Abelian groups

A group is abelian or commutative if gh=hg for all g and h, in other words if all elements commute. Such a group is a direct product of cyclic groups (structure theorem)

G = C_n₁x···xC_{n_k}, in a unique way if we require n₁|n₂|x···|n_k. We say that G is of type [n₁,n₂,...,n_k]. A group C_pxC_px···xC_p for a prime number p is elementary abelian - these are the additive groups of finite fields. Abelian groups are soluble, nilpotent and monomial. Classes extending abelian groups are metabelian groups (commutator is abelian) and A-groups (abelian Sylows). See also non-abelian groups.

Groups of order 1

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

Groups of order 2

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

Groups of order 3

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

Groups of order 4

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

Groups of order 5

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

Groups of order 6

		d	ρ	Label	ID
C₆	Cyclic group; = hexagon rotations	6	1	C6	6,2

Groups of order 7

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

Groups of order 8

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

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
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

Groups of order 15

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

Groups of order 16

		d	ρ	Label	ID
C₁₆	Cyclic group	16	1	C16	16,1
C₄²	Abelian group of type [4,4]	16		C4^2	16,2
C₂⁴	Elementary abelian group of type [2,2,2,2]	16		C2^4	16,14
C₂xC₈	Abelian group of type [2,8]	16		C2xC8	16,5
C₂²xC₄	Abelian group of type [2,2,4]	16		C2^2xC4	16,10

Groups of order 17

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

Groups of order 18

		d	ρ	Label	ID
C₁₈	Cyclic group	18	1	C18	18,2
C₃xC₆	Abelian group of type [3,6]	18		C3xC6	18,5

Groups of order 19

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

Groups of order 20

		d	ρ	Label	ID
C₂₀	Cyclic group	20	1	C20	20,2
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

Groups of order 22

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

Groups of order 23

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

Groups of order 24

		d	ρ	Label	ID
C₂₄	Cyclic group	24	1	C24	24,2
C₂xC₁₂	Abelian group of type [2,12]	24		C2xC12	24,9
C₂²xC₆	Abelian group of type [2,2,6]	24		C2^2xC6	24,15

Groups of order 25

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

Groups of order 26

		d	ρ	Label	ID
C₂₆	Cyclic group	26	1	C26	26,2

Groups of order 27

		d	ρ	Label	ID
C₂₇	Cyclic group	27	1	C27	27,1
C₃³	Elementary abelian group of type [3,3,3]	27		C3^3	27,5
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
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

Groups of order 31

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

Groups of order 32

		d	ρ	Label	ID
C₃₂	Cyclic group	32	1	C32	32,1
C₂⁵	Elementary abelian group of type [2,2,2,2,2]	32		C2^5	32,51
C₄xC₈	Abelian group of type [4,8]	32		C4xC8	32,3
C₂xC₁₆	Abelian group of type [2,16]	32		C2xC16	32,16
C₂xC₄²	Abelian group of type [2,4,4]	32		C2xC4^2	32,21
C₂²xC₈	Abelian group of type [2,2,8]	32		C2^2xC8	32,36
C₂³xC₄	Abelian group of type [2,2,2,4]	32		C2^3xC4	32,45

Groups of order 33

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

Groups of order 34

		d	ρ	Label	ID
C₃₄	Cyclic group	34	1	C34	34,2

Groups of order 35

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

Groups of order 36

		d	ρ	Label	ID
C₃₆	Cyclic group	36	1	C36	36,2
C₆²	Abelian group of type [6,6]	36		C6^2	36,14
C₂xC₁₈	Abelian group of type [2,18]	36		C2xC18	36,5
C₃xC₁₂	Abelian group of type [3,12]	36		C3xC12	36,8

Groups of order 37

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

Groups of order 38

		d	ρ	Label	ID
C₃₈	Cyclic group	38	1	C38	38,2

Groups of order 39

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

Groups of order 40

		d	ρ	Label	ID
C₄₀	Cyclic group	40	1	C40	40,2
C₂xC₂₀	Abelian group of type [2,20]	40		C2xC20	40,9
C₂²xC₁₀	Abelian group of type [2,2,10]	40		C2^2xC10	40,14

Groups of order 41

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

Groups of order 42

		d	ρ	Label	ID
C₄₂	Cyclic group	42	1	C42	42,6

Groups of order 43

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

Groups of order 44

		d	ρ	Label	ID
C₄₄	Cyclic group	44	1	C44	44,2
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

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
C₄xC₁₂	Abelian group of type [4,12]	48		C4xC12	48,20
C₂xC₂₄	Abelian group of type [2,24]	48		C2xC24	48,23
C₂³xC₆	Abelian group of type [2,2,2,6]	48		C2^3xC6	48,52
C₂²xC₁₂	Abelian group of type [2,2,12]	48		C2^2xC12	48,44

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
C₅xC₁₀	Abelian group of type [5,10]	50		C5xC10	50,5

Groups of order 51

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

Groups of order 52

		d	ρ	Label	ID
C₅₂	Cyclic group	52	1	C52	52,2
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
C₃xC₁₈	Abelian group of type [3,18]	54		C3xC18	54,9
C₃²xC₆	Abelian group of type [3,3,6]	54		C3^2xC6	54,15

Groups of order 55

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

Groups of order 56

		d	ρ	Label	ID
C₅₆	Cyclic group	56	1	C56	56,2
C₂xC₂₈	Abelian group of type [2,28]	56		C2xC28	56,8
C₂²xC₁₄	Abelian group of type [2,2,14]	56		C2^2xC14	56,13

Groups of order 57

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

Groups of order 58

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

Groups of order 59

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

Groups of order 60

		d	ρ	Label	ID
C₆₀	Cyclic group	60	1	C60	60,4
C₂xC₃₀	Abelian group of type [2,30]	60		C2xC30	60,13

