Soluble groups

A group is soluble or solvable if there are nested normal subgroups Ni◃G

{1}=N0 < N1 < N2 <...< Nk = G
with all successive quotients Ni+1/Ni abelian. All abelian, nilpotent, monomial, super​soluble, metabelian groups, p-groups, Z-groups and A-groups are soluble, and the class of soluble groups is closed under subgroups, quotients and extensions. Among all groups of order <120 only A5 is not soluble. See also non-soluble groups.

Groups of order 1

dρLabelID
C1Trivial group11+C11,1

Groups of order 2

dρLabelID
C2Cyclic group21+C22,1

Groups of order 3

dρLabelID
C3Cyclic group; = A3 = triangle rotations31C33,1

Groups of order 4

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

Groups of order 5

dρLabelID
C5Cyclic group; = pentagon rotations51C55,1

Groups of order 6

dρLabelID
C6Cyclic group; = hexagon rotations61C66,2
S3Symmetric group on 3 letters; = D3 = GL2(F2) = triangle symmetries = 1st non-abelian group32+S36,1

Groups of order 7

dρLabelID
C7Cyclic group71C77,1

Groups of order 8

dρLabelID
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
C2xC4Abelian group of type [2,4]8C2xC48,2

Groups of order 9

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

Groups of order 10

dρLabelID
C10Cyclic group101C1010,2
D5Dihedral group; = pentagon symmetries52+D510,1

Groups of order 11

dρLabelID
C11Cyclic group111C1111,1

Groups of order 12

dρLabelID
C12Cyclic group121C1212,2
A4Alternating group on 4 letters; = PSL2(F3) = L2(3) = tetrahedron rotations43+A412,3
D6Dihedral group; = C2xS3 = hexagon symmetries62+D612,4
Dic3Dicyclic group; = C3:C4122-Dic312,1
C2xC6Abelian group of type [2,6]12C2xC612,5

Groups of order 13

dρLabelID
C13Cyclic group131C1313,1

Groups of order 14

dρLabelID
C14Cyclic group141C1414,2
D7Dihedral group72+D714,1

Groups of order 15

dρLabelID
C15Cyclic group151C1515,1

Groups of order 16

dρLabelID
C16Cyclic group161C1616,1
D8Dihedral group82+D816,7
Q16Generalised quaternion group; = C8.C2 = Dic4162-Q1616,9
SD16Semidihedral group; = Q8:C2 = QD1682SD1616,8
M4(2)Modular maximal-cyclic group; = C8:3C282M4(2)16,6
C4oD4Pauli 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
C2xC8Abelian group of type [2,8]16C2xC816,5
C22xC4Abelian group of type [2,2,4]16C2^2xC416,10
C2xD4Direct product of C2 and D48C2xD416,11
C2xQ8Direct product of C2 and Q816C2xQ816,12

Groups of order 17

dρLabelID
C17Cyclic group171C1717,1

Groups of order 18

dρLabelID
C18Cyclic group181C1818,2
D9Dihedral group92+D918,1
C3:S3The semidirect product of C3 and S3 acting via S3/C3=C29C3:S318,4
C3xC6Abelian group of type [3,6]18C3xC618,5
C3xS3Direct product of C3 and S3; = U2(F2)62C3xS318,3

Groups of order 19

dρLabelID
C19Cyclic group191C1919,1

Groups of order 20

dρLabelID
C20Cyclic group201C2020,2
D10Dihedral group; = C2xD5102+D1020,4
F5Frobenius group; = C5:C4 = AGL1(F5) = Aut(D5) = Hol(C5) = Sz(2)54+F520,3
Dic5Dicyclic group; = C5:2C4202-Dic520,1
C2xC10Abelian group of type [2,10]20C2xC1020,5

Groups of order 21

dρLabelID
C21Cyclic group211C2121,2
C7:C3The semidirect product of C7 and C3 acting faithfully73C7:C321,1

Groups of order 22

dρLabelID
C22Cyclic group221C2222,2
D11Dihedral group112+D1122,1

Groups of order 23

dρLabelID
C23Cyclic group231C2323,1

Groups of order 24

dρLabelID
C24Cyclic group241C2424,2
S4Symmetric group on 4 letters; = PGL2(F3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotations43+S424,12
D12Dihedral group122+D1224,6
Dic6Dicyclic group; = C3:Q8242-Dic624,4
SL2(F3)Special linear group on F32; = Q8:C3 = 2T = <2,3,3> = 1st non-monomial group82-SL(2,3)24,3
C3:D4The semidirect product of C3 and D4 acting via D4/C22=C2122C3:D424,8
C3:C8The semidirect product of C3 and C8 acting via C8/C4=C2242C3:C824,1
C2xC12Abelian group of type [2,12]24C2xC1224,9
C22xC6Abelian group of type [2,2,6]24C2^2xC624,15
C2xA4Direct product of C2 and A4; = AΣL1(F8)63+C2xA424,13
C4xS3Direct product of C4 and S3122C4xS324,5
C3xD4Direct product of C3 and D4122C3xD424,10
C22xS3Direct product of C22 and S312C2^2xS324,14
C3xQ8Direct product of C3 and Q8242C3xQ824,11
C2xDic3Direct product of C2 and Dic324C2xDic324,7

Groups of order 25

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

Groups of order 26

dρLabelID
C26Cyclic group261C2626,2
D13Dihedral group132+D1326,1

Groups of order 27

dρLabelID
C27Cyclic group271C2727,1
He3Heisenberg group; = C32:C3 = 3+ 1+293He327,3
3- 1+2Extraspecial group93ES-(3,1)27,4
C33Elementary abelian group of type [3,3,3]27C3^327,5
C3xC9Abelian group of type [3,9]27C3xC927,2

Groups of order 28

dρLabelID
C28Cyclic group281C2828,2
D14Dihedral group; = C2xD7142+D1428,3
Dic7Dicyclic group; = C7:C4282-Dic728,1
C2xC14Abelian group of type [2,14]28C2xC1428,4

Groups of order 29

dρLabelID
C29Cyclic group291C2929,1

Groups of order 30

dρLabelID
C30Cyclic group301C3030,4
D15Dihedral group152+D1530,3
C5xS3Direct product of C5 and S3152C5xS330,1
C3xD5Direct product of C3 and D5152C3xD530,2

Groups of order 31

dρLabelID
C31Cyclic group311C3131,1

Groups of order 32

dρLabelID
C32Cyclic group321C3232,1
D16Dihedral group162+D1632,18
Q32Generalised quaternion group; = C16.C2 = Dic8322-Q3232,20
2+ 1+4Extraspecial group; = D4oD484+ES+(2,2)32,49
SD32Semidihedral group; = C16:2C2 = QD32162SD3232,19
2- 1+4Gamma matrices = Extraspecial group; = D4oQ8164-ES-(2,2)32,50
M5(2)Modular maximal-cyclic group; = C16:3C2162M5(2)32,17
C4wrC2Wreath product of C4 by C282C4wrC232,11
C22wrC2Wreath product of C22 by C28C2^2wrC232,27
C8oD4Central product of C8 and D4162C8oD432,38
C4oD8Central 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
C4:1D4The 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
C42:2C22nd 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
C4xC8Abelian group of type [4,8]32C4xC832,3
C2xC16Abelian group of type [2,16]32C2xC1632,16
C2xC42Abelian group of type [2,4,4]32C2xC4^232,21
C22xC8Abelian group of type [2,2,8]32C2^2xC832,36
C23xC4Abelian group of type [2,2,2,4]32C2^3xC432,45
C4xD4Direct product of C4 and D416C4xD432,25
C2xD8Direct product of C2 and D816C2xD832,39
C2xSD16Direct product of C2 and SD1616C2xSD1632,40
C22xD4Direct product of C22 and D416C2^2xD432,46
C2xM4(2)Direct product of C2 and M4(2)16C2xM4(2)32,37
C4xQ8Direct product of C4 and Q832C4xQ832,26
C2xQ16Direct product of C2 and Q1632C2xQ1632,41
C22xQ8Direct product of C22 and Q832C2^2xQ832,47
C2xC4oD4Direct product of C2 and C4oD416C2xC4oD432,48
C2xC22:C4Direct product of C2 and C22:C416C2xC2^2:C432,22
C2xC4:C4Direct product of C2 and C4:C432C2xC4:C432,23

Groups of order 33

dρLabelID
C33Cyclic group331C3333,1

Groups of order 34

dρLabelID
C34Cyclic group341C3434,2
D17Dihedral group172+D1734,1

Groups of order 35

dρLabelID
C35Cyclic group351C3535,1

Groups of order 36

dρLabelID
C36Cyclic group361C3636,2
D18Dihedral group; = C2xD9182+D1836,4
Dic9Dicyclic group; = C9:C4362-Dic936,1
C32:C4The semidirect product of C32 and C4 acting faithfully64+C3^2:C436,9
C3:Dic3The semidirect product of C3 and Dic3 acting via Dic3/C6=C236C3:Dic336,7
C3.A4The central extension by C3 of A4183C3.A436,3
C62Abelian group of type [6,6]36C6^236,14
C2xC18Abelian group of type [2,18]36C2xC1836,5
C3xC12Abelian group of type [3,12]36C3xC1236,8
S32Direct product of S3 and S3; = Spin+4(F2) = Hol(S3)64+S3^236,10
S3xC6Direct product of C6 and S3122S3xC636,12
C3xA4Direct product of C3 and A4123C3xA436,11
C3xDic3Direct product of C3 and Dic3122C3xDic336,6
C2xC3:S3Direct product of C2 and C3:S318C2xC3:S336,13

Groups of order 37

dρLabelID
C37Cyclic group371C3737,1

Groups of order 38

dρLabelID
C38Cyclic group381C3838,2
D19Dihedral group192+D1938,1

Groups of order 39

dρLabelID
C39Cyclic group391C3939,2
C13:C3The semidirect product of C13 and C3 acting faithfully133C13:C339,1

