Direct products

Groups of order 4

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

Groups of order 6

C6Cyclic group; = hexagon rotations61C66,2

Groups of order 8

C23Elementary abelian group of type [2,2,2]8C2^38,5
C2×C4Abelian group of type [2,4]8C2xC48,2

Groups of order 9

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

Groups of order 10

C10Cyclic group101C1010,2

Groups of order 12

C12Cyclic group121C1212,2
D6Dihedral group; = C2×S3 = hexagon symmetries62+D612,4
C2×C6Abelian group of type [2,6]12C2xC612,5

Groups of order 14

C14Cyclic group141C1414,2

Groups of order 15

C15Cyclic group151C1515,1

Groups of order 16

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 18

C18Cyclic group181C1818,2
C3×C6Abelian group of type [3,6]18C3xC618,5
C3×S3Direct product of C3 and S3; = U2(𝔽2)62C3xS318,3

Groups of order 20

C20Cyclic group201C2020,2
D10Dihedral group; = C2×D5102+D1020,4
C2×C10Abelian group of type [2,10]20C2xC1020,5

Groups of order 21

C21Cyclic group211C2121,2

Groups of order 22

C22Cyclic group221C2222,2

Groups of order 24

C24Cyclic group241C2424,2
C2×C12Abelian group of type [2,12]24C2xC1224,9
C22×C6Abelian group of type [2,2,6]24C2^2xC624,15
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)63+C2xA424,13
C4×S3Direct product of C4 and S3122C4xS324,5
C3×D4Direct product of C3 and D4122C3xD424,10
C22×S3Direct product of C22 and S312C2^2xS324,14
C3×Q8Direct product of C3 and Q8242C3xQ824,11
C2×Dic3Direct product of C2 and Dic324C2xDic324,7

Groups of order 25

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

Groups of order 26

C26Cyclic group261C2626,2

Groups of order 27

C33Elementary abelian group of type [3,3,3]27C3^327,5
C3×C9Abelian group of type [3,9]27C3xC927,2

Groups of order 28

C28Cyclic group281C2828,2
D14Dihedral group; = C2×D7142+D1428,3
C2×C14Abelian group of type [2,14]28C2xC1428,4

Groups of order 30

C30Cyclic group301C3030,4
C5×S3Direct product of C5 and S3152C5xS330,1
C3×D5Direct product of C3 and D5152C3xD530,2

Groups of order 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

C33Cyclic group331C3333,1

Groups of order 34

C34Cyclic group341C3434,2

Groups of order 35

C35Cyclic group351C3535,1

Groups of order 36

C36Cyclic group361C3636,2
D18Dihedral group; = C2×D9182+D1836,4
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
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)64+S3^236,10
S3×C6Direct product of C6 and S3122S3xC636,12
C3×A4Direct product of C3 and A4123C3xA436,11
C3×Dic3Direct product of C3 and Dic3122C3xDic336,6
C2×C3⋊S3Direct product of C2 and C3⋊S318C2xC3:S336,13

Groups of order 38

C38Cyclic group381C3838,2

Groups of order 39

C39Cyclic group391C3939,2

Groups of order 40

C40Cyclic group401C4040,2
C2×C20Abelian group of type [2,20]40C2xC2040,9
C22×C10Abelian group of type [2,2,10]40C2^2xC1040,14
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)104+C2xF540,12
C4×D5Direct product of C4 and D5202C4xD540,5
C5×D4Direct product of C5 and D4202C5xD440,10
C22×D5Direct product of C22 and D520C2^2xD540,13
C5×Q8Direct product of C5 and Q8402C5xQ840,11
C2×Dic5Direct product of C2 and Dic540C2xDic540,7

Groups of order 42

C42Cyclic group421C4242,6
S3×C7Direct product of C7 and S3212S3xC742,3
C3×D7Direct product of C3 and D7212C3xD742,4
C2×C7⋊C3Direct product of C2 and C7⋊C3143C2xC7:C342,2