Groups of order 61

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

Groups of order 62

		d	ρ	Label	ID
C₆₂	Cyclic group	62	1	C62	62,2

Groups of order 63

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

Groups of order 64

		d	ρ	Label	ID
C₆₄	Cyclic group	64	1	C64	64,1
C₈²	Abelian group of type [8,8]	64		C8^2	64,2
C₄³	Abelian group of type [4,4,4]	64		C4^3	64,55
C₂⁶	Elementary abelian group of type [2,2,2,2,2,2]	64		C2^6	64,267
C₄xC₁₆	Abelian group of type [4,16]	64		C4xC16	64,26
C₂xC₃₂	Abelian group of type [2,32]	64		C2xC32	64,50
C₂³xC₈	Abelian group of type [2,2,2,8]	64		C2^3xC8	64,246
C₂⁴xC₄	Abelian group of type [2,2,2,2,4]	64		C2^4xC4	64,260
C₂²xC₁₆	Abelian group of type [2,2,16]	64		C2^2xC16	64,183
C₂²xC₄²	Abelian group of type [2,2,4,4]	64		C2^2xC4^2	64,192
C₂xC₄xC₈	Abelian group of type [2,4,8]	64		C2xC4xC8	64,83

Groups of order 65

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

Groups of order 66

		d	ρ	Label	ID
C₆₆	Cyclic group	66	1	C66	66,4

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
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

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
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
C₂xC₆²	Abelian group of type [2,6,6]	72		C2xC6^2	72,50
C₂²xC₁₈	Abelian group of type [2,2,18]	72		C2^2xC18	72,18

Groups of order 73

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

Groups of order 74

		d	ρ	Label	ID
C₇₄	Cyclic group	74	1	C74	74,2

Groups of order 75

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

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
C₄xC₂₀	Abelian group of type [4,20]	80		C4xC20	80,20
C₂xC₄₀	Abelian group of type [2,40]	80		C2xC40	80,23
C₂²xC₂₀	Abelian group of type [2,2,20]	80		C2^2xC20	80,45
C₂³xC₁₀	Abelian group of type [2,2,2,10]	80		C2^3xC10	80,52

Groups of order 81

		d	ρ	Label	ID
C₈₁	Cyclic group	81	1	C81	81,1
C₉²	Abelian group of type [9,9]	81		C9^2	81,2
C₃⁴	Elementary abelian group of type [3,3,3,3]	81		C3^4	81,15
C₃xC₂₇	Abelian group of type [3,27]	81		C3xC27	81,5
C₃²xC₉	Abelian group of type [3,3,9]	81		C3^2xC9	81,11

Groups of order 82

		d	ρ	Label	ID
C₈₂	Cyclic group	82	1	C82	82,2

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

Groups of order 85

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

Groups of order 86

		d	ρ	Label	ID
C₈₆	Cyclic group	86	1	C86	86,2

Groups of order 87

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

Groups of order 88

		d	ρ	Label	ID
C₈₈	Cyclic group	88	1	C88	88,2
C₂xC₄₄	Abelian group of type [2,44]	88		C2xC44	88,8
C₂²xC₂₂	Abelian group of type [2,2,22]	88		C2^2xC22	88,12

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

Groups of order 91

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

Groups of order 92

		d	ρ	Label	ID
C₉₂	Cyclic group	92	1	C92	92,2
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

Groups of order 94

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

Groups of order 95

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

Groups of order 96

		d	ρ	Label	ID
C₉₆	Cyclic group	96	1	C96	96,2
C₄xC₂₄	Abelian group of type [4,24]	96		C4xC24	96,46
C₂xC₄₈	Abelian group of type [2,48]	96		C2xC48	96,59
C₂⁴xC₆	Abelian group of type [2,2,2,2,6]	96		C2^4xC6	96,231
C₂²xC₂₄	Abelian group of type [2,2,24]	96		C2^2xC24	96,176
C₂³xC₁₂	Abelian group of type [2,2,2,12]	96		C2^3xC12	96,220
C₂xC₄xC₁₂	Abelian group of type [2,4,12]	96		C2xC4xC12	96,161

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
C₇xC₁₄	Abelian group of type [7,14]	98		C7xC14	98,5

Groups of order 99

		d	ρ	Label	ID
C₉₉	Cyclic group	99	1	C99	99,1
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
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

Groups of order 101

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

Groups of order 102

		d	ρ	Label	ID
C₁₀₂	Cyclic group	102	1	C102	102,4

Groups of order 103

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

Groups of order 104

		d	ρ	Label	ID
C₁₀₄	Cyclic group	104	1	C104	104,2
C₂xC₅₂	Abelian group of type [2,52]	104		C2xC52	104,9
C₂²xC₂₆	Abelian group of type [2,2,26]	104		C2^2xC26	104,14

Groups of order 105

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

Groups of order 106

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

Groups of order 107

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

Groups of order 108

		d	ρ	Label	ID
C₁₀₈	Cyclic group	108	1	C108	108,2
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
C₃xC₆²	Abelian group of type [3,6,6]	108		C3xC6^2	108,45
C₃²xC₁₂	Abelian group of type [3,3,12]	108		C3^2xC12	108,35

Groups of order 109

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

Groups of order 110

		d	ρ	Label	ID
C₁₁₀	Cyclic group	110	1	C110	110,6

Groups of order 111

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

Groups of order 112

		d	ρ	Label	ID
C₁₁₂	Cyclic group	112	1	C112	112,2
C₄xC₂₈	Abelian group of type [4,28]	112		C4xC28	112,19
C₂xC₅₆	Abelian group of type [2,56]	112		C2xC56	112,22
C₂²xC₂₈	Abelian group of type [2,2,28]	112		C2^2xC28	112,37
C₂³xC₁₄	Abelian group of type [2,2,2,14]	112		C2^3xC14	112,43

Groups of order 113

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

Groups of order 114

		d	ρ	Label	ID
C₁₁₄	Cyclic group	114	1	C114	114,6

Groups of order 115

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

Groups of order 116

		d	ρ	Label	ID
C₁₁₆	Cyclic group	116	1	C116	116,2
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
C₃xC₃₉	Abelian group of type [3,39]	117		C3xC39	117,4

