# Nilpotent groups

A finite group G is nilpotent if it is a direct product of p-groups. Equivalently, all Sylow subgroups of G are normal. Equivalently, G has a central series

{1}=G0 ◃ G1 ◃ N2 ◃...◃ Gk = G,
a nested sequence of normal subgroups with [G,Gi+1]≤Gi. The smallest such k is the nilpotency class of G. It is 0 for C1, 1 for non-trivial abelian groups, and ≥2 for all other nilpotent groups. Nilpotent groups are closed under subgroups and quotients (but not extensions), and are soluble, super​soluble and monomial. See also non-​nilpotent groups.

### Groups of order 1

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C1Trivial group11+C11,1

### Groups of order 2

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C2Cyclic group21+C22,1

### Groups of order 3

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C3Cyclic group; = A3 = triangle rotations31C33,1

### Groups of order 4

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C4Cyclic group; = square rotations41C44,1
C22Klein 4-group V4 = elementary abelian group of type [2,2]; = rectangle symmetries4C2^24,2

### Groups of order 5

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C5Cyclic group; = pentagon rotations51C55,1

### Groups of order 6

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C6Cyclic group; = hexagon rotations61C66,2

### Groups of order 7

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C7Cyclic group71C77,1

### Groups of order 8

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C8Cyclic group81C88,1
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetries42+D48,3
Q8Quaternion group; = C4.C2 = Dic2 = 2- 1+282-Q88,4
C23Elementary abelian group of type [2,2,2]8C2^38,5
C2×C4Abelian group of type [2,4]8C2xC48,2

### Groups of order 9

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C9Cyclic group91C99,1
C32Elementary abelian group of type [3,3]9C3^29,2

### Groups of order 10

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C10Cyclic group101C1010,2

### Groups of order 11

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C11Cyclic group111C1111,1

### Groups of order 12

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C12Cyclic group121C1212,2
C2×C6Abelian group of type [2,6]12C2xC612,5

### Groups of order 13

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C13Cyclic group131C1313,1

### Groups of order 14

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C14Cyclic group141C1414,2

### Groups of order 15

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C15Cyclic group151C1515,1

### Groups of order 16

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C16Cyclic group161C1616,1
D8Dihedral group82+D816,7
Q16Generalised quaternion group; = C8.C2 = Dic4162-Q1616,9
SD16Semidihedral group; = Q8C2 = QD1682SD1616,8
M4(2)Modular maximal-cyclic group; = C83C282M4(2)16,6
C4○D4Pauli group = central product of C4 and D482C4oD416,13
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C28C2^2:C416,3
C4⋊C4The semidirect product of C4 and C4 acting via C4/C2=C216C4:C416,4
C42Abelian group of type [4,4]16C4^216,2
C24Elementary abelian group of type [2,2,2,2]16C2^416,14
C2×C8Abelian group of type [2,8]16C2xC816,5
C22×C4Abelian group of type [2,2,4]16C2^2xC416,10
C2×D4Direct product of C2 and D48C2xD416,11
C2×Q8Direct product of C2 and Q816C2xQ816,12

### Groups of order 17

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C17Cyclic group171C1717,1

### Groups of order 18

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C18Cyclic group181C1818,2
C3×C6Abelian group of type [3,6]18C3xC618,5

### Groups of order 19

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C19Cyclic group191C1919,1

### Groups of order 20

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C20Cyclic group201C2020,2
C2×C10Abelian group of type [2,10]20C2xC1020,5

### Groups of order 21

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C21Cyclic group211C2121,2

### Groups of order 22

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C22Cyclic group221C2222,2

### Groups of order 23

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C23Cyclic group231C2323,1

### Groups of order 24

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C24Cyclic group241C2424,2
C2×C12Abelian group of type [2,12]24C2xC1224,9
C22×C6Abelian group of type [2,2,6]24C2^2xC624,15
C3×D4Direct product of C3 and D4122C3xD424,10
C3×Q8Direct product of C3 and Q8242C3xQ824,11

### Groups of order 25

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C25Cyclic group251C2525,1
C52Elementary abelian group of type [5,5]25C5^225,2

### Groups of order 26

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C26Cyclic group261C2626,2

### Groups of order 27

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C27Cyclic group271C2727,1
He3Heisenberg group; = C32C3 = 3+ 1+293He327,3
3- 1+2Extraspecial group93ES-(3,1)27,4
C33Elementary abelian group of type [3,3,3]27C3^327,5
C3×C9Abelian group of type [3,9]27C3xC927,2

### Groups of order 28

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C28Cyclic group281C2828,2
C2×C14Abelian group of type [2,14]28C2xC1428,4