Groups of order 44

C44Cyclic group441C4444,2
D22Dihedral group; = C2×D11222+D2244,3
C2×C22Abelian group of type [2,22]44C2xC2244,4

Groups of order 45

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

Groups of order 46

C46Cyclic group461C4646,2

Groups of order 48

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
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetries63+C2xS448,48
C4×A4Direct product of C4 and A4123C4xA448,31
S3×D4Direct product of S3 and D4; = Aut(D12) = Hol(C12)124+S3xD448,38
C22×A4Direct product of C22 and A412C2^2xA448,49
C2×SL2(𝔽3)Direct product of C2 and SL2(𝔽3)16C2xSL(2,3)48,32
S3×C8Direct product of C8 and S3242S3xC848,4
C3×D8Direct product of C3 and D8242C3xD848,25
C6×D4Direct product of C6 and D424C6xD448,45
S3×Q8Direct product of S3 and Q8244-S3xQ848,40
C2×D12Direct product of C2 and D1224C2xD1248,36
S3×C23Direct product of C23 and S324S3xC2^348,51
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
C4×Dic3Direct product of C4 and Dic348C4xDic348,11
C2×Dic6Direct product of C2 and Dic648C2xDic648,34
C22×Dic3Direct product of C22 and Dic348C2^2xDic348,42
S3×C2×C4Direct product of C2×C4 and S324S3xC2xC448,35
C2×C3⋊D4Direct product of C2 and C3⋊D424C2xC3:D448,43
C3×C4○D4Direct product of C3 and C4○D4242C3xC4oD448,47
C3×C22⋊C4Direct product of C3 and C22⋊C424C3xC2^2:C448,21
C2×C3⋊C8Direct product of C2 and C3⋊C848C2xC3:C848,9
C3×C4⋊C4Direct product of C3 and C4⋊C448C3xC4:C448,22

Groups of order 49

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

Groups of order 50

C50Cyclic group501C5050,2
C5×C10Abelian group of type [5,10]50C5xC1050,5
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)102C5xD550,3

Groups of order 51

C51Cyclic group511C5151,1

Groups of order 52

C52Cyclic group521C5252,2
D26Dihedral group; = C2×D13262+D2652,4
C2×C26Abelian group of type [2,26]52C2xC2652,5

Groups of order 54

C54Cyclic group541C5454,2
C3×C18Abelian group of type [3,18]54C3xC1854,9
C32×C6Abelian group of type [3,3,6]54C3^2xC654,15
S3×C9Direct product of C9 and S3182S3xC954,4
C3×D9Direct product of C3 and D9182C3xD954,3
C2×He3Direct product of C2 and He3183C2xHe354,10
S3×C32Direct product of C32 and S318S3xC3^254,12
C2×3- 1+2Direct product of C2 and 3- 1+2183C2xES-(3,1)54,11
C3×C3⋊S3Direct product of C3 and C3⋊S318C3xC3:S354,13

Groups of order 55

C55Cyclic group551C5555,2

Groups of order 56

C56Cyclic group561C5656,2
C2×C28Abelian group of type [2,28]56C2xC2856,8
C22×C14Abelian group of type [2,2,14]56C2^2xC1456,13
C4×D7Direct product of C4 and D7282C4xD756,4
C7×D4Direct product of C7 and D4282C7xD456,9
C22×D7Direct product of C22 and D728C2^2xD756,12
C7×Q8Direct product of C7 and Q8562C7xQ856,10
C2×Dic7Direct product of C2 and Dic756C2xDic756,6

