:C₈	Direct product of C₂ and C₁₃:C₈	208		C2xC13:C8	208,32
C₁₃xC₄:C₄	Direct product of C₁₃ and C₄:C₄	208		C13xC4:C4	208,22
C₂xC₁₃:₂C₈	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
C₅xF₇	Direct product of C₅ and F₇	35	6	C5xF7	210,1
S₃xC₃₅	Direct product of C₃₅ and S₃	105	2	S3xC35	210,8
D₇xC₁₅	Direct product of C₁₅ and D₇	105	2	D7xC15	210,5
D₅xC₂₁	Direct product of C₂₁ and D₅	105	2	D5xC21	210,6
C₃xD₃₅	Direct product of C₃ and D₃₅	105	2	C3xD35	210,7
C₅xD₂₁	Direct product of C₅ and D₂₁	105	2	C5xD21	210,9
C₇xD₁₅	Direct product of C₇ and D₁₅	105	2	C7xD15	210,10
D₅xC₇:C₃	Direct product of D₅ and C₇:C₃	35	6	D5xC7:C3	210,2
C₁₀xC₇: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; = C₂xD₅₃	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
C₂xC₁₀₆	Abelian group of type [2,106]	212		C2xC106	212,5

Groups of order 213

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

Groups of order 214

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

Groups of order 215

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

Groups of order 216

		d	ρ	Label	ID
C₂₁₆	Cyclic group	216	1	C216	216,2
D₁₀₈	Dihedral group	108	2+	D108	216,6
Dic₅₄	Dicyclic group; = C₂₇ :Q₈	216	2-	Dic54	216,4
D₃₆:C₃	The semidirect product of D₃₆ and C₃ acting faithfully	36	6+	D36:C3	216,54
C₉:C₂₄	The semidirect product of C₉ and C₂₄ acting via C₂₄/C₄=C₆	72	6	C9:C24	216,15
C₂₇:C₈	The semidirect product of C₂₇ and C₈ acting via C₈/C₄=C₂	216	2	C27:C8	216,1
C₃₆.C₆	1^st non-split extension by C₃₆ of C₆ acting faithfully	72	6-	C36.C6	216,52
C₃xC₇₂	Abelian group of type [3,72]	216		C3xC72	216,18
C₆xC₃₆	Abelian group of type [6,36]	216		C6xC36	216,73
C₂xC₁₀₈	Abelian group of type [2,108]	216		C2xC108	216,9
D₄x3_-¹⁺²	Direct product of D₄ and 3_-¹⁺²	36	6	D4xES-(3,1)	216,78
S₃xC₃₆	Direct product of C₃₆ and S₃	72	2	S3xC36	216,47
C₁₂xD₉	Direct product of C₁₂ and D₉	72	2	C12xD9	216,45
C₃xD₃₆	Direct product of C₃ and D₃₆	72	2	C3xD36	216,46
C₉xD₁₂	Direct product of C₉ and D₁₂	72	2	C9xD12	216,48
C₉xDic₆	Direct product of C₉ and Dic₆	72	2	C9xDic6	216,44
C₆xDic₉	Direct product of C₆ and Dic₉	72		C6xDic9	216,55
C₃xDic₁₈	Direct product of C₃ and Dic₁₈	72	2	C3xDic18	216,43
Dic₃xC₁₈	Direct product of C₁₈ and Dic₃	72		Dic3xC18	216,56
C₈x3_-¹⁺²	Direct product of C₈ and 3_-¹⁺²	72	3	C8xES-(3,1)	216,20
Q₈x3_-¹⁺²	Direct product of Q₈ and 3_-¹⁺²	72	6	Q8xES-(3,1)	216,81
C₄xD₂₇	Direct product of C₄ and D₂₇	108	2	C4xD27	216,5
D₄xC₂₇	Direct product of C₂₇ and D₄	108	2	D4xC27	216,10
Q₈xC₂₇	Direct product of C₂₇ and Q₈	216	2	Q8xC27	216,11
C₂xDic₂₇	Direct product of C₂ and Dic₂₇	216		C2xDic27	216,7
C₄xC₉:C₆	Direct product of C₄ and C₉:C₆	36	6	C4xC9:C6	216,53
C₃xC₉:C₈	Direct product of C₃ and C₉:C₈	72	2	C3xC9:C8	216,12
C₉xC₃:C₈	Direct product of C₉ and C₃:C₈	72	2	C9xC3:C8	216,13
C₂xC₉:C₁₂	Direct product of C₂ and C₉:C₁₂	72		C2xC9:C12	216,61
C₂xC₄x3_-¹⁺²	Direct product of C₂xC₄ and 3_-¹⁺²	72		C2xC4xES-(3,1)	216,75
D₄xC₃xC₉	Direct product of C₃xC₉ and D₄	108		D4xC3xC9	216,76
Q₈xC₃xC₉	Direct product of C₃xC₉ and Q₈	216		Q8xC3xC9	216,79

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; = C₂xD₅₅	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
C₂xC₁₁₀	Abelian group of type [2,110]	220		C2xC110	220,15
C₂xF₁₁	Direct product of C₂ and F₁₁; = Aut(D₂₂) = Hol(C₂₂)	22	10+	C2xF11	220,7
C₁₁xF₅	Direct product of C₁₁ and F₅	55	4	C11xF5	220,9
D₅xC₂₂	Direct product of C₂₂ and D₅	110	2	D5xC22	220,13
C₁₀xD₁₁	Direct product of C₁₀ and D₁₁	110	2	C10xD11	220,12
C₁₁xDic₅	Direct product of C₁₁ and Dic₅	220	2	C11xDic5	220,3
C₅xDic₁₁	Direct product of C₅ and Dic₁₁	220	2	C5xDic11	220,4
C₄xC₁₁:C₅	Direct product of C₄ and C₁₁:C₅	44	5	C4xC11:C5	220,2
C₂²xC₁₁: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
S₃xC₃₇	Direct product of C₃₇ and S₃	111	2	S3xC37	222,3
C₃xD₃₇	Direct product of C₃ and D₃₇	111	2	C3xD37	222,4
C₂xC₃₇:C₃	Direct product of C₂ and C₃₇:C₃	74	3	C2xC37:C3	222,2

Groups of order 223

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

Groups of order 224

		d	ρ	Label	ID
C₂₂₄	Cyclic group	224	1	C224	224,2
D₁₁₂	Dihedral group	112	2+	D112	224,5
Dic₅₆	Dicyclic group; = C₇ :₁ Q₃₂	224	2-	Dic56	224,7
C₁₆:D₇	3^rd semidirect product of C₁₆ and D₇ acting via D₇/C₇=C₂	112	2	C16:D7	224,4
C₁₁₂:C₂	2^nd semidirect product of C₁₁₂ and C₂ acting faithfully	112	2	C112:C2	224,6
C₇:C₃₂	The semidirect product of C₇ and C₃₂ acting via C₃₂/C₁₆=C₂	224	2	C7:C32	224,1
C₂₈:C₈	1^st semidirect product of C₂₈ and C₈ acting via C₈/C₄=C₂	224		C28:C8	224,10
C₅₆:C₄	4^th semidirect product of C₅₆ and C₄ acting via C₄/C₂=C₂	224		C56:C4	224,21
C₅₆:₁C₄	1^st semidirect product of C₅₆ and C₄ acting via C₄/C₂=C₂	224		C56:1C4	224,24
C₈:Dic₇	2^nd semidirect product of C₈ and Dic₇ acting via Dic₇/C₁₄=C₂	224		C8:Dic7	224,23
C₂₈.C₈	1^st non-split extension by C₂₈ of C₈ acting via C₈/C₄=C₂	112	2	C28.C8	224,18
C₅₆.C₄	1^st non-split extension by C₅₆ of C₄ acting via C₄/C₂=C₂	112	2	C56.C4	224,25
C₄xC₅₆	Abelian group of type [4,56]	224		C4xC56	224,45
C₂xC₁₁₂	Abelian group of type [2,112]	224		C2xC112	224,58
D₇xC₁₆	Direct product of C₁₆ and D₇	112	2	D7xC16	224,3
C₇xD₁₆	Direct product of C₇ and D₁₆	112	2	C7xD16	224,60
C₇xSD₃₂	Direct product of C₇ and SD₃₂	112	2	C7xSD32	224,61
C₇xM₅(2)	Direct product of C₇ and M₅(2)	112	2	C7xM5(2)	224,59
C₇xQ₃₂	Direct product of C₇ and Q₃₂	224	2	C7xQ32	224,62
C₈xDic₇	Direct product of C₈ and Dic₇	224		C8xDic7	224,19
C₇xC₈.C₄	Direct product of C₇ and C₈.C₄	112	2	C7xC8.C4	224,57
C₄xC₇:C₈	Direct product of C₄ and C₇:C₈	224		C4xC7:C8	224,8
C₇xC₄:C₈	Direct product of C₇ and C₄:C₈	224		C7xC4:C8	224,54
C₂xC₇:C₁₆	Direct product of C₂ and C₇:C₁₆	224		C2xC7:C16	224,17
C₇xC₈:C₄	Direct product of C₇ and C₈:C₄	224		C7xC8:C4	224,46
C₇xC₂.D₈	Direct product of C₇ and C₂.D₈	224		C7xC2.D8	224,56
C₇xC₄.Q₈	Direct product of C₇ and C₄.Q₈	224		C7xC4.Q8	224,55

Groups of order 225

		d	ρ	Label	ID
C₂₂₅	Cyclic group	225	1	C225	225,1
C₁₅²	Abelian group of type [15,15]	225		C15^2	225,6
C₃xC₇₅	Abelian group of type [3,75]	225		C3xC75	225,2
C₅xC₄₅	Abelian group of type [5,45]	225		C5xC45	225,4

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; = C₂xD₅₇	114	2+	D114	228,14
Dic₅₇	Dicyclic group; = C₅₇ :₁ C₄	228	2-	Dic57	228,5
C₁₉:C₁₂	The semidirect product of C₁₉ and C₁₂ acting via C₁₂/C₂=C₆	76	6-	C19:C12	228,1
C₂xC₁₁₄	Abelian group of type [2,114]	228		C2xC114	228,15
S₃xC₃₈	Direct product of C₃₈ and S₃	114	2	S3xC38	228,13
C₆xD₁₉	Direct product of C₆ and D₁₉	114	2	C6xD19	228,12
Dic₃xC₁₉	Direct product of C₁₉ and Dic₃	228	2	Dic3xC19	228,3
C₃xDic₁₉	Direct product of C₃ and Dic₁₉	228	2	C3xDic19	228,4
C₂xC₁₉:C₆	Direct product of C₂ and C₁₉:C₆	38	6+	C2xC19:C6	228,7
C₄xC₁₉:C₃	Direct product of C₄ and C₁₉:C₃	76	3	C4xC19:C3	228,2
C₂²xC₁₉: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
D₅xC₂₃	Direct product of C₂₃ and D₅	115	2	D5xC23	230,1
C₅xD₂₃	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
C₁₁xC₇:C₃	Direct product of C₁₁ and C₇:C₃	77	3	C11xC7:C3	231,1

Groups of order 232

		d	ρ	Label	ID
C₂₃₂	Cyclic group	232	1	C232	232,2
D₁₁₆	Dihedral group	116	2+	D116	232,6
Dic₅₈	Dicyclic group; = C₂₉ :Q₈	232	2-	Dic58	232,4
C₂₉: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
C₂xC₁₁₆	Abelian group of type [2,116]	232		C2xC116	232,9
C₄xD₂₉	Direct product of C₄ and D₂₉	116	2	C4xD29	232,5
D₄xC₂₉	Direct product of C₂₉ and D₄	116	2	D4xC29	232,10
Q₈xC₂₉	Direct product of C₂₉ and Q₈	232	2	Q8xC29	232,11
C₂xDic₂₉	Direct product of C₂ and Dic₂₉	232		C2xDic29	232,7
C₂xC₂₉: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
C₃xC₇₈	Abelian group of type [3,78]	234		C3xC78	234,16
S₃xC₃₉	Direct product of C₃₉ and S₃	78	2	S3xC39	234,12
C₃xD₃₉	Direct product of C₃ and D₃₉	78	2	C3xD39	234,13
C₁₃xD₉	Direct product of C₁₃ and D₉	117	2	C13xD9	234,3
C₉xD₁₃	Direct product of C₉ and D₁₃	117	2	C9xD13	234,4
C₃²xD₁₃	Direct product of C₃² and D₁₃	117		C3^2xD13	234,11
C₃xC₁₃:C₆	Direct product of C₃ and C₁₃:C₆	39	6	C3xC13:C6	234,7
S₃xC₁₃:C₃	Direct product of S₃ and C₁₃:C₃	39	6	S3xC13:C3	234,8
C₆xC₁₃:C₃	Direct product of C₆ and C₁₃:C₃	78	3	C6xC13:C3	234,10
C₂xC₁₃: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; = C₂xD₅₉	118	2+	D118	236,3
Dic₅₉	Dicyclic group; = C₅₉ :C₄	236	2-	Dic59	236,1
C₂xC₁₁₈	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
D₇xC₁₇	Direct product of C₁₇ and D₇	119	2	D7xC17	238,1
C₇xD₁₇	Direct product of C₇ and D₁₇	119	2	C7xD17	238,2

Groups of order 239

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

Groups of order 240

		d	ρ	Label	ID
C₂₄₀	Cyclic group	240	1	C240	240,4
D₁₂₀	Dihedral group	120	2+	D120	240,68
Dic₆₀	Dicyclic group; = C₁₅ :₄ Q₁₆	240	2-	Dic60	240,69
C₆₀:C₄	1^st semidirect product of C₆₀ and C₄ acting faithfully	60	4	C60:C4	240,121
C₄₀:S₃	4^th semidirect product of C₄₀ and S₃ acting via S₃/C₃=C₂	120	2	C40:S3	240,66
C₂₄:D₅	2^nd semidirect product of C₂₄ and D₅ acting via D₅/C₅=C₂	120	2	C24:D5	240,67
C₆₀:₅C₄	1^st semidirect product of C₆₀ and C₄ acting via C₄/C₂=C₂	240		C60:5C4	240,74
C₁₅:₃C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₈=C₂	240	2	C15:3C16	240,3
C₁₅:C₁₆	1^st semidirect product of C₁₅ and C₁₆ acting via C₁₆/C₄=C₄	240	4	C15:C16	240,6
C₆₀.₇C₄	1^st non-split extension by C₆₀ of C₄ acting via C₄/C₂=C₂	120	2	C60.7C4	240,71
C₆₀.C₄	3^rd non-split extension by C₆₀ of C₄ acting faithfully	120	4	C60.C4	240,118
C₁₂.F₅	1^st non-split extension by C₁₂ of F₅ acting via F₅/D₅=C₂	120	4	C12.F5	240,119
C₄xC₆₀	Abelian group of type [4,60]	240		C4xC60	240,81
C₂xC₁₂₀	Abelian group of type [2,120]	240		C2xC120	240,84
C₁₂xF₅	Direct product of C₁₂ and F₅	60	4	C12xF5	240,113
S₃xC₄₀	Direct product of C₄₀ and S₃	120	2	S3xC40	240,49
D₅xC₂₄	Direct product of C₂₄ and D₅	120	2	D5xC24	240,33
C₃xD₄₀	Direct product of C₃ and D₄₀	120	2	C3xD40	240,36
C₅xD₂₄	Direct product of C₅ and D₂₄	120	2	C5xD24	240,52
C₈xD₁₅	Direct product of C₈ and D₁₅	120	2	C8xD15	240,65
C₁₅xD₈	Direct product of C₁₅ and D₈	120	2	C15xD8	240,86
C₁₅xSD₁₆	Direct product of C₁₅ and SD₁₆	120	2	C15xSD16	240,87
C₁₅xM₄(2)	Direct product of C₁₅ and M₄(2)	120	2	C15xM4(2)	240,85
C₁₅xQ₁₆	Direct product of C₁₅ and Q₁₆	240	2	C15xQ16	240,88
C₃xDic₂₀	Direct product of C₃ and Dic₂₀	240	2	C3xDic20	240,37
C₁₂xDic₅	Direct product of C₁₂ and Dic₅	240		C12xDic5	240,40
C₅xDic₁₂	Direct product of C₅ and Dic₁₂	240	2	C5xDic12	240,53
Dic₃xC₂₀	Direct product of C₂₀ and Dic₃	240		Dic3xC20	240,56
C₄xDic₁₅	Direct product of C₄ and Dic₁₅	240		C4xDic15	240,72
C₄xC₃:F₅	Direct product of C₄ and C₃:F₅	60	4	C4xC3:F5	240,120
C₃xC₄:F₅	Direct product of C₃ and C₄:F₅	60	4	C3xC4:F5	240,114
C₅xC₈:S₃	Direct product of C₅ and C₈:S₃	120	2	C5xC8:S3	240,50
C₃xD₅:C₈	Direct product of C₃ and D₅:C₈	120	4	C3xD5:C8	240,111
C₃xC₈:D₅	Direct product of C₃ and C₈:D₅	120	2	C3xC8:D5	240,34
C₃xC₄₀:C₂	Direct product of C₃ and C₄₀:C₂	120	2	C3xC40:C2	240,35
C₅xC₂₄:C₂	Direct product of C₅ and C₂₄:C₂	120	2	C5xC24:C2	240,51
C₃xC₄.F₅	Direct product of C₃ and C₄.F₅	120	4	C3xC4.F5	240,112
C₃xC₄.Dic₅	Direct product of C₃ and C₄.Dic₅	120	2	C3xC4.Dic5	240,39
C₅xC₄.Dic₃	Direct product of C₅ and C₄.Dic₃	120	2	C5xC4.Dic3	240,55
C₆xC₅:C₈	Direct product of C₆ and C₅:C₈	240		C6xC5:C8	240,115
C₅xC₃:C₁₆	Direct product of C₅ and C₃:C₁₆	240	2	C5xC3:C16	240,1
C₃xC₅:C₁₆	Direct product of C₃ and C₅:C₁₆	240	4	C3xC5:C16	240,5
C₁₀xC₃:C₈	Direct product of C₁₀ and C₃:C₈	240		C10xC3:C8	240,54
C₁₅xC₄:C₄	Direct product of C₁₅ and C₄:C₄	240		C15xC4:C4	240,83
C₆xC₅:₂C₈	Direct product of C₆ and C₅:₂C₈	240		C6xC5:2C8	240,38
C₂xC₁₅:C₈	Direct product of C₂ and C₁₅:C₈	240		C2xC15:C8	240,122
C₃xC₅:₂C₁₆	Direct product of C₃ and C₅:₂C₁₆	240	2	C3xC5:2C16	240,2
C₂xC₁₅:₃C₈	Direct product of C₂ and C₁₅:₃C₈	240		C2xC15:3C8	240,70
C₃xC₄:Dic₅	Direct product of C₃ and C₄:Dic₅	240		C3xC4:Dic5	240,42
C₅xC₄:Dic₃	Direct product of C₅ and C₄:Dic₃	240		C5xC4:Dic3	240,58

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
C₁₁xC₂₂	Abelian group of type [11,22]	242		C11xC22	242,5
C₁₁xD₁₁	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
C₂₇:C₉	The semidirect product of C₂₇ and C₉ acting faithfully	27	9	C27:C9	243,22
C₈₁:C₃	The semidirect product of C₈₁ and C₃ acting faithfully	81	3	C81:C3	243,24
C₉:C₂₇	The semidirect product of C₉ and C₂₇ acting via C₂₇/C₉=C₃	243		C9:C27	243,21
C₂₇:₂C₉	The semidirect product of C₂₇ and C₉ acting via C₉/C₃=C₃	243		C27:2C9	243,11
C₉xC₂₇	Abelian group of type [9,27]	243		C9xC27	243,10
C₃xC₈₁	Abelian group of type [3,81]	243		C3xC81	243,23

Groups of order 244

		d	ρ	Label	ID
C₂₄₄	Cyclic group	244	1	C244	244,2
D₁₂₂	Dihedral group; = C₂xD₆₁	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
C₂xC₁₂₂	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
C₇xC₃₅	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
S₃xC₄₁	Direct product of C₄₁ and S₃	123	2	S3xC41	246,1
C₃xD₄₁	Direct product of C₃ and D₄₁	123	2	C3xD41	246,2

Groups of order 247

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

Groups of order 248

		d	ρ	Label	ID
C₂₄₈	Cyclic group	248	1	C248	248,2
D₁₂₄	Dihedral group	124	2+	D124	248,5
Dic₆₂	Dicyclic group; = C₃₁ :Q₈	248	2-	Dic62	248,3
C₃₁:C₈	The semidirect product of C₃₁ and C₈ acting via C₈/C₄=C₂	248	2	C31:C8	248,1
C₂xC₁₂₄	Abelian group of type [2,124]	248		C2xC124	248,8
C₄xD₃₁	Direct product of C₄ and D₃₁	124	2	C4xD31	248,4
D₄xC₃₁	Direct product of C₃₁ and D₄	124	2	D4xC31	248,9
Q₈xC₃₁	Direct product of C₃₁ and Q₈	248	2	Q8xC31	248,10
C₂xDic₃₁	Direct product of C₂ and Dic₃₁	248		C2xDic31	248,6

Groups of order 249

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

Groups of order 250

		d	ρ	Label	ID
C₂₅₀	Cyclic group	250	1	C250	250,2
D₁₂₅	Dihedral group	125	2+	D125	250,1
C₂₅:C₁₀	The semidirect product of C₂₅ and C₁₀ acting faithfully	25	10+	C25:C10	250,6
C₅xC₅₀	Abelian group of type [5,50]	250		C5xC50	250,9
C₅xD₂₅	Direct product of C₅ and D₂₅	50	2	C5xD25	250,3
D₅xC₂₅	Direct product of C₂₅ and D₅	50	2	D5xC25	250,4
C₂x5_-¹⁺²	Direct product of C₂ and 5_-¹⁺²	50	5	C2xES-(5,1)	250,11