Groups of order 40

dρLabelID
C40Cyclic group401C4040,2
D20Dihedral group202+D2040,6
Dic10Dicyclic group; = C5:Q8402-Dic1040,4
C5:D4The semidirect product of C5 and D4 acting via D4/C22=C2202C5:D440,8
C5:C8The semidirect product of C5 and C8 acting via C8/C2=C4404-C5:C840,3
C5:2C8The semidirect product of C5 and C8 acting via C8/C4=C2402C5:2C840,1
C2xC20Abelian group of type [2,20]40C2xC2040,9
C22xC10Abelian group of type [2,2,10]40C2^2xC1040,14
C2xF5Direct product of C2 and F5; = Aut(D10) = Hol(C10)104+C2xF540,12
C4xD5Direct product of C4 and D5202C4xD540,5
C5xD4Direct product of C5 and D4202C5xD440,10
C22xD5Direct product of C22 and D520C2^2xD540,13
C5xQ8Direct product of C5 and Q8402C5xQ840,11
C2xDic5Direct product of C2 and Dic540C2xDic540,7

Groups of order 41

dρLabelID
C41Cyclic group411C4141,1

Groups of order 42

dρLabelID
C42Cyclic group421C4242,6
D21Dihedral group212+D2142,5
F7Frobenius group; = C7:C6 = AGL1(F7) = Aut(D7) = Hol(C7)76+F742,1
S3xC7Direct product of C7 and S3212S3xC742,3
C3xD7Direct product of C3 and D7212C3xD742,4
C2xC7:C3Direct product of C2 and C7:C3143C2xC7:C342,2

Groups of order 43

dρLabelID
C43Cyclic group431C4343,1

Groups of order 44

dρLabelID
C44Cyclic group441C4444,2
D22Dihedral group; = C2xD11222+D2244,3
Dic11Dicyclic group; = C11:C4442-Dic1144,1
C2xC22Abelian group of type [2,22]44C2xC2244,4

Groups of order 45

dρLabelID
C45Cyclic group451C4545,1
C3xC15Abelian group of type [3,15]45C3xC1545,2

Groups of order 46

dρLabelID
C46Cyclic group461C4646,2
D23Dihedral group232+D2346,1

Groups of order 47

dρLabelID
C47Cyclic group471C4747,1

Groups of order 48

dρLabelID
C48Cyclic group481C4848,2
D24Dihedral group242+D2448,7
Dic12Dicyclic group; = C3:1Q16482-Dic1248,8
GL2(F3)General linear group on F32; = Q8:S3 = Aut(C32)82GL(2,3)48,29
CSU2(F3)Conformal special unitary group on F32; = Q8.S3 = 2O = <2,3,4>162-CSU(2,3)48,28
C4oD12Central product of C4 and D12242C4oD1248,37
A4:C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(Z/4Z)123A4:C448,30
C42:C3The semidirect product of C42 and C3 acting faithfully123C4^2:C348,3
C22:A4The semidirect product of C22 and A4 acting via A4/C22=C312C2^2:A448,50
D6:C4The semidirect product of D6 and C4 acting via C4/C2=C224D6:C448,14
D4:S3The semidirect product of D4 and S3 acting via S3/C3=C2244+D4:S348,15
C8:S33rd semidirect product of C8 and S3 acting via S3/C3=C2242C8:S348,5
C24:C22nd semidirect product of C24 and C2 acting faithfully242C24:C248,6
D4:2S3The semidirect product of D4 and S3 acting through Inn(D4)244-D4:2S348,39
Q8:2S3The semidirect product of Q8 and S3 acting via S3/C3=C2244+Q8:2S348,17
Q8:3S3The semidirect product of Q8 and S3 acting through Inn(Q8)244+Q8:3S348,41
C3:C16The semidirect product of C3 and C16 acting via C16/C8=C2482C3:C1648,1
C4:Dic3The semidirect product of C4 and Dic3 acting via Dic3/C6=C248C4:Dic348,13
C3:Q16The semidirect product of C3 and Q16 acting via Q16/Q8=C2484-C3:Q1648,18
Dic3:C4The semidirect product of Dic3 and C4 acting via C4/C2=C248Dic3:C448,12
C4.A4The central extension by C4 of A4162C4.A448,33
D4.S3The non-split extension by D4 of S3 acting via S3/C3=C2244-D4.S348,16
C4.Dic3The non-split extension by C4 of Dic3 acting via Dic3/C6=C2242C4.Dic348,10
C6.D47th non-split extension by C6 of D4 acting via D4/C22=C224C6.D448,19
C4xC12Abelian group of type [4,12]48C4xC1248,20
C2xC24Abelian group of type [2,24]48C2xC2448,23
C23xC6Abelian group of type [2,2,2,6]48C2^3xC648,52
C22xC12Abelian group of type [2,2,12]48C2^2xC1248,44
C2xS4Direct product of C2 and S4; = O3(F3) = cube/octahedron symmetries63+C2xS448,48
C4xA4Direct product of C4 and A4123C4xA448,31
S3xD4Direct product of S3 and D4; = Aut(D12) = Hol(C12)124+S3xD448,38
C22xA4Direct product of C22 and A412C2^2xA448,49
C2xSL2(F3)Direct product of C2 and SL2(F3)16C2xSL(2,3)48,32
S3xC8Direct product of C8 and S3242S3xC848,4
C3xD8Direct product of C3 and D8242C3xD848,25
C6xD4Direct product of C6 and D424C6xD448,45
S3xQ8Direct product of S3 and Q8244-S3xQ848,40
C2xD12Direct product of C2 and D1224C2xD1248,36
S3xC23Direct product of C23 and S324S3xC2^348,51
C3xSD16Direct product of C3 and SD16242C3xSD1648,26
C3xM4(2)Direct product of C3 and M4(2)242C3xM4(2)48,24
C6xQ8Direct product of C6 and Q848C6xQ848,46
C3xQ16Direct product of C3 and Q16482C3xQ1648,27
C4xDic3Direct product of C4 and Dic348C4xDic348,11
C2xDic6Direct product of C2 and Dic648C2xDic648,34
C22xDic3Direct product of C22 and Dic348C2^2xDic348,42
S3xC2xC4Direct product of C2xC4 and S324S3xC2xC448,35
C2xC3:D4Direct product of C2 and C3:D424C2xC3:D448,43
C3xC4oD4Direct product of C3 and C4oD4242C3xC4oD448,47
C3xC22:C4Direct product of C3 and C22:C424C3xC2^2:C448,21
C2xC3:C8Direct product of C2 and C3:C848C2xC3:C848,9
C3xC4:C4Direct product of C3 and C4:C448C3xC4:C448,22

Groups of order 49

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

Groups of order 50

dρLabelID
C50Cyclic group501C5050,2
D25Dihedral group252+D2550,1
C5:D5The semidirect product of C5 and D5 acting via D5/C5=C225C5:D550,4
C5xC10Abelian group of type [5,10]50C5xC1050,5
C5xD5Direct product of C5 and D5; = AΣL1(F25)102C5xD550,3

Groups of order 51

dρLabelID
C51Cyclic group511C5151,1

Groups of order 52

dρLabelID
C52Cyclic group521C5252,2
D26Dihedral group; = C2xD13262+D2652,4
Dic13Dicyclic group; = C13:2C4522-Dic1352,1
C13:C4The semidirect product of C13 and C4 acting faithfully134+C13:C452,3
C2xC26Abelian group of type [2,26]52C2xC2652,5

Groups of order 53

dρLabelID
C53Cyclic group531C5353,1

Groups of order 54

dρLabelID
C54Cyclic group541C5454,2
D27Dihedral group272+D2754,1
C9:C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)96+C9:C654,6
C32:C6The semidirect product of C32 and C6 acting faithfully96+C3^2:C654,5
He3:C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)93He3:C254,8
C9:S3The semidirect product of C9 and S3 acting via S3/C3=C227C9:S354,7
C33:C23rd semidirect product of C33 and C2 acting faithfully27C3^3:C254,14
C3xC18Abelian group of type [3,18]54C3xC1854,9
C32xC6Abelian group of type [3,3,6]54C3^2xC654,15
S3xC9Direct product of C9 and S3182S3xC954,4
C3xD9Direct product of C3 and D9182C3xD954,3
C2xHe3Direct product of C2 and He3183C2xHe354,10
S3xC32Direct product of C32 and S318S3xC3^254,12
C2x3- 1+2Direct product of C2 and 3- 1+2183C2xES-(3,1)54,11
C3xC3:S3Direct product of C3 and C3:S318C3xC3:S354,13

Groups of order 55

dρLabelID
C55Cyclic group551C5555,2
C11:C5The semidirect product of C11 and C5 acting faithfully115C11:C555,1

Groups of order 56

dρLabelID
C56Cyclic group561C5656,2
D28Dihedral group282+D2856,5
F8Frobenius group; = C23:C7 = AGL1(F8)87+F856,11
Dic14Dicyclic group; = C7:Q8562-Dic1456,3
C7:D4The semidirect product of C7 and D4 acting via D4/C22=C2282C7:D456,7
C7:C8The semidirect product of C7 and C8 acting via C8/C4=C2562C7:C856,1
C2xC28Abelian group of type [2,28]56C2xC2856,8
C22xC14Abelian group of type [2,2,14]56C2^2xC1456,13
C4xD7Direct product of C4 and D7282C4xD756,4
C7xD4Direct product of C7 and D4282C7xD456,9
C22xD7Direct product of C22 and D728C2^2xD756,12
C7xQ8Direct product of C7 and Q8562C7xQ856,10
C2xDic7Direct product of C2 and Dic756C2xDic756,6

Groups of order 57

dρLabelID
C57Cyclic group571C5757,2
C19:C3The semidirect product of C19 and C3 acting faithfully193C19:C357,1

Groups of order 58

dρLabelID
C58Cyclic group581C5858,2
D29Dihedral group292+D2958,1

Groups of order 59

dρLabelID
C59Cyclic group591C5959,1

Groups of order 60

dρLabelID
C60Cyclic group601C6060,4
D30Dihedral group; = C2xD15302+D3060,12
Dic15Dicyclic group; = C3:Dic5602-Dic1560,3
C3:F5The semidirect product of C3 and F5 acting via F5/D5=C2154C3:F560,7
C2xC30Abelian group of type [2,30]60C2xC3060,13
S3xD5Direct product of S3 and D5154+S3xD560,8
C3xF5Direct product of C3 and F5154C3xF560,6
C5xA4Direct product of C5 and A4203C5xA460,9
C6xD5Direct product of C6 and D5302C6xD560,10
S3xC10Direct product of C10 and S3302S3xC1060,11
C5xDic3Direct product of C5 and Dic3602C5xDic360,1
C3xDic5Direct product of C3 and Dic5602C3xDic560,2

