Direct products

Groups of order 4

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

Groups of order 6

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

Groups of order 8

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

Groups of order 9

		d	ρ	Label	ID
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 12

		d	ρ	Label	ID
C₁₂	Cyclic group	12	1	C12	12,2
D₆	Dihedral group; = C₂×S₃ = hexagon symmetries	6	2+	D6	12,4
C₂×C₆	Abelian group of type [2,6]	12		C2xC6	12,5

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	Label	ID
C₄²	Abelian group of type [4,4]	16	C4^2	16,2
C₂⁴	Elementary abelian group of type [2,2,2,2]	16	C2^4	16,14
C₂×C₈	Abelian group of type [2,8]	16	C2xC8	16,5
C₂²×C₄	Abelian group of type [2,2,4]	16	C2^2xC4	16,10
C₂×D₄	Direct product of C₂ and D₄	8	C2xD4	16,11
C₂×Q₈	Direct product of C₂ and Q₈	16	C2xQ8	16,12

Groups of order 18

		d	ρ	Label	ID
C₁₈	Cyclic group	18	1	C18	18,2
C₃×C₆	Abelian group of type [3,6]	18		C3xC6	18,5
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	6	2	C3xS3	18,3

Groups of order 20

		d	ρ	Label	ID
C₂₀	Cyclic group	20	1	C20	20,2
D₁₀	Dihedral group; = C₂×D₅	10	2+	D10	20,4
C₂×C₁₀	Abelian group of type [2,10]	20		C2xC10	20,5

Groups of order 21

		d	ρ	Label	ID
C₂₁	Cyclic group	21	1	C21	21,2

Groups of order 22

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

Groups of order 24

		d	ρ	Label	ID
C₂₄	Cyclic group	24	1	C24	24,2
C₂×C₁₂	Abelian group of type [2,12]	24		C2xC12	24,9
C₂²×C₆	Abelian group of type [2,2,6]	24		C2^2xC6	24,15
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	6	3+	C2xA4	24,13
C₄×S₃	Direct product of C₄ and S₃	12	2	C4xS3	24,5
C₃×D₄	Direct product of C₃ and D₄	12	2	C3xD4	24,10
C₂²×S₃	Direct product of C₂² and S₃	12		C2^2xS3	24,14
C₃×Q₈	Direct product of C₃ and Q₈	24	2	C3xQ8	24,11
C₂×Dic₃	Direct product of C₂ and Dic₃	24		C2xDic3	24,7

Groups of order 25

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

Groups of order 28

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

Groups of order 30

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

Groups of order 32

		d	Label	ID
C₂⁵	Elementary abelian group of type [2,2,2,2,2]	32	C2^5	32,51
C₄×C₈	Abelian group of type [4,8]	32	C4xC8	32,3
C₂×C₁₆	Abelian group of type [2,16]	32	C2xC16	32,16
C₂×C₄²	Abelian group of type [2,4,4]	32	C2xC4^2	32,21
C₂²×C₈	Abelian group of type [2,2,8]	32	C2^2xC8	32,36
C₂³×C₄	Abelian group of type [2,2,2,4]	32	C2^3xC4	32,45
C₄×D₄	Direct product of C₄ and D₄	16	C4xD4	32,25
C₂×D₈	Direct product of C₂ and D₈	16	C2xD8	32,39
C₂×SD₁₆	Direct product of C₂ and SD₁₆	16	C2xSD16	32,40
C₂²×D₄	Direct product of C₂² and D₄	16	C2^2xD4	32,46
C₂×M₄(2)	Direct product of C₂ and M₄(2)	16	C2xM4(2)	32,37
C₄×Q₈	Direct product of C₄ and Q₈	32	C4xQ8	32,26
C₂×Q₁₆	Direct product of C₂ and Q₁₆	32	C2xQ16	32,41
C₂²×Q₈	Direct product of C₂² and Q₈	32	C2^2xQ8	32,47
C₂×C₄○D₄	Direct product of C₂ and C₄○D₄	16	C2xC4oD4	32,48
C₂×C₂²⋊C₄	Direct product of C₂ and C₂²⋊C₄	16	C2xC2^2:C4	32,22
C₂×C₄⋊C₄	Direct product of C₂ and C₄⋊C₄	32	C2xC4:C4	32,23

Groups of order 33

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

Groups of order 34

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

Groups of order 35

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

Groups of order 36

		d	ρ	Label	ID
C₃₆	Cyclic group	36	1	C36	36,2
D₁₈	Dihedral group; = C₂×D₉	18	2+	D18	36,4
C₆²	Abelian group of type [6,6]	36		C6^2	36,14
C₂×C₁₈	Abelian group of type [2,18]	36		C2xC18	36,5
C₃×C₁₂	Abelian group of type [3,12]	36		C3xC12	36,8
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	6	4+	S3^2	36,10
S₃×C₆	Direct product of C₆ and S₃	12	2	S3xC6	36,12
C₃×A₄	Direct product of C₃ and A₄	12	3	C3xA4	36,11
C₃×Dic₃	Direct product of C₃ and Dic₃	12	2	C3xDic3	36,6
C₂×C₃⋊S₃	Direct product of C₂ and C₃⋊S₃	18		C2xC3:S3	36,13

Groups of order 38

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

Groups of order 39

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

Groups of order 40

		d	ρ	Label	ID
C₄₀	Cyclic group	40	1	C40	40,2
C₂×C₂₀	Abelian group of type [2,20]	40		C2xC20	40,9
C₂²×C₁₀	Abelian group of type [2,2,10]	40		C2^2xC10	40,14
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	10	4+	C2xF5	40,12
C₄×D₅	Direct product of C₄ and D₅	20	2	C4xD5	40,5
C₅×D₄	Direct product of C₅ and D₄	20	2	C5xD4	40,10
C₂²×D₅	Direct product of C₂² and D₅	20		C2^2xD5	40,13
C₅×Q₈	Direct product of C₅ and Q₈	40	2	C5xQ8	40,11
C₂×Dic₅	Direct product of C₂ and Dic₅	40		C2xDic5	40,7

Groups of order 42

		d	ρ	Label	ID
C₄₂	Cyclic group	42	1	C42	42,6
S₃×C₇	Direct product of C₇ and S₃	21	2	S3xC7	42,3
C₃×D₇	Direct product of C₃ and D₇	21	2	C3xD7	42,4
C₂×C₇⋊C₃	Direct product of C₂ and C₇⋊C₃	14	3	C2xC7:C3	42,2