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; = C₂xD₆₃	126	2+	D126	252,14
Dic₆₃	Dicyclic group; = C₉ :Dic₇	252	2-	Dic63	252,5
C₇:C₃₆	The semidirect product of C₇ and C₃₆ acting via C₃₆/C₆=C₆	252	6	C7:C36	252,1
C₆.F₇	The non-split extension by C₆ of F₇ acting via F₇/C₇:C₃=C₂	84	6-	C6.F7	252,18
C₃xC₈₄	Abelian group of type [3,84]	252		C3xC84	252,25
C₆xC₄₂	Abelian group of type [6,42]	252		C6xC42	252,46
C₂xC₁₂₆	Abelian group of type [2,126]	252		C2xC126	252,15
C₆xF₇	Direct product of C₆ and F₇	42	6	C6xF7	252,28
S₃xC₄₂	Direct product of C₄₂ and S₃	84	2	S3xC42	252,42
C₆xD₂₁	Direct product of C₆ and D₂₁	84	2	C6xD21	252,43
Dic₃xC₂₁	Direct product of C₂₁ and Dic₃	84	2	Dic3xC21	252,21
C₃xDic₂₁	Direct product of C₃ and Dic₂₁	84	2	C3xDic21	252,22
D₇xC₁₈	Direct product of C₁₈ and D₇	126	2	D7xC18	252,12
C₁₄xD₉	Direct product of C₁₄ and D₉	126	2	C14xD9	252,13
C₇xDic₉	Direct product of C₇ and Dic₉	252	2	C7xDic9	252,3
C₉xDic₇	Direct product of C₉ and Dic₇	252	2	C9xDic7	252,4
C₃²xDic₇	Direct product of C₃² and Dic₇	252		C3^2xDic7	252,20
C₂xC₃:F₇	Direct product of C₂ and C₃:F₇	42	6+	C2xC3:F7	252,30
C₃xC₇:C₁₂	Direct product of C₃ and C₇:C₁₂	84	6	C3xC7:C12	252,16
C₁₂xC₇:C₃	Direct product of C₁₂ and C₇:C₃	84	3	C12xC7:C3	252,19
Dic₃xC₇:C₃	Direct product of Dic₃ and C₇:C₃	84	6	Dic3xC7:C3	252,17
D₇xC₃xC₆	Direct product of C₃xC₆ and D₇	126		D7xC3xC6	252,41
C₂xC₇:C₁₈	Direct product of C₂ and C₇:C₁₈	126	6	C2xC7:C18	252,7
C₄xC₇:C₉	Direct product of C₄ and C₇:C₉	252	3	C4xC7:C9	252,2
C₂²xC₇:C₉	Direct product of C₂² and C₇:C₉	252		C2^2xC7:C9	252,9
C₂xS₃xC₇:C₃	Direct product of C₂, S₃ and C₇:C₃	42	6	C2xS3xC7:C3	252,29
C₂xC₆xC₇:C₃	Direct product of C₂xC₆ 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
S₃xC₄₃	Direct product of C₄₃ and S₃	129	2	S3xC43	258,3
C₃xD₄₃	Direct product of C₃ and D₄₃	129	2	C3xD43	258,4
C₂xC₄₃: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; = C₂xD₆₅	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
C₂xC₁₃₀	Abelian group of type [2,130]	260		C2xC130	260,15
C₁₃xF₅	Direct product of C₁₃ and F₅	65	4	C13xF5	260,7
D₅xC₂₆	Direct product of C₂₆ and D₅	130	2	D5xC26	260,13
C₁₀xD₁₃	Direct product of C₁₀ and D₁₃	130	2	C10xD13	260,12
C₁₃xDic₅	Direct product of C₁₃ and Dic₅	260	2	C13xDic5	260,1
C₅xDic₁₃	Direct product of C₅ and Dic₁₃	260	2	C5xDic13	260,2
C₅xC₁₃: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
C₃xC₈₇	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
D₁₃₂	Dihedral group	132	2+	D132	264,25
Dic₆₆	Dicyclic group; = C₃₃ :₂ Q₈	264	2-	Dic66	264,23
C₃₃:C₈	1^st semidirect product of C₃₃ and C₈ acting via C₈/C₄=C₂	264	2	C33:C8	264,3
C₂xC₁₃₂	Abelian group of type [2,132]	264		C2xC132	264,28
S₃xC₄₄	Direct product of C₄₄ and S₃	132	2	S3xC44	264,19
C₃xD₄₄	Direct product of C₃ and D₄₄	132	2	C3xD44	264,15
C₄xD₃₃	Direct product of C₄ and D₃₃	132	2	C4xD33	264,24
D₄xC₃₃	Direct product of C₃₃ and D₄	132	2	D4xC33	264,29
C₁₂xD₁₁	Direct product of C₁₂ and D₁₁	132	2	C12xD11	264,14
C₁₁xD₁₂	Direct product of C₁₁ and D₁₂	132	2	C11xD12	264,20
Q₈xC₃₃	Direct product of C₃₃ and Q₈	264	2	Q8xC33	264,30
C₃xDic₂₂	Direct product of C₃ and Dic₂₂	264	2	C3xDic22	264,13
C₆xDic₁₁	Direct product of C₆ and Dic₁₁	264		C6xDic11	264,16
C₁₁xDic₆	Direct product of C₁₁ and Dic₆	264	2	C11xDic6	264,18
Dic₃xC₂₂	Direct product of C₂₂ and Dic₃	264		Dic3xC22	264,21
C₂xDic₃₃	Direct product of C₂ and Dic₃₃	264		C2xDic33	264,26
C₁₁xC₃:C₈	Direct product of C₁₁ and C₃:C₈	264	2	C11xC3:C8	264,1
C₃xC₁₁: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
D₇xC₁₉	Direct product of C₁₉ and D₇	133	2	D7xC19	266,1
C₇xD₁₉	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; = C₂xD₆₇	134	2+	D134	268,3
Dic₆₇	Dicyclic group; = C₆₇ :C₄	268	2-	Dic67	268,1
C₂xC₁₃₄	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
D₄₅:C₃	The semidirect product of D₄₅ and C₃ acting faithfully	45	6+	D45:C3	270,15
C₃xC₉₀	Abelian group of type [3,90]	270		C3xC90	270,20
D₅x3_-¹⁺²	Direct product of D₅ and 3_-¹⁺²	45	6	D5xES-(3,1)	270,7
S₃xC₄₅	Direct product of C₄₅ and S₃	90	2	S3xC45	270,9
C₁₅xD₉	Direct product of C₁₅ and D₉	90	2	C15xD9	270,8
C₃xD₄₅	Direct product of C₃ and D₄₅	90	2	C3xD45	270,12
C₉xD₁₅	Direct product of C₉ and D₁₅	90	2	C9xD15	270,13
C₁₀x3_-¹⁺²	Direct product of C₁₀ and 3_-¹⁺²	90	3	C10xES-(3,1)	270,22
C₅xD₂₇	Direct product of C₅ and D₂₇	135	2	C5xD27	270,1
D₅xC₂₇	Direct product of C₂₇ and D₅	135	2	D5xC27	270,2
C₅xC₉:C₆	Direct product of C₅ and C₉:C₆	45	6	C5xC9:C6	270,11
D₅xC₃xC₉	Direct product of C₃xC₉ and D₅	135		D5xC3xC9	270,5

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
D₁₃₆	Dihedral group	136	2+	D136	272,7
F₁₇	Frobenius group; = C₁₇ :C₁₆ = AGL₁(F₁₇) = Aut(D₁₇) = Hol(C₁₇)	17	16+	F17	272,50
Dic₆₈	Dicyclic group; = C₁₇ :₁ Q₁₆	272	2-	Dic68	272,8
C₆₈:C₄	1^st semidirect product of C₆₈ and C₄ acting faithfully	68	4	C68:C4	272,32
C₈:D₁₇	3^rd semidirect product of C₈ and D₁₇ acting via D₁₇/C₁₇=C₂	136	2	C8:D17	272,5
C₁₃₆:C₂	2^nd semidirect product of C₁₃₆ and C₂ acting faithfully	136	2	C136:C2	272,6
C₆₈:₃C₄	1^st semidirect product of C₆₈ and C₄ acting via C₄/C₂=C₂	272		C68:3C4	272,13
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
C₆₈.₄C₄	1^st non-split extension by C₆₈ of C₄ acting via C₄/C₂=C₂	136	2	C68.4C4	272,10
C₆₈.C₄	3^rd non-split extension by C₆₈ of C₄ acting faithfully	136	4	C68.C4	272,29
D₃₄.₄C₄	3^rd non-split extension by D₃₄ of C₄ acting via C₄/C₂=C₂	136	4	D34.4C4	272,30
C₃₄.C₈	The non-split extension by C₃₄ of C₈ acting faithfully	272	8-	C34.C8	272,28
C₄xC₆₈	Abelian group of type [4,68]	272		C4xC68	272,20
C₂xC₁₃₆	Abelian group of type [2,136]	272		C2xC136	272,23
C₈xD₁₇	Direct product of C₈ and D₁₇	136	2	C8xD17	272,4
D₈xC₁₇	Direct product of C₁₇ and D₈	136	2	D8xC17	272,25
SD₁₆xC₁₇	Direct product of C₁₇ and SD₁₆	136	2	SD16xC17	272,26
M₄(2)xC₁₇	Direct product of C₁₇ and M₄(2)	136	2	M4(2)xC17	272,24
Q₁₆xC₁₇	Direct product of C₁₇ and Q₁₆	272	2	Q16xC17	272,27
C₄xDic₁₇	Direct product of C₄ and Dic₁₇	272		C4xDic17	272,11
C₂xC₁₇:C₈	Direct product of C₂ and C₁₇:C₈	34	8+	C2xC17:C8	272,51
C₄xC₁₇:C₄	Direct product of C₄ and C₁₇:C₄	68	4	C4xC17:C4	272,31
C₄:C₄xC₁₇	Direct product of C₁₇ and C₄:C₄	272		C4:C4xC17	272,22
C₂xC₁₇:₃C₈	Direct product of C₂ and C₁₇:₃C₈	272		C2xC17:3C8	272,9
C₂xC₁₇:₂C₈	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
C₁₃xC₇:C₃	Direct product of C₁₃ and C₇:C₃	91	3	C13xC7:C3	273,1
C₇xC₁₃: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
C₅xC₅₅	Abelian group of type [5,55]	275		C5xC55	275,4
C₅xC₁₁: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; = C₂xD₆₉	138	2+	D138	276,9
Dic₆₉	Dicyclic group; = C₆₉ :₁ C₄	276	2-	Dic69	276,3
C₂xC₁₃₈	Abelian group of type [2,138]	276		C2xC138	276,10
S₃xC₄₆	Direct product of C₄₆ and S₃	138	2	S3xC46	276,8
C₆xD₂₃	Direct product of C₆ and D₂₃	138	2	C6xD23	276,7
Dic₃xC₂₃	Direct product of C₂₃ and Dic₃	276	2	Dic3xC23	276,1
C₃xDic₂₃	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
C₃xC₉₃	Abelian group of type [3,93]	279		C3xC93	279,4
C₃xC₃₁: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
D₁₄₀	Dihedral group	140	2+	D140	280,26
Dic₇₀	Dicyclic group; = C₃₅ :₂ Q₈	280	2-	Dic70	280,24
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
C₂xC₁₄₀	Abelian group of type [2,140]	280		C2xC140	280,29
C₁₄xF₅	Direct product of C₁₄ and F₅	70	4	C14xF5	280,34
D₇xC₂₀	Direct product of C₂₀ and D₇	140	2	D7xC20	280,15
C₅xD₂₈	Direct product of C₅ and D₂₈	140	2	C5xD28	280,16
D₅xC₂₈	Direct product of C₂₈ and D₅	140	2	D5xC28	280,20
C₇xD₂₀	Direct product of C₇ and D₂₀	140	2	C7xD20	280,21
C₄xD₃₅	Direct product of C₄ and D₃₅	140	2	C4xD35	280,25
D₄xC₃₅	Direct product of C₃₅ and D₄	140	2	D4xC35	280,30
Q₈xC₃₅	Direct product of C₃₅ and Q₈	280	2	Q8xC35	280,31
C₅xDic₁₄	Direct product of C₅ and Dic₁₄	280	2	C5xDic14	280,14
C₁₀xDic₇	Direct product of C₁₀ and Dic₇	280		C10xDic7	280,17
C₇xDic₁₀	Direct product of C₇ and Dic₁₀	280	2	C7xDic10	280,19
C₁₄xDic₅	Direct product of C₁₄ and Dic₅	280		C14xDic5	280,22
C₂xDic₃₅	Direct product of C₂ and Dic₃₅	280		C2xDic35	280,27
C₂xC₇:F₅	Direct product of C₂ and C₇:F₅	70	4	C2xC7:F5	280,35
C₅xC₇:C₈	Direct product of C₅ and C₇:C₈	280	2	C5xC7:C8	280,2
C₇xC₅:C₈	Direct product of C₇ and C₅:C₈	280	4	C7xC5:C8	280,5
C₇xC₅:₂C₈	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
S₃xC₄₇	Direct product of C₄₇ and S₃	141	2	S3xC47	282,1
C₃xD₄₇	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; = C₂xD₇₁	142	2+	D142	284,3
Dic₇₁	Dicyclic group; = C₇₁ :C₄	284	2-	Dic71	284,1
C₂xC₁₄₂	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
C₅xC₁₉: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
C₁₃xD₁₁	Direct product of C₁₃ and D₁₁	143	2	C13xD11	286,1
C₁₁xD₁₃	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
D₁₄₄	Dihedral group	144	2+	D144	288,6
Dic₇₂	Dicyclic group; = C₉ :₁ Q₃₂	288	2-	Dic72	288,8
C₁₆:D₉	3^rd semidirect product of C₁₆ and D₉ acting via D₉/C₉=C₂	144	2	C16:D9	288,5
C₁₄₄:C₂	2^nd semidirect product of C₁₄₄ and C₂ acting faithfully	144	2	C144:C2	288,7
C₉:C₃₂	The semidirect product of C₉ and C₃₂ acting via C₃₂/C₁₆=C₂	288	2	C9:C32	288,1
C₃₆:C₈	1^st semidirect product of C₃₆ and C₈ acting via C₈/C₄=C₂	288		C36:C8	288,11
C₇₂:C₄	4^th semidirect product of C₇₂ and C₄ acting via C₄/C₂=C₂	288		C72:C4	288,23
C₇₂:₁C₄	1^st semidirect product of C₇₂ and C₄ acting via C₄/C₂=C₂	288		C72:1C4	288,26
C₈:Dic₉	2^nd semidirect product of C₈ and Dic₉ acting via Dic₉/C₁₈=C₂	288		C8:Dic9	288,25
C₃₆.C₈	1^st non-split extension by C₃₆ of C₈ acting via C₈/C₄=C₂	144	2	C36.C8	288,19
C₇₂.C₄	1^st non-split extension by C₇₂ of C₄ acting via C₄/C₂=C₂	144	2	C72.C4	288,20
C₄xC₇₂	Abelian group of type [4,72]	288		C4xC72	288,46
C₃xC₉₆	Abelian group of type [3,96]	288		C3xC96	288,66
C₆xC₄₈	Abelian group of type [6,48]	288		C6xC48	288,327
C₂xC₁₄₄	Abelian group of type [2,144]	288		C2xC144	288,59
C₁₂xC₂₄	Abelian group of type [12,24]	288		C12xC24	288,314
S₃xC₄₈	Direct product of C₄₈ and S₃	96	2	S3xC48	288,231
C₃xD₄₈	Direct product of C₃ and D₄₈	96	2	C3xD48	288,233
C₃xDic₂₄	Direct product of C₃ and Dic₂₄	96	2	C3xDic24	288,235
Dic₃xC₂₄	Direct product of C₂₄ and Dic₃	96		Dic3xC24	288,247
C₁₆xD₉	Direct product of C₁₆ and D₉	144	2	C16xD9	288,4
C₉xD₁₆	Direct product of C₉ and D₁₆	144	2	C9xD16	288,61
C₉xSD₃₂	Direct product of C₉ and SD₃₂	144	2	C9xSD32	288,62
C₃²xD₁₆	Direct product of C₃² and D₁₆	144		C3^2xD16	288,329
C₉xM₅(2)	Direct product of C₉ and M₅(2)	144	2	C9xM5(2)	288,60
C₃²xSD₃₂	Direct product of C₃² and SD₃₂	144		C3^2xSD32	288,330
C₃²xM₅(2)	Direct product of C₃² and M₅(2)	144		C3^2xM5(2)	288,328
C₉xQ₃₂	Direct product of C₉ and Q₃₂	288	2	C9xQ32	288,63
C₈xDic₉	Direct product of C₈ and Dic₉	288		C8xDic9	288,21
C₃²xQ₃₂	Direct product of C₃² and Q₃₂	288		C3^2xQ32	288,331
C₃xC₁₂.C₈	Direct product of C₃ and C₁₂.C₈	48	2	C3xC12.C8	288,246
C₃xC₂₄.C₄	Direct product of C₃ and C₂₄.C₄	48	2	C3xC24.C4	288,253
C₃xC₃:C₃₂	Direct product of C₃ and C₃:C₃₂	96	2	C3xC3:C32	288,64
C₁₂xC₃:C₈	Direct product of C₁₂ and C₃:C₈	96		C12xC3:C8	288,236
C₆xC₃:C₁₆	Direct product of C₆ and C₃:C₁₆	96		C6xC3:C16	288,245
C₃xC₄₈:C₂	Direct product of C₃ and C₄₈:C₂	96	2	C3xC48:C2	288,234
C₃xC₁₂:C₈	Direct product of C₃ and C₁₂:C₈	96		C3xC12:C8	288,238
C₃xC₂₄:C₄	Direct product of C₃ and C₂₄:C₄	96		C3xC24:C4	288,249
C₃xD₆.C₈	Direct product of C₃ and D₆.C₈	96	2	C3xD6.C8	288,232
C₃xC₂₄:₁C₄	Direct product of C₃ and C₂₄:₁C₄	96		C3xC24:1C4	288,252
C₃xC₈:Dic₃	Direct product of C₃ and C₈:Dic₃	96		C3xC8:Dic3	288,251
C₉xC₈.C₄	Direct product of C₉ and C₈.C₄	144	2	C9xC8.C4	288,58
C₃²xC₈.C₄	Direct product of C₃² and C₈.C₄	144		C3^2xC8.C4	288,326
C₄xC₉:C₈	Direct product of C₄ and C₉:C₈	288		C4xC9:C8	288,9
C₉xC₄:C₈	Direct product of C₉ and C₄:C₈	288		C9xC4:C8	288,55
C₂xC₉:C₁₆	Direct product of C₂ and C₉:C₁₆	288		C2xC9:C16	288,18
C₉xC₈:C₄	Direct product of C₉ and C₈:C₄	288		C9xC8:C4	288,47
C₃²xC₄:C₈	Direct product of C₃² and C₄:C₈	288		C3^2xC4:C8	288,323
C₉xC₂.D₈	Direct product of C₉ and C₂.D₈	288		C9xC2.D8	288,57
C₉xC₄.Q₈	Direct product of C₉ and C₄.Q₈	288		C9xC4.Q8	288,56
C₃²xC₈:C₄	Direct product of C₃² and C₈:C₄	288		C3^2xC8:C4	288,315
C₃²xC₂.D₈	Direct product of C₃² and C₂.D₈	288		C3^2xC2.D8	288,325
C₃²xC₄.Q₈	Direct product of C₃² and C₄.Q₈	288		C3^2xC4.Q8	288,324

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
D₅xC₂₉	Direct product of C₂₉ and D₅	145	2	D5xC29	290,1
C₅xD₂₉	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; = C₂xD₇₃	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
C₂xC₁₄₆	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
C₄₉:C₆	The semidirect product of C₄₉ and C₆ acting faithfully	49	6+	C49:C6	294,1
C₇xC₄₂	Abelian group of type [7,42]	294		C7xC42	294,23
C₇xF₇	Direct product of C₇ and F₇	42	6	C7xF7	294,8
D₇xC₂₁	Direct product of C₂₁ and D₇	42	2	D7xC21	294,18
C₇xD₂₁	Direct product of C₇ and D₂₁	42	2	C7xD21	294,21
S₃xC₄₉	Direct product of C₄₉ and S₃	147	2	S3xC49	294,3
C₃xD₄₉	Direct product of C₃ and D₄₉	147	2	C3xD49	294,4
S₃xC₇²	Direct product of C₇² and S₃	147		S3xC7^2	294,20
C₁₄xC₇:C₃	Direct product of C₁₄ and C₇:C₃	42	3	C14xC7:C3	294,15
C₂xC₄₉:C₃	Direct product of C₂ and C₄₉:C₃	98	3	C2xC49:C3	294,2

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
D₁₄₈	Dihedral group	148	2+	D148	296,6
Dic₇₄	Dicyclic group; = C₃₇ :Q₈	296	2-	Dic74	296,4
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
C₂xC₁₄₈	Abelian group of type [2,148]	296		C2xC148	296,9
C₄xD₃₇	Direct product of C₄ and D₃₇	148	2	C4xD37	296,5
D₄xC₃₇	Direct product of C₃₇ and D₄	148	2	D4xC37	296,10
Q₈xC₃₇	Direct product of C₃₇ and Q₈	296	2	Q8xC37	296,11
C₂xDic₃₇	Direct product of C₂ and Dic₃₇	296		C2xDic37	296,7
C₂xC₃₇: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
C₃xC₉₉	Abelian group of type [3,99]	297		C3xC99	297,2
C₁₁x3_-¹⁺²	Direct product of C₁₁ and 3_-¹⁺²	99	3	C11xES-(3,1)	297,4

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; = C₂xD₇₅	150	2+	D150	300,11
Dic₇₅	Dicyclic group; = C₇₅ :₃ C₄	300	2-	Dic75	300,3
C₇₅:C₄	1^st semidirect product of C₇₅ and C₄ acting faithfully	75	4	C75:C4	300,6
C₅xC₆₀	Abelian group of type [5,60]	300		C5xC60	300,21
C₂xC₁₅₀	Abelian group of type [2,150]	300		C2xC150	300,12
C₁₀xC₃₀	Abelian group of type [10,30]	300		C10xC30	300,49
D₅xC₃₀	Direct product of C₃₀ and D₅	60	2	D5xC30	300,44
C₁₅xF₅	Direct product of C₁₅ and F₅	60	4	C15xF5	300,28
C₁₀xD₁₅	Direct product of C₁₀ and D₁₅	60	2	C10xD15	300,47
C₁₅xDic₅	Direct product of C₁₅ and Dic₅	60	2	C15xDic5	300,16
C₅xDic₁₅	Direct product of C₅ and Dic₁₅	60	2	C5xDic15	300,19
S₃xC₅₀	Direct product of C₅₀ and S₃	150	2	S3xC50	300,10
C₆xD₂₅	Direct product of C₆ and D₂₅	150	2	C6xD25	300,9
Dic₃xC₂₅	Direct product of C₂₅ and Dic₃	300	2	Dic3xC25	300,1
C₃xDic₂₅	Direct product of C₃ and Dic₂₅	300	2	C3xDic25	300,2
Dic₃xC₅²	Direct product of C₅² and Dic₃	300		Dic3xC5^2	300,18
C₅xC₃:F₅	Direct product of C₅ and C₃:F₅	60	4	C5xC3:F5	300,32
C₃xC₂₅:C₄	Direct product of C₃ and C₂₅:C₄	75	4	C3xC25:C4	300,5
S₃xC₅xC₁₀	Direct product of C₅xC₁₀ and S₃	150		S3xC5xC10	300,46

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
D₁₅₂	Dihedral group	152	2+	D152	304,6
Dic₇₆	Dicyclic group; = C₁₉ :₁ Q₁₆	304	2-	Dic76	304,7
C₈:D₁₉	3^rd semidirect product of C₈ and D₁₉ acting via D₁₉/C₁₉=C₂	152	2	C8:D19	304,4
C₁₅₂:C₂	2^nd semidirect product of C₁₅₂ and C₂ acting faithfully	152	2	C152:C2	304,5
C₁₉:C₁₆	The semidirect product of C₁₉ and C₁₆ acting via C₁₆/C₈=C₂	304	2	C19:C16	304,1
C₇₆:C₄	1^st semidirect product of C₇₆ and C₄ acting via C₄/C₂=C₂	304		C76:C4	304,12
C₇₆.C₄	1^st non-split extension by C₇₆ of C₄ acting via C₄/C₂=C₂	152	2	C76.C4	304,9
C₄xC₇₆	Abelian group of type [4,76]	304		C4xC76	304,19
C₂xC₁₅₂	Abelian group of type [2,152]	304		C2xC152	304,22
C₈xD₁₉	Direct product of C₈ and D₁₉	152	2	C8xD19	304,3
D₈xC₁₉	Direct product of C₁₉ and D₈	152	2	D8xC19	304,24
SD₁₆xC₁₉	Direct product of C₁₉ and SD₁₆	152	2	SD16xC19	304,25
M₄(2)xC₁₉	Direct product of C₁₉ and M₄(2)	152	2	M4(2)xC19	304,23
Q₁₆xC₁₉	Direct product of C₁₉ and Q₁₆	304	2	Q16xC19	304,26
C₄xDic₁₉	Direct product of C₄ and Dic₁₉	304		C4xDic19	304,10
C₂xC₁₉:C₈	Direct product of C₂ and C₁₉:C₈	304		C2xC19:C8	304,8
C₄:C₄xC₁₉	Direct product of C₁₉ and C₄:C₄	304		C4:C4xC19	304,21