Groups of order 61

dρLabelID
C61Cyclic group611C6161,1

Groups of order 62

dρLabelID
C62Cyclic group621C6262,2
D31Dihedral group312+D3162,1

Groups of order 63

dρLabelID
C63Cyclic group631C6363,2
C7:C9The semidirect product of C7 and C9 acting via C9/C3=C3633C7:C963,1
C3xC21Abelian group of type [3,21]63C3xC2163,4
C3xC7:C3Direct product of C3 and C7:C3213C3xC7:C363,3

Groups of order 64

dρLabelID
C64Cyclic group641C6464,1
D32Dihedral group322+D3264,52
Q64Generalised quaternion group; = C32.C2 = Dic16642-Q6464,54
SD64Semidihedral group; = C32:2C2 = QD64322SD6464,53
M6(2)Modular maximal-cyclic group; = C32:3C2322M6(2)64,51
C2wrC4Wreath product of C2 by C4; = AΣL1(F16)84+C2wrC464,32
C2wrC22Wreath product of C2 by C22; = Hol(C2xC4)84+C2wrC2^264,138
C8oD8Central product of C8 and D8162C8oD864,124
D4oD8Central product of D4 and D8164+D4oD864,257
D4oSD16Central product of D4 and SD16164D4oSD1664,258
Q8oM4(2)Central product of Q8 and M4(2)164Q8oM4(2)64,249
Q8oD8Central product of Q8 and D8324-Q8oD864,259
D4oC16Central product of D4 and C16322D4oC1664,185
C4oD16Central product of C4 and D16322C4oD1664,189
C8o2M4(2)Central product of C8 and M4(2)32C8o2M4(2)64,86
D4:4D43rd 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
D8:2C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
D4:5D41st 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
C42:6C43rd semidirect product of C42 and C4 acting via C4/C2=C216C4^2:6C464,20
C42:3C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
C24:3C41st 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
C23:3D42nd semidirect product of C23 and D4 acting via D4/C2=C2216C2^3:3D464,215
C23:2Q82nd 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
C8:9D43rd semidirect product of C8 and D4 acting via D4/C22=C232C8:9D464,116
C8:6D43rd 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
C8:8D42nd semidirect product of C8 and D4 acting via D4/C22=C232C8:8D464,146
C8:7D41st 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
C8:2D42nd semidirect product of C8 and D4 acting via D4/C2=C2232C8:2D464,150
C8:5D42nd semidirect product of C8 and D4 acting via D4/C4=C232C8:5D464,173
C8:4D41st semidirect product of C8 and D4 acting via D4/C4=C232C8:4D464,174
C8:3D43rd 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
D4:6D42nd 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
D4:2Q82nd semidirect product of D4 and Q8 acting via Q8/C4=C232D4:2Q864,157
Q8:5D41st semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:5D464,229
Q8:6D42nd semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:6D464,231
D4:3Q8The 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
C23:2D41st 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)/C2xC4=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
C8:2C82nd semidirect product of C8 and C8 acting via C8/C4=C264C8:2C864,15
C8:1C81st semidirect product of C8 and C8 acting via C8/C4=C264C8:1C864,16
C8:4Q83rd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:4Q864,127
C8:3Q82nd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:3Q864,179
C8:2Q81st semidirect product of C8 and Q8 acting via Q8/C4=C264C8:2Q864,181
C16:5C43rd semidirect product of C16 and C4 acting via C4/C2=C264C16:5C464,27
C16:3C41st semidirect product of C16 and C4 acting via C4/C2=C264C16:3C464,47
C16:4C42nd 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
Q8:3Q8The semidirect product of Q8 and Q8 acting through Inn(Q8)64Q8:3Q864,238
C4:2Q16The 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
C42:4C41st semidirect product of C42 and C4 acting via C4/C2=C264C4^2:4C464,57
C42:8C45th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:8C464,63
C42:5C42nd semidirect product of C42 and C4 acting via C4/C2=C264C4^2:5C464,64
C42:9C46th 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
(C22xC8):C22nd semidirect product of C22xC8 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/C2xC4=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/C2xC4=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)/C2xC4=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
C4xC16Abelian group of type [4,16]64C4xC1664,26
C2xC32Abelian group of type [2,32]64C2xC3264,50
C23xC8Abelian group of type [2,2,2,8]64C2^3xC864,246
C24xC4Abelian group of type [2,2,2,2,4]64C2^4xC464,260
C22xC16Abelian group of type [2,2,16]64C2^2xC1664,183
C22xC42Abelian group of type [2,2,4,4]64C2^2xC4^264,192
C2xC4xC8Abelian group of type [2,4,8]64C2xC4xC864,83
D42Direct product of D4 and D416D4^264,226
C2x2+ 1+4Direct product of C2 and 2+ 1+416C2xES+(2,2)64,264
C8xD4Direct product of C8 and D432C8xD464,115
C4xD8Direct product of C4 and D832C4xD864,118
D4xQ8Direct product of D4 and Q832D4xQ864,230
C2xD16Direct product of C2 and D1632C2xD1664,186
C4xSD16Direct product of C4 and SD1632C4xSD1664,119
C2xSD32Direct product of C2 and SD3232C2xSD3264,187
C22xD8Direct product of C22 and D832C2^2xD864,250
D4xC23Direct product of C23 and D432D4xC2^364,261
C4xM4(2)Direct product of C4 and M4(2)32C4xM4(2)64,85
C2xM5(2)Direct product of C2 and M5(2)32C2xM5(2)64,184
C22xSD16Direct product of C22 and SD1632C2^2xSD1664,251
C22xM4(2)Direct product of C22 and M4(2)32C2^2xM4(2)64,247
C2x2- 1+4Direct product of C2 and 2- 1+432C2xES-(2,2)64,265
Q82Direct product of Q8 and Q864Q8^264,239
C8xQ8Direct product of C8 and Q864C8xQ864,126
C4xQ16Direct product of C4 and Q1664C4xQ1664,120
C2xQ32Direct product of C2 and Q3264C2xQ3264,188
Q8xC23Direct product of C23 and Q864Q8xC2^364,262
C22xQ16Direct product of C22 and Q1664C2^2xQ1664,252
C2xC4wrC2Direct product of C2 and C4wrC216C2xC4wrC264,101
C2xC23:C4Direct product of C2 and C23:C416C2xC2^3:C464,90
C2xC8:C22Direct product of C2 and C8:C2216C2xC8:C2^264,254
C2xC4.D4Direct product of C2 and C4.D416C2xC4.D464,92
C2xC22wrC2Direct product of C2 and C22wrC216C2xC2^2wrC264,202
C2xC4xD4Direct product of C2xC4 and D432C2xC4xD464,196
C4xC4oD4Direct product of C4 and C4oD432C4xC4oD464,198
C2xC8oD4Direct product of C2 and C8oD432C2xC8oD464,248
C2xC4oD8Direct product of C2 and C4oD832C2xC4oD864,253
C2xC4:D4Direct product of C2 and C4:D432C2xC4:D464,203
C2xD4:C4Direct product of C2 and D4:C432C2xD4:C464,95
C2xC8.C4Direct product of C2 and C8.C432C2xC8.C464,110
C2xC4:1D4Direct product of C2 and C4:1D432C2xC4:1D464,211
C4xC22:C4Direct product of C4 and C22:C432C4xC2^2:C464,58
C2xC22:C8Direct product of C2 and C22:C832C2xC2^2:C864,87
C2xC22:Q8Direct product of C2 and C22:Q832C2xC2^2:Q864,204
C2xC42:C2Direct product of C2 and C42:C232C2xC4^2:C264,195
C2xC4.4D4Direct product of C2 and C4.4D432C2xC4.4D464,207
C22xC4oD4Direct product of C22 and C4oD432C2^2xC4oD464,263
C2xC8.C22Direct product of C2 and C8.C2232C2xC8.C2^264,255
C2xC42:2C2Direct product of C2 and C42:2C232C2xC4^2:2C264,209
C2xC4.10D4Direct product of C2 and C4.10D432C2xC4.10D464,93
C22xC22:C4Direct product of C22 and C22:C432C2^2xC2^2:C464,193
C2xC22.D4Direct product of C2 and C22.D432C2xC2^2.D464,205
C4xC4:C4Direct product of C4 and C4:C464C4xC4:C464,59
C2xC4:C8Direct product of C2 and C4:C864C2xC4:C864,103
C2xC4xQ8Direct product of C2xC4 and Q864C2xC4xQ864,197
C2xC4:Q8Direct product of C2 and C4:Q864C2xC4:Q864,212
C2xC8:C4Direct product of C2 and C8:C464C2xC8:C464,84
C22xC4:C4Direct product of C22 and C4:C464C2^2xC4:C464,194
C2xQ8:C4Direct product of C2 and Q8:C464C2xQ8:C464,96
C2xC2.D8Direct product of C2 and C2.D864C2xC2.D864,107
C2xC4.Q8Direct product of C2 and C4.Q864C2xC4.Q864,106
C2xC2.C42Direct product of C2 and C2.C4264C2xC2.C4^264,56
C2xC42.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
D33Dihedral group332+D3366,3
S3xC11Direct product of C11 and S3332S3xC1166,1
C3xD11Direct product of C3 and D11332C3xD1166,2

Groups of order 67

dρLabelID
C67Cyclic group671C6767,1

Groups of order 68

dρLabelID
C68Cyclic group681C6868,2
D34Dihedral group; = C2xD17342+D3468,4
Dic17Dicyclic group; = C17:2C4682-Dic1768,1
C17:C4The semidirect product of C17 and C4 acting faithfully174+C17:C468,3
C2xC34Abelian group of type [2,34]68C2xC3468,5

Groups of order 69

dρLabelID
C69Cyclic group691C6969,1

Groups of order 70

dρLabelID
C70Cyclic group701C7070,4
D35Dihedral group352+D3570,3
C7xD5Direct product of C7 and D5352C7xD570,1
C5xD7Direct product of C5 and D7352C5xD770,2

