Group​Names [Beta]

Finite groups of order ≤500, group names, extensions, presentations, properties and character tables.

Order  ≤60≤120≤250≤500

Orders with >300 groups of order n
n = 128, 192, 256, 288, 320, 384, 432, 448, 480.

[non]​abelian, [non]​soluble, super​soluble, [non]​monomial, Z-groups, A-groups, metacyclic, metabelian, p-groups, elementary, hyper​elementary, linear, perfect, simple, almost simple, quasisimple, rational 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
C2×C4Abelian 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; = C2×S3 = hexagon symmetries62+D612,4
Dic3Dicyclic group; = C3C4122-Dic312,1
C2×C6Abelian 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; = Q8C2 = QD1682SD1616,8
M4(2)Modular maximal-cyclic group; = C83C282M4(2)16,6
C4○D4Pauli group = central product of C4 and D482C4oD416,13
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C28C2^2:C416,3
C4⋊C4The semidirect product of C4 and C4 acting via C4/C2=C216C4:C416,4
C42Abelian group of type [4,4]16C4^216,2
C24Elementary abelian group of type [2,2,2,2]16C2^416,14
C2×C8Abelian group of type [2,8]16C2xC816,5
C22×C4Abelian group of type [2,2,4]16C2^2xC416,10
C2×D4Direct product of C2 and D48C2xD416,11
C2×Q8Direct product of C2 and Q816C2xQ816,12

Groups of order 17

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
C3×C6Abelian group of type [3,6]18C3xC618,5
C3×S3Direct 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; = C2×D5102+D1020,4
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)54+F520,3
Dic5Dicyclic group; = C52C4202-Dic520,1
C2×C10Abelian 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; = C3Q8242-Dic624,4
SL2(𝔽3)Special linear group on 𝔽32; = Q8C3 = 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
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

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

Groups of order 28

dρLabelID
C28Cyclic group281C2828,2
D14Dihedral group; = C2×D7142+D1428,3
Dic7Dicyclic group; = C7C4282-Dic728,1
C2×C14Abelian 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
C5×S3Direct product of C5 and S3152C5xS330,1
C3×D5Direct 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; = D4D484+ES+(2,2)32,49
SD32Semidihedral group; = C162C2 = QD32162SD3232,19
2- 1+4Gamma matrices = Extraspecial group; = D4Q8164-ES-(2,2)32,50
M5(2)Modular maximal-cyclic group; = C163C2162M5(2)32,17
C4≀C2Wreath product of C4 by C282C4wrC232,11
C22≀C2Wreath product of C22 by C28C2^2wrC232,27
C8○D4Central product of C8 and D4162C8oD432,38
C4○D8Central product of C4 and D8162C4oD832,42
C23⋊C4The semidirect product of C23 and C4 acting faithfully84+C2^3:C432,6
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)84+C8:C2^232,43
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C216C4:D432,28
C41D4The semidirect product of C4 and D4 acting via D4/C4=C216C4:1D432,34
C22⋊C8The semidirect product of C22 and C8 acting via C8/C4=C216C2^2:C832,5
C22⋊Q8The semidirect product of C22 and Q8 acting via Q8/C4=C216C2^2:Q832,29
D4⋊C41st semidirect product of D4 and C4 acting via C4/C2=C216D4:C432,9
C42⋊C21st semidirect product of C42 and C2 acting faithfully16C4^2:C232,24
C422C22nd semidirect product of C42 and C2 acting faithfully16C4^2:2C232,33
C4⋊C8The semidirect product of C4 and C8 acting via C8/C4=C232C4:C832,12
C4⋊Q8The semidirect product of C4 and Q8 acting via Q8/C4=C232C4:Q832,35
C8⋊C43rd semidirect product of C8 and C4 acting via C4/C2=C232C8:C432,4
Q8⋊C41st semidirect product of Q8 and C4 acting via C4/C2=C232Q8:C432,10
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C284+C4.D432,7
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2162C8.C432,15
C4.4D44th non-split extension by C4 of D4 acting via D4/C4=C216C4.4D432,31
C8.C22The non-split extension by C8 of C22 acting faithfully164-C8.C2^232,44
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2164-C4.10D432,8
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C216C2^2.D432,30
C2.D82nd central extension by C2 of D832C2.D832,14
C4.Q81st non-split extension by C4 of Q8 acting via Q8/C4=C232C4.Q832,13
C2.C421st central stem extension by C2 of C4232C2.C4^232,2
C42.C24th non-split extension by C42 of C2 acting faithfully32C4^2.C232,32
C25Elementary abelian group of type [2,2,2,2,2]32C2^532,51
C4×C8Abelian group of type [4,8]32C4xC832,3
C2×C16Abelian group of type [2,16]32C2xC1632,16
C2×C42Abelian group of type [2,4,4]32C2xC4^232,21
C22×C8Abelian group of type [2,2,8]32C2^2xC832,36
C23×C4Abelian group of type [2,2,2,4]32C2^3xC432,45
C4×D4Direct product of C4 and D416C4xD432,25
C2×D8Direct product of C2 and D816C2xD832,39
C2×SD16Direct product of C2 and SD1616C2xSD1632,40
C22×D4Direct product of C22 and D416C2^2xD432,46
C2×M4(2)Direct product of C2 and M4(2)16C2xM4(2)32,37
C4×Q8Direct product of C4 and Q832C4xQ832,26
C2×Q16Direct product of C2 and Q1632C2xQ1632,41
C22×Q8Direct product of C22 and Q832C2^2xQ832,47
C2×C4○D4Direct product of C2 and C4○D416C2xC4oD432,48
C2×C22⋊C4Direct product of C2 and C22⋊C416C2xC2^2:C432,22
C2×C4⋊C4Direct product of C2 and C4⋊C432C2xC4:C432,23

Groups of order 33

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; = C2×D9182+D1836,4
Dic9Dicyclic group; = C9C4362-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
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 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; = C5Q8402-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
C52C8The semidirect product of C5 and C8 acting via C8/C4=C2402C5:2C840,1
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 41

dρLabelID
C41Cyclic group411C4141,1

Groups of order 42

dρLabelID
C42Cyclic group421C4242,6
D21Dihedral group212+D2142,5
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)76+F742,1
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 43

dρLabelID
C43Cyclic group431C4343,1

Groups of order 44

dρLabelID
C44Cyclic group441C4444,2
D22Dihedral group; = C2×D11222+D2244,3
Dic11Dicyclic group; = C11C4442-Dic1144,1
C2×C22Abelian group of type [2,22]44C2xC2244,4

Groups of order 45

dρLabelID
C45Cyclic group451C4545,1
C3×C15Abelian 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; = C31Q16482-Dic1248,8
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = 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
C4○D12Central 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
D42S3The semidirect product of D4 and S3 acting through Inn(D4)244-D4:2S348,39
Q82S3The semidirect product of Q8 and S3 acting via S3/C3=C2244+Q8:2S348,17
Q83S3The 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
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

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
C5×C10Abelian group of type [5,10]50C5xC1050,5
C5×D5Direct 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; = C2×D13262+D2652,4
Dic13Dicyclic group; = C132C4522-Dic1352,1
C13⋊C4The semidirect product of C13 and C4 acting faithfully134+C13:C452,3
C2×C26Abelian 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
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

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; = C23C7 = AGL1(𝔽8)87+F856,11
Dic14Dicyclic group; = C7Q8562-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
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

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
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simple53+A560,5
D30Dihedral group; = C2×D15302+D3060,12
Dic15Dicyclic group; = C3Dic5602-Dic1560,3
C3⋊F5The semidirect product of C3 and F5 acting via F5/D5=C2154C3:F560,7
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 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
C3×C21Abelian group of type [3,21]63C3xC2163,4
C3×C7⋊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; = C322C2 = QD64322SD6464,53
M6(2)Modular maximal-cyclic group; = C323C2322M6(2)64,51
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)84+C2wrC464,32
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)84+C2wrC2^264,138
C8○D8Central product of C8 and D8162C8oD864,124
D4○D8Central product of D4 and D8164+D4oD864,257
D4○SD16Central product of D4 and SD16164D4oSD1664,258
Q8○M4(2)Central product of Q8 and M4(2)164Q8oM4(2)64,249
Q8○D8Central product of Q8 and D8324-Q8oD864,259
D4○C16Central product of D4 and C16322D4oC1664,185
C4○D16Central product of C4 and D16322C4oD1664,189
C82M4(2)Central product of C8 and M4(2)32C8o2M4(2)64,86
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)84+D4:4D464,134
C42⋊C42nd semidirect product of C42 and C4 acting faithfully84+C4^2:C464,34
C23⋊C8The semidirect product of C23 and C8 acting via C8/C2=C416C2^3:C864,4
C16⋊C42nd semidirect product of C16 and C4 acting faithfully164C16:C464,28
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
D45D41st semidirect product of D4 and D4 acting through Inn(D4)16D4:5D464,227
C16⋊C22The semidirect product of C16 and C22 acting faithfully164+C16:C2^264,190
C426C43rd semidirect product of C42 and C4 acting via C4/C2=C216C4^2:6C464,20
C423C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
C243C41st semidirect product of C24 and C4 acting via C4/C2=C216C2^4:3C464,60
C22⋊D8The semidirect product of C22 and D8 acting via D8/D4=C216C2^2:D864,128
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C2216C2^3:3D464,215
C232Q82nd semidirect product of C23 and Q8 acting via Q8/C2=C2216C2^3:2Q864,224
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2164D8:C2^264,256
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2164M4(2):4C464,25
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfully164+M5(2):C264,42
C42⋊C221st semidirect product of C42 and C22 acting faithfully164C4^2:C2^264,102
C24⋊C224th semidirect product of C24 and C22 acting faithfully16C2^4:C2^264,242
C22⋊SD16The semidirect product of C22 and SD16 acting via SD16/D4=C216C2^2:SD1664,131
D4⋊C8The semidirect product of D4 and C8 acting via C8/C4=C232D4:C864,6
C89D43rd semidirect product of C8 and D4 acting via D4/C22=C232C8:9D464,116
C86D43rd semidirect product of C8 and D4 acting via D4/C4=C232C8:6D464,117
C4⋊D8The semidirect product of C4 and D8 acting via D8/D4=C232C4:D864,140
C88D42nd semidirect product of C8 and D4 acting via D4/C22=C232C8:8D464,146
C87D41st semidirect product of C8 and D4 acting via D4/C22=C232C8:7D464,147
C8⋊D41st semidirect product of C8 and D4 acting via D4/C2=C2232C8:D464,149
C82D42nd semidirect product of C8 and D4 acting via D4/C2=C2232C8:2D464,150
C85D42nd semidirect product of C8 and D4 acting via D4/C4=C232C8:5D464,173
C84D41st semidirect product of C8 and D4 acting via D4/C4=C232C8:4D464,174
C83D43rd semidirect product of C8 and D4 acting via D4/C2=C2232C8:3D464,177
D8⋊C43rd semidirect product of D8 and C4 acting via C4/C2=C2; = Aut(SD32)32D8:C464,123
D4⋊D42nd semidirect product of D4 and D4 acting via D4/C22=C232D4:D464,130
D46D42nd semidirect product of D4 and D4 acting through Inn(D4)32D4:6D464,228
C22⋊C16The semidirect product of C22 and C16 acting via C16/C8=C232C2^2:C1664,29
Q8⋊D41st semidirect product of Q8 and D4 acting via D4/C22=C232Q8:D464,129
D4⋊Q81st semidirect product of D4 and Q8 acting via Q8/C4=C232D4:Q864,155
D42Q82nd semidirect product of D4 and Q8 acting via Q8/C4=C232D4:2Q864,157
Q85D41st semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:5D464,229
Q86D42nd semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:6D464,231
D43Q8The semidirect product of D4 and Q8 acting through Inn(D4)32D4:3Q864,235
Q32⋊C22nd semidirect product of Q32 and C2 acting faithfully324-Q32:C264,191
C4⋊SD16The semidirect product of C4 and SD16 acting via SD16/Q8=C232C4:SD1664,141
C232D41st semidirect product of C23 and D4 acting via D4/C2=C2232C2^3:2D464,73
C23⋊Q81st semidirect product of C23 and Q8 acting via Q8/C2=C2232C2^3:Q864,74
SD16⋊C41st semidirect product of SD16 and C4 acting via C4/C2=C232SD16:C464,121
C4⋊M4(2)The semidirect product of C4 and M4(2) acting via M4(2)/C2×C4=C232C4:M4(2)64,104
C22⋊Q16The semidirect product of C22 and Q16 acting via Q16/Q8=C232C2^2:Q1664,132
M4(2)⋊C41st semidirect product of M4(2) and C4 acting via C4/C2=C232M4(2):C464,109
C8⋊Q8The semidirect product of C8 and Q8 acting via Q8/C2=C2264C8:Q864,182
C4⋊C16The semidirect product of C4 and C16 acting via C16/C8=C264C4:C1664,44
Q8⋊C8The semidirect product of Q8 and C8 acting via C8/C4=C264Q8:C864,7
C8⋊C83rd semidirect product of C8 and C8 acting via C8/C4=C264C8:C864,3
C82C82nd semidirect product of C8 and C8 acting via C8/C4=C264C8:2C864,15
C81C81st semidirect product of C8 and C8 acting via C8/C4=C264C8:1C864,16
C84Q83rd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:4Q864,127
C83Q82nd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:3Q864,179
C82Q81st semidirect product of C8 and Q8 acting via Q8/C4=C264C8:2Q864,181
C165C43rd semidirect product of C16 and C4 acting via C4/C2=C264C16:5C464,27
C163C41st semidirect product of C16 and C4 acting via C4/C2=C264C16:3C464,47
C164C42nd semidirect product of C16 and C4 acting via C4/C2=C264C16:4C464,48
Q8⋊Q81st semidirect product of Q8 and Q8 acting via Q8/C4=C264Q8:Q864,156
Q83Q8The semidirect product of Q8 and Q8 acting through Inn(Q8)64Q8:3Q864,238
C42Q16The semidirect product of C4 and Q16 acting via Q16/Q8=C264C4:2Q1664,143
C4⋊Q16The semidirect product of C4 and Q16 acting via Q16/C8=C264C4:Q1664,175
C424C41st semidirect product of C42 and C4 acting via C4/C2=C264C4^2:4C464,57
C428C45th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:8C464,63
C425C42nd semidirect product of C42 and C4 acting via C4/C2=C264C4^2:5C464,64
C429C46th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:9C464,65
Q16⋊C43rd semidirect product of Q16 and C4 acting via C4/C2=C264Q16:C464,122
(C22×C8)⋊C22nd semidirect product of C22×C8 and C2 acting faithfully32(C2^2xC8):C264,89
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22164C8.Q864,46
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2162C8.C864,45
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4164C2^3.C864,30
D4.8D43rd non-split extension by D4 of D4 acting via D4/C22=C2164D4.8D464,135
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2164D4.9D464,136
D4.3D43rd non-split extension by D4 of D4 acting via D4/C4=C2164D4.3D464,152
D4.4D44th non-split extension by D4 of D4 acting via D4/C4=C2164+D4.4D464,153
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2164C8.26D464,125
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2164-D4.10D464,137
C4.9C421st central stem extension by C4 of C42164C4.9C4^264,18
C42.C42nd non-split extension by C42 of C4 acting faithfully164C4^2.C464,36
C42.3C43rd non-split extension by C42 of C4 acting faithfully164-C4^2.3C464,37
C24.4C42nd non-split extension by C24 of C4 acting via C4/C2=C216C2^4.4C464,88
C2.C256th central stem extension by C2 of C25164C2.C2^564,266
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C2216C2^3.9D464,23
C23.D42nd non-split extension by C23 of D4 acting faithfully164C2^3.D464,33
C23.7D47th non-split extension by C23 of D4 acting faithfully164C2^3.7D464,139
C4.10C422nd central stem extension by C4 of C42164C4.10C4^264,19
C23.31D42nd non-split extension by C23 of D4 acting via D4/C22=C216C2^3.31D464,9
C23.37D48th non-split extension by C23 of D4 acting via D4/C22=C216C2^3.37D464,99
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2164M4(2).C464,111
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22164C2^3.C2^364,91
C22.SD161st non-split extension by C22 of SD16 acting via SD16/Q8=C216C2^2.SD1664,8
C22.11C247th central extension by C22 of C2416C2^2.11C2^464,199
C22.19C245th central stem extension by C22 of C2416C2^2.19C2^464,206
C22.29C2415th central stem extension by C22 of C2416C2^2.29C2^464,216
C22.32C2418th central stem extension by C22 of C2416C2^2.32C2^464,219
C22.45C2431st central stem extension by C22 of C2416C2^2.45C2^464,232
C22.54C2440th central stem extension by C22 of C2416C2^2.54C2^464,241
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2164M4(2).8C2^264,94
D4.C8The non-split extension by D4 of C8 acting via C8/C4=C2322D4.C864,31
D4.Q8The non-split extension by D4 of Q8 acting via Q8/C4=C232D4.Q864,159
C4.D81st non-split extension by C4 of D8 acting via D8/D4=C232C4.D864,12
C8.D41st non-split extension by C8 of D4 acting via D4/C2=C2232C8.D464,151
C4.4D84th non-split extension by C4 of D8 acting via D8/C8=C232C4.4D864,167
C8.2D42nd non-split extension by C8 of D4 acting via D4/C2=C2232C8.2D464,178
C8.4Q83rd non-split extension by C8 of Q8 acting via Q8/C4=C2322C8.4Q864,49
D8.C41st non-split extension by D8 of C4 acting via C4/C2=C2322D8.C464,40
D4.7D42nd non-split extension by D4 of D4 acting via D4/C22=C232D4.7D464,133
D4.D41st non-split extension by D4 of D4 acting via D4/C4=C232D4.D464,142
D4.2D42nd non-split extension by D4 of D4 acting via D4/C4=C232D4.2D464,144
D4.5D45th non-split extension by D4 of D4 acting via D4/C4=C2324-D4.5D464,154
C2.D161st central extension by C2 of D1632C2.D1664,38
C8.17D44th non-split extension by C8 of D4 acting via D4/C22=C2324-C8.17D464,43
C8.18D45th non-split extension by C8 of D4 acting via D4/C22=C232C8.18D464,148
C8.12D48th non-split extension by C8 of D4 acting via D4/C4=C232C8.12D464,176
Q8.D42nd non-split extension by Q8 of D4 acting via D4/C4=C232Q8.D464,145
C4.C423rd non-split extension by C4 of C42 acting via C42/C2×C4=C232C4.C4^264,22
C42.6C43rd non-split extension by C42 of C4 acting via C4/C2=C232C4^2.6C464,113
C22.D83rd non-split extension by C22 of D8 acting via D8/D4=C232C2^2.D864,161
C23.7Q82nd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.7Q864,61
C23.8Q83rd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.8Q864,66
C23.Q83rd non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.Q864,77
C23.4Q84th non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.4Q864,80
C42.12C49th non-split extension by C42 of C4 acting via C4/C2=C232C4^2.12C464,112
C23.34D45th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.34D464,62
C23.23D42nd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.23D464,67
C23.10D43rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.10D464,75
C23.11D44th non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.11D464,78
C23.24D43rd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.24D464,97
C23.36D47th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.36D464,98
C23.38D49th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.38D464,100
C23.25D44th non-split extension by C23 of D4 acting via D4/C4=C232C2^3.25D464,108
C23.46D417th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.46D464,162
C23.19D412nd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.19D464,163
C23.47D418th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.47D464,164
C23.48D419th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.48D464,165
C23.20D413rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.20D464,166
C42.C221st non-split extension by C42 of C22 acting faithfully32C4^2.C2^264,10
C22.C422nd non-split extension by C22 of C42 acting via C42/C2×C4=C232C2^2.C4^264,24
C24.C222nd non-split extension by C24 of C22 acting faithfully32C2^4.C2^264,69
C24.3C223rd non-split extension by C24 of C22 acting faithfully32C2^4.3C2^264,71
C42.6C226th non-split extension by C42 of C22 acting faithfully32C4^2.6C2^264,105
C42.7C227th non-split extension by C42 of C22 acting faithfully32C4^2.7C2^264,114
C42.78C2221st non-split extension by C42 of C22 acting via C22/C2=C232C4^2.78C2^264,169
C42.28C2228th non-split extension by C42 of C22 acting faithfully32C4^2.28C2^264,170
C42.29C2229th non-split extension by C42 of C22 acting faithfully32C4^2.29C2^264,171
C23.32C235th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.32C2^364,200
C23.33C236th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.33C2^364,201
C23.36C239th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.36C2^364,210
C22.26C2412nd central stem extension by C22 of C2432C2^2.26C2^464,213
C23.37C2310th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.37C2^364,214
C23.38C2311st non-split extension by C23 of C23 acting via C23/C22=C232C2^3.38C2^364,217
C22.31C2417th central stem extension by C22 of C2432C2^2.31C2^464,218
C22.33C2419th central stem extension by C22 of C2432C2^2.33C2^464,220
C22.34C2420th central stem extension by C22 of C2432C2^2.34C2^464,221
C22.35C2421st central stem extension by C22 of C2432C2^2.35C2^464,222
C22.36C2422nd central stem extension by C22 of C2432C2^2.36C2^464,223
C23.41C2314th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.41C2^364,225
C22.46C2432nd central stem extension by C22 of C2432C2^2.46C2^464,233
C22.47C2433rd central stem extension by C22 of C2432C2^2.47C2^464,234
C22.49C2435th central stem extension by C22 of C2432C2^2.49C2^464,236
C22.50C2436th central stem extension by C22 of C2432C2^2.50C2^464,237
C22.53C2439th central stem extension by C22 of C2432C2^2.53C2^464,240
C22.56C2442nd central stem extension by C22 of C2432C2^2.56C2^464,243
C22.57C2443rd central stem extension by C22 of C2432C2^2.57C2^464,244
C22.M4(2)2nd non-split extension by C22 of M4(2) acting via M4(2)/C2×C4=C232C2^2.M4(2)64,5
Q8.Q8The non-split extension by Q8 of Q8 acting via Q8/C4=C264Q8.Q864,160
C8.5Q84th non-split extension by C8 of Q8 acting via Q8/C4=C264C8.5Q864,180
C4.10D82nd non-split extension by C4 of D8 acting via D8/D4=C264C4.10D864,13
C4.6Q162nd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.6Q1664,14
C2.Q321st central extension by C2 of Q3264C2.Q3264,39
C4.Q163rd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.Q1664,158
C4.SD164th non-split extension by C4 of SD16 acting via SD16/C8=C264C4.SD1664,168
C22.4Q161st central extension by C22 of Q1664C2^2.4Q1664,21
C42.2C222nd non-split extension by C42 of C22 acting faithfully64C4^2.2C2^264,11
C22.7C422nd central extension by C22 of C4264C2^2.7C4^264,17
C23.63C2313rd central extension by C23 of C2364C2^3.63C2^364,68
C23.65C2315th central extension by C23 of C2364C2^3.65C2^364,70
C23.67C2317th central extension by C23 of C2364C2^3.67C2^364,72
C23.78C234th central stem extension by C23 of C2364C2^3.78C2^364,76
C23.81C237th central stem extension by C23 of C2364C2^3.81C2^364,79
C23.83C239th central stem extension by C23 of C2364C2^3.83C2^364,81
C23.84C2310th central stem extension by C23 of C2364C2^3.84C2^364,82
C42.30C2230th non-split extension by C42 of C22 acting faithfully64C4^2.30C2^264,172
C22.58C2444th central stem extension by C22 of C2464C2^2.58C2^464,245
C82Abelian group of type [8,8]64C8^264,2
C43Abelian group of type [4,4,4]64C4^364,55
C26Elementary abelian group of type [2,2,2,2,2,2]64C2^664,267
C4×C16Abelian group of type [4,16]64C4xC1664,26
C2×C32Abelian group of type [2,32]64C2xC3264,50
C23×C8Abelian group of type [2,2,2,8]64C2^3xC864,246
C24×C4Abelian group of type [2,2,2,2,4]64C2^4xC464,260
C22×C16Abelian group of type [2,2,16]64C2^2xC1664,183
C22×C42Abelian group of type [2,2,4,4]64C2^2xC4^264,192
C2×C4×C8Abelian group of type [2,4,8]64C2xC4xC864,83
D42Direct product of D4 and D416D4^264,226
C2×2+ 1+4Direct product of C2 and 2+ 1+416C2xES+(2,2)64,264
C8×D4Direct product of C8 and D432C8xD464,115
C4×D8Direct product of C4 and D832C4xD864,118
D4×Q8Direct product of D4 and Q832D4xQ864,230
C2×D16Direct product of C2 and D1632C2xD1664,186
C4×SD16Direct product of C4 and SD1632C4xSD1664,119
C2×SD32Direct product of C2 and SD3232C2xSD3264,187
C22×D8Direct product of C22 and D832C2^2xD864,250
D4×C23Direct product of C23 and D432D4xC2^364,261
C4×M4(2)Direct product of C4 and M4(2)32C4xM4(2)64,85
C2×M5(2)Direct product of C2 and M5(2)32C2xM5(2)64,184
C22×SD16Direct product of C22 and SD1632C2^2xSD1664,251
C22×M4(2)Direct product of C22 and M4(2)32C2^2xM4(2)64,247
C2×2- 1+4Direct product of C2 and 2- 1+432C2xES-(2,2)64,265
Q82Direct product of Q8 and Q864Q8^264,239
C8×Q8Direct product of C8 and Q864C8xQ864,126
C4×Q16Direct product of C4 and Q1664C4xQ1664,120
C2×Q32Direct product of C2 and Q3264C2xQ3264,188
Q8×C23Direct product of C23 and Q864Q8xC2^364,262
C22×Q16Direct product of C22 and Q1664C2^2xQ1664,252
C2×C4≀C2Direct product of C2 and C4≀C216C2xC4wrC264,101
C2×C23⋊C4Direct product of C2 and C23⋊C416C2xC2^3:C464,90
C2×C8⋊C22Direct product of C2 and C8⋊C2216C2xC8:C2^264,254
C2×C4.D4Direct product of C2 and C4.D416C2xC4.D464,92
C2×C22≀C2Direct product of C2 and C22≀C216C2xC2^2wrC264,202
C2×C4×D4Direct product of C2×C4 and D432C2xC4xD464,196
C4×C4○D4Direct product of C4 and C4○D432C4xC4oD464,198
C2×C8○D4Direct product of C2 and C8○D432C2xC8oD464,248
C2×C4○D8Direct product of C2 and C4○D832C2xC4oD864,253
C2×C4⋊D4Direct product of C2 and C4⋊D432C2xC4:D464,203
C2×D4⋊C4Direct product of C2 and D4⋊C432C2xD4:C464,95
C2×C8.C4Direct product of C2 and C8.C432C2xC8.C464,110
C2×C41D4Direct product of C2 and C41D432C2xC4:1D464,211
C4×C22⋊C4Direct product of C4 and C22⋊C432C4xC2^2:C464,58
C2×C22⋊C8Direct product of C2 and C22⋊C832C2xC2^2:C864,87
C2×C22⋊Q8Direct product of C2 and C22⋊Q832C2xC2^2:Q864,204
C2×C42⋊C2Direct product of C2 and C42⋊C232C2xC4^2:C264,195
C2×C4.4D4Direct product of C2 and C4.4D432C2xC4.4D464,207
C22×C4○D4Direct product of C22 and C4○D432C2^2xC4oD464,263
C2×C8.C22Direct product of C2 and C8.C2232C2xC8.C2^264,255
C2×C422C2Direct product of C2 and C422C232C2xC4^2:2C264,209
C2×C4.10D4Direct product of C2 and C4.10D432C2xC4.10D464,93
C22×C22⋊C4Direct product of C22 and C22⋊C432C2^2xC2^2:C464,193
C2×C22.D4Direct product of C2 and C22.D432C2xC2^2.D464,205
C4×C4⋊C4Direct product of C4 and C4⋊C464C4xC4:C464,59
C2×C4⋊C8Direct product of C2 and C4⋊C864C2xC4:C864,103
C2×C4×Q8Direct product of C2×C4 and Q864C2xC4xQ864,197
C2×C4⋊Q8Direct product of C2 and C4⋊Q864C2xC4:Q864,212
C2×C8⋊C4Direct product of C2 and C8⋊C464C2xC8:C464,84
C22×C4⋊C4Direct product of C22 and C4⋊C464C2^2xC4:C464,194
C2×Q8⋊C4Direct product of C2 and Q8⋊C464C2xQ8:C464,96
C2×C2.D8Direct product of C2 and C2.D864C2xC2.D864,107
C2×C4.Q8Direct product of C2 and C4.Q864C2xC4.Q864,106
C2×C2.C42Direct product of C2 and C2.C4264C2xC2.C4^264,56
C2×C42.C2Direct product of C2 and C42.C264C2xC4^2.C264,208