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
C₃xC₁₀₂	Abelian group of type [3,102]	306		C3xC102	306,10
S₃xC₅₁	Direct product of C₅₁ and S₃	102	2	S3xC51	306,6
C₃xD₅₁	Direct product of C₃ and D₅₁	102	2	C3xD51	306,7
C₁₇xD₉	Direct product of C₁₇ and D₉	153	2	C17xD9	306,1
C₉xD₁₇	Direct product of C₉ and D₁₇	153	2	C9xD17	306,2
C₃²xD₁₇	Direct product of C₃² and D₁₇	153		C3^2xD17	306,5

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; = C₂xD₇₇	154	2+	D154	308,8
Dic₇₇	Dicyclic group; = C₇₇ :₁ C₄	308	2-	Dic77	308,3
C₂xC₁₅₄	Abelian group of type [2,154]	308		C2xC154	308,9
D₇xC₂₂	Direct product of C₂₂ and D₇	154	2	D7xC22	308,7
C₁₄xD₁₁	Direct product of C₁₄ and D₁₁	154	2	C14xD11	308,6
C₁₁xDic₇	Direct product of C₁₁ and Dic₇	308	2	C11xDic7	308,1
C₇xDic₁₁	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
D₅xC₃₁	Direct product of C₃₁ and D₅	155	2	D5xC31	310,3
C₅xD₃₁	Direct product of C₅ and D₃₁	155	2	C5xD31	310,4
C₂xC₃₁: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
D₁₅₆	Dihedral group	156	2+	D156	312,39
Dic₇₈	Dicyclic group; = C₃₉ :₂ Q₈	312	2-	Dic78	312,37
D₅₂:C₃	The semidirect product of D₅₂ and C₃ acting faithfully	52	6+	D52:C3	312,10
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
Dic₂₆:C₃	The semidirect product of Dic₂₆ and C₃ acting faithfully	104	6-	Dic26:C3	312,8
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
C₂xC₁₅₆	Abelian group of type [2,156]	312		C2xC156	312,42
C₂xF₁₃	Direct product of C₂ and F₁₃; = Aut(D₂₆) = Hol(C₂₆)	26	12+	C2xF13	312,45
S₃xC₅₂	Direct product of C₅₂ and S₃	156	2	S3xC52	312,33
C₃xD₅₂	Direct product of C₃ and D₅₂	156	2	C3xD52	312,29
C₄xD₃₉	Direct product of C₄ and D₃₉	156	2	C4xD39	312,38
D₄xC₃₉	Direct product of C₃₉ and D₄	156	2	D4xC39	312,43
C₁₂xD₁₃	Direct product of C₁₂ and D₁₃	156	2	C12xD13	312,28
C₁₃xD₁₂	Direct product of C₁₃ and D₁₂	156	2	C13xD12	312,34
Q₈xC₃₉	Direct product of C₃₉ and Q₈	312	2	Q8xC39	312,44
C₃xDic₂₆	Direct product of C₃ and Dic₂₆	312	2	C3xDic26	312,27
C₆xDic₁₃	Direct product of C₆ and Dic₁₃	312		C6xDic13	312,30
C₁₃xDic₆	Direct product of C₁₃ and Dic₆	312	2	C13xDic6	312,32
Dic₃xC₂₆	Direct product of C₂₆ and Dic₃	312		Dic3xC26	312,35
C₂xDic₃₉	Direct product of C₂ and Dic₃₉	312		C2xDic39	312,40
C₄xC₁₃:C₆	Direct product of C₄ and C₁₃:C₆	52	6	C4xC13:C6	312,9
D₄xC₁₃:C₃	Direct product of D₄ and C₁₃:C₃	52	6	D4xC13:C3	312,23
C₆xC₁₃:C₄	Direct product of C₆ and C₁₃:C₄	78	4	C6xC13:C4	312,52
C₂xC₃₉:C₄	Direct product of C₂ and C₃₉:C₄	78	4	C2xC39:C4	312,53
C₈xC₁₃:C₃	Direct product of C₈ and C₁₃:C₃	104	3	C8xC13:C3	312,2
Q₈xC₁₃:C₃	Direct product of Q₈ and C₁₃:C₃	104	6	Q8xC13:C3	312,24
C₂xC₂₆.C₆	Direct product of C₂ and C₂₆.C₆	104		C2xC26.C6	312,11
C₁₃xC₃:C₈	Direct product of C₁₃ and C₃:C₈	312	2	C13xC3:C8	312,3
C₃xC₁₃:C₈	Direct product of C₃ and C₁₃:C₈	312	4	C3xC13:C8	312,13
C₃xC₁₃:₂C₈	Direct product of C₃ and C₁₃:₂C₈	312	2	C3xC13:2C8	312,4
C₂xC₄xC₁₃:C₃	Direct product of C₂xC₄ 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
C₃xC₁₀₅	Abelian group of type [3,105]	315		C3xC105	315,4
C₁₅xC₇:C₃	Direct product of C₁₅ and C₇:C₃	105	3	C15xC7:C3	315,3
C₅xC₇: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; = C₂xD₇₉	158	2+	D158	316,3
Dic₇₉	Dicyclic group; = C₇₉ :C₄	316	2-	Dic79	316,1
C₂xC₁₅₈	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
S₃xC₅₃	Direct product of C₅₃ and S₃	159	2	S3xC53	318,1
C₃xD₅₃	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
D₁₆₀	Dihedral group	160	2+	D160	320,6
Dic₈₀	Dicyclic group; = C₅ :₁ Q₆₄	320	2-	Dic80	320,8
C₈₀:C₄	6^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:C4	320,70
C₈₀:₄C₄	4^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:4C4	320,185
C₈₀:₅C₄	5^th semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:5C4	320,186
C₈₀:₂C₄	2^nd semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:2C4	320,187
C₈₀:₃C₄	3^rd semidirect product of C₈₀ and C₄ acting faithfully	80	4	C80:3C4	320,188
C₁₆:₇F₅	3^rd semidirect product of C₁₆ and F₅ acting via F₅/D₅=C₂	80	4	C16:7F5	320,182
C₁₆:F₅	3^rd semidirect product of C₁₆ and F₅ acting via F₅/C₅=C₄	80	4	C16:F5	320,183
C₁₆:₄F₅	4^th semidirect product of C₁₆ and F₅ acting via F₅/C₅=C₄	80	4	C16:4F5	320,184
D₅:C₃₂	The semidirect product of D₅ and C₃₂ acting via C₃₂/C₁₆=C₂	160	4	D5:C32	320,179
C₃₂:D₅	3^rd semidirect product of C₃₂ and D₅ acting via D₅/C₅=C₂	160	2	C32:D5	320,5
C₁₆₀:C₂	2^nd semidirect product of C₁₆₀ and C₂ acting faithfully	160	2	C160:C2	320,7
C₅:M₆(2)	The semidirect product of C₅ and M₆(2) acting via M₆(2)/C₂xC₈=C₄	160	4	C5:M6(2)	320,215
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
C₄₀:₈C₈	4^th semidirect product of C₄₀ and C₈ acting via C₈/C₄=C₂	320		C40:8C8	320,13
C₄₀:₆C₈	2^nd semidirect product of C₄₀ and C₈ acting via C₈/C₄=C₂	320		C40:6C8	320,15
C₄₀:₅C₈	1^st semidirect product of C₄₀ and C₈ acting via C₈/C₄=C₂	320		C40:5C8	320,16
C₄₀:C₈	4^th semidirect product of C₄₀ and C₈ acting via C₈/C₂=C₄	320		C40:C8	320,217
C₄₀:₂C₈	2^nd semidirect product of C₄₀ and C₈ acting via C₈/C₂=C₄	320		C40:2C8	320,219
C₄₀:₁C₈	1^st semidirect product of C₄₀ and C₈ acting via C₈/C₂=C₄	320		C40:1C8	320,220
C₂₀:₃C₁₆	1^st semidirect product of C₂₀ and C₁₆ acting via C₁₆/C₈=C₂	320		C20:3C16	320,20
C₈₀:₁₇C₄	5^th semidirect product of C₈₀ and C₄ acting via C₄/C₂=C₂	320		C80:17C4	320,60
C₈₀:₁₃C₄	1^st semidirect product of C₈₀ and C₄ acting via C₄/C₂=C₂	320		C80:13C4	320,62
C₈₀:₁₄C₄	2^nd semidirect product of C₈₀ and C₄ acting via C₄/C₂=C₂	320		C80:14C4	320,63
C₂₀:C₁₆	1^st semidirect product of C₂₀ and C₁₆ acting via C₁₆/C₄=C₄	320		C20:C16	320,196
Dic₅:C₁₆	2^nd semidirect product of Dic₅ and C₁₆ acting via C₁₆/C₈=C₂	320		Dic5:C16	320,223
C₄₀.₇C₈	1^st non-split extension by C₄₀ of C₈ acting via C₈/C₄=C₂	80	2	C40.7C8	320,21
C₄₀.₁C₈	1^st non-split extension by C₄₀ of C₈ acting via C₈/C₂=C₄	80	4	C40.1C8	320,227
C₄₀.Q₈	1^st non-split extension by C₄₀ of Q₈ acting via Q₈/C₂=C₂²	80	4	C40.Q8	320,71
C₈₀.₉C₄	4^th non-split extension by C₈₀ of C₄ acting via C₄/C₂=C₂	160	2	C80.9C4	320,57
C₈₀.₆C₄	1^st non-split extension by C₈₀ of C₄ acting via C₄/C₂=C₂	160	2	C80.6C4	320,64
C₈₀.C₄	5^th non-split extension by C₈₀ of C₄ acting faithfully	160	4	C80.C4	320,180
C₈₀.₂C₄	2^nd non-split extension by C₈₀ of C₄ acting faithfully	160	4	C80.2C4	320,190
C₁₆.F₅	1^st non-split extension by C₁₆ of F₅ acting via F₅/D₅=C₂	160	4	C16.F5	320,189
C₄₀.C₈	6^th non-split extension by C₄₀ of C₈ acting via C₈/C₂=C₄	320		C40.C8	320,224
C₄₀.₁₀C₈	4^th non-split extension by C₄₀ of C₈ acting via C₈/C₄=C₂	320		C40.10C8	320,19
C₈xC₄₀	Abelian group of type [8,40]	320		C8xC40	320,126
C₄xC₈₀	Abelian group of type [4,80]	320		C4xC80	320,150
C₂xC₁₆₀	Abelian group of type [2,160]	320		C2xC160	320,174
C₁₆xF₅	Direct product of C₁₆ and F₅	80	4	C16xF5	320,181
D₅xC₃₂	Direct product of C₃₂ and D₅	160	2	D5xC32	320,4
C₅xD₃₂	Direct product of C₅ and D₃₂	160	2	C5xD32	320,176
C₅xSD₆₄	Direct product of C₅ and SD₆₄	160	2	C5xSD64	320,177
C₅xM₆(2)	Direct product of C₅ and M₆(2)	160	2	C5xM6(2)	320,175
C₅xQ₆₄	Direct product of C₅ and Q₆₄	320	2	C5xQ64	320,178
C₁₆xDic₅	Direct product of C₁₆ and Dic₅	320		C16xDic5	320,58
C₅xC₁₆:C₄	Direct product of C₅ and C₁₆:C₄	80	4	C5xC16:C4	320,152
C₅xC₈.Q₈	Direct product of C₅ and C₈.Q₈	80	4	C5xC8.Q8	320,170
C₅xC₈.C₈	Direct product of C₅ and C₈.C₈	80	2	C5xC8.C8	320,169
C₅xC₈.₄Q₈	Direct product of C₅ and C₈.₄Q₈	160	2	C5xC8.4Q8	320,173
C₈xC₅:C₈	Direct product of C₈ and C₅:C₈	320		C8xC5:C8	320,216
C₄xC₅:C₁₆	Direct product of C₄ and C₅:C₁₆	320		C4xC5:C16	320,195
C₂xC₅:C₃₂	Direct product of C₂ and C₅:C₃₂	320		C2xC5:C32	320,214
C₅xC₄:C₁₆	Direct product of C₅ and C₄:C₁₆	320		C5xC4:C16	320,168
C₅xC₈:C₈	Direct product of C₅ and C₈:C₈	320		C5xC8:C8	320,127
C₈xC₅:₂C₈	Direct product of C₈ and C₅:₂C₈	320		C8xC5:2C8	320,11
C₅xC₈:₂C₈	Direct product of C₅ and C₈:₂C₈	320		C5xC8:2C8	320,139
C₅xC₈:₁C₈	Direct product of C₅ and C₈:₁C₈	320		C5xC8:1C8	320,140
C₄xC₅:₂C₁₆	Direct product of C₄ and C₅:₂C₁₆	320		C4xC5:2C16	320,18
C₂xC₅:₂C₃₂	Direct product of C₂ and C₅:₂C₃₂	320		C2xC5:2C32	320,56
C₅xC₁₆:₅C₄	Direct product of C₅ and C₁₆:₅C₄	320		C5xC16:5C4	320,151
C₅xC₁₆:₃C₄	Direct product of C₅ and C₁₆:₃C₄	320		C5xC16:3C4	320,171
C₅xC₁₆:₄C₄	Direct product of C₅ and C₁₆:₄C₄	320		C5xC16:4C4	320,172

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
D₇xC₂₃	Direct product of C₂₃ and D₇	161	2	D7xC23	322,1
C₇xD₂₃	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; = C₂xD₈₁	162	2+	D162	324,4
Dic₈₁	Dicyclic group; = C₈₁ :C₄	324	2-	Dic81	324,1
C₉:C₃₆	The semidirect product of C₉ and C₃₆ acting via C₃₆/C₆=C₆	36	6	C9:C36	324,9
C₂₇:C₁₂	The semidirect product of C₂₇ and C₁₂ acting via C₁₂/C₂=C₆	108	6-	C27:C12	324,12
C₁₈²	Abelian group of type [18,18]	324		C18^2	324,81
C₉xC₃₆	Abelian group of type [9,36]	324		C9xC36	324,26
C₆xC₅₄	Abelian group of type [6,54]	324		C6xC54	324,84
C₂xC₁₆₂	Abelian group of type [2,162]	324		C2xC162	324,5
C₃xC₁₀₈	Abelian group of type [3,108]	324		C3xC108	324,29
D₉xC₁₈	Direct product of C₁₈ and D₉	36	2	D9xC18	324,61
C₉xDic₉	Direct product of C₉ and Dic₉	36	2	C9xDic9	324,6
S₃xC₅₄	Direct product of C₅₄ and S₃	108	2	S3xC54	324,66
C₆xD₂₇	Direct product of C₆ and D₂₇	108	2	C6xD27	324,65
C₃xDic₂₇	Direct product of C₃ and Dic₂₇	108	2	C3xDic27	324,10
Dic₃xC₂₇	Direct product of C₂₇ and Dic₃	108	2	Dic3xC27	324,11
C₂xC₉:C₁₈	Direct product of C₂ and C₉:C₁₈	36	6	C2xC9:C18	324,64
C₂xC₂₇:C₆	Direct product of C₂ and C₂₇:C₆	54	6+	C2xC27:C6	324,67
C₄xC₂₇:C₃	Direct product of C₄ and C₂₇:C₃	108	3	C4xC27:C3	324,30
C₂²xC₂₇:C₃	Direct product of C₂² and C₂₇:C₃	108		C2^2xC27:C3	324,85
C₄xC₉:C₉	Direct product of C₄ and C₉:C₉	324		C4xC9:C9	324,28
C₂²xC₉:C₉	Direct product of C₂² and C₉:C₉	324		C2^2xC9:C9	324,83

Groups of order 325

		d	ρ	Label	ID
C₃₂₅	Cyclic group	325	1	C325	325,1
C₅xC₆₅	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
D₁₆₄	Dihedral group	164	2+	D164	328,6
Dic₈₂	Dicyclic group; = C₄₁ :Q₈	328	2-	Dic82	328,4
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
C₂xC₁₆₄	Abelian group of type [2,164]	328		C2xC164	328,9
C₄xD₄₁	Direct product of C₄ and D₄₁	164	2	C4xD41	328,5
D₄xC₄₁	Direct product of C₄₁ and D₄	164	2	D4xC41	328,10
Q₈xC₄₁	Direct product of C₄₁ and Q₈	328	2	Q8xC41	328,11
C₂xDic₄₁	Direct product of C₂ and Dic₄₁	328		C2xDic41	328,7
C₂xC₄₁: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
C₃xF₁₁	Direct product of C₃ and F₁₁	33	10	C3xF11	330,1
S₃xC₅₅	Direct product of C₅₅ and S₃	165	2	S3xC55	330,8
D₅xC₃₃	Direct product of C₃₃ and D₅	165	2	D5xC33	330,6
C₃xD₅₅	Direct product of C₃ and D₅₅	165	2	C3xD55	330,7
C₅xD₃₃	Direct product of C₅ and D₃₃	165	2	C5xD33	330,9
C₁₅xD₁₁	Direct product of C₁₅ and D₁₁	165	2	C15xD11	330,5
C₁₁xD₁₅	Direct product of C₁₁ and D₁₅	165	2	C11xD15	330,10
S₃xC₁₁:C₅	Direct product of S₃ and C₁₁:C₅	33	10	S3xC11:C5	330,2
C₆xC₁₁: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; = C₂xD₈₃	166	2+	D166	332,3
Dic₈₃	Dicyclic group; = C₈₃ :C₄	332	2-	Dic83	332,1
C₂xC₁₆₆	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
C₃xC₁₁₁	Abelian group of type [3,111]	333		C3xC111	333,5
C₃xC₃₇: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
D₁₆₈	Dihedral group	168	2+	D168	336,93
Dic₈₄	Dicyclic group; = C₂₁ :₄ Q₁₆	336	2-	Dic84	336,94
D₅₆:C₃	The semidirect product of D₅₆ and C₃ acting faithfully	56	6+	D56:C3	336,10
C₈:F₇	3^rd semidirect product of C₈ and F₇ acting via F₇/C₇:C₃=C₂	56	6	C8:F7	336,8
C₅₆:C₆	2^nd semidirect product of C₅₆ and C₆ acting faithfully	56	6	C56:C6	336,9
C₇:C₄₈	The semidirect product of C₇ and C₄₈ acting via C₄₈/C₈=C₆	112	6	C7:C48	336,1
C₂₈:C₁₂	1^st semidirect product of C₂₈ and C₁₂ acting via C₁₂/C₂=C₆	112		C28:C12	336,16
C₅₆:S₃	4^th semidirect product of C₅₆ and S₃ acting via S₃/C₃=C₂	168	2	C56:S3	336,91
C₈:D₂₁	2^nd semidirect product of C₈ and D₂₁ acting via D₂₁/C₂₁=C₂	168	2	C8:D21	336,92
C₈₄:C₄	1^st semidirect product of C₈₄ and C₄ acting via C₄/C₂=C₂	336		C84:C4	336,99
C₂₁:C₁₆	1^st semidirect product of C₂₁ and C₁₆ acting via C₁₆/C₈=C₂	336	2	C21:C16	336,5
C₂₈.C₁₂	1^st non-split extension by C₂₈ of C₁₂ acting via C₁₂/C₂=C₆	56	6	C28.C12	336,13
C₈.F₇	The non-split extension by C₈ of F₇ acting via F₇/C₇:C₃=C₂	112	6-	C8.F7	336,11
C₈₄.C₄	1^st non-split extension by C₈₄ of C₄ acting via C₄/C₂=C₂	168	2	C84.C4	336,96
C₄xC₈₄	Abelian group of type [4,84]	336		C4xC84	336,106
C₂xC₁₆₈	Abelian group of type [2,168]	336		C2xC168	336,109
C₈xF₇	Direct product of C₈ and F₇	56	6	C8xF7	336,7
S₃xC₅₆	Direct product of C₅₆ and S₃	168	2	S3xC56	336,74
D₇xC₂₄	Direct product of C₂₄ and D₇	168	2	D7xC24	336,58
C₃xD₅₆	Direct product of C₃ and D₅₆	168	2	C3xD56	336,61
C₇xD₂₄	Direct product of C₇ and D₂₄	168	2	C7xD24	336,77
C₈xD₂₁	Direct product of C₈ and D₂₁	168	2	C8xD21	336,90
D₈xC₂₁	Direct product of C₂₁ and D₈	168	2	D8xC21	336,111
SD₁₆xC₂₁	Direct product of C₂₁ and SD₁₆	168	2	SD16xC21	336,112
M₄(2)xC₂₁	Direct product of C₂₁ and M₄(2)	168	2	M4(2)xC21	336,110
Q₁₆xC₂₁	Direct product of C₂₁ and Q₁₆	336	2	Q16xC21	336,113
C₃xDic₂₈	Direct product of C₃ and Dic₂₈	336	2	C3xDic28	336,62
C₁₂xDic₇	Direct product of C₁₂ and Dic₇	336		C12xDic7	336,65
C₇xDic₁₂	Direct product of C₇ and Dic₁₂	336	2	C7xDic12	336,78
Dic₃xC₂₈	Direct product of C₂₈ and Dic₃	336		Dic3xC28	336,81
C₄xDic₂₁	Direct product of C₄ and Dic₂₁	336		C4xDic21	336,97
D₈xC₇:C₃	Direct product of D₈ and C₇:C₃	56	6	D8xC7:C3	336,53
SD₁₆xC₇:C₃	Direct product of SD₁₆ and C₇:C₃	56	6	SD16xC7:C3	336,54
M₄(2)xC₇:C₃	Direct product of M₄(2) and C₇:C₃	56	6	M4(2)xC7:C3	336,52
C₁₆xC₇:C₃	Direct product of C₁₆ and C₇:C₃	112	3	C16xC7:C3	336,2
C₂xC₇:C₂₄	Direct product of C₂ and C₇:C₂₄	112		C2xC7:C24	336,12
C₄xC₇:C₁₂	Direct product of C₄ and C₇:C₁₂	112		C4xC7:C12	336,14
Q₁₆xC₇:C₃	Direct product of Q₁₆ and C₇:C₃	112	6	Q16xC7:C3	336,55
C₄²xC₇:C₃	Direct product of C₄² and C₇:C₃	112		C4^2xC7:C3	336,48
C₇xC₈:S₃	Direct product of C₇ and C₈:S₃	168	2	C7xC8:S3	336,75
C₃xC₈:D₇	Direct product of C₃ and C₈:D₇	168	2	C3xC8:D7	336,59
C₃xC₅₆:C₂	Direct product of C₃ and C₅₆:C₂	168	2	C3xC56:C2	336,60
C₇xC₂₄:C₂	Direct product of C₇ and C₂₄:C₂	168	2	C7xC24:C2	336,76
C₃xC₄.Dic₇	Direct product of C₃ and C₄.Dic₇	168	2	C3xC4.Dic7	336,64
C₇xC₄.Dic₃	Direct product of C₇ and C₄.Dic₃	168	2	C7xC4.Dic3	336,80
C₆xC₇:C₈	Direct product of C₆ and C₇:C₈	336		C6xC7:C8	336,63
C₇xC₃:C₁₆	Direct product of C₇ and C₃:C₁₆	336	2	C7xC3:C16	336,3
C₃xC₇:C₁₆	Direct product of C₃ and C₇:C₁₆	336	2	C3xC7:C16	336,4
C₁₄xC₃:C₈	Direct product of C₁₄ and C₃:C₈	336		C14xC3:C8	336,79
C₄:C₄xC₂₁	Direct product of C₂₁ and C₄:C₄	336		C4:C4xC21	336,108
C₂xC₂₁:C₈	Direct product of C₂ and C₂₁:C₈	336		C2xC21:C8	336,95
C₃xC₄:Dic₇	Direct product of C₃ and C₄:Dic₇	336		C3xC4:Dic7	336,67
C₇xC₄:Dic₃	Direct product of C₇ and C₄:Dic₃	336		C7xC4:Dic3	336,83
C₂xC₈xC₇:C₃	Direct product of C₂xC₈ and C₇:C₃	112		C2xC8xC7:C3	336,51
C₄:C₄xC₇:C₃	Direct product of C₄:C₄ and C₇:C₃	112		C4:C4xC7:C3	336,50