Groups of order 44

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

Groups of order 45

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

Groups of order 46

		d	ρ	Label	ID
C₄₆	Cyclic group	46	1	C46	46,2

Groups of order 48

		d	ρ	Label	ID
C₄₈	Cyclic group	48	1	C48	48,2
C₄×C₁₂	Abelian group of type [4,12]	48		C4xC12	48,20
C₂×C₂₄	Abelian group of type [2,24]	48		C2xC24	48,23
C₂³×C₆	Abelian group of type [2,2,2,6]	48		C2^3xC6	48,52
C₂²×C₁₂	Abelian group of type [2,2,12]	48		C2^2xC12	48,44
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	6	3+	C2xS4	48,48
C₄×A₄	Direct product of C₄ and A₄	12	3	C4xA4	48,31
S₃×D₄	Direct product of S₃ and D₄; = Aut(D₁₂) = Hol(C₁₂)	12	4+	S3xD4	48,38
C₂²×A₄	Direct product of C₂² and A₄	12		C2^2xA4	48,49
C₂×SL₂(𝔽₃)	Direct product of C₂ and SL₂(𝔽₃)	16		C2xSL(2,3)	48,32
S₃×C₈	Direct product of C₈ and S₃	24	2	S3xC8	48,4
C₃×D₈	Direct product of C₃ and D₈	24	2	C3xD8	48,25
C₆×D₄	Direct product of C₆ and D₄	24		C6xD4	48,45
S₃×Q₈	Direct product of S₃ and Q₈	24	4-	S3xQ8	48,40
C₂×D₁₂	Direct product of C₂ and D₁₂	24		C2xD12	48,36
S₃×C₂³	Direct product of C₂³ and S₃	24		S3xC2^3	48,51
C₃×SD₁₆	Direct product of C₃ and SD₁₆	24	2	C3xSD16	48,26
C₃×M₄(2)	Direct product of C₃ and M₄(2)	24	2	C3xM4(2)	48,24
C₆×Q₈	Direct product of C₆ and Q₈	48		C6xQ8	48,46
C₃×Q₁₆	Direct product of C₃ and Q₁₆	48	2	C3xQ16	48,27
C₄×Dic₃	Direct product of C₄ and Dic₃	48		C4xDic3	48,11
C₂×Dic₆	Direct product of C₂ and Dic₆	48		C2xDic6	48,34
C₂²×Dic₃	Direct product of C₂² and Dic₃	48		C2^2xDic3	48,42
S₃×C₂×C₄	Direct product of C₂×C₄ and S₃	24		S3xC2xC4	48,35
C₂×C₃⋊D₄	Direct product of C₂ and C₃⋊D₄	24		C2xC3:D4	48,43
C₃×C₄○D₄	Direct product of C₃ and C₄○D₄	24	2	C3xC4oD4	48,47
C₃×C₂²⋊C₄	Direct product of C₃ and C₂²⋊C₄	24		C3xC2^2:C4	48,21
C₂×C₃⋊C₈	Direct product of C₂ and C₃⋊C₈	48		C2xC3:C8	48,9
C₃×C₄⋊C₄	Direct product of C₃ and C₄⋊C₄	48		C3xC4:C4	48,22

Groups of order 49

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

Groups of order 50

		d	ρ	Label	ID
C₅₀	Cyclic group	50	1	C50	50,2
C₅×C₁₀	Abelian group of type [5,10]	50		C5xC10	50,5
C₅×D₅	Direct product of C₅ and D₅; = AΣL₁(𝔽₂₅)	10	2	C5xD5	50,3

Groups of order 51

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

Groups of order 52

		d	ρ	Label	ID
C₅₂	Cyclic group	52	1	C52	52,2
D₂₆	Dihedral group; = C₂×D₁₃	26	2+	D26	52,4
C₂×C₂₆	Abelian group of type [2,26]	52		C2xC26	52,5

Groups of order 54

		d	ρ	Label	ID
C₅₄	Cyclic group	54	1	C54	54,2
C₃×C₁₈	Abelian group of type [3,18]	54		C3xC18	54,9
C₃²×C₆	Abelian group of type [3,3,6]	54		C3^2xC6	54,15
S₃×C₉	Direct product of C₉ and S₃	18	2	S3xC9	54,4
C₃×D₉	Direct product of C₃ and D₉	18	2	C3xD9	54,3
C₂×He₃	Direct product of C₂ and He₃	18	3	C2xHe3	54,10
S₃×C₃²	Direct product of C₃² and S₃	18		S3xC3^2	54,12
C₂×3_-¹⁺²	Direct product of C₂ and 3_-¹⁺²	18	3	C2xES-(3,1)	54,11
C₃×C₃⋊S₃	Direct product of C₃ and C₃⋊S₃	18		C3xC3:S3	54,13

Groups of order 55

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

Groups of order 56

		d	ρ	Label	ID
C₅₆	Cyclic group	56	1	C56	56,2
C₂×C₂₈	Abelian group of type [2,28]	56		C2xC28	56,8
C₂²×C₁₄	Abelian group of type [2,2,14]	56		C2^2xC14	56,13
C₄×D₇	Direct product of C₄ and D₇	28	2	C4xD7	56,4
C₇×D₄	Direct product of C₇ and D₄	28	2	C7xD4	56,9
C₂²×D₇	Direct product of C₂² and D₇	28		C2^2xD7	56,12
C₇×Q₈	Direct product of C₇ and Q₈	56	2	C7xQ8	56,10
C₂×Dic₇	Direct product of C₂ and Dic₇	56		C2xDic7	56,6

Groups of order 57

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

Groups of order 58

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

Groups of order 60

		d	ρ	Label	ID
C₆₀	Cyclic group	60	1	C60	60,4
D₃₀	Dihedral group; = C₂×D₁₅	30	2+	D30	60,12
C₂×C₃₀	Abelian group of type [2,30]	60		C2xC30	60,13
S₃×D₅	Direct product of S₃ and D₅	15	4+	S3xD5	60,8
C₃×F₅	Direct product of C₃ and F₅	15	4	C3xF5	60,6
C₅×A₄	Direct product of C₅ and A₄	20	3	C5xA4	60,9
C₆×D₅	Direct product of C₆ and D₅	30	2	C6xD5	60,10
S₃×C₁₀	Direct product of C₁₀ and S₃	30	2	S3xC10	60,11
C₅×Dic₃	Direct product of C₅ and Dic₃	60	2	C5xDic3	60,1
C₃×Dic₅	Direct product of C₃ and Dic₅	60	2	C3xDic5	60,2