### Groups of order 29

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C29Cyclic group291C2929,1

### Groups of order 30

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C30Cyclic group301C3030,4

### Groups of order 31

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C31Cyclic group311C3131,1

### Groups of order 32

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C32Cyclic group321C3232,1
D16Dihedral group162+D1632,18
Q32Generalised quaternion group; = C16.C2 = Dic8322-Q3232,20
2+ 1+4Extraspecial group; = D4D484+ES+(2,2)32,49
SD32Semidihedral group; = C162C2 = QD32162SD3232,19
2- 1+4Gamma matrices = Extraspecial group; = D4Q8164-ES-(2,2)32,50
M5(2)Modular maximal-cyclic group; = C163C2162M5(2)32,17
C4≀C2Wreath product of C4 by C282C4wrC232,11
C22≀C2Wreath product of C22 by C28C2^2wrC232,27
C8○D4Central product of C8 and D4162C8oD432,38
C4○D8Central product of C4 and D8162C4oD832,42
C23⋊C4The semidirect product of C23 and C4 acting faithfully84+C2^3:C432,6
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)84+C8:C2^232,43
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C216C4:D432,28
C41D4The semidirect product of C4 and D4 acting via D4/C4=C216C4:1D432,34
C22⋊C8The semidirect product of C22 and C8 acting via C8/C4=C216C2^2:C832,5
C22⋊Q8The semidirect product of C22 and Q8 acting via Q8/C4=C216C2^2:Q832,29
D4⋊C41st semidirect product of D4 and C4 acting via C4/C2=C216D4:C432,9
C42⋊C21st semidirect product of C42 and C2 acting faithfully16C4^2:C232,24
C422C22nd semidirect product of C42 and C2 acting faithfully16C4^2:2C232,33
C4⋊C8The semidirect product of C4 and C8 acting via C8/C4=C232C4:C832,12
C4⋊Q8The semidirect product of C4 and Q8 acting via Q8/C4=C232C4:Q832,35
C8⋊C43rd semidirect product of C8 and C4 acting via C4/C2=C232C8:C432,4
Q8⋊C41st semidirect product of Q8 and C4 acting via C4/C2=C232Q8:C432,10
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C284+C4.D432,7
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2162C8.C432,15
C4.4D44th non-split extension by C4 of D4 acting via D4/C4=C216C4.4D432,31
C8.C22The non-split extension by C8 of C22 acting faithfully164-C8.C2^232,44
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2164-C4.10D432,8
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C216C2^2.D432,30
C2.D82nd central extension by C2 of D832C2.D832,14
C4.Q81st non-split extension by C4 of Q8 acting via Q8/C4=C232C4.Q832,13
C2.C421st central stem extension by C2 of C4232C2.C4^232,2
C42.C24th non-split extension by C42 of C2 acting faithfully32C4^2.C232,32
C25Elementary abelian group of type [2,2,2,2,2]32C2^532,51
C4×C8Abelian group of type [4,8]32C4xC832,3
C2×C16Abelian group of type [2,16]32C2xC1632,16
C2×C42Abelian group of type [2,4,4]32C2xC4^232,21
C22×C8Abelian group of type [2,2,8]32C2^2xC832,36
C23×C4Abelian group of type [2,2,2,4]32C2^3xC432,45
C4×D4Direct product of C4 and D416C4xD432,25
C2×D8Direct product of C2 and D816C2xD832,39
C2×SD16Direct product of C2 and SD1616C2xSD1632,40
C22×D4Direct product of C22 and D416C2^2xD432,46
C2×M4(2)Direct product of C2 and M4(2)16C2xM4(2)32,37
C4×Q8Direct product of C4 and Q832C4xQ832,26
C2×Q16Direct product of C2 and Q1632C2xQ1632,41
C22×Q8Direct product of C22 and Q832C2^2xQ832,47
C2×C4○D4Direct product of C2 and C4○D416C2xC4oD432,48
C2×C22⋊C4Direct product of C2 and C22⋊C416C2xC2^2:C432,22
C2×C4⋊C4Direct product of C2 and C4⋊C432C2xC4:C432,23

### Groups of order 33

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C33Cyclic group331C3333,1

### Groups of order 34

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C34Cyclic group341C3434,2

### Groups of order 35

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C35Cyclic group351C3535,1

### Groups of order 36

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C36Cyclic group361C3636,2
C62Abelian group of type [6,6]36C6^236,14
C2×C18Abelian group of type [2,18]36C2xC1836,5
C3×C12Abelian group of type [3,12]36C3xC1236,8

### Groups of order 37

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C37Cyclic group371C3737,1

### Groups of order 38

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C38Cyclic group381C3838,2

### Groups of order 39

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C39Cyclic group391C3939,2

### Groups of order 40

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C40Cyclic group401C4040,2
C2×C20Abelian group of type [2,20]40C2xC2040,9
C22×C10Abelian group of type [2,2,10]40C2^2xC1040,14
C5×D4Direct product of C5 and D4202C5xD440,10
C5×Q8Direct product of C5 and Q8402C5xQ840,11

### Groups of order 41

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C41Cyclic group411C4141,1

### Groups of order 42

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C42Cyclic group421C4242,6

### Groups of order 43

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C43Cyclic group431C4343,1

### Groups of order 44

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C44Cyclic group441C4444,2
C2×C22Abelian group of type [2,22]44C2xC2244,4

### Groups of order 45

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C45Cyclic group451C4545,1
C3×C15Abelian group of type [3,15]45C3xC1545,2

### Groups of order 46

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C46Cyclic group461C4646,2

### Groups of order 47

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C47Cyclic group471C4747,1

### Groups of order 48

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C48Cyclic group481C4848,2
C4×C12Abelian group of type [4,12]48C4xC1248,20
C2×C24Abelian group of type [2,24]48C2xC2448,23
C23×C6Abelian group of type [2,2,2,6]48C2^3xC648,52
C22×C12Abelian group of type [2,2,12]48C2^2xC1248,44
C3×D8Direct product of C3 and D8242C3xD848,25
C6×D4Direct product of C6 and D424C6xD448,45
C3×SD16Direct product of C3 and SD16242C3xSD1648,26
C3×M4(2)Direct product of C3 and M4(2)242C3xM4(2)48,24
C6×Q8Direct product of C6 and Q848C6xQ848,46
C3×Q16Direct product of C3 and Q16482C3xQ1648,27
C3×C4○D4Direct product of C3 and C4○D4242C3xC4oD448,47
C3×C22⋊C4Direct product of C3 and C22⋊C424C3xC2^2:C448,21
C3×C4⋊C4Direct product of C3 and C4⋊C448C3xC4:C448,22

### Groups of order 49

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C49Cyclic group491C4949,1
C72Elementary abelian group of type [7,7]49C7^249,2

### Groups of order 50

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C50Cyclic group501C5050,2
C5×C10Abelian group of type [5,10]50C5xC1050,5

### Groups of order 51

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C51Cyclic group511C5151,1

### Groups of order 52

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C52Cyclic group521C5252,2
C2×C26Abelian group of type [2,26]52C2xC2652,5

### Groups of order 53

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C53Cyclic group531C5353,1

### Groups of order 54

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C54Cyclic group541C5454,2
C3×C18Abelian group of type [3,18]54C3xC1854,9
C32×C6Abelian group of type [3,3,6]54C3^2xC654,15
C2×He3Direct product of C2 and He3183C2xHe354,10
C2×3- 1+2Direct product of C2 and 3- 1+2183C2xES-(3,1)54,11

### Groups of order 55

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C55Cyclic group551C5555,2

### Groups of order 56

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C56Cyclic group561C5656,2
C2×C28Abelian group of type [2,28]56C2xC2856,8
C22×C14Abelian group of type [2,2,14]56C2^2xC1456,13
C7×D4Direct product of C7 and D4282C7xD456,9
C7×Q8Direct product of C7 and Q8562C7xQ856,10