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
C₁₃xC₂₆	Abelian group of type [13,26]	338		C13xC26	338,5
C₁₃xD₁₃	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; = C₂xD₈₅	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
C₂xC₁₇₀	Abelian group of type [2,170]	340		C2xC170	340,15
C₁₇xF₅	Direct product of C₁₇ and F₅	85	4	C17xF5	340,7
D₅xC₃₄	Direct product of C₃₄ and D₅	170	2	D5xC34	340,13
C₁₀xD₁₇	Direct product of C₁₀ and D₁₇	170	2	C10xD17	340,12
C₁₇xDic₅	Direct product of C₁₇ and Dic₅	340	2	C17xDic5	340,1
C₅xDic₁₇	Direct product of C₅ and Dic₁₇	340	2	C5xDic17	340,2
C₅xC₁₇: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
C₅₇.C₆	The non-split extension by C₅₇ of C₆ acting faithfully	171	6	C57.C6	342,1
C₃xC₁₁₄	Abelian group of type [3,114]	342		C3xC114	342,18
S₃xC₅₇	Direct product of C₅₇ and S₃	114	2	S3xC57	342,14
C₃xD₅₇	Direct product of C₃ and D₅₇	114	2	C3xD57	342,15
D₉xC₁₉	Direct product of C₁₉ and D₉	171	2	D9xC19	342,3
C₉xD₁₉	Direct product of C₉ and D₁₉	171	2	C9xD19	342,4
C₃²xD₁₉	Direct product of C₃² and D₁₉	171		C3^2xD19	342,13
C₂xC₁₉:C₉	Direct product of C₂ and C₁₉:C₉	38	9	C2xC19:C9	342,8
C₃xC₁₉:C₆	Direct product of C₃ and C₁₉:C₆	57	6	C3xC19:C6	342,9
S₃xC₁₉:C₃	Direct product of S₃ and C₁₉:C₃	57	6	S3xC19:C3	342,10
C₆xC₁₉:C₃	Direct product of C₆ and C₁₉:C₃	114	3	C6xC19:C3	342,12
C₂xC₁₉:₂C₉	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
7_-¹⁺²	Extraspecial group	49	7	ES-(7,1)	343,4
C₇xC₄₉	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
D₁₇₂	Dihedral group	172	2+	D172	344,5
Dic₈₆	Dicyclic group; = C₄₃ :Q₈	344	2-	Dic86	344,3
C₄₃:C₈	The semidirect product of C₄₃ and C₈ acting via C₈/C₄=C₂	344	2	C43:C8	344,1
C₂xC₁₇₂	Abelian group of type [2,172]	344		C2xC172	344,8
C₄xD₄₃	Direct product of C₄ and D₄₃	172	2	C4xD43	344,4
D₄xC₄₃	Direct product of C₄₃ and D₄	172	2	D4xC43	344,9
Q₈xC₄₃	Direct product of C₄₃ and Q₈	344	2	Q8xC43	344,10
C₂xDic₄₃	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; = C₂xD₈₇	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
C₂xC₁₇₄	Abelian group of type [2,174]	348		C2xC174	348,12
S₃xC₅₈	Direct product of C₅₈ and S₃	174	2	S3xC58	348,10
C₆xD₂₉	Direct product of C₆ and D₂₉	174	2	C6xD29	348,9
Dic₃xC₂₉	Direct product of C₂₉ and Dic₃	348	2	Dic3xC29	348,1
C₃xDic₂₉	Direct product of C₃ and Dic₂₉	348	2	C3xDic29	348,2
C₃xC₂₉: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
C₅xC₇₀	Abelian group of type [5,70]	350		C5xC70	350,10
D₅xC₃₅	Direct product of C₃₅ and D₅	70	2	D5xC35	350,6
C₅xD₃₅	Direct product of C₅ and D₃₅	70	2	C5xD35	350,7
C₇xD₂₅	Direct product of C₇ and D₂₅	175	2	C7xD25	350,1
D₇xC₂₅	Direct product of C₂₅ and D₇	175	2	D7xC25	350,2
D₇xC₅²	Direct product of C₅² and D₇	175		D7xC5^2	350,5

Groups of order 351

		d	ρ	Label	ID
C₃₅₁	Cyclic group	351	1	C351	351,2
C₁₁₇:C₃	2^nd semidirect product of C₁₁₇ and C₃ acting faithfully	117	3	C117:C3	351,4
C₁₁₇:₃C₃	3^rd semidirect product of C₁₁₇ and C₃ acting faithfully	117	3	C117:3C3	351,5
C₁₃:C₂₇	The semidirect product of C₁₃ and C₂₇ acting via C₂₇/C₉=C₃	351	3	C13:C27	351,1
C₃xC₁₁₇	Abelian group of type [3,117]	351		C3xC117	351,9
C₁₃x3_-¹⁺²	Direct product of C₁₃ and 3_-¹⁺²	117	3	C13xES-(3,1)	351,11
C₉xC₁₃:C₃	Direct product of C₉ and C₁₃:C₃	117	3	C9xC13:C3	351,3
C₃xC₁₃: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
D₁₇₆	Dihedral group	176	2+	D176	352,5
Dic₈₈	Dicyclic group; = C₁₁ :₁ Q₃₂	352	2-	Dic88	352,7
C₁₇₆:C₂	2^nd semidirect product of C₁₇₆ and C₂ acting faithfully	176	2	C176:C2	352,6
C₁₁:C₃₂	The semidirect product of C₁₁ and C₃₂ acting via C₃₂/C₁₆=C₂	352	2	C11:C32	352,1
C₄₄:C₈	1^st semidirect product of C₄₄ and C₈ acting via C₈/C₄=C₂	352		C44:C8	352,10
C₈₈:C₄	4^th semidirect product of C₈₈ and C₄ acting via C₄/C₂=C₂	352		C88:C4	352,21
D₂₂.C₈	The non-split extension by D₂₂ of C₈ acting via C₈/C₄=C₂	176	2	D22.C8	352,4
C₄₄.C₈	1^st non-split extension by C₄₄ of C₈ acting via C₈/C₄=C₂	176	2	C44.C8	352,18
C₈₈.C₄	1^st non-split extension by C₈₈ of C₄ acting via C₄/C₂=C₂	176	2	C88.C4	352,25
C₄₄.₄Q₈	1^st non-split extension by C₄₄ of Q₈ acting via Q₈/C₄=C₂	352		C44.4Q8	352,23
C₄₄.₅Q₈	2^nd non-split extension by C₄₄ of Q₈ acting via Q₈/C₄=C₂	352		C44.5Q8	352,24
C₄xC₈₈	Abelian group of type [4,88]	352		C4xC88	352,45
C₂xC₁₇₆	Abelian group of type [2,176]	352		C2xC176	352,58
C₁₆xD₁₁	Direct product of C₁₆ and D₁₁	176	2	C16xD11	352,3
C₁₁xD₁₆	Direct product of C₁₁ and D₁₆	176	2	C11xD16	352,60
C₁₁xSD₃₂	Direct product of C₁₁ and SD₃₂	176	2	C11xSD32	352,61
C₁₁xM₅(2)	Direct product of C₁₁ and M₅(2)	176	2	C11xM5(2)	352,59
C₁₁xQ₃₂	Direct product of C₁₁ and Q₃₂	352	2	C11xQ32	352,62
C₈xDic₁₁	Direct product of C₈ and Dic₁₁	352		C8xDic11	352,19
C₁₁xC₈.C₄	Direct product of C₁₁ and C₈.C₄	176	2	C11xC8.C4	352,57
C₄xC₁₁:C₈	Direct product of C₄ and C₁₁:C₈	352		C4xC11:C8	352,8
C₁₁xC₄:C₈	Direct product of C₁₁ and C₄:C₈	352		C11xC4:C8	352,54
C₂xC₁₁:C₁₆	Direct product of C₂ and C₁₁:C₁₆	352		C2xC11:C16	352,17
C₁₁xC₈:C₄	Direct product of C₁₁ and C₈:C₄	352		C11xC8:C4	352,46
C₁₁xC₂.D₈	Direct product of C₁₁ and C₂.D₈	352		C11xC2.D8	352,56
C₁₁xC₄.Q₈	Direct product of C₁₁ and C₄.Q₈	352		C11xC4.Q8	352,55

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
S₃xC₅₉	Direct product of C₅₉ and S₃	177	2	S3xC59	354,1
C₃xD₅₉	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; = C₂xD₈₉	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
C₂xC₁₇₈	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
C₁₇xC₇: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
D₁₈₀	Dihedral group	180	2+	D180	360,27
Dic₉₀	Dicyclic group; = C₄₅ :₂ Q₈	360	2-	Dic90	360,25
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
C₆xC₆₀	Abelian group of type [6,60]	360		C6xC60	360,115
C₂xC₁₈₀	Abelian group of type [2,180]	360		C2xC180	360,30
C₃xC₁₂₀	Abelian group of type [3,120]	360		C3xC120	360,38
C₁₈xF₅	Direct product of C₁₈ and F₅	90	4	C18xF5	360,43
S₃xC₆₀	Direct product of C₆₀ and S₃	120	2	S3xC60	360,96
C₃xD₆₀	Direct product of C₃ and D₆₀	120	2	C3xD60	360,102
C₁₅xD₁₂	Direct product of C₁₅ and D₁₂	120	2	C15xD12	360,97
C₁₂xD₁₅	Direct product of C₁₂ and D₁₅	120	2	C12xD15	360,101
C₁₅xDic₆	Direct product of C₁₅ and Dic₆	120	2	C15xDic6	360,95
Dic₃xC₃₀	Direct product of C₃₀ and Dic₃	120		Dic3xC30	360,98
C₃xDic₃₀	Direct product of C₃ and Dic₃₀	120	2	C3xDic30	360,100
C₆xDic₁₅	Direct product of C₆ and Dic₁₅	120		C6xDic15	360,103
D₅xC₃₆	Direct product of C₃₆ and D₅	180	2	D5xC36	360,16
C₉xD₂₀	Direct product of C₉ and D₂₀	180	2	C9xD20	360,17
D₉xC₂₀	Direct product of C₂₀ and D₉	180	2	D9xC20	360,21
C₅xD₃₆	Direct product of C₅ and D₃₆	180	2	C5xD36	360,22
C₄xD₄₅	Direct product of C₄ and D₄₅	180	2	C4xD45	360,26
D₄xC₄₅	Direct product of C₄₅ and D₄	180	2	D4xC45	360,31
C₃²xD₂₀	Direct product of C₃² and D₂₀	180		C3^2xD20	360,92
Q₈xC₄₅	Direct product of C₄₅ and Q₈	360	2	Q8xC45	360,32
C₉xDic₁₀	Direct product of C₉ and Dic₁₀	360	2	C9xDic10	360,15
C₁₈xDic₅	Direct product of C₁₈ and Dic₅	360		C18xDic5	360,18
C₅xDic₁₈	Direct product of C₅ and Dic₁₈	360	2	C5xDic18	360,20
C₁₀xDic₉	Direct product of C₁₀ and Dic₉	360		C10xDic9	360,23
C₂xDic₄₅	Direct product of C₂ and Dic₄₅	360		C2xDic45	360,28
C₃²xDic₁₀	Direct product of C₃² and Dic₁₀	360		C3^2xDic10	360,90
C₆xC₃:F₅	Direct product of C₆ and C₃:F₅	60	4	C6xC3:F5	360,146
C₂xC₉:F₅	Direct product of C₂ and C₉:F₅	90	4	C2xC9:F5	360,44
C₃xC₆xF₅	Direct product of C₃xC₆ and F₅	90		C3xC6xF5	360,145
C₁₅xC₃:C₈	Direct product of C₁₅ and C₃:C₈	120	2	C15xC3:C8	360,34
C₃xC₁₅:C₈	Direct product of C₃ and C₁₅:C₈	120	4	C3xC15:C8	360,53
C₃xC₁₅:₃C₈	Direct product of C₃ and C₁₅:₃C₈	120	2	C3xC15:3C8	360,35
D₅xC₃xC₁₂	Direct product of C₃xC₁₂ and D₅	180		D5xC3xC12	360,91
D₄xC₃xC₁₅	Direct product of C₃xC₁₅ and D₄	180		D4xC3xC15	360,116
C₅xC₉:C₈	Direct product of C₅ and C₉:C₈	360	2	C5xC9:C8	360,1
C₉xC₅:C₈	Direct product of C₉ and C₅:C₈	360	4	C9xC5:C8	360,5
Q₈xC₃xC₁₅	Direct product of C₃xC₁₅ and Q₈	360		Q8xC3xC15	360,117
C₉xC₅:₂C₈	Direct product of C₉ and C₅:₂C₈	360	2	C9xC5:2C8	360,2
C₃²xC₅:C₈	Direct product of C₃² and C₅:C₈	360		C3^2xC5:C8	360,52
C₃xC₆xDic₅	Direct product of C₃xC₆ and Dic₅	360		C3xC6xDic5	360,93
C₃²xC₅:₂C₈	Direct product of C₃² and C₅:₂C₈	360		C3^2xC5:2C8	360,33

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
C₁₁xC₃₃	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; = C₂xD₉₁	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
C₂xC₁₈₂	Abelian group of type [2,182]	364		C2xC182	364,11
D₇xC₂₆	Direct product of C₂₆ and D₇	182	2	D7xC26	364,9
C₁₄xD₁₃	Direct product of C₁₄ and D₁₃	182	2	C14xD13	364,8
C₁₃xDic₇	Direct product of C₁₃ and Dic₇	364	2	C13xDic7	364,1
C₇xDic₁₃	Direct product of C₇ and Dic₁₃	364	2	C7xDic13	364,2
C₇xC₁₃: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
S₃xC₆₁	Direct product of C₆₁ and S₃	183	2	S3xC61	366,3
C₃xD₆₁	Direct product of C₃ and D₆₁	183	2	C3xD61	366,4
C₂xC₆₁: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
D₁₈₄	Dihedral group	184	2+	D184	368,6
Dic₉₂	Dicyclic group; = C₂₃ :₁ Q₁₆	368	2-	Dic92	368,7
C₈:D₂₃	3^rd semidirect product of C₈ and D₂₃ acting via D₂₃/C₂₃=C₂	184	2	C8:D23	368,4
C₁₈₄:C₂	2^nd semidirect product of C₁₈₄ and C₂ acting faithfully	184	2	C184:C2	368,5
C₂₃:C₁₆	The semidirect product of C₂₃ and C₁₆ acting via C₁₆/C₈=C₂	368	2	C23:C16	368,1
C₉₂:C₄	1^st semidirect product of C₉₂ and C₄ acting via C₄/C₂=C₂	368		C92:C4	368,12
C₉₂.C₄	1^st non-split extension by C₉₂ of C₄ acting via C₄/C₂=C₂	184	2	C92.C4	368,9
C₄xC₉₂	Abelian group of type [4,92]	368		C4xC92	368,19
C₂xC₁₈₄	Abelian group of type [2,184]	368		C2xC184	368,22
C₈xD₂₃	Direct product of C₈ and D₂₃	184	2	C8xD23	368,3
D₈xC₂₃	Direct product of C₂₃ and D₈	184	2	D8xC23	368,24
SD₁₆xC₂₃	Direct product of C₂₃ and SD₁₆	184	2	SD16xC23	368,25
M₄(2)xC₂₃	Direct product of C₂₃ and M₄(2)	184	2	M4(2)xC23	368,23
Q₁₆xC₂₃	Direct product of C₂₃ and Q₁₆	368	2	Q16xC23	368,26
C₄xDic₂₃	Direct product of C₄ and Dic₂₃	368		C4xDic23	368,10
C₂xC₂₃:C₈	Direct product of C₂ and C₂₃:C₈	368		C2xC23:C8	368,8
C₄:C₄xC₂₃	Direct product of C₂₃ and C₄:C₄	368		C4:C4xC23	368,21

Groups of order 369

		d	ρ	Label	ID
C₃₆₉	Cyclic group	369	1	C369	369,1
C₃xC₁₂₃	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
D₅xC₃₇	Direct product of C₃₇ and D₅	185	2	D5xC37	370,1
C₅xD₃₇	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; = C₂xD₉₃	186	2+	D186	372,14
Dic₉₃	Dicyclic group; = C₉₃ :₁ C₄	372	2-	Dic93	372,5
C₃₁:C₁₂	The semidirect product of C₃₁ and C₁₂ acting via C₁₂/C₂=C₆	124	6-	C31:C12	372,1
C₂xC₁₈₆	Abelian group of type [2,186]	372		C2xC186	372,15
S₃xC₆₂	Direct product of C₆₂ and S₃	186	2	S3xC62	372,13
C₆xD₃₁	Direct product of C₆ and D₃₁	186	2	C6xD31	372,12
Dic₃xC₃₁	Direct product of C₃₁ and Dic₃	372	2	Dic3xC31	372,3
C₃xDic₃₁	Direct product of C₃ and Dic₃₁	372	2	C3xDic31	372,4
C₂xC₃₁:C₆	Direct product of C₂ and C₃₁:C₆	62	6+	C2xC31:C6	372,7
C₄xC₃₁:C₃	Direct product of C₄ and C₃₁:C₃	124	3	C4xC31:C3	372,2
C₂²xC₃₁: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
C₁₇xD₁₁	Direct product of C₁₇ and D₁₁	187	2	C17xD11	374,1
C₁₁xD₁₇	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
C₅xC₇₅	Abelian group of type [5,75]	375		C5xC75	375,3
C₃x5_-¹⁺²	Direct product of C₃ and 5_-¹⁺²	75	5	C3xES-(5,1)	375,5

Groups of order 376

		d	ρ	Label	ID
C₃₇₆	Cyclic group	376	1	C376	376,2
D₁₈₈	Dihedral group	188	2+	D188	376,5
Dic₉₄	Dicyclic group; = C₄₇ :Q₈	376	2-	Dic94	376,3
C₄₇:C₈	The semidirect product of C₄₇ and C₈ acting via C₈/C₄=C₂	376	2	C47:C8	376,1
C₂xC₁₈₈	Abelian group of type [2,188]	376		C2xC188	376,8
C₄xD₄₇	Direct product of C₄ and D₄₇	188	2	C4xD47	376,4
D₄xC₄₇	Direct product of C₄₇ and D₄	188	2	D4xC47	376,9
Q₈xC₄₇	Direct product of C₄₇ and Q₈	376	2	Q8xC47	376,10
C₂xDic₄₇	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
C₉:₃F₇	1^st semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:3F7	378,8
C₉:₄F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/D₇=C₃	63	6	C9:4F7	378,9
C₉:F₇	1^st semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:F7	378,18
C₉:₂F₇	2^nd semidirect product of C₉ and F₇ acting via F₇/C₇=C₆	63	6+	C9:2F7	378,19
C₉:₅F₇	The semidirect product of C₉ and F₇ acting via F₇/C₇:C₃=C₂	63	6+	C9:5F7	378,20
C₆₃:C₆	5^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:C6	378,13
C₆₃:₆C₆	6^th semidirect product of C₆₃ and C₆ acting faithfully	63	6	C63:6C6	378,14
D₆₃:C₃	1^st semidirect product of D₆₃ and C₃ acting faithfully	63	6+	D63:C3	378,39
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
C₃xC₁₂₆	Abelian group of type [3,126]	378		C3xC126	378,44
C₉xF₇	Direct product of C₉ and F₇	63	6	C9xF7	378,7
D₇x3_-¹⁺²	Direct product of D₇ and 3_-¹⁺²	63	6	D7xES-(3,1)	378,31
S₃xC₆₃	Direct product of C₆₃ and S₃	126	2	S3xC63	378,33
D₉xC₂₁	Direct product of C₂₁ and D₉	126	2	D9xC21	378,32
C₃xD₆₃	Direct product of C₃ and D₆₃	126	2	C3xD63	378,36
C₉xD₂₁	Direct product of C₉ and D₂₁	126	2	C9xD21	378,37
C₁₄x3_-¹⁺²	Direct product of C₁₄ and 3_-¹⁺²	126	3	C14xES-(3,1)	378,46
C₇xD₂₇	Direct product of C₇ and D₂₇	189	2	C7xD27	378,3
D₇xC₂₇	Direct product of C₂₇ and D₇	189	2	D7xC27	378,4
D₉xC₇:C₃	Direct product of D₉ and C₇:C₃	63	6	D9xC7:C3	378,15
C₇xC₉:C₆	Direct product of C₇ and C₉:C₆	63	6	C7xC9:C6	378,35
S₃xC₇:C₉	Direct product of S₃ and C₇:C₉	126	6	S3xC7:C9	378,16
C₁₈xC₇:C₃	Direct product of C₁₈ and C₇:C₃	126	3	C18xC7:C3	378,23
C₂xC₆₃:C₃	Direct product of C₂ and C₆₃:C₃	126	3	C2xC63:C3	378,24
C₂xC₆₃:₃C₃	Direct product of C₂ and C₆₃:₃C₃	126	3	C2xC63:3C3	378,25
D₇xC₃xC₉	Direct product of C₃xC₉ and D₇	189		D7xC3xC9	378,29
C₃xC₇:C₁₈	Direct product of C₃ and C₇:C₁₈	189		C3xC7:C18	378,10
C₆xC₇:C₉	Direct product of C₆ and C₇:C₉	378		C6xC7:C9	378,26
C₂xC₇:C₂₇	Direct product of C₂ and C₇:C₂₇	378	3	C2xC7:C27	378,2