Groups of order 57

C57Cyclic group571C5757,2

Groups of order 58

C58Cyclic group581C5858,2

Groups of order 60

C60Cyclic group601C6060,4
D30Dihedral group; = C2×D15302+D3060,12
C2×C30Abelian group of type [2,30]60C2xC3060,13
S3×D5Direct product of S3 and D5154+S3xD560,8
C3×F5Direct product of C3 and F5154C3xF560,6
C5×A4Direct product of C5 and A4203C5xA460,9
C6×D5Direct product of C6 and D5302C6xD560,10
S3×C10Direct product of C10 and S3302S3xC1060,11
C5×Dic3Direct product of C5 and Dic3602C5xDic360,1
C3×Dic5Direct product of C3 and Dic5602C3xDic560,2

Groups of order 62

C62Cyclic group621C6262,2

Groups of order 63

C63Cyclic group631C6363,2
C3×C21Abelian group of type [3,21]63C3xC2163,4
C3×C7⋊C3Direct product of C3 and C7⋊C3213C3xC7:C363,3

Groups of order 64

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

C65Cyclic group651C6565,1

Groups of order 66

C66Cyclic group661C6666,4
S3×C11Direct product of C11 and S3332S3xC1166,1
C3×D11Direct product of C3 and D11332C3xD1166,2

Groups of order 68

C68Cyclic group681C6868,2
D34Dihedral group; = C2×D17342+D3468,4
C2×C34Abelian group of type [2,34]68C2xC3468,5

Groups of order 69

C69Cyclic group691C6969,1

Groups of order 70

C70Cyclic group701C7070,4
C7×D5Direct product of C7 and D5352C7xD570,1
C5×D7Direct product of C5 and D7352C5xD770,2

Groups of order 72

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
C3×S4Direct product of C3 and S4123C3xS472,42
S3×A4Direct product of S3 and A4126+S3xA472,44
C6×A4Direct product of C6 and A4183C6xA472,47
S3×C12Direct product of C12 and S3242S3xC1272,27
C3×D12Direct product of C3 and D12242C3xD1272,28
S3×Dic3Direct product of S3 and Dic3244-S3xDic372,20
C3×Dic6Direct product of C3 and Dic6242C3xDic672,26
C6×Dic3Direct product of C6 and Dic324C6xDic372,29
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)242C3xSL(2,3)72,25
C4×D9Direct product of C4 and D9362C4xD972,5
D4×C9Direct product of C9 and D4362D4xC972,10
C22×D9Direct product of C22 and D936C2^2xD972,17
D4×C32Direct product of C32 and D436D4xC3^272,37
Q8×C9Direct product of C9 and Q8722Q8xC972,11
C2×Dic9Direct product of C2 and Dic972C2xDic972,7
Q8×C32Direct product of C32 and Q872Q8xC3^272,38
C2×S32Direct product of C2, S3 and S3124+C2xS3^272,46
C3×C3⋊D4Direct product of C3 and C3⋊D4122C3xC3:D472,30
C2×C32⋊C4Direct product of C2 and C32⋊C4124+C2xC3^2:C472,45
C2×C3.A4Direct product of C2 and C3.A4183C2xC3.A472,16
C3×C3⋊C8Direct product of C3 and C3⋊C8242C3xC3:C872,12
S3×C2×C6Direct product of C2×C6 and S324S3xC2xC672,48
C4×C3⋊S3Direct product of C4 and C3⋊S336C4xC3:S372,32
C22×C3⋊S3Direct product of C22 and C3⋊S336C2^2xC3:S372,49
C2×C3⋊Dic3Direct product of C2 and C3⋊Dic372C2xC3:Dic372,34

Groups of order 74

C74Cyclic group741C7474,2

Groups of order 75

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

Groups of order 76

C76Cyclic group761C7676,2
D38Dihedral group; = C2×D19382+D3876,3
C2×C38Abelian group of type [2,38]76C2xC3876,4

Groups of order 77

C77Cyclic group771C7777,1

Groups of order 78

C78Cyclic group781C7878,6
S3×C13Direct product of C13 and S3392S3xC1378,3
C3×D13Direct product of C3 and D13392C3xD1378,4
C2×C13⋊C3Direct product of C2 and C13⋊C3263C2xC13:C378,2