Groups of order 71

dρLabelID
C71Cyclic group711C7171,1

Groups of order 72

dρLabelID
C72Cyclic group721C7272,2
D36Dihedral group362+D3672,6
F9Frobenius group; = C32:C8 = AGL1(F9)98+F972,39
Dic18Dicyclic group; = C9:Q8722-Dic1872,4
PSU3(F2)Projective special unitary group on F23; = C32:Q8 = M998+PSU(3,2)72,41
S3wrC2Wreath product of S3 by C2; = SO+4(F2)64+S3wrC272,40
C3:S4The semidirect product of C3 and S4 acting via S4/A4=C2126+C3:S472,43
C3:D12The semidirect product of C3 and D12 acting via D12/D6=C2124+C3:D1272,23
D6:S31st semidirect product of D6 and S3 acting via S3/C3=C2244-D6:S372,22
C32:2C8The semidirect product of C32 and C8 acting via C8/C2=C4244-C3^2:2C872,19
C32:2Q8The semidirect product of C32 and Q8 acting via Q8/C2=C22244-C3^2:2Q872,24
C9:D4The semidirect product of C9 and D4 acting via D4/C22=C2362C9:D472,8
C12:S31st semidirect product of C12 and S3 acting via S3/C3=C236C12:S372,33
C32:7D42nd semidirect product of C32 and D4 acting via D4/C22=C236C3^2:7D472,35
C9:C8The semidirect product of C9 and C8 acting via C8/C4=C2722C9:C872,1
Q8:C9The semidirect product of Q8 and C9 acting via C9/C3=C3722Q8:C972,3
C32:4C82nd semidirect product of C32 and C8 acting via C8/C4=C272C3^2:4C872,13
C32:4Q82nd semidirect product of C32 and Q8 acting via Q8/C4=C272C3^2:4Q872,31
C6.D62nd non-split extension by C6 of D6 acting via D6/S3=C2124+C6.D672,21
C3.S4The non-split extension by C3 of S4 acting via S4/A4=C2186+C3.S472,15
C2xC36Abelian group of type [2,36]72C2xC3672,9
C3xC24Abelian group of type [3,24]72C3xC2472,14
C6xC12Abelian group of type [6,12]72C6xC1272,36
C2xC62Abelian group of type [2,6,6]72C2xC6^272,50
C22xC18Abelian group of type [2,2,18]72C2^2xC1872,18
C3xS4Direct product of C3 and S4123C3xS472,42
S3xA4Direct product of S3 and A4126+S3xA472,44
C6xA4Direct product of C6 and A4183C6xA472,47
S3xC12Direct product of C12 and S3242S3xC1272,27
C3xD12Direct product of C3 and D12242C3xD1272,28
S3xDic3Direct product of S3 and Dic3244-S3xDic372,20
C3xDic6Direct product of C3 and Dic6242C3xDic672,26
C6xDic3Direct product of C6 and Dic324C6xDic372,29
C3xSL2(F3)Direct product of C3 and SL2(F3)242C3xSL(2,3)72,25
C4xD9Direct product of C4 and D9362C4xD972,5
D4xC9Direct product of C9 and D4362D4xC972,10
C22xD9Direct product of C22 and D936C2^2xD972,17
D4xC32Direct product of C32 and D436D4xC3^272,37
Q8xC9Direct product of C9 and Q8722Q8xC972,11
C2xDic9Direct product of C2 and Dic972C2xDic972,7
Q8xC32Direct product of C32 and Q872Q8xC3^272,38
C2xS32Direct product of C2, S3 and S3124+C2xS3^272,46
C3xC3:D4Direct product of C3 and C3:D4122C3xC3:D472,30
C2xC32:C4Direct product of C2 and C32:C4124+C2xC3^2:C472,45
C2xC3.A4Direct product of C2 and C3.A4183C2xC3.A472,16
C3xC3:C8Direct product of C3 and C3:C8242C3xC3:C872,12
S3xC2xC6Direct product of C2xC6 and S324S3xC2xC672,48
C4xC3:S3Direct product of C4 and C3:S336C4xC3:S372,32
C22xC3:S3Direct product of C22 and C3:S336C2^2xC3:S372,49
C2xC3:Dic3Direct product of C2 and C3:Dic372C2xC3:Dic372,34

Groups of order 73

dρLabelID
C73Cyclic group731C7373,1

Groups of order 74

dρLabelID
C74Cyclic group741C7474,2
D37Dihedral group372+D3774,1

Groups of order 75

dρLabelID
C75Cyclic group751C7575,1
C52:C3The semidirect product of C52 and C3 acting faithfully153C5^2:C375,2
C5xC15Abelian group of type [5,15]75C5xC1575,3

Groups of order 76

dρLabelID
C76Cyclic group761C7676,2
D38Dihedral group; = C2xD19382+D3876,3
Dic19Dicyclic group; = C19:C4762-Dic1976,1
C2xC38Abelian group of type [2,38]76C2xC3876,4

Groups of order 77

dρLabelID
C77Cyclic group771C7777,1

Groups of order 78

dρLabelID
C78Cyclic group781C7878,6
D39Dihedral group392+D3978,5
C13:C6The semidirect product of C13 and C6 acting faithfully136+C13:C678,1
S3xC13Direct product of C13 and S3392S3xC1378,3
C3xD13Direct product of C3 and D13392C3xD1378,4
C2xC13:C3Direct product of C2 and C13:C3263C2xC13:C378,2

Groups of order 79

dρLabelID
C79Cyclic group791C7979,1

Groups of order 80

dρLabelID
C80Cyclic group801C8080,2
D40Dihedral group402+D4080,7
Dic20Dicyclic group; = C5:1Q16802-Dic2080,8
C4oD20Central product of C4 and D20402C4oD2080,38
C24:C5The semidirect product of C24 and C5 acting faithfully105+C2^4:C580,49
C4:F5The semidirect product of C4 and F5 acting via F5/D5=C2204C4:F580,31
C22:F5The semidirect product of C22 and F5 acting via F5/D5=C2204+C2^2:F580,34
D4:D5The semidirect product of D4 and D5 acting via D5/C5=C2404+D4:D580,15
D5:C8The semidirect product of D5 and C8 acting via C8/C4=C2404D5:C880,28
Q8:D5The semidirect product of Q8 and D5 acting via D5/C5=C2404+Q8:D580,17
C8:D53rd semidirect product of C8 and D5 acting via D5/C5=C2402C8:D580,5
C40:C22nd semidirect product of C40 and C2 acting faithfully402C40:C280,6
D4:2D5The semidirect product of D4 and D5 acting through Inn(D4)404-D4:2D580,40
Q8:2D5The semidirect product of Q8 and D5 acting through Inn(Q8)404+Q8:2D580,42
D10:C41st semidirect product of D10 and C4 acting via C4/C2=C240D10:C480,14
C5:C16The semidirect product of C5 and C16 acting via C16/C4=C4804C5:C1680,3
C5:2C16The semidirect product of C5 and C16 acting via C16/C8=C2802C5:2C1680,1
C4:Dic5The semidirect product of C4 and Dic5 acting via Dic5/C10=C280C4:Dic580,13
C5:Q16The semidirect product of C5 and Q16 acting via Q16/Q8=C2804-C5:Q1680,18
C4.F5The non-split extension by C4 of F5 acting via F5/D5=C2404C4.F580,29
D4.D5The non-split extension by D4 of D5 acting via D5/C5=C2404-D4.D580,16
C4.Dic5The non-split extension by C4 of Dic5 acting via Dic5/C10=C2402C4.Dic580,10
C23.D5The non-split extension by C23 of D5 acting via D5/C5=C240C2^3.D580,19
C22.F5The non-split extension by C22 of F5 acting via F5/D5=C2404-C2^2.F580,33
C10.D41st non-split extension by C10 of D4 acting via D4/C22=C280C10.D480,12
C4xC20Abelian group of type [4,20]80C4xC2080,20
C2xC40Abelian group of type [2,40]80C2xC4080,23
C22xC20Abelian group of type [2,2,20]80C2^2xC2080,45
C23xC10Abelian group of type [2,2,2,10]80C2^3xC1080,52
D4xD5Direct product of D4 and D5204+D4xD580,39
C4xF5Direct product of C4 and F5204C4xF580,30
C22xF5Direct product of C22 and F520C2^2xF580,50
C8xD5Direct product of C8 and D5402C8xD580,4
C5xD8Direct product of C5 and D8402C5xD880,25
Q8xD5Direct product of Q8 and D5404-Q8xD580,41
C2xD20Direct product of C2 and D2040C2xD2080,37
D4xC10Direct product of C10 and D440D4xC1080,46
C5xSD16Direct product of C5 and SD16402C5xSD1680,26
C23xD5Direct product of C23 and D540C2^3xD580,51
C5xM4(2)Direct product of C5 and M4(2)402C5xM4(2)80,24
C5xQ16Direct product of C5 and Q16802C5xQ1680,27
Q8xC10Direct product of C10 and Q880Q8xC1080,47
C4xDic5Direct product of C4 and Dic580C4xDic580,11
C2xDic10Direct product of C2 and Dic1080C2xDic1080,35
C22xDic5Direct product of C22 and Dic580C2^2xDic580,43
C2xC4xD5Direct product of C2xC4 and D540C2xC4xD580,36
C2xC5:D4Direct product of C2 and C5:D440C2xC5:D480,44
C5xC4oD4Direct product of C5 and C4oD4402C5xC4oD480,48
C5xC22:C4Direct product of C5 and C22:C440C5xC2^2:C480,21
C2xC5:C8Direct product of C2 and C5:C880C2xC5:C880,32
C5xC4:C4Direct product of C5 and C4:C480C5xC4:C480,22
C2xC5:2C8Direct product of C2 and C5:2C880C2xC5:2C880,9

Groups of order 81

dρLabelID
C81Cyclic group811C8181,1
C3wrC3Wreath product of C3 by C3; = AΣL1(F27)93C3wrC381,7
C9oHe3Central 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
C3xC27Abelian group of type [3,27]81C3xC2781,5
C32xC9Abelian group of type [3,3,9]81C3^2xC981,11
C3xHe3Direct product of C3 and He327C3xHe381,12
C3x3- 1+2Direct product of C3 and 3- 1+227C3xES-(3,1)81,13