### Groups of order 57

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C57Cyclic group571C5757,2

### Groups of order 58

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C58Cyclic group581C5858,2

### Groups of order 59

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C59Cyclic group591C5959,1

### Groups of order 60

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C60Cyclic group601C6060,4
C2×C30Abelian group of type [2,30]60C2xC3060,13

### Groups of order 61

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C61Cyclic group611C6161,1

### Groups of order 62

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C62Cyclic group621C6262,2

### Groups of order 63

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C63Cyclic group631C6363,2
C3×C21Abelian group of type [3,21]63C3xC2163,4

### Groups of order 64

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C64Cyclic group641C6464,1
D32Dihedral group322+D3264,52
Q64Generalised quaternion group; = C32.C2 = Dic16642-Q6464,54
SD64Semidihedral group; = C322C2 = QD64322SD6464,53
M6(2)Modular maximal-cyclic group; = C323C2322M6(2)64,51
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)84+C2wrC464,32
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)84+C2wrC2^264,138
C8○D8Central product of C8 and D8162C8oD864,124
D4○D8Central product of D4 and D8164+D4oD864,257
D4○SD16Central product of D4 and SD16164D4oSD1664,258
Q8○M4(2)Central product of Q8 and M4(2)164Q8oM4(2)64,249
Q8○D8Central product of Q8 and D8324-Q8oD864,259
D4○C16Central product of D4 and C16322D4oC1664,185
C4○D16Central product of C4 and D16322C4oD1664,189
C82M4(2)Central product of C8 and M4(2)32C8o2M4(2)64,86
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)84+D4:4D464,134
C42⋊C42nd semidirect product of C42 and C4 acting faithfully84+C4^2:C464,34
C23⋊C8The semidirect product of C23 and C8 acting via C8/C2=C416C2^3:C864,4
C16⋊C42nd semidirect product of C16 and C4 acting faithfully164C16:C464,28
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
D45D41st semidirect product of D4 and D4 acting through Inn(D4)16D4:5D464,227
C16⋊C22The semidirect product of C16 and C22 acting faithfully164+C16:C2^264,190
C426C43rd semidirect product of C42 and C4 acting via C4/C2=C216C4^2:6C464,20
C423C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
C243C41st semidirect product of C24 and C4 acting via C4/C2=C216C2^4:3C464,60
C22⋊D8The semidirect product of C22 and D8 acting via D8/D4=C216C2^2:D864,128
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C2216C2^3:3D464,215
C232Q82nd semidirect product of C23 and Q8 acting via Q8/C2=C2216C2^3:2Q864,224
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2164D8:C2^264,256
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2164M4(2):4C464,25
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfully164+M5(2):C264,42
C42⋊C221st semidirect product of C42 and C22 acting faithfully164C4^2:C2^264,102
C24⋊C224th semidirect product of C24 and C22 acting faithfully16C2^4:C2^264,242
C22⋊SD16The semidirect product of C22 and SD16 acting via SD16/D4=C216C2^2:SD1664,131
D4⋊C8The semidirect product of D4 and C8 acting via C8/C4=C232D4:C864,6
C89D43rd semidirect product of C8 and D4 acting via D4/C22=C232C8:9D464,116
C86D43rd semidirect product of C8 and D4 acting via D4/C4=C232C8:6D464,117
C4⋊D8The semidirect product of C4 and D8 acting via D8/D4=C232C4:D864,140
C88D42nd semidirect product of C8 and D4 acting via D4/C22=C232C8:8D464,146
C87D41st semidirect product of C8 and D4 acting via D4/C22=C232C8:7D464,147
C8⋊D41st semidirect product of C8 and D4 acting via D4/C2=C2232C8:D464,149
C82D42nd semidirect product of C8 and D4 acting via D4/C2=C2232C8:2D464,150
C85D42nd semidirect product of C8 and D4 acting via D4/C4=C232C8:5D464,173
C84D41st semidirect product of C8 and D4 acting via D4/C4=C232C8:4D464,174
C83D43rd semidirect product of C8 and D4 acting via D4/C2=C2232C8:3D464,177
D8⋊C43rd semidirect product of D8 and C4 acting via C4/C2=C2; = Aut(SD32)32D8:C464,123
D4⋊D42nd semidirect product of D4 and D4 acting via D4/C22=C232D4:D464,130
D46D42nd semidirect product of D4 and D4 acting through Inn(D4)32D4:6D464,228
C22⋊C16The semidirect product of C22 and C16 acting via C16/C8=C232C2^2:C1664,29
Q8⋊D41st semidirect product of Q8 and D4 acting via D4/C22=C232Q8:D464,129
D4⋊Q81st semidirect product of D4 and Q8 acting via Q8/C4=C232D4:Q864,155
D42Q82nd semidirect product of D4 and Q8 acting via Q8/C4=C232D4:2Q864,157
Q85D41st semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:5D464,229
Q86D42nd semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:6D464,231
D43Q8The semidirect product of D4 and Q8 acting through Inn(D4)32D4:3Q864,235
Q32⋊C22nd semidirect product of Q32 and C2 acting faithfully324-Q32:C264,191
C4⋊SD16The semidirect product of C4 and SD16 acting via SD16/Q8=C232C4:SD1664,141
C232D41st semidirect product of C23 and D4 acting via D4/C2=C2232C2^3:2D464,73
C23⋊Q81st semidirect product of C23 and Q8 acting via Q8/C2=C2232C2^3:Q864,74
SD16⋊C41st semidirect product of SD16 and C4 acting via C4/C2=C232SD16:C464,121
C4⋊M4(2)The semidirect product of C4 and M4(2) acting via M4(2)/C2×C4=C232C4:M4(2)64,104
C22⋊Q16The semidirect product of C22 and Q16 acting via Q16/Q8=C232C2^2:Q1664,132
M4(2)⋊C41st semidirect product of M4(2) and C4 acting via C4/C2=C232M4(2):C464,109
C8⋊Q8The semidirect product of C8 and Q8 acting via Q8/C2=C2264C8:Q864,182
C4⋊C16The semidirect product of C4 and C16 acting via C16/C8=C264C4:C1664,44
Q8⋊C8The semidirect product of Q8 and C8 acting via C8/C4=C264Q8:C864,7
C8⋊C83rd semidirect product of C8 and C8 acting via C8/C4=C264C8:C864,3
C82C82nd semidirect product of C8 and C8 acting via C8/C4=C264C8:2C864,15
C81C81st semidirect product of C8 and C8 acting via C8/C4=C264C8:1C864,16
C84Q83rd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:4Q864,127
C83Q82nd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:3Q864,179
C82Q81st semidirect product of C8 and Q8 acting via Q8/C4=C264C8:2Q864,181
C165C43rd semidirect product of C16 and C4 acting via C4/C2=C264C16:5C464,27
C163C41st semidirect product of C16 and C4 acting via C4/C2=C264C16:3C464,47
C164C42nd semidirect product of C16 and C4 acting via C4/C2=C264C16:4C464,48
Q8⋊Q81st semidirect product of Q8 and Q8 acting via Q8/C4=C264Q8:Q864,156
Q83Q8The semidirect product of Q8 and Q8 acting through Inn(Q8)64Q8:3Q864,238