Groups of order 62

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

Groups of order 63

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

Groups of order 64

		d	Label	ID
C₈²	Abelian group of type [8,8]	64	C8^2	64,2
C₄³	Abelian group of type [4,4,4]	64	C4^3	64,55
C₂⁶	Elementary abelian group of type [2,2,2,2,2,2]	64	C2^6	64,267
C₄×C₁₆	Abelian group of type [4,16]	64	C4xC16	64,26
C₂×C₃₂	Abelian group of type [2,32]	64	C2xC32	64,50
C₂³×C₈	Abelian group of type [2,2,2,8]	64	C2^3xC8	64,246
C₂⁴×C₄	Abelian group of type [2,2,2,2,4]	64	C2^4xC4	64,260
C₂²×C₁₆	Abelian group of type [2,2,16]	64	C2^2xC16	64,183
C₂²×C₄²	Abelian group of type [2,2,4,4]	64	C2^2xC4^2	64,192
C₂×C₄×C₈	Abelian group of type [2,4,8]	64	C2xC4xC8	64,83
D₄²	Direct product of D₄ and D₄	16	D4^2	64,226
C₂×2₊¹⁺⁴	Direct product of C₂ and 2₊¹⁺⁴	16	C2xES+(2,2)	64,264
C₈×D₄	Direct product of C₈ and D₄	32	C8xD4	64,115
C₄×D₈	Direct product of C₄ and D₈	32	C4xD8	64,118
D₄×Q₈	Direct product of D₄ and Q₈	32	D4xQ8	64,230
C₂×D₁₆	Direct product of C₂ and D₁₆	32	C2xD16	64,186
C₄×SD₁₆	Direct product of C₄ and SD₁₆	32	C4xSD16	64,119
C₂×SD₃₂	Direct product of C₂ and SD₃₂	32	C2xSD32	64,187
C₂²×D₈	Direct product of C₂² and D₈	32	C2^2xD8	64,250
D₄×C₂³	Direct product of C₂³ and D₄	32	D4xC2^3	64,261
C₄×M₄(2)	Direct product of C₄ and M₄(2)	32	C4xM4(2)	64,85
C₂×M₅(2)	Direct product of C₂ and M₅(2)	32	C2xM5(2)	64,184
C₂²×SD₁₆	Direct product of C₂² and SD₁₆	32	C2^2xSD16	64,251
C₂²×M₄(2)	Direct product of C₂² and M₄(2)	32	C2^2xM4(2)	64,247
C₂×2_-¹⁺⁴	Direct product of C₂ and 2_-¹⁺⁴	32	C2xES-(2,2)	64,265
Q₈²	Direct product of Q₈ and Q₈	64	Q8^2	64,239
C₈×Q₈	Direct product of C₈ and Q₈	64	C8xQ8	64,126
C₄×Q₁₆	Direct product of C₄ and Q₁₆	64	C4xQ16	64,120
C₂×Q₃₂	Direct product of C₂ and Q₃₂	64	C2xQ32	64,188
Q₈×C₂³	Direct product of C₂³ and Q₈	64	Q8xC2^3	64,262
C₂²×Q₁₆	Direct product of C₂² and Q₁₆	64	C2^2xQ16	64,252
C₂×C₄≀C₂	Direct product of C₂ and C₄≀C₂	16	C2xC4wrC2	64,101
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	16	C2xC2^3:C4	64,90
C₂×C₈⋊C₂²	Direct product of C₂ and C₈⋊C₂²	16	C2xC8:C2^2	64,254
C₂×C₄.D₄	Direct product of C₂ and C₄.D₄	16	C2xC4.D4	64,92
C₂×C₂²≀C₂	Direct product of C₂ and C₂²≀C₂	16	C2xC2^2wrC2	64,202
C₂×C₄×D₄	Direct product of C₂×C₄ and D₄	32	C2xC4xD4	64,196
C₄×C₄○D₄	Direct product of C₄ and C₄○D₄	32	C4xC4oD4	64,198
C₂×C₈○D₄	Direct product of C₂ and C₈○D₄	32	C2xC8oD4	64,248
C₂×C₄○D₈	Direct product of C₂ and C₄○D₈	32	C2xC4oD8	64,253
C₂×C₄⋊D₄	Direct product of C₂ and C₄⋊D₄	32	C2xC4:D4	64,203
C₂×D₄⋊C₄	Direct product of C₂ and D₄⋊C₄	32	C2xD4:C4	64,95
C₂×C₈.C₄	Direct product of C₂ and C₈.C₄	32	C2xC8.C4	64,110
C₂×C₄⋊₁D₄	Direct product of C₂ and C₄⋊₁D₄	32	C2xC4:1D4	64,211
C₄×C₂²⋊C₄	Direct product of C₄ and C₂²⋊C₄	32	C4xC2^2:C4	64,58
C₂×C₂²⋊C₈	Direct product of C₂ and C₂²⋊C₈	32	C2xC2^2:C8	64,87
C₂×C₂²⋊Q₈	Direct product of C₂ and C₂²⋊Q₈	32	C2xC2^2:Q8	64,204
C₂×C₄²⋊C₂	Direct product of C₂ and C₄²⋊C₂	32	C2xC4^2:C2	64,195
C₂×C₄.₄D₄	Direct product of C₂ and C₄.₄D₄	32	C2xC4.4D4	64,207
C₂²×C₄○D₄	Direct product of C₂² and C₄○D₄	32	C2^2xC4oD4	64,263
C₂×C₈.C₂²	Direct product of C₂ and C₈.C₂²	32	C2xC8.C2^2	64,255
C₂×C₄²⋊₂C₂	Direct product of C₂ and C₄²⋊₂C₂	32	C2xC4^2:2C2	64,209
C₂×C₄.₁₀D₄	Direct product of C₂ and C₄.₁₀D₄	32	C2xC4.10D4	64,93
C₂²×C₂²⋊C₄	Direct product of C₂² and C₂²⋊C₄	32	C2^2xC2^2:C4	64,193
C₂×C₂².D₄	Direct product of C₂ and C₂².D₄	32	C2xC2^2.D4	64,205
C₄×C₄⋊C₄	Direct product of C₄ and C₄⋊C₄	64	C4xC4:C4	64,59
C₂×C₄⋊C₈	Direct product of C₂ and C₄⋊C₈	64	C2xC4:C8	64,103
C₂×C₄×Q₈	Direct product of C₂×C₄ and Q₈	64	C2xC4xQ8	64,197
C₂×C₄⋊Q₈	Direct product of C₂ and C₄⋊Q₈	64	C2xC4:Q8	64,212
C₂×C₈⋊C₄	Direct product of C₂ and C₈⋊C₄	64	C2xC8:C4	64,84
C₂²×C₄⋊C₄	Direct product of C₂² and C₄⋊C₄	64	C2^2xC4:C4	64,194
C₂×Q₈⋊C₄	Direct product of C₂ and Q₈⋊C₄	64	C2xQ8:C4	64,96
C₂×C₂.D₈	Direct product of C₂ and C₂.D₈	64	C2xC2.D8	64,107
C₂×C₄.Q₈	Direct product of C₂ and C₄.Q₈	64	C2xC4.Q8	64,106
C₂×C₂.C₄²	Direct product of C₂ and C₂.C₄²	64	C2xC2.C4^2	64,56
C₂×C₄².C₂	Direct product of C₂ and C₄².C₂	64	C2xC4^2.C2	64,208

Groups of order 65

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

Groups of order 66

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

Groups of order 68

		d	ρ	Label	ID
C₆₈	Cyclic group	68	1	C68	68,2
D₃₄	Dihedral group; = C₂×D₁₇	34	2+	D34	68,4
C₂×C₃₄	Abelian group of type [2,34]	68		C2xC34	68,5