Groups of order 82

dρLabelID
C82Cyclic group821C8282,2
D41Dihedral group412+D4182,1

Groups of order 83

dρLabelID
C83Cyclic group831C8383,1

Groups of order 84

dρLabelID
C84Cyclic group841C8484,6
D42Dihedral group; = C2xD21422+D4284,14
Dic21Dicyclic group; = C3:Dic7842-Dic2184,5
C7:A4The semidirect product of C7 and A4 acting via A4/C22=C3283C7:A484,11
C7:C12The semidirect product of C7 and C12 acting via C12/C2=C6286-C7:C1284,1
C2xC42Abelian group of type [2,42]84C2xC4284,15
C2xF7Direct product of C2 and F7; = Aut(D14) = Hol(C14)146+C2xF784,7
S3xD7Direct product of S3 and D7214+S3xD784,8
C7xA4Direct product of C7 and A4283C7xA484,10
C6xD7Direct product of C6 and D7422C6xD784,12
S3xC14Direct product of C14 and S3422S3xC1484,13
C7xDic3Direct product of C7 and Dic3842C7xDic384,3
C3xDic7Direct product of C3 and Dic7842C3xDic784,4
C4xC7:C3Direct product of C4 and C7:C3283C4xC7:C384,2
C22xC7:C3Direct product of C22 and C7:C328C2^2xC7:C384,9

Groups of order 85

dρLabelID
C85Cyclic group851C8585,1

Groups of order 86

dρLabelID
C86Cyclic group861C8686,2
D43Dihedral group432+D4386,1

Groups of order 87

dρLabelID
C87Cyclic group871C8787,1

Groups of order 88

dρLabelID
C88Cyclic group881C8888,2
D44Dihedral group442+D4488,5
Dic22Dicyclic group; = C11:Q8882-Dic2288,3
C11:D4The semidirect product of C11 and D4 acting via D4/C22=C2442C11:D488,7
C11:C8The semidirect product of C11 and C8 acting via C8/C4=C2882C11:C888,1
C2xC44Abelian group of type [2,44]88C2xC4488,8
C22xC22Abelian group of type [2,2,22]88C2^2xC2288,12
C4xD11Direct product of C4 and D11442C4xD1188,4
D4xC11Direct product of C11 and D4442D4xC1188,9
C22xD11Direct product of C22 and D1144C2^2xD1188,11
Q8xC11Direct product of C11 and Q8882Q8xC1188,10
C2xDic11Direct product of C2 and Dic1188C2xDic1188,6

Groups of order 89

dρLabelID
C89Cyclic group891C8989,1

Groups of order 90

dρLabelID
C90Cyclic group901C9090,4
D45Dihedral group452+D4590,3
C3:D15The semidirect product of C3 and D15 acting via D15/C15=C245C3:D1590,9
C3xC30Abelian group of type [3,30]90C3xC3090,10
S3xC15Direct product of C15 and S3302S3xC1590,6
C3xD15Direct product of C3 and D15302C3xD1590,7
C5xD9Direct product of C5 and D9452C5xD990,1
C9xD5Direct product of C9 and D5452C9xD590,2
C32xD5Direct product of C32 and D545C3^2xD590,5
C5xC3:S3Direct product of C5 and C3:S345C5xC3:S390,8

Groups of order 91

dρLabelID
C91Cyclic group911C9191,1

Groups of order 92

dρLabelID
C92Cyclic group921C9292,2
D46Dihedral group; = C2xD23462+D4692,3
Dic23Dicyclic group; = C23:C4922-Dic2392,1
C2xC46Abelian group of type [2,46]92C2xC4692,4

Groups of order 93

dρLabelID
C93Cyclic group931C9393,2
C31:C3The semidirect product of C31 and C3 acting faithfully313C31:C393,1