Groups of order 118

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

Groups of order 119

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

Groups of order 120

		d	ρ	Label	ID
C₁₂₀	Cyclic group	120	1	C120	120,4
C₂xC₆₀	Abelian group of type [2,60]	120		C2xC60	120,31
C₂²xC₃₀	Abelian group of type [2,2,30]	120		C2^2xC30	120,47

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

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
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
C₅³	Elementary abelian group of type [5,5,5]	125		C5^3	125,5
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
C₃xC₄₂	Abelian group of type [3,42]	126		C3xC42	126,16

Groups of order 127

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

Groups of order 128

		d	ρ	Label	ID
C₁₂₈	Cyclic group	128	1	C128	128,1
C₂⁷	Elementary abelian group of type [2,2,2,2,2,2,2]	128		C2^7	128,2328
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
C₂xC₈²	Abelian group of type [2,8,8]	128		C2xC8^2	128,179
C₄²xC₈	Abelian group of type [4,4,8]	128		C4^2xC8	128,456
C₂xC₄³	Abelian group of type [2,4,4,4]	128		C2xC4^3	128,997
C₂⁴xC₈	Abelian group of type [2,2,2,2,8]	128		C2^4xC8	128,2301
C₂⁵xC₄	Abelian group of type [2,2,2,2,2,4]	128		C2^5xC4	128,2319
C₂²xC₃₂	Abelian group of type [2,2,32]	128		C2^2xC32	128,988
C₂³xC₁₆	Abelian group of type [2,2,2,16]	128		C2^3xC16	128,2136
C₂³xC₄²	Abelian group of type [2,2,2,4,4]	128		C2^3xC4^2	128,2150
C₂xC₄xC₁₆	Abelian group of type [2,4,16]	128		C2xC4xC16	128,837
C₂²xC₄xC₈	Abelian group of type [2,2,4,8]	128		C2^2xC4xC8	128,1601

Groups of order 129

		d	ρ	Label	ID
C₁₂₉	Cyclic group	129	1	C129	129,2

Groups of order 130

		d	ρ	Label	ID
C₁₃₀	Cyclic group	130	1	C130	130,4

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
C₂xC₆₆	Abelian group of type [2,66]	132		C2xC66	132,10

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

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
C₃²xC₁₅	Abelian group of type [3,3,15]	135		C3^2xC15	135,5

Groups of order 136

		d	ρ	Label	ID
C₁₃₆	Cyclic group	136	1	C136	136,2
C₂xC₆₈	Abelian group of type [2,68]	136		C2xC68	136,9
C₂²xC₃₄	Abelian group of type [2,2,34]	136		C2^2xC34	136,15

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

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
C₂xC₇₀	Abelian group of type [2,70]	140		C2xC70	140,11

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

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
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
C₂²xC₃₆	Abelian group of type [2,2,36]	144		C2^2xC36	144,47
C₂³xC₁₈	Abelian group of type [2,2,2,18]	144		C2^3xC18	144,113
C₂²xC₆²	Abelian group of type [2,2,6,6]	144		C2^2xC6^2	144,197
C₂xC₆xC₁₂	Abelian group of type [2,6,12]	144		C2xC6xC12	144,178

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

Groups of order 147

		d	ρ	Label	ID
C₁₄₇	Cyclic group	147	1	C147	147,2
C₇xC₂₁	Abelian group of type [7,21]	147		C7xC21	147,6

Groups of order 148

		d	ρ	Label	ID
C₁₄₈	Cyclic group	148	1	C148	148,2
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
C₅xC₃₀	Abelian group of type [5,30]	150		C5xC30	150,13

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
C₂xC₇₆	Abelian group of type [2,76]	152		C2xC76	152,8
C₂²xC₃₈	Abelian group of type [2,2,38]	152		C2^2xC38	152,12

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

Groups of order 155

		d	ρ	Label	ID
C₁₅₅	Cyclic group	155	1	C155	155,2

Groups of order 156

		d	ρ	Label	ID
C₁₅₆	Cyclic group	156	1	C156	156,6
C₂xC₇₈	Abelian group of type [2,78]	156		C2xC78	156,18

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

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
C₄xC₄₀	Abelian group of type [4,40]	160		C4xC40	160,46
C₂xC₈₀	Abelian group of type [2,80]	160		C2xC80	160,59
C₂²xC₄₀	Abelian group of type [2,2,40]	160		C2^2xC40	160,190
C₂³xC₂₀	Abelian group of type [2,2,2,20]	160		C2^3xC20	160,228
C₂⁴xC₁₀	Abelian group of type [2,2,2,2,10]	160		C2^4xC10	160,238
C₂xC₄xC₂₀	Abelian group of type [2,4,20]	160		C2xC4xC20	160,175

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
C₉xC₁₈	Abelian group of type [9,18]	162		C9xC18	162,23
C₃xC₅₄	Abelian group of type [3,54]	162		C3xC54	162,26
C₃³xC₆	Abelian group of type [3,3,3,6]	162		C3^3xC6	162,55
C₃²xC₁₈	Abelian group of type [3,3,18]	162		C3^2xC18	162,47

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
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

Groups of order 166

		d	ρ	Label	ID
C₁₆₆	Cyclic group	166	1	C166	166,2

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
C₂xC₈₄	Abelian group of type [2,84]	168		C2xC84	168,39
C₂²xC₄₂	Abelian group of type [2,2,42]	168		C2^2xC42	168,57

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

Groups of order 171

		d	ρ	Label	ID
C₁₇₁	Cyclic group	171	1	C171	171,2
C₃xC₅₇	Abelian group of type [3,57]	171		C3xC57	171,5

Groups of order 172

		d	ρ	Label	ID
C₁₇₂	Cyclic group	172	1	C172	172,2
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

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
C₄xC₄₄	Abelian group of type [4,44]	176		C4xC44	176,19
C₂xC₈₈	Abelian group of type [2,88]	176		C2xC88	176,22
C₂²xC₄₄	Abelian group of type [2,2,44]	176		C2^2xC44	176,37
C₂³xC₂₂	Abelian group of type [2,2,2,22]	176		C2^3xC22	176,42