Groups of order 69

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

Groups of order 70

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

Groups of order 72

		d	ρ	Label	ID
C₇₂	Cyclic group	72	1	C72	72,2
C₂×C₃₆	Abelian group of type [2,36]	72		C2xC36	72,9
C₃×C₂₄	Abelian group of type [3,24]	72		C3xC24	72,14
C₆×C₁₂	Abelian group of type [6,12]	72		C6xC12	72,36
C₂×C₆²	Abelian group of type [2,6,6]	72		C2xC6^2	72,50
C₂²×C₁₈	Abelian group of type [2,2,18]	72		C2^2xC18	72,18
C₃×S₄	Direct product of C₃ and S₄	12	3	C3xS4	72,42
S₃×A₄	Direct product of S₃ and A₄	12	6+	S3xA4	72,44
C₆×A₄	Direct product of C₆ and A₄	18	3	C6xA4	72,47
S₃×C₁₂	Direct product of C₁₂ and S₃	24	2	S3xC12	72,27
C₃×D₁₂	Direct product of C₃ and D₁₂	24	2	C3xD12	72,28
S₃×Dic₃	Direct product of S₃ and Dic₃	24	4-	S3xDic3	72,20
C₃×Dic₆	Direct product of C₃ and Dic₆	24	2	C3xDic6	72,26
C₆×Dic₃	Direct product of C₆ and Dic₃	24		C6xDic3	72,29
C₃×SL₂(𝔽₃)	Direct product of C₃ and SL₂(𝔽₃)	24	2	C3xSL(2,3)	72,25
C₄×D₉	Direct product of C₄ and D₉	36	2	C4xD9	72,5
D₄×C₉	Direct product of C₉ and D₄	36	2	D4xC9	72,10
C₂²×D₉	Direct product of C₂² and D₉	36		C2^2xD9	72,17
D₄×C₃²	Direct product of C₃² and D₄	36		D4xC3^2	72,37
Q₈×C₉	Direct product of C₉ and Q₈	72	2	Q8xC9	72,11
C₂×Dic₉	Direct product of C₂ and Dic₉	72		C2xDic9	72,7
Q₈×C₃²	Direct product of C₃² and Q₈	72		Q8xC3^2	72,38
C₂×S₃²	Direct product of C₂, S₃ and S₃	12	4+	C2xS3^2	72,46
C₃×C₃⋊D₄	Direct product of C₃ and C₃⋊D₄	12	2	C3xC3:D4	72,30
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	12	4+	C2xC3^2:C4	72,45
C₂×C₃.A₄	Direct product of C₂ and C₃.A₄	18	3	C2xC3.A4	72,16
C₃×C₃⋊C₈	Direct product of C₃ and C₃⋊C₈	24	2	C3xC3:C8	72,12
S₃×C₂×C₆	Direct product of C₂×C₆ and S₃	24		S3xC2xC6	72,48
C₄×C₃⋊S₃	Direct product of C₄ and C₃⋊S₃	36		C4xC3:S3	72,32
C₂²×C₃⋊S₃	Direct product of C₂² and C₃⋊S₃	36		C2^2xC3:S3	72,49
C₂×C₃⋊Dic₃	Direct product of C₂ and C₃⋊Dic₃	72		C2xC3:Dic3	72,34

Groups of order 74

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

Groups of order 75

		d	ρ	Label	ID
C₇₅	Cyclic group	75	1	C75	75,1
C₅×C₁₅	Abelian group of type [5,15]	75		C5xC15	75,3

Groups of order 76

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

Groups of order 77

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

Groups of order 78

		d	ρ	Label	ID
C₇₈	Cyclic group	78	1	C78	78,6
S₃×C₁₃	Direct product of C₁₃ and S₃	39	2	S3xC13	78,3
C₃×D₁₃	Direct product of C₃ and D₁₃	39	2	C3xD13	78,4
C₂×C₁₃⋊C₃	Direct product of C₂ and C₁₃⋊C₃	26	3	C2xC13:C3	78,2

Groups of order 80

		d	ρ	Label	ID
C₈₀	Cyclic group	80	1	C80	80,2
C₄×C₂₀	Abelian group of type [4,20]	80		C4xC20	80,20
C₂×C₄₀	Abelian group of type [2,40]	80		C2xC40	80,23
C₂²×C₂₀	Abelian group of type [2,2,20]	80		C2^2xC20	80,45
C₂³×C₁₀	Abelian group of type [2,2,2,10]	80		C2^3xC10	80,52
D₄×D₅	Direct product of D₄ and D₅	20	4+	D4xD5	80,39
C₄×F₅	Direct product of C₄ and F₅	20	4	C4xF5	80,30
C₂²×F₅	Direct product of C₂² and F₅	20		C2^2xF5	80,50
C₈×D₅	Direct product of C₈ and D₅	40	2	C8xD5	80,4
C₅×D₈	Direct product of C₅ and D₈	40	2	C5xD8	80,25
Q₈×D₅	Direct product of Q₈ and D₅	40	4-	Q8xD5	80,41
C₂×D₂₀	Direct product of C₂ and D₂₀	40		C2xD20	80,37
D₄×C₁₀	Direct product of C₁₀ and D₄	40		D4xC10	80,46
C₅×SD₁₆	Direct product of C₅ and SD₁₆	40	2	C5xSD16	80,26
C₂³×D₅	Direct product of C₂³ and D₅	40		C2^3xD5	80,51
C₅×M₄(2)	Direct product of C₅ and M₄(2)	40	2	C5xM4(2)	80,24
C₅×Q₁₆	Direct product of C₅ and Q₁₆	80	2	C5xQ16	80,27
Q₈×C₁₀	Direct product of C₁₀ and Q₈	80		Q8xC10	80,47
C₄×Dic₅	Direct product of C₄ and Dic₅	80		C4xDic5	80,11
C₂×Dic₁₀	Direct product of C₂ and Dic₁₀	80		C2xDic10	80,35
C₂²×Dic₅	Direct product of C₂² and Dic₅	80		C2^2xDic5	80,43
C₂×C₄×D₅	Direct product of C₂×C₄ and D₅	40		C2xC4xD5	80,36
C₂×C₅⋊D₄	Direct product of C₂ and C₅⋊D₄	40		C2xC5:D4	80,44
C₅×C₄○D₄	Direct product of C₅ and C₄○D₄	40	2	C5xC4oD4	80,48
C₅×C₂²⋊C₄	Direct product of C₅ and C₂²⋊C₄	40		C5xC2^2:C4	80,21
C₂×C₅⋊C₈	Direct product of C₂ and C₅⋊C₈	80		C2xC5:C8	80,32
C₅×C₄⋊C₄	Direct product of C₅ and C₄⋊C₄	80		C5xC4:C4	80,22
C₂×C₅⋊₂C₈	Direct product of C₂ and C₅⋊₂C₈	80		C2xC5:2C8	80,9