Groups of order 80

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
D4×D5Direct product of D4 and D5204+D4xD580,39
C4×F5Direct product of C4 and F5204C4xF580,30
C22×F5Direct product of C22 and F520C2^2xF580,50
C8×D5Direct product of C8 and D5402C8xD580,4
C5×D8Direct product of C5 and D8402C5xD880,25
Q8×D5Direct product of Q8 and D5404-Q8xD580,41
C2×D20Direct product of C2 and D2040C2xD2080,37
D4×C10Direct product of C10 and D440D4xC1080,46
C5×SD16Direct product of C5 and SD16402C5xSD1680,26
C23×D5Direct product of C23 and D540C2^3xD580,51
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
C4×Dic5Direct product of C4 and Dic580C4xDic580,11
C2×Dic10Direct product of C2 and Dic1080C2xDic1080,35
C22×Dic5Direct product of C22 and Dic580C2^2xDic580,43
C2×C4×D5Direct product of C2×C4 and D540C2xC4xD580,36
C2×C5⋊D4Direct product of C2 and C5⋊D440C2xC5:D480,44
C5×C4○D4Direct product of C5 and C4○D4402C5xC4oD480,48
C5×C22⋊C4Direct product of C5 and C22⋊C440C5xC2^2:C480,21
C2×C5⋊C8Direct product of C2 and C5⋊C880C2xC5:C880,32
C5×C4⋊C4Direct product of C5 and C4⋊C480C5xC4:C480,22
C2×C52C8Direct product of C2 and C52C880C2xC5:2C880,9

Groups of order 81

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

C82Cyclic group821C8282,2

Groups of order 84

C84Cyclic group841C8484,6
D42Dihedral group; = C2×D21422+D4284,14
C2×C42Abelian group of type [2,42]84C2xC4284,15
C2×F7Direct product of C2 and F7; = Aut(D14) = Hol(C14)146+C2xF784,7
S3×D7Direct product of S3 and D7214+S3xD784,8
C7×A4Direct product of C7 and A4283C7xA484,10
C6×D7Direct product of C6 and D7422C6xD784,12
S3×C14Direct product of C14 and S3422S3xC1484,13
C7×Dic3Direct product of C7 and Dic3842C7xDic384,3
C3×Dic7Direct product of C3 and Dic7842C3xDic784,4
C4×C7⋊C3Direct product of C4 and C7⋊C3283C4xC7:C384,2
C22×C7⋊C3Direct product of C22 and C7⋊C328C2^2xC7:C384,9

Groups of order 85

C85Cyclic group851C8585,1

Groups of order 86

C86Cyclic group861C8686,2

Groups of order 87

C87Cyclic group871C8787,1

Groups of order 88

C88Cyclic group881C8888,2
C2×C44Abelian group of type [2,44]88C2xC4488,8
C22×C22Abelian group of type [2,2,22]88C2^2xC2288,12
C4×D11Direct product of C4 and D11442C4xD1188,4
D4×C11Direct product of C11 and D4442D4xC1188,9
C22×D11Direct product of C22 and D1144C2^2xD1188,11
Q8×C11Direct product of C11 and Q8882Q8xC1188,10
C2×Dic11Direct product of C2 and Dic1188C2xDic1188,6

Groups of order 90

C90Cyclic group901C9090,4
C3×C30Abelian group of type [3,30]90C3xC3090,10
S3×C15Direct product of C15 and S3302S3xC1590,6
C3×D15Direct product of C3 and D15302C3xD1590,7
C5×D9Direct product of C5 and D9452C5xD990,1
C9×D5Direct product of C9 and D5452C9xD590,2
C32×D5Direct product of C32 and D545C3^2xD590,5
C5×C3⋊S3Direct product of C5 and C3⋊S345C5xC3:S390,8

Groups of order 91

C91Cyclic group911C9191,1

Groups of order 92

C92Cyclic group921C9292,2
D46Dihedral group; = C2×D23462+D4692,3
C2×C46Abelian group of type [2,46]92C2xC4692,4