C42Q16The semidirect product of C4 and Q16 acting via Q16/Q8=C264C4:2Q1664,143
C4⋊Q16The semidirect product of C4 and Q16 acting via Q16/C8=C264C4:Q1664,175
C424C41st semidirect product of C42 and C4 acting via C4/C2=C264C4^2:4C464,57
C428C45th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:8C464,63
C425C42nd semidirect product of C42 and C4 acting via C4/C2=C264C4^2:5C464,64
C429C46th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:9C464,65
Q16⋊C43rd semidirect product of Q16 and C4 acting via C4/C2=C264Q16:C464,122
(C22×C8)⋊C22nd semidirect product of C22×C8 and C2 acting faithfully32(C2^2xC8):C264,89
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22164C8.Q864,46
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2162C8.C864,45
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4164C2^3.C864,30
D4.8D43rd non-split extension by D4 of D4 acting via D4/C22=C2164D4.8D464,135
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2164D4.9D464,136
D4.3D43rd non-split extension by D4 of D4 acting via D4/C4=C2164D4.3D464,152
D4.4D44th non-split extension by D4 of D4 acting via D4/C4=C2164+D4.4D464,153
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2164C8.26D464,125
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2164-D4.10D464,137
C4.9C421st central stem extension by C4 of C42164C4.9C4^264,18
C42.C42nd non-split extension by C42 of C4 acting faithfully164C4^2.C464,36
C42.3C43rd non-split extension by C42 of C4 acting faithfully164-C4^2.3C464,37
C24.4C42nd non-split extension by C24 of C4 acting via C4/C2=C216C2^4.4C464,88
C2.C256th central stem extension by C2 of C25164C2.C2^564,266
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C2216C2^3.9D464,23
C23.D42nd non-split extension by C23 of D4 acting faithfully164C2^3.D464,33
C23.7D47th non-split extension by C23 of D4 acting faithfully164C2^3.7D464,139
C4.10C422nd central stem extension by C4 of C42164C4.10C4^264,19
C23.31D42nd non-split extension by C23 of D4 acting via D4/C22=C216C2^3.31D464,9
C23.37D48th non-split extension by C23 of D4 acting via D4/C22=C216C2^3.37D464,99
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2164M4(2).C464,111
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22164C2^3.C2^364,91
C22.SD161st non-split extension by C22 of SD16 acting via SD16/Q8=C216C2^2.SD1664,8
C22.11C247th central extension by C22 of C2416C2^2.11C2^464,199
C22.19C245th central stem extension by C22 of C2416C2^2.19C2^464,206
C22.29C2415th central stem extension by C22 of C2416C2^2.29C2^464,216
C22.32C2418th central stem extension by C22 of C2416C2^2.32C2^464,219
C22.45C2431st central stem extension by C22 of C2416C2^2.45C2^464,232
C22.54C2440th central stem extension by C22 of C2416C2^2.54C2^464,241
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2164M4(2).8C2^264,94
D4.C8The non-split extension by D4 of C8 acting via C8/C4=C2322D4.C864,31
D4.Q8The non-split extension by D4 of Q8 acting via Q8/C4=C232D4.Q864,159
C4.D81st non-split extension by C4 of D8 acting via D8/D4=C232C4.D864,12
C8.D41st non-split extension by C8 of D4 acting via D4/C2=C2232C8.D464,151
C4.4D84th non-split extension by C4 of D8 acting via D8/C8=C232C4.4D864,167
C8.2D42nd non-split extension by C8 of D4 acting via D4/C2=C2232C8.2D464,178
C8.4Q83rd non-split extension by C8 of Q8 acting via Q8/C4=C2322C8.4Q864,49
D8.C41st non-split extension by D8 of C4 acting via C4/C2=C2322D8.C464,40
D4.7D42nd non-split extension by D4 of D4 acting via D4/C22=C232D4.7D464,133
D4.D41st non-split extension by D4 of D4 acting via D4/C4=C232D4.D464,142
D4.2D42nd non-split extension by D4 of D4 acting via D4/C4=C232D4.2D464,144
D4.5D45th non-split extension by D4 of D4 acting via D4/C4=C2324-D4.5D464,154
C2.D161st central extension by C2 of D1632C2.D1664,38
C8.17D44th non-split extension by C8 of D4 acting via D4/C22=C2324-C8.17D464,43
C8.18D45th non-split extension by C8 of D4 acting via D4/C22=C232C8.18D464,148
C8.12D48th non-split extension by C8 of D4 acting via D4/C4=C232C8.12D464,176
Q8.D42nd non-split extension by Q8 of D4 acting via D4/C4=C232Q8.D464,145
C4.C423rd non-split extension by C4 of C42 acting via C42/C2×C4=C232C4.C4^264,22
C42.6C43rd non-split extension by C42 of C4 acting via C4/C2=C232C4^2.6C464,113
C22.D83rd non-split extension by C22 of D8 acting via D8/D4=C232C2^2.D864,161
C23.7Q82nd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.7Q864,61
C23.8Q83rd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.8Q864,66
C23.Q83rd non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.Q864,77
C23.4Q84th non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.4Q864,80
C42.12C49th non-split extension by C42 of C4 acting via C4/C2=C232C4^2.12C464,112
C23.34D45th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.34D464,62
C23.23D42nd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.23D464,67
C23.10D43rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.10D464,75
C23.11D44th non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.11D464,78
C23.24D43rd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.24D464,97
C23.36D47th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.36D464,98
C23.38D49th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.38D464,100
C23.25D44th non-split extension by C23 of D4 acting via D4/C4=C232C2^3.25D464,108
C23.46D417th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.46D464,162
C23.19D412nd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.19D464,163
C23.47D418th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.47D464,164
C23.48D419th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.48D464,165
C23.20D413rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.20D464,166
C42.C221st non-split extension by C42 of C22 acting faithfully32C4^2.C2^264,10
C22.C422nd non-split extension by C22 of C42 acting via C42/C2×C4=C232C2^2.C4^264,24
C24.C222nd non-split extension by C24 of C22 acting faithfully32C2^4.C2^264,69
C24.3C223rd non-split extension by C24 of C22 acting faithfully32C2^4.3C2^264,71
C42.6C226th non-split extension by C42 of C22 acting faithfully32C4^2.6C2^264,105
C42.7C227th non-split extension by C42 of C22 acting faithfully32C4^2.7C2^264,114
C42.78C2221st non-split extension by C42 of C22 acting via C22/C2=C232C4^2.78C2^264,169
C42.28C2228th non-split extension by C42 of C22 acting faithfully32C4^2.28C2^264,170
C42.29C2229th non-split extension by C42 of C22 acting faithfully32C4^2.29C2^264,171