Groups of order 81

		d	Label	ID
C₉²	Abelian group of type [9,9]	81	C9^2	81,2
C₃⁴	Elementary abelian group of type [3,3,3,3]	81	C3^4	81,15
C₃×C₂₇	Abelian group of type [3,27]	81	C3xC27	81,5
C₃²×C₉	Abelian group of type [3,3,9]	81	C3^2xC9	81,11
C₃×He₃	Direct product of C₃ and He₃	27	C3xHe3	81,12
C₃×3_-¹⁺²	Direct product of C₃ and 3_-¹⁺²	27	C3xES-(3,1)	81,13

Groups of order 82

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

Groups of order 84

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

Groups of order 85

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

Groups of order 86

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

Groups of order 87

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

Groups of order 88

		d	ρ	Label	ID
C₈₈	Cyclic group	88	1	C88	88,2
C₂×C₄₄	Abelian group of type [2,44]	88		C2xC44	88,8
C₂²×C₂₂	Abelian group of type [2,2,22]	88		C2^2xC22	88,12
C₄×D₁₁	Direct product of C₄ and D₁₁	44	2	C4xD11	88,4
D₄×C₁₁	Direct product of C₁₁ and D₄	44	2	D4xC11	88,9
C₂²×D₁₁	Direct product of C₂² and D₁₁	44		C2^2xD11	88,11
Q₈×C₁₁	Direct product of C₁₁ and Q₈	88	2	Q8xC11	88,10
C₂×Dic₁₁	Direct product of C₂ and Dic₁₁	88		C2xDic11	88,6