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; = C₂xD₉₅	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
C₂xC₁₉₀	Abelian group of type [2,190]	380		C2xC190	380,11
C₁₉xF₅	Direct product of C₁₉ and F₅	95	4	C19xF5	380,5
D₅xC₃₈	Direct product of C₃₈ and D₅	190	2	D5xC38	380,9
C₁₀xD₁₉	Direct product of C₁₀ and D₁₉	190	2	C10xD19	380,8
C₁₉xDic₅	Direct product of C₁₉ and Dic₅	380	2	C19xDic5	380,1
C₅xDic₁₉	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
C₇xC₁₁: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
C₃xC₁₂₉	Abelian group of type [3,129]	387		C3xC129	387,4
C₃xC₄₃: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; = C₂xD₉₇	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
C₂xC₁₉₄	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
S₃xC₆₅	Direct product of C₆₅ and S₃	195	2	S3xC65	390,8
D₅xC₃₉	Direct product of C₃₉ and D₅	195	2	D5xC39	390,6
C₃xD₆₅	Direct product of C₃ and D₆₅	195	2	C3xD65	390,7
C₅xD₃₉	Direct product of C₅ and D₃₉	195	2	C5xD39	390,9
C₁₅xD₁₃	Direct product of C₁₅ and D₁₃	195	2	C15xD13	390,5
C₁₃xD₁₅	Direct product of C₁₃ and D₁₅	195	2	C13xD15	390,10
C₅xC₁₃:C₆	Direct product of C₅ and C₁₃:C₆	65	6	C5xC13:C6	390,1
D₅xC₁₃:C₃	Direct product of D₅ and C₁₃:C₃	65	6	D5xC13:C3	390,2
C₁₀xC₁₃: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
D₁₉₆	Dihedral group	196	2+	D196	392,5
Dic₉₈	Dicyclic group; = C₄₉ :Q₈	392	2-	Dic98	392,3
C₄₉:C₈	The semidirect product of C₄₉ and C₈ acting via C₈/C₄=C₂	392	2	C49:C8	392,1
C₇xC₅₆	Abelian group of type [7,56]	392		C7xC56	392,16
C₂xC₁₉₆	Abelian group of type [2,196]	392		C2xC196	392,8
C₁₄xC₂₈	Abelian group of type [14,28]	392		C14xC28	392,33
D₇xC₂₈	Direct product of C₂₈ and D₇	56	2	D7xC28	392,24
C₇xD₂₈	Direct product of C₇ and D₂₈	56	2	C7xD28	392,25
C₇xDic₁₄	Direct product of C₇ and Dic₁₄	56	2	C7xDic14	392,23
C₁₄xDic₇	Direct product of C₁₄ and Dic₇	56		C14xDic7	392,26
C₄xD₄₉	Direct product of C₄ and D₄₉	196	2	C4xD49	392,4
D₄xC₄₉	Direct product of C₄₉ and D₄	196	2	D4xC49	392,9
D₄xC₇²	Direct product of C₇² and D₄	196		D4xC7^2	392,34
Q₈xC₄₉	Direct product of C₄₉ and Q₈	392	2	Q8xC49	392,10
Q₈xC₇²	Direct product of C₇² and Q₈	392		Q8xC7^2	392,35
C₂xDic₄₉	Direct product of C₂ and Dic₄₉	392		C2xDic49	392,6
C₇xC₇:C₈	Direct product of C₇ and C₇:C₈	56	2	C7xC7:C8	392,14

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; = C₂xD₉₉	198	2+	D198	396,9
Dic₉₉	Dicyclic group; = C₉₉ :₁ C₄	396	2-	Dic99	396,3
C₆xC₆₆	Abelian group of type [6,66]	396		C6xC66	396,30
C₂xC₁₉₈	Abelian group of type [2,198]	396		C2xC198	396,10
C₃xC₁₃₂	Abelian group of type [3,132]	396		C3xC132	396,16
S₃xC₆₆	Direct product of C₆₆ and S₃	132	2	S3xC66	396,26
C₆xD₃₃	Direct product of C₆ and D₃₃	132	2	C6xD33	396,27
Dic₃xC₃₃	Direct product of C₃₃ and Dic₃	132	2	Dic3xC33	396,12
C₃xDic₃₃	Direct product of C₃ and Dic₃₃	132	2	C3xDic33	396,13
D₉xC₂₂	Direct product of C₂₂ and D₉	198	2	D9xC22	396,8
C₁₈xD₁₁	Direct product of C₁₈ and D₁₁	198	2	C18xD11	396,7
C₁₁xDic₉	Direct product of C₁₁ and Dic₉	396	2	C11xDic9	396,1
C₉xDic₁₁	Direct product of C₉ and Dic₁₁	396	2	C9xDic11	396,2
C₃²xDic₁₁	Direct product of C₃² and Dic₁₁	396		C3^2xDic11	396,11
C₃xC₆xD₁₁	Direct product of C₃xC₆ and D₁₁	198		C3xC6xD11	396,25

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
C₁₉xC₇:C₃	Direct product of C₁₉ and C₇:C₃	133	3	C19xC7:C3	399,1
C₇xC₁₉: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
D₂₀₀	Dihedral group	200	2+	D200	400,8
Dic₁₀₀	Dicyclic group; = C₂₅ :₁ Q₁₆	400	2-	Dic100	400,4
C₁₀₀:C₄	1^st semidirect product of C₁₀₀ and C₄ acting faithfully	100	4	C100:C4	400,31
D₂₅:C₈	The semidirect product of D₂₅ and C₈ acting via C₈/C₄=C₂	200	4	D25:C8	400,28
C₈:D₂₅	3^rd semidirect product of C₈ and D₂₅ acting via D₂₅/C₂₅=C₂	200	2	C8:D25	400,6
C₂₀₀:C₂	2^nd semidirect product of C₂₀₀ and C₂ acting faithfully	200	2	C200:C2	400,7
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
C₄:Dic₂₅	The semidirect product of C₄ and Dic₂₅ acting via Dic₂₅/C₅₀=C₂	400		C4:Dic25	400,13
C₄.Dic₂₅	The non-split extension by C₄ of Dic₂₅ acting via Dic₂₅/C₅₀=C₂	200	2	C4.Dic25	400,10
C₁₀₀.C₄	1^st non-split extension by C₁₀₀ of C₄ acting faithfully	200	4	C100.C4	400,29
C₂₀²	Abelian group of type [20,20]	400		C20^2	400,108
C₅xC₈₀	Abelian group of type [5,80]	400		C5xC80	400,51
C₄xC₁₀₀	Abelian group of type [4,100]	400		C4xC100	400,20
C₂xC₂₀₀	Abelian group of type [2,200]	400		C2xC200	400,23
C₁₀xC₄₀	Abelian group of type [10,40]	400		C10xC40	400,111
D₅xC₄₀	Direct product of C₄₀ and D₅	80	2	D5xC40	400,76
C₅xD₄₀	Direct product of C₅ and D₄₀	80	2	C5xD40	400,79
C₂₀xF₅	Direct product of C₂₀ and F₅	80	4	C20xF5	400,137
C₅xDic₂₀	Direct product of C₅ and Dic₂₀	80	2	C5xDic20	400,80
Dic₅xC₂₀	Direct product of C₂₀ and Dic₅	80		Dic5xC20	400,83
C₈xD₂₅	Direct product of C₈ and D₂₅	200	2	C8xD25	400,5
D₈xC₂₅	Direct product of C₂₅ and D₈	200	2	D8xC25	400,25
D₈xC₅²	Direct product of C₅² and D₈	200		D8xC5^2	400,113
SD₁₆xC₂₅	Direct product of C₂₅ and SD₁₆	200	2	SD16xC25	400,26
M₄(2)xC₂₅	Direct product of C₂₅ and M₄(2)	200	2	M4(2)xC25	400,24
SD₁₆xC₅²	Direct product of C₅² and SD₁₆	200		SD16xC5^2	400,114
M₄(2)xC₅²	Direct product of C₅² and M₄(2)	200		M4(2)xC5^2	400,112
Q₁₆xC₂₅	Direct product of C₂₅ and Q₁₆	400	2	Q16xC25	400,27
C₄xDic₂₅	Direct product of C₄ and Dic₂₅	400		C4xDic25	400,11
Q₁₆xC₅²	Direct product of C₅² and Q₁₆	400		Q16xC5^2	400,115
C₅xC₄.Dic₅	Direct product of C₅ and C₄.Dic₅	40	2	C5xC4.Dic5	400,82
C₅xC₅:C₁₆	Direct product of C₅ and C₅:C₁₆	80	4	C5xC5:C16	400,56
C₁₀xC₅:C₈	Direct product of C₁₀ and C₅:C₈	80		C10xC5:C8	400,139
C₅xC₄:F₅	Direct product of C₅ and C₄:F₅	80	4	C5xC4:F5	400,138
C₅xD₅:C₈	Direct product of C₅ and D₅:C₈	80	4	C5xD5:C8	400,135
C₅xC₈:D₅	Direct product of C₅ and C₈:D₅	80	2	C5xC8:D5	400,77
C₅xC₄₀:C₂	Direct product of C₅ and C₄₀:C₂	80	2	C5xC40:C2	400,78
C₅xC₅:₂C₁₆	Direct product of C₅ and C₅:₂C₁₆	80	2	C5xC5:2C16	400,49
C₁₀xC₅:₂C₈	Direct product of C₁₀ and C₅:₂C₈	80		C10xC5:2C8	400,81
C₅xC₄.F₅	Direct product of C₅ and C₄.F₅	80	4	C5xC4.F5	400,136
C₅xC₄:Dic₅	Direct product of C₅ and C₄:Dic₅	80		C5xC4:Dic5	400,85
C₄xC₂₅:C₄	Direct product of C₄ and C₂₅:C₄	100	4	C4xC25:C4	400,30
C₂xC₂₅:C₈	Direct product of C₂ and C₂₅:C₈	400		C2xC25:C8	400,32
C₄:C₄xC₂₅	Direct product of C₂₅ and C₄:C₄	400		C4:C4xC25	400,22
C₂xC₂₅:₂C₈	Direct product of C₂ and C₂₅:₂C₈	400		C2xC25:2C8	400,9
C₄:C₄xC₅²	Direct product of C₅² and C₄:C₄	400		C4:C4xC5^2	400,110

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
S₃xC₆₇	Direct product of C₆₇ and S₃	201	2	S3xC67	402,3
C₃xD₆₇	Direct product of C₃ and D₆₇	201	2	C3xD67	402,4
C₂xC₆₇: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; = C₂xD₁₀₁	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
C₂xC₂₀₂	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
C₉xC₄₅	Abelian group of type [9,45]	405		C9xC45	405,2
C₃xC₁₃₅	Abelian group of type [3,135]	405		C3xC135	405,5
C₅xC₂₇:C₃	Direct product of C₅ and C₂₇:C₃	135	3	C5xC27:C3	405,6
C₅xC₉:C₉	Direct product of C₅ and C₉:C₉	405		C5xC9:C9	405,4

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
D₇xC₂₉	Direct product of C₂₉ and D₇	203	2	D7xC29	406,3
C₇xD₂₉	Direct product of C₇ and D₂₉	203	2	C7xD29	406,4
C₂xC₂₉: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
D₂₀₄	Dihedral group	204	2+	D204	408,27
Dic₁₀₂	Dicyclic group; = C₅₁ :₂ Q₈	408	2-	Dic102	408,25
C₅₁:C₈	1^st semidirect product of C₅₁ and C₈ acting faithfully	51	8	C51:C8	408,34
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
C₂xC₂₀₄	Abelian group of type [2,204]	408		C2xC204	408,30
S₃xC₆₈	Direct product of C₆₈ and S₃	204	2	S3xC68	408,21
C₃xD₆₈	Direct product of C₃ and D₆₈	204	2	C3xD68	408,17
C₄xD₅₁	Direct product of C₄ and D₅₁	204	2	C4xD51	408,26
D₄xC₅₁	Direct product of C₅₁ and D₄	204	2	D4xC51	408,31
C₁₂xD₁₇	Direct product of C₁₂ and D₁₇	204	2	C12xD17	408,16
C₁₇xD₁₂	Direct product of C₁₇ and D₁₂	204	2	C17xD12	408,22
Q₈xC₅₁	Direct product of C₅₁ and Q₈	408	2	Q8xC51	408,32
C₃xDic₃₄	Direct product of C₃ and Dic₃₄	408	2	C3xDic34	408,15
C₆xDic₁₇	Direct product of C₆ and Dic₁₇	408		C6xDic17	408,18
C₁₇xDic₆	Direct product of C₁₇ and Dic₆	408	2	C17xDic6	408,20
Dic₃xC₃₄	Direct product of C₃₄ and Dic₃	408		Dic3xC34	408,23
C₂xDic₅₁	Direct product of C₂ and Dic₅₁	408		C2xDic51	408,28
C₃xC₁₇:C₈	Direct product of C₃ and C₁₇:C₈	51	8	C3xC17:C8	408,33
C₆xC₁₇:C₄	Direct product of C₆ and C₁₇:C₄	102	4	C6xC17:C4	408,39
C₂xC₅₁:C₄	Direct product of C₂ and C₅₁:C₄	102	4	C2xC51:C4	408,40
C₁₇xC₃:C₈	Direct product of C₁₇ and C₃:C₈	408	2	C17xC3:C8	408,1
C₃xC₁₇:₃C₈	Direct product of C₃ and C₁₇:₃C₈	408	2	C3xC17:3C8	408,2
C₃xC₁₇:₂C₈	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
D₅xC₄₁	Direct product of C₄₁ and D₅	205	2	D5xC41	410,3
C₅xD₄₁	Direct product of C₅ and D₄₁	205	2	C5xD41	410,4
C₂xC₄₁:C₅	Direct product of C₂ and C₄₁:C₅	82	5	C2xC41:C5	410,2

Groups of order 411

		d	ρ	Label	ID
C₄₁₁	Cyclic group	411	1	C411	411,1

Groups of order 412

		d	ρ	Label	ID
C₄₁₂	Cyclic group	412	1	C412	412,2
D₂₀₆	Dihedral group; = C₂xD₁₀₃	206	2+	D206	412,3
Dic₁₀₃	Dicyclic group; = C₁₀₃ :C₄	412	2-	Dic103	412,1
C₂xC₂₀₆	Abelian group of type [2,206]	412		C2xC206	412,4

Groups of order 413

		d	ρ	Label	ID
C₄₁₃	Cyclic group	413	1	C413	413,1

Groups of order 414

		d	ρ	Label	ID
C₄₁₄	Cyclic group	414	1	C414	414,4
D₂₀₇	Dihedral group	207	2+	D207	414,3
C₃xC₁₃₈	Abelian group of type [3,138]	414		C3xC138	414,10
S₃xC₆₉	Direct product of C₆₉ and S₃	138	2	S3xC69	414,6
C₃xD₆₉	Direct product of C₃ and D₆₉	138	2	C3xD69	414,7
D₉xC₂₃	Direct product of C₂₃ and D₉	207	2	D9xC23	414,1
C₉xD₂₃	Direct product of C₉ and D₂₃	207	2	C9xD23	414,2
C₃²xD₂₃	Direct product of C₃² and D₂₃	207		C3^2xD23	414,5

Groups of order 415

		d	ρ	Label	ID
C₄₁₅	Cyclic group	415	1	C415	415,1

Groups of order 416

		d	ρ	Label	ID
C₄₁₆	Cyclic group	416	1	C416	416,2
D₂₀₈	Dihedral group	208	2+	D208	416,6
Dic₁₀₄	Dicyclic group; = C₁₃ :₁ Q₃₂	416	2-	Dic104	416,8
C₁₀₄:C₄	4^th semidirect product of C₁₀₄ and C₄ acting faithfully	104	4	C104:C4	416,67
D₁₃:C₁₆	The semidirect product of D₁₃ and C₁₆ acting via C₁₆/C₈=C₂	208	4	D13:C16	416,64
C₂₀₈:C₂	4^th semidirect product of C₂₀₈ and C₂ acting faithfully	208	2	C208:C2	416,5
C₁₆:D₁₃	2^nd semidirect product of C₁₆ and D₁₃ acting via D₁₃/C₁₃=C₂	208	2	C16:D13	416,7
C₁₃:C₃₂	The semidirect product of C₁₃ and C₃₂ acting via C₃₂/C₈=C₄	416	4	C13:C32	416,3
C₅₂:₃C₈	1^st semidirect product of C₅₂ and C₈ acting via C₈/C₄=C₂	416		C52:3C8	416,11
C₅₂:C₈	1^st semidirect product of C₅₂ and C₈ acting via C₈/C₂=C₄	416		C52:C8	416,76
C₁₃:₂C₃₂	The semidirect product of C₁₃ and C₃₂ acting via C₃₂/C₁₆=C₂	416	2	C13:2C32	416,1
C₁₀₄:₈C₄	4^th semidirect product of C₁₀₄ and C₄ acting via C₄/C₂=C₂	416		C104:8C4	416,22
C₁₀₄:₆C₄	2^nd semidirect product of C₁₀₄ and C₄ acting via C₄/C₂=C₂	416		C104:6C4	416,24
C₁₀₄:₅C₄	1^st semidirect product of C₁₀₄ and C₄ acting via C₄/C₂=C₂	416		C104:5C4	416,25
D₂₆.₈D₄	4^th non-split extension by D₂₆ of D₄ acting via D₄/C₄=C₂	104	4	D26.8D4	416,68
D₁₃.D₈	The non-split extension by D₁₃ of D₈ acting via D₈/C₈=C₂	104	4	D13.D8	416,69
C₅₂.₄C₈	1^st non-split extension by C₅₂ of C₈ acting via C₈/C₄=C₂	208	2	C52.4C8	416,19
C₅₂.C₈	1^st non-split extension by C₅₂ of C₈ acting via C₈/C₂=C₄	208	4	C52.C8	416,73
C₁₀₄.₆C₄	1^st non-split extension by C₁₀₄ of C₄ acting via C₄/C₂=C₂	208	2	C104.6C4	416,26
C₁₀₄.C₄	2^nd non-split extension by C₁₀₄ of C₄ acting faithfully	208	4	C104.C4	416,70
C₁₀₄.₁C₄	1^st non-split extension by C₁₀₄ of C₄ acting faithfully	208	4	C104.1C4	416,71
D₂₆.C₈	3^rd non-split extension by D₂₆ of C₈ acting via C₈/C₄=C₂	208	4	D26.C8	416,65
C₄xC₁₀₄	Abelian group of type [4,104]	416		C4xC104	416,46
C₂xC₂₀₈	Abelian group of type [2,208]	416		C2xC208	416,59
C₁₆xD₁₃	Direct product of C₁₆ and D₁₃	208	2	C16xD13	416,4
C₁₃xD₁₆	Direct product of C₁₃ and D₁₆	208	2	C13xD16	416,61
C₁₃xSD₃₂	Direct product of C₁₃ and SD₃₂	208	2	C13xSD32	416,62
C₁₃xM₅(2)	Direct product of C₁₃ and M₅(2)	208	2	C13xM5(2)	416,60
C₁₃xQ₃₂	Direct product of C₁₃ and Q₃₂	416	2	C13xQ32	416,63
C₈xDic₁₃	Direct product of C₈ and Dic₁₃	416		C8xDic13	416,20
C₈xC₁₃:C₄	Direct product of C₈ and C₁₃:C₄	104	4	C8xC13:C4	416,66
C₁₃xC₈.C₄	Direct product of C₁₃ and C₈.C₄	208	2	C13xC8.C4	416,58
C₄xC₁₃:C₈	Direct product of C₄ and C₁₃:C₈	416		C4xC13:C8	416,75
C₁₃xC₄:C₈	Direct product of C₁₃ and C₄:C₈	416		C13xC4:C8	416,55
C₂xC₁₃:C₁₆	Direct product of C₂ and C₁₃:C₁₆	416		C2xC13:C16	416,72
C₁₃xC₈:C₄	Direct product of C₁₃ and C₈:C₄	416		C13xC8:C4	416,47
C₄xC₁₃:₂C₈	Direct product of C₄ and C₁₃:₂C₈	416		C4xC13:2C8	416,9
C₂xC₁₃:₂C₁₆	Direct product of C₂ and C₁₃:₂C₁₆	416		C2xC13:2C16	416,18
C₁₃xC₂.D₈	Direct product of C₁₃ and C₂.D₈	416		C13xC2.D8	416,57
C₁₃xC₄.Q₈	Direct product of C₁₃ and C₄.Q₈	416		C13xC4.Q8	416,56

Groups of order 417

		d	ρ	Label	ID
C₄₁₇	Cyclic group	417	1	C417	417,2
C₁₃₉:C₃	The semidirect product of C₁₃₉ and C₃ acting faithfully	139	3	C139:C3	417,1

Groups of order 418

		d	ρ	Label	ID
C₄₁₈	Cyclic group	418	1	C418	418,4
D₂₀₉	Dihedral group	209	2+	D209	418,3
C₁₉xD₁₁	Direct product of C₁₉ and D₁₁	209	2	C19xD11	418,1
C₁₁xD₁₉	Direct product of C₁₁ and D₁₉	209	2	C11xD19	418,2

Groups of order 419

		d	ρ	Label	ID
C₄₁₉	Cyclic group	419	1	C419	419,1

Groups of order 420

		d	ρ	Label	ID
C₄₂₀	Cyclic group	420	1	C420	420,12
D₂₁₀	Dihedral group; = C₂xD₁₀₅	210	2+	D210	420,40
Dic₁₀₅	Dicyclic group; = C₃ :Dic₃₅	420	2-	Dic105	420,11
C₃₅:C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting faithfully	35	12	C35:C12	420,15
C₅:Dic₂₁	The semidirect product of C₅ and Dic₂₁ acting via Dic₂₁/C₂₁=C₄	105	4	C5:Dic21	420,23
C₃₅:₃C₁₂	1^st semidirect product of C₃₅ and C₁₂ acting via C₁₂/C₂=C₆	140	6-	C35:3C12	420,3
C₂xC₂₁₀	Abelian group of type [2,210]	420		C2xC210	420,41
C₁₀xF₇	Direct product of C₁₀ and F₇	70	6	C10xF7	420,17
F₅xC₂₁	Direct product of C₂₁ and F₅	105	4	F5xC21	420,20
S₃xC₇₀	Direct product of C₇₀ and S₃	210	2	S3xC70	420,37
D₇xC₃₀	Direct product of C₃₀ and D₇	210	2	D7xC30	420,34
D₅xC₄₂	Direct product of C₄₂ and D₅	210	2	D5xC42	420,35
C₆xD₃₅	Direct product of C₆ and D₃₅	210	2	C6xD35	420,36
C₁₀xD₂₁	Direct product of C₁₀ and D₂₁	210	2	C10xD21	420,38
C₁₄xD₁₅	Direct product of C₁₄ and D₁₅	210	2	C14xD15	420,39
C₁₅xDic₇	Direct product of C₁₅ and Dic₇	420	2	C15xDic7	420,5
Dic₅xC₂₁	Direct product of C₂₁ and Dic₅	420	2	Dic5xC21	420,6
C₃xDic₃₅	Direct product of C₃ and Dic₃₅	420	2	C3xDic35	420,7
Dic₃xC₃₅	Direct product of C₃₅ and Dic₃	420	2	Dic3xC35	420,8
C₅xDic₂₁	Direct product of C₅ and Dic₂₁	420	2	C5xDic21	420,9
C₇xDic₁₅	Direct product of C₇ and Dic₁₅	420	2	C7xDic15	420,10
F₅xC₇:C₃	Direct product of F₅ and C₇:C₃	35	12	F5xC7:C3	420,14
C₂xC₅:F₇	Direct product of C₂ and C₅:F₇	70	6+	C2xC5:F7	420,19
C₃xC₇:F₅	Direct product of C₃ and C₇:F₅	105	4	C3xC7:F5	420,21
C₇xC₃:F₅	Direct product of C₇ and C₃:F₅	105	4	C7xC3:F5	420,22
C₅xC₇:C₁₂	Direct product of C₅ and C₇:C₁₂	140	6	C5xC7:C12	420,1
C₂₀xC₇:C₃	Direct product of C₂₀ and C₇:C₃	140	3	C20xC7:C3	420,4
Dic₅xC₇:C₃	Direct product of Dic₅ and C₇:C₃	140	6	Dic5xC7:C3	420,2
C₂xD₅xC₇:C₃	Direct product of C₂, D₅ and C₇:C₃	70	6	C2xD5xC7:C3	420,18
C₂xC₁₀xC₇:C₃	Direct product of C₂xC₁₀ and C₇:C₃	140		C2xC10xC7:C3	420,31