Groups of order 65

dρLabelID
C65Cyclic group651C6565,1

Groups of order 66

dρLabelID
C66Cyclic group661C6666,4
D33Dihedral group332+D3366,3
S3×C11Direct product of C11 and S3332S3xC1166,1
C3×D11Direct product of C3 and D11332C3xD1166,2

Groups of order 67

dρLabelID
C67Cyclic group671C6767,1

Groups of order 68

dρLabelID
C68Cyclic group681C6868,2
D34Dihedral group; = C2×D17342+D3468,4
Dic17Dicyclic group; = C172C4682-Dic1768,1
C17⋊C4The semidirect product of C17 and C4 acting faithfully174+C17:C468,3
C2×C34Abelian group of type [2,34]68C2xC3468,5

Groups of order 69

dρLabelID
C69Cyclic group691C6969,1

Groups of order 70

dρLabelID
C70Cyclic group701C7070,4
D35Dihedral group352+D3570,3
C7×D5Direct product of C7 and D5352C7xD570,1
C5×D7Direct 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; = C32C8 = AGL1(𝔽9)98+F972,39
Dic18Dicyclic group; = C9Q8722-Dic1872,4
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M998+PSU(3,2)72,41
S3≀C2Wreath 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
C322C8The semidirect product of C32 and C8 acting via C8/C2=C4244-C3^2:2C872,19
C322Q8The 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
C327D42nd 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
C324C82nd semidirect product of C32 and C8 acting via C8/C4=C272C3^2:4C872,13
C324Q82nd 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
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 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
C5×C15Abelian group of type [5,15]75C5xC1575,3

Groups of order 76

dρLabelID
C76Cyclic group761C7676,2
D38Dihedral group; = C2×D19382+D3876,3
Dic19Dicyclic group; = C19C4762-Dic1976,1
C2×C38Abelian group of type [2,38]76C2xC3876,4

Groups of order 77

dρLabelID
C77Cyclic group771C7777,1

Groups of order 78

dρLabelID
C78Cyclic group781C7878,6
D39Dihedral group392+D3978,5
C13⋊C6The semidirect product of C13 and C6 acting faithfully136+C13:C678,1
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 79

dρLabelID
C79Cyclic group791C7979,1

Groups of order 80

dρLabelID
C80Cyclic group801C8080,2
D40Dihedral group402+D4080,7
Dic20Dicyclic group; = C51Q16802-Dic2080,8
C4○D20Central 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
D42D5The semidirect product of D4 and D5 acting through Inn(D4)404-D4:2D580,40
Q82D5The 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
C52C16The 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
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

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

Groups of order 82

dρLabelID
C82Cyclic group821C8282,2
D41Dihedral group412+D4182,1

Groups of order 83

dρLabelID
C83Cyclic group831C8383,1

Groups of order 84

dρLabelID
C84Cyclic group841C8484,6
D42Dihedral group; = C2×D21422+D4284,14
Dic21Dicyclic group; = C3Dic7842-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
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

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; = C11Q8882-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
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 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
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

dρLabelID
C91Cyclic group911C9191,1

Groups of order 92

dρLabelID
C92Cyclic group921C9292,2
D46Dihedral group; = C2×D23462+D4692,3
Dic23Dicyclic group; = C23C4922-Dic2392,1
C2×C46Abelian 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; = C31Q32962-Dic2496,8
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4242U(2,3)96,67
D4○D12Central product of D4 and D12244+D4oD1296,216
C8○D12Central product of C8 and D12482C8oD1296,108
C4○D24Central product of C4 and D24482C4oD2496,111
Q8○D12Central 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
D46D62nd semidirect product of D4 and D6 acting through Inn(D4)244D4:6D696,211
Q83D62nd 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
C424S33rd semidirect product of C42 and S3 acting via S3/C3=C2242C4^2:4S396,12
C244S31st semidirect product of C24 and S3 acting via S3/C3=C224C2^4:4S396,160
C232D61st semidirect product of C23 and D6 acting via D6/C3=C2224C2^3:2D696,144
Q83Dic32nd semidirect product of Q8 and Dic3 acting via Dic3/C6=C2244Q8:3Dic396,44
D126C224th 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
D83S3The semidirect product of D8 and S3 acting through Inn(D8)484-D8:3S396,119
D63D43rd 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
C127D41st semidirect product of C12 and D4 acting via D4/C22=C248C12:7D496,137
C123D43rd 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
D63Q83rd 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
C422S31st semidirect product of C42 and S3 acting via S3/C3=C248C4^2:2S396,79
C427S36th semidirect product of C42 and S3 acting via S3/C3=C248C4^2:7S396,82
C423S32nd 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
Dic34D41st 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
Dic35D42nd 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
C241C41st 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
C122Q81st 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
Q82Dic31st 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⋊C47S31st 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/C2×C4=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
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 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
C7×C14Abelian group of type [7,14]98C7xC1498,5
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)142C7xD798,3

Groups of order 99

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

Groups of order 100

dρLabelID
C100Cyclic group1001C100100,2
D50Dihedral group; = C2×D25502+D50100,4
Dic25Dicyclic group; = C252C41002-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
C526C42nd 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
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 101

dρLabelID
C101Cyclic group1011C101101,1

Groups of order 102

dρLabelID
C102Cyclic group1021C102102,4
D51Dihedral group512+D51102,3
S3×C17Direct product of C17 and S3512S3xC17102,1
C3×D17Direct 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; = C13Q81042-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
C132C8The semidirect product of C13 and C8 acting via C8/C4=C21042C13:2C8104,1
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

dρLabelID
C105Cyclic group1051C105105,2
C5×C7⋊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; = C2×D27542+D54108,4
Dic27Dicyclic group; = C27C41082-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
C324D6The 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
He33C42nd 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
C335C43rd 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
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 109

dρLabelID
C109Cyclic group1091C109109,1

Groups of order 110

dρLabelID
C110Cyclic group1101C110110,6
D55Dihedral group552+D55110,5
F11Frobenius group; = C11C10 = AGL1(𝔽11) = Aut(D11) = Hol(C11)1110+F11110,1
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

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; = C71Q161122-Dic28112,7
C4○D28Central 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
D42D7The semidirect product of D4 and D7 acting through Inn(D4)564-D4:2D7112,32
Q82D7The 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
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 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
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

dρLabelID
C115Cyclic group1151C115115,1

Groups of order 116

dρLabelID
C116Cyclic group1161C116116,2
D58Dihedral group; = C2×D29582+D58116,4
Dic29Dicyclic group; = C292C41162-Dic29116,1
C29⋊C4The semidirect product of C29 and C4 acting faithfully294+C29:C4116,3
C2×C58Abelian 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
C3×C39Abelian group of type [3,39]117C3xC39117,4
C3×C13⋊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
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simple54+S5120,34
D60Dihedral group602+D60120,28
Dic30Dicyclic group; = C152Q81202-Dic30120,26
SL2(𝔽5)Special linear group on 𝔽52; = C2.A5 = 2I = <2,3,5>242-SL(2,5)120,5
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
C157D41st 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
C153C81st 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
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

Groups of order 121

dρLabelID
C121Cyclic group1211C121121,1
C112Elementary abelian group of type [11,11]121C11^2121,2

Groups of order 122

dρLabelID
C122Cyclic group1221C122122,2
D61Dihedral group612+D61122,1

Groups of order 123

dρLabelID
C123Cyclic group1231C123123,1

Groups of order 124

dρLabelID
C124Cyclic group1241C124124,2
D62Dihedral group; = C2×D31622+D62124,3
Dic31Dicyclic group; = C31C41242-Dic31124,1
C2×C62Abelian group of type [2,62]124C2xC62124,4

Groups of order 125

dρLabelID
C125Cyclic group1251C125125,1
He5Heisenberg group; = C52C5 = 5+ 1+2255He5125,3
5- 1+2Extraspecial group255ES-(5,1)125,4
C53Elementary abelian group of type [5,5,5]125C5^3125,5
C5×C25Abelian group of type [5,25]125C5xC25125,2

Groups of order 126

dρLabelID
C126Cyclic group1261C126126,6
D63Dihedral group632+D63126,5
C3⋊F7The semidirect product of C3 and F7 acting via F7/C7⋊C3=C2216+C3:F7126,9
C7⋊C18The semidirect product of C7 and C18 acting via C18/C3=C6636C7:C18126,1
C3⋊D21The semidirect product of C3 and D21 acting via D21/C21=C263C3:D21126,15
C3×C42Abelian group of type [3,42]126C3xC42126,16
C3×F7Direct product of C3 and F7216C3xF7126,7
S3×C21Direct product of C21 and S3422S3xC21126,12
C3×D21Direct product of C3 and D21422C3xD21126,13
C7×D9Direct product of C7 and D9632C7xD9126,3
C9×D7Direct product of C9 and D7632C9xD7126,4
C32×D7Direct product of C32 and D763C3^2xD7126,11
S3×C7⋊C3Direct product of S3 and C7⋊C3216S3xC7:C3126,8
C6×C7⋊C3Direct product of C6 and C7⋊C3423C6xC7:C3126,10
C7×C3⋊S3Direct product of C7 and C3⋊S363C7xC3:S3126,14
C2×C7⋊C9Direct product of C2 and C7⋊C91263C2xC7:C9126,2

Groups of order 127

dρLabelID
C127Cyclic group1271C127127,1

Groups of order 128

dρLabelID
C128Cyclic group1281C128128,1
D64Dihedral group642+D64128,161
Q128Generalised quaternion group; = C64.C2 = Dic321282-Q128128,163
2+ 1+6Extraspecial group; = D42+ 1+4168+ES+(2,3)128,2326
2- 1+6Extraspecial group; = D42- 1+4328-ES-(2,3)128,2327
SD128Semidihedral group; = C642C2 = QD128642SD128128,162
M7(2)Modular maximal-cyclic group; = C643C2642M7(2)128,160
D4≀C2Wreath product of D4 by C284+D4wrC2128,928
C8≀C2Wreath product of C8 by C2162C8wrC2128,67
Q8≀C2Wreath product of Q8 by C2164-Q8wrC2128,937
C23≀C2Wreath product of C23 by C216C2^3wrC2128,1578
(C2×C4)≀C2Wreath product of C2×C4 by C216(C2xC4)wrC2128,628
D8○D8Central product of D8 and D8164+D8oD8128,2024
C16○D8Central product of C16 and D8322C16oD8128,902
C8○D16Central product of C8 and D16322C8oD16128,910
D4○D16Central product of D4 and D16324+D4oD16128,2147
D8○Q16Central product of D8 and Q16324-D8oQ16128,2025
D8○SD16Central product of D8 and SD16324D8oSD16128,2022
D4○SD32Central product of D4 and SD32324D4oSD32128,2148
M4(2)○D8Central product of M4(2) and D8324M4(2)oD8128,1689
Q8○M5(2)Central product of Q8 and M5(2)324Q8oM5(2)128,2139
M4(2)○2M4(2)Central product of M4(2) and M4(2)32M4(2)o2M4(2)128,1605
D4○C32Central product of D4 and C32642D4oC32128,990
C4○D32Central product of C4 and D32642C4oD32128,994
Q8○D16Central product of Q8 and D16644-Q8oD16128,2149
C162M5(2)Central product of C16 and M5(2)64C16o2M5(2)128,840
C4○C2≀C4Central product of C4 and C2≀C4164C4oC2wrC4128,852
D4○(C22⋊C8)Central product of D4 and C22⋊C832D4o(C2^2:C8)128,1612
D8⋊D4The semidirect product of D8 and D4 acting via D4/C2=C22168+D8:D4128,922
D16⋊C4The semidirect product of D16 and C4 acting faithfully; = Aut(D16) = Hol(C16)168+D16:C4128,913
C23⋊D8The semidirect product of C23 and D8 acting via D8/C2=D416C2^3:D8128,327
C24⋊Q8The semidirect product of C24 and Q8 acting faithfully168+C2^4:Q8128,764
D83D42nd semidirect product of D8 and D4 acting via D4/C4=C2164+D8:3D4128,945
D86D45th semidirect product of D8 and D4 acting via D4/C4=C2164D8:6D4128,2023
D83Q83rd semidirect product of D8 and Q8 acting via Q8/C4=C2164D8:3Q8128,962
D811D45th semidirect product of D8 and D4 acting via D4/C22=C2168+D8:11D4128,2020
C24⋊C81st semidirect product of C24 and C8 acting via C8/C2=C416C2^4:C8128,48
C25⋊C41st semidirect product of C25 and C4 acting faithfully16C2^5:C4128,513
C42⋊D41st semidirect product of C42 and D4 acting faithfully168+C4^2:D4128,643
C429D43rd semidirect product of C42 and D4 acting via D4/C2=C2216C4^2:9D4128,734
C422D42nd semidirect product of C42 and D4 acting faithfully164C4^2:2D4128,742
C24⋊D41st semidirect product of C24 and D4 acting faithfully16C2^4:D4128,753
C424D44th semidirect product of C42 and D4 acting faithfully164C4^2:4D4128,929
C425D45th semidirect product of C42 and D4 acting faithfully168+C4^2:5D4128,931
C426D46th semidirect product of C42 and D4 acting faithfully168+C4^2:6D4128,932
C242Q81st semidirect product of C24 and Q8 acting via Q8/C2=C2216C2^4:2Q8128,761
D8⋊C236th semidirect product of D8 and C23 acting via C23/C22=C2168+D8:C2^3128,2317
M4(2)⋊5D45th semidirect product of M4(2) and D4 acting via D4/C2=C22168+M4(2):5D4128,740
C24⋊C232nd semidirect product of C24 and C23 acting faithfully168+C2^4:C2^3128,1758
C42⋊C234th semidirect product of C42 and C23 acting faithfully16C4^2:C2^3128,2264

Full list: Groups of order 128 (2328 groups)

Groups of order 129

dρLabelID
C129Cyclic group1291C129129,2
C43⋊C3The semidirect product of C43 and C3 acting faithfully433C43:C3129,1

Groups of order 130

dρLabelID
C130Cyclic group1301C130130,4
D65Dihedral group652+D65130,3
D5×C13Direct product of C13 and D5652D5xC13130,1
C5×D13Direct product of C5 and D13652C5xD13130,2

Groups of order 131

dρLabelID
C131Cyclic group1311C131131,1

Groups of order 132

dρLabelID
C132Cyclic group1321C132132,4
D66Dihedral group; = C2×D33662+D66132,9
Dic33Dicyclic group; = C331C41322-Dic33132,3
C2×C66Abelian group of type [2,66]132C2xC66132,10
S3×D11Direct product of S3 and D11334+S3xD11132,5
C11×A4Direct product of C11 and A4443C11xA4132,6
S3×C22Direct product of C22 and S3662S3xC22132,8
C6×D11Direct product of C6 and D11662C6xD11132,7
C11×Dic3Direct product of C11 and Dic31322C11xDic3132,1
C3×Dic11Direct product of C3 and Dic111322C3xDic11132,2

Groups of order 133

dρLabelID
C133Cyclic group1331C133133,1

Groups of order 134

dρLabelID
C134Cyclic group1341C134134,2
D67Dihedral group672+D67134,1

Groups of order 135

dρLabelID
C135Cyclic group1351C135135,1
C3×C45Abelian group of type [3,45]135C3xC45135,2
C32×C15Abelian group of type [3,3,15]135C3^2xC15135,5
C5×He3Direct product of C5 and He3453C5xHe3135,3
C5×3- 1+2Direct product of C5 and 3- 1+2453C5xES-(3,1)135,4

Groups of order 136

dρLabelID
C136Cyclic group1361C136136,2
D68Dihedral group682+D68136,6
Dic34Dicyclic group; = C17Q81362-Dic34136,4
C17⋊C8The semidirect product of C17 and C8 acting faithfully178+C17:C8136,12
C17⋊D4The semidirect product of C17 and D4 acting via D4/C22=C2682C17:D4136,8
C173C8The semidirect product of C17 and C8 acting via C8/C4=C21362C17:3C8136,1
C172C8The semidirect product of C17 and C8 acting via C8/C2=C41364-C17:2C8136,3
C2×C68Abelian group of type [2,68]136C2xC68136,9
C22×C34Abelian group of type [2,2,34]136C2^2xC34136,15
C4×D17Direct product of C4 and D17682C4xD17136,5
D4×C17Direct product of C17 and D4682D4xC17136,10
C22×D17Direct product of C22 and D1768C2^2xD17136,14
Q8×C17Direct product of C17 and Q81362Q8xC17136,11
C2×Dic17Direct product of C2 and Dic17136C2xDic17136,7
C2×C17⋊C4Direct product of C2 and C17⋊C4344+C2xC17:C4136,13

Groups of order 137

dρLabelID
C137Cyclic group1371C137137,1

Groups of order 138

dρLabelID
C138Cyclic group1381C138138,4
D69Dihedral group692+D69138,3
S3×C23Direct product of C23 and S3692S3xC23138,1
C3×D23Direct product of C3 and D23692C3xD23138,2

Groups of order 139

dρLabelID
C139Cyclic group1391C139139,1

Groups of order 140

dρLabelID
C140Cyclic group1401C140140,4
D70Dihedral group; = C2×D35702+D70140,10
Dic35Dicyclic group; = C7Dic51402-Dic35140,3
C7⋊F5The semidirect product of C7 and F5 acting via F5/D5=C2354C7:F5140,6
C2×C70Abelian group of type [2,70]140C2xC70140,11
D5×D7Direct product of D5 and D7354+D5xD7140,7
C7×F5Direct product of C7 and F5354C7xF5140,5
C10×D7Direct product of C10 and D7702C10xD7140,8
D5×C14Direct product of C14 and D5702D5xC14140,9
C7×Dic5Direct product of C7 and Dic51402C7xDic5140,1
C5×Dic7Direct product of C5 and Dic71402C5xDic7140,2