Groups of order 90

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

Groups of order 91

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

Groups of order 92

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

Groups of order 93

		d	ρ	Label	ID
C₉₃	Cyclic group	93	1	C93	93,2

Groups of order 94

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

Groups of order 95

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

Groups of order 96

		d	ρ	Label	ID
C₉₆	Cyclic group	96	1	C96	96,2
C₄×C₂₄	Abelian group of type [4,24]	96		C4xC24	96,46
C₂×C₄₈	Abelian group of type [2,48]	96		C2xC48	96,59
C₂⁴×C₆	Abelian group of type [2,2,2,2,6]	96		C2^4xC6	96,231
C₂²×C₂₄	Abelian group of type [2,2,24]	96		C2^2xC24	96,176
C₂³×C₁₂	Abelian group of type [2,2,2,12]	96		C2^3xC12	96,220
C₂×C₄×C₁₂	Abelian group of type [2,4,12]	96		C2xC4xC12	96,161
C₄×S₄	Direct product of C₄ and S₄	12	3	C4xS4	96,186
D₄×A₄	Direct product of D₄ and A₄	12	6+	D4xA4	96,197
C₂²×S₄	Direct product of C₂² and S₄	12		C2^2xS4	96,226
C₂×GL₂(𝔽₃)	Direct product of C₂ and GL₂(𝔽₃)	16		C2xGL(2,3)	96,189
C₈×A₄	Direct product of C₈ and A₄	24	3	C8xA4	96,73
S₃×D₈	Direct product of S₃ and D₈	24	4+	S3xD8	96,117
Q₈×A₄	Direct product of Q₈ and A₄	24	6-	Q8xA4	96,199
C₂³×A₄	Direct product of C₂³ and A₄	24		C2^3xA4	96,228
S₃×SD₁₆	Direct product of S₃ and SD₁₆	24	4	S3xSD16	96,120
S₃×M₄(2)	Direct product of S₃ and M₄(2)	24	4	S3xM4(2)	96,113
C₃×2₊¹⁺⁴	Direct product of C₃ and 2₊¹⁺⁴	24	4	C3xES+(2,2)	96,224
C₄×SL₂(𝔽₃)	Direct product of C₄ and SL₂(𝔽₃)	32		C4xSL(2,3)	96,69
C₂×CSU₂(𝔽₃)	Direct product of C₂ and CSU₂(𝔽₃)	32		C2xCSU(2,3)	96,188
C₂²×SL₂(𝔽₃)	Direct product of C₂² and SL₂(𝔽₃)	32		C2^2xSL(2,3)	96,198
C₆×D₈	Direct product of C₆ and D₈	48		C6xD8	96,179
S₃×C₁₆	Direct product of C₁₆ and S₃	48	2	S3xC16	96,4
C₃×D₁₆	Direct product of C₃ and D₁₆	48	2	C3xD16	96,61
C₄×D₁₂	Direct product of C₄ and D₁₂	48		C4xD12	96,80
C₂×D₂₄	Direct product of C₂ and D₂₄	48		C2xD24	96,110
D₄×C₁₂	Direct product of C₁₂ and D₄	48		D4xC12	96,165
S₃×Q₁₆	Direct product of S₃ and Q₁₆	48	4-	S3xQ16	96,124
S₃×C₄²	Direct product of C₄² and S₃	48		S3xC4^2	96,78
S₃×C₂⁴	Direct product of C₂⁴ and S₃	48		S3xC2^4	96,230
C₃×SD₃₂	Direct product of C₃ and SD₃₂	48	2	C3xSD32	96,62
D₄×Dic₃	Direct product of D₄ and Dic₃	48		D4xDic3	96,141
C₆×SD₁₆	Direct product of C₆ and SD₁₆	48		C6xSD16	96,180
C₂²×D₁₂	Direct product of C₂² and D₁₂	48		C2^2xD12	96,207
C₃×M₅(2)	Direct product of C₃ and M₅(2)	48	2	C3xM5(2)	96,60
C₆×M₄(2)	Direct product of C₆ and M₄(2)	48		C6xM4(2)	96,177
C₃×2_-¹⁺⁴	Direct product of C₃ and 2_-¹⁺⁴	48	4	C3xES-(2,2)	96,225
C₃×Q₃₂	Direct product of C₃ and Q₃₂	96	2	C3xQ32	96,63
Q₈×C₁₂	Direct product of C₁₂ and Q₈	96		Q8xC12	96,166
C₆×Q₁₆	Direct product of C₆ and Q₁₆	96		C6xQ16	96,181
C₈×Dic₃	Direct product of C₈ and Dic₃	96		C8xDic3	96,20
C₄×Dic₆	Direct product of C₄ and Dic₆	96		C4xDic6	96,75
Q₈×Dic₃	Direct product of Q₈ and Dic₃	96		Q8xDic3	96,152
C₂×Dic₁₂	Direct product of C₂ and Dic₁₂	96		C2xDic12	96,112
C₂²×Dic₆	Direct product of C₂² and Dic₆	96		C2^2xDic6	96,205
C₂³×Dic₃	Direct product of C₂³ and Dic₃	96		C2^3xDic3	96,218
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	12	3	C2xC4^2:C3	96,68
C₂×C₂²⋊A₄	Direct product of C₂ and C₂²⋊A₄	12		C2xC2^2:A4	96,229
C₂×C₄×A₄	Direct product of C₂×C₄ and A₄	24		C2xC4xA4	96,196
C₂×S₃×D₄	Direct product of C₂, S₃ and D₄	24		C2xS3xD4	96,209
C₃×C₄≀C₂	Direct product of C₃ and C₄≀C₂	24	2	C3xC4wrC2	96,54
C₂×A₄⋊C₄	Direct product of C₂ and A₄⋊C₄	24		C2xA4:C4	96,194
S₃×C₄○D₄	Direct product of S₃ and C₄○D₄	24	4	S3xC4oD4	96,215
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	24	4	C3xC2^3:C4	96,49
S₃×C₂²⋊C₄	Direct product of S₃ and C₂²⋊C₄	24		S3xC2^2:C4	96,87
C₃×C₈⋊C₂²	Direct product of C₃ and C₈⋊C₂²	24	4	C3xC8:C2^2	96,183
C₃×C₄.D₄	Direct product of C₃ and C₄.D₄	24	4	C3xC4.D4	96,50
C₃×C₂²≀C₂	Direct product of C₃ and C₂²≀C₂	24		C3xC2^2wrC2	96,167
C₂×C₄.A₄	Direct product of C₂ and C₄.A₄	32		C2xC4.A4	96,200
S₃×C₂×C₈	Direct product of C₂×C₈ and S₃	48		S3xC2xC8	96,106
D₄×C₂×C₆	Direct product of C₂×C₆ and D₄	48		D4xC2xC6	96,221
S₃×C₄⋊C₄	Direct product of S₃ and C₄⋊C₄	48		S3xC4:C4	96,98
C₂×S₃×Q₈	Direct product of C₂, S₃ and Q₈	48		C2xS3xQ8	96,212
C₄×C₃⋊D₄	Direct product of C₄ and C₃⋊D₄	48		C4xC3:D4	96,135
C₂×C₈⋊S₃	Direct product of C₂ and C₈⋊S₃	48		C2xC8:S3	96,107
C₂×D₆⋊C₄	Direct product of C₂ and D₆⋊C₄	48		C2xD6:C4	96,134
C₂×D₄⋊S₃	Direct product of C₂ and D₄⋊S₃	48		C2xD4:S3	96,138
C₃×C₈○D₄	Direct product of C₃ and C₈○D₄	48	2	C3xC8oD4	96,178
C₃×C₄○D₈	Direct product of C₃ and C₄○D₈	48	2	C3xC4oD8	96,182
C₆×C₄○D₄	Direct product of C₆ and C₄○D₄	48		C6xC4oD4	96,223
C₃×C₄⋊D₄	Direct product of C₃ and C₄⋊D₄	48		C3xC4:D4	96,168
S₃×C₂²×C₄	Direct product of C₂²×C₄ and S₃	48		S3xC2^2xC4	96,206
C₂×C₂₄⋊C₂	Direct product of C₂ and C₂₄⋊C₂	48		C2xC24:C2	96,109
C₂×C₄○D₁₂	Direct product of C₂ and C₄○D₁₂	48		C2xC4oD12	96,208
C₃×D₄⋊C₄	Direct product of C₃ and D₄⋊C₄	48		C3xD4:C4	96,52
C₃×C₈.C₄	Direct product of C₃ and C₈.C₄	48	2	C3xC8.C4	96,58
C₃×C₄⋊₁D₄	Direct product of C₃ and C₄⋊₁D₄	48		C3xC4:1D4	96,174
C₃×C₂²⋊C₈	Direct product of C₃ and C₂²⋊C₈	48		C3xC2^2:C8	96,48
C₆×C₂²⋊C₄	Direct product of C₆ and C₂²⋊C₄	48		C6xC2^2:C4	96,162
C₂×D₄.S₃	Direct product of C₂ and D₄.S₃	48		C2xD4.S3	96,140
C₂×C₆.D₄	Direct product of C₂ and C₆.D₄	48		C2xC6.D4	96,159
C₂²×C₃⋊D₄	Direct product of C₂² and C₃⋊D₄	48		C2^2xC3:D4	96,219
C₃×C₂²⋊Q₈	Direct product of C₃ and C₂²⋊Q₈	48		C3xC2^2:Q8	96,169
C₂×D₄⋊₂S₃	Direct product of C₂ and D₄⋊₂S₃	48		C2xD4:2S3	96,210
C₃×C₄²⋊C₂	Direct product of C₃ and C₄²⋊C₂	48		C3xC4^2:C2	96,164
C₂×Q₈⋊₂S₃	Direct product of C₂ and Q₈⋊₂S₃	48		C2xQ8:2S3	96,148
C₂×Q₈⋊₃S₃	Direct product of C₂ and Q₈⋊₃S₃	48		C2xQ8:3S3	96,213
C₃×C₄.₄D₄	Direct product of C₃ and C₄.₄D₄	48		C3xC4.4D4	96,171
C₃×C₈.C₂²	Direct product of C₃ and C₈.C₂²	48	4	C3xC8.C2^2	96,184
C₂×C₄.Dic₃	Direct product of C₂ and C₄.Dic₃	48		C2xC4.Dic3	96,128
C₃×C₄²⋊₂C₂	Direct product of C₃ and C₄²⋊₂C₂	48		C3xC4^2:2C2	96,173
C₃×C₄.₁₀D₄	Direct product of C₃ and C₄.₁₀D₄	48	4	C3xC4.10D4	96,51
C₃×C₂².D₄	Direct product of C₃ and C₂².D₄	48		C3xC2^2.D4	96,170
C₄×C₃⋊C₈	Direct product of C₄ and C₃⋊C₈	96		C4xC3:C8	96,9
C₃×C₄⋊C₈	Direct product of C₃ and C₄⋊C₈	96		C3xC4:C8	96,55
C₆×C₄⋊C₄	Direct product of C₆ and C₄⋊C₄	96		C6xC4:C4	96,163
C₂×C₃⋊C₁₆	Direct product of C₂ and C₃⋊C₁₆	96		C2xC3:C16	96,18
Q₈×C₂×C₆	Direct product of C₂×C₆ and Q₈	96		Q8xC2xC6	96,222
C₃×C₄⋊Q₈	Direct product of C₃ and C₄⋊Q₈	96		C3xC4:Q8	96,175
C₃×C₈⋊C₄	Direct product of C₃ and C₈⋊C₄	96		C3xC8:C4	96,47
C₂²×C₃⋊C₈	Direct product of C₂² and C₃⋊C₈	96		C2^2xC3:C8	96,127
C₂×C₄×Dic₃	Direct product of C₂×C₄ and Dic₃	96		C2xC4xDic3	96,129
C₂×C₃⋊Q₁₆	Direct product of C₂ and C₃⋊Q₁₆	96		C2xC3:Q16	96,150
C₂×C₄⋊Dic₃	Direct product of C₂ and C₄⋊Dic₃	96		C2xC4:Dic3	96,132
C₃×Q₈⋊C₄	Direct product of C₃ and Q₈⋊C₄	96		C3xQ8:C4	96,53
C₃×C₂.D₈	Direct product of C₃ and C₂.D₈	96		C3xC2.D8	96,57
C₃×C₄.Q₈	Direct product of C₃ and C₄.Q₈	96		C3xC4.Q8	96,56
C₂×Dic₃⋊C₄	Direct product of C₂ and Dic₃⋊C₄	96		C2xDic3:C4	96,130
C₃×C₂.C₄²	Direct product of C₃ and C₂.C₄²	96		C3xC2.C4^2	96,45
C₃×C₄².C₂	Direct product of C₃ and C₄².C₂	96		C3xC4^2.C2	96,172