Groups of order 93

C93Cyclic group931C9393,2

Groups of order 94

C94Cyclic group941C9494,2

Groups of order 95

C95Cyclic group951C9595,1

Groups of order 96

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
C4×S4Direct product of C4 and S4123C4xS496,186
D4×A4Direct product of D4 and A4126+D4xA496,197
C22×S4Direct product of C22 and S412C2^2xS496,226
C2×GL2(𝔽3)Direct product of C2 and GL2(𝔽3)16C2xGL(2,3)96,189
C8×A4Direct product of C8 and A4243C8xA496,73
S3×D8Direct product of S3 and D8244+S3xD896,117
Q8×A4Direct product of Q8 and A4246-Q8xA496,199
C23×A4Direct product of C23 and A424C2^3xA496,228
S3×SD16Direct product of S3 and SD16244S3xSD1696,120
S3×M4(2)Direct product of S3 and M4(2)244S3xM4(2)96,113
C3×2+ 1+4Direct product of C3 and 2+ 1+4244C3xES+(2,2)96,224
C4×SL2(𝔽3)Direct product of C4 and SL2(𝔽3)32C4xSL(2,3)96,69
C2×CSU2(𝔽3)Direct product of C2 and CSU2(𝔽3)32C2xCSU(2,3)96,188
C22×SL2(𝔽3)Direct product of C22 and SL2(𝔽3)32C2^2xSL(2,3)96,198
C6×D8Direct product of C6 and D848C6xD896,179
S3×C16Direct product of C16 and S3482S3xC1696,4
C3×D16Direct product of C3 and D16482C3xD1696,61
C4×D12Direct product of C4 and D1248C4xD1296,80
C2×D24Direct product of C2 and D2448C2xD2496,110
D4×C12Direct product of C12 and D448D4xC1296,165
S3×Q16Direct product of S3 and Q16484-S3xQ1696,124
S3×C42Direct product of C42 and S348S3xC4^296,78
S3×C24Direct product of C24 and S348S3xC2^496,230
C3×SD32Direct product of C3 and SD32482C3xSD3296,62
D4×Dic3Direct product of D4 and Dic348D4xDic396,141
C6×SD16Direct product of C6 and SD1648C6xSD1696,180
C22×D12Direct product of C22 and D1248C2^2xD1296,207
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
C8×Dic3Direct product of C8 and Dic396C8xDic396,20
C4×Dic6Direct product of C4 and Dic696C4xDic696,75
Q8×Dic3Direct product of Q8 and Dic396Q8xDic396,152
C2×Dic12Direct product of C2 and Dic1296C2xDic1296,112
C22×Dic6Direct product of C22 and Dic696C2^2xDic696,205
C23×Dic3Direct product of C23 and Dic396C2^3xDic396,218
C2×C42⋊C3Direct product of C2 and C42⋊C3123C2xC4^2:C396,68
C2×C22⋊A4Direct product of C2 and C22⋊A412C2xC2^2:A496,229
C2×C4×A4Direct product of C2×C4 and A424C2xC4xA496,196
C2×S3×D4Direct product of C2, S3 and D424C2xS3xD496,209
C3×C4≀C2Direct product of C3 and C4≀C2242C3xC4wrC296,54
C2×A4⋊C4Direct product of C2 and A4⋊C424C2xA4:C496,194
S3×C4○D4Direct product of S3 and C4○D4244S3xC4oD496,215
C3×C23⋊C4Direct product of C3 and C23⋊C4244C3xC2^3:C496,49
S3×C22⋊C4Direct product of S3 and C22⋊C424S3xC2^2:C496,87
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
C2×C4.A4Direct product of C2 and C4.A432C2xC4.A496,200
S3×C2×C8Direct product of C2×C8 and S348S3xC2xC896,106
D4×C2×C6Direct product of C2×C6 and D448D4xC2xC696,221
S3×C4⋊C4Direct product of S3 and C4⋊C448S3xC4:C496,98
C2×S3×Q8Direct product of C2, S3 and Q848C2xS3xQ896,212
C4×C3⋊D4Direct product of C4 and C3⋊D448C4xC3:D496,135
C2×C8⋊S3Direct product of C2 and C8⋊S348C2xC8:S396,107
C2×D6⋊C4Direct product of C2 and D6⋊C448C2xD6:C496,134
C2×D4⋊S3Direct product of C2 and D4⋊S348C2xD4:S396,138
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
S3×C22×C4Direct product of C22×C4 and S348S3xC2^2xC496,206
C2×C24⋊C2Direct product of C2 and C24⋊C248C2xC24:C296,109
C2×C4○D12Direct product of C2 and C4○D1248C2xC4oD1296,208
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
C2×D4.S3Direct product of C2 and D4.S348C2xD4.S396,140
C2×C6.D4Direct product of C2 and C6.D448C2xC6.D496,159
C22×C3⋊D4Direct product of C22 and C3⋊D448C2^2xC3:D496,219
C3×C22⋊Q8Direct product of C3 and C22⋊Q848C3xC2^2:Q896,169
C2×D42S3Direct product of C2 and D42S348C2xD4:2S396,210
C3×C42⋊C2Direct product of C3 and C42⋊C248C3xC4^2:C296,164
C2×Q82S3Direct product of C2 and Q82S348C2xQ8:2S396,148
C2×Q83S3Direct product of C2 and Q83S348C2xQ8:3S396,213
C3×C4.4D4Direct product of C3 and C4.4D448C3xC4.4D496,171
C3×C8.C22Direct product of C3 and C8.C22484C3xC8.C2^296,184
C2×C4.Dic3Direct product of C2 and C4.Dic348C2xC4.Dic396,128
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
C4×C3⋊C8Direct product of C4 and C3⋊C896C4xC3:C896,9
C3×C4⋊C8Direct product of C3 and C4⋊C896C3xC4:C896,55
C6×C4⋊C4Direct product of C6 and C4⋊C496C6xC4:C496,163
C2×C3⋊C16Direct product of C2 and C3⋊C1696C2xC3:C1696,18
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
C22×C3⋊C8Direct product of C22 and C3⋊C896C2^2xC3:C896,127
C2×C4×Dic3Direct product of C2×C4 and Dic396C2xC4xDic396,129
C2×C3⋊Q16Direct product of C2 and C3⋊Q1696C2xC3:Q1696,150
C2×C4⋊Dic3Direct product of C2 and C4⋊Dic396C2xC4:Dic396,132
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
C2×Dic3⋊C4Direct product of C2 and Dic3⋊C496C2xDic3:C496,130
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 98