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

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
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

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

Groups of order 183

		d	ρ	Label	ID
C₁₈₃	Cyclic group	183	1	C183	183,2

Groups of order 184

		d	ρ	Label	ID
C₁₈₄	Cyclic group	184	1	C184	184,2
C₂xC₉₂	Abelian group of type [2,92]	184		C2xC92	184,8
C₂²xC₄₆	Abelian group of type [2,2,46]	184		C2^2xC46	184,12

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

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
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
C₃xC₆₃	Abelian group of type [3,63]	189		C3xC63	189,9
C₃²xC₂₁	Abelian group of type [3,3,21]	189		C3^2xC21	189,13

Groups of order 190

		d	ρ	Label	ID
C₁₉₀	Cyclic group	190	1	C190	190,4

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
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
C₂⁵xC₆	Abelian group of type [2,2,2,2,2,6]	192		C2^5xC6	192,1543
C₄²xC₁₂	Abelian group of type [4,4,12]	192		C4^2xC12	192,807
C₂²xC₄₈	Abelian group of type [2,2,48]	192		C2^2xC48	192,935
C₂³xC₂₄	Abelian group of type [2,2,2,24]	192		C2^3xC24	192,1454
C₂⁴xC₁₂	Abelian group of type [2,2,2,2,12]	192		C2^4xC12	192,1530
C₂xC₄xC₂₄	Abelian group of type [2,4,24]	192		C2xC4xC24	192,835
C₂²xC₄xC₁₂	Abelian group of type [2,2,4,12]	192		C2^2xC4xC12	192,1400

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

Groups of order 195

		d	ρ	Label	ID
C₁₉₅	Cyclic group	195	1	C195	195,2

Groups of order 196

		d	ρ	Label	ID
C₁₉₆	Cyclic group	196	1	C196	196,2
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

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
C₃xC₆₆	Abelian group of type [3,66]	198		C3xC66	198,10

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
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
C₂²xC₅₀	Abelian group of type [2,2,50]	200		C2^2xC50	200,14
C₂xC₁₀²	Abelian group of type [2,10,10]	200		C2xC10^2	200,52

Groups of order 201

		d	ρ	Label	ID
C₂₀₁	Cyclic group	201	1	C201	201,2

Groups of order 202

		d	ρ	Label	ID
C₂₀₂	Cyclic group	202	1	C202	202,2

Groups of order 203

		d	ρ	Label	ID
C₂₀₃	Cyclic group	203	1	C203	203,2

Groups of order 204

		d	ρ	Label	ID
C₂₀₄	Cyclic group	204	1	C204	204,4
C₂xC₁₀₂	Abelian group of type [2,102]	204		C2xC102	204,12

Groups of order 205

		d	ρ	Label	ID
C₂₀₅	Cyclic group	205	1	C205	205,2

Groups of order 206

		d	ρ	Label	ID
C₂₀₆	Cyclic group	206	1	C206	206,2

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
C₄xC₅₂	Abelian group of type [4,52]	208		C4xC52	208,20
C₂xC₁₀₄	Abelian group of type [2,104]	208		C2xC104	208,23
C₂²xC₅₂	Abelian group of type [2,2,52]	208		C2^2xC52	208,45
C₂³xC₂₆	Abelian group of type [2,2,2,26]	208		C2^3xC26	208,51

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

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
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

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
C₆³	Abelian group of type [6,6,6]	216		C6^3	216,177
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
C₂²xC₅₄	Abelian group of type [2,2,54]	216		C2^2xC54	216,24
C₃²xC₂₄	Abelian group of type [3,3,24]	216		C3^2xC24	216,85
C₂xC₆xC₁₈	Abelian group of type [2,6,18]	216		C2xC6xC18	216,114
C₃xC₆xC₁₂	Abelian group of type [3,6,12]	216		C3xC6xC12	216,150

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

Groups of order 219

		d	ρ	Label	ID
C₂₁₉	Cyclic group	219	1	C219	219,2

Groups of order 220

		d	ρ	Label	ID
C₂₂₀	Cyclic group	220	1	C220	220,6
C₂xC₁₁₀	Abelian group of type [2,110]	220		C2xC110	220,15

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

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
C₄xC₅₆	Abelian group of type [4,56]	224		C4xC56	224,45
C₂xC₁₁₂	Abelian group of type [2,112]	224		C2xC112	224,58
C₂²xC₅₆	Abelian group of type [2,2,56]	224		C2^2xC56	224,164
C₂³xC₂₈	Abelian group of type [2,2,2,28]	224		C2^3xC28	224,189
C₂⁴xC₁₄	Abelian group of type [2,2,2,2,14]	224		C2^4xC14	224,197
C₂xC₄xC₂₈	Abelian group of type [2,4,28]	224		C2xC4xC28	224,149

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

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
C₂xC₁₁₄	Abelian group of type [2,114]	228		C2xC114	228,15

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

Groups of order 231

		d	ρ	Label	ID
C₂₃₁	Cyclic group	231	1	C231	231,2

Groups of order 232

		d	ρ	Label	ID
C₂₃₂	Cyclic group	232	1	C232	232,2
C₂xC₁₁₆	Abelian group of type [2,116]	232		C2xC116	232,9
C₂²xC₅₈	Abelian group of type [2,2,58]	232		C2^2xC58	232,14

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
C₃xC₇₈	Abelian group of type [3,78]	234		C3xC78	234,16

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
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

Groups of order 238

		d	ρ	Label	ID
C₂₃₈	Cyclic group	238	1	C238	238,4

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
C₄xC₆₀	Abelian group of type [4,60]	240		C4xC60	240,81
C₂xC₁₂₀	Abelian group of type [2,120]	240		C2xC120	240,84
C₂²xC₆₀	Abelian group of type [2,2,60]	240		C2^2xC60	240,185
C₂³xC₃₀	Abelian group of type [2,2,2,30]	240		C2^3xC30	240,208