Groups of order 421

		d	ρ	Label	ID
C₄₂₁	Cyclic group	421	1	C421	421,1

Groups of order 422

		d	ρ	Label	ID
C₄₂₂	Cyclic group	422	1	C422	422,2
D₂₁₁	Dihedral group	211	2+	D211	422,1

Groups of order 423

		d	ρ	Label	ID
C₄₂₃	Cyclic group	423	1	C423	423,1
C₃xC₁₄₁	Abelian group of type [3,141]	423		C3xC141	423,2

Groups of order 424

		d	ρ	Label	ID
C₄₂₄	Cyclic group	424	1	C424	424,2
D₂₁₂	Dihedral group	212	2+	D212	424,6
Dic₁₀₆	Dicyclic group; = C₅₃ :Q₈	424	2-	Dic106	424,4
C₅₃:C₈	The semidirect product of C₅₃ and C₈ acting via C₈/C₂=C₄	424	4-	C53:C8	424,3
C₅₃:₂C₈	The semidirect product of C₅₃ and C₈ acting via C₈/C₄=C₂	424	2	C53:2C8	424,1
C₂xC₂₁₂	Abelian group of type [2,212]	424		C2xC212	424,9
C₄xD₅₃	Direct product of C₄ and D₅₃	212	2	C4xD53	424,5
D₄xC₅₃	Direct product of C₅₃ and D₄	212	2	D4xC53	424,10
Q₈xC₅₃	Direct product of C₅₃ and Q₈	424	2	Q8xC53	424,11
C₂xDic₅₃	Direct product of C₂ and Dic₅₃	424		C2xDic53	424,7
C₂xC₅₃:C₄	Direct product of C₂ and C₅₃:C₄	106	4+	C2xC53:C4	424,12

Groups of order 425

		d	ρ	Label	ID
C₄₂₅	Cyclic group	425	1	C425	425,1
C₅xC₈₅	Abelian group of type [5,85]	425		C5xC85	425,2

Groups of order 426

		d	ρ	Label	ID
C₄₂₆	Cyclic group	426	1	C426	426,4
D₂₁₃	Dihedral group	213	2+	D213	426,3
S₃xC₇₁	Direct product of C₇₁ and S₃	213	2	S3xC71	426,1
C₃xD₇₁	Direct product of C₃ and D₇₁	213	2	C3xD71	426,2

Groups of order 427

		d	ρ	Label	ID
C₄₂₇	Cyclic group	427	1	C427	427,1

Groups of order 428

		d	ρ	Label	ID
C₄₂₈	Cyclic group	428	1	C428	428,2
D₂₁₄	Dihedral group; = C₂xD₁₀₇	214	2+	D214	428,3
Dic₁₀₇	Dicyclic group; = C₁₀₇ :C₄	428	2-	Dic107	428,1
C₂xC₂₁₄	Abelian group of type [2,214]	428		C2xC214	428,4

Groups of order 429

		d	ρ	Label	ID
C₄₂₉	Cyclic group	429	1	C429	429,2
C₁₁xC₁₃:C₃	Direct product of C₁₁ and C₁₃:C₃	143	3	C11xC13:C3	429,1

Groups of order 430

		d	ρ	Label	ID
C₄₃₀	Cyclic group	430	1	C430	430,4
D₂₁₅	Dihedral group	215	2+	D215	430,3
D₅xC₄₃	Direct product of C₄₃ and D₅	215	2	D5xC43	430,1
C₅xD₄₃	Direct product of C₅ and D₄₃	215	2	C5xD43	430,2

Groups of order 431

		d	ρ	Label	ID
C₄₃₁	Cyclic group	431	1	C431	431,1

Groups of order 432

		d	ρ	Label	ID
C₄₃₂	Cyclic group	432	1	C432	432,2
D₂₁₆	Dihedral group	216	2+	D216	432,8
Dic₁₀₈	Dicyclic group; = C₂₇ :₁ Q₁₆	432	2-	Dic108	432,4
D₇₂:C₃	The semidirect product of D₇₂ and C₃ acting faithfully	72	6+	D72:C3	432,123
C₇₂:C₆	4^th semidirect product of C₇₂ and C₆ acting faithfully	72	6	C72:C6	432,121
C₇₂:₂C₆	2^nd semidirect product of C₇₂ and C₆ acting faithfully	72	6	C72:2C6	432,122
C₉:C₄₈	The semidirect product of C₉ and C₄₈ acting via C₄₈/C₈=C₆	144	6	C9:C48	432,31
C₃₆:C₁₂	1^st semidirect product of C₃₆ and C₁₂ acting via C₁₂/C₂=C₆	144		C36:C12	432,146
C₈:D₂₇	3^rd semidirect product of C₈ and D₂₇ acting via D₂₇/C₂₇=C₂	216	2	C8:D27	432,6
C₂₁₆:C₂	2^nd semidirect product of C₂₁₆ and C₂ acting faithfully	216	2	C216:C2	432,7
C₂₇:C₁₆	The semidirect product of C₂₇ and C₁₆ acting via C₁₆/C₈=C₂	432	2	C27:C16	432,1
C₄:Dic₂₇	The semidirect product of C₄ and Dic₂₇ acting via Dic₂₇/C₅₄=C₂	432		C4:Dic27	432,13
C₃₆.C₁₂	1^st non-split extension by C₃₆ of C₁₂ acting via C₁₂/C₂=C₆	72	6	C36.C12	432,143
C₇₂.C₆	1^st non-split extension by C₇₂ of C₆ acting faithfully	144	6-	C72.C6	432,119
C₄.Dic₂₇	The non-split extension by C₄ of Dic₂₇ acting via Dic₂₇/C₅₄=C₂	216	2	C4.Dic27	432,10
C₆xC₇₂	Abelian group of type [6,72]	432		C6xC72	432,209
C₄xC₁₀₈	Abelian group of type [4,108]	432		C4xC108	432,20
C₂xC₂₁₆	Abelian group of type [2,216]	432		C2xC216	432,23
C₃xC₁₄₄	Abelian group of type [3,144]	432		C3xC144	432,34
C₁₂xC₃₆	Abelian group of type [12,36]	432		C12xC36	432,200
D₈x3_-¹⁺²	Direct product of D₈ and 3_-¹⁺²	72	6	D8xES-(3,1)	432,217
SD₁₆x3_-¹⁺²	Direct product of SD₁₆ and 3_-¹⁺²	72	6	SD16xES-(3,1)	432,220
M₄(2)x3_-¹⁺²	Direct product of M₄(2) and 3_-¹⁺²	72	6	M4(2)xES-(3,1)	432,214
S₃xC₇₂	Direct product of C₇₂ and S₃	144	2	S3xC72	432,109
D₉xC₂₄	Direct product of C₂₄ and D₉	144	2	D9xC24	432,105
C₃xD₇₂	Direct product of C₃ and D₇₂	144	2	C3xD72	432,108
C₉xD₂₄	Direct product of C₉ and D₂₄	144	2	C9xD24	432,112
C₃xDic₃₆	Direct product of C₃ and Dic₃₆	144	2	C3xDic36	432,104
C₉xDic₁₂	Direct product of C₉ and Dic₁₂	144	2	C9xDic12	432,113
C₁₂xDic₉	Direct product of C₁₂ and Dic₉	144		C12xDic9	432,128
Dic₃xC₃₆	Direct product of C₃₆ and Dic₃	144		Dic3xC36	432,131
C₁₆x3_-¹⁺²	Direct product of C₁₆ and 3_-¹⁺²	144	3	C16xES-(3,1)	432,36
Q₁₆x3_-¹⁺²	Direct product of Q₁₆ and 3_-¹⁺²	144	6	Q16xES-(3,1)	432,223
C₄²x3_-¹⁺²	Direct product of C₄² and 3_-¹⁺²	144		C4^2xES-(3,1)	432,202
C₈xD₂₇	Direct product of C₈ and D₂₇	216	2	C8xD27	432,5
D₈xC₂₇	Direct product of C₂₇ and D₈	216	2	D8xC27	432,25
SD₁₆xC₂₇	Direct product of C₂₇ and SD₁₆	216	2	SD16xC27	432,26
M₄(2)xC₂₇	Direct product of C₂₇ and M₄(2)	216	2	M4(2)xC27	432,24
Q₁₆xC₂₇	Direct product of C₂₇ and Q₁₆	432	2	Q16xC27	432,27
C₄xDic₂₇	Direct product of C₄ and Dic₂₇	432		C4xDic27	432,11
C₈xC₉:C₆	Direct product of C₈ and C₉:C₆	72	6	C8xC9:C6	432,120
C₃xC₄.Dic₉	Direct product of C₃ and C₄.Dic₉	72	2	C3xC4.Dic9	432,125
C₉xC₄.Dic₃	Direct product of C₉ and C₄.Dic₃	72	2	C9xC4.Dic3	432,127
C₆xC₉:C₈	Direct product of C₆ and C₉:C₈	144		C6xC9:C8	432,124
C₃xC₉:C₁₆	Direct product of C₃ and C₉:C₁₆	144	2	C3xC9:C16	432,28
C₉xC₃:C₁₆	Direct product of C₉ and C₃:C₁₆	144	2	C9xC3:C16	432,29
C₁₈xC₃:C₈	Direct product of C₁₈ and C₃:C₈	144		C18xC3:C8	432,126
C₂xC₉:C₂₄	Direct product of C₂ and C₉:C₂₄	144		C2xC9:C24	432,142
C₄xC₉:C₁₂	Direct product of C₄ and C₉:C₁₂	144		C4xC9:C12	432,144
C₉xC₈:S₃	Direct product of C₉ and C₈:S₃	144	2	C9xC8:S3	432,110
C₃xC₈:D₉	Direct product of C₃ and C₈:D₉	144	2	C3xC8:D9	432,106
C₃xC₇₂:C₂	Direct product of C₃ and C₇₂:C₂	144	2	C3xC72:C2	432,107
C₉xC₂₄:C₂	Direct product of C₉ and C₂₄:C₂	144	2	C9xC24:C2	432,111
C₃xC₄:Dic₉	Direct product of C₃ and C₄:Dic₉	144		C3xC4:Dic9	432,130
C₉xC₄:Dic₃	Direct product of C₉ and C₄:Dic₃	144		C9xC4:Dic3	432,133
C₂xC₈x3_-¹⁺²	Direct product of C₂xC₈ and 3_-¹⁺²	144		C2xC8xES-(3,1)	432,211
C₄:C₄x3_-¹⁺²	Direct product of C₄:C₄ and 3_-¹⁺²	144		C4:C4xES-(3,1)	432,208
D₈xC₃xC₉	Direct product of C₃xC₉ and D₈	216		D8xC3xC9	432,215
SD₁₆xC₃xC₉	Direct product of C₃xC₉ and SD₁₆	216		SD16xC3xC9	432,218
M₄(2)xC₃xC₉	Direct product of C₃xC₉ and M₄(2)	216		M4(2)xC3xC9	432,212
C₂xC₂₇:C₈	Direct product of C₂ and C₂₇:C₈	432		C2xC27:C8	432,9
C₄:C₄xC₂₇	Direct product of C₂₇ and C₄:C₄	432		C4:C4xC27	432,22
Q₁₆xC₃xC₉	Direct product of C₃xC₉ and Q₁₆	432		Q16xC3xC9	432,221
C₄:C₄xC₃xC₉	Direct product of C₃xC₉ and C₄:C₄	432		C4:C4xC3xC9	432,206

Groups of order 433

		d	ρ	Label	ID
C₄₃₃	Cyclic group	433	1	C433	433,1

Groups of order 434

		d	ρ	Label	ID
C₄₃₄	Cyclic group	434	1	C434	434,4
D₂₁₇	Dihedral group	217	2+	D217	434,3
D₇xC₃₁	Direct product of C₃₁ and D₇	217	2	D7xC31	434,1
C₇xD₃₁	Direct product of C₇ and D₃₁	217	2	C7xD31	434,2

Groups of order 435

		d	ρ	Label	ID
C₄₃₅	Cyclic group	435	1	C435	435,1

Groups of order 436

		d	ρ	Label	ID
C₄₃₆	Cyclic group	436	1	C436	436,2
D₂₁₈	Dihedral group; = C₂xD₁₀₉	218	2+	D218	436,4
Dic₁₀₉	Dicyclic group; = C₁₀₉ :₂ C₄	436	2-	Dic109	436,1
C₁₀₉:C₄	The semidirect product of C₁₀₉ and C₄ acting faithfully	109	4+	C109:C4	436,3
C₂xC₂₁₈	Abelian group of type [2,218]	436		C2xC218	436,5

Groups of order 437

		d	ρ	Label	ID
C₄₃₇	Cyclic group	437	1	C437	437,1

Groups of order 438

		d	ρ	Label	ID
C₄₃₈	Cyclic group	438	1	C438	438,6
D₂₁₉	Dihedral group	219	2+	D219	438,5
C₇₃:C₆	The semidirect product of C₇₃ and C₆ acting faithfully	73	6+	C73:C6	438,1
S₃xC₇₃	Direct product of C₇₃ and S₃	219	2	S3xC73	438,3
C₃xD₇₃	Direct product of C₃ and D₇₃	219	2	C3xD73	438,4
C₂xC₇₃:C₃	Direct product of C₂ and C₇₃:C₃	146	3	C2xC73:C3	438,2

Groups of order 439

		d	ρ	Label	ID
C₄₃₉	Cyclic group	439	1	C439	439,1

Groups of order 440

		d	ρ	Label	ID
C₄₄₀	Cyclic group	440	1	C440	440,6
D₂₂₀	Dihedral group	220	2+	D220	440,36
Dic₁₁₀	Dicyclic group; = C₅₅ :₂ Q₈	440	2-	Dic110	440,34
D₄₄:C₅	The semidirect product of D₄₄ and C₅ acting faithfully	44	10+	D44:C5	440,9
C₁₁:C₄₀	The semidirect product of C₁₁ and C₄₀ acting via C₄₀/C₄=C₁₀	88	10	C11:C40	440,1
C₅₅:₃C₈	1^st semidirect product of C₅₅ and C₈ acting via C₈/C₄=C₂	440	2	C55:3C8	440,5
C₅₅:C₈	1^st semidirect product of C₅₅ and C₈ acting via C₈/C₂=C₄	440	4	C55:C8	440,16
C₄.F₁₁	The non-split extension by C₄ of F₁₁ acting via F₁₁/C₁₁:C₅=C₂	88	10-	C4.F11	440,7
C₂xC₂₂₀	Abelian group of type [2,220]	440		C2xC220	440,39
C₄xF₁₁	Direct product of C₄ and F₁₁	44	10	C4xF11	440,8
F₅xC₂₂	Direct product of C₂₂ and F₅	110	4	F5xC22	440,45
C₅xD₄₄	Direct product of C₅ and D₄₄	220	2	C5xD44	440,26
D₅xC₄₄	Direct product of C₄₄ and D₅	220	2	D5xC44	440,30
C₄xD₅₅	Direct product of C₄ and D₅₅	220	2	C4xD55	440,35
D₄xC₅₅	Direct product of C₅₅ and D₄	220	2	D4xC55	440,40
C₂₀xD₁₁	Direct product of C₂₀ and D₁₁	220	2	C20xD11	440,25
C₁₁xD₂₀	Direct product of C₁₁ and D₂₀	220	2	C11xD20	440,31
Q₈xC₅₅	Direct product of C₅₅ and Q₈	440	2	Q8xC55	440,41
C₅xDic₂₂	Direct product of C₅ and Dic₂₂	440	2	C5xDic22	440,24
Dic₅xC₂₂	Direct product of C₂₂ and Dic₅	440		Dic5xC22	440,32
C₂xDic₅₅	Direct product of C₂ and Dic₅₅	440		C2xDic55	440,37
C₁₀xDic₁₁	Direct product of C₁₀ and Dic₁₁	440		C10xDic11	440,27
C₁₁xDic₁₀	Direct product of C₁₁ and Dic₁₀	440	2	C11xDic10	440,29
D₄xC₁₁:C₅	Direct product of D₄ and C₁₁:C₅	44	10	D4xC11:C5	440,13
C₈xC₁₁:C₅	Direct product of C₈ and C₁₁:C₅	88	5	C8xC11:C5	440,2
Q₈xC₁₁:C₅	Direct product of Q₈ and C₁₁:C₅	88	10	Q8xC11:C5	440,14
C₂xC₁₁:C₂₀	Direct product of C₂ and C₁₁:C₂₀	88		C2xC11:C20	440,10
C₂xC₁₁:F₅	Direct product of C₂ and C₁₁:F₅	110	4	C2xC11:F5	440,46
C₅xC₁₁:C₈	Direct product of C₅ and C₁₁:C₈	440	2	C5xC11:C8	440,4
C₁₁xC₅:C₈	Direct product of C₁₁ and C₅:C₈	440	4	C11xC5:C8	440,15
C₁₁xC₅:₂C₈	Direct product of C₁₁ and C₅:₂C₈	440	2	C11xC5:2C8	440,3
C₂xC₄xC₁₁:C₅	Direct product of C₂xC₄ and C₁₁:C₅	88		C2xC4xC11:C5	440,12

Groups of order 441

		d	ρ	Label	ID
C₄₄₁	Cyclic group	441	1	C441	441,2
C₄₉:C₉	The semidirect product of C₄₉ and C₉ acting via C₉/C₃=C₃	441	3	C49:C9	441,1
C₂₁²	Abelian group of type [21,21]	441		C21^2	441,13
C₇xC₆₃	Abelian group of type [7,63]	441		C7xC63	441,8
C₃xC₁₄₇	Abelian group of type [3,147]	441		C3xC147	441,4
C₇xC₇:C₉	Direct product of C₇ and C₇:C₉	63	3	C7xC7:C9	441,5
C₇:C₃xC₂₁	Direct product of C₂₁ and C₇:C₃	63	3	C7:C3xC21	441,10
C₃xC₄₉:C₃	Direct product of C₃ and C₄₉:C₃	147	3	C3xC49:C3	441,3

Groups of order 442

		d	ρ	Label	ID
C₄₄₂	Cyclic group	442	1	C442	442,4
D₂₂₁	Dihedral group	221	2+	D221	442,3
C₁₇xD₁₃	Direct product of C₁₇ and D₁₃	221	2	C17xD13	442,1
C₁₃xD₁₇	Direct product of C₁₃ and D₁₇	221	2	C13xD17	442,2

Groups of order 443

		d	ρ	Label	ID
C₄₄₃	Cyclic group	443	1	C443	443,1

Groups of order 444

		d	ρ	Label	ID
C₄₄₄	Cyclic group	444	1	C444	444,6
D₂₂₂	Dihedral group; = C₂xD₁₁₁	222	2+	D222	444,17
Dic₁₁₁	Dicyclic group; = C₃ :Dic₃₇	444	2-	Dic111	444,5
C₃₇:C₁₂	The semidirect product of C₃₇ and C₁₂ acting faithfully	37	12+	C37:C12	444,7
C₃₇:Dic₃	The semidirect product of C₃₇ and Dic₃ acting via Dic₃/C₃=C₄	111	4	C37:Dic3	444,10
C₇₄.C₆	The non-split extension by C₇₄ of C₆ acting faithfully	148	6-	C74.C6	444,1
C₂xC₂₂₂	Abelian group of type [2,222]	444		C2xC222	444,18
S₃xC₇₄	Direct product of C₇₄ and S₃	222	2	S3xC74	444,16
C₆xD₃₇	Direct product of C₆ and D₃₇	222	2	C6xD37	444,15
Dic₃xC₃₇	Direct product of C₃₇ and Dic₃	444	2	Dic3xC37	444,3
C₃xDic₃₇	Direct product of C₃ and Dic₃₇	444	2	C3xDic37	444,4
C₂xC₃₇:C₆	Direct product of C₂ and C₃₇:C₆	74	6+	C2xC37:C6	444,8
C₃xC₃₇:C₄	Direct product of C₃ and C₃₇:C₄	111	4	C3xC37:C4	444,9
C₄xC₃₇:C₃	Direct product of C₄ and C₃₇:C₃	148	3	C4xC37:C3	444,2
C₂²xC₃₇:C₃	Direct product of C₂² and C₃₇:C₃	148		C2^2xC37:C3	444,12

Groups of order 445

		d	ρ	Label	ID
C₄₄₅	Cyclic group	445	1	C445	445,1

Groups of order 446

		d	ρ	Label	ID
C₄₄₆	Cyclic group	446	1	C446	446,2
D₂₂₃	Dihedral group	223	2+	D223	446,1

Groups of order 447

		d	ρ	Label	ID
C₄₄₇	Cyclic group	447	1	C447	447,1

Groups of order 448

		d	ρ	Label	ID
C₄₄₈	Cyclic group	448	1	C448	448,2
D₂₂₄	Dihedral group	224	2+	D224	448,5
Dic₁₁₂	Dicyclic group; = C₇ :₁ Q₆₄	448	2-	Dic112	448,7
C₁₁₂:C₄	2^nd semidirect product of C₁₁₂ and C₄ acting faithfully	112	4	C112:C4	448,69
C₁₆:Dic₇	1^st semidirect product of C₁₆ and Dic₇ acting via Dic₇/C₇=C₄	112	4	C16:Dic7	448,70
C₃₂:D₇	3^rd semidirect product of C₃₂ and D₇ acting via D₇/C₇=C₂	224	2	C32:D7	448,4
C₂₂₄:C₂	2^nd semidirect product of C₂₂₄ and C₂ acting faithfully	224	2	C224:C2	448,6
C₇:M₆(2)	The semidirect product of C₇ and M₆(2) acting via M₆(2)/C₂xC₁₆=C₂	224	2	C7:M6(2)	448,56
C₇:C₆₄	The semidirect product of C₇ and C₆₄ acting via C₆₄/C₃₂=C₂	448	2	C7:C64	448,1
C₅₆:C₈	4^th semidirect product of C₅₆ and C₈ acting via C₈/C₄=C₂	448		C56:C8	448,12
C₅₆:₂C₈	2^nd semidirect product of C₅₆ and C₈ acting via C₈/C₄=C₂	448		C56:2C8	448,14
C₅₆:₁C₈	1^st semidirect product of C₅₆ and C₈ acting via C₈/C₄=C₂	448		C56:1C8	448,15
C₂₈:C₁₆	1^st semidirect product of C₂₈ and C₁₆ acting via C₁₆/C₈=C₂	448		C28:C16	448,19
C₁₁₂:₉C₄	5^th semidirect product of C₁₁₂ and C₄ acting via C₄/C₂=C₂	448		C112:9C4	448,59
C₁₁₂:₅C₄	1^st semidirect product of C₁₁₂ and C₄ acting via C₄/C₂=C₂	448		C112:5C4	448,61
C₁₁₂:₆C₄	2^nd semidirect product of C₁₁₂ and C₄ acting via C₄/C₂=C₂	448		C112:6C4	448,62
C₅₆.₁₆Q₈	6^th non-split extension by C₅₆ of Q₈ acting via Q₈/C₄=C₂	112	2	C56.16Q8	448,20
C₁₁₂.C₄	1^st non-split extension by C₁₁₂ of C₄ acting via C₄/C₂=C₂	224	2	C112.C4	448,63
C₅₆.C₈	4^th non-split extension by C₅₆ of C₈ acting via C₈/C₄=C₂	448		C56.C8	448,18
C₈xC₅₆	Abelian group of type [8,56]	448		C8xC56	448,125
C₄xC₁₁₂	Abelian group of type [4,112]	448		C4xC112	448,149
C₂xC₂₂₄	Abelian group of type [2,224]	448		C2xC224	448,173
D₇xC₃₂	Direct product of C₃₂ and D₇	224	2	D7xC32	448,3
C₇xD₃₂	Direct product of C₇ and D₃₂	224	2	C7xD32	448,175
C₇xSD₆₄	Direct product of C₇ and SD₆₄	224	2	C7xSD64	448,176
C₇xM₆(2)	Direct product of C₇ and M₆(2)	224	2	C7xM6(2)	448,174
C₇xQ₆₄	Direct product of C₇ and Q₆₄	448	2	C7xQ64	448,177
C₁₆xDic₇	Direct product of C₁₆ and Dic₇	448		C16xDic7	448,57
C₇xC₁₆:C₄	Direct product of C₇ and C₁₆:C₄	112	4	C7xC16:C4	448,151
C₇xC₈.Q₈	Direct product of C₇ and C₈.Q₈	112	4	C7xC8.Q8	448,169
C₇xC₈.C₈	Direct product of C₇ and C₈.C₈	112	2	C7xC8.C8	448,168
C₇xC₈.₄Q₈	Direct product of C₇ and C₈.₄Q₈	224	2	C7xC8.4Q8	448,172
C₈xC₇:C₈	Direct product of C₈ and C₇:C₈	448		C8xC7:C8	448,10
C₄xC₇:C₁₆	Direct product of C₄ and C₇:C₁₆	448		C4xC7:C16	448,17
C₂xC₇:C₃₂	Direct product of C₂ and C₇:C₃₂	448		C2xC7:C32	448,55
C₇xC₄:C₁₆	Direct product of C₇ and C₄:C₁₆	448		C7xC4:C16	448,167
C₇xC₈:C₈	Direct product of C₇ and C₈:C₈	448		C7xC8:C8	448,126
C₇xC₈:₂C₈	Direct product of C₇ and C₈:₂C₈	448		C7xC8:2C8	448,138
C₇xC₈:₁C₈	Direct product of C₇ and C₈:₁C₈	448		C7xC8:1C8	448,139
C₇xC₁₆:₅C₄	Direct product of C₇ and C₁₆:₅C₄	448		C7xC16:5C4	448,150
C₇xC₁₆:₃C₄	Direct product of C₇ and C₁₆:₃C₄	448		C7xC16:3C4	448,170
C₇xC₁₆:₄C₄	Direct product of C₇ and C₁₆:₄C₄	448		C7xC16:4C4	448,171