Groups of order 141

dρLabelID
C141Cyclic group1411C141141,1

Groups of order 142

dρLabelID
C142Cyclic group1421C142142,2
D71Dihedral group712+D71142,1

Groups of order 143

dρLabelID
C143Cyclic group1431C143143,1

Groups of order 144

dρLabelID
C144Cyclic group1441C144144,2
D72Dihedral group722+D72144,8
Dic36Dicyclic group; = C91Q161442-Dic36144,4
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)98+AGammaL(1,9)144,182
C62⋊C41st semidirect product of C62 and C4 acting faithfully124+C6^2:C4144,136
Dic3⋊D62nd semidirect product of Dic3 and D6 acting via D6/S3=C2; = Hol(Dic3)124+Dic3:D6144,154
C32⋊D8The semidirect product of C32 and D8 acting via D8/C2=D4244C3^2:D8144,117
D6⋊D62nd semidirect product of D6 and D6 acting via D6/S3=C2244D6:D6144,145
C3⋊D24The semidirect product of C3 and D24 acting via D24/D12=C2244+C3:D24144,57
D12⋊S33rd semidirect product of D12 and S3 acting via S3/C3=C2244D12:S3144,139
C325SD163rd semidirect product of C32 and SD16 acting via SD16/C4=C22244+C3^2:5SD16144,60
C322SD16The semidirect product of C32 and SD16 acting via SD16/C2=D4244-C3^2:2SD16144,118
C32⋊M4(2)The semidirect product of C32 and M4(2) acting via M4(2)/C4=C4244C3^2:M4(2)144,131
C42⋊C9The semidirect product of C42 and C9 acting via C9/C3=C3363C4^2:C9144,3
C24⋊C92nd semidirect product of C24 and C9 acting via C9/C3=C336C2^4:C9144,111
C32⋊Q16The semidirect product of C32 and Q16 acting via Q16/C2=D4484-C3^2:Q16144,119
D6⋊Dic3The semidirect product of D6 and Dic3 acting via Dic3/C6=C248D6:Dic3144,64
C322D81st semidirect product of C32 and D8 acting via D8/C4=C22484C3^2:2D8144,56
D125S3The semidirect product of D12 and S3 acting through Inn(D12)484-D12:5S3144,138
C322C16The semidirect product of C32 and C16 acting via C16/C4=C4484C3^2:2C16144,51
C322Q161st semidirect product of C32 and Q16 acting via Q16/C4=C22484C3^2:2Q16144,61
C323Q162nd semidirect product of C32 and Q16 acting via Q16/C4=C22484-C3^2:3Q16144,62
Dic3⋊Dic3The semidirect product of Dic3 and Dic3 acting via Dic3/C6=C248Dic3:Dic3144,66
Dic6⋊S32nd semidirect product of Dic6 and S3 acting via S3/C3=C2484Dic6:S3144,58
D4⋊D9The semidirect product of D4 and D9 acting via D9/C9=C2724+D4:D9144,16
Q8⋊D9The semidirect product of Q8 and D9 acting via D9/C3=S3724+Q8:D9144,32
D18⋊C4The semidirect product of D18 and C4 acting via C4/C2=C272D18:C4144,14
C8⋊D93rd semidirect product of C8 and D9 acting via D9/C9=C2722C8:D9144,6
C72⋊C22nd semidirect product of C72 and C2 acting faithfully722C72:C2144,7
C24⋊S35th semidirect product of C24 and S3 acting via S3/C3=C272C24:S3144,86
C242S32nd semidirect product of C24 and S3 acting via S3/C3=C272C24:2S3144,87
D42D9The semidirect product of D4 and D9 acting through Inn(D4)724-D4:2D9144,42
Q82D9The semidirect product of Q8 and D9 acting via D9/C9=C2724+Q8:2D9144,18
Q83D9The semidirect product of Q8 and D9 acting through Inn(Q8)724+Q8:3D9144,44
C325D82nd semidirect product of C32 and D8 acting via D8/C8=C272C3^2:5D8144,88
C327D82nd semidirect product of C32 and D8 acting via D8/D4=C272C3^2:7D8144,96
D365C2The semidirect product of D36 and C2 acting through Inn(D36)722D36:5C2144,40
C625C43rd semidirect product of C62 and C4 acting via C4/C2=C272C6^2:5C4144,100
C329SD162nd semidirect product of C32 and SD16 acting via SD16/D4=C272C3^2:9SD16144,97
C3211SD162nd semidirect product of C32 and SD16 acting via SD16/Q8=C272C3^2:11SD16144,98
C9⋊C16The semidirect product of C9 and C16 acting via C16/C8=C21442C9:C16144,1
C4⋊Dic9The semidirect product of C4 and Dic9 acting via Dic9/C18=C2144C4:Dic9144,13
C9⋊Q16The semidirect product of C9 and Q16 acting via Q16/Q8=C21444-C9:Q16144,17
Dic9⋊C4The semidirect product of Dic9 and C4 acting via C4/C2=C2144Dic9:C4144,12
C325Q162nd semidirect product of C32 and Q16 acting via Q16/C8=C2144C3^2:5Q16144,89
C327Q162nd semidirect product of C32 and Q16 acting via Q16/Q8=C2144C3^2:7Q16144,99
C12⋊Dic31st semidirect product of C12 and Dic3 acting via Dic3/C6=C2144C12:Dic3144,94
S32⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2124+S3^2:C4144,115
C3⋊S33C82nd semidirect product of C3⋊S3 and C8 acting via C8/C4=C2244C3:S3:3C8144,130
C4⋊(C32⋊C4)The semidirect product of C4 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2244C4:(C3^2:C4)144,133
C6.6S46th non-split extension by C6 of S4 acting via S4/A4=C2244+C6.6S4144,125
D6.D61st non-split extension by D6 of D6 acting via D6/C6=C2244D6.D6144,141
D6.6D62nd non-split extension by D6 of D6 acting via D6/C6=C2244+D6.6D6144,142
D6.3D63rd non-split extension by D6 of D6 acting via D6/S3=C2244D6.3D6144,147
D6.4D64th non-split extension by D6 of D6 acting via D6/S3=C2244-D6.4D6144,148
C12.29D63rd non-split extension by C12 of D6 acting via D6/S3=C2244C12.29D6144,53
C12.31D65th non-split extension by C12 of D6 acting via D6/S3=C2244C12.31D6144,55
C6.D126th non-split extension by C6 of D12 acting via D12/D6=C224C6.D12144,65
C62.C42nd non-split extension by C62 of C4 acting faithfully244-C6^2.C4144,135
Dic3.D62nd non-split extension by Dic3 of D6 acting via D6/S3=C2244Dic3.D6144,140
C2.PSU3(𝔽2)The central extension by C2 of PSU3(𝔽2)248+C2.PSU(3,2)144,120
C6.S43rd non-split extension by C6 of S4 acting via S4/A4=C2366-C6.S4144,33
C6.7S47th non-split extension by C6 of S4 acting via S4/A4=C2366-C6.7S4144,126
C2.F9The central extension by C2 of F9488-C2.F9144,114
C6.5S45th non-split extension by C6 of S4 acting via S4/A4=C2484-C6.5S4144,124
D6.Dic3The non-split extension by D6 of Dic3 acting via Dic3/C6=C2484D6.Dic3144,54
Dic3.A4The non-split extension by Dic3 of A4 acting through Inn(Dic3)484+Dic3.A4144,127
D12.S31st non-split extension by D12 of S3 acting via S3/C3=C2484-D12.S3144,59
C62.C225th non-split extension by C62 of C22 acting faithfully48C6^2.C2^2144,67
D4.D9The non-split extension by D4 of D9 acting via D9/C9=C2724-D4.D9144,15
Q8.C18The non-split extension by Q8 of C18 acting via C18/C6=C3722Q8.C18144,36
C4.Dic9The non-split extension by C4 of Dic9 acting via Dic9/C18=C2722C4.Dic9144,10
C18.D47th non-split extension by C18 of D4 acting via D4/C22=C272C18.D4144,19
C12.58D619th non-split extension by C12 of D6 acting via D6/C6=C272C12.58D6144,91
C6.11D1211st non-split extension by C6 of D12 acting via D12/C12=C272C6.11D12144,95
C12.59D620th non-split extension by C12 of D6 acting via D6/C6=C272C12.59D6144,171
C12.D624th non-split extension by C12 of D6 acting via D6/C3=C2272C12.D6144,173
C12.26D626th non-split extension by C12 of D6 acting via D6/C3=C2272C12.26D6144,175
Q8.D9The non-split extension by Q8 of D9 acting via D9/C3=S31444-Q8.D9144,31
C24.S39th non-split extension by C24 of S3 acting via S3/C3=C2144C24.S3144,29
C6.Dic64th non-split extension by C6 of Dic6 acting via Dic6/C12=C2144C6.Dic6144,93
C3⋊S3.Q8The non-split extension by C3⋊S3 of Q8 acting via Q8/C2=C22244C3:S3.Q8144,116
C122Abelian group of type [12,12]144C12^2144,101
C4×C36Abelian group of type [4,36]144C4xC36144,20
C2×C72Abelian group of type [2,72]144C2xC72144,23
C3×C48Abelian group of type [3,48]144C3xC48144,30
C6×C24Abelian group of type [6,24]144C6xC24144,104
C22×C36Abelian group of type [2,2,36]144C2^2xC36144,47
C23×C18Abelian group of type [2,2,2,18]144C2^3xC18144,113
C22×C62Abelian group of type [2,2,6,6]144C2^2xC6^2144,197
C2×C6×C12Abelian group of type [2,6,12]144C2xC6xC12144,178
A42Direct product of A4 and A4; = PΩ+4(𝔽3)129+A4^2144,184
S3×S4Direct product of S3 and S4; = Hol(C2×C6)126+S3xS4144,183
C6×S4Direct product of C6 and S4183C6xS4144,188
C2×F9Direct product of C2 and F9188+C2xF9144,185
C2×PSU3(𝔽2)Direct product of C2 and PSU3(𝔽2)188+C2xPSU(3,2)144,187
S3×D12Direct product of S3 and D12244+S3xD12144,144
C3×GL2(𝔽3)Direct product of C3 and GL2(𝔽3)242C3xGL(2,3)144,122
S3×SL2(𝔽3)Direct product of S3 and SL2(𝔽3); = SL2(ℤ/6ℤ)244-S3xSL(2,3)144,128
D4×D9Direct product of D4 and D9364+D4xD9144,41
C12×A4Direct product of C12 and A4363C12xA4144,155
Dic3×A4Direct product of Dic3 and A4366-Dic3xA4144,129
S3×C24Direct product of C24 and S3482S3xC24144,69
C3×D24Direct product of C3 and D24482C3xD24144,72
C6×D12Direct product of C6 and D1248C6xD12144,160
Dic32Direct product of Dic3 and Dic348Dic3^2144,63
S3×Dic6Direct product of S3 and Dic6484-S3xDic6144,137
C6×Dic6Direct product of C6 and Dic648C6xDic6144,158
C3×Dic12Direct product of C3 and Dic12482C3xDic12144,73
Dic3×C12Direct product of C12 and Dic348Dic3xC12144,76
C6×SL2(𝔽3)Direct product of C6 and SL2(𝔽3)48C6xSL(2,3)144,156
C3×CSU2(𝔽3)Direct product of C3 and CSU2(𝔽3)482C3xCSU(2,3)144,121
C8×D9Direct product of C8 and D9722C8xD9144,5
C9×D8Direct product of C9 and D8722C9xD8144,25
Q8×D9Direct product of Q8 and D9724-Q8xD9144,43
C2×D36Direct product of C2 and D3672C2xD36144,39
D4×C18Direct product of C18 and D472D4xC18144,48
C9×SD16Direct product of C9 and SD16722C9xSD16144,26
C32×D8Direct product of C32 and D872C3^2xD8144,106
C23×D9Direct product of C23 and D972C2^3xD9144,112
C9×M4(2)Direct product of C9 and M4(2)722C9xM4(2)144,24
C32×SD16Direct product of C32 and SD1672C3^2xSD16144,107
C32×M4(2)Direct product of C32 and M4(2)72C3^2xM4(2)144,105
C9×Q16Direct product of C9 and Q161442C9xQ16144,27
Q8×C18Direct product of C18 and Q8144Q8xC18144,49
C4×Dic9Direct product of C4 and Dic9144C4xDic9144,11
C2×Dic18Direct product of C2 and Dic18144C2xDic18144,37
C32×Q16Direct product of C32 and Q16144C3^2xQ16144,108
C22×Dic9Direct product of C22 and Dic9144C2^2xDic9144,45
C2×S3≀C2Direct product of C2 and S3≀C2124+C2xS3wrC2144,186
C2×S3×A4Direct product of C2, S3 and A4186+C2xS3xA4144,190
C2×C3⋊S4Direct product of C2 and C3⋊S4186+C2xC3:S4144,189
C2×C3.S4Direct product of C2 and C3.S4186+C2xC3.S4144,109
C4×S32Direct product of C4, S3 and S3244C4xS3^2144,143
C3×S3×D4Direct product of C3, S3 and D4244C3xS3xD4144,162
S3×C3⋊D4Direct product of S3 and C3⋊D4244S3xC3:D4144,153
C6×C3⋊D4Direct product of C6 and C3⋊D424C6xC3:D4144,167
C3×D4⋊S3Direct product of C3 and D4⋊S3244C3xD4:S3144,80
C22×S32Direct product of C22, S3 and S324C2^2xS3^2144,192
C4×C32⋊C4Direct product of C4 and C32⋊C4244C4xC3^2:C4144,132
C3×C4○D12Direct product of C3 and C4○D12242C3xC4oD12144,161
C2×C3⋊D12Direct product of C2 and C3⋊D1224C2xC3:D12144,151
C3×D4.S3Direct product of C3 and D4.S3244C3xD4.S3144,81
C3×C6.D4Direct product of C3 and C6.D424C3xC6.D4144,84
C2×C6.D6Direct product of C2 and C6.D624C2xC6.D6144,149
C3×D42S3Direct product of C3 and D42S3244C3xD4:2S3144,163
C22×C32⋊C4Direct product of C22 and C32⋊C424C2^2xC3^2:C4144,191
C3×C4.Dic3Direct product of C3 and C4.Dic3242C3xC4.Dic3144,75
A4×C2×C6Direct product of C2×C6 and A436A4xC2xC6144,193
D4×C3⋊S3Direct product of D4 and C3⋊S336D4xC3:S3144,172
C3×A4⋊C4Direct product of C3 and A4⋊C4363C3xA4:C4144,123
C4×C3.A4Direct product of C4 and C3.A4363C4xC3.A4144,34
C3×C42⋊C3Direct product of C3 and C42⋊C3363C3xC4^2:C3144,68
C3×C22⋊A4Direct product of C3 and C22⋊A436C3xC2^2:A4144,194
C22×C3.A4Direct product of C22 and C3.A436C2^2xC3.A4144,110
C6×C3⋊C8Direct product of C6 and C3⋊C848C6xC3:C8144,74
S3×C3⋊C8Direct product of S3 and C3⋊C8484S3xC3:C8144,52
C3×C3⋊C16Direct product of C3 and C3⋊C16482C3xC3:C16144,28
C3×S3×Q8Direct product of C3, S3 and Q8484C3xS3xQ8144,164
S3×C2×C12Direct product of C2×C12 and S348S3xC2xC12144,159
C3×C8⋊S3Direct product of C3 and C8⋊S3482C3xC8:S3144,70
C3×D6⋊C4Direct product of C3 and D6⋊C448C3xD6:C4144,79
C3×C4.A4Direct product of C3 and C4.A4482C3xC4.A4144,157
S3×C22×C6Direct product of C22×C6 and S348S3xC2^2xC6144,195
C2×S3×Dic3Direct product of C2, S3 and Dic348C2xS3xDic3144,146
Dic3×C2×C6Direct product of C2×C6 and Dic348Dic3xC2xC6144,166
C3×C24⋊C2Direct product of C3 and C24⋊C2482C3xC24:C2144,71
C3×C3⋊Q16Direct product of C3 and C3⋊Q16484C3xC3:Q16144,83
C2×D6⋊S3Direct product of C2 and D6⋊S348C2xD6:S3144,150
C3×C4⋊Dic3Direct product of C3 and C4⋊Dic348C3xC4:Dic3144,78
C3×Dic3⋊C4Direct product of C3 and Dic3⋊C448C3xDic3:C4144,77
C2×C322C8Direct product of C2 and C322C848C2xC3^2:2C8144,134
C3×Q82S3Direct product of C3 and Q82S3484C3xQ8:2S3144,82
C3×Q83S3Direct product of C3 and Q83S3484C3xQ8:3S3144,165
C2×C322Q8Direct product of C2 and C322Q848C2xC3^2:2Q8144,152
C2×C4×D9Direct product of C2×C4 and D972C2xC4xD9144,38
D4×C3×C6Direct product of C3×C6 and D472D4xC3xC6144,179
C8×C3⋊S3Direct product of C8 and C3⋊S372C8xC3:S3144,85
C2×C9⋊D4Direct product of C2 and C9⋊D472C2xC9:D4144,46
Q8×C3⋊S3Direct product of Q8 and C3⋊S372Q8xC3:S3144,174
C9×C4○D4Direct product of C9 and C4○D4722C9xC4oD4144,50
C2×C12⋊S3Direct product of C2 and C12⋊S372C2xC12:S3144,170
C9×C22⋊C4Direct product of C9 and C22⋊C472C9xC2^2:C4144,21
C23×C3⋊S3Direct product of C23 and C3⋊S372C2^3xC3:S3144,196
C32×C4○D4Direct product of C32 and C4○D472C3^2xC4oD4144,181
C2×C327D4Direct product of C2 and C327D472C2xC3^2:7D4144,177
C32×C22⋊C4Direct product of C32 and C22⋊C472C3^2xC2^2:C4144,102
C2×C9⋊C8Direct product of C2 and C9⋊C8144C2xC9:C8144,9
C9×C4⋊C4Direct product of C9 and C4⋊C4144C9xC4:C4144,22
Q8×C3×C6Direct product of C3×C6 and Q8144Q8xC3xC6144,180
C2×Q8⋊C9Direct product of C2 and Q8⋊C9144C2xQ8:C9144,35
C32×C4⋊C4Direct product of C32 and C4⋊C4144C3^2xC4:C4144,103
C4×C3⋊Dic3Direct product of C4 and C3⋊Dic3144C4xC3:Dic3144,92
C2×C324C8Direct product of C2 and C324C8144C2xC3^2:4C8144,90
C2×C324Q8Direct product of C2 and C324Q8144C2xC3^2:4Q8144,168
C22×C3⋊Dic3Direct product of C22 and C3⋊Dic3144C2^2xC3:Dic3144,176
C2×C4×C3⋊S3Direct product of C2×C4 and C3⋊S372C2xC4xC3:S3144,169

Groups of order 145

dρLabelID
C145Cyclic group1451C145145,1

Groups of order 146

dρLabelID
C146Cyclic group1461C146146,2
D73Dihedral group732+D73146,1

Groups of order 147

dρLabelID
C147Cyclic group1471C147147,2
C723C33rd semidirect product of C72 and C3 acting faithfully213C7^2:3C3147,5
C49⋊C3The semidirect product of C49 and C3 acting faithfully493C49:C3147,1
C72⋊C32nd semidirect product of C72 and C3 acting faithfully49C7^2:C3147,4
C7×C21Abelian group of type [7,21]147C7xC21147,6
C7×C7⋊C3Direct product of C7 and C7⋊C3213C7xC7:C3147,3

Groups of order 148

dρLabelID
C148Cyclic group1481C148148,2
D74Dihedral group; = C2×D37742+D74148,4
Dic37Dicyclic group; = C372C41482-Dic37148,1
C37⋊C4The semidirect product of C37 and C4 acting faithfully374+C37:C4148,3
C2×C74Abelian group of type [2,74]148C2xC74148,5

Groups of order 149

dρLabelID
C149Cyclic group1491C149149,1

Groups of order 150

dρLabelID
C150Cyclic group1501C150150,4
D75Dihedral group752+D75150,3
C52⋊S3The semidirect product of C52 and S3 acting faithfully153C5^2:S3150,5
C52⋊C6The semidirect product of C52 and C6 acting faithfully156+C5^2:C6150,6
C5⋊D15The semidirect product of C5 and D15 acting via D15/C15=C275C5:D15150,12
C5×C30Abelian group of type [5,30]150C5xC30150,13
D5×C15Direct product of C15 and D5302D5xC15150,8
C5×D15Direct product of C5 and D15302C5xD15150,11
S3×C25Direct product of C25 and S3752S3xC25150,1
C3×D25Direct product of C3 and D25752C3xD25150,2
S3×C52Direct product of C52 and S375S3xC5^2150,10
C2×C52⋊C3Direct product of C2 and C52⋊C3303C2xC5^2:C3150,7
C3×C5⋊D5Direct product of C3 and C5⋊D575C3xC5:D5150,9

Groups of order 151

dρLabelID
C151Cyclic group1511C151151,1

Groups of order 152

dρLabelID
C152Cyclic group1521C152152,2
D76Dihedral group762+D76152,5
Dic38Dicyclic group; = C19Q81522-Dic38152,3
C19⋊D4The semidirect product of C19 and D4 acting via D4/C22=C2762C19:D4152,7
C19⋊C8The semidirect product of C19 and C8 acting via C8/C4=C21522C19:C8152,1
C2×C76Abelian group of type [2,76]152C2xC76152,8
C22×C38Abelian group of type [2,2,38]152C2^2xC38152,12
C4×D19Direct product of C4 and D19762C4xD19152,4
D4×C19Direct product of C19 and D4762D4xC19152,9
C22×D19Direct product of C22 and D1976C2^2xD19152,11
Q8×C19Direct product of C19 and Q81522Q8xC19152,10
C2×Dic19Direct product of C2 and Dic19152C2xDic19152,6

Groups of order 153

dρLabelID
C153Cyclic group1531C153153,1
C3×C51Abelian group of type [3,51]153C3xC51153,2

Groups of order 154

dρLabelID
C154Cyclic group1541C154154,4
D77Dihedral group772+D77154,3
C11×D7Direct product of C11 and D7772C11xD7154,1
C7×D11Direct product of C7 and D11772C7xD11154,2

Groups of order 155

dρLabelID
C155Cyclic group1551C155155,2
C31⋊C5The semidirect product of C31 and C5 acting faithfully315C31:C5155,1

Groups of order 156

dρLabelID
C156Cyclic group1561C156156,6
D78Dihedral group; = C2×D39782+D78156,17
F13Frobenius group; = C13C12 = AGL1(𝔽13) = Aut(D13) = Hol(C13)1312+F13156,7
Dic39Dicyclic group; = C393C41562-Dic39156,5
C39⋊C41st semidirect product of C39 and C4 acting faithfully394C39:C4156,10
C13⋊A4The semidirect product of C13 and A4 acting via A4/C22=C3523C13:A4156,14
C26.C6The non-split extension by C26 of C6 acting faithfully526-C26.C6156,1
C2×C78Abelian group of type [2,78]156C2xC78156,18
S3×D13Direct product of S3 and D13394+S3xD13156,11
A4×C13Direct product of C13 and A4523A4xC13156,13
S3×C26Direct product of C26 and S3782S3xC26156,16
C6×D13Direct product of C6 and D13782C6xD13156,15
Dic3×C13Direct product of C13 and Dic31562Dic3xC13156,3
C3×Dic13Direct product of C3 and Dic131562C3xDic13156,4
C2×C13⋊C6Direct product of C2 and C13⋊C6266+C2xC13:C6156,8
C3×C13⋊C4Direct product of C3 and C13⋊C4394C3xC13:C4156,9
C4×C13⋊C3Direct product of C4 and C13⋊C3523C4xC13:C3156,2
C22×C13⋊C3Direct product of C22 and C13⋊C352C2^2xC13:C3156,12