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
C₁₁xC₂₂	Abelian group of type [11,22]	242		C11xC22	242,5

Groups of order 243

		d	ρ	Label	ID
C₂₄₃	Cyclic group	243	1	C243	243,1
C₃⁵	Elementary abelian group of type [3,3,3,3,3]	243		C3^5	243,67
C₉xC₂₇	Abelian group of type [9,27]	243		C9xC27	243,10
C₃xC₈₁	Abelian group of type [3,81]	243		C3xC81	243,23
C₃xC₉²	Abelian group of type [3,9,9]	243		C3xC9^2	243,31
C₃³xC₉	Abelian group of type [3,3,3,9]	243		C3^3xC9	243,61
C₃²xC₂₇	Abelian group of type [3,3,27]	243		C3^2xC27	243,48

Groups of order 244

		d	ρ	Label	ID
C₂₄₄	Cyclic group	244	1	C244	244,2
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

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
C₂xC₁₂₄	Abelian group of type [2,124]	248		C2xC124	248,8
C₂²xC₆₂	Abelian group of type [2,2,62]	248		C2^2xC62	248,12

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
C₅xC₅₀	Abelian group of type [5,50]	250		C5xC50	250,9
C₅²xC₁₀	Abelian group of type [5,5,10]	250		C5^2xC10	250,15

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
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

Groups of order 253

		d	ρ	Label	ID
C₂₅₃	Cyclic group	253	1	C253	253,2

Groups of order 254

		d	ρ	Label	ID
C₂₅₄	Cyclic group	254	1	C254	254,2

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

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
C₂xC₁₃₀	Abelian group of type [2,130]	260		C2xC130	260,15

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

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
C₂xC₁₃₂	Abelian group of type [2,132]	264		C2xC132	264,28
C₂²xC₆₆	Abelian group of type [2,2,66]	264		C2^2xC66	264,39

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

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
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
C₃xC₉₀	Abelian group of type [3,90]	270		C3xC90	270,20
C₃²xC₃₀	Abelian group of type [3,3,30]	270		C3^2xC30	270,30

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
C₄xC₆₈	Abelian group of type [4,68]	272		C4xC68	272,20
C₂xC₁₃₆	Abelian group of type [2,136]	272		C2xC136	272,23
C₂²xC₆₈	Abelian group of type [2,2,68]	272		C2^2xC68	272,46
C₂³xC₃₄	Abelian group of type [2,2,2,34]	272		C2^3xC34	272,54

Groups of order 273

		d	ρ	Label	ID
C₂₇₃	Cyclic group	273	1	C273	273,5

Groups of order 274

		d	ρ	Label	ID
C₂₇₄	Cyclic group	274	1	C274	274,2

Groups of order 275

		d	ρ	Label	ID
C₂₇₅	Cyclic group	275	1	C275	275,2
C₅xC₅₅	Abelian group of type [5,55]	275		C5xC55	275,4

Groups of order 276

		d	ρ	Label	ID
C₂₇₆	Cyclic group	276	1	C276	276,4
C₂xC₁₃₈	Abelian group of type [2,138]	276		C2xC138	276,10

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

Groups of order 279

		d	ρ	Label	ID
C₂₇₉	Cyclic group	279	1	C279	279,2
C₃xC₉₃	Abelian group of type [3,93]	279		C3xC93	279,4

Groups of order 280

		d	ρ	Label	ID
C₂₈₀	Cyclic group	280	1	C280	280,4
C₂xC₁₄₀	Abelian group of type [2,140]	280		C2xC140	280,29
C₂²xC₇₀	Abelian group of type [2,2,70]	280		C2^2xC70	280,40

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

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
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

Groups of order 286

		d	ρ	Label	ID
C₂₈₆	Cyclic group	286	1	C286	286,4

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
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
C₂²xC₇₂	Abelian group of type [2,2,72]	288		C2^2xC72	288,179
C₂³xC₃₆	Abelian group of type [2,2,2,36]	288		C2^3xC36	288,367
C₂xC₁₂²	Abelian group of type [2,12,12]	288		C2xC12^2	288,811
C₂⁴xC₁₈	Abelian group of type [2,2,2,2,18]	288		C2^4xC18	288,840
C₂³xC₆²	Abelian group of type [2,2,2,6,6]	288		C2^3xC6^2	288,1045
C₂xC₄xC₃₆	Abelian group of type [2,4,36]	288		C2xC4xC36	288,164
C₂xC₆xC₂₄	Abelian group of type [2,6,24]	288		C2xC6xC24	288,826
C₂²xC₆xC₁₂	Abelian group of type [2,2,6,12]	288		C2^2xC6xC12	288,1018

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

Groups of order 291

		d	ρ	Label	ID
C₂₉₁	Cyclic group	291	1	C291	291,2

Groups of order 292

		d	ρ	Label	ID
C₂₉₂	Cyclic group	292	1	C292	292,2
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
C₇xC₄₂	Abelian group of type [7,42]	294		C7xC42	294,23

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
C₂xC₁₄₈	Abelian group of type [2,148]	296		C2xC148	296,9
C₂²xC₇₄	Abelian group of type [2,2,74]	296		C2^2xC74	296,14

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
C₃²xC₃₃	Abelian group of type [3,3,33]	297		C3^2xC33	297,5

Groups of order 298

		d	ρ	Label	ID
C₂₉₈	Cyclic group	298	1	C298	298,2

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
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

Groups of order 301

		d	ρ	Label	ID
C₃₀₁	Cyclic group	301	1	C301	301,2

Groups of order 302

		d	ρ	Label	ID
C₃₀₂	Cyclic group	302	1	C302	302,2

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
C₄xC₇₆	Abelian group of type [4,76]	304		C4xC76	304,19
C₂xC₁₅₂	Abelian group of type [2,152]	304		C2xC152	304,22
C₂²xC₇₆	Abelian group of type [2,2,76]	304		C2^2xC76	304,37
C₂³xC₃₈	Abelian group of type [2,2,2,38]	304		C2^3xC38	304,42