C98Cyclic group981C9898,2
C7×C14Abelian group of type [7,14]98C7xC1498,5
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)142C7xD798,3

Groups of order 99

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

Groups of order 100

C100Cyclic group1001C100100,2
D50Dihedral group; = C2×D25502+D50100,4
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
D52Direct product of D5 and D5104+D5^2100,13
C5×F5Direct product of C5 and F5204C5xF5100,9
D5×C10Direct product of C10 and D5202D5xC10100,14
C5×Dic5Direct product of C5 and Dic5202C5xDic5100,6
C2×C5⋊D5Direct product of C2 and C5⋊D550C2xC5:D5100,15

Groups of order 102

C102Cyclic group1021C102102,4
S3×C17Direct product of C17 and S3512S3xC17102,1
C3×D17Direct product of C3 and D17512C3xD17102,2

Groups of order 104

C104Cyclic group1041C104104,2
C2×C52Abelian group of type [2,52]104C2xC52104,9
C22×C26Abelian group of type [2,2,26]104C2^2xC26104,14
C4×D13Direct product of C4 and D13522C4xD13104,5
D4×C13Direct product of C13 and D4522D4xC13104,10
C22×D13Direct product of C22 and D1352C2^2xD13104,13
Q8×C13Direct product of C13 and Q81042Q8xC13104,11
C2×Dic13Direct product of C2 and Dic13104C2xDic13104,7
C2×C13⋊C4Direct product of C2 and C13⋊C4264+C2xC13:C4104,12