Groups of order 157

dρLabelID
C157Cyclic group1571C157157,1

Groups of order 158

dρLabelID
C158Cyclic group1581C158158,2
D79Dihedral group792+D79158,1

Groups of order 159

dρLabelID
C159Cyclic group1591C159159,1

Groups of order 160

dρLabelID
C160Cyclic group1601C160160,2
D80Dihedral group802+D80160,6
Dic40Dicyclic group; = C51Q321602-Dic40160,8
C24⋊D5The semidirect product of C24 and D5 acting faithfully105+C2^4:D5160,234
2- 1+4⋊C5The semidirect product of 2- 1+4 and C5 acting faithfully324-ES-(2,2):C5160,199
C8⋊F53rd semidirect product of C8 and F5 acting via F5/D5=C2404C8:F5160,67
C40⋊C42nd semidirect product of C40 and C4 acting faithfully404C40:C4160,68
C23⋊F5The semidirect product of C23 and F5 acting via F5/C5=C4404C2^3:F5160,86
D8⋊D52nd semidirect product of D8 and D5 acting via D5/C5=C2404D8:D5160,132
C8⋊D101st semidirect product of C8 and D10 acting via D10/C5=C22404+C8:D10160,129
D4⋊F52nd semidirect product of D4 and F5 acting via F5/D5=C2408-D4:F5160,83
Q8⋊F51st semidirect product of Q8 and F5 acting via F5/D5=C2408-Q8:F5160,84
Q82F52nd semidirect product of Q8 and F5 acting via F5/D5=C2408+Q8:2F5160,85
D204C41st semidirect product of D20 and C4 acting via C4/C2=C2402D20:4C4160,12
D207C44th semidirect product of D20 and C4 acting via C4/C2=C2404D20:7C4160,32
D20⋊C41st semidirect product of D20 and C4 acting faithfully408+D20:C4160,82
D40⋊C26th semidirect product of D40 and C2 acting faithfully404+D40:C2160,135
D4⋊D102nd semidirect product of D4 and D10 acting via D10/C10=C2404+D4:D10160,170
D46D102nd semidirect product of D4 and D10 acting through Inn(D4)404D4:6D10160,219
D48D104th semidirect product of D4 and D10 acting through Inn(D4)404+D4:8D10160,224
D5⋊M4(2)The semidirect product of D5 and M4(2) acting via M4(2)/C2×C4=C2404D5:M4(2)160,202
C242D51st semidirect product of C24 and D5 acting via D5/C5=C240C2^4:2D5160,174
C23⋊Dic5The semidirect product of C23 and Dic5 acting via Dic5/C5=C4404C2^3:Dic5160,41
D42Dic52nd semidirect product of D4 and Dic5 acting via Dic5/C10=C2404D4:2Dic5160,44
C22⋊D20The semidirect product of C22 and D20 acting via D20/D10=C240C2^2:D20160,103
C23⋊D101st semidirect product of C23 and D10 acting via D10/C5=C2240C2^3:D10160,158
D5⋊C16The semidirect product of D5 and C16 acting via C16/C8=C2804D5:C16160,64
C5⋊D16The semidirect product of C5 and D16 acting via D16/D8=C2804+C5:D16160,33
C80⋊C25th semidirect product of C80 and C2 acting faithfully802C80:C2160,5
D83D5The semidirect product of D8 and D5 acting through Inn(D8)804-D8:3D5160,133
C16⋊D52nd semidirect product of C16 and D5 acting via D5/C5=C2802C16:D5160,7
C204D41st semidirect product of C20 and D4 acting via D4/C4=C280C20:4D4160,95
C4⋊D20The semidirect product of C4 and D20 acting via D20/D10=C280C4:D20160,116
C207D41st semidirect product of C20 and D4 acting via D4/C22=C280C20:7D4160,151
C202D42nd semidirect product of C20 and D4 acting via D4/C2=C2280C20:2D4160,159
C20⋊D43rd semidirect product of C20 and D4 acting via D4/C2=C2280C20:D4160,161
C5⋊SD32The semidirect product of C5 and SD32 acting via SD32/Q16=C2804+C5:SD32160,35
D206C43rd semidirect product of D20 and C4 acting via C4/C2=C280D20:6C4160,16
D101C81st semidirect product of D10 and C8 acting via C8/C4=C280D10:1C8160,27
D205C42nd semidirect product of D20 and C4 acting via C4/C2=C280D20:5C4160,28
D10⋊C82nd semidirect product of D10 and C8 acting via C8/C4=C280D10:C8160,78
D10⋊D41st semidirect product of D10 and D4 acting via D4/C4=C280D10:D4160,105
D208C45th semidirect product of D20 and C4 acting via C4/C2=C280D20:8C4160,114
D407C2The semidirect product of D40 and C2 acting through Inn(D40)802D40:7C2160,125
D10⋊Q81st semidirect product of D10 and Q8 acting via Q8/C4=C280D10:Q8160,117
D102Q82nd semidirect product of D10 and Q8 acting via Q8/C4=C280D10:2Q8160,118
Q16⋊D52nd semidirect product of Q16 and D5 acting via D5/C5=C2804Q16:D5160,139
D103Q83rd semidirect product of D10 and Q8 acting via Q8/C4=C280D10:3Q8160,167
C42⋊D51st semidirect product of C42 and D5 acting via D5/C5=C280C4^2:D5160,93
C422D52nd semidirect product of C42 and D5 acting via D5/C5=C280C4^2:2D5160,97
D4⋊Dic51st semidirect product of D4 and Dic5 acting via Dic5/C10=C280D4:Dic5160,39
Dic54D41st semidirect product of Dic5 and D4 acting through Inn(Dic5)80Dic5:4D4160,102
SD16⋊D52nd semidirect product of SD16 and D5 acting via D5/C5=C2804-SD16:D5160,136
SD163D5The semidirect product of SD16 and D5 acting through Inn(SD16)804SD16:3D5160,137
Dic5⋊D42nd semidirect product of Dic5 and D4 acting via D4/C22=C280Dic5:D4160,160
C5⋊C32The semidirect product of C5 and C32 acting via C32/C8=C41604C5:C32160,3
C20⋊Q8The semidirect product of C20 and Q8 acting via Q8/C2=C22160C20:Q8160,109
C52C32The semidirect product of C5 and C32 acting via C32/C16=C21602C5:2C32160,1
C203C81st semidirect product of C20 and C8 acting via C8/C4=C2160C20:3C8160,11
C408C44th semidirect product of C40 and C4 acting via C4/C2=C2160C40:8C4160,22
C406C42nd semidirect product of C40 and C4 acting via C4/C2=C2160C40:6C4160,24
C405C41st semidirect product of C40 and C4 acting via C4/C2=C2160C40:5C4160,25
C5⋊Q32The semidirect product of C5 and Q32 acting via Q32/Q16=C21604-C5:Q32160,36
C20⋊C81st semidirect product of C20 and C8 acting via C8/C2=C4160C20:C8160,76
C202Q81st semidirect product of C20 and Q8 acting via Q8/C4=C2160C20:2Q8160,90
Q8⋊Dic51st semidirect product of Q8 and Dic5 acting via Dic5/C10=C2160Q8:Dic5160,42
Dic5⋊C83rd semidirect product of Dic5 and C8 acting via C8/C4=C2160Dic5:C8160,79
Dic53Q8The semidirect product of Dic5 and Q8 acting through Inn(Dic5)160Dic5:3Q8160,108
Dic5⋊Q82nd semidirect product of Dic5 and Q8 acting via Q8/C4=C2160Dic5:Q8160,165
C4⋊C47D51st semidirect product of C4⋊C4 and D5 acting through Inn(C4⋊C4)80C4:C4:7D5160,113
C4⋊C4⋊D56th semidirect product of C4⋊C4 and D5 acting via D5/C5=C280C4:C4:D5160,119
C23.F5The non-split extension by C23 of F5 acting via F5/C5=C4404C2^3.F5160,88
D5.D8The non-split extension by D5 of D8 acting via D8/C8=C2404D5.D8160,69
C20.D48th non-split extension by C20 of D4 acting via D4/C2=C22404C20.D4160,40
D10.D41st non-split extension by D10 of D4 acting via D4/C2=C22404+D10.D4160,74
D4.D101st non-split extension by D4 of D10 acting via D10/C10=C2404D4.D10160,153
C20.46D43rd non-split extension by C20 of D4 acting via D4/C22=C2404+C20.46D4160,30
D10.3Q83rd non-split extension by D10 of Q8 acting via Q8/C4=C240D10.3Q8160,81
C23.1D101st non-split extension by C23 of D10 acting via D10/C5=C22404C2^3.1D10160,13
D10.C2311st non-split extension by D10 of C23 acting via C23/C22=C2404D10.C2^3160,205
D8.D5The non-split extension by D8 of D5 acting via D5/C5=C2804-D8.D5160,34
D4.F5The non-split extension by D4 of F5 acting through Inn(D4)808-D4.F5160,206
Q8.F5The non-split extension by Q8 of F5 acting through Inn(Q8)808+Q8.F5160,208
C8.F53rd non-split extension by C8 of F5 acting via F5/D5=C2804C8.F5160,65
C20.4C81st non-split extension by C20 of C8 acting via C8/C4=C2802C20.4C8160,19
C40.6C41st non-split extension by C40 of C4 acting via C4/C2=C2802C40.6C4160,26
C40.C42nd non-split extension by C40 of C4 acting faithfully804C40.C4160,70
C20.C81st non-split extension by C20 of C8 acting via C8/C2=C4804C20.C8160,73
C4.D205th non-split extension by C4 of D20 acting via D20/C20=C280C4.D20160,96
C8.D101st non-split extension by C8 of D10 acting via D10/C5=C22804-C8.D10160,130
D4.Dic5The non-split extension by D4 of Dic5 acting through Inn(D4)804D4.Dic5160,169
D20.3C4The non-split extension by D20 of C4 acting through Inn(D20)802D20.3C4160,122
D20.2C4The non-split extension by D20 of C4 acting via C4/C2=C2804D20.2C4160,128
D4.8D103rd non-split extension by D4 of D10 acting via D10/C10=C2804D4.8D10160,171
D4.9D104th non-split extension by D4 of D10 acting via D10/C10=C2804-D4.9D10160,172
C20.53D410th non-split extension by C20 of D4 acting via D4/C22=C2804C20.53D4160,29
C4.12D204th non-split extension by C4 of D20 acting via D20/D10=C2804-C4.12D20160,31
C20.55D412nd non-split extension by C20 of D4 acting via D4/C22=C280C20.55D4160,37
C20.10D410th non-split extension by C20 of D4 acting via D4/C2=C22804C20.10D4160,43
C20.48D45th non-split extension by C20 of D4 acting via D4/C22=C280C20.48D4160,145
C20.17D417th non-split extension by C20 of D4 acting via D4/C2=C2280C20.17D4160,157
C20.23D423rd non-split extension by C20 of D4 acting via D4/C2=C2280C20.23D4160,168
D10.Q82nd non-split extension by D10 of Q8 acting via Q8/C4=C2804D10.Q8160,71
Q8.D105th non-split extension by Q8 of D10 acting via D10/D5=C2804+Q8.D10160,140
C23.2F51st non-split extension by C23 of F5 acting via F5/D5=C280C2^3.2F5160,87
D10.12D41st non-split extension by D10 of D4 acting via D4/C22=C280D10.12D4160,104
D10.13D42nd non-split extension by D10 of D4 acting via D4/C22=C280D10.13D4160,115
D4.10D10The non-split extension by D4 of D10 acting through Inn(D4)804-D4.10D10160,225
Q8.10D101st non-split extension by Q8 of D10 acting through Inn(Q8)804Q8.10D10160,222
Dic5.D41st non-split extension by Dic5 of D4 acting via D4/C2=C22804-Dic5.D4160,80
Dic5.5D41st non-split extension by Dic5 of D4 acting via D4/C4=C280Dic5.5D4160,106
C23.D103rd non-split extension by C23 of D10 acting via D10/C5=C2280C2^3.D10160,100
C22.D203rd non-split extension by C22 of D20 acting via D20/D10=C280C2^2.D20160,107
C20.C2315th non-split extension by C20 of C23 acting via C23/C2=C22804C20.C2^3160,163
Dic5.14D41st non-split extension by Dic5 of D4 acting via D4/C22=C280Dic5.14D4160,99
C23.11D101st non-split extension by C23 of D10 acting via D10/D5=C280C2^3.11D10160,98
C23.21D102nd non-split extension by C23 of D10 acting via D10/C10=C280C2^3.21D10160,147
C23.23D104th non-split extension by C23 of D10 acting via D10/C10=C280C2^3.23D10160,150
C23.18D108th non-split extension by C23 of D10 acting via D10/D5=C280C2^3.18D10160,156
C10.D81st non-split extension by C10 of D8 acting via D8/D4=C2160C10.D8160,14
C20.Q82nd non-split extension by C20 of Q8 acting via Q8/C2=C22160C20.Q8160,15
C20.8Q85th non-split extension by C20 of Q8 acting via Q8/C4=C2160C20.8Q8160,21
C20.6Q83rd non-split extension by C20 of Q8 acting via Q8/C4=C2160C20.6Q8160,91
C20.44D41st non-split extension by C20 of D4 acting via D4/C22=C2160C20.44D4160,23
C10.Q162nd non-split extension by C10 of Q16 acting via Q16/Q8=C2160C10.Q16160,17
C42.D51st non-split extension by C42 of D5 acting via D5/C5=C2160C4^2.D5160,10
C10.C424th non-split extension by C10 of C42 acting via C42/C4=C4160C10.C4^2160,77
Dic5.Q81st non-split extension by Dic5 of Q8 acting via Q8/C4=C2160Dic5.Q8160,110
C4.Dic103rd non-split extension by C4 of Dic10 acting via Dic10/Dic5=C2160C4.Dic10160,111
C10.10C425th non-split extension by C10 of C42 acting via C42/C2×C4=C2160C10.10C4^2160,38
C4×C40Abelian group of type [4,40]160C4xC40160,46
C2×C80Abelian group of type [2,80]160C2xC80160,59
C22×C40Abelian group of type [2,2,40]160C2^2xC40160,190
C23×C20Abelian group of type [2,2,2,20]160C2^3xC20160,228
C24×C10Abelian group of type [2,2,2,2,10]160C2^4xC10160,238
C2×C4×C20Abelian group of type [2,4,20]160C2xC4xC20160,175
D4×F5Direct product of D4 and F5; = Aut(D20) = Hol(C20)208+D4xF5160,207
D5×D8Direct product of D5 and D8404+D5xD8160,131
C8×F5Direct product of C8 and F5404C8xF5160,66
Q8×F5Direct product of Q8 and F5408-Q8xF5160,209
D5×SD16Direct product of D5 and SD16404D5xSD16160,134
C23×F5Direct product of C23 and F540C2^3xF5160,236
D5×M4(2)Direct product of D5 and M4(2)404D5xM4(2)160,127
C5×2+ 1+4Direct product of C5 and 2+ 1+4404C5xES+(2,2)160,232
D5×C16Direct product of C16 and D5802D5xC16160,4
C5×D16Direct product of C5 and D16802C5xD16160,61
C4×D20Direct product of C4 and D2080C4xD20160,94
C2×D40Direct product of C2 and D4080C2xD40160,124
D4×C20Direct product of C20 and D480D4xC20160,179
C10×D8Direct product of C10 and D880C10xD8160,193
D5×Q16Direct product of D5 and Q16804-D5xQ16160,138
C5×SD32Direct product of C5 and SD32802C5xSD32160,62
D4×Dic5Direct product of D4 and Dic580D4xDic5160,155
D5×C42Direct product of C42 and D580D5xC4^2160,92
D5×C24Direct product of C24 and D580D5xC2^4160,237
C10×SD16Direct product of C10 and SD1680C10xSD16160,194
C22×D20Direct product of C22 and D2080C2^2xD20160,215
C5×M5(2)Direct product of C5 and M5(2)802C5xM5(2)160,60
C10×M4(2)Direct product of C10 and M4(2)80C10xM4(2)160,191
C5×2- 1+4Direct product of C5 and 2- 1+4804C5xES-(2,2)160,233
C5×Q32Direct product of C5 and Q321602C5xQ32160,63
Q8×C20Direct product of C20 and Q8160Q8xC20160,180
C10×Q16Direct product of C10 and Q16160C10xQ16160,195
C8×Dic5Direct product of C8 and Dic5160C8xDic5160,20
Q8×Dic5Direct product of Q8 and Dic5160Q8xDic5160,166
C4×Dic10Direct product of C4 and Dic10160C4xDic10160,89
C2×Dic20Direct product of C2 and Dic20160C2xDic20160,126
C23×Dic5Direct product of C23 and Dic5160C2^3xDic5160,226
C22×Dic10Direct product of C22 and Dic10160C2^2xDic10160,213
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)105+C2xC2^4:C5160,235
C2×D4×D5Direct product of C2, D4 and D540C2xD4xD5160,217
C2×C4×F5Direct product of C2×C4 and F540C2xC4xF5160,203
C5×C4≀C2Direct product of C5 and C4≀C2402C5xC4wrC2160,54
C2×C4⋊F5Direct product of C2 and C4⋊F540C2xC4:F5160,204
D5×C4○D4Direct product of D5 and C4○D4404D5xC4oD4160,223
C5×C23⋊C4Direct product of C5 and C23⋊C4404C5xC2^3:C4160,49
C5×C8⋊C22Direct product of C5 and C8⋊C22404C5xC8:C2^2160,197
D5×C22⋊C4Direct product of D5 and C22⋊C440D5xC2^2:C4160,101
C5×C4.D4Direct product of C5 and C4.D4404C5xC4.D4160,50
C2×C22⋊F5Direct product of C2 and C22⋊F540C2xC2^2:F5160,212
C5×C22≀C2Direct product of C5 and C22≀C240C5xC2^2wrC2160,181
D5×C2×C8Direct product of C2×C8 and D580D5xC2xC8160,120
C2×Q8×D5Direct product of C2, Q8 and D580C2xQ8xD5160,220
D5×C4⋊C4Direct product of D5 and C4⋊C480D5xC4:C4160,112
D4×C2×C10Direct product of C2×C10 and D480D4xC2xC10160,229
C4×C5⋊D4Direct product of C4 and C5⋊D480C4xC5:D4160,149
C2×D4⋊D5Direct product of C2 and D4⋊D580C2xD4:D5160,152
C2×D5⋊C8Direct product of C2 and D5⋊C880C2xD5:C8160,200
C5×C8○D4Direct product of C5 and C8○D4802C5xC8oD4160,192
C5×C4○D8Direct product of C5 and C4○D8802C5xC4oD8160,196
C2×C8⋊D5Direct product of C2 and C8⋊D580C2xC8:D5160,121
C5×C4⋊D4Direct product of C5 and C4⋊D480C5xC4:D4160,182
C2×Q8⋊D5Direct product of C2 and Q8⋊D580C2xQ8:D5160,162
C2×C40⋊C2Direct product of C2 and C40⋊C280C2xC40:C2160,123
D5×C22×C4Direct product of C22×C4 and D580D5xC2^2xC4160,214
C2×C4.F5Direct product of C2 and C4.F580C2xC4.F5160,201
C2×C4○D20Direct product of C2 and C4○D2080C2xC4oD20160,216
C10×C4○D4Direct product of C10 and C4○D480C10xC4oD4160,231
C5×D4⋊C4Direct product of C5 and D4⋊C480C5xD4:C4160,52
C5×C8.C4Direct product of C5 and C8.C4802C5xC8.C4160,58
C5×C41D4Direct product of C5 and C41D480C5xC4:1D4160,188
C5×C22⋊C8Direct product of C5 and C22⋊C880C5xC2^2:C8160,48
C2×D4.D5Direct product of C2 and D4.D580C2xD4.D5160,154
C22×C5⋊D4Direct product of C22 and C5⋊D480C2^2xC5:D4160,227
C5×C22⋊Q8Direct product of C5 and C22⋊Q880C5xC2^2:Q8160,183
C2×D10⋊C4Direct product of C2 and D10⋊C480C2xD10:C4160,148
C2×D42D5Direct product of C2 and D42D580C2xD4:2D5160,218
C10×C22⋊C4Direct product of C10 and C22⋊C480C10xC2^2:C4160,176
C5×C42⋊C2Direct product of C5 and C42⋊C280C5xC4^2:C2160,178
C2×Q82D5Direct product of C2 and Q82D580C2xQ8:2D5160,221
C5×C4.4D4Direct product of C5 and C4.4D480C5xC4.4D4160,185
C5×C8.C22Direct product of C5 and C8.C22804C5xC8.C2^2160,198
C2×C4.Dic5Direct product of C2 and C4.Dic580C2xC4.Dic5160,142
C2×C23.D5Direct product of C2 and C23.D580C2xC2^3.D5160,173
C2×C22.F5Direct product of C2 and C22.F580C2xC2^2.F5160,211
C5×C422C2Direct product of C5 and C422C280C5xC4^2:2C2160,187
C5×C4.10D4Direct product of C5 and C4.10D4804C5xC4.10D4160,51
C5×C22.D4Direct product of C5 and C22.D480C5xC2^2.D4160,184
C4×C5⋊C8Direct product of C4 and C5⋊C8160C4xC5:C8160,75
C5×C4⋊C8Direct product of C5 and C4⋊C8160C5xC4:C8160,55
C2×C5⋊C16Direct product of C2 and C5⋊C16160C2xC5:C16160,72
C5×C4⋊Q8Direct product of C5 and C4⋊Q8160C5xC4:Q8160,189
C10×C4⋊C4Direct product of C10 and C4⋊C4160C10xC4:C4160,177
Q8×C2×C10Direct product of C2×C10 and Q8160Q8xC2xC10160,230
C5×C8⋊C4Direct product of C5 and C8⋊C4160C5xC8:C4160,47
C4×C52C8Direct product of C4 and C52C8160C4xC5:2C8160,9
C22×C5⋊C8Direct product of C22 and C5⋊C8160C2^2xC5:C8160,210
C2×C4×Dic5Direct product of C2×C4 and Dic5160C2xC4xDic5160,143
C2×C5⋊Q16Direct product of C2 and C5⋊Q16160C2xC5:Q16160,164
C2×C52C16Direct product of C2 and C52C16160C2xC5:2C16160,18
C2×C4⋊Dic5Direct product of C2 and C4⋊Dic5160C2xC4:Dic5160,146
C5×Q8⋊C4Direct product of C5 and Q8⋊C4160C5xQ8:C4160,53
C5×C2.D8Direct product of C5 and C2.D8160C5xC2.D8160,57
C5×C4.Q8Direct product of C5 and C4.Q8160C5xC4.Q8160,56
C22×C52C8Direct product of C22 and C52C8160C2^2xC5:2C8160,141
C2×C10.D4Direct product of C2 and C10.D4160C2xC10.D4160,144
C5×C2.C42Direct product of C5 and C2.C42160C5xC2.C4^2160,45
C5×C42.C2Direct product of C5 and C42.C2160C5xC4^2.C2160,186