Groups of order 305

		d	ρ	Label	ID
C₃₀₅	Cyclic group	305	1	C305	305,2

Groups of order 306

		d	ρ	Label	ID
C₃₀₆	Cyclic group	306	1	C306	306,4
C₃xC₁₀₂	Abelian group of type [3,102]	306		C3xC102	306,10

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
C₂xC₁₅₄	Abelian group of type [2,154]	308		C2xC154	308,9

Groups of order 309

		d	ρ	Label	ID
C₃₀₉	Cyclic group	309	1	C309	309,2

Groups of order 310

		d	ρ	Label	ID
C₃₁₀	Cyclic group	310	1	C310	310,6

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
C₂xC₁₅₆	Abelian group of type [2,156]	312		C2xC156	312,42
C₂²xC₇₈	Abelian group of type [2,2,78]	312		C2^2xC78	312,61

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

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

Groups of order 316

		d	ρ	Label	ID
C₃₁₆	Cyclic group	316	1	C316	316,2
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

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
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
C₄²xC₂₀	Abelian group of type [4,4,20]	320		C4^2xC20	320,875
C₂²xC₈₀	Abelian group of type [2,2,80]	320		C2^2xC80	320,1003
C₂³xC₄₀	Abelian group of type [2,2,2,40]	320		C2^3xC40	320,1567
C₂⁴xC₂₀	Abelian group of type [2,2,2,2,20]	320		C2^4xC20	320,1628
C₂⁵xC₁₀	Abelian group of type [2,2,2,2,2,10]	320		C2^5xC10	320,1640
C₂xC₄xC₄₀	Abelian group of type [2,4,40]	320		C2xC4xC40	320,903
C₂²xC₄xC₂₀	Abelian group of type [2,2,4,20]	320		C2^2xC4xC20	320,1513

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

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
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
C₃²xC₃₆	Abelian group of type [3,3,36]	324		C3^2xC36	324,105
C₃³xC₁₂	Abelian group of type [3,3,3,12]	324		C3^3xC12	324,159
C₃²xC₆²	Abelian group of type [3,3,6,6]	324		C3^2xC6^2	324,176
C₃xC₆xC₁₈	Abelian group of type [3,6,18]	324		C3xC6xC18	324,151

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

Groups of order 327

		d	ρ	Label	ID
C₃₂₇	Cyclic group	327	1	C327	327,2

Groups of order 328

		d	ρ	Label	ID
C₃₂₈	Cyclic group	328	1	C328	328,2
C₂xC₁₆₄	Abelian group of type [2,164]	328		C2xC164	328,9
C₂²xC₈₂	Abelian group of type [2,2,82]	328		C2^2xC82	328,15

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

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
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
C₃xC₁₁₁	Abelian group of type [3,111]	333		C3xC111	333,5

Groups of order 334

		d	ρ	Label	ID
C₃₃₄	Cyclic group	334	1	C334	334,2

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
C₄xC₈₄	Abelian group of type [4,84]	336		C4xC84	336,106
C₂xC₁₆₈	Abelian group of type [2,168]	336		C2xC168	336,109
C₂²xC₈₄	Abelian group of type [2,2,84]	336		C2^2xC84	336,204
C₂³xC₄₂	Abelian group of type [2,2,2,42]	336		C2^3xC42	336,228

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
C₁₃xC₂₆	Abelian group of type [13,26]	338		C13xC26	338,5

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
C₂xC₁₇₀	Abelian group of type [2,170]	340		C2xC170	340,15

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
C₃xC₁₁₄	Abelian group of type [3,114]	342		C3xC114	342,18

Groups of order 343

		d	ρ	Label	ID
C₃₄₃	Cyclic group	343	1	C343	343,1
C₇³	Elementary abelian group of type [7,7,7]	343		C7^3	343,5
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
C₂xC₁₇₂	Abelian group of type [2,172]	344		C2xC172	344,8
C₂²xC₈₆	Abelian group of type [2,2,86]	344		C2^2xC86	344,12

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

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
C₂xC₁₇₄	Abelian group of type [2,174]	348		C2xC174	348,12

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
C₅xC₇₀	Abelian group of type [5,70]	350		C5xC70	350,10

Groups of order 351

		d	ρ	Label	ID
C₃₅₁	Cyclic group	351	1	C351	351,2
C₃xC₁₁₇	Abelian group of type [3,117]	351		C3xC117	351,9
C₃²xC₃₉	Abelian group of type [3,3,39]	351		C3^2xC39	351,14

Groups of order 352

		d	ρ	Label	ID
C₃₅₂	Cyclic group	352	1	C352	352,2
C₄xC₈₈	Abelian group of type [4,88]	352		C4xC88	352,45
C₂xC₁₇₆	Abelian group of type [2,176]	352		C2xC176	352,58
C₂²xC₈₈	Abelian group of type [2,2,88]	352		C2^2xC88	352,164
C₂³xC₄₄	Abelian group of type [2,2,2,44]	352		C2^3xC44	352,188
C₂⁴xC₂₂	Abelian group of type [2,2,2,2,22]	352		C2^4xC22	352,195
C₂xC₄xC₄₄	Abelian group of type [2,4,44]	352		C2xC4xC44	352,149

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

Groups of order 355

		d	ρ	Label	ID
C₃₅₅	Cyclic group	355	1	C355	355,2

Groups of order 356

		d	ρ	Label	ID
C₃₅₆	Cyclic group	356	1	C356	356,2
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

Groups of order 358

		d	ρ	Label	ID
C₃₅₈	Cyclic group	358	1	C358	358,2

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
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
C₂²xC₉₀	Abelian group of type [2,2,90]	360		C2^2xC90	360,50
C₂xC₆xC₃₀	Abelian group of type [2,6,30]	360		C2xC6xC30	360,162

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

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
C₂xC₁₈₂	Abelian group of type [2,182]	364		C2xC182	364,11