Groups of order 94

dρLabelID
C94Cyclic group941C9494,2
D47Dihedral group472+D4794,1

Groups of order 95

dρLabelID
C95Cyclic group951C9595,1

Groups of order 96

dρLabelID
C96Cyclic group961C9696,2
D48Dihedral group482+D4896,6
Dic24Dicyclic group; = C3:1Q32962-Dic2496,8
U2(F3)Unitary group on F32; = SL2(F3):2C4242U(2,3)96,67
D4oD12Central product of D4 and D12244+D4oD1296,216
C8oD12Central product of C8 and D12482C8oD1296,108
C4oD24Central product of C4 and D24482C4oD2496,111
Q8oD12Central product of Q8 and D12484-Q8oD1296,217
C22:S4The semidirect product of C22 and S4 acting via S4/C22=S386+C2^2:S496,227
C24:C61st semidirect product of C24 and C6 acting faithfully86+C2^4:C696,70
C23:A42nd semidirect product of C23 and A4 acting faithfully84+C2^3:A496,204
C4:S4The semidirect product of C4 and S4 acting via S4/A4=C2126+C4:S496,187
C42:S3The semidirect product of C42 and S3 acting faithfully123C4^2:S396,64
A4:D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(Z/4Z)126+A4:D496,195
C42:C61st semidirect product of C42 and C6 acting faithfully166C4^2:C696,71
A4:C8The semidirect product of A4 and C8 acting via C8/C4=C2243A4:C896,65
A4:Q8The semidirect product of A4 and Q8 acting via Q8/C4=C2246-A4:Q896,185
C8:D61st semidirect product of C8 and D6 acting via D6/C3=C22244+C8:D696,115
D6:D41st semidirect product of D6 and D4 acting via D4/C22=C224D6:D496,89
D8:S32nd semidirect product of D8 and S3 acting via S3/C3=C2244D8:S396,118
D4:D62nd semidirect product of D4 and D6 acting via D6/C6=C2244+D4:D696,156
D4:6D62nd semidirect product of D4 and D6 acting through Inn(D4)244D4:6D696,211
Q8:3D62nd semidirect product of Q8 and D6 acting via D6/S3=C2244+Q8:3D696,121
Q8:A41st semidirect product of Q8 and A4 acting via A4/C22=C3246-Q8:A496,203
D12:C44th semidirect product of D12 and C4 acting via C4/C2=C2244D12:C496,32
C42:4S33rd semidirect product of C42 and S3 acting via S3/C3=C2242C4^2:4S396,12
C24:4S31st semidirect product of C24 and S3 acting via S3/C3=C224C2^4:4S396,160
C23:2D61st semidirect product of C23 and D6 acting via D6/C3=C2224C2^3:2D696,144
Q8:3Dic32nd semidirect product of Q8 and Dic3 acting via Dic3/C6=C2244Q8:3Dic396,44
D12:6C224th semidirect product of D12 and C22 acting via C22/C2=C2244D12:6C2^296,139
Q8:Dic3The semidirect product of Q8 and Dic3 acting via Dic3/C2=S332Q8:Dic396,66
D6:C8The semidirect product of D6 and C8 acting via C8/C4=C248D6:C896,27
C3:D16The semidirect product of C3 and D16 acting via D16/D8=C2484+C3:D1696,33
C48:C22nd semidirect product of C48 and C2 acting faithfully482C48:C296,7
D8:3S3The semidirect product of D8 and S3 acting through Inn(D8)484-D8:3S396,119
D6:3D43rd semidirect product of D6 and D4 acting via D4/C4=C248D6:3D496,145
C4:D12The semidirect product of C4 and D12 acting via D12/C12=C248C4:D1296,81
C12:D41st semidirect product of C12 and D4 acting via D4/C2=C2248C12:D496,102
C12:7D41st semidirect product of C12 and D4 acting via D4/C22=C248C12:7D496,137
C12:3D43rd semidirect product of C12 and D4 acting via D4/C2=C2248C12:3D496,147
D6:Q81st semidirect product of D6 and Q8 acting via Q8/C4=C248D6:Q896,103
D6:3Q83rd semidirect product of D6 and Q8 acting via Q8/C4=C248D6:3Q896,153
D24:C25th semidirect product of D24 and C2 acting faithfully484+D24:C296,126
C42:2S31st semidirect product of C42 and S3 acting via S3/C3=C248C4^2:2S396,79
C42:7S36th semidirect product of C42 and S3 acting via S3/C3=C248C4^2:7S396,82
C42:3S32nd semidirect product of C42 and S3 acting via S3/C3=C248C4^2:3S396,83
Q16:S32nd semidirect product of Q16 and S3 acting via S3/C3=C2484Q16:S396,125
D4:Dic31st semidirect product of D4 and Dic3 acting via Dic3/C6=C248D4:Dic396,39
Dic3:4D41st semidirect product of Dic3 and D4 acting through Inn(Dic3)48Dic3:4D496,88
Dic3:D41st semidirect product of Dic3 and D4 acting via D4/C22=C248Dic3:D496,91
Dic3:5D42nd semidirect product of Dic3 and D4 acting through Inn(Dic3)48Dic3:5D496,100
C3:C32The semidirect product of C3 and C32 acting via C32/C16=C2962C3:C3296,1
C12:Q8The semidirect product of C12 and Q8 acting via Q8/C2=C2296C12:Q896,95
C12:C81st semidirect product of C12 and C8 acting via C8/C4=C296C12:C896,11
C24:C45th semidirect product of C24 and C4 acting via C4/C2=C296C24:C496,22
C24:1C41st semidirect product of C24 and C4 acting via C4/C2=C296C24:1C496,25
C3:Q32The semidirect product of C3 and Q32 acting via Q32/Q16=C2964-C3:Q3296,36
Dic3:C8The semidirect product of Dic3 and C8 acting via C8/C4=C296Dic3:C896,21
C12:2Q81st semidirect product of C12 and Q8 acting via Q8/C4=C296C12:2Q896,76
C8:Dic32nd semidirect product of C8 and Dic3 acting via Dic3/C6=C296C8:Dic396,24
Q8:2Dic31st semidirect product of Q8 and Dic3 acting via Dic3/C6=C296Q8:2Dic396,42
Dic6:C45th semidirect product of Dic6 and C4 acting via C4/C2=C296Dic6:C496,94
Dic3:Q82nd semidirect product of Dic3 and Q8 acting via Q8/C4=C296Dic3:Q896,151
C4:C4:7S31st semidirect product of C4:C4 and S3 acting through Inn(C4:C4)48C4:C4:7S396,99
C4:C4:S36th semidirect product of C4:C4 and S3 acting via S3/C3=C248C4:C4:S396,105
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3126+C2^3.3A496,3
C23.A42nd non-split extension by C23 of A4 acting faithfully126+C2^3.A496,72
D4.A4The non-split extension by D4 of A4 acting through Inn(D4)164-D4.A496,202
C4.6S43rd central extension by C4 of S4162C4.6S496,192
C4.3S43rd non-split extension by C4 of S4 acting via S4/A4=C2164+C4.3S496,193
Q8.D62nd non-split extension by Q8 of D6 acting via D6/C2=S3164-Q8.D696,190
Q8.A4The non-split extension by Q8 of A4 acting through Inn(Q8)244+Q8.A496,201
C12.D48th non-split extension by C12 of D4 acting via D4/C2=C22244C12.D496,40
C12.46D43rd non-split extension by C12 of D4 acting via D4/C22=C2244+C12.46D496,30
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.6D696,13
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.7D696,41
C8.A4The central extension by C8 of A4322C8.A496,74
C4.S42nd non-split extension by C4 of S4 acting via S4/A4=C2324-C4.S496,191
D6.C8The non-split extension by D6 of C8 acting via C8/C4=C2482D6.C896,5
D8.S3The non-split extension by D8 of S3 acting via S3/C3=C2484-D8.S396,34
D12.C4The non-split extension by D12 of C4 acting via C4/C2=C2484D12.C496,114
C6.D82nd non-split extension by C6 of D8 acting via D8/D4=C248C6.D896,16
C8.6D63rd non-split extension by C8 of D6 acting via D6/S3=C2484+C8.6D696,35
C8.D61st non-split extension by C8 of D6 acting via D6/C3=C22484-C8.D696,116
C12.C81st non-split extension by C12 of C8 acting via C8/C4=C2482C12.C896,19
C24.C41st non-split extension by C24 of C4 acting via C4/C2=C2482C24.C496,26
D6.D42nd non-split extension by D6 of D4 acting via D4/C22=C248D6.D496,101
D4.D64th non-split extension by D4 of D6 acting via D6/S3=C2484-D4.D696,122
C2.D242nd central extension by C2 of D2448C2.D2496,28
D4.Dic3The non-split extension by D4 of Dic3 acting through Inn(D4)484D4.Dic396,155
Q8.7D62nd non-split extension by Q8 of D6 acting via D6/S3=C2484Q8.7D696,123
C12.53D410th non-split extension by C12 of D4 acting via D4/C22=C2484C12.53D496,29
C12.47D44th non-split extension by C12 of D4 acting via D4/C22=C2484-C12.47D496,31
C12.55D412nd non-split extension by C12 of D4 acting via D4/C22=C248C12.55D496,37
C12.10D410th non-split extension by C12 of D4 acting via D4/C2=C22484C12.10D496,43
C4.D125th non-split extension by C4 of D12 acting via D12/D6=C248C4.D1296,104
C12.48D45th non-split extension by C12 of D4 acting via D4/C22=C248C12.48D496,131
C12.23D423rd non-split extension by C12 of D4 acting via D4/C2=C2248C12.23D496,154
Q8.11D61st non-split extension by Q8 of D6 acting via D6/C6=C2484Q8.11D696,149
Q8.13D63rd non-split extension by Q8 of D6 acting via D6/C6=C2484Q8.13D696,157
Q8.14D64th non-split extension by Q8 of D6 acting via D6/C6=C2484-Q8.14D696,158
Q8.15D61st non-split extension by Q8 of D6 acting through Inn(Q8)484Q8.15D696,214
C23.8D63rd non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.8D696,86
C23.9D64th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.9D696,90
Dic3.D41st non-split extension by Dic3 of D4 acting via D4/C22=C248Dic3.D496,85
C23.16D61st non-split extension by C23 of D6 acting via D6/S3=C248C2^3.16D696,84
C23.11D66th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.11D696,92
C23.21D66th non-split extension by C23 of D6 acting via D6/S3=C248C2^3.21D696,93
C23.26D62nd non-split extension by C23 of D6 acting via D6/C6=C248C2^3.26D696,133
C23.28D64th non-split extension by C23 of D6 acting via D6/C6=C248C2^3.28D696,136
C23.23D68th non-split extension by C23 of D6 acting via D6/S3=C248C2^3.23D696,142
C23.12D67th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.12D696,143
C23.14D69th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.14D696,146
Dic3.Q8The non-split extension by Dic3 of Q8 acting via Q8/C4=C296Dic3.Q896,96
C6.Q161st non-split extension by C6 of Q16 acting via Q16/Q8=C296C6.Q1696,14
C12.Q82nd non-split extension by C12 of Q8 acting via Q8/C2=C2296C12.Q896,15
C12.6Q83rd non-split extension by C12 of Q8 acting via Q8/C4=C296C12.6Q896,77
C42.S31st non-split extension by C42 of S3 acting via S3/C3=C296C4^2.S396,10
C6.C425th non-split extension by C6 of C42 acting via C42/C2xC4=C296C6.C4^296,38
C6.SD162nd non-split extension by C6 of SD16 acting via SD16/D4=C296C6.SD1696,17
C4.Dic63rd non-split extension by C4 of Dic6 acting via Dic6/Dic3=C296C4.Dic696,97
C2.Dic121st central extension by C2 of Dic1296C2.Dic1296,23
C4xC24Abelian group of type [4,24]96C4xC2496,46
C2xC48Abelian group of type [2,48]96C2xC4896,59
C24xC6Abelian group of type [2,2,2,2,6]96C2^4xC696,231
C22xC24Abelian group of type [2,2,24]96C2^2xC2496,176
C23xC12Abelian group of type [2,2,2,12]96C2^3xC1296,220
C2xC4xC12Abelian group of type [2,4,12]96C2xC4xC1296,161
C4xS4Direct product of C4 and S4123C4xS496,186
D4xA4Direct product of D4 and A4126+D4xA496,197
C22xS4Direct product of C22 and S412C2^2xS496,226
C2xGL2(F3)Direct product of C2 and GL2(F3)16C2xGL(2,3)96,189
C8xA4Direct product of C8 and A4243C8xA496,73
S3xD8Direct product of S3 and D8244+S3xD896,117
Q8xA4Direct product of Q8 and A4246-Q8xA496,199
C23xA4Direct product of C23 and A424C2^3xA496,228
S3xSD16Direct product of S3 and SD16244S3xSD1696,120
S3xM4(2)Direct product of S3 and M4(2)244S3xM4(2)96,113
C3x2+ 1+4Direct product of C3 and 2+ 1+4244C3xES+(2,2)96,224
C4xSL2(F3)Direct product of C4 and SL2(F3)32C4xSL(2,3)96,69
C2xCSU2(F3)Direct product of C2 and CSU2(F3)32C2xCSU(2,3)96,188
C22xSL2(F3)Direct product of C22 and SL2(F3)32C2^2xSL(2,3)96,198
C6xD8Direct product of C6 and D848C6xD896,179
S3xC16Direct product of C16 and S3482S3xC1696,4
C3xD16Direct product of C3 and D16482C3xD1696,61
C4xD12Direct product of C4 and D1248C4xD1296,80
C2xD24Direct product of C2 and D2448C2xD2496,110
D4xC12Direct product of C12 and D448D4xC1296,165
S3xQ16Direct product of S3 and Q16484-S3xQ1696,124
S3xC42Direct product of C42 and S348S3xC4^296,78
S3xC24Direct product of C24 and S348S3xC2^496,230
C3xSD32Direct product of C3 and SD32482C3xSD3296,62
D4xDic3Direct product of D4 and Dic348D4xDic396,141
C6xSD16Direct product of C6 and SD1648C6xSD1696,180
C22xD12Direct product of C22 and D1248C2^2xD1296,207
C3xM5(2)Direct product of C3 and M5(2)482C3xM5(2)96,60
C6xM4(2)Direct product of C6 and M4(2)48C6xM4(2)96,177
C3x2- 1+4Direct product of C3 and 2- 1+4484C3xES-(2,2)96,225
C3xQ32Direct product of C3 and Q32962C3xQ3296,63
Q8xC12Direct product of C12 and Q896Q8xC1296,166
C6xQ16Direct product of C6 and Q1696C6xQ1696,181
C8xDic3Direct product of C8 and Dic396C8xDic396,20
C4xDic6Direct product of C4 and Dic696C4xDic696,75
Q8xDic3Direct product of Q8 and Dic396Q8xDic396,152
C2xDic12Direct product of C2 and Dic1296C2xDic1296,112
C22xDic6Direct product of C22 and Dic696C2^2xDic696,205
C23xDic3Direct product of C23 and Dic396C2^3xDic396,218
C2xC42:C3Direct product of C2 and C42:C3123C2xC4^2:C396,68
C2xC22:A4Direct product of C2 and C22:A412C2xC2^2:A496,229
C2xC4xA4Direct product of C2xC4 and A424C2xC4xA496,196
C2xS3xD4Direct product of C2, S3 and D424C2xS3xD496,209
C3xC4wrC2Direct product of C3 and C4wrC2242C3xC4wrC296,54
C2xA4:C4Direct product of C2 and A4:C424C2xA4:C496,194
S3xC4oD4Direct product of S3 and C4oD4244S3xC4oD496,215
C3xC23:C4Direct product of C3 and C23:C4244C3xC2^3:C496,49
S3xC22:C4Direct product of S3 and C22:C424S3xC2^2:C496,87
C3xC8:C22Direct product of C3 and C8:C22244C3xC8:C2^296,183
C3xC4.D4Direct product of C3 and C4.D4244C3xC4.D496,50
C3xC22wrC2Direct product of C3 and C22wrC224C3xC2^2wrC296,167
C2xC4.A4Direct product of C2 and C4.A432C2xC4.A496,200
S3xC2xC8Direct product of C2xC8 and S348S3xC2xC896,106
D4xC2xC6Direct product of C2xC6 and D448D4xC2xC696,221
S3xC4:C4Direct product of S3 and C4:C448S3xC4:C496,98
C2xS3xQ8Direct product of C2, S3 and Q848C2xS3xQ896,212
C4xC3:D4Direct product of C4 and C3:D448C4xC3:D496,135
C2xC8:S3Direct product of C2 and C8:S348C2xC8:S396,107
C2xD6:C4Direct product of C2 and D6:C448C2xD6:C496,134
C2xD4:S3Direct product of C2 and D4:S348C2xD4:S396,138
C3xC8oD4Direct product of C3 and C8oD4482C3xC8oD496,178
C3xC4oD8Direct product of C3 and C4oD8482C3xC4oD896,182
C6xC4oD4Direct product of C6 and C4oD448C6xC4oD496,223
C3xC4:D4Direct product of C3 and C4:D448C3xC4:D496,168
S3xC22xC4Direct product of C22xC4 and S348S3xC2^2xC496,206
C2xC24:C2Direct product of C2 and C24:C248C2xC24:C296,109
C2xC4oD12Direct product of C2 and C4oD1248C2xC4oD1296,208
C3xD4:C4Direct product of C3 and D4:C448C3xD4:C496,52
C3xC8.C4Direct product of C3 and C8.C4482C3xC8.C496,58
C3xC4:1D4Direct product of C3 and C4:1D448C3xC4:1D496,174
C3xC22:C8Direct product of C3 and C22:C848C3xC2^2:C896,48
C6xC22:C4Direct product of C6 and C22:C448C6xC2^2:C496,162
C2xD4.S3Direct product of C2 and D4.S348C2xD4.S396,140
C2xC6.D4Direct product of C2 and C6.D448C2xC6.D496,159
C22xC3:D4Direct product of C22 and C3:D448C2^2xC3:D496,219
C3xC22:Q8Direct product of C3 and C22:Q848C3xC2^2:Q896,169
C2xD4:2S3Direct product of C2 and D4:2S348C2xD4:2S396,210
C3xC42:C2Direct product of C3 and C42:C248C3xC4^2:C296,164
C2xQ8:2S3Direct product of C2 and Q8:2S348C2xQ8:2S396,148
C2xQ8:3S3Direct product of C2 and Q8:3S348C2xQ8:3S396,213
C3xC4.4D4Direct product of C3 and C4.4D448C3xC4.4D496,171
C3xC8.C22Direct product of C3 and C8.C22484C3xC8.C2^296,184
C2xC4.Dic3Direct product of C2 and C4.Dic348C2xC4.Dic396,128
C3xC42:2C2Direct product of C3 and C42:2C248C3xC4^2:2C296,173
C3xC4.10D4Direct product of C3 and C4.10D4484C3xC4.10D496,51
C3xC22.D4Direct product of C3 and C22.D448C3xC2^2.D496,170
C4xC3:C8Direct product of C4 and C3:C896C4xC3:C896,9
C3xC4:C8Direct product of C3 and C4:C896C3xC4:C896,55
C6xC4:C4Direct product of C6 and C4:C496C6xC4:C496,163
C2xC3:C16Direct product of C2 and C3:C1696C2xC3:C1696,18
Q8xC2xC6Direct product of C2xC6 and Q896Q8xC2xC696,222
C3xC4:Q8Direct product of C3 and C4:Q896C3xC4:Q896,175
C3xC8:C4Direct product of C3 and C8:C496C3xC8:C496,47
C22xC3:C8Direct product of C22 and C3:C896C2^2xC3:C896,127
C2xC4xDic3Direct product of C2xC4 and Dic396C2xC4xDic396,129
C2xC3:Q16Direct product of C2 and C3:Q1696C2xC3:Q1696,150
C2xC4:Dic3Direct product of C2 and C4:Dic396C2xC4:Dic396,132
C3xQ8:C4Direct product of C3 and Q8:C496C3xQ8:C496,53
C3xC2.D8Direct product of C3 and C2.D896C3xC2.D896,57
C3xC4.Q8Direct product of C3 and C4.Q896C3xC4.Q896,56
C2xDic3:C4Direct product of C2 and Dic3:C496C2xDic3:C496,130
C3xC2.C42Direct product of C3 and C2.C4296C3xC2.C4^296,45
C3xC42.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
D49Dihedral group492+D4998,1
C7:D7The semidirect product of C7 and D7 acting via D7/C7=C249C7:D798,4
C7xC14Abelian group of type [7,14]98C7xC1498,5
C7xD7Direct product of C7 and D7; = AΣL1(F49)142C7xD798,3