Groups of order 161

dρLabelID
C161Cyclic group1611C161161,1

Groups of order 162

dρLabelID
C162Cyclic group1621C162162,2
D81Dihedral group812+D81162,1
C3≀S3Wreath product of C3 by S393C3wrS3162,10
C33⋊C61st semidirect product of C33 and C6 acting faithfully96+C3^3:C6162,11
C33⋊S32nd semidirect product of C33 and S3 acting faithfully96+C3^3:S3162,19
C9⋊C18The semidirect product of C9 and C18 acting via C18/C3=C6186C9:C18162,6
C32⋊C18The semidirect product of C32 and C18 acting via C18/C3=C6186C3^2:C18162,4
He35S32nd semidirect product of He3 and S3 acting via S3/C3=C2186He3:5S3162,46
C322D92nd semidirect product of C32 and D9 acting via D9/C3=S3186C3^2:2D9162,17
C27⋊C6The semidirect product of C27 and C6 acting faithfully276+C27:C6162,9
He3⋊S33rd semidirect product of He3 and S3 acting faithfully276+He3:S3162,21
He34S31st semidirect product of He3 and S3 acting via S3/C3=C227He3:4S3162,40
C32⋊D91st semidirect product of C32 and D9 acting via D9/C3=S327C3^2:D9162,5
C9⋊D9The semidirect product of C9 and D9 acting via D9/C9=C281C9:D9162,16
C27⋊S3The semidirect product of C27 and S3 acting via S3/C3=C281C27:S3162,18
C34⋊C24th semidirect product of C34 and C2 acting faithfully81C3^4:C2162,54
C324D92nd semidirect product of C32 and D9 acting via D9/C9=C281C3^2:4D9162,45
He3.C61st non-split extension by He3 of C6 acting faithfully273He3.C6162,12
He3.S31st non-split extension by He3 of S3 acting faithfully276+He3.S3162,13
He3.2C62nd non-split extension by He3 of C6 acting faithfully273He3.2C6162,14
He3.2S32nd non-split extension by He3 of S3 acting faithfully276+He3.2S3162,15
He3.3S33rd non-split extension by He3 of S3 acting faithfully276+He3.3S3162,20
He3.4S3The non-split extension by He3 of S3 acting via S3/C3=C2276+He3.4S3162,43
He3.4C6The non-split extension by He3 of C6 acting via C6/C3=C2273He3.4C6162,44
C33.S34th non-split extension by C33 of S3 acting faithfully27C3^3.S3162,42
3- 1+2.S3The non-split extension by 3- 1+2 of S3 acting faithfully276+ES-(3,1).S3162,22
C9×C18Abelian group of type [9,18]162C9xC18162,23
C3×C54Abelian group of type [3,54]162C3xC54162,26
C33×C6Abelian group of type [3,3,3,6]162C3^3xC6162,55
C32×C18Abelian group of type [3,3,18]162C3^2xC18162,47
C9×D9Direct product of C9 and D9182C9xD9162,3
S3×He3Direct product of S3 and He3186S3xHe3162,35
S3×3- 1+2Direct product of S3 and 3- 1+2186S3xES-(3,1)162,37
S3×C27Direct product of C27 and S3542S3xC27162,8
C3×D27Direct product of C3 and D27542C3xD27162,7
C6×He3Direct product of C6 and He354C6xHe3162,48
S3×C33Direct product of C33 and S354S3xC3^3162,51
C32×D9Direct product of C32 and D954C3^2xD9162,32
C6×3- 1+2Direct product of C6 and 3- 1+254C6xES-(3,1)162,49
C3×C9⋊C6Direct product of C3 and C9⋊C6186C3xC9:C6162,36
C2×C3≀C3Direct product of C2 and C3≀C3183C2xC3wrC3162,28
C3×C32⋊C6Direct product of C3 and C32⋊C6186C3xC3^2:C6162,34
C32×C3⋊S3Direct product of C32 and C3⋊S318C3^2xC3:S3162,52
C3×He3⋊C2Direct product of C3 and He3⋊C227C3xHe3:C2162,41
S3×C3×C9Direct product of C3×C9 and S354S3xC3xC9162,33
C3×C9⋊S3Direct product of C3 and C9⋊S354C3xC9:S3162,38
C9×C3⋊S3Direct product of C9 and C3⋊S354C9xC3:S3162,39
C2×C27⋊C3Direct product of C2 and C27⋊C3543C2xC27:C3162,27
C2×C32⋊C9Direct product of C2 and C32⋊C954C2xC3^2:C9162,24
C2×C9○He3Direct product of C2 and C9○He3543C2xC9oHe3162,50
C3×C33⋊C2Direct product of C3 and C33⋊C254C3xC3^3:C2162,53
C2×He3⋊C3Direct product of C2 and He3⋊C3543C2xHe3:C3162,30
C2×He3.C3Direct product of C2 and He3.C3543C2xHe3.C3162,29
C2×C3.He3Direct product of C2 and C3.He3543C2xC3.He3162,31
C2×C9⋊C9Direct product of C2 and C9⋊C9162C2xC9:C9162,25

Groups of order 163

dρLabelID
C163Cyclic group1631C163163,1

Groups of order 164

dρLabelID
C164Cyclic group1641C164164,2
D82Dihedral group; = C2×D41822+D82164,4
Dic41Dicyclic group; = C412C41642-Dic41164,1
C41⋊C4The semidirect product of C41 and C4 acting faithfully414+C41:C4164,3
C2×C82Abelian group of type [2,82]164C2xC82164,5

Groups of order 165

dρLabelID
C165Cyclic group1651C165165,2
C3×C11⋊C5Direct product of C3 and C11⋊C5335C3xC11:C5165,1

Groups of order 166

dρLabelID
C166Cyclic group1661C166166,2
D83Dihedral group832+D83166,1

Groups of order 167

dρLabelID
C167Cyclic group1671C167167,1

Groups of order 168

dρLabelID
C168Cyclic group1681C168168,6
D84Dihedral group842+D84168,36
Dic42Dicyclic group; = C212Q81682-Dic42168,34
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simple73GL(3,2)168,42
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)87+AGammaL(1,8)168,43
C7⋊S4The semidirect product of C7 and S4 acting via S4/A4=C2286+C7:S4168,46
C4⋊F7The semidirect product of C4 and F7 acting via F7/C7⋊C3=C2286+C4:F7168,9
D7⋊A4The semidirect product of D7 and A4 acting via A4/C22=C3286+D7:A4168,49
Dic7⋊C6The semidirect product of Dic7 and C6 acting faithfully286Dic7:C6168,11
C7⋊C24The semidirect product of C7 and C24 acting via C24/C4=C6566C7:C24168,1
D21⋊C4The semidirect product of D21 and C4 acting via C4/C2=C2844+D21:C4168,14
C21⋊D41st semidirect product of C21 and D4 acting via D4/C2=C22844-C21:D4168,15
C3⋊D28The semidirect product of C3 and D28 acting via D28/D14=C2844+C3:D28168,16
C7⋊D12The semidirect product of C7 and D12 acting via D12/D6=C2844+C7:D12168,17
C217D41st semidirect product of C21 and D4 acting via D4/C22=C2842C21:7D4168,38
C21⋊Q8The semidirect product of C21 and Q8 acting via Q8/C2=C221684-C21:Q8168,18
C21⋊C81st semidirect product of C21 and C8 acting via C8/C4=C21682C21:C8168,5
C4.F7The non-split extension by C4 of F7 acting via F7/C7⋊C3=C2566-C4.F7168,7
C14.A4The non-split extension by C14 of A4 acting via A4/C22=C3566C14.A4168,23
C2×C84Abelian group of type [2,84]168C2xC84168,39
C22×C42Abelian group of type [2,2,42]168C2^2xC42168,57
C3×F8Direct product of C3 and F8247C3xF8168,44
C7×S4Direct product of C7 and S4283C7xS4168,45
A4×D7Direct product of A4 and D7286+A4xD7168,48
C4×F7Direct product of C4 and F7286C4xF7168,8
C22×F7Direct product of C22 and F728C2^2xF7168,47
A4×C14Direct product of C14 and A4423A4xC14168,52
C7×SL2(𝔽3)Direct product of C7 and SL2(𝔽3)562C7xSL(2,3)168,22
S3×C28Direct product of C28 and S3842S3xC28168,30
C12×D7Direct product of C12 and D7842C12xD7168,25
C3×D28Direct product of C3 and D28842C3xD28168,26
C7×D12Direct product of C7 and D12842C7xD12168,31
C4×D21Direct product of C4 and D21842C4xD21168,35
D4×C21Direct product of C21 and D4842D4xC21168,40
Dic3×D7Direct product of Dic3 and D7844-Dic3xD7168,12
S3×Dic7Direct product of S3 and Dic7844-S3xDic7168,13
C22×D21Direct product of C22 and D2184C2^2xD21168,56
Q8×C21Direct product of C21 and Q81682Q8xC21168,41
C6×Dic7Direct product of C6 and Dic7168C6xDic7168,27
C7×Dic6Direct product of C7 and Dic61682C7xDic6168,29
C3×Dic14Direct product of C3 and Dic141682C3xDic14168,24
Dic3×C14Direct product of C14 and Dic3168Dic3xC14168,32
C2×Dic21Direct product of C2 and Dic21168C2xDic21168,37
D4×C7⋊C3Direct product of D4 and C7⋊C3286D4xC7:C3168,20
C2×C7⋊A4Direct product of C2 and C7⋊A4423C2xC7:A4168,53
C2×S3×D7Direct product of C2, S3 and D7424+C2xS3xD7168,50
C8×C7⋊C3Direct product of C8 and C7⋊C3563C8xC7:C3168,2
Q8×C7⋊C3Direct product of Q8 and C7⋊C3566Q8xC7:C3168,21
C2×C7⋊C12Direct product of C2 and C7⋊C1256C2xC7:C12168,10
C23×C7⋊C3Direct product of C23 and C7⋊C356C2^3xC7:C3168,51
C2×C6×D7Direct product of C2×C6 and D784C2xC6xD7168,54
S3×C2×C14Direct product of C2×C14 and S384S3xC2xC14168,55
C3×C7⋊D4Direct product of C3 and C7⋊D4842C3xC7:D4168,28
C7×C3⋊D4Direct product of C7 and C3⋊D4842C7xC3:D4168,33
C7×C3⋊C8Direct product of C7 and C3⋊C81682C7xC3:C8168,3
C3×C7⋊C8Direct product of C3 and C7⋊C81682C3xC7:C8168,4
C2×C4×C7⋊C3Direct product of C2×C4 and C7⋊C356C2xC4xC7:C3168,19

Groups of order 169

dρLabelID
C169Cyclic group1691C169169,1
C132Elementary abelian group of type [13,13]169C13^2169,2

Groups of order 170

dρLabelID
C170Cyclic group1701C170170,4
D85Dihedral group852+D85170,3
D5×C17Direct product of C17 and D5852D5xC17170,1
C5×D17Direct product of C5 and D17852C5xD17170,2

Groups of order 171

dρLabelID
C171Cyclic group1711C171171,2
C19⋊C9The semidirect product of C19 and C9 acting faithfully199C19:C9171,3
C192C9The semidirect product of C19 and C9 acting via C9/C3=C31713C19:2C9171,1
C3×C57Abelian group of type [3,57]171C3xC57171,5
C3×C19⋊C3Direct product of C3 and C19⋊C3573C3xC19:C3171,4

Groups of order 172

dρLabelID
C172Cyclic group1721C172172,2
D86Dihedral group; = C2×D43862+D86172,3
Dic43Dicyclic group; = C43C41722-Dic43172,1
C2×C86Abelian group of type [2,86]172C2xC86172,4

Groups of order 173

dρLabelID
C173Cyclic group1731C173173,1

Groups of order 174

dρLabelID
C174Cyclic group1741C174174,4
D87Dihedral group872+D87174,3
S3×C29Direct product of C29 and S3872S3xC29174,1
C3×D29Direct product of C3 and D29872C3xD29174,2

Groups of order 175

dρLabelID
C175Cyclic group1751C175175,1
C5×C35Abelian group of type [5,35]175C5xC35175,2

Groups of order 176

dρLabelID
C176Cyclic group1761C176176,2
D88Dihedral group882+D88176,6
Dic44Dicyclic group; = C111Q161762-Dic44176,7
D22⋊C4The semidirect product of D22 and C4 acting via C4/C2=C288D22:C4176,13
D4⋊D11The semidirect product of D4 and D11 acting via D11/C11=C2884+D4:D11176,14
Q8⋊D11The semidirect product of Q8 and D11 acting via D11/C11=C2884+Q8:D11176,16
C88⋊C24th semidirect product of C88 and C2 acting faithfully882C88:C2176,4
C8⋊D112nd semidirect product of C8 and D11 acting via D11/C11=C2882C8:D11176,5
D445C2The semidirect product of D44 and C2 acting through Inn(D44)882D44:5C2176,30
D42D11The semidirect product of D4 and D11 acting through Inn(D4)884-D4:2D11176,32
D44⋊C24th semidirect product of D44 and C2 acting faithfully884+D44:C2176,34
C11⋊C16The semidirect product of C11 and C16 acting via C16/C8=C21762C11:C16176,1
C44⋊C41st semidirect product of C44 and C4 acting via C4/C2=C2176C44:C4176,12
C11⋊Q16The semidirect product of C11 and Q16 acting via Q16/Q8=C21764-C11:Q16176,17
Dic11⋊C4The semidirect product of Dic11 and C4 acting via C4/C2=C2176Dic11:C4176,11
D4.D11The non-split extension by D4 of D11 acting via D11/C11=C2884-D4.D11176,15
C44.C41st non-split extension by C44 of C4 acting via C4/C2=C2882C44.C4176,9
C23.D11The non-split extension by C23 of D11 acting via D11/C11=C288C2^3.D11176,18
C4×C44Abelian group of type [4,44]176C4xC44176,19
C2×C88Abelian group of type [2,88]176C2xC88176,22
C22×C44Abelian group of type [2,2,44]176C2^2xC44176,37
C23×C22Abelian group of type [2,2,2,22]176C2^3xC22176,42
D4×D11Direct product of D4 and D11444+D4xD11176,31
C8×D11Direct product of C8 and D11882C8xD11176,3
C11×D8Direct product of C11 and D8882C11xD8176,24
C2×D44Direct product of C2 and D4488C2xD44176,29
D4×C22Direct product of C22 and D488D4xC22176,38
Q8×D11Direct product of Q8 and D11884-Q8xD11176,33
C11×SD16Direct product of C11 and SD16882C11xSD16176,25
C23×D11Direct product of C23 and D1188C2^3xD11176,41
C11×M4(2)Direct product of C11 and M4(2)882C11xM4(2)176,23
Q8×C22Direct product of C22 and Q8176Q8xC22176,39
C11×Q16Direct product of C11 and Q161762C11xQ16176,26
C4×Dic11Direct product of C4 and Dic11176C4xDic11176,10
C2×Dic22Direct product of C2 and Dic22176C2xDic22176,27
C22×Dic11Direct product of C22 and Dic11176C2^2xDic11176,35
C2×C4×D11Direct product of C2×C4 and D1188C2xC4xD11176,28
C2×C11⋊D4Direct product of C2 and C11⋊D488C2xC11:D4176,36
C11×C4○D4Direct product of C11 and C4○D4882C11xC4oD4176,40
C11×C22⋊C4Direct product of C11 and C22⋊C488C11xC2^2:C4176,20
C2×C11⋊C8Direct product of C2 and C11⋊C8176C2xC11:C8176,8
C11×C4⋊C4Direct product of C11 and C4⋊C4176C11xC4:C4176,21

Groups of order 177

dρLabelID
C177Cyclic group1771C177177,1

Groups of order 178

dρLabelID
C178Cyclic group1781C178178,2
D89Dihedral group892+D89178,1

Groups of order 179

dρLabelID
C179Cyclic group1791C179179,1

Groups of order 180

dρLabelID
C180Cyclic group1801C180180,4
D90Dihedral group; = C2×D45902+D90180,11
Dic45Dicyclic group; = C9Dic51802-Dic45180,3
C32⋊F5The semidirect product of C32 and F5 acting via F5/C5=C4304+C3^2:F5180,25
D15⋊S3The semidirect product of D15 and S3 acting via S3/C3=C2304D15:S3180,30
C32⋊Dic5The semidirect product of C32 and Dic5 acting via Dic5/C5=C4304C3^2:Dic5180,24
C9⋊F5The semidirect product of C9 and F5 acting via F5/D5=C2454C9:F5180,6
C323F52nd semidirect product of C32 and F5 acting via F5/D5=C245C3^2:3F5180,22
C3⋊Dic15The semidirect product of C3 and Dic15 acting via Dic15/C30=C2180C3:Dic15180,17
C2×C90Abelian group of type [2,90]180C2xC90180,12
C3×C60Abelian group of type [3,60]180C3xC60180,18
C6×C30Abelian group of type [6,30]180C6xC30180,37
C3×A5Direct product of C3 and A5; = GL2(𝔽4)153C3xA5180,19
S3×D15Direct product of S3 and D15304+S3xD15180,29
D5×D9Direct product of D5 and D9454+D5xD9180,7
C9×F5Direct product of C9 and F5454C9xF5180,5
C32×F5Direct product of C32 and F545C3^2xF5180,20
S3×C30Direct product of C30 and S3602S3xC30180,33
A4×C15Direct product of C15 and A4603A4xC15180,31
C6×D15Direct product of C6 and D15602C6xD15180,34
Dic3×C15Direct product of C15 and Dic3602Dic3xC15180,14
C3×Dic15Direct product of C3 and Dic15602C3xDic15180,15
D5×C18Direct product of C18 and D5902D5xC18180,9
C10×D9Direct product of C10 and D9902C10xD9180,10
C5×Dic9Direct product of C5 and Dic91802C5xDic9180,1
C9×Dic5Direct product of C9 and Dic51802C9xDic5180,2
C32×Dic5Direct product of C32 and Dic5180C3^2xDic5180,13
C5×S32Direct product of C5, S3 and S3304C5xS3^2180,28
C3×S3×D5Direct product of C3, S3 and D5304C3xS3xD5180,26
C3×C3⋊F5Direct product of C3 and C3⋊F5304C3xC3:F5180,21
C5×C32⋊C4Direct product of C5 and C32⋊C4304C5xC3^2:C4180,23
D5×C3⋊S3Direct product of D5 and C3⋊S345D5xC3:S3180,27
D5×C3×C6Direct product of C3×C6 and D590D5xC3xC6180,32
C10×C3⋊S3Direct product of C10 and C3⋊S390C10xC3:S3180,35
C2×C3⋊D15Direct product of C2 and C3⋊D1590C2xC3:D15180,36
C5×C3.A4Direct product of C5 and C3.A4903C5xC3.A4180,8
C5×C3⋊Dic3Direct product of C5 and C3⋊Dic3180C5xC3:Dic3180,16

Groups of order 181

dρLabelID
C181Cyclic group1811C181181,1

Groups of order 182

dρLabelID
C182Cyclic group1821C182182,4
D91Dihedral group912+D91182,3
C13×D7Direct product of C13 and D7912C13xD7182,1
C7×D13Direct product of C7 and D13912C7xD13182,2

Groups of order 183

dρLabelID
C183Cyclic group1831C183183,2
C61⋊C3The semidirect product of C61 and C3 acting faithfully613C61:C3183,1

Groups of order 184

dρLabelID
C184Cyclic group1841C184184,2
D92Dihedral group922+D92184,5
Dic46Dicyclic group; = C23Q81842-Dic46184,3
C23⋊D4The semidirect product of C23 and D4 acting via D4/C22=C2922C23:D4184,7
C23⋊C8The semidirect product of C23 and C8 acting via C8/C4=C21842C23:C8184,1
C2×C92Abelian group of type [2,92]184C2xC92184,8
C22×C46Abelian group of type [2,2,46]184C2^2xC46184,12
C4×D23Direct product of C4 and D23922C4xD23184,4
D4×C23Direct product of C23 and D4922D4xC23184,9
C22×D23Direct product of C22 and D2392C2^2xD23184,11
Q8×C23Direct product of C23 and Q81842Q8xC23184,10
C2×Dic23Direct product of C2 and Dic23184C2xDic23184,6

Groups of order 185

dρLabelID
C185Cyclic group1851C185185,1

Groups of order 186

dρLabelID
C186Cyclic group1861C186186,6
D93Dihedral group932+D93186,5
C31⋊C6The semidirect product of C31 and C6 acting faithfully316+C31:C6186,1
S3×C31Direct product of C31 and S3932S3xC31186,3
C3×D31Direct product of C3 and D31932C3xD31186,4
C2×C31⋊C3Direct product of C2 and C31⋊C3623C2xC31:C3186,2

Groups of order 187

dρLabelID
C187Cyclic group1871C187187,1

Groups of order 188

dρLabelID
C188Cyclic group1881C188188,2
D94Dihedral group; = C2×D47942+D94188,3
Dic47Dicyclic group; = C47C41882-Dic47188,1
C2×C94Abelian group of type [2,94]188C2xC94188,4

Groups of order 189

dρLabelID
C189Cyclic group1891C189189,2
C7⋊He3The semidirect product of C7 and He3 acting via He3/C32=C3633C7:He3189,8
C63⋊C32nd semidirect product of C63 and C3 acting faithfully633C63:C3189,4
C633C33rd semidirect product of C63 and C3 acting faithfully633C63:3C3189,5
C7⋊C27The semidirect product of C7 and C27 acting via C27/C9=C31893C7:C27189,1
C21.C325th non-split extension by C21 of C32 acting via C32/C3=C3633C21.C3^2189,7
C3×C63Abelian group of type [3,63]189C3xC63189,9
C32×C21Abelian group of type [3,3,21]189C3^2xC21189,13
C7×He3Direct product of C7 and He3633C7xHe3189,10
C7×3- 1+2Direct product of C7 and 3- 1+2633C7xES-(3,1)189,11
C9×C7⋊C3Direct product of C9 and C7⋊C3633C9xC7:C3189,3
C32×C7⋊C3Direct product of C32 and C7⋊C363C3^2xC7:C3189,12
C3×C7⋊C9Direct product of C3 and C7⋊C9189C3xC7:C9189,6

Groups of order 190

dρLabelID
C190Cyclic group1901C190190,4
D95Dihedral group952+D95190,3
D5×C19Direct product of C19 and D5952D5xC19190,1
C5×D19Direct product of C5 and D19952C5xD19190,2