Groups of order 105

C105Cyclic group1051C105105,2
C5×C7⋊C3Direct product of C5 and C7⋊C3353C5xC7:C3105,1

Groups of order 106

C106Cyclic group1061C106106,2

Groups of order 108

C108Cyclic group1081C108108,2
D54Dihedral group; = C2×D27542+D54108,4
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
S3×D9Direct product of S3 and D9184+S3xD9108,16
C9×A4Direct product of C9 and A4363C9xA4108,18
C6×D9Direct product of C6 and D9362C6xD9108,23
S3×C18Direct product of C18 and S3362S3xC18108,24
C4×He3Direct product of C4 and He3363C4xHe3108,13
C32×A4Direct product of C32 and A436C3^2xA4108,41
C3×Dic9Direct product of C3 and Dic9362C3xDic9108,6
C9×Dic3Direct product of C9 and Dic3362C9xDic3108,7
C22×He3Direct product of C22 and He336C2^2xHe3108,30
C32×Dic3Direct product of C32 and Dic336C3^2xDic3108,32
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
C3×S32Direct product of C3, S3 and S3124C3xS3^2108,38
C3×C32⋊C4Direct product of C3 and C32⋊C4124C3xC3^2:C4108,36
C2×C9⋊C6Direct product of C2 and C9⋊C6; = Aut(D18) = Hol(C18)186+C2xC9:C6108,26
S3×C3⋊S3Direct product of S3 and C3⋊S318S3xC3:S3108,39
C2×C32⋊C6Direct product of C2 and C32⋊C6186+C2xC3^2:C6108,25
C2×He3⋊C2Direct product of C2 and He3⋊C2183C2xHe3:C2108,28
S3×C3×C6Direct product of C3×C6 and S336S3xC3xC6108,42
C6×C3⋊S3Direct product of C6 and C3⋊S336C6xC3:S3108,43
C3×C3⋊Dic3Direct product of C3 and C3⋊Dic336C3xC3:Dic3108,33
C2×C9⋊S3Direct product of C2 and C9⋊S354C2xC9:S3108,27
C3×C3.A4Direct product of C3 and C3.A454C3xC3.A4108,20
C2×C33⋊C2Direct product of C2 and C33⋊C254C2xC3^3:C2108,44

Groups of order 110

C110Cyclic group1101C110110,6
D5×C11Direct product of C11 and D5552D5xC11110,3
C5×D11Direct product of C5 and D11552C5xD11110,4
C2×C11⋊C5Direct product of C2 and C11⋊C5225C2xC11:C5110,2

Groups of order 111

C111Cyclic group1111C111111,2

Groups of order 112

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
C2×F8Direct product of C2 and F8147+C2xF8112,41
D4×D7Direct product of D4 and D7284+D4xD7112,31
C8×D7Direct product of C8 and D7562C8xD7112,3
C7×D8Direct product of C7 and D8562C7xD8112,24
Q8×D7Direct product of Q8 and D7564-Q8xD7112,33
C2×D28Direct product of C2 and D2856C2xD28112,29
D4×C14Direct product of C14 and D456D4xC14112,38
C7×SD16Direct product of C7 and SD16562C7xSD16112,25
C23×D7Direct product of C23 and D756C2^3xD7112,42
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
C4×Dic7Direct product of C4 and Dic7112C4xDic7112,10
C2×Dic14Direct product of C2 and Dic14112C2xDic14112,27
C22×Dic7Direct product of C22 and Dic7112C2^2xDic7112,35
C2×C4×D7Direct product of C2×C4 and D756C2xC4xD7112,28
C2×C7⋊D4Direct product of C2 and C7⋊D456C2xC7:D4112,36
C7×C4○D4Direct product of C7 and C4○D4562C7xC4oD4112,40
C7×C22⋊C4Direct product of C7 and C22⋊C456C7xC2^2:C4112,20
C2×C7⋊C8Direct product of C2 and C7⋊C8112C2xC7:C8112,8
C7×C4⋊C4Direct product of C7 and C4⋊C4112C7xC4:C4112,21