C23.32C235th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.32C2^364,200
C23.33C236th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.33C2^364,201
C23.36C239th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.36C2^364,210
C22.26C2412nd central stem extension by C22 of C2432C2^2.26C2^464,213
C23.37C2310th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.37C2^364,214
C23.38C2311st non-split extension by C23 of C23 acting via C23/C22=C232C2^3.38C2^364,217
C22.31C2417th central stem extension by C22 of C2432C2^2.31C2^464,218
C22.33C2419th central stem extension by C22 of C2432C2^2.33C2^464,220
C22.34C2420th central stem extension by C22 of C2432C2^2.34C2^464,221
C22.35C2421st central stem extension by C22 of C2432C2^2.35C2^464,222
C22.36C2422nd central stem extension by C22 of C2432C2^2.36C2^464,223
C23.41C2314th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.41C2^364,225
C22.46C2432nd central stem extension by C22 of C2432C2^2.46C2^464,233
C22.47C2433rd central stem extension by C22 of C2432C2^2.47C2^464,234
C22.49C2435th central stem extension by C22 of C2432C2^2.49C2^464,236
C22.50C2436th central stem extension by C22 of C2432C2^2.50C2^464,237
C22.53C2439th central stem extension by C22 of C2432C2^2.53C2^464,240
C22.56C2442nd central stem extension by C22 of C2432C2^2.56C2^464,243
C22.57C2443rd central stem extension by C22 of C2432C2^2.57C2^464,244
C22.M4(2)2nd non-split extension by C22 of M4(2) acting via M4(2)/C2×C4=C232C2^2.M4(2)64,5
Q8.Q8The non-split extension by Q8 of Q8 acting via Q8/C4=C264Q8.Q864,160
C8.5Q84th non-split extension by C8 of Q8 acting via Q8/C4=C264C8.5Q864,180
C4.10D82nd non-split extension by C4 of D8 acting via D8/D4=C264C4.10D864,13
C4.6Q162nd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.6Q1664,14
C2.Q321st central extension by C2 of Q3264C2.Q3264,39
C4.Q163rd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.Q1664,158
C4.SD164th non-split extension by C4 of SD16 acting via SD16/C8=C264C4.SD1664,168
C22.4Q161st central extension by C22 of Q1664C2^2.4Q1664,21
C42.2C222nd non-split extension by C42 of C22 acting faithfully64C4^2.2C2^264,11
C22.7C422nd central extension by C22 of C4264C2^2.7C4^264,17
C23.63C2313rd central extension by C23 of C2364C2^3.63C2^364,68
C23.65C2315th central extension by C23 of C2364C2^3.65C2^364,70
C23.67C2317th central extension by C23 of C2364C2^3.67C2^364,72
C23.78C234th central stem extension by C23 of C2364C2^3.78C2^364,76
C23.81C237th central stem extension by C23 of C2364C2^3.81C2^364,79
C23.83C239th central stem extension by C23 of C2364C2^3.83C2^364,81
C23.84C2310th central stem extension by C23 of C2364C2^3.84C2^364,82
C42.30C2230th non-split extension by C42 of C22 acting faithfully64C4^2.30C2^264,172
C22.58C2444th central stem extension by C22 of C2464C2^2.58C2^464,245
C82Abelian group of type [8,8]64C8^264,2
C43Abelian group of type [4,4,4]64C4^364,55
C26Elementary abelian group of type [2,2,2,2,2,2]64C2^664,267
C4×C16Abelian group of type [4,16]64C4xC1664,26
C2×C32Abelian group of type [2,32]64C2xC3264,50
C23×C8Abelian group of type [2,2,2,8]64C2^3xC864,246
C24×C4Abelian group of type [2,2,2,2,4]64C2^4xC464,260
C22×C16Abelian group of type [2,2,16]64C2^2xC1664,183
C22×C42Abelian group of type [2,2,4,4]64C2^2xC4^264,192
C2×C4×C8Abelian group of type [2,4,8]64C2xC4xC864,83
D42Direct product of D4 and D416D4^264,226
C2×2+ 1+4Direct product of C2 and 2+ 1+416C2xES+(2,2)64,264
C8×D4Direct product of C8 and D432C8xD464,115
C4×D8Direct product of C4 and D832C4xD864,118
D4×Q8Direct product of D4 and Q832D4xQ864,230
C2×D16Direct product of C2 and D1632C2xD1664,186
C4×SD16Direct product of C4 and SD1632C4xSD1664,119
C2×SD32Direct product of C2 and SD3232C2xSD3264,187
C22×D8Direct product of C22 and D832C2^2xD864,250
D4×C23Direct product of C23 and D432D4xC2^364,261
C4×M4(2)Direct product of C4 and M4(2)32C4xM4(2)64,85
C2×M5(2)Direct product of C2 and M5(2)32C2xM5(2)64,184
C22×SD16Direct product of C22 and SD1632C2^2xSD1664,251
C22×M4(2)Direct product of C22 and M4(2)32C2^2xM4(2)64,247
C2×2- 1+4Direct product of C2 and 2- 1+432C2xES-(2,2)64,265
Q82Direct product of Q8 and Q864Q8^264,239
C8×Q8Direct product of C8 and Q864C8xQ864,126
C4×Q16Direct product of C4 and Q1664C4xQ1664,120
C2×Q32Direct product of C2 and Q3264C2xQ3264,188
Q8×C23Direct product of C23 and Q864Q8xC2^364,262
C22×Q16Direct product of C22 and Q1664C2^2xQ1664,252
C2×C4≀C2Direct product of C2 and C4≀C216C2xC4wrC264,101
C2×C23⋊C4Direct product of C2 and C23⋊C416C2xC2^3:C464,90
C2×C8⋊C22Direct product of C2 and C8⋊C2216C2xC8:C2^264,254
C2×C4.D4Direct product of C2 and C4.D416C2xC4.D464,92
C2×C22≀C2Direct product of C2 and C22≀C216C2xC2^2wrC264,202
C2×C4×D4Direct product of C2×C4 and D432C2xC4xD464,196
C4×C4○D4Direct product of C4 and C4○D432C4xC4oD464,198
C2×C8○D4Direct product of C2 and C8○D432C2xC8oD464,248
C2×C4○D8Direct product of C2 and C4○D832C2xC4oD864,253
C2×C4⋊D4Direct product of C2 and C4⋊D432C2xC4:D464,203
C2×D4⋊C4Direct product of C2 and D4⋊C432C2xD4:C464,95
C2×C8.C4Direct product of C2 and C8.C432C2xC8.C464,110
C2×C41D4Direct product of C2 and C41D432C2xC4:1D464,211
C4×C22⋊C4Direct product of C4 and C22⋊C432C4xC2^2:C464,58
C2×C22⋊C8Direct product of C2 and C22⋊C832C2xC2^2:C864,87
C2×C22⋊Q8Direct product of C2 and C22⋊Q832C2xC2^2:Q864,204
C2×C42⋊C2Direct product of C2 and C42⋊C232C2xC4^2:C264,195
C2×C4.4D4Direct product of C2 and C4.4D432C2xC4.4D464,207
C22×C4○D4Direct product of C22 and C4○D432C2^2xC4oD464,263
C2×C8.C22Direct product of C2 and C8.C2232C2xC8.C2^264,255
C2×C422C2Direct product of C2 and C422C232C2xC4^2:2C264,209
C2×C4.10D4Direct product of C2 and C4.10D432C2xC4.10D464,93
C22×C22⋊C4Direct product of C22 and C22⋊C432C2^2xC2^2:C464,193
C2×C22.D4Direct product of C2 and C22.D432C2xC2^2.D464,205
C4×C4⋊C4Direct product of C4 and C4⋊C464C4xC4:C464,59
C2×C4⋊C8Direct product of C2 and C4⋊C864C2xC4:C864,103
C2×C4×Q8Direct product of C2×C4 and Q864C2xC4xQ864,197
C2×C4⋊Q8Direct product of C2 and C4⋊Q864C2xC4:Q864,212
C2×C8⋊C4Direct product of C2 and C8⋊C464C2xC8:C464,84
C22×C4⋊C4Direct product of C22 and C4⋊C464C2^2xC4:C464,194
C2×Q8⋊C4Direct product of C2 and Q8⋊C464C2xQ8:C464,96
C2×C2.D8Direct product of C2 and C2.D864C2xC2.D864,107
C2×C4.Q8Direct product of C2 and C4.Q864C2xC4.Q864,106
C2×C2.C42Direct product of C2 and C2.C4264C2xC2.C4^264,56
C2×C42.C2Direct product of C2 and C42.C264C2xC4^2.C264,208