Groups of order 99

dρLabelID
C99Cyclic group991C9999,1
C3xC33Abelian group of type [3,33]99C3xC3399,2

Groups of order 100

dρLabelID
C100Cyclic group1001C100100,2
D50Dihedral group; = C2xD25502+D50100,4
Dic25Dicyclic group; = C25:2C41002-Dic25100,1
C52:C44th semidirect product of C52 and C4 acting faithfully104+C5^2:C4100,12
C25:C4The semidirect product of C25 and C4 acting faithfully254+C25:C4100,3
C5:F51st semidirect product of C5 and F5 acting via F5/C5=C425C5:F5100,11
C52:6C42nd semidirect product of C52 and C4 acting via C4/C2=C2100C5^2:6C4100,7
D5.D5The non-split extension by D5 of D5 acting via D5/C5=C2204D5.D5100,10
C102Abelian group of type [10,10]100C10^2100,16
C2xC50Abelian group of type [2,50]100C2xC50100,5
C5xC20Abelian group of type [5,20]100C5xC20100,8
D52Direct product of D5 and D5104+D5^2100,13
C5xF5Direct product of C5 and F5204C5xF5100,9
D5xC10Direct product of C10 and D5202D5xC10100,14
C5xDic5Direct product of C5 and Dic5202C5xDic5100,6
C2xC5:D5Direct product of C2 and C5:D550C2xC5:D5100,15

Groups of order 101

dρLabelID
C101Cyclic group1011C101101,1

Groups of order 102

dρLabelID
C102Cyclic group1021C102102,4
D51Dihedral group512+D51102,3
S3xC17Direct product of C17 and S3512S3xC17102,1
C3xD17Direct product of C3 and D17512C3xD17102,2

Groups of order 103

dρLabelID
C103Cyclic group1031C103103,1

Groups of order 104

dρLabelID
C104Cyclic group1041C104104,2
D52Dihedral group522+D52104,6
Dic26Dicyclic group; = C13:Q81042-Dic26104,4
C13:D4The semidirect product of C13 and D4 acting via D4/C22=C2522C13:D4104,8
C13:C8The semidirect product of C13 and C8 acting via C8/C2=C41044-C13:C8104,3
C13:2C8The semidirect product of C13 and C8 acting via C8/C4=C21042C13:2C8104,1
C2xC52Abelian group of type [2,52]104C2xC52104,9
C22xC26Abelian group of type [2,2,26]104C2^2xC26104,14
C4xD13Direct product of C4 and D13522C4xD13104,5
D4xC13Direct product of C13 and D4522D4xC13104,10
C22xD13Direct product of C22 and D1352C2^2xD13104,13
Q8xC13Direct product of C13 and Q81042Q8xC13104,11
C2xDic13Direct product of C2 and Dic13104C2xDic13104,7
C2xC13:C4Direct product of C2 and C13:C4264+C2xC13:C4104,12

Groups of order 105

dρLabelID
C105Cyclic group1051C105105,2
C5xC7:C3Direct product of C5 and C7:C3353C5xC7:C3105,1

Groups of order 106

dρLabelID
C106Cyclic group1061C106106,2
D53Dihedral group532+D53106,1

Groups of order 107

dρLabelID
C107Cyclic group1071C107107,1

Groups of order 108

dρLabelID
C108Cyclic group1081C108108,2
D54Dihedral group; = C2xD27542+D54108,4
Dic27Dicyclic group; = C27:C41082-Dic27108,1
C32:D6The semidirect product of C32 and D6 acting faithfully96+C3^2:D6108,17
C33:C42nd semidirect product of C33 and C4 acting faithfully124C3^3:C4108,37
C32:4D6The semidirect product of C32 and D6 acting via D6/C3=C22124C3^2:4D6108,40
He3:C4The semidirect product of He3 and C4 acting faithfully183He3:C4108,15
C32:A4The semidirect product of C32 and A4 acting via A4/C22=C3183C3^2:A4108,22
C9:A4The semidirect product of C9 and A4 acting via A4/C22=C3363C9:A4108,19
C9:C12The semidirect product of C9 and C12 acting via C12/C2=C6366-C9:C12108,9
C32:C12The semidirect product of C32 and C12 acting via C12/C2=C6366-C3^2:C12108,8
He3:3C42nd semidirect product of He3 and C4 acting via C4/C2=C2363He3:3C4108,11
C9:Dic3The semidirect product of C9 and Dic3 acting via Dic3/C6=C2108C9:Dic3108,10
C33:5C43rd semidirect product of C33 and C4 acting via C4/C2=C2108C3^3:5C4108,34
C32.A4The non-split extension by C32 of A4 acting via A4/C22=C3183C3^2.A4108,21
C9.A4The central extension by C9 of A4543C9.A4108,3
C2xC54Abelian group of type [2,54]108C2xC54108,5
C3xC36Abelian group of type [3,36]108C3xC36108,12
C6xC18Abelian group of type [6,18]108C6xC18108,29
C3xC62Abelian group of type [3,6,6]108C3xC6^2108,45
C32xC12Abelian group of type [3,3,12]108C3^2xC12108,35
S3xD9Direct product of S3 and D9184+S3xD9108,16
C9xA4Direct product of C9 and A4363C9xA4108,18
C6xD9Direct product of C6 and D9362C6xD9108,23
S3xC18Direct product of C18 and S3362S3xC18108,24
C4xHe3Direct product of C4 and He3363C4xHe3108,13
C32xA4Direct product of C32 and A436C3^2xA4108,41
C3xDic9Direct product of C3 and Dic9362C3xDic9108,6
C9xDic3Direct product of C9 and Dic3362C9xDic3108,7
C22xHe3Direct product of C22 and He336C2^2xHe3108,30
C32xDic3Direct product of C32 and Dic336C3^2xDic3108,32
C4x3- 1+2Direct product of C4 and 3- 1+2363C4xES-(3,1)108,14
C22x3- 1+2Direct product of C22 and 3- 1+236C2^2xES-(3,1)108,31
C3xS32Direct product of C3, S3 and S3124C3xS3^2108,38
C3xC32:C4Direct product of C3 and C32:C4124C3xC3^2:C4108,36
C2xC9:C6Direct product of C2 and C9:C6; = Aut(D18) = Hol(C18)186+C2xC9:C6108,26
S3xC3:S3Direct product of S3 and C3:S318S3xC3:S3108,39
C2xC32:C6Direct product of C2 and C32:C6186+C2xC3^2:C6108,25
C2xHe3:C2Direct product of C2 and He3:C2183C2xHe3:C2108,28
S3xC3xC6Direct product of C3xC6 and S336S3xC3xC6108,42
C6xC3:S3Direct product of C6 and C3:S336C6xC3:S3108,43
C3xC3:Dic3Direct product of C3 and C3:Dic336C3xC3:Dic3108,33
C2xC9:S3Direct product of C2 and C9:S354C2xC9:S3108,27
C3xC3.A4Direct product of C3 and C3.A454C3xC3.A4108,20
C2xC33:C2Direct product of C2 and C33:C254C2xC3^3:C2108,44