Groups of order 191

dρLabelID
C191Cyclic group1911C191191,1

Groups of order 192

dρLabelID
C192Cyclic group1921C192192,2
D96Dihedral group962+D96192,7
Dic48Dicyclic group; = C31Q641922-Dic48192,9
CU2(𝔽3)Conformal unitary group on 𝔽32; = U2(𝔽3)7C2322CU(2,3)192,963
C2≀A4Wreath product of C2 by A484+C2wrA4192,201
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)84+Q8:2S4192,1494
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)84+C2^3:S4192,1493
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)86+C2^4:D6192,955
C42⋊D6The semidirect product of C42 and D6 acting faithfully126+C4^2:D6192,956
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6126+C2^4:C12192,191
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3126+C2^4:4Dic3192,1495
C42⋊A4The semidirect product of C42 and A4 acting faithfully1612+C4^2:A4192,1023
C24⋊A43rd semidirect product of C24 and A4 acting faithfully1612+C2^4:A4192,1009
C245A45th semidirect product of C24 and A4 acting faithfully16C2^4:5A4192,1024
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfully1612+C2^4:Dic3192,184
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfully1612+C4^2:Dic3192,185
D4⋊S4The semidirect product of D4 and S4 acting via S4/A4=C2246+D4:S4192,974
C82⋊C3The semidirect product of C82 and C3 acting faithfully243C8^2:C3192,3
C8⋊S43rd semidirect product of C8 and S4 acting via S4/A4=C2246C8:S4192,959
C82S42nd semidirect product of C8 and S4 acting via S4/A4=C2246C8:2S4192,960
A4⋊D8The semidirect product of A4 and D8 acting via D8/C8=C2246+A4:D8192,961
D42S4The semidirect product of D4 and S4 acting through Inn(D4)246D4:2S4192,1473
C26⋊C33rd semidirect product of C26 and C3 acting faithfully24C2^6:C3192,1541
Q83S4The semidirect product of Q8 and S4 acting via S4/A4=C2246Q8:3S4192,976
Q84S4The semidirect product of Q8 and S4 acting through Inn(Q8)246Q8:4S4192,1478
Q8⋊S41st semidirect product of Q8 and S4 acting via S4/C22=S3246Q8:S4192,1490
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4248+C2^3:D12192,300
D121D41st semidirect product of D12 and D4 acting via D4/C2=C22248+D12:1D4192,306
C422A4The semidirect product of C42 and A4 acting via A4/C22=C324C4^2:2A4192,1020
Q85D123rd semidirect product of Q8 and D12 acting via D12/D6=C2244+Q8:5D12192,381
C246D61st semidirect product of C24 and D6 acting via D6/C3=C22244C2^4:6D6192,591
C428D66th semidirect product of C42 and D6 acting via D6/C3=C22244C4^2:8D6192,636
D1218D46th semidirect product of D12 and D4 acting via D4/C22=C2248+D12:18D4192,757
C42⋊C121st semidirect product of C42 and C12 acting via C12/C2=C6246C4^2:C12192,192
C422C122nd semidirect product of C42 and C12 acting via C12/C2=C6246-C4^2:2C12192,193
A4⋊SD16The semidirect product of A4 and SD16 acting via SD16/D4=C2246A4:SD16192,973
A4⋊M4(2)The semidirect product of A4 and M4(2) acting via M4(2)/C2×C4=C2246A4:M4(2)192,968
C245Dic31st semidirect product of C24 and Dic3 acting via Dic3/C3=C4244C2^4:5Dic3192,95
C425Dic33rd semidirect product of C42 and Dic3 acting via Dic3/C3=C4244C4^2:5Dic3192,104
2+ 1+46S31st semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2248+ES+(2,2):6S3192,800
2+ 1+47S32nd semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2248+ES+(2,2):7S3192,803
Q8⋊D12The semidirect product of Q8 and D12 acting via D12/C4=S332Q8:D12192,952
U2(𝔽3)⋊C26th semidirect product of U2(𝔽3) and C2 acting faithfully324U(2,3):C2192,982
GL2(𝔽3)⋊C41st semidirect product of GL2(𝔽3) and C4 acting via C4/C2=C232GL(2,3):C4192,953
SL2(𝔽3)⋊D42nd semidirect product of SL2(𝔽3) and D4 acting via D4/C22=C232SL(2,3):D4192,986
SL2(𝔽3)⋊5D41st semidirect product of SL2(𝔽3) and D4 acting through Inn(SL2(𝔽3))32SL(2,3):5D4192,1003
2- 1+43C62nd semidirect product of 2- 1+4 and C6 acting via C6/C2=C3324ES-(2,2):3C6192,1504
GL2(𝔽3)⋊C223rd semidirect product of GL2(𝔽3) and C22 acting via C22/C2=C2324GL(2,3):C2^2192,1482
A4⋊C16The semidirect product of A4 and C16 acting via C16/C8=C2483A4:C16192,186
C48⋊C42nd semidirect product of C48 and C4 acting faithfully484C48:C4192,71

Full list: Groups of order 192 (1543 groups)

Groups of order 193

dρLabelID
C193Cyclic group1931C193193,1

Groups of order 194

dρLabelID
C194Cyclic group1941C194194,2
D97Dihedral group972+D97194,1

Groups of order 195

dρLabelID
C195Cyclic group1951C195195,2
C5×C13⋊C3Direct product of C5 and C13⋊C3653C5xC13:C3195,1

Groups of order 196

dρLabelID
C196Cyclic group1961C196196,2
D98Dihedral group; = C2×D49982+D98196,3
Dic49Dicyclic group; = C49C41962-Dic49196,1
C72⋊C4The semidirect product of C72 and C4 acting faithfully144+C7^2:C4196,8
C7⋊Dic7The semidirect product of C7 and Dic7 acting via Dic7/C14=C2196C7:Dic7196,6
C142Abelian group of type [14,14]196C14^2196,12
C2×C98Abelian group of type [2,98]196C2xC98196,4
C7×C28Abelian group of type [7,28]196C7xC28196,7
D72Direct product of D7 and D7144+D7^2196,9
D7×C14Direct product of C14 and D7282D7xC14196,10
C7×Dic7Direct product of C7 and Dic7282C7xDic7196,5
C2×C7⋊D7Direct product of C2 and C7⋊D798C2xC7:D7196,11

Groups of order 197

dρLabelID
C197Cyclic group1971C197197,1

Groups of order 198

dρLabelID
C198Cyclic group1981C198198,4
D99Dihedral group992+D99198,3
C3⋊D33The semidirect product of C3 and D33 acting via D33/C33=C299C3:D33198,9
C3×C66Abelian group of type [3,66]198C3xC66198,10
S3×C33Direct product of C33 and S3662S3xC33198,6
C3×D33Direct product of C3 and D33662C3xD33198,7
C11×D9Direct product of C11 and D9992C11xD9198,1
C9×D11Direct product of C9 and D11992C9xD11198,2
C32×D11Direct product of C32 and D1199C3^2xD11198,5
C11×C3⋊S3Direct product of C11 and C3⋊S399C11xC3:S3198,8

Groups of order 199

dρLabelID
C199Cyclic group1991C199199,1

Groups of order 200

dρLabelID
C200Cyclic group2001C200200,2
D100Dihedral group1002+D100200,6
Dic50Dicyclic group; = C25Q82002-Dic50200,4
D5≀C2Wreath product of D5 by C2104+D5wrC2200,43
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)108+D5:F5200,42
C52⋊C8The semidirect product of C52 and C8 acting faithfully108+C5^2:C8200,40
C52⋊Q8The semidirect product of C52 and Q8 acting faithfully108+C5^2:Q8200,44
C5⋊D20The semidirect product of C5 and D20 acting via D20/D10=C2204+C5:D20200,25
Dic52D5The semidirect product of Dic5 and D5 acting through Inn(Dic5)204+Dic5:2D5200,23
C523C82nd semidirect product of C52 and C8 acting via C8/C2=C4404C5^2:3C8200,19
C525C84th semidirect product of C52 and C8 acting via C8/C2=C4404-C5^2:5C8200,21
C522D41st semidirect product of C52 and D4 acting via D4/C2=C22404-C5^2:2D4200,24
C522Q8The semidirect product of C52 and Q8 acting via Q8/C2=C22404-C5^2:2Q8200,26
C25⋊D4The semidirect product of C25 and D4 acting via D4/C22=C21002C25:D4200,8
C20⋊D51st semidirect product of C20 and D5 acting via D5/C5=C2100C20:D5200,34
C527D42nd semidirect product of C52 and D4 acting via D4/C22=C2100C5^2:7D4200,36
C25⋊C8The semidirect product of C25 and C8 acting via C8/C2=C42004-C25:C8200,3
C252C8The semidirect product of C25 and C8 acting via C8/C4=C22002C25:2C8200,1
C527C82nd semidirect product of C52 and C8 acting via C8/C4=C2200C5^2:7C8200,16
C524C83rd semidirect product of C52 and C8 acting via C8/C2=C4200C5^2:4C8200,20
C524Q82nd semidirect product of C52 and Q8 acting via Q8/C4=C2200C5^2:4Q8200,32
C5×C40Abelian group of type [5,40]200C5xC40200,17
C2×C100Abelian group of type [2,100]200C2xC100200,9
C10×C20Abelian group of type [10,20]200C10xC20200,37
C22×C50Abelian group of type [2,2,50]200C2^2xC50200,14
C2×C102Abelian group of type [2,10,10]200C2xC10^2200,52
D5×F5Direct product of D5 and F5208+D5xF5200,41
D5×C20Direct product of C20 and D5402D5xC20200,28
C5×D20Direct product of C5 and D20402C5xD20200,29
C10×F5Direct product of C10 and F5404C10xF5200,45
D5×Dic5Direct product of D5 and Dic5404-D5xDic5200,22
C5×Dic10Direct product of C5 and Dic10402C5xDic10200,27
C10×Dic5Direct product of C10 and Dic540C10xDic5200,30
C4×D25Direct product of C4 and D251002C4xD25200,5
D4×C25Direct product of C25 and D41002D4xC25200,10
D4×C52Direct product of C52 and D4100D4xC5^2200,38
C22×D25Direct product of C22 and D25100C2^2xD25200,13
Q8×C25Direct product of C25 and Q82002Q8xC25200,11
Q8×C52Direct product of C52 and Q8200Q8xC5^2200,39
C2×Dic25Direct product of C2 and Dic25200C2xDic25200,7
C2×D52Direct product of C2, D5 and D5204+C2xD5^2200,49
C5×C5⋊D4Direct product of C5 and C5⋊D4202C5xC5:D4200,31
C2×C52⋊C4Direct product of C2 and C52⋊C4204+C2xC5^2:C4200,48
C5×C5⋊C8Direct product of C5 and C5⋊C8404C5xC5:C8200,18
D5×C2×C10Direct product of C2×C10 and D540D5xC2xC10200,50
C5×C52C8Direct product of C5 and C52C8402C5xC5:2C8200,15
C2×D5.D5Direct product of C2 and D5.D5404C2xD5.D5200,46
C2×C25⋊C4Direct product of C2 and C25⋊C4504+C2xC25:C4200,12
C2×C5⋊F5Direct product of C2 and C5⋊F550C2xC5:F5200,47
C4×C5⋊D5Direct product of C4 and C5⋊D5100C4xC5:D5200,33
C22×C5⋊D5Direct product of C22 and C5⋊D5100C2^2xC5:D5200,51
C2×C526C4Direct product of C2 and C526C4200C2xC5^2:6C4200,35

Groups of order 201

dρLabelID
C201Cyclic group2011C201201,2
C67⋊C3The semidirect product of C67 and C3 acting faithfully673C67:C3201,1

Groups of order 202

dρLabelID
C202Cyclic group2021C202202,2
D101Dihedral group1012+D101202,1

Groups of order 203

dρLabelID
C203Cyclic group2031C203203,2
C29⋊C7The semidirect product of C29 and C7 acting faithfully297C29:C7203,1

Groups of order 204

dρLabelID
C204Cyclic group2041C204204,4
D102Dihedral group; = C2×D511022+D102204,11
Dic51Dicyclic group; = C513C42042-Dic51204,3
C51⋊C41st semidirect product of C51 and C4 acting faithfully514C51:C4204,6
C2×C102Abelian group of type [2,102]204C2xC102204,12
S3×D17Direct product of S3 and D17514+S3xD17204,7
A4×C17Direct product of C17 and A4683A4xC17204,8
S3×C34Direct product of C34 and S31022S3xC34204,10
C6×D17Direct product of C6 and D171022C6xD17204,9
Dic3×C17Direct product of C17 and Dic32042Dic3xC17204,1
C3×Dic17Direct product of C3 and Dic172042C3xDic17204,2
C3×C17⋊C4Direct product of C3 and C17⋊C4514C3xC17:C4204,5

Groups of order 205

dρLabelID
C205Cyclic group2051C205205,2
C41⋊C5The semidirect product of C41 and C5 acting faithfully415C41:C5205,1

Groups of order 206

dρLabelID
C206Cyclic group2061C206206,2
D103Dihedral group1032+D103206,1

Groups of order 207

dρLabelID
C207Cyclic group2071C207207,1
C3×C69Abelian group of type [3,69]207C3xC69207,2

Groups of order 208

dρLabelID
C208Cyclic group2081C208208,2
D104Dihedral group1042+D104208,7
Dic52Dicyclic group; = C131Q162082-Dic52208,8
C52⋊C41st semidirect product of C52 and C4 acting faithfully524C52:C4208,31
D4⋊D13The semidirect product of D4 and D13 acting via D13/C13=C21044+D4:D13208,15
D13⋊C8The semidirect product of D13 and C8 acting via C8/C4=C21044D13:C8208,28
Q8⋊D13The semidirect product of Q8 and D13 acting via D13/C13=C21044+Q8:D13208,17
C8⋊D133rd semidirect product of C8 and D13 acting via D13/C13=C21042C8:D13208,5
C104⋊C22nd semidirect product of C104 and C2 acting faithfully1042C104:C2208,6
D26⋊C41st semidirect product of D26 and C4 acting via C4/C2=C2104D26:C4208,14
D525C2The semidirect product of D52 and C2 acting through Inn(D52)1042D52:5C2208,38
D42D13The semidirect product of D4 and D13 acting through Inn(D4)1044-D4:2D13208,40
D52⋊C24th semidirect product of D52 and C2 acting faithfully1044+D52:C2208,42
C13⋊M4(2)The semidirect product of C13 and M4(2) acting via M4(2)/C22=C41044-C13:M4(2)208,33
C13⋊C16The semidirect product of C13 and C16 acting via C16/C4=C42084C13:C16208,3
C523C41st semidirect product of C52 and C4 acting via C4/C2=C2208C52:3C4208,13
C132C16The semidirect product of C13 and C16 acting via C16/C8=C22082C13:2C16208,1
C13⋊Q16The semidirect product of C13 and Q16 acting via Q16/Q8=C22084-C13:Q16208,18
D13.D4The non-split extension by D13 of D4 acting via D4/C22=C2524+D13.D4208,34
D4.D13The non-split extension by D4 of D13 acting via D13/C13=C21044-D4.D13208,16
C52.4C41st non-split extension by C52 of C4 acting via C4/C2=C21042C52.4C4208,10
C52.C41st non-split extension by C52 of C4 acting faithfully1044C52.C4208,29
C23.D13The non-split extension by C23 of D13 acting via D13/C13=C2104C2^3.D13208,19
C26.D41st non-split extension by C26 of D4 acting via D4/C22=C2208C26.D4208,12
C4×C52Abelian group of type [4,52]208C4xC52208,20
C2×C104Abelian group of type [2,104]208C2xC104208,23
C22×C52Abelian group of type [2,2,52]208C2^2xC52208,45
C23×C26Abelian group of type [2,2,2,26]208C2^3xC26208,51
D4×D13Direct product of D4 and D13524+D4xD13208,39
C8×D13Direct product of C8 and D131042C8xD13208,4
C13×D8Direct product of C13 and D81042C13xD8208,25
C2×D52Direct product of C2 and D52104C2xD52208,37
D4×C26Direct product of C26 and D4104D4xC26208,46
Q8×D13Direct product of Q8 and D131044-Q8xD13208,41
C13×SD16Direct product of C13 and SD161042C13xSD16208,26
C23×D13Direct product of C23 and D13104C2^3xD13208,50
C13×M4(2)Direct product of C13 and M4(2)1042C13xM4(2)208,24
Q8×C26Direct product of C26 and Q8208Q8xC26208,47
C13×Q16Direct product of C13 and Q162082C13xQ16208,27
C4×Dic13Direct product of C4 and Dic13208C4xDic13208,11
C2×Dic26Direct product of C2 and Dic26208C2xDic26208,35
C22×Dic13Direct product of C22 and Dic13208C2^2xDic13208,43
C4×C13⋊C4Direct product of C4 and C13⋊C4524C4xC13:C4208,30
C22×C13⋊C4Direct product of C22 and C13⋊C452C2^2xC13:C4208,49
C2×C4×D13Direct product of C2×C4 and D13104C2xC4xD13208,36
C2×C13⋊D4Direct product of C2 and C13⋊D4104C2xC13:D4208,44
C13×C4○D4Direct product of C13 and C4○D41042C13xC4oD4208,48
C13×C22⋊C4Direct product of C13 and C22⋊C4104C13xC2^2:C4208,21
C2×C13⋊C8Direct product of C2 and C13⋊C8208C2xC13:C8208,32
C13×C4⋊C4Direct product of C13 and C4⋊C4208C13xC4:C4208,22
C2×C132C8Direct product of C2 and C132C8208C2xC13:2C8208,9

Groups of order 209

dρLabelID
C209Cyclic group2091C209209,1

Groups of order 210

dρLabelID
C210Cyclic group2101C210210,12
D105Dihedral group1052+D105210,11
C5⋊F7The semidirect product of C5 and F7 acting via F7/C7⋊C3=C2356+C5:F7210,3
C5×F7Direct product of C5 and F7356C5xF7210,1
S3×C35Direct product of C35 and S31052S3xC35210,8
D7×C15Direct product of C15 and D71052D7xC15210,5
D5×C21Direct product of C21 and D51052D5xC21210,6
C3×D35Direct product of C3 and D351052C3xD35210,7
C5×D21Direct product of C5 and D211052C5xD21210,9
C7×D15Direct product of C7 and D151052C7xD15210,10
D5×C7⋊C3Direct product of D5 and C7⋊C3356D5xC7:C3210,2
C10×C7⋊C3Direct product of C10 and C7⋊C3703C10xC7:C3210,4

Groups of order 211

dρLabelID
C211Cyclic group2111C211211,1

Groups of order 212

dρLabelID
C212Cyclic group2121C212212,2
D106Dihedral group; = C2×D531062+D106212,4
Dic53Dicyclic group; = C532C42122-Dic53212,1
C53⋊C4The semidirect product of C53 and C4 acting faithfully534+C53:C4212,3
C2×C106Abelian group of type [2,106]212C2xC106212,5