### Groups of order 65

dρLabelID
C65Cyclic group651C6565,1

### Groups of order 66

dρLabelID
C66Cyclic group661C6666,4

### Groups of order 67

dρLabelID
C67Cyclic group671C6767,1

### Groups of order 68

dρLabelID
C68Cyclic group681C6868,2
C2×C34Abelian group of type [2,34]68C2xC3468,5

### Groups of order 69

dρLabelID
C69Cyclic group691C6969,1

### Groups of order 70

dρLabelID
C70Cyclic group701C7070,4

### Groups of order 71

dρLabelID
C71Cyclic group711C7171,1

### Groups of order 72

dρLabelID
C72Cyclic group721C7272,2
C2×C36Abelian group of type [2,36]72C2xC3672,9
C3×C24Abelian group of type [3,24]72C3xC2472,14
C6×C12Abelian group of type [6,12]72C6xC1272,36
C2×C62Abelian group of type [2,6,6]72C2xC6^272,50
C22×C18Abelian group of type [2,2,18]72C2^2xC1872,18
D4×C9Direct product of C9 and D4362D4xC972,10
D4×C32Direct product of C32 and D436D4xC3^272,37
Q8×C9Direct product of C9 and Q8722Q8xC972,11
Q8×C32Direct product of C32 and Q872Q8xC3^272,38

### Groups of order 73

dρLabelID
C73Cyclic group731C7373,1

### Groups of order 74

dρLabelID
C74Cyclic group741C7474,2

### Groups of order 75

dρLabelID
C75Cyclic group751C7575,1
C5×C15Abelian group of type [5,15]75C5xC1575,3

### Groups of order 76

dρLabelID
C76Cyclic group761C7676,2
C2×C38Abelian group of type [2,38]76C2xC3876,4