Groups of order 109

dρLabelID
C109Cyclic group1091C109109,1

Groups of order 110

dρLabelID
C110Cyclic group1101C110110,6
D55Dihedral group552+D55110,5
F11Frobenius group; = C11:C10 = AGL1(F11) = Aut(D11) = Hol(C11)1110+F11110,1
D5xC11Direct product of C11 and D5552D5xC11110,3
C5xD11Direct product of C5 and D11552C5xD11110,4
C2xC11:C5Direct product of C2 and C11:C5225C2xC11:C5110,2

Groups of order 111

dρLabelID
C111Cyclic group1111C111111,2
C37:C3The semidirect product of C37 and C3 acting faithfully373C37:C3111,1

Groups of order 112

dρLabelID
C112Cyclic group1121C112112,2
D56Dihedral group562+D56112,6
Dic28Dicyclic group; = C7:1Q161122-Dic28112,7
C4oD28Central product of C4 and D28562C4oD28112,30
D4:D7The semidirect product of D4 and D7 acting via D7/C7=C2564+D4:D7112,14
Q8:D7The semidirect product of Q8 and D7 acting via D7/C7=C2564+Q8:D7112,16
D14:C4The semidirect product of D14 and C4 acting via C4/C2=C256D14:C4112,13
C8:D73rd semidirect product of C8 and D7 acting via D7/C7=C2562C8:D7112,4
C56:C22nd semidirect product of C56 and C2 acting faithfully562C56:C2112,5
D4:2D7The semidirect product of D4 and D7 acting through Inn(D4)564-D4:2D7112,32
Q8:2D7The semidirect product of Q8 and D7 acting through Inn(Q8)564+Q8:2D7112,34
C7:C16The semidirect product of C7 and C16 acting via C16/C8=C21122C7:C16112,1
C4:Dic7The semidirect product of C4 and Dic7 acting via Dic7/C14=C2112C4:Dic7112,12
C7:Q16The semidirect product of C7 and Q16 acting via Q16/Q8=C21124-C7:Q16112,17
Dic7:C4The semidirect product of Dic7 and C4 acting via C4/C2=C2112Dic7:C4112,11
D4.D7The non-split extension by D4 of D7 acting via D7/C7=C2564-D4.D7112,15
C4.Dic7The non-split extension by C4 of Dic7 acting via Dic7/C14=C2562C4.Dic7112,9
C23.D7The non-split extension by C23 of D7 acting via D7/C7=C256C2^3.D7112,18
C4xC28Abelian group of type [4,28]112C4xC28112,19
C2xC56Abelian group of type [2,56]112C2xC56112,22
C22xC28Abelian group of type [2,2,28]112C2^2xC28112,37
C23xC14Abelian group of type [2,2,2,14]112C2^3xC14112,43
C2xF8Direct product of C2 and F8147+C2xF8112,41
D4xD7Direct product of D4 and D7284+D4xD7112,31
C8xD7Direct product of C8 and D7562C8xD7112,3
C7xD8Direct product of C7 and D8562C7xD8112,24
Q8xD7Direct product of Q8 and D7564-Q8xD7112,33
C2xD28Direct product of C2 and D2856C2xD28112,29
D4xC14Direct product of C14 and D456D4xC14112,38
C7xSD16Direct product of C7 and SD16562C7xSD16112,25
C23xD7Direct product of C23 and D756C2^3xD7112,42
C7xM4(2)Direct product of C7 and M4(2)562C7xM4(2)112,23
C7xQ16Direct product of C7 and Q161122C7xQ16112,26
Q8xC14Direct product of C14 and Q8112Q8xC14112,39
C4xDic7Direct product of C4 and Dic7112C4xDic7112,10
C2xDic14Direct product of C2 and Dic14112C2xDic14112,27
C22xDic7Direct product of C22 and Dic7112C2^2xDic7112,35
C2xC4xD7Direct product of C2xC4 and D756C2xC4xD7112,28
C2xC7:D4Direct product of C2 and C7:D456C2xC7:D4112,36
C7xC4oD4Direct product of C7 and C4oD4562C7xC4oD4112,40
C7xC22:C4Direct product of C7 and C22:C456C7xC2^2:C4112,20
C2xC7:C8Direct product of C2 and C7:C8112C2xC7:C8112,8
C7xC4: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
D57Dihedral group572+D57114,5
C19:C6The semidirect product of C19 and C6 acting faithfully196+C19:C6114,1
S3xC19Direct product of C19 and S3572S3xC19114,3
C3xD19Direct product of C3 and D19572C3xD19114,4
C2xC19:C3Direct product of C2 and C19:C3383C2xC19:C3114,2

Groups of order 115

dρLabelID
C115Cyclic group1151C115115,1

Groups of order 116

dρLabelID
C116Cyclic group1161C116116,2
D58Dihedral group; = C2xD29582+D58116,4
Dic29Dicyclic group; = C29:2C41162-Dic29116,1
C29:C4The semidirect product of C29 and C4 acting faithfully294+C29:C4116,3
C2xC58Abelian group of type [2,58]116C2xC58116,5

Groups of order 117

dρLabelID
C117Cyclic group1171C117117,2
C13:C9The semidirect product of C13 and C9 acting via C9/C3=C31173C13:C9117,1
C3xC39Abelian group of type [3,39]117C3xC39117,4
C3xC13:C3Direct product of C3 and C13:C3393C3xC13:C3117,3

Groups of order 118

dρLabelID
C118Cyclic group1181C118118,2
D59Dihedral group592+D59118,1

Groups of order 119

dρLabelID
C119Cyclic group1191C119119,1

Groups of order 120

dρLabelID
C120Cyclic group1201C120120,4
D60Dihedral group602+D60120,28
Dic30Dicyclic group; = C15:2Q81202-Dic30120,26
C5:S4The semidirect product of C5 and S4 acting via S4/A4=C2206+C5:S4120,38
C15:D41st semidirect product of C15 and D4 acting via D4/C2=C22604-C15:D4120,11
C3:D20The semidirect product of C3 and D20 acting via D20/D10=C2604+C3:D20120,12
C5:D12The semidirect product of C5 and D12 acting via D12/D6=C2604+C5:D12120,13
C15:7D41st semidirect product of C15 and D4 acting via D4/C22=C2602C15:7D4120,30
C15:Q8The semidirect product of C15 and Q8 acting via Q8/C2=C221204-C15:Q8120,14
C15:3C81st semidirect product of C15 and C8 acting via C8/C4=C21202C15:3C8120,3
C15:C81st semidirect product of C15 and C8 acting via C8/C2=C41204C15:C8120,7
D30.C2The non-split extension by D30 of C2 acting faithfully604+D30.C2120,10
C2xC60Abelian group of type [2,60]120C2xC60120,31
C22xC30Abelian group of type [2,2,30]120C2^2xC30120,47
S3xF5Direct product of S3 and F5; = Aut(D15) = Hol(C15)158+S3xF5120,36
C5xS4Direct product of C5 and S4203C5xS4120,37
D5xA4Direct product of D5 and A4206+D5xA4120,39
C6xF5Direct product of C6 and F5304C6xF5120,40
C10xA4Direct product of C10 and A4303C10xA4120,43
C5xSL2(F3)Direct product of C5 and SL2(F3)402C5xSL(2,3)120,15
S3xC20Direct product of C20 and S3602S3xC20120,22
D5xC12Direct product of C12 and D5602D5xC12120,17
C3xD20Direct product of C3 and D20602C3xD20120,18
C5xD12Direct product of C5 and D12602C5xD12120,23
C4xD15Direct product of C4 and D15602C4xD15120,27
D4xC15Direct product of C15 and D4602D4xC15120,32
D5xDic3Direct product of D5 and Dic3604-D5xDic3120,8
S3xDic5Direct product of S3 and Dic5604-S3xDic5120,9
C22xD15Direct product of C22 and D1560C2^2xD15120,46
Q8xC15Direct product of C15 and Q81202Q8xC15120,33
C6xDic5Direct product of C6 and Dic5120C6xDic5120,19
C5xDic6Direct product of C5 and Dic61202C5xDic6120,21
C3xDic10Direct product of C3 and Dic101202C3xDic10120,16
C10xDic3Direct product of C10 and Dic3120C10xDic3120,24
C2xDic15Direct product of C2 and Dic15120C2xDic15120,29
C2xS3xD5Direct product of C2, S3 and D5304+C2xS3xD5120,42
C2xC3:F5Direct product of C2 and C3:F5304C2xC3:F5120,41
D5xC2xC6Direct product of C2xC6 and D560D5xC2xC6120,44
S3xC2xC10Direct product of C2xC10 and S360S3xC2xC10120,45
C3xC5:D4Direct product of C3 and C5:D4602C3xC5:D4120,20
C5xC3:D4Direct product of C5 and C3:D4602C5xC3:D4120,25
C5xC3:C8Direct product of C5 and C3:C81202C5xC3:C8120,1
C3xC5:C8Direct product of C3 and C5:C81204C3xC5:C8120,6
C3xC5:2C8Direct product of C3 and C5:2C81202C3xC5:2C8120,2
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