Groups of order 114

C114Cyclic group1141C114114,6
S3×C19Direct product of C19 and S3572S3xC19114,3
C3×D19Direct product of C3 and D19572C3xD19114,4
C2×C19⋊C3Direct product of C2 and C19⋊C3383C2xC19:C3114,2

Groups of order 115

C115Cyclic group1151C115115,1

Groups of order 116

C116Cyclic group1161C116116,2
D58Dihedral group; = C2×D29582+D58116,4
C2×C58Abelian group of type [2,58]116C2xC58116,5

Groups of order 117

C117Cyclic group1171C117117,2
C3×C39Abelian group of type [3,39]117C3xC39117,4
C3×C13⋊C3Direct product of C3 and C13⋊C3393C3xC13:C3117,3

Groups of order 118

C118Cyclic group1181C118118,2

Groups of order 119

C119Cyclic group1191C119119,1

Groups of order 120

C120Cyclic group1201C120120,4
C2×C60Abelian group of type [2,60]120C2xC60120,31
C22×C30Abelian group of type [2,2,30]120C2^2xC30120,47
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetries103+C2xA5120,35
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)158+S3xF5120,36
C5×S4Direct product of C5 and S4203C5xS4120,37
D5×A4Direct product of D5 and A4206+D5xA4120,39
C6×F5Direct product of C6 and F5304C6xF5120,40
C10×A4Direct product of C10 and A4303C10xA4120,43
C5×SL2(𝔽3)Direct product of C5 and SL2(𝔽3)402C5xSL(2,3)120,15
S3×C20Direct product of C20 and S3602S3xC20120,22
D5×C12Direct product of C12 and D5602D5xC12120,17
C3×D20Direct product of C3 and D20602C3xD20120,18
C5×D12Direct product of C5 and D12602C5xD12120,23
C4×D15Direct product of C4 and D15602C4xD15120,27
D4×C15Direct product of C15 and D4602D4xC15120,32
D5×Dic3Direct product of D5 and Dic3604-D5xDic3120,8
S3×Dic5Direct product of S3 and Dic5604-S3xDic5120,9
C22×D15Direct product of C22 and D1560C2^2xD15120,46
Q8×C15Direct product of C15 and Q81202Q8xC15120,33
C6×Dic5Direct product of C6 and Dic5120C6xDic5120,19
C5×Dic6Direct product of C5 and Dic61202C5xDic6120,21
C3×Dic10Direct product of C3 and Dic101202C3xDic10120,16
C10×Dic3Direct product of C10 and Dic3120C10xDic3120,24
C2×Dic15Direct product of C2 and Dic15120C2xDic15120,29
C2×S3×D5Direct product of C2, S3 and D5304+C2xS3xD5120,42
C2×C3⋊F5Direct product of C2 and C3⋊F5304C2xC3:F5120,41
D5×C2×C6Direct product of C2×C6 and D560D5xC2xC6120,44
S3×C2×C10Direct product of C2×C10 and S360S3xC2xC10120,45
C3×C5⋊D4Direct product of C3 and C5⋊D4602C3xC5:D4120,20
C5×C3⋊D4Direct product of C5 and C3⋊D4602C5xC3:D4120,25
C5×C3⋊C8Direct product of C5 and C3⋊C81202C5xC3:C8120,1
C3×C5⋊C8Direct product of C3 and C5⋊C81204C3xC5:C8120,6
C3×C52C8Direct product of C3 and C52C81202C3xC5:2C8120,2