Groups of order 213

dρLabelID
C213Cyclic group2131C213213,1

Groups of order 214

dρLabelID
C214Cyclic group2141C214214,2
D107Dihedral group1072+D107214,1

Groups of order 215

dρLabelID
C215Cyclic group2151C215215,1

Groups of order 216

dρLabelID
C216Cyclic group2161C216216,2
D108Dihedral group1082+D108216,6
Dic54Dicyclic group; = C27Q82162-Dic54216,4
SU3(𝔽2)Special unitary group on 𝔽23; = He3Q8273SU(3,2)216,88
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C398+ASL(2,3)216,153
C33⋊D42nd semidirect product of C33 and D4 acting faithfully124C3^3:D4216,158
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4128+C3^2:2D12216,159
He3⋊D4The semidirect product of He3 and D4 acting faithfully186+He3:D4216,87
C62⋊S34th semidirect product of C62 and S3 acting faithfully186+C6^2:S3216,92
C32⋊S42nd semidirect product of C32 and S4 acting via S4/C22=S3183C3^2:S4216,95
C62⋊C63rd semidirect product of C62 and C6 acting faithfully186+C6^2:C6216,99
C3⋊F9The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2248C3:F9216,155
C334C82nd semidirect product of C33 and C8 acting via C8/C2=C4244C3^3:4C8216,118
C339D46th semidirect product of C33 and D4 acting via D4/C2=C22244C3^3:9D4216,132
C335Q83rd semidirect product of C33 and Q8 acting via Q8/C2=C22244C3^3:5Q8216,133
C33⋊Q82nd semidirect product of C33 and Q8 acting faithfully248C3^3:Q8216,161
He3⋊C8The semidirect product of He3 and C8 acting faithfully276+He3:C8216,86
C9⋊S4The semidirect product of C9 and S4 acting via S4/A4=C2366+C9:S4216,93
D9⋊A4The semidirect product of D9 and A4 acting via A4/C22=C3366+D9:A4216,96
D36⋊C3The semidirect product of D36 and C3 acting faithfully366+D36:C3216,54
C3⋊D36The semidirect product of C3 and D36 acting via D36/D18=C2364+C3:D36216,29
C9⋊D12The semidirect product of C9 and D12 acting via D12/D6=C2364+C9:D12216,32
Dic9⋊C6The semidirect product of Dic9 and C6 acting faithfully366Dic9:C6216,62
He32D41st semidirect product of He3 and D4 acting via D4/C2=C22366+He3:2D4216,35
He33D42nd semidirect product of He3 and D4 acting via D4/C2=C22366He3:3D4216,37
He34D41st semidirect product of He3 and D4 acting via D4/C4=C2366+He3:4D4216,51
He36D41st semidirect product of He3 and D4 acting via D4/C22=C2366He3:6D4216,60
He35D42nd semidirect product of He3 and D4 acting via D4/C4=C2366He3:5D4216,68
He37D42nd semidirect product of He3 and D4 acting via D4/C22=C2366He3:7D4216,72
C337D44th semidirect product of C33 and D4 acting via D4/C2=C2236C3^3:7D4216,128
C338D45th semidirect product of C33 and D4 acting via D4/C2=C2236C3^3:8D4216,129
C324S42nd semidirect product of C32 and S4 acting via S4/A4=C236C3^2:4S4216,165
C9⋊C24The semidirect product of C9 and C24 acting via C24/C4=C6726C9:C24216,15
Q8⋊He3The semidirect product of Q8 and He3 acting via He3/C32=C3726Q8:He3216,42
D6⋊D91st semidirect product of D6 and D9 acting via D9/C9=C2724-D6:D9216,31
He33C81st semidirect product of He3 and C8 acting via C8/C4=C2726He3:3C8216,14
He34C82nd semidirect product of He3 and C8 acting via C8/C4=C2723He3:4C8216,17
He32C8The semidirect product of He3 and C8 acting via C8/C2=C4723He3:2C8216,25
He32Q8The semidirect product of He3 and Q8 acting via Q8/C2=C22726-He3:2Q8216,33
He33Q81st semidirect product of He3 and Q8 acting via Q8/C4=C2726-He3:3Q8216,49
He34Q82nd semidirect product of He3 and Q8 acting via Q8/C4=C2726He3:4Q8216,66
C336D43rd semidirect product of C33 and D4 acting via D4/C2=C2272C3^3:6D4216,127
C334Q82nd semidirect product of C33 and Q8 acting via Q8/C2=C2272C3^3:4Q8216,130
C9⋊Dic6The semidirect product of C9 and Dic6 acting via Dic6/Dic3=C2724-C9:Dic6216,26
Q8⋊3- 1+2The semidirect product of Q8 and 3- 1+2 acting via 3- 1+2/C32=C3726Q8:ES-(3,1)216,41
C27⋊D4The semidirect product of C27 and D4 acting via D4/C22=C21082C27:D4216,8
C36⋊S31st semidirect product of C36 and S3 acting via S3/C3=C2108C36:S3216,65
C3312D43rd semidirect product of C33 and D4 acting via D4/C4=C2108C3^3:12D4216,147
C3315D43rd semidirect product of C33 and D4 acting via D4/C22=C2108C3^3:15D4216,149
C27⋊C8The semidirect product of C27 and C8 acting via C8/C4=C22162C27:C8216,1
Q8⋊C27The semidirect product of Q8 and C27 acting via C27/C9=C32162Q8:C27216,3
C337C83rd semidirect product of C33 and C8 acting via C8/C4=C2216C3^3:7C8216,84
C338Q83rd semidirect product of C33 and Q8 acting via Q8/C4=C2216C3^3:8Q8216,145
C339(C2×C4)6th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22244C3^3:9(C2xC4)216,131
He3⋊(C2×C4)2nd semidirect product of He3 and C2×C4 acting via C2×C4/C2=C22366-He3:(C2xC4)216,36
C338(C2×C4)5th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C2236C3^3:8(C2xC4)216,126
C32.S4The non-split extension by C32 of S4 acting via S4/C22=S3186+C3^2.S4216,90
C18.D63rd non-split extension by C18 of D6 acting via D6/S3=C2364+C18.D6216,28
C9.S4The non-split extension by C9 of S4 acting via S4/A4=C2546+C9.S4216,21
C32.3S42nd non-split extension by C32 of S4 acting via S4/A4=C254C3^2.3S4216,94
C18.A4The non-split extension by C18 of A4 acting via A4/C22=C3726C18.A4216,39
C36.C61st non-split extension by C36 of C6 acting faithfully726-C36.C6216,52
C6.D1811st non-split extension by C6 of D18 acting via D18/C18=C2108C6.D18216,70
C36.S36th non-split extension by C36 of S3 acting via S3/C3=C2216C36.S3216,16
C12.D93rd non-split extension by C12 of D9 acting via D9/C9=C2216C12.D9216,63
C6.S322nd non-split extension by C6 of S32 acting via S32/C3⋊S3=C2366C6.S3^2216,34
C63Abelian group of type [6,6,6]216C6^3216,177
C3×C72Abelian group of type [3,72]216C3xC72216,18
C6×C36Abelian group of type [6,36]216C6xC36216,73
C2×C108Abelian group of type [2,108]216C2xC108216,9
C22×C54Abelian group of type [2,2,54]216C2^2xC54216,24
C32×C24Abelian group of type [3,3,24]216C3^2xC24216,85
C2×C6×C18Abelian group of type [2,6,18]216C2xC6xC18216,114
C3×C6×C12Abelian group of type [3,6,12]216C3xC6xC12216,150
C3×F9Direct product of C3 and F9248C3xF9216,154
C3×PSU3(𝔽2)Direct product of C3 and PSU3(𝔽2)248C3xPSU(3,2)216,160
C9×S4Direct product of C9 and S4363C9xS4216,89
A4×D9Direct product of A4 and D9366+A4xD9216,97
D4×He3Direct product of D4 and He3366D4xHe3216,77
C32×S4Direct product of C32 and S436C3^2xS4216,163
D4×3- 1+2Direct product of D4 and 3- 1+2366D4xES-(3,1)216,78
A4×C18Direct product of C18 and A4543A4xC18216,103
S3×C36Direct product of C36 and S3722S3xC36216,47
C12×D9Direct product of C12 and D9722C12xD9216,45
C3×D36Direct product of C3 and D36722C3xD36216,46
C9×D12Direct product of C9 and D12722C9xD12216,48
C8×He3Direct product of C8 and He3723C8xHe3216,19
Q8×He3Direct product of Q8 and He3726Q8xHe3216,80
S3×C62Direct product of C62 and S372S3xC6^2216,174
Dic3×D9Direct product of Dic3 and D9724-Dic3xD9216,27
S3×Dic9Direct product of S3 and Dic9724-S3xDic9216,30
C9×Dic6Direct product of C9 and Dic6722C9xDic6216,44
C6×Dic9Direct product of C6 and Dic972C6xDic9216,55
C3×Dic18Direct product of C3 and Dic18722C3xDic18216,43
Dic3×C18Direct product of C18 and Dic372Dic3xC18216,56
C32×D12Direct product of C32 and D1272C3^2xD12216,137
C23×He3Direct product of C23 and He372C2^3xHe3216,115
C32×Dic6Direct product of C32 and Dic672C3^2xDic6216,135
C9×SL2(𝔽3)Direct product of C9 and SL2(𝔽3)722C9xSL(2,3)216,38
C8×3- 1+2Direct product of C8 and 3- 1+2723C8xES-(3,1)216,20
Q8×3- 1+2Direct product of Q8 and 3- 1+2726Q8xES-(3,1)216,81
C32×SL2(𝔽3)Direct product of C32 and SL2(𝔽3)72C3^2xSL(2,3)216,134
C23×3- 1+2Direct product of C23 and 3- 1+272C2^3xES-(3,1)216,116
C4×D27Direct product of C4 and D271082C4xD27216,5
D4×C27Direct product of C27 and D41082D4xC27216,10
D4×C33Direct product of C33 and D4108D4xC3^3216,151
C22×D27Direct product of C22 and D27108C2^2xD27216,23
Q8×C27Direct product of C27 and Q82162Q8xC27216,11
Q8×C33Direct product of C33 and Q8216Q8xC3^3216,152
C2×Dic27Direct product of C2 and Dic27216C2xDic27216,7
S33Direct product of S3, S3 and S3; = Hol(C3×S3)128+S3^3216,162
C3×S3≀C2Direct product of C3 and S3≀C2124C3xS3wrC2216,157
S3×C32⋊C4Direct product of S3 and C32⋊C4128+S3xC3^2:C4216,156
C2×C32⋊A4Direct product of C2 and C32⋊A4183C2xC3^2:A4216,107
C2×C32⋊D6Direct product of C2 and C32⋊D6186+C2xC3^2:D6216,102
C2×C32.A4Direct product of C2 and C32.A4183C2xC3^2.A4216,106
S32×C6Direct product of C6, S3 and S3244S3^2xC6216,170
C3×S3×A4Direct product of C3, S3 and A4246C3xS3xA4216,166
C3×C3⋊S4Direct product of C3 and C3⋊S4246C3xC3:S4216,164
C6×C32⋊C4Direct product of C6 and C32⋊C4244C6xC3^2:C4216,168
C3×S3×Dic3Direct product of C3, S3 and Dic3244C3xS3xDic3216,119
C3×D6⋊S3Direct product of C3 and D6⋊S3244C3xD6:S3216,121
C3×C3⋊D12Direct product of C3 and C3⋊D12244C3xC3:D12216,122
C2×C33⋊C4Direct product of C2 and C33⋊C4244C2xC3^3:C4216,169
C3×C6.D6Direct product of C3 and C6.D6244C3xC6.D6216,120
C3×C322C8Direct product of C3 and C322C8244C3xC3^2:2C8216,117
C3×C322Q8Direct product of C3 and C322Q8244C3xC3^2:2Q8216,123
C2×C324D6Direct product of C2 and C324D6244C2xC3^2:4D6216,172
C2×S3×D9Direct product of C2, S3 and D9364+C2xS3xD9216,101
C4×C9⋊C6Direct product of C4 and C9⋊C6366C4xC9:C6216,53
A4×C3⋊S3Direct product of A4 and C3⋊S336A4xC3:S3216,167
C3×C9⋊D4Direct product of C3 and C9⋊D4362C3xC9:D4216,57
C9×C3⋊D4Direct product of C9 and C3⋊D4362C9xC3:D4216,58
C3×C3.S4Direct product of C3 and C3.S4366C3xC3.S4216,91
S3×C3.A4Direct product of S3 and C3.A4366S3xC3.A4216,98
C2×He3⋊C4Direct product of C2 and He3⋊C4363C2xHe3:C4216,100
C4×C32⋊C6Direct product of C4 and C32⋊C6366C4xC3^2:C6216,50
C22×C9⋊C6Direct product of C22 and C9⋊C636C2^2xC9:C6216,111
C4×He3⋊C2Direct product of C4 and He3⋊C2363C4xHe3:C2216,67
C32×C3⋊D4Direct product of C32 and C3⋊D436C3^2xC3:D4216,139
C3×C327D4Direct product of C3 and C327D436C3xC3^2:7D4216,144
C22×C32⋊C6Direct product of C22 and C32⋊C636C2^2xC3^2:C6216,110
C22×He3⋊C2Direct product of C22 and He3⋊C236C2^2xHe3:C2216,113
A4×C3×C6Direct product of C3×C6 and A454A4xC3xC6216,173
C2×C9⋊A4Direct product of C2 and C9⋊A4543C2xC9:A4216,104
C2×C9.A4Direct product of C2 and C9.A4543C2xC9.A4216,22
C6×C3.A4Direct product of C6 and C3.A454C6xC3.A4216,105
C3×C9⋊C8Direct product of C3 and C9⋊C8722C3xC9:C8216,12
C9×C3⋊C8Direct product of C9 and C3⋊C8722C9xC3:C8216,13
C2×C6×D9Direct product of C2×C6 and D972C2xC6xD9216,108
S3×C2×C18Direct product of C2×C18 and S372S3xC2xC18216,109
S3×C3×C12Direct product of C3×C12 and S372S3xC3xC12216,136
C2×C9⋊C12Direct product of C2 and C9⋊C1272C2xC9:C12216,61
C2×C4×He3Direct product of C2×C4 and He372C2xC4xHe3216,74
C12×C3⋊S3Direct product of C12 and C3⋊S372C12xC3:S3216,141
C32×C3⋊C8Direct product of C32 and C3⋊C872C3^2xC3:C8216,82
Dic3×C3×C6Direct product of C3×C6 and Dic372Dic3xC3xC6216,138
C3×C12⋊S3Direct product of C3 and C12⋊S372C3xC12:S3216,142
S3×C3⋊Dic3Direct product of S3 and C3⋊Dic372S3xC3:Dic3216,124
Dic3×C3⋊S3Direct product of Dic3 and C3⋊S372Dic3xC3:S3216,125
C6×C3⋊Dic3Direct product of C6 and C3⋊Dic372C6xC3:Dic3216,143
C2×C32⋊C12Direct product of C2 and C32⋊C1272C2xC3^2:C12216,59
C2×He33C4Direct product of C2 and He33C472C2xHe3:3C4216,71
C3×C324C8Direct product of C3 and C324C872C3xC3^2:4C8216,83
C3×C324Q8Direct product of C3 and C324Q872C3xC3^2:4Q8216,140
C2×C4×3- 1+2Direct product of C2×C4 and 3- 1+272C2xC4xES-(3,1)216,75
D4×C3×C9Direct product of C3×C9 and D4108D4xC3xC9216,76
C4×C9⋊S3Direct product of C4 and C9⋊S3108C4xC9:S3216,64
C22×C9⋊S3Direct product of C22 and C9⋊S3108C2^2xC9:S3216,112
C4×C33⋊C2Direct product of C4 and C33⋊C2108C4xC3^3:C2216,146
C22×C33⋊C2Direct product of C22 and C33⋊C2108C2^2xC3^3:C2216,176
Q8×C3×C9Direct product of C3×C9 and Q8216Q8xC3xC9216,79
C3×Q8⋊C9Direct product of C3 and Q8⋊C9216C3xQ8:C9216,40
C2×C9⋊Dic3Direct product of C2 and C9⋊Dic3216C2xC9:Dic3216,69
C2×C335C4Direct product of C2 and C335C4216C2xC3^3:5C4216,148
C2×S3×C3⋊S3Direct product of C2, S3 and C3⋊S336C2xS3xC3:S3216,171
C2×C6×C3⋊S3Direct product of C2×C6 and C3⋊S372C2xC6xC3:S3216,175

Groups of order 217

dρLabelID
C217Cyclic group2171C217217,1

Groups of order 218

dρLabelID
C218Cyclic group2181C218218,2
D109Dihedral group1092+D109218,1

Groups of order 219

dρLabelID
C219Cyclic group2191C219219,2
C73⋊C3The semidirect product of C73 and C3 acting faithfully733C73:C3219,1

Groups of order 220

dρLabelID
C220Cyclic group2201C220220,6
D110Dihedral group; = C2×D551102+D110220,14
Dic55Dicyclic group; = C553C42202-Dic55220,5
C11⋊C20The semidirect product of C11 and C20 acting via C20/C2=C104410-C11:C20220,1
C11⋊F5The semidirect product of C11 and F5 acting via F5/D5=C2554C11:F5220,10
C2×C110Abelian group of type [2,110]220C2xC110220,15
C2×F11Direct product of C2 and F11; = Aut(D22) = Hol(C22)2210+C2xF11220,7
D5×D11Direct product of D5 and D11554+D5xD11220,11
C11×F5Direct product of C11 and F5554C11xF5220,9
D5×C22Direct product of C22 and D51102D5xC22220,13
C10×D11Direct product of C10 and D111102C10xD11220,12
C11×Dic5Direct product of C11 and Dic52202C11xDic5220,3
C5×Dic11Direct product of C5 and Dic112202C5xDic11220,4
C4×C11⋊C5Direct product of C4 and C11⋊C5445C4xC11:C5220,2
C22×C11⋊C5Direct product of C22 and C11⋊C544C2^2xC11:C5220,8

Groups of order 221

dρLabelID
C221Cyclic group2211C221221,1

Groups of order 222

dρLabelID
C222Cyclic group2221C222222,6
D111Dihedral group1112+D111222,5
C37⋊C6The semidirect product of C37 and C6 acting faithfully376+C37:C6222,1
S3×C37Direct product of C37 and S31112S3xC37222,3
C3×D37Direct product of C3 and D371112C3xD37222,4
C2×C37⋊C3Direct product of C2 and C37⋊C3743C2xC37:C3222,2

Groups of order 223

dρLabelID
C223Cyclic group2231C223223,1

Groups of order 224

dρLabelID
C224Cyclic group2241C224224,2
D112Dihedral group1122+D112224,5
Dic56Dicyclic group; = C71Q322242-Dic56224,7
D8⋊D72nd semidirect product of D8 and D7 acting via D7/C7=C2564D8:D7224,106
C8⋊D141st semidirect product of C8 and D14 acting via D14/C7=C22564+C8:D14224,103
D284C44th semidirect product of D28 and C4 acting via C4/C2=C2564D28:4C4224,31
D56⋊C26th semidirect product of D56 and C2 acting faithfully564+D56:C2224,109
D4⋊D142nd semidirect product of D4 and D14 acting via D14/C14=C2564+D4:D14224,144
D46D142nd semidirect product of D4 and D14 acting through Inn(D4)564D4:6D14224,180
D48D144th semidirect product of D4 and D14 acting through Inn(D4)564+D4:8D14224,185
C24⋊D71st semidirect product of C24 and D7 acting via D7/C7=C256C2^4:D7224,148
C23⋊Dic7The semidirect product of C23 and Dic7 acting via Dic7/C7=C4564C2^3:Dic7224,40
D42Dic72nd semidirect product of D4 and Dic7 acting via Dic7/C14=C2564D4:2Dic7224,43
C22⋊D28The semidirect product of C22 and D28 acting via D28/D14=C256C2^2:D28224,77
C23⋊D141st semidirect product of C23 and D14 acting via D14/C7=C2256C2^3:D14224,132
Dic14⋊C41st semidirect product of Dic14 and C4 acting via C4/C2=C2562Dic14:C4224,11
D14⋊C8The semidirect product of D14 and C8 acting via C8/C4=C2112D14:C8224,26
C7⋊D16The semidirect product of C7 and D16 acting via D16/D8=C21124+C7:D16224,32
D83D7The semidirect product of D8 and D7 acting through Inn(D8)1124-D8:3D7224,107
C16⋊D73rd semidirect product of C16 and D7 acting via D7/C7=C21122C16:D7224,4
C284D41st semidirect product of C28 and D4 acting via D4/C4=C2112C28:4D4224,69
C4⋊D28The semidirect product of C4 and D28 acting via D28/D14=C2112C4:D28224,90
C287D41st semidirect product of C28 and D4 acting via D4/C22=C2112C28:7D4224,125
C282D42nd semidirect product of C28 and D4 acting via D4/C2=C22112C28:2D4224,133
C28⋊D43rd semidirect product of C28 and D4 acting via D4/C2=C22112C28:D4224,135
C112⋊C22nd semidirect product of C112 and C2 acting faithfully1122C112:C2224,6
C7⋊SD32The semidirect product of C7 and SD32 acting via SD32/Q16=C21124+C7:SD32224,34
D14⋊D41st semidirect product of D14 and D4 acting via D4/C4=C2112D14:D4224,79
D28⋊C45th semidirect product of D28 and C4 acting via C4/C2=C2112D28:C4224,88
D567C2The semidirect product of D56 and C2 acting through Inn(D56)1122D56:7C2224,99
D14⋊Q81st semidirect product of D14 and Q8 acting via Q8/C4=C2112D14:Q8224,91
D142Q82nd semidirect product of D14 and Q8 acting via Q8/C4=C2112D14:2Q8224,92
Q16⋊D72nd semidirect product of Q16 and D7 acting via D7/C7=C21124Q16:D7224,113
D143Q83rd semidirect product of D14 and Q8 acting via Q8/C4=C2112D14:3Q8224,141
C42⋊D71st semidirect product of C42 and D7 acting via D7/C7=C2112C4^2:D7224,67
C422D72nd semidirect product of C42 and D7 acting via D7/C7=C2112C4^2:2D7224,71
D4⋊Dic71st semidirect product of D4 and Dic7 acting via Dic7/C14=C2112D4:Dic7224,38
Dic74D41st semidirect product of Dic7 and D4 acting through Inn(Dic7)112Dic7:4D4224,76
SD16⋊D72nd semidirect product of SD16 and D7 acting via D7/C7=C21124-SD16:D7224,110
SD163D7The semidirect product of SD16 and D7 acting through Inn(SD16)1124SD16:3D7224,111
Dic7⋊D42nd semidirect product of Dic7 and D4 acting via D4/C22=C2112Dic7:D4224,134
C22⋊Dic14The semidirect product of C22 and Dic14 acting via Dic14/Dic7=C2112C2^2:Dic14224,73
C7⋊C32The semidirect product of C7 and C32 acting via C32/C16=C22242C7:C32224,1
C28⋊Q8The semidirect product of C28 and Q8 acting via Q8/C2=C22224C28:Q8224,83
C28⋊C81st semidirect product of C28 and C8 acting via C8/C4=C2224C28:C8224,10
C56⋊C44th semidirect product of C56 and C4 acting via C4/C2=C2224C56:C4224,21
C561C41st semidirect product of C56 and C4 acting via C4/C2=C2224C56:1C4224,24
C7⋊Q32The semidirect product of C7 and Q32 acting via Q32/Q16=C22244-C7:Q32224,35
Dic7⋊C8The semidirect product of Dic7 and C8 acting via C8/C4=C2224Dic7:C8224,20
C282Q81st semidirect product of C28 and Q8 acting via Q8/C4=C2224C28:2Q8224,64
C8⋊Dic72nd semidirect product of C8 and Dic7 acting via Dic7/C14=C2224C8:Dic7224,23
Q8⋊Dic71st semidirect product of Q8 and Dic7 acting via Dic7/C14=C2224Q8:Dic7224,41
Dic73Q8The semidirect product of Dic7 and Q8 acting through Inn(Dic7)224Dic7:3Q8224,82
Dic7⋊Q82nd semidirect product of Dic7 and Q8 acting via Q8/C4=C2224Dic7:Q8224,139
C4⋊C47D71st semidirect product of C4⋊C4 and D7 acting through Inn(C4⋊C4)112C4:C4:7D7224,87
C4⋊C4⋊D76th semidirect product of C4⋊C4 and D7 acting via D7/C7=C2112C4:C4:D7224,93
C28.D48th non-split extension by C28 of D4 acting via D4/C2=C22564C28.D4224,39
D4.D141st non-split extension by D4 of D14 acting via D14/C14=C2564D4.D14224,127
C28.46D43rd non-split extension by C28 of D4 acting via D4/C22=C2564+C28.46D4224,29
C23.1D141st non-split extension by C23 of D14 acting via D14/C7=C22564C2^3.1D14224,12
D8.D7The non-split extension by D8 of D7 acting via D7/C7=C21124-D8.D7224,33
D28.C4The non-split extension by D28 of C4 acting via C4/C2=C21124D28.C4224,102
C28.C81st non-split extension by C28 of C8 acting via C8/C4=C21122C28.C8224,18
C56.C41st non-split extension by C56 of C4 acting via C4/C2=C21122C56.C4224,25
C14.D82nd non-split extension by C14 of D8 acting via D8/D4=C2112C14.D8224,15
C2.D562nd central extension by C2 of D56112C2.D56224,27
C4.D285th non-split extension by C4 of D28 acting via D28/C28=C2112C4.D28224,70
C8.D141st non-split extension by C8 of D14 acting via D14/C7=C221124-C8.D14224,104
Q8.Dic7The non-split extension by Q8 of Dic7 acting through Inn(Q8)1124Q8.Dic7224,143
D14.D41st non-split extension by D14 of D4 acting via D4/C22=C2112D14.D4224,78
D14.5D42nd non-split extension by D14 of D4 acting via D4/C22=C2112D14.5D4224,89
D28.2C4The non-split extension by D28 of C4 acting through Inn(D28)1122D28.2C4224,96
D4.8D143rd non-split extension by D4 of D14 acting via D14/C14=C21124D4.8D14224,145
D4.9D144th non-split extension by D4 of D14 acting via D14/C14=C21124-D4.9D14224,146
C28.53D410th non-split extension by C28 of D4 acting via D4/C22=C21124C28.53D4224,28
C4.12D284th non-split extension by C4 of D28 acting via D28/D14=C21124-C4.12D28224,30
C28.55D412nd non-split extension by C28 of D4 acting via D4/C22=C2112C28.55D4224,36
C28.10D410th non-split extension by C28 of D4 acting via D4/C2=C221124C28.10D4224,42
C28.48D45th non-split extension by C28 of D4 acting via D4/C22=C2112C28.48D4224,119
C28.17D417th non-split extension by C28 of D4 acting via D4/C2=C22112C28.17D4224,131
C28.23D423rd non-split extension by C28 of D4 acting via D4/C2=C22112C28.23D4224,142
Q8.D145th non-split extension by Q8 of D14 acting via D14/D7=C21124+Q8.D14224,114
D4.10D14The non-split extension by D4 of D14 acting through Inn(D4)1124-D4.10D14224,186
Q8.10D141st non-split extension by Q8 of D14 acting through Inn(Q8)1124Q8.10D14224,183
Dic7.D41st non-split extension by Dic7 of D4 acting via D4/C4=C2112Dic7.D4224,80
C23.D143rd non-split extension by C23 of D14 acting via D14/C7=C22112C2^3.D14224,74
C22.D283rd non-split extension by C22 of D28 acting via D28/D14=C2112C2^2.D28224,81
C28.C2315th non-split extension by C28 of C23 acting via C23/C2=C221124C28.C2^3224,137
C23.11D141st non-split extension by C23 of D14 acting via D14/D7=C2112C2^3.11D14224,72
C23.21D142nd non-split extension by C23 of D14 acting via D14/C14=C2112C2^3.21D14224,121
C23.23D144th non-split extension by C23 of D14 acting via D14/C14=C2112C2^3.23D14224,124
C23.18D148th non-split extension by C23 of D14 acting via D14/D7=C2112C2^3.18D14224,130
Dic7.Q8The non-split extension by Dic7 of Q8 acting via Q8/C4=C2224Dic7.Q8224,84
C28.Q81st non-split extension by C28 of Q8 acting via Q8/C2=C22224C28.Q8224,13
C28.6Q83rd non-split extension by C28 of Q8 acting via Q8/C4=C2224C28.6Q8224,65
C28.3Q83rd non-split extension by C28 of Q8 acting via Q8/C2=C22224C28.3Q8224,85
C28.44D41st non-split extension by C28 of D4 acting via D4/C22=C2224C28.44D4224,22
C14.Q162nd non-split extension by C14 of Q16 acting via Q16/Q8=C2224C14.Q16224,16
C42.D71st non-split extension by C42 of D7 acting via D7/C7=C2224C4^2.D7224,9
C14.C425th non-split extension by C14 of C42 acting via C42/C2×C4=C2224C14.C4^2224,37
C4.Dic142nd non-split extension by C4 of Dic14 acting via Dic14/Dic7=C2224C4.Dic14224,14
C4×C56Abelian group of type [4,56]224C4xC56224,45
C2×C112Abelian group of type [2,112]224C2xC112224,58
C22×C56Abelian group of type [2,2,56]224C2^2xC56224,164
C23×C28Abelian group of type [2,2,2,28]224C2^3xC28224,189
C24×C14Abelian group of type [2,2,2,2,14]224C2^4xC14224,197
C2×C4×C28Abelian group of type [2,4,28]224C2xC4xC28224,149
C4×F8Direct product of C4 and F8287C4xF8224,173
C22×F8Direct product of C22 and F828C2^2xF8224,195
D7×D8Direct product of D7 and D8564+D7xD8224,105
D7×SD16Direct product of D7 and SD16564D7xSD16224,108
D7×M4(2)Direct product of D7 and M4(2)564D7xM4(2)224,101
C7×2+ 1+4Direct product of C7 and 2+ 1+4564C7xES+(2,2)224,193
D7×C16Direct product of C16 and D71122D7xC16224,3
C7×D16Direct product of C7 and D161122C7xD16224,60
C4×D28Direct product of C4 and D28112C4xD28224,68
C2×D56Direct product of C2 and D56112C2xD56224,98
D4×C28Direct product of C28 and D4112D4xC28224,153
C14×D8Direct product of C14 and D8112C14xD8224,167
D7×Q16Direct product of D7 and Q161124-D7xQ16224,112
C7×SD32Direct product of C7 and SD321122C7xSD32224,61
D4×Dic7Direct product of D4 and Dic7112D4xDic7224,129
D7×C42Direct product of C42 and D7112D7xC4^2224,66
D7×C24Direct product of C24 and D7112D7xC2^4224,196
C14×SD16Direct product of C14 and SD16112C14xSD16224,168
C22×D28Direct product of C22 and D28112C2^2xD28224,176
C7×M5(2)Direct product of C7 and M5(2)1122C7xM5(2)224,59
C14×M4(2)Direct product of C14 and M4(2)112C14xM4(2)224,165
C7×2- 1+4Direct product of C7 and 2- 1+41124C7xES-(2,2)224,194
C7×Q32Direct product of C7 and Q322242C7xQ32224,62
Q8×C28Direct product of C28 and Q8224Q8xC28224,154
C14×Q16Direct product of C14 and Q16224C14xQ16224,169
C8×Dic7Direct product of C8 and Dic7224C8xDic7224,19
Q8×Dic7Direct product of Q8 and Dic7224Q8xDic7224,140
C4×Dic14Direct product of C4 and Dic14224C4xDic14224,63
C2×Dic28Direct product of C2 and Dic28224C2xDic28224,100
C23×Dic7Direct product of C23 and Dic7224C2^3xDic7224,187
C22×Dic14Direct product of C22 and Dic14224C2^2xDic14224,174
C2×D4×D7Direct product of C2, D4 and D756C2xD4xD7224,178
C7×C4≀C2Direct product of C7 and C4≀C2562C7xC4wrC2224,53
D7×C4○D4Direct product of D7 and C4○D4564D7xC4oD4224,184
C7×C23⋊C4Direct product of C7 and C23⋊C4564C7xC2^3:C4224,48
C7×C8⋊C22Direct product of C7 and C8⋊C22564C7xC8:C2^2224,171
D7×C22⋊C4Direct product of D7 and C22⋊C456D7xC2^2:C4224,75
C7×C4.D4Direct product of C7 and C4.D4564C7xC4.D4224,49
C7×C22≀C2Direct product of C7 and C22≀C256C7xC2^2wrC2224,155
D7×C2×C8Direct product of C2×C8 and D7112D7xC2xC8224,94
C2×Q8×D7Direct product of C2, Q8 and D7112C2xQ8xD7224,181
D7×C4⋊C4Direct product of D7 and C4⋊C4112D7xC4:C4224,86
D4×C2×C14Direct product of C2×C14 and D4112D4xC2xC14224,190
C4×C7⋊D4Direct product of C4 and C7⋊D4112C4xC7:D4224,123
C2×D4⋊D7Direct product of C2 and D4⋊D7112C2xD4:D7224,126
C7×C8○D4Direct product of C7 and C8○D41122C7xC8oD4224,166
C7×C4○D8Direct product of C7 and C4○D81122C7xC4oD8224,170
C2×C8⋊D7Direct product of C2 and C8⋊D7112C2xC8:D7224,95
C7×C4⋊D4Direct product of C7 and C4⋊D4112C7xC4:D4224,156
C2×Q8⋊D7Direct product of C2 and Q8⋊D7112C2xQ8:D7224,136
C2×C56⋊C2Direct product of C2 and C56⋊C2112C2xC56:C2224,97
D7×C22×C4Direct product of C22×C4 and D7112D7xC2^2xC4224,175
C2×D14⋊C4Direct product of C2 and D14⋊C4112C2xD14:C4224,122
C2×C4○D28Direct product of C2 and C4○D28112C2xC4oD28224,177
C14×C4○D4Direct product of C14 and C4○D4112C14xC4oD4224,192
C7×D4⋊C4Direct product of C7 and D4⋊C4112C7xD4:C4224,51
C7×C8.C4Direct product of C7 and C8.C41122C7xC8.C4224,57
C7×C41D4Direct product of C7 and C41D4112C7xC4:1D4224,162
C7×C22⋊C8Direct product of C7 and C22⋊C8112C7xC2^2:C8224,47
C2×D4.D7Direct product of C2 and D4.D7112C2xD4.D7224,128
C22×C7⋊D4Direct product of C22 and C7⋊D4112C2^2xC7:D4224,188
C7×C22⋊Q8Direct product of C7 and C22⋊Q8112C7xC2^2:Q8224,157
C2×D42D7Direct product of C2 and D42D7112C2xD4:2D7224,179
C14×C22⋊C4Direct product of C14 and C22⋊C4112C14xC2^2:C4224,150
C7×C42⋊C2Direct product of C7 and C42⋊C2112C7xC4^2:C2224,152
C2×Q82D7Direct product of C2 and Q82D7112C2xQ8:2D7224,182
C7×C4.4D4Direct product of C7 and C4.4D4112C7xC4.4D4224,159
C7×C8.C22Direct product of C7 and C8.C221124C7xC8.C2^2224,172
C2×C4.Dic7Direct product of C2 and C4.Dic7112C2xC4.Dic7224,116
C2×C23.D7Direct product of C2 and C23.D7112C2xC2^3.D7224,147
C7×C422C2Direct product of C7 and C422C2112C7xC4^2:2C2224,161
C7×C4.10D4Direct product of C7 and C4.10D41124C7xC4.10D4224,50
C7×C22.D4Direct product of C7 and C22.D4112C7xC2^2.D4224,158
C4×C7⋊C8Direct product of C4 and C7⋊C8224C4xC7:C8224,8
C7×C4⋊C8Direct product of C7 and C4⋊C8224C7xC4:C8224,54
C2×C7⋊C16Direct product of C2 and C7⋊C16224C2xC7:C16224,17
C7×C4⋊Q8Direct product of C7 and C4⋊Q8224C7xC4:Q8224,163
C14×C4⋊C4Direct product of C14 and C4⋊C4224C14xC4:C4224,151
Q8×C2×C14Direct product of C2×C14 and Q8224Q8xC2xC14224,191
C7×C8⋊C4Direct product of C7 and C8⋊C4224C7xC8:C4224,46
C22×C7⋊C8Direct product of C22 and C7⋊C8224C2^2xC7:C8224,115
C2×C4×Dic7Direct product of C2×C4 and Dic7224C2xC4xDic7224,117
C2×C7⋊Q16Direct product of C2 and C7⋊Q16224C2xC7:Q16224,138
C2×C4⋊Dic7Direct product of C2 and C4⋊Dic7224C2xC4:Dic7224,120
C7×Q8⋊C4Direct product of C7 and Q8⋊C4224C7xQ8:C4224,52
C7×C2.D8Direct product of C7 and C2.D8224C7xC2.D8224,56
C7×C4.Q8Direct product of C7 and C4.Q8224C7xC4.Q8224,55
C2×Dic7⋊C4Direct product of C2 and Dic7⋊C4224C2xDic7:C4224,118
C7×C2.C42Direct product of C7 and C2.C42224C7xC2.C4^2224,44
C7×C42.C2Direct product of C7 and C42.C2224C7xC4^2.C2224,160