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

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
C₄xC₉₂	Abelian group of type [4,92]	368		C4xC92	368,19
C₂xC₁₈₄	Abelian group of type [2,184]	368		C2xC184	368,22
C₂²xC₉₂	Abelian group of type [2,2,92]	368		C2^2xC92	368,37
C₂³xC₄₆	Abelian group of type [2,2,2,46]	368		C2^3xC46	368,42

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

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
C₂xC₁₈₆	Abelian group of type [2,186]	372		C2xC186	372,15

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

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
C₅²xC₁₅	Abelian group of type [5,5,15]	375		C5^2xC15	375,7

Groups of order 376

		d	ρ	Label	ID
C₃₇₆	Cyclic group	376	1	C376	376,2
C₂xC₁₈₈	Abelian group of type [2,188]	376		C2xC188	376,8
C₂²xC₉₄	Abelian group of type [2,2,94]	376		C2^2xC94	376,12

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
C₃xC₁₂₆	Abelian group of type [3,126]	378		C3xC126	378,44
C₃²xC₄₂	Abelian group of type [3,3,42]	378		C3^2xC42	378,60

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
C₂xC₁₉₀	Abelian group of type [2,190]	380		C2xC190	380,11

Groups of order 381

		d	ρ	Label	ID
C₃₈₁	Cyclic group	381	1	C381	381,2

Groups of order 382

		d	ρ	Label	ID
C₃₈₂	Cyclic group	382	1	C382	382,2

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

Groups of order 386

		d	ρ	Label	ID
C₃₈₆	Cyclic group	386	1	C386	386,2

Groups of order 387

		d	ρ	Label	ID
C₃₈₇	Cyclic group	387	1	C387	387,2
C₃xC₁₂₉	Abelian group of type [3,129]	387		C3xC129	387,4

Groups of order 388

		d	ρ	Label	ID
C₃₈₈	Cyclic group	388	1	C388	388,2
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

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
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
C₂²xC₉₈	Abelian group of type [2,2,98]	392		C2^2xC98	392,13
C₂xC₁₄²	Abelian group of type [2,14,14]	392		C2xC14^2	392,44

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

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
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

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

Groups of order 399

		d	ρ	Label	ID
C₃₉₉	Cyclic group	399	1	C399	399,5

Groups of order 400

		d	ρ	Label	ID
C₄₀₀	Cyclic group	400	1	C400	400,2
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
C₂³xC₅₀	Abelian group of type [2,2,2,50]	400		C2^3xC50	400,55
C₂²xC₁₀₀	Abelian group of type [2,2,100]	400		C2^2xC100	400,45
C₂²xC₁₀²	Abelian group of type [2,2,10,10]	400		C2^2xC10^2	400,221
C₂xC₁₀xC₂₀	Abelian group of type [2,10,20]	400		C2xC10xC20	400,201

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

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
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
C₃²xC₄₅	Abelian group of type [3,3,45]	405		C3^2xC45	405,11
C₃³xC₁₅	Abelian group of type [3,3,3,15]	405		C3^3xC15	405,16

Groups of order 406

		d	ρ	Label	ID
C₄₀₆	Cyclic group	406	1	C406	406,6

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
C₂xC₂₀₄	Abelian group of type [2,204]	408		C2xC204	408,30
C₂²xC₁₀₂	Abelian group of type [2,2,102]	408		C2^2xC102	408,46

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

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
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
C₃xC₁₃₈	Abelian group of type [3,138]	414		C3xC138	414,10

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
C₄xC₁₀₄	Abelian group of type [4,104]	416		C4xC104	416,46
C₂xC₂₀₈	Abelian group of type [2,208]	416		C2xC208	416,59
C₂³xC₅₂	Abelian group of type [2,2,2,52]	416		C2^3xC52	416,227
C₂⁴xC₂₆	Abelian group of type [2,2,2,2,26]	416		C2^4xC26	416,235
C₂²xC₁₀₄	Abelian group of type [2,2,104]	416		C2^2xC104	416,190
C₂xC₄xC₅₂	Abelian group of type [2,4,52]	416		C2xC4xC52	416,175

Groups of order 417

		d	ρ	Label	ID
C₄₁₇	Cyclic group	417	1	C417	417,2

Groups of order 418

		d	ρ	Label	ID
C₄₁₈	Cyclic group	418	1	C418	418,4

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
C₂xC₂₁₀	Abelian group of type [2,210]	420		C2xC210	420,41

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

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
C₂xC₂₁₂	Abelian group of type [2,212]	424		C2xC212	424,9
C₂²xC₁₀₆	Abelian group of type [2,2,106]	424		C2^2xC106	424,14

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

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
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

Groups of order 430

		d	ρ	Label	ID
C₄₃₀	Cyclic group	430	1	C430	430,4

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
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
C₂xC₆³	Abelian group of type [2,6,6,6]	432		C2xC6^3	432,775
C₂³xC₅₄	Abelian group of type [2,2,2,54]	432		C2^3xC54	432,228
C₃²xC₄₈	Abelian group of type [3,3,48]	432		C3^2xC48	432,232
C₃xC₁₂²	Abelian group of type [3,12,12]	432		C3xC12^2	432,512
C₆²xC₁₂	Abelian group of type [6,6,12]	432		C6^2xC12	432,730
C₂²xC₁₀₈	Abelian group of type [2,2,108]	432		C2^2xC108	432,53
C₂xC₆xC₃₆	Abelian group of type [2,6,36]	432		C2xC6xC36	432,400
C₃xC₆xC₂₄	Abelian group of type [3,6,24]	432		C3xC6xC24	432,515
C₂²xC₆xC₁₈	Abelian group of type [2,2,6,18]	432		C2^2xC6xC18	432,562

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

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
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

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
C₂xC₂₂₀	Abelian group of type [2,220]	440		C2xC220	440,39
C₂²xC₁₁₀	Abelian group of type [2,2,110]	440		C2^2xC110	440,51

Groups of order 441

		d	ρ	Label	ID
C₄₄₁	Cyclic group	441	1	C441	441,2
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