Groups of order 449

		d	ρ	Label	ID
C₄₄₉	Cyclic group	449	1	C449	449,1

Groups of order 450

		d	ρ	Label	ID
C₄₅₀	Cyclic group	450	1	C450	450,4
D₂₂₅	Dihedral group	225	2+	D225	450,3
C₅xC₉₀	Abelian group of type [5,90]	450		C5xC90	450,19
C₃xC₁₅₀	Abelian group of type [3,150]	450		C3xC150	450,10
C₁₅xC₃₀	Abelian group of type [15,30]	450		C15xC30	450,34
C₁₅xD₁₅	Direct product of C₁₅ and D₁₅	30	2	C15xD15	450,29
D₅xC₄₅	Direct product of C₄₅ and D₅	90	2	D5xC45	450,14
C₅xD₄₅	Direct product of C₅ and D₄₅	90	2	C5xD45	450,17
S₃xC₇₅	Direct product of C₇₅ and S₃	150	2	S3xC75	450,6
C₃xD₇₅	Direct product of C₃ and D₇₅	150	2	C3xD75	450,7
D₉xC₂₅	Direct product of C₂₅ and D₉	225	2	D9xC25	450,1
C₉xD₂₅	Direct product of C₉ and D₂₅	225	2	C9xD25	450,2
D₉xC₅²	Direct product of C₅² and D₉	225		D9xC5^2	450,16
C₃²xD₂₅	Direct product of C₃² and D₂₅	225		C3^2xD25	450,5
D₅xC₃xC₁₅	Direct product of C₃xC₁₅ and D₅	90		D5xC3xC15	450,26
S₃xC₅xC₁₅	Direct product of C₅xC₁₅ and S₃	150		S3xC5xC15	450,28

Groups of order 451

		d	ρ	Label	ID
C₄₅₁	Cyclic group	451	1	C451	451,1

Groups of order 452

		d	ρ	Label	ID
C₄₅₂	Cyclic group	452	1	C452	452,2
D₂₂₆	Dihedral group; = C₂xD₁₁₃	226	2+	D226	452,4
Dic₁₁₃	Dicyclic group; = C₁₁₃ :₂ C₄	452	2-	Dic113	452,1
C₁₁₃:C₄	The semidirect product of C₁₁₃ and C₄ acting faithfully	113	4+	C113:C4	452,3
C₂xC₂₂₆	Abelian group of type [2,226]	452		C2xC226	452,5

Groups of order 453

		d	ρ	Label	ID
C₄₅₃	Cyclic group	453	1	C453	453,2
C₁₅₁:C₃	The semidirect product of C₁₅₁ and C₃ acting faithfully	151	3	C151:C3	453,1

Groups of order 454

		d	ρ	Label	ID
C₄₅₄	Cyclic group	454	1	C454	454,2
D₂₂₇	Dihedral group	227	2+	D227	454,1

Groups of order 455

		d	ρ	Label	ID
C₄₅₅	Cyclic group	455	1	C455	455,1

Groups of order 456

		d	ρ	Label	ID
C₄₅₆	Cyclic group	456	1	C456	456,6
D₂₂₈	Dihedral group	228	2+	D228	456,36
Dic₁₁₄	Dicyclic group; = C₅₇ :₂ Q₈	456	2-	Dic114	456,34
D₇₆:C₃	The semidirect product of D₇₆ and C₃ acting faithfully	76	6+	D76:C3	456,9
C₁₉:C₂₄	The semidirect product of C₁₉ and C₂₄ acting via C₂₄/C₄=C₆	152	6	C19:C24	456,1
Dic₃₈:C₃	The semidirect product of Dic₃₈ and C₃ acting faithfully	152	6-	Dic38:C3	456,7
C₅₇:C₈	1^st semidirect product of C₅₇ and C₈ acting via C₈/C₄=C₂	456	2	C57:C8	456,5
C₂xC₂₂₈	Abelian group of type [2,228]	456		C2xC228	456,39
S₃xC₇₆	Direct product of C₇₆ and S₃	228	2	S3xC76	456,30
C₃xD₇₆	Direct product of C₃ and D₇₆	228	2	C3xD76	456,26
C₄xD₅₇	Direct product of C₄ and D₅₇	228	2	C4xD57	456,35
D₄xC₅₇	Direct product of C₅₇ and D₄	228	2	D4xC57	456,40
C₁₂xD₁₉	Direct product of C₁₂ and D₁₉	228	2	C12xD19	456,25
C₁₉xD₁₂	Direct product of C₁₉ and D₁₂	228	2	C19xD12	456,31
Q₈xC₅₇	Direct product of C₅₇ and Q₈	456	2	Q8xC57	456,41
C₃xDic₃₈	Direct product of C₃ and Dic₃₈	456	2	C3xDic38	456,24
C₆xDic₁₉	Direct product of C₆ and Dic₁₉	456		C6xDic19	456,27
C₁₉xDic₆	Direct product of C₁₉ and Dic₆	456	2	C19xDic6	456,29
Dic₃xC₃₈	Direct product of C₃₈ and Dic₃	456		Dic3xC38	456,32
C₂xDic₅₇	Direct product of C₂ and Dic₅₇	456		C2xDic57	456,37
C₄xC₁₉:C₆	Direct product of C₄ and C₁₉:C₆	76	6	C4xC19:C6	456,8
D₄xC₁₉:C₃	Direct product of D₄ and C₁₉:C₃	76	6	D4xC19:C3	456,20
C₈xC₁₉:C₃	Direct product of C₈ and C₁₉:C₃	152	3	C8xC19:C3	456,2
Q₈xC₁₉:C₃	Direct product of Q₈ and C₁₉:C₃	152	6	Q8xC19:C3	456,21
C₂xC₁₉:C₁₂	Direct product of C₂ and C₁₉:C₁₂	152		C2xC19:C12	456,10
C₁₉xC₃:C₈	Direct product of C₁₉ and C₃:C₈	456	2	C19xC3:C8	456,3
C₃xC₁₉:C₈	Direct product of C₃ and C₁₉:C₈	456	2	C3xC19:C8	456,4
C₂xC₄xC₁₉:C₃	Direct product of C₂xC₄ and C₁₉:C₃	152		C2xC4xC19:C3	456,19

Groups of order 457

		d	ρ	Label	ID
C₄₅₇	Cyclic group	457	1	C457	457,1

Groups of order 458

		d	ρ	Label	ID
C₄₅₈	Cyclic group	458	1	C458	458,2
D₂₂₉	Dihedral group	229	2+	D229	458,1

Groups of order 459

		d	ρ	Label	ID
C₄₅₉	Cyclic group	459	1	C459	459,1
C₃xC₁₅₃	Abelian group of type [3,153]	459		C3xC153	459,2
C₁₇x3_-¹⁺²	Direct product of C₁₇ and 3_-¹⁺²	153	3	C17xES-(3,1)	459,4

Groups of order 460

		d	ρ	Label	ID
C₄₆₀	Cyclic group	460	1	C460	460,4
D₂₃₀	Dihedral group; = C₂xD₁₁₅	230	2+	D230	460,10
Dic₁₁₅	Dicyclic group; = C₂₃ :Dic₅	460	2-	Dic115	460,3
C₂₃:F₅	The semidirect product of C₂₃ and F₅ acting via F₅/D₅=C₂	115	4	C23:F5	460,6
C₂xC₂₃₀	Abelian group of type [2,230]	460		C2xC230	460,11
F₅xC₂₃	Direct product of C₂₃ and F₅	115	4	F5xC23	460,5
D₅xC₄₆	Direct product of C₄₆ and D₅	230	2	D5xC46	460,9
C₁₀xD₂₃	Direct product of C₁₀ and D₂₃	230	2	C10xD23	460,8
Dic₅xC₂₃	Direct product of C₂₃ and Dic₅	460	2	Dic5xC23	460,1
C₅xDic₂₃	Direct product of C₅ and Dic₂₃	460	2	C5xDic23	460,2

Groups of order 461

		d	ρ	Label	ID
C₄₆₁	Cyclic group	461	1	C461	461,1

Groups of order 462

		d	ρ	Label	ID
C₄₆₂	Cyclic group	462	1	C462	462,12
D₂₃₁	Dihedral group	231	2+	D231	462,11
C₁₁:F₇	The semidirect product of C₁₁ and F₇ acting via F₇/C₇:C₃=C₂	77	6+	C11:F7	462,3
C₁₁xF₇	Direct product of C₁₁ and F₇	77	6	C11xF7	462,2
S₃xC₇₇	Direct product of C₇₇ and S₃	231	2	S3xC77	462,8
D₇xC₃₃	Direct product of C₃₃ and D₇	231	2	D7xC33	462,6
C₃xD₇₇	Direct product of C₃ and D₇₇	231	2	C3xD77	462,7
C₇xD₃₃	Direct product of C₇ and D₃₃	231	2	C7xD33	462,9
C₂₁xD₁₁	Direct product of C₂₁ and D₁₁	231	2	C21xD11	462,5
C₁₁xD₂₁	Direct product of C₁₁ and D₂₁	231	2	C11xD21	462,10
C₇:C₃xD₁₁	Direct product of C₇:C₃ and D₁₁	77	6	C7:C3xD11	462,1
C₇:C₃xC₂₂	Direct product of C₂₂ and C₇:C₃	154	3	C7:C3xC22	462,4

Groups of order 463

		d	ρ	Label	ID
C₄₆₃	Cyclic group	463	1	C463	463,1

Groups of order 464

		d	ρ	Label	ID
C₄₆₄	Cyclic group	464	1	C464	464,2
D₂₃₂	Dihedral group	232	2+	D232	464,7
Dic₁₁₆	Dicyclic group; = C₂₉ :₁ Q₁₆	464	2-	Dic116	464,8
C₁₁₆:C₄	1^st semidirect product of C₁₁₆ and C₄ acting faithfully	116	4	C116:C4	464,31
D₂₉:C₈	The semidirect product of D₂₉ and C₈ acting via C₈/C₄=C₂	232	4	D29:C8	464,28
C₈:D₂₉	3^rd semidirect product of C₈ and D₂₉ acting via D₂₉/C₂₉=C₂	232	2	C8:D29	464,5
C₂₃₂:C₂	2^nd semidirect product of C₂₃₂ and C₂ acting faithfully	232	2	C232:C2	464,6
C₂₉:C₁₆	The semidirect product of C₂₉ and C₁₆ acting via C₁₆/C₄=C₄	464	4	C29:C16	464,3
C₂₉:₂C₁₆	The semidirect product of C₂₉ and C₁₆ acting via C₁₆/C₈=C₂	464	2	C29:2C16	464,1
C₄:Dic₂₉	The semidirect product of C₄ and Dic₂₉ acting via Dic₂₉/C₅₈=C₂	464		C4:Dic29	464,13
C₄.Dic₂₉	The non-split extension by C₄ of Dic₂₉ acting via Dic₂₉/C₅₈=C₂	232	2	C4.Dic29	464,10
C₁₁₆.C₄	1^st non-split extension by C₁₁₆ of C₄ acting faithfully	232	4	C116.C4	464,29
C₄xC₁₁₆	Abelian group of type [4,116]	464		C4xC116	464,20
C₂xC₂₃₂	Abelian group of type [2,232]	464		C2xC232	464,23
C₈xD₂₉	Direct product of C₈ and D₂₉	232	2	C8xD29	464,4
D₈xC₂₉	Direct product of C₂₉ and D₈	232	2	D8xC29	464,25
SD₁₆xC₂₉	Direct product of C₂₉ and SD₁₆	232	2	SD16xC29	464,26
M₄(2)xC₂₉	Direct product of C₂₉ and M₄(2)	232	2	M4(2)xC29	464,24
Q₁₆xC₂₉	Direct product of C₂₉ and Q₁₆	464	2	Q16xC29	464,27
C₄xDic₂₉	Direct product of C₄ and Dic₂₉	464		C4xDic29	464,11
C₄xC₂₉:C₄	Direct product of C₄ and C₂₉:C₄	116	4	C4xC29:C4	464,30
C₂xC₂₉:C₈	Direct product of C₂ and C₂₉:C₈	464		C2xC29:C8	464,32
C₄:C₄xC₂₉	Direct product of C₂₉ and C₄:C₄	464		C4:C4xC29	464,22
C₂xC₂₉:₂C₈	Direct product of C₂ and C₂₉:₂C₈	464		C2xC29:2C8	464,9

Groups of order 465

		d	ρ	Label	ID
C₄₆₅	Cyclic group	465	1	C465	465,4
C₃₁:C₁₅	The semidirect product of C₃₁ and C₁₅ acting faithfully	31	15	C31:C15	465,1
C₃xC₃₁:C₅	Direct product of C₃ and C₃₁:C₅	93	5	C3xC31:C5	465,2
C₅xC₃₁:C₃	Direct product of C₅ and C₃₁:C₃	155	3	C5xC31:C3	465,3

Groups of order 466

		d	ρ	Label	ID
C₄₆₆	Cyclic group	466	1	C466	466,2
D₂₃₃	Dihedral group	233	2+	D233	466,1

Groups of order 467

		d	ρ	Label	ID
C₄₆₇	Cyclic group	467	1	C467	467,1

Groups of order 468

		d	ρ	Label	ID
C₄₆₈	Cyclic group	468	1	C468	468,6
D₂₃₄	Dihedral group; = C₂xD₁₁₇	234	2+	D234	468,17
Dic₁₁₇	Dicyclic group; = C₉ :Dic₁₃	468	2-	Dic117	468,5
C₃:F₁₃	The semidirect product of C₃ and F₁₃ acting via F₁₃/C₁₃:C₆=C₂	39	12	C3:F13	468,30
C₁₃:C₃₆	The semidirect product of C₁₃ and C₃₆ acting via C₃₆/C₃=C₁₂	117	12	C13:C36	468,7
C₁₃:Dic₉	The semidirect product of C₁₃ and Dic₉ acting via Dic₉/C₉=C₄	117	4	C13:Dic9	468,10
C₃₉:₃C₁₂	1^st semidirect product of C₃₉ and C₁₂ acting via C₁₂/C₂=C₆	156	6-	C39:3C12	468,21
C₁₃:₂C₃₆	The semidirect product of C₁₃ and C₃₆ acting via C₃₆/C₆=C₆	468	6	C13:2C36	468,1
C₆xC₇₈	Abelian group of type [6,78]	468		C6xC78	468,55
C₂xC₂₃₄	Abelian group of type [2,234]	468		C2xC234	468,18
C₃xC₁₅₆	Abelian group of type [3,156]	468		C3xC156	468,28
C₃xF₁₃	Direct product of C₃ and F₁₃	39	12	C3xF13	468,29
S₃xC₇₈	Direct product of C₇₈ and S₃	156	2	S3xC78	468,51
C₆xD₃₉	Direct product of C₆ and D₃₉	156	2	C6xD39	468,52
Dic₃xC₃₉	Direct product of C₃₉ and Dic₃	156	2	Dic3xC39	468,24
C₃xDic₃₉	Direct product of C₃ and Dic₃₉	156	2	C3xDic39	468,25
D₉xC₂₆	Direct product of C₂₆ and D₉	234	2	D9xC26	468,16
C₁₈xD₁₃	Direct product of C₁₈ and D₁₃	234	2	C18xD13	468,15
C₁₃xDic₉	Direct product of C₁₃ and Dic₉	468	2	C13xDic9	468,3
C₉xDic₁₃	Direct product of C₉ and Dic₁₃	468	2	C9xDic13	468,4
C₃²xDic₁₃	Direct product of C₃² and Dic₁₃	468		C3^2xDic13	468,23
C₆xC₁₃:C₆	Direct product of C₆ and C₁₃:C₆	78	6	C6xC13:C6	468,33
C₃xC₃₉:C₄	Direct product of C₃ and C₃₉:C₄	78	4	C3xC39:C4	468,37
C₂xD₃₉:C₃	Direct product of C₂ and D₃₉:C₃	78	6+	C2xD39:C3	468,35
C₉xC₁₃:C₄	Direct product of C₉ and C₁₃:C₄	117	4	C9xC13:C4	468,9
C₃²xC₁₃:C₄	Direct product of C₃² and C₁₃:C₄	117		C3^2xC13:C4	468,36
C₁₂xC₁₃:C₃	Direct product of C₁₂ and C₁₃:C₃	156	3	C12xC13:C3	468,22
C₃xC₂₆.C₆	Direct product of C₃ and C₂₆.C₆	156	6	C3xC26.C6	468,19
Dic₃xC₁₃:C₃	Direct product of Dic₃ and C₁₃:C₃	156	6	Dic3xC13:C3	468,20
C₃xC₆xD₁₃	Direct product of C₃xC₆ and D₁₃	234		C3xC6xD13	468,50
C₂xC₁₃:C₁₈	Direct product of C₂ and C₁₃:C₁₈	234	6	C2xC13:C18	468,8
C₄xC₁₃:C₉	Direct product of C₄ and C₁₃:C₉	468	3	C4xC13:C9	468,2
C₂²xC₁₃:C₉	Direct product of C₂² and C₁₃:C₉	468		C2^2xC13:C9	468,12
C₂xS₃xC₁₃:C₃	Direct product of C₂, S₃ and C₁₃:C₃	78	6	C2xS3xC13:C3	468,34
C₂xC₆xC₁₃:C₃	Direct product of C₂xC₆ and C₁₃:C₃	156		C2xC6xC13:C3	468,47

Groups of order 469

		d	ρ	Label	ID
C₄₆₉	Cyclic group	469	1	C469	469,1

Groups of order 470

		d	ρ	Label	ID
C₄₇₀	Cyclic group	470	1	C470	470,4
D₂₃₅	Dihedral group	235	2+	D235	470,3
D₅xC₄₇	Direct product of C₄₇ and D₅	235	2	D5xC47	470,1
C₅xD₄₇	Direct product of C₅ and D₄₇	235	2	C5xD47	470,2

Groups of order 471

		d	ρ	Label	ID
C₄₇₁	Cyclic group	471	1	C471	471,2
C₁₅₇:C₃	The semidirect product of C₁₅₇ and C₃ acting faithfully	157	3	C157:C3	471,1

Groups of order 472

		d	ρ	Label	ID
C₄₇₂	Cyclic group	472	1	C472	472,2
D₂₃₆	Dihedral group	236	2+	D236	472,5
Dic₁₁₈	Dicyclic group; = C₅₉ :Q₈	472	2-	Dic118	472,3
C₅₉:C₈	The semidirect product of C₅₉ and C₈ acting via C₈/C₄=C₂	472	2	C59:C8	472,1
C₂xC₂₃₆	Abelian group of type [2,236]	472		C2xC236	472,8
C₄xD₅₉	Direct product of C₄ and D₅₉	236	2	C4xD59	472,4
D₄xC₅₉	Direct product of C₅₉ and D₄	236	2	D4xC59	472,9
Q₈xC₅₉	Direct product of C₅₉ and Q₈	472	2	Q8xC59	472,10
C₂xDic₅₉	Direct product of C₂ and Dic₅₉	472		C2xDic59	472,6

Groups of order 473

		d	ρ	Label	ID
C₄₇₃	Cyclic group	473	1	C473	473,1

Groups of order 474

		d	ρ	Label	ID
C₄₇₄	Cyclic group	474	1	C474	474,6
D₂₃₇	Dihedral group	237	2+	D237	474,5
C₇₉:C₆	The semidirect product of C₇₉ and C₆ acting faithfully	79	6+	C79:C6	474,1
S₃xC₇₉	Direct product of C₇₉ and S₃	237	2	S3xC79	474,3
C₃xD₇₉	Direct product of C₃ and D₇₉	237	2	C3xD79	474,4
C₂xC₇₉:C₃	Direct product of C₂ and C₇₉:C₃	158	3	C2xC79:C3	474,2

Groups of order 475

		d	ρ	Label	ID
C₄₇₅	Cyclic group	475	1	C475	475,1
C₅xC₉₅	Abelian group of type [5,95]	475		C5xC95	475,2

Groups of order 476

		d	ρ	Label	ID
C₄₇₆	Cyclic group	476	1	C476	476,4
D₂₃₈	Dihedral group; = C₂xD₁₁₉	238	2+	D238	476,10
Dic₁₁₉	Dicyclic group; = C₇ :Dic₁₇	476	2-	Dic119	476,3
C₁₇:Dic₇	The semidirect product of C₁₇ and Dic₇ acting via Dic₇/C₇=C₄	119	4	C17:Dic7	476,6
C₂xC₂₃₈	Abelian group of type [2,238]	476		C2xC238	476,11
D₇xC₃₄	Direct product of C₃₄ and D₇	238	2	D7xC34	476,9
C₁₄xD₁₇	Direct product of C₁₄ and D₁₇	238	2	C14xD17	476,8
C₁₇xDic₇	Direct product of C₁₇ and Dic₇	476	2	C17xDic7	476,1
C₇xDic₁₇	Direct product of C₇ and Dic₁₇	476	2	C7xDic17	476,2
C₇xC₁₇:C₄	Direct product of C₇ and C₁₇:C₄	119	4	C7xC17:C4	476,5