Groups of order 98

		d	ρ	Label	ID
C₉₈	Cyclic group	98	1	C98	98,2
C₇×C₁₄	Abelian group of type [7,14]	98		C7xC14	98,5
C₇×D₇	Direct product of C₇ and D₇; = AΣL₁(𝔽₄₉)	14	2	C7xD7	98,3

Groups of order 99

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

Groups of order 100

		d	ρ	Label	ID
C₁₀₀	Cyclic group	100	1	C100	100,2
D₅₀	Dihedral group; = C₂×D₂₅	50	2+	D50	100,4
C₁₀²	Abelian group of type [10,10]	100		C10^2	100,16
C₂×C₅₀	Abelian group of type [2,50]	100		C2xC50	100,5
C₅×C₂₀	Abelian group of type [5,20]	100		C5xC20	100,8
D₅²	Direct product of D₅ and D₅	10	4+	D5^2	100,13
C₅×F₅	Direct product of C₅ and F₅	20	4	C5xF5	100,9
D₅×C₁₀	Direct product of C₁₀ and D₅	20	2	D5xC10	100,14
C₅×Dic₅	Direct product of C₅ and Dic₅	20	2	C5xDic5	100,6
C₂×C₅⋊D₅	Direct product of C₂ and C₅⋊D₅	50		C2xC5:D5	100,15

Groups of order 102

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

Groups of order 104

		d	ρ	Label	ID
C₁₀₄	Cyclic group	104	1	C104	104,2
C₂×C₅₂	Abelian group of type [2,52]	104		C2xC52	104,9
C₂²×C₂₆	Abelian group of type [2,2,26]	104		C2^2xC26	104,14
C₄×D₁₃	Direct product of C₄ and D₁₃	52	2	C4xD13	104,5
D₄×C₁₃	Direct product of C₁₃ and D₄	52	2	D4xC13	104,10
C₂²×D₁₃	Direct product of C₂² and D₁₃	52		C2^2xD13	104,13
Q₈×C₁₃	Direct product of C₁₃ and Q₈	104	2	Q8xC13	104,11
C₂×Dic₁₃	Direct product of C₂ and Dic₁₃	104		C2xDic13	104,7
C₂×C₁₃⋊C₄	Direct product of C₂ and C₁₃⋊C₄	26	4+	C2xC13:C4	104,12

Groups of order 105

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

Groups of order 106

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

Groups of order 108

		d	ρ	Label	ID
C₁₀₈	Cyclic group	108	1	C108	108,2
D₅₄	Dihedral group; = C₂×D₂₇	54	2+	D54	108,4
C₂×C₅₄	Abelian group of type [2,54]	108		C2xC54	108,5
C₃×C₃₆	Abelian group of type [3,36]	108		C3xC36	108,12
C₆×C₁₈	Abelian group of type [6,18]	108		C6xC18	108,29
C₃×C₆²	Abelian group of type [3,6,6]	108		C3xC6^2	108,45
C₃²×C₁₂	Abelian group of type [3,3,12]	108		C3^2xC12	108,35
S₃×D₉	Direct product of S₃ and D₉	18	4+	S3xD9	108,16
C₉×A₄	Direct product of C₉ and A₄	36	3	C9xA4	108,18
C₆×D₉	Direct product of C₆ and D₉	36	2	C6xD9	108,23
S₃×C₁₈	Direct product of C₁₈ and S₃	36	2	S3xC18	108,24
C₄×He₃	Direct product of C₄ and He₃	36	3	C4xHe3	108,13
C₃²×A₄	Direct product of C₃² and A₄	36		C3^2xA4	108,41
C₃×Dic₉	Direct product of C₃ and Dic₉	36	2	C3xDic9	108,6
C₉×Dic₃	Direct product of C₉ and Dic₃	36	2	C9xDic3	108,7
C₂²×He₃	Direct product of C₂² and He₃	36		C2^2xHe3	108,30
C₃²×Dic₃	Direct product of C₃² and Dic₃	36		C3^2xDic3	108,32
C₄×3_-¹⁺²	Direct product of C₄ and 3_-¹⁺²	36	3	C4xES-(3,1)	108,14
C₂²×3_-¹⁺²	Direct product of C₂² and 3_-¹⁺²	36		C2^2xES-(3,1)	108,31
C₃×S₃²	Direct product of C₃, S₃ and S₃	12	4	C3xS3^2	108,38
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	12	4	C3xC3^2:C4	108,36
C₂×C₉⋊C₆	Direct product of C₂ and C₉⋊C₆; = Aut(D₁₈) = Hol(C₁₈)	18	6+	C2xC9:C6	108,26
S₃×C₃⋊S₃	Direct product of S₃ and C₃⋊S₃	18		S3xC3:S3	108,39
C₂×C₃²⋊C₆	Direct product of C₂ and C₃²⋊C₆	18	6+	C2xC3^2:C6	108,25
C₂×He₃⋊C₂	Direct product of C₂ and He₃⋊C₂	18	3	C2xHe3:C2	108,28
S₃×C₃×C₆	Direct product of C₃×C₆ and S₃	36		S3xC3xC6	108,42
C₆×C₃⋊S₃	Direct product of C₆ and C₃⋊S₃	36		C6xC3:S3	108,43
C₃×C₃⋊Dic₃	Direct product of C₃ and C₃⋊Dic₃	36		C3xC3:Dic3	108,33
C₂×C₉⋊S₃	Direct product of C₂ and C₉⋊S₃	54		C2xC9:S3	108,27
C₃×C₃.A₄	Direct product of C₃ and C₃.A₄	54		C3xC3.A4	108,20
C₂×C₃³⋊C₂	Direct product of C₂ and C₃³⋊C₂	54		C2xC3^3:C2	108,44

Groups of order 110

		d	ρ	Label	ID
C₁₁₀	Cyclic group	110	1	C110	110,6
D₅×C₁₁	Direct product of C₁₁ and D₅	55	2	D5xC11	110,3
C₅×D₁₁	Direct product of C₅ and D₁₁	55	2	C5xD11	110,4
C₂×C₁₁⋊C₅	Direct product of C₂ and C₁₁⋊C₅	22	5	C2xC11:C5	110,2