### Groups of order 77

dρLabelID
C77Cyclic group771C7777,1

### Groups of order 78

dρLabelID
C78Cyclic group781C7878,6

### Groups of order 79

dρLabelID
C79Cyclic group791C7979,1

### Groups of order 80

dρLabelID
C80Cyclic group801C8080,2
C4×C20Abelian group of type [4,20]80C4xC2080,20
C2×C40Abelian group of type [2,40]80C2xC4080,23
C22×C20Abelian group of type [2,2,20]80C2^2xC2080,45
C23×C10Abelian group of type [2,2,2,10]80C2^3xC1080,52
C5×D8Direct product of C5 and D8402C5xD880,25
D4×C10Direct product of C10 and D440D4xC1080,46
C5×SD16Direct product of C5 and SD16402C5xSD1680,26
C5×M4(2)Direct product of C5 and M4(2)402C5xM4(2)80,24
C5×Q16Direct product of C5 and Q16802C5xQ1680,27
Q8×C10Direct product of C10 and Q880Q8xC1080,47
C5×C4○D4Direct product of C5 and C4○D4402C5xC4oD480,48
C5×C22⋊C4Direct product of C5 and C22⋊C440C5xC2^2:C480,21
C5×C4⋊C4Direct product of C5 and C4⋊C480C5xC4:C480,22

### Groups of order 81

dρLabelID
C81Cyclic group811C8181,1
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)93C3wrC381,7
C9○He3Central product of C9 and He3273C9oHe381,14
C27⋊C3The semidirect product of C27 and C3 acting faithfully273C27:C381,6
C32⋊C9The semidirect product of C32 and C9 acting via C9/C3=C327C3^2:C981,3
He3⋊C32nd semidirect product of He3 and C3 acting faithfully273He3:C381,9
C9⋊C9The semidirect product of C9 and C9 acting via C9/C3=C381C9:C981,4
He3.C3The non-split extension by He3 of C3 acting faithfully273He3.C381,8
C3.He34th central stem extension by C3 of He3273C3.He381,10
C92Abelian group of type [9,9]81C9^281,2
C34Elementary abelian group of type [3,3,3,3]81C3^481,15
C3×C27Abelian group of type [3,27]81C3xC2781,5
C32×C9Abelian group of type [3,3,9]81C3^2xC981,11
C3×He3Direct product of C3 and He327C3xHe381,12
C3×3- 1+2Direct product of C3 and 3- 1+227C3xES-(3,1)81,13

### Groups of order 82

dρLabelID
C82Cyclic group821C8282,2

### Groups of order 83

dρLabelID
C83Cyclic group831C8383,1

### Groups of order 84

dρLabelID
C84Cyclic group841C8484,6
C2×C42Abelian group of type [2,42]84C2xC4284,15

### Groups of order 85

dρLabelID
C85Cyclic group851C8585,1

### Groups of order 86

dρLabelID
C86Cyclic group861C8686,2

### Groups of order 87

dρLabelID
C87Cyclic group871C8787,1

### Groups of order 88

dρLabelID
C88Cyclic group881C8888,2
C2×C44Abelian group of type [2,44]88C2xC4488,8
C22×C22Abelian group of type [2,2,22]88C2^2xC2288,12
D4×C11Direct product of C11 and D4442D4xC1188,9
Q8×C11Direct product of C11 and Q8882Q8xC1188,10

### Groups of order 89

dρLabelID
C89Cyclic group891C8989,1

### Groups of order 90

dρLabelID
C90Cyclic group901C9090,4
C3×C30Abelian group of type [3,30]90C3xC3090,10

### Groups of order 91

dρLabelID
C91Cyclic group911C9191,1

### Groups of order 92

dρLabelID
C92Cyclic group921C9292,2
C2×C46Abelian group of type [2,46]92C2xC4692,4

### Groups of order 93

dρLabelID
C93Cyclic group931C9393,2

### Groups of order 94

dρLabelID
C94Cyclic group941C9494,2

### Groups of order 95

dρLabelID
C95Cyclic group951C9595,1

### Groups of order 96

dρLabelID
C96Cyclic group961C9696,2
C4×C24Abelian group of type [4,24]96C4xC2496,46
C2×C48Abelian group of type [2,48]96C2xC4896,59
C24×C6Abelian group of type [2,2,2,2,6]96C2^4xC696,231
C22×C24Abelian group of type [2,2,24]96C2^2xC2496,176
C23×C12Abelian group of type [2,2,2,12]96C2^3xC1296,220
C2×C4×C12Abelian group of type [2,4,12]96C2xC4xC1296,161
C3×2+ 1+4Direct product of C3 and 2+ 1+4244C3xES+(2,2)96,224
C6×D8Direct product of C6 and D848C6xD896,179
C3×D16Direct product of C3 and D16482C3xD1696,61
D4×C12Direct product of C12 and D448D4xC1296,165
C3×SD32Direct product of C3 and SD32482C3xSD3296,62
C6×SD16Direct product of C6 and SD1648C6xSD1696,180
C3×M5(2)Direct product of C3 and M5(2)482C3xM5(2)96,60
C6×M4(2)Direct product of C6 and M4(2)48C6xM4(2)96,177
C3×2- 1+4Direct product of C3 and 2- 1+4484C3xES-(2,2)96,225
C3×Q32Direct product of C3 and Q32962C3xQ3296,63
Q8×C12Direct product of C12 and Q896Q8xC1296,166
C6×Q16Direct product of C6 and Q1696C6xQ1696,181
C3×C4≀C2Direct product of C3 and C4≀C2242C3xC4wrC296,54
C3×C23⋊C4Direct product of C3 and C23⋊C4244C3xC2^3:C496,49
C3×C8⋊C22Direct product of C3 and C8⋊C22244C3xC8:C2^296,183
C3×C4.D4Direct product of C3 and C4.D4244C3xC4.D496,50
C3×C22≀C2Direct product of C3 and C22≀C224C3xC2^2wrC296,167
D4×C2×C6Direct product of C2×C6 and D448D4xC2xC696,221
C3×C8○D4Direct product of C3 and C8○D4482C3xC8oD496,178
C3×C4○D8Direct product of C3 and C4○D8482C3xC4oD896,182
C6×C4○D4Direct product of C6 and C4○D448C6xC4oD496,223
C3×C4⋊D4Direct product of C3 and C4⋊D448C3xC4:D496,168
C3×D4⋊C4Direct product of C3 and D4⋊C448C3xD4:C496,52
C3×C8.C4Direct product of C3 and C8.C4482C3xC8.C496,58
C3×C41D4Direct product of C3 and C41D448C3xC4:1D496,174
C3×C22⋊C8Direct product of C3 and C22⋊C848C3xC2^2:C896,48
C6×C22⋊C4Direct product of C6 and C22⋊C448C6xC2^2:C496,162
C3×C22⋊Q8Direct product of C3 and C22⋊Q848C3xC2^2:Q896,169
C3×C42⋊C2Direct product of C3 and C42⋊C248C3xC4^2:C296,164
C3×C4.4D4Direct product of C3 and C4.4D448C3xC4.4D496,171
C3×C8.C22Direct product of C3 and C8.C22484C3xC8.C2^296,184
C3×C422C2Direct product of C3 and C422C248C3xC4^2:2C296,173
C3×C4.10D4Direct product of C3 and C4.10D4484C3xC4.10D496,51
C3×C22.D4Direct product of C3 and C22.D448C3xC2^2.D496,170
C3×C4⋊C8Direct product of C3 and C4⋊C896C3xC4:C896,55
C6×C4⋊C4Direct product of C6 and C4⋊C496C6xC4:C496,163
Q8×C2×C6Direct product of C2×C6 and Q896Q8xC2xC696,222
C3×C4⋊Q8Direct product of C3 and C4⋊Q896C3xC4:Q896,175
C3×C8⋊C4Direct product of C3 and C8⋊C496C3xC8:C496,47
C3×Q8⋊C4Direct product of C3 and Q8⋊C496C3xQ8:C496,53
C3×C2.D8Direct product of C3 and C2.D896C3xC2.D896,57
C3×C4.Q8Direct product of C3 and C4.Q896C3xC4.Q896,56
C3×C2.C42Direct product of C3 and C2.C4296C3xC2.C4^296,45
C3×C42.C2Direct product of C3 and C42.C296C3xC4^2.C296,172