Groups of order 477

		d	ρ	Label	ID
C₄₇₇	Cyclic group	477	1	C477	477,1
C₃xC₁₅₉	Abelian group of type [3,159]	477		C3xC159	477,2

Groups of order 478

		d	ρ	Label	ID
C₄₇₈	Cyclic group	478	1	C478	478,2
D₂₃₉	Dihedral group	239	2+	D239	478,1

Groups of order 479

		d	ρ	Label	ID
C₄₇₉	Cyclic group	479	1	C479	479,1

Groups of order 480

		d	ρ	Label	ID
C₄₈₀	Cyclic group	480	1	C480	480,4
D₂₄₀	Dihedral group	240	2+	D240	480,159
Dic₁₂₀	Dicyclic group; = C₁₅ :₄ Q₃₂	480	2-	Dic120	480,161
C₂₄:F₅	5^th semidirect product of C₂₄ and F₅ acting via F₅/D₅=C₂	120	4	C24:F5	480,297
C₁₂₀:C₄	2^nd semidirect product of C₁₂₀ and C₄ acting faithfully	120	4	C120:C4	480,298
C₈₀:S₃	5^th semidirect product of C₈₀ and S₃ acting via S₃/C₃=C₂	240	2	C80:S3	480,158
C₄₈:D₅	2^nd semidirect product of C₄₈ and D₅ acting via D₅/C₅=C₂	240	2	C48:D5	480,160
C₆₀:₅C₈	1^st semidirect product of C₆₀ and C₈ acting via C₈/C₄=C₂	480		C60:5C8	480,164
C₆₀:C₈	1^st semidirect product of C₆₀ and C₈ acting via C₈/C₂=C₄	480		C60:C8	480,306
C₁₅:₃C₃₂	1^st semidirect product of C₁₅ and C₃₂ acting via C₃₂/C₁₆=C₂	480	2	C15:3C32	480,3
C₁₅:C₃₂	1^st semidirect product of C₁₅ and C₃₂ acting via C₃₂/C₈=C₄	480	4	C15:C32	480,6
C₁₂₀:₉C₄	1^st semidirect product of C₁₂₀ and C₄ acting via C₄/C₂=C₂	480		C120:9C4	480,178
C₁₂₀:₁₃C₄	5^th semidirect product of C₁₂₀ and C₄ acting via C₄/C₂=C₂	480		C120:13C4	480,175
C₁₂₀:₁₀C₄	2^nd semidirect product of C₁₂₀ and C₄ acting via C₄/C₂=C₂	480		C120:10C4	480,177
D₅.D₂₄	The non-split extension by D₅ of D₂₄ acting via D₂₄/C₂₄=C₂	120	4	D5.D24	480,299
C₆₀.₇C₈	1^st non-split extension by C₆₀ of C₈ acting via C₈/C₄=C₂	240	2	C60.7C8	480,172
C₆₀.C₈	1^st non-split extension by C₆₀ of C₈ acting via C₈/C₂=C₄	240	4	C60.C8	480,303
C₂₄.F₅	5^th non-split extension by C₂₄ of F₅ acting via F₅/D₅=C₂	240	4	C24.F5	480,294
C₂₄.₁F₅	1^st non-split extension by C₂₄ of F₅ acting via F₅/D₅=C₂	240	4	C24.1F5	480,301
C₁₂₀.C₄	6^th non-split extension by C₁₂₀ of C₄ acting faithfully	240	4	C120.C4	480,295
C₄.₁₈D₆₀	3^rd central extension by C₄ of D₆₀	240	2	C4.18D60	480,179
C₄₀.Dic₃	2^nd non-split extension by C₄₀ of Dic₃ acting via Dic₃/C₃=C₄	240	4	C40.Dic3	480,300
C₄xC₁₂₀	Abelian group of type [4,120]	480		C4xC120	480,199
C₂xC₂₄₀	Abelian group of type [2,240]	480		C2xC240	480,212
F₅xC₂₄	Direct product of C₂₄ and F₅	120	4	F5xC24	480,271
S₃xC₈₀	Direct product of C₈₀ and S₃	240	2	S3xC80	480,116
D₅xC₄₈	Direct product of C₄₈ and D₅	240	2	D5xC48	480,75
C₃xD₈₀	Direct product of C₃ and D₈₀	240	2	C3xD80	480,77
C₅xD₄₈	Direct product of C₅ and D₄₈	240	2	C5xD48	480,118
C₁₆xD₁₅	Direct product of C₁₆ and D₁₅	240	2	C16xD15	480,157
C₁₅xD₁₆	Direct product of C₁₅ and D₁₆	240	2	C15xD16	480,214
C₁₅xSD₃₂	Direct product of C₁₅ and SD₃₂	240	2	C15xSD32	480,215
C₁₅xM₅(2)	Direct product of C₁₅ and M₅(2)	240	2	C15xM5(2)	480,213
C₁₅xQ₃₂	Direct product of C₁₅ and Q₃₂	480	2	C15xQ32	480,216
C₃xDic₄₀	Direct product of C₃ and Dic₄₀	480	2	C3xDic40	480,79
Dic₅xC₂₄	Direct product of C₂₄ and Dic₅	480		Dic5xC24	480,91
C₅xDic₂₄	Direct product of C₅ and Dic₂₄	480	2	C5xDic24	480,120
Dic₃xC₄₀	Direct product of C₄₀ and Dic₃	480		Dic3xC40	480,132
C₈xDic₁₅	Direct product of C₈ and Dic₁₅	480		C8xDic15	480,173
C₈xC₃:F₅	Direct product of C₈ and C₃:F₅	120	4	C8xC3:F5	480,296
C₃xC₈:F₅	Direct product of C₃ and C₈:F₅	120	4	C3xC8:F5	480,272
C₃xC₄₀:C₄	Direct product of C₃ and C₄₀:C₄	120	4	C3xC40:C4	480,273
C₃xD₅.D₈	Direct product of C₃ and D₅.D₈	120	4	C3xD5.D8	480,274
C₃xC₈₀:C₂	Direct product of C₃ and C₈₀:C₂	240	2	C3xC80:C2	480,76
C₅xC₄₈:C₂	Direct product of C₅ and C₄₈:C₂	240	2	C5xC48:C2	480,119
C₃xD₅:C₁₆	Direct product of C₃ and D₅:C₁₆	240	4	C3xD5:C16	480,269
C₃xC₁₆:D₅	Direct product of C₃ and C₁₆:D₅	240	2	C3xC16:D5	480,78
C₅xD₆.C₈	Direct product of C₅ and D₆.C₈	240	2	C5xD6.C8	480,117
C₃xC₈.F₅	Direct product of C₃ and C₈.F₅	240	4	C3xC8.F5	480,270
C₅xC₁₂.C₈	Direct product of C₅ and C₁₂.C₈	240	2	C5xC12.C8	480,131
C₅xC₂₄.C₄	Direct product of C₅ and C₂₄.C₄	240	2	C5xC24.C4	480,138
C₁₅xC₈.C₄	Direct product of C₁₅ and C₈.C₄	240	2	C15xC8.C4	480,211
C₃xC₄₀.C₄	Direct product of C₃ and C₄₀.C₄	240	4	C3xC40.C4	480,275
C₃xC₂₀.C₈	Direct product of C₃ and C₂₀.C₈	240	4	C3xC20.C8	480,278
C₃xC₂₀.₄C₈	Direct product of C₃ and C₂₀.₄C₈	240	2	C3xC20.4C8	480,90
C₃xC₄₀.₆C₄	Direct product of C₃ and C₄₀.₆C₄	240	2	C3xC40.6C4	480,97
C₃xD₁₀.Q₈	Direct product of C₃ and D₁₀.Q₈	240	4	C3xD10.Q8	480,276
C₅xC₃:C₃₂	Direct product of C₅ and C₃:C₃₂	480	2	C5xC3:C32	480,1
C₃xC₅:C₃₂	Direct product of C₃ and C₅:C₃₂	480	4	C3xC5:C32	480,5
C₂₀xC₃:C₈	Direct product of C₂₀ and C₃:C₈	480		C20xC3:C8	480,121
C₆xC₅:C₁₆	Direct product of C₆ and C₅:C₁₆	480		C6xC5:C16	480,277
C₁₂xC₅:C₈	Direct product of C₁₂ and C₅:C₈	480		C12xC5:C8	480,280
C₁₅xC₄:C₈	Direct product of C₁₅ and C₄:C₈	480		C15xC4:C8	480,208
C₁₀xC₃:C₁₆	Direct product of C₁₀ and C₃:C₁₆	480		C10xC3:C16	480,130
C₄xC₁₅:C₈	Direct product of C₄ and C₁₅:C₈	480		C4xC15:C8	480,305
C₅xC₁₂:C₈	Direct product of C₅ and C₁₂:C₈	480		C5xC12:C8	480,123
C₅xC₂₄:C₄	Direct product of C₅ and C₂₄:C₄	480		C5xC24:C4	480,134
C₁₅xC₈:C₄	Direct product of C₁₅ and C₈:C₄	480		C15xC8:C4	480,200
C₃xC₂₀:C₈	Direct product of C₃ and C₂₀:C₈	480		C3xC20:C8	480,281
C₃xC₅:₂C₃₂	Direct product of C₃ and C₅:₂C₃₂	480	2	C3xC5:2C32	480,2
C₁₂xC₅:₂C₈	Direct product of C₁₂ and C₅:₂C₈	480		C12xC5:2C8	480,80
C₆xC₅:₂C₁₆	Direct product of C₆ and C₅:₂C₁₆	480		C6xC5:2C16	480,89
C₄xC₁₅:₃C₈	Direct product of C₄ and C₁₅:₃C₈	480		C4xC15:3C8	480,162
C₂xC₁₅:C₁₆	Direct product of C₂ and C₁₅:C₁₆	480		C2xC15:C16	480,302
C₃xC₂₀:₃C₈	Direct product of C₃ and C₂₀:₃C₈	480		C3xC20:3C8	480,82
C₃xC₄₀:₈C₄	Direct product of C₃ and C₄₀:₈C₄	480		C3xC40:8C4	480,93
C₃xC₄₀:₆C₄	Direct product of C₃ and C₄₀:₆C₄	480		C3xC40:6C4	480,95
C₃xC₄₀:₅C₄	Direct product of C₃ and C₄₀:₅C₄	480		C3xC40:5C4	480,96
C₅xC₂₄:₁C₄	Direct product of C₅ and C₂₄:₁C₄	480		C5xC24:1C4	480,137
C₂xC₁₅:₃C₁₆	Direct product of C₂ and C₁₅:₃C₁₆	480		C2xC15:3C16	480,171
C₅xC₈:Dic₃	Direct product of C₅ and C₈:Dic₃	480		C5xC8:Dic3	480,136
C₁₅xC₂.D₈	Direct product of C₁₅ and C₂.D₈	480		C15xC2.D8	480,210
C₁₅xC₄.Q₈	Direct product of C₁₅ and C₄.Q₈	480		C15xC4.Q8	480,209

Groups of order 481

		d	ρ	Label	ID
C₄₈₁	Cyclic group	481	1	C481	481,1

Groups of order 482

		d	ρ	Label	ID
C₄₈₂	Cyclic group	482	1	C482	482,2
D₂₄₁	Dihedral group	241	2+	D241	482,1

Groups of order 483

		d	ρ	Label	ID
C₄₈₃	Cyclic group	483	1	C483	483,2
C₇:C₃xC₂₃	Direct product of C₂₃ and C₇:C₃	161	3	C7:C3xC23	483,1

Groups of order 484

		d	ρ	Label	ID
C₄₈₄	Cyclic group	484	1	C484	484,2
D₂₄₂	Dihedral group; = C₂xD₁₂₁	242	2+	D242	484,3
Dic₁₂₁	Dicyclic group; = C₁₂₁ :C₄	484	2-	Dic121	484,1
C₂₂²	Abelian group of type [22,22]	484		C22^2	484,12
C₂xC₂₄₂	Abelian group of type [2,242]	484		C2xC242	484,4
C₁₁xC₄₄	Abelian group of type [11,44]	484		C11xC44	484,7
D₁₁xC₂₂	Direct product of C₂₂ and D₁₁	44	2	D11xC22	484,10
C₁₁xDic₁₁	Direct product of C₁₁ and Dic₁₁	44	2	C11xDic11	484,5

Groups of order 485

		d	ρ	Label	ID
C₄₈₅	Cyclic group	485	1	C485	485,1

Groups of order 486

		d	ρ	Label	ID
C₄₈₆	Cyclic group	486	1	C486	486,2
D₂₄₃	Dihedral group	243	2+	D243	486,1
C₂₇:C₁₈	The semidirect product of C₂₇ and C₁₈ acting faithfully; = Aut(D₂₇) = Hol(C₂₇)	27	18+	C27:C18	486,31
C₉:C₅₄	The semidirect product of C₉ and C₅₄ acting via C₅₄/C₉=C₆	54	6	C9:C54	486,30
C₂₇:₃C₁₈	The semidirect product of C₂₇ and C₁₈ acting via C₁₈/C₃=C₆	54	6	C27:3C18	486,15
C₈₁:C₆	The semidirect product of C₈₁ and C₆ acting faithfully	81	6+	C81:C6	486,34
C₉xC₅₄	Abelian group of type [9,54]	486		C9xC54	486,70
C₃xC₁₆₂	Abelian group of type [3,162]	486		C3xC162	486,83
C₉xD₂₇	Direct product of C₉ and D₂₇	54	2	C9xD27	486,13
D₉xC₂₇	Direct product of C₂₇ and D₉	54	2	D9xC27	486,14
S₃xC₈₁	Direct product of C₈₁ and S₃	162	2	S3xC81	486,33
C₃xD₈₁	Direct product of C₃ and D₈₁	162	2	C3xD81	486,32
C₂xC₂₇:C₉	Direct product of C₂ and C₂₇:C₉	54	9	C2xC27:C9	486,82
C₂xC₈₁:C₃	Direct product of C₂ and C₈₁:C₃	162	3	C2xC81:C3	486,84
C₂xC₉:C₂₇	Direct product of C₂ and C₉:C₂₇	486		C2xC9:C27	486,81
C₂xC₂₇:₂C₉	Direct product of C₂ and C₂₇:₂C₉	486		C2xC27:2C9	486,71

Groups of order 487

		d	ρ	Label	ID
C₄₈₇	Cyclic group	487	1	C487	487,1

Groups of order 488

		d	ρ	Label	ID
C₄₈₈	Cyclic group	488	1	C488	488,2
D₂₄₄	Dihedral group	244	2+	D244	488,6
Dic₁₂₂	Dicyclic group; = C₆₁ :Q₈	488	2-	Dic122	488,4
C₆₁:C₈	The semidirect product of C₆₁ and C₈ acting via C₈/C₂=C₄	488	4-	C61:C8	488,3
C₆₁:₂C₈	The semidirect product of C₆₁ and C₈ acting via C₈/C₄=C₂	488	2	C61:2C8	488,1
C₂xC₂₄₄	Abelian group of type [2,244]	488		C2xC244	488,9
C₄xD₆₁	Direct product of C₄ and D₆₁	244	2	C4xD61	488,5
D₄xC₆₁	Direct product of C₆₁ and D₄	244	2	D4xC61	488,10
Q₈xC₆₁	Direct product of C₆₁ and Q₈	488	2	Q8xC61	488,11
C₂xDic₆₁	Direct product of C₂ and Dic₆₁	488		C2xDic61	488,7
C₂xC₆₁:C₄	Direct product of C₂ and C₆₁:C₄	122	4+	C2xC61:C4	488,12

Groups of order 489

		d	ρ	Label	ID
C₄₈₉	Cyclic group	489	1	C489	489,2
C₁₆₃:C₃	The semidirect product of C₁₆₃ and C₃ acting faithfully	163	3	C163:C3	489,1

Groups of order 490

		d	ρ	Label	ID
C₄₉₀	Cyclic group	490	1	C490	490,4
D₂₄₅	Dihedral group	245	2+	D245	490,3
C₇xC₇₀	Abelian group of type [7,70]	490		C7xC70	490,10
D₇xC₃₅	Direct product of C₃₅ and D₇	70	2	D7xC35	490,5
C₇xD₃₅	Direct product of C₇ and D₃₅	70	2	C7xD35	490,8
D₅xC₄₉	Direct product of C₄₉ and D₅	245	2	D5xC49	490,1
C₅xD₄₉	Direct product of C₅ and D₄₉	245	2	C5xD49	490,2
D₅xC₇²	Direct product of C₇² and D₅	245		D5xC7^2	490,7

Groups of order 491

		d	ρ	Label	ID
C₄₉₁	Cyclic group	491	1	C491	491,1

Groups of order 492

		d	ρ	Label	ID
C₄₉₂	Cyclic group	492	1	C492	492,4
D₂₄₆	Dihedral group; = C₂xD₁₂₃	246	2+	D246	492,11
Dic₁₂₃	Dicyclic group; = C₃ :Dic₄₁	492	2-	Dic123	492,3
C₄₁:Dic₃	The semidirect product of C₄₁ and Dic₃ acting via Dic₃/C₃=C₄	123	4	C41:Dic3	492,6
C₂xC₂₄₆	Abelian group of type [2,246]	492		C2xC246	492,12
S₃xC₈₂	Direct product of C₈₂ and S₃	246	2	S3xC82	492,10
C₆xD₄₁	Direct product of C₆ and D₄₁	246	2	C6xD41	492,9
Dic₃xC₄₁	Direct product of C₄₁ and Dic₃	492	2	Dic3xC41	492,1
C₃xDic₄₁	Direct product of C₃ and Dic₄₁	492	2	C3xDic41	492,2
C₃xC₄₁:C₄	Direct product of C₃ and C₄₁:C₄	123	4	C3xC41:C4	492,5

Groups of order 493

		d	ρ	Label	ID
C₄₉₃	Cyclic group	493	1	C493	493,1

Groups of order 494

		d	ρ	Label	ID
C₄₉₄	Cyclic group	494	1	C494	494,4
D₂₄₇	Dihedral group	247	2+	D247	494,3
C₁₉xD₁₃	Direct product of C₁₉ and D₁₃	247	2	C19xD13	494,1
C₁₃xD₁₉	Direct product of C₁₃ and D₁₉	247	2	C13xD19	494,2

Groups of order 495

		d	ρ	Label	ID
C₄₉₅	Cyclic group	495	1	C495	495,2
C₃xC₁₆₅	Abelian group of type [3,165]	495		C3xC165	495,4
C₉xC₁₁:C₅	Direct product of C₉ and C₁₁:C₅	99	5	C9xC11:C5	495,1
C₃²xC₁₁:C₅	Direct product of C₃² and C₁₁:C₅	99		C3^2xC11:C5	495,3

Groups of order 496

		d	ρ	Label	ID
C₄₉₆	Cyclic group	496	1	C496	496,2
D₂₄₈	Dihedral group	248	2+	D248	496,6
Dic₁₂₄	Dicyclic group; = C₃₁ :₁ Q₁₆	496	2-	Dic124	496,7
C₈:D₃₁	3^rd semidirect product of C₈ and D₃₁ acting via D₃₁/C₃₁=C₂	248	2	C8:D31	496,4
C₂₄₈:C₂	2^nd semidirect product of C₂₄₈ and C₂ acting faithfully	248	2	C248:C2	496,5
C₃₁:C₁₆	The semidirect product of C₃₁ and C₁₆ acting via C₁₆/C₈=C₂	496	2	C31:C16	496,1
C₄:Dic₃₁	The semidirect product of C₄ and Dic₃₁ acting via Dic₃₁/C₆₂=C₂	496		C4:Dic31	496,12
C₄.Dic₃₁	The non-split extension by C₄ of Dic₃₁ acting via Dic₃₁/C₆₂=C₂	248	2	C4.Dic31	496,9
C₄xC₁₂₄	Abelian group of type [4,124]	496		C4xC124	496,19
C₂xC₂₄₈	Abelian group of type [2,248]	496		C2xC248	496,22
C₈xD₃₁	Direct product of C₈ and D₃₁	248	2	C8xD31	496,3
D₈xC₃₁	Direct product of C₃₁ and D₈	248	2	D8xC31	496,24
SD₁₆xC₃₁	Direct product of C₃₁ and SD₁₆	248	2	SD16xC31	496,25
M₄(2)xC₃₁	Direct product of C₃₁ and M₄(2)	248	2	M4(2)xC31	496,23
Q₁₆xC₃₁	Direct product of C₃₁ and Q₁₆	496	2	Q16xC31	496,26
C₄xDic₃₁	Direct product of C₄ and Dic₃₁	496		C4xDic31	496,10
C₂xC₃₁:C₈	Direct product of C₂ and C₃₁:C₈	496		C2xC31:C8	496,8
C₄:C₄xC₃₁	Direct product of C₃₁ and C₄:C₄	496		C4:C4xC31	496,21

Groups of order 497

		d	ρ	Label	ID
C₄₉₇	Cyclic group	497	1	C497	497,2
C₇₁:C₇	The semidirect product of C₇₁ and C₇ acting faithfully	71	7	C71:C7	497,1

Groups of order 498

		d	ρ	Label	ID
C₄₉₈	Cyclic group	498	1	C498	498,4
D₂₄₉	Dihedral group	249	2+	D249	498,3
S₃xC₈₃	Direct product of C₈₃ and S₃	249	2	S3xC83	498,1
C₃xD₈₃	Direct product of C₃ and D₈₃	249	2	C3xD83	498,2

Groups of order 499

		d	ρ	Label	ID
C₄₉₉	Cyclic group	499	1	C499	499,1

Groups of order 500

		d	ρ	Label	ID
C₅₀₀	Cyclic group	500	1	C500	500,2
D₂₅₀	Dihedral group; = C₂xD₁₂₅	250	2+	D250	500,4
Dic₁₂₅	Dicyclic group; = C₁₂₅ :₂ C₄	500	2-	Dic125	500,1
C₂₅:C₂₀	The semidirect product of C₂₅ and C₂₀ acting faithfully; = Aut(D₂₅) = Hol(C₂₅)	25	20+	C25:C20	500,18
C₁₂₅:C₄	The semidirect product of C₁₂₅ and C₄ acting faithfully	125	4+	C125:C4	500,3
C₅₀.C₁₀	The non-split extension by C₅₀ of C₁₀ acting faithfully	100	10-	C50.C10	500,9
C₂xC₂₅₀	Abelian group of type [2,250]	500		C2xC250	500,5
C₅xC₁₀₀	Abelian group of type [5,100]	500		C5xC100	500,12
C₁₀xC₅₀	Abelian group of type [10,50]	500		C10xC50	500,34
D₅xC₅₀	Direct product of C₅₀ and D₅	100	2	D5xC50	500,29
F₅xC₂₅	Direct product of C₂₅ and F₅	100	4	F5xC25	500,15
C₁₀xD₂₅	Direct product of C₁₀ and D₂₅	100	2	C10xD25	500,28
C₅xDic₂₅	Direct product of C₅ and Dic₂₅	100	2	C5xDic25	500,6
Dic₅xC₂₅	Direct product of C₂₅ and Dic₅	100	2	Dic5xC25	500,7
C₄x5_-¹⁺²	Direct product of C₄ and 5_-¹⁺²	100	5	C4xES-(5,1)	500,14
C₂²x5_-¹⁺²	Direct product of C₂² and 5_-¹⁺²	100		C2^2xES-(5,1)	500,36
C₂xC₂₅:C₁₀	Direct product of C₂ and C₂₅:C₁₀	50	10+	C2xC25:C10	500,31
C₅xC₂₅:C₄	Direct product of C₅ and C₂₅:C₄	100	4	C5xC25:C4	500,16