Groups of order 111

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

Groups of order 112

		d	ρ	Label	ID
C₁₁₂	Cyclic group	112	1	C112	112,2
C₄×C₂₈	Abelian group of type [4,28]	112		C4xC28	112,19
C₂×C₅₆	Abelian group of type [2,56]	112		C2xC56	112,22
C₂²×C₂₈	Abelian group of type [2,2,28]	112		C2^2xC28	112,37
C₂³×C₁₄	Abelian group of type [2,2,2,14]	112		C2^3xC14	112,43
C₂×F₈	Direct product of C₂ and F₈	14	7+	C2xF8	112,41
D₄×D₇	Direct product of D₄ and D₇	28	4+	D4xD7	112,31
C₈×D₇	Direct product of C₈ and D₇	56	2	C8xD7	112,3
C₇×D₈	Direct product of C₇ and D₈	56	2	C7xD8	112,24
Q₈×D₇	Direct product of Q₈ and D₇	56	4-	Q8xD7	112,33
C₂×D₂₈	Direct product of C₂ and D₂₈	56		C2xD28	112,29
D₄×C₁₄	Direct product of C₁₄ and D₄	56		D4xC14	112,38
C₇×SD₁₆	Direct product of C₇ and SD₁₆	56	2	C7xSD16	112,25
C₂³×D₇	Direct product of C₂³ and D₇	56		C2^3xD7	112,42
C₇×M₄(2)	Direct product of C₇ and M₄(2)	56	2	C7xM4(2)	112,23
C₇×Q₁₆	Direct product of C₇ and Q₁₆	112	2	C7xQ16	112,26
Q₈×C₁₄	Direct product of C₁₄ and Q₈	112		Q8xC14	112,39
C₄×Dic₇	Direct product of C₄ and Dic₇	112		C4xDic7	112,10
C₂×Dic₁₄	Direct product of C₂ and Dic₁₄	112		C2xDic14	112,27
C₂²×Dic₇	Direct product of C₂² and Dic₇	112		C2^2xDic7	112,35
C₂×C₄×D₇	Direct product of C₂×C₄ and D₇	56		C2xC4xD7	112,28
C₂×C₇⋊D₄	Direct product of C₂ and C₇⋊D₄	56		C2xC7:D4	112,36
C₇×C₄○D₄	Direct product of C₇ and C₄○D₄	56	2	C7xC4oD4	112,40
C₇×C₂²⋊C₄	Direct product of C₇ and C₂²⋊C₄	56		C7xC2^2:C4	112,20
C₂×C₇⋊C₈	Direct product of C₂ and C₇⋊C₈	112		C2xC7:C8	112,8
C₇×C₄⋊C₄	Direct product of C₇ and C₄⋊C₄	112		C7xC4:C4	112,21

Groups of order 114

		d	ρ	Label	ID
C₁₁₄	Cyclic group	114	1	C114	114,6
S₃×C₁₉	Direct product of C₁₉ and S₃	57	2	S3xC19	114,3
C₃×D₁₉	Direct product of C₃ and D₁₉	57	2	C3xD19	114,4
C₂×C₁₉⋊C₃	Direct product of C₂ and C₁₉⋊C₃	38	3	C2xC19:C3	114,2

Groups of order 115

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

Groups of order 116

		d	ρ	Label	ID
C₁₁₆	Cyclic group	116	1	C116	116,2
D₅₈	Dihedral group; = C₂×D₂₉	58	2+	D58	116,4
C₂×C₅₈	Abelian group of type [2,58]	116		C2xC58	116,5

Groups of order 117

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

Groups of order 118

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

Groups of order 119

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

Groups of order 120

		d	ρ	Label	ID
C₁₂₀	Cyclic group	120	1	C120	120,4
C₂×C₆₀	Abelian group of type [2,60]	120		C2xC60	120,31
C₂²×C₃₀	Abelian group of type [2,2,30]	120		C2^2xC30	120,47
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	15	8+	S3xF5	120,36
C₅×S₄	Direct product of C₅ and S₄	20	3	C5xS4	120,37
D₅×A₄	Direct product of D₅ and A₄	20	6+	D5xA4	120,39
C₆×F₅	Direct product of C₆ and F₅	30	4	C6xF5	120,40
C₁₀×A₄	Direct product of C₁₀ and A₄	30	3	C10xA4	120,43
C₅×SL₂(𝔽₃)	Direct product of C₅ and SL₂(𝔽₃)	40	2	C5xSL(2,3)	120,15
S₃×C₂₀	Direct product of C₂₀ and S₃	60	2	S3xC20	120,22
D₅×C₁₂	Direct product of C₁₂ and D₅	60	2	D5xC12	120,17
C₃×D₂₀	Direct product of C₃ and D₂₀	60	2	C3xD20	120,18
C₅×D₁₂	Direct product of C₅ and D₁₂	60	2	C5xD12	120,23
C₄×D₁₅	Direct product of C₄ and D₁₅	60	2	C4xD15	120,27
D₄×C₁₅	Direct product of C₁₅ and D₄	60	2	D4xC15	120,32
D₅×Dic₃	Direct product of D₅ and Dic₃	60	4-	D5xDic3	120,8
S₃×Dic₅	Direct product of S₃ and Dic₅	60	4-	S3xDic5	120,9
C₂²×D₁₅	Direct product of C₂² and D₁₅	60		C2^2xD15	120,46
Q₈×C₁₅	Direct product of C₁₅ and Q₈	120	2	Q8xC15	120,33
C₆×Dic₅	Direct product of C₆ and Dic₅	120		C6xDic5	120,19
C₅×Dic₆	Direct product of C₅ and Dic₆	120	2	C5xDic6	120,21
C₃×Dic₁₀	Direct product of C₃ and Dic₁₀	120	2	C3xDic10	120,16
C₁₀×Dic₃	Direct product of C₁₀ and Dic₃	120		C10xDic3	120,24
C₂×Dic₁₅	Direct product of C₂ and Dic₁₅	120		C2xDic15	120,29
C₂×S₃×D₅	Direct product of C₂, S₃ and D₅	30	4+	C2xS3xD5	120,42
C₂×C₃⋊F₅	Direct product of C₂ and C₃⋊F₅	30	4	C2xC3:F5	120,41
D₅×C₂×C₆	Direct product of C₂×C₆ and D₅	60		D5xC2xC6	120,44
S₃×C₂×C₁₀	Direct product of C₂×C₁₀ and S₃	60		S3xC2xC10	120,45
C₃×C₅⋊D₄	Direct product of C₃ and C₅⋊D₄	60	2	C3xC5:D4	120,20
C₅×C₃⋊D₄	Direct product of C₅ and C₃⋊D₄	60	2	C5xC3:D4	120,25
C₅×C₃⋊C₈	Direct product of C₅ and C₃⋊C₈	120	2	C5xC3:C8	120,1
C₃×C₅⋊C₈	Direct product of C₃ and C₅⋊C₈	120	4	C3xC5:C8	120,6
C₃×C₅⋊₂C₈	Direct product of C₃ and C₅⋊₂C₈	120	2	C3xC5:2C8	120,2

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