Groups of order 442

		d	ρ	Label	ID
C₄₄₂	Cyclic group	442	1	C442	442,4

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
C₂xC₂₂₂	Abelian group of type [2,222]	444		C2xC222	444,18

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

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
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
C₄²xC₂₈	Abelian group of type [4,4,28]	448		C4^2xC28	448,782
C₂³xC₅₆	Abelian group of type [2,2,2,56]	448		C2^3xC56	448,1348
C₂⁴xC₂₈	Abelian group of type [2,2,2,2,28]	448		C2^4xC28	448,1385
C₂⁵xC₁₄	Abelian group of type [2,2,2,2,2,14]	448		C2^5xC14	448,1396
C₂²xC₁₁₂	Abelian group of type [2,2,112]	448		C2^2xC112	448,910
C₂xC₄xC₅₆	Abelian group of type [2,4,56]	448		C2xC4xC56	448,810
C₂²xC₄xC₂₈	Abelian group of type [2,2,4,28]	448		C2^2xC4xC28	448,1294

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
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

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
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

Groups of order 454

		d	ρ	Label	ID
C₄₅₄	Cyclic group	454	1	C454	454,2

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
C₂xC₂₂₈	Abelian group of type [2,228]	456		C2xC228	456,39
C₂²xC₁₁₄	Abelian group of type [2,2,114]	456		C2^2xC114	456,54

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

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
C₃²xC₅₁	Abelian group of type [3,3,51]	459		C3^2xC51	459,5

Groups of order 460

		d	ρ	Label	ID
C₄₆₀	Cyclic group	460	1	C460	460,4
C₂xC₂₃₀	Abelian group of type [2,230]	460		C2xC230	460,11

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

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
C₄xC₁₁₆	Abelian group of type [4,116]	464		C4xC116	464,20
C₂xC₂₃₂	Abelian group of type [2,232]	464		C2xC232	464,23
C₂³xC₅₈	Abelian group of type [2,2,2,58]	464		C2^3xC58	464,51
C₂²xC₁₁₆	Abelian group of type [2,2,116]	464		C2^2xC116	464,45

Groups of order 465

		d	ρ	Label	ID
C₄₆₅	Cyclic group	465	1	C465	465,4

Groups of order 466

		d	ρ	Label	ID
C₄₆₆	Cyclic group	466	1	C466	466,2

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
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

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

Groups of order 471

		d	ρ	Label	ID
C₄₇₁	Cyclic group	471	1	C471	471,2

Groups of order 472

		d	ρ	Label	ID
C₄₇₂	Cyclic group	472	1	C472	472,2
C₂xC₂₃₆	Abelian group of type [2,236]	472		C2xC236	472,8
C₂²xC₁₁₈	Abelian group of type [2,2,118]	472		C2^2xC118	472,12

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

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
C₂xC₂₃₈	Abelian group of type [2,238]	476		C2xC238	476,11

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

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
C₄xC₁₂₀	Abelian group of type [4,120]	480		C4xC120	480,199
C₂xC₂₄₀	Abelian group of type [2,240]	480		C2xC240	480,212
C₂³xC₆₀	Abelian group of type [2,2,2,60]	480		C2^3xC60	480,1180
C₂⁴xC₃₀	Abelian group of type [2,2,2,2,30]	480		C2^4xC30	480,1213
C₂²xC₁₂₀	Abelian group of type [2,2,120]	480		C2^2xC120	480,934
C₂xC₄xC₆₀	Abelian group of type [2,4,60]	480		C2xC4xC60	480,919

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

Groups of order 483

		d	ρ	Label	ID
C₄₈₃	Cyclic group	483	1	C483	483,2

Groups of order 484

		d	ρ	Label	ID
C₄₈₄	Cyclic group	484	1	C484	484,2
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

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
C₉xC₅₄	Abelian group of type [9,54]	486		C9xC54	486,70
C₃xC₁₆₂	Abelian group of type [3,162]	486		C3xC162	486,83
C₃⁴xC₆	Abelian group of type [3,3,3,3,6]	486		C3^4xC6	486,261
C₃²xC₅₄	Abelian group of type [3,3,54]	486		C3^2xC54	486,207
C₃³xC₁₈	Abelian group of type [3,3,3,18]	486		C3^3xC18	486,250
C₃xC₉xC₁₈	Abelian group of type [3,9,18]	486		C3xC9xC18	486,190

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
C₂xC₂₄₄	Abelian group of type [2,244]	488		C2xC244	488,9
C₂²xC₁₂₂	Abelian group of type [2,2,122]	488		C2^2xC122	488,14

Groups of order 489

		d	ρ	Label	ID
C₄₈₉	Cyclic group	489	1	C489	489,2

Groups of order 490

		d	ρ	Label	ID
C₄₉₀	Cyclic group	490	1	C490	490,4
C₇xC₇₀	Abelian group of type [7,70]	490		C7xC70	490,10

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
C₂xC₂₄₆	Abelian group of type [2,246]	492		C2xC246	492,12

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

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

Groups of order 496

		d	ρ	Label	ID
C₄₉₆	Cyclic group	496	1	C496	496,2
C₄xC₁₂₄	Abelian group of type [4,124]	496		C4xC124	496,19
C₂xC₂₄₈	Abelian group of type [2,248]	496		C2xC248	496,22
C₂³xC₆₂	Abelian group of type [2,2,2,62]	496		C2^3xC62	496,42
C₂²xC₁₂₄	Abelian group of type [2,2,124]	496		C2^2xC124	496,37

Groups of order 497

		d	ρ	Label	ID
C₄₉₇	Cyclic group	497	1	C497	497,2

Groups of order 498

		d	ρ	Label	ID
C₄₉₈	Cyclic group	498	1	C498	498,4

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
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
C₅²xC₂₀	Abelian group of type [5,5,20]	500		C5^2xC20	500,40
C₅xC₁₀²	Abelian group of type [5,10,10]	500		C5xC10^2	500,56