### Groups of order 97

dρLabelID
C97Cyclic group971C9797,1

### Groups of order 98

dρLabelID
C98Cyclic group981C9898,2
C7×C14Abelian group of type [7,14]98C7xC1498,5

### Groups of order 99

dρLabelID
C99Cyclic group991C9999,1
C3×C33Abelian group of type [3,33]99C3xC3399,2

### Groups of order 100

dρLabelID
C100Cyclic group1001C100100,2
C102Abelian group of type [10,10]100C10^2100,16
C2×C50Abelian group of type [2,50]100C2xC50100,5
C5×C20Abelian group of type [5,20]100C5xC20100,8

### Groups of order 101

dρLabelID
C101Cyclic group1011C101101,1

### Groups of order 102

dρLabelID
C102Cyclic group1021C102102,4

### Groups of order 103

dρLabelID
C103Cyclic group1031C103103,1

### Groups of order 104

dρLabelID
C104Cyclic group1041C104104,2
C2×C52Abelian group of type [2,52]104C2xC52104,9
C22×C26Abelian group of type [2,2,26]104C2^2xC26104,14
D4×C13Direct product of C13 and D4522D4xC13104,10
Q8×C13Direct product of C13 and Q81042Q8xC13104,11

### Groups of order 105

dρLabelID
C105Cyclic group1051C105105,2

### Groups of order 106

dρLabelID
C106Cyclic group1061C106106,2

### Groups of order 107

dρLabelID
C107Cyclic group1071C107107,1

### Groups of order 108

dρLabelID
C108Cyclic group1081C108108,2
C2×C54Abelian group of type [2,54]108C2xC54108,5
C3×C36Abelian group of type [3,36]108C3xC36108,12
C6×C18Abelian group of type [6,18]108C6xC18108,29
C3×C62Abelian group of type [3,6,6]108C3xC6^2108,45
C32×C12Abelian group of type [3,3,12]108C3^2xC12108,35
C4×He3Direct product of C4 and He3363C4xHe3108,13
C22×He3Direct product of C22 and He336C2^2xHe3108,30
C4×3- 1+2Direct product of C4 and 3- 1+2363C4xES-(3,1)108,14
C22×3- 1+2Direct product of C22 and 3- 1+236C2^2xES-(3,1)108,31

### Groups of order 109

dρLabelID
C109Cyclic group1091C109109,1

### Groups of order 110

dρLabelID
C110Cyclic group1101C110110,6

### Groups of order 111

dρLabelID
C111Cyclic group1111C111111,2

### Groups of order 112

dρLabelID
C112Cyclic group1121C112112,2
C4×C28Abelian group of type [4,28]112C4xC28112,19
C2×C56Abelian group of type [2,56]112C2xC56112,22
C22×C28Abelian group of type [2,2,28]112C2^2xC28112,37
C23×C14Abelian group of type [2,2,2,14]112C2^3xC14112,43
C7×D8Direct product of C7 and D8562C7xD8112,24
D4×C14Direct product of C14 and D456D4xC14112,38
C7×SD16Direct product of C7 and SD16562C7xSD16112,25
C7×M4(2)Direct product of C7 and M4(2)562C7xM4(2)112,23
C7×Q16Direct product of C7 and Q161122C7xQ16112,26
Q8×C14Direct product of C14 and Q8112Q8xC14112,39
C7×C4○D4Direct product of C7 and C4○D4562C7xC4oD4112,40
C7×C22⋊C4Direct product of C7 and C22⋊C456C7xC2^2:C4112,20
C7×C4⋊C4Direct product of C7 and C4⋊C4112C7xC4:C4112,21

### Groups of order 113

dρLabelID
C113Cyclic group1131C113113,1

### Groups of order 114

dρLabelID
C114Cyclic group1141C114114,6

### Groups of order 115

dρLabelID
C115Cyclic group1151C115115,1

### Groups of order 116

dρLabelID
C116Cyclic group1161C116116,2
C2×C58Abelian group of type [2,58]116C2xC58116,5

### Groups of order 117

dρLabelID
C117Cyclic group1171C117117,2
C3×C39Abelian group of type [3,39]117C3xC39117,4

### Groups of order 118

dρLabelID
C118Cyclic group1181C118118,2

### Groups of order 119

dρLabelID
C119Cyclic group1191C119119,1

### Groups of order 120

dρLabelID
C120Cyclic group1201C120120,4
C2×C60Abelian group of type [2,60]120C2xC60120,31
C22×C30Abelian group of type [2,2,30]120C2^2xC30120,47
D4×C15Direct product of C15 and D4602D4xC15120,32
Q8×C15Direct product of C15 and Q81202Q8xC15120,33
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