Groups of order 225

dρLabelID
C225Cyclic group2251C225225,1
C52⋊C9The semidirect product of C52 and C9 acting via C9/C3=C3453C5^2:C9225,3
C152Abelian group of type [15,15]225C15^2225,6
C3×C75Abelian group of type [3,75]225C3xC75225,2
C5×C45Abelian group of type [5,45]225C5xC45225,4
C3×C52⋊C3Direct product of C3 and C52⋊C3453C3xC5^2:C3225,5

Groups of order 226

dρLabelID
C226Cyclic group2261C226226,2
D113Dihedral group1132+D113226,1

Groups of order 227

dρLabelID
C227Cyclic group2271C227227,1

Groups of order 228

dρLabelID
C228Cyclic group2281C228228,6
D114Dihedral group; = C2×D571142+D114228,14
Dic57Dicyclic group; = C571C42282-Dic57228,5
C19⋊A4The semidirect product of C19 and A4 acting via A4/C22=C3763C19:A4228,11
C19⋊C12The semidirect product of C19 and C12 acting via C12/C2=C6766-C19:C12228,1
C2×C114Abelian group of type [2,114]228C2xC114228,15
S3×D19Direct product of S3 and D19574+S3xD19228,8
A4×C19Direct product of C19 and A4763A4xC19228,10
S3×C38Direct product of C38 and S31142S3xC38228,13
C6×D19Direct product of C6 and D191142C6xD19228,12
Dic3×C19Direct product of C19 and Dic32282Dic3xC19228,3
C3×Dic19Direct product of C3 and Dic192282C3xDic19228,4
C2×C19⋊C6Direct product of C2 and C19⋊C6386+C2xC19:C6228,7
C4×C19⋊C3Direct product of C4 and C19⋊C3763C4xC19:C3228,2
C22×C19⋊C3Direct product of C22 and C19⋊C376C2^2xC19:C3228,9

Groups of order 229

dρLabelID
C229Cyclic group2291C229229,1

Groups of order 230

dρLabelID
C230Cyclic group2301C230230,4
D115Dihedral group1152+D115230,3
D5×C23Direct product of C23 and D51152D5xC23230,1
C5×D23Direct product of C5 and D231152C5xD23230,2

Groups of order 231

dρLabelID
C231Cyclic group2311C231231,2
C11×C7⋊C3Direct product of C11 and C7⋊C3773C11xC7:C3231,1

Groups of order 232

dρLabelID
C232Cyclic group2321C232232,2
D116Dihedral group1162+D116232,6
Dic58Dicyclic group; = C29Q82322-Dic58232,4
C29⋊D4The semidirect product of C29 and D4 acting via D4/C22=C21162C29:D4232,8
C29⋊C8The semidirect product of C29 and C8 acting via C8/C2=C42324-C29:C8232,3
C292C8The semidirect product of C29 and C8 acting via C8/C4=C22322C29:2C8232,1
C2×C116Abelian group of type [2,116]232C2xC116232,9
C22×C58Abelian group of type [2,2,58]232C2^2xC58232,14
C4×D29Direct product of C4 and D291162C4xD29232,5
D4×C29Direct product of C29 and D41162D4xC29232,10
C22×D29Direct product of C22 and D29116C2^2xD29232,13
Q8×C29Direct product of C29 and Q82322Q8xC29232,11
C2×Dic29Direct product of C2 and Dic29232C2xDic29232,7
C2×C29⋊C4Direct product of C2 and C29⋊C4584+C2xC29:C4232,12

Groups of order 233

dρLabelID
C233Cyclic group2331C233233,1

Groups of order 234

dρLabelID
C234Cyclic group2341C234234,6
D117Dihedral group1172+D117234,5
D39⋊C3The semidirect product of D39 and C3 acting faithfully396+D39:C3234,9
C13⋊C18The semidirect product of C13 and C18 acting via C18/C3=C61176C13:C18234,1
C3⋊D39The semidirect product of C3 and D39 acting via D39/C39=C2117C3:D39234,15
C3×C78Abelian group of type [3,78]234C3xC78234,16
S3×C39Direct product of C39 and S3782S3xC39234,12
C3×D39Direct product of C3 and D39782C3xD39234,13
C13×D9Direct product of C13 and D91172C13xD9234,3
C9×D13Direct product of C9 and D131172C9xD13234,4
C32×D13Direct product of C32 and D13117C3^2xD13234,11
C3×C13⋊C6Direct product of C3 and C13⋊C6396C3xC13:C6234,7
S3×C13⋊C3Direct product of S3 and C13⋊C3396S3xC13:C3234,8
C6×C13⋊C3Direct product of C6 and C13⋊C3783C6xC13:C3234,10
C13×C3⋊S3Direct product of C13 and C3⋊S3117C13xC3:S3234,14
C2×C13⋊C9Direct product of C2 and C13⋊C92343C2xC13:C9234,2

Groups of order 235

dρLabelID
C235Cyclic group2351C235235,1

Groups of order 236

dρLabelID
C236Cyclic group2361C236236,2
D118Dihedral group; = C2×D591182+D118236,3
Dic59Dicyclic group; = C59C42362-Dic59236,1
C2×C118Abelian group of type [2,118]236C2xC118236,4

Groups of order 237

dρLabelID
C237Cyclic group2371C237237,2
C79⋊C3The semidirect product of C79 and C3 acting faithfully793C79:C3237,1

Groups of order 238

dρLabelID
C238Cyclic group2381C238238,4
D119Dihedral group1192+D119238,3
D7×C17Direct product of C17 and D71192D7xC17238,1
C7×D17Direct product of C7 and D171192C7xD17238,2

Groups of order 239

dρLabelID
C239Cyclic group2391C239239,1

Groups of order 240

dρLabelID
C240Cyclic group2401C240240,4
D120Dihedral group1202+D120240,68
F16Frobenius group; = C24C15 = AGL1(𝔽16)1615+F16240,191
Dic60Dicyclic group; = C154Q162402-Dic60240,69
CSU2(𝔽5)Conformal special unitary group on 𝔽52; = C2.2S5484-CSU(2,5)240,89
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2124A5:C4240,91
A4⋊F5The semidirect product of A4 and F5 acting via F5/D5=C22012+A4:F5240,192
Q8⋊D15The semidirect product of Q8 and D15 acting via D15/C5=S3404+Q8:D15240,106
D6⋊F5The semidirect product of D6 and F5 acting via F5/D5=C2608+D6:F5240,96
C60⋊C41st semidirect product of C60 and C4 acting faithfully604C60:C4240,121
C20⋊D62nd semidirect product of C20 and D6 acting via D6/C3=C22604C20:D6240,138
Dic3⋊F5The semidirect product of Dic3 and F5 acting via F5/D5=C2608-Dic3:F5240,97
A4⋊Dic5The semidirect product of A4 and Dic5 acting via Dic5/C10=C2606-A4:Dic5240,107
D10⋊D64th semidirect product of D10 and D6 acting via D6/S3=C2604+D10:D6240,151
D4⋊D15The semidirect product of D4 and D15 acting via D15/C15=C21204+D4:D15240,76
D15⋊C8The semidirect product of D15 and C8 acting via C8/C2=C41208+D15:C8240,99
C15⋊D81st semidirect product of C15 and D8 acting via D8/C4=C221204C15:D8240,13
C3⋊D40The semidirect product of C3 and D40 acting via D40/D20=C21204+C3:D40240,14
C5⋊D24The semidirect product of C5 and D24 acting via D24/D12=C21204+C5:D24240,15
D15⋊Q8The semidirect product of D15 and Q8 acting via Q8/C4=C21204D15:Q8240,131
C40⋊S34th semidirect product of C40 and S3 acting via S3/C3=C21202C40:S3240,66
C24⋊D52nd semidirect product of C24 and D5 acting via D5/C5=C21202C24:D5240,67
D6⋊Dic5The semidirect product of D6 and Dic5 acting via Dic5/C10=C2120D6:Dic5240,27
D152C8The semidirect product of D15 and C8 acting via C8/C4=C21204D15:2C8240,9
D304C42nd semidirect product of D30 and C4 acting via C4/C2=C2120D30:4C4240,28
D303C41st semidirect product of D30 and C4 acting via C4/C2=C2120D30:3C4240,75
D205S3The semidirect product of D20 and S3 acting through Inn(D20)1204-D20:5S3240,126
D20⋊S33rd semidirect product of D20 and S3 acting via S3/C3=C21204D20:S3240,127
D12⋊D53rd semidirect product of D12 and D5 acting via D5/C5=C21204D12:D5240,129
D60⋊C26th semidirect product of D60 and C2 acting faithfully1204+D60:C2240,130
D125D5The semidirect product of D12 and D5 acting through Inn(D12)1204-D12:5D5240,133
D42D15The semidirect product of D4 and D15 acting through Inn(D4)1204-D4:2D15240,180
Q82D15The semidirect product of Q8 and D15 acting via D15/C15=C21204+Q8:2D15240,78
Q83D15The semidirect product of Q8 and D15 acting through Inn(Q8)1204+Q8:3D15240,182
C15⋊SD164th semidirect product of C15 and SD16 acting via SD16/C4=C221204+C15:SD16240,19
D6011C2The semidirect product of D60 and C2 acting through Inn(D60)1202D60:11C2240,178
Dic6⋊D51st semidirect product of Dic6 and D5 acting via D5/C5=C21204+Dic6:D5240,21
C158M4(2)1st semidirect product of C15 and M4(2) acting via M4(2)/C22=C41204C15:8M4(2)240,123
D10⋊Dic31st semidirect product of D10 and Dic3 acting via Dic3/C6=C2120D10:Dic3240,26
C605C41st semidirect product of C60 and C4 acting via C4/C2=C2240C60:5C4240,74
C153C161st semidirect product of C15 and C16 acting via C16/C8=C22402C15:3C16240,3
C15⋊C161st semidirect product of C15 and C16 acting via C16/C4=C42404C15:C16240,6
C15⋊Q161st semidirect product of C15 and Q16 acting via Q16/C4=C222404C15:Q16240,22
C157Q161st semidirect product of C15 and Q16 acting via Q16/Q8=C22404-C15:7Q16240,79
C3⋊Dic20The semidirect product of C3 and Dic20 acting via Dic20/Dic10=C22404-C3:Dic20240,23
C5⋊Dic12The semidirect product of C5 and Dic12 acting via Dic12/Dic6=C22404-C5:Dic12240,24
Dic155C43rd semidirect product of Dic15 and C4 acting via C4/C2=C2240Dic15:5C4240,30
C4.A5The central extension by C4 of A5242C4.A5240,93
C2.S52nd central stem extension by C2 of S5404-C2.S5240,90
D10.D66th non-split extension by D10 of D6 acting via D6/C6=C2604D10.D6240,124
Q8.D15The non-split extension by Q8 of D15 acting via D15/C5=S3804-Q8.D15240,105
Dic5.A4The non-split extension by Dic5 of A4 acting through Inn(Dic5)804+Dic5.A4240,108
D6.F5The non-split extension by D6 of F5 acting via F5/D5=C21208-D6.F5240,100
D4.D15The non-split extension by D4 of D15 acting via D15/C15=C21204-D4.D15240,77
C60.7C41st non-split extension by C60 of C4 acting via C4/C2=C21202C60.7C4240,71
C60.C43rd non-split extension by C60 of C4 acting faithfully1204C60.C4240,118
C30.D44th non-split extension by C30 of D4 acting via D4/C2=C221204C30.D4240,16
C20.D64th non-split extension by C20 of D6 acting via D6/C3=C221204C20.D6240,17
C6.D202nd non-split extension by C6 of D20 acting via D20/D10=C21204-C6.D20240,18
D6.Dic5The non-split extension by D6 of Dic5 acting via Dic5/C10=C21204D6.Dic5240,11
Dic3.F5The non-split extension by Dic3 of F5 acting via F5/D5=C21208+Dic3.F5240,101
C12.F51st non-split extension by C12 of F5 acting via F5/D5=C21204C12.F5240,119
D30.5C43rd non-split extension by D30 of C4 acting via C4/C2=C21204D30.5C4240,12
D12.D51st non-split extension by D12 of D5 acting via D5/C5=C21204-D12.D5240,20
D6.D103rd non-split extension by D6 of D10 acting via D10/C10=C21204D6.D10240,132
C20.32D611st non-split extension by C20 of D6 acting via D6/S3=C21204C20.32D6240,10
C30.38D47th non-split extension by C30 of D4 acting via D4/C22=C2120C30.38D4240,80
C12.28D107th non-split extension by C12 of D10 acting via D10/D5=C21204+C12.28D10240,134
Dic5.D65th non-split extension by Dic5 of D6 acting via D6/S3=C21204Dic5.D6240,140
C30.C2317th non-split extension by C30 of C23 acting via C23/C2=C221204-C30.C2^3240,141
Dic3.D106th non-split extension by Dic3 of D10 acting via D10/D5=C21204Dic3.D10240,143
C30.Q81st non-split extension by C30 of Q8 acting via Q8/C2=C22240C30.Q8240,29
C30.4Q81st non-split extension by C30 of Q8 acting via Q8/C4=C2240C30.4Q8240,73
C6.Dic103rd non-split extension by C6 of Dic10 acting via Dic10/Dic5=C2240C6.Dic10240,31
C4×C60Abelian group of type [4,60]240C4xC60240,81
C2×C120Abelian group of type [2,120]240C2xC120240,84
C22×C60Abelian group of type [2,2,60]240C2^2xC60240,185
C23×C30Abelian group of type [2,2,2,30]240C2^3xC30240,208
C2×S5Direct product of C2 and S5; = O3(𝔽5)104+C2xS5240,189
C4×A5Direct product of C4 and A5203C4xA5240,92
D5×S4Direct product of D5 and S4206+D5xS4240,194
A4×F5Direct product of A4 and F52012+A4xF5240,193
C22×A5Direct product of C22 and A520C2^2xA5240,190
C10×S4Direct product of C10 and S4303C10xS4240,196
C5×GL2(𝔽3)Direct product of C5 and GL2(𝔽3)402C5xGL(2,3)240,103
D5×SL2(𝔽3)Direct product of D5 and SL2(𝔽3)404-D5xSL(2,3)240,109
C2×SL2(𝔽5)Direct product of C2 and SL2(𝔽5)48C2xSL(2,5)240,94
A4×C20Direct product of C20 and A4603A4xC20240,152
D5×D12Direct product of D5 and D12604+D5xD12240,136
S3×D20Direct product of S3 and D20604+S3xD20240,137
D4×D15Direct product of D4 and D15604+D4xD15240,179
C12×F5Direct product of C12 and F5604C12xF5240,113
Dic3×F5Direct product of Dic3 and F5608-Dic3xF5240,95
A4×Dic5Direct product of A4 and Dic5606-A4xDic5240,110
C5×CSU2(𝔽3)Direct product of C5 and CSU2(𝔽3)802C5xCSU(2,3)240,102
C10×SL2(𝔽3)Direct product of C10 and SL2(𝔽3)80C10xSL(2,3)240,153
S3×C40Direct product of C40 and S31202S3xC40240,49
D5×C24Direct product of C24 and D51202D5xC24240,33
C3×D40Direct product of C3 and D401202C3xD40240,36
C5×D24Direct product of C5 and D241202C5xD24240,52
C8×D15Direct product of C8 and D151202C8xD15240,65
C15×D8Direct product of C15 and D81202C15xD8240,86
C6×D20Direct product of C6 and D20120C6xD20240,157
C2×D60Direct product of C2 and D60120C2xD60240,177
D4×C30Direct product of C30 and D4120D4xC30240,186
Q8×D15Direct product of Q8 and D151204-Q8xD15240,181
C10×D12Direct product of C10 and D12120C10xD12240,167
D5×Dic6Direct product of D5 and Dic61204-D5xDic6240,125
C15×SD16Direct product of C15 and SD161202C15xSD16240,87
S3×Dic10Direct product of S3 and Dic101204-S3xDic10240,128
C23×D15Direct product of C23 and D15120C2^3xD15240,207
C15×M4(2)Direct product of C15 and M4(2)1202C15xM4(2)240,85
Q8×C30Direct product of C30 and Q8240Q8xC30240,187
C15×Q16Direct product of C15 and Q162402C15xQ16240,88
C3×Dic20Direct product of C3 and Dic202402C3xDic20240,37
C12×Dic5Direct product of C12 and Dic5240C12xDic5240,40
C5×Dic12Direct product of C5 and Dic122402C5xDic12240,53
Dic3×C20Direct product of C20 and Dic3240Dic3xC20240,56
C4×Dic15Direct product of C4 and Dic15240C4xDic15240,72
C6×Dic10Direct product of C6 and Dic10240C6xDic10240,155
C10×Dic6Direct product of C10 and Dic6240C10xDic6240,165
C2×Dic30Direct product of C2 and Dic30240C2xDic30240,175
Dic3×Dic5Direct product of Dic3 and Dic5240Dic3xDic5240,25
C22×Dic15Direct product of C22 and Dic15240C2^2xDic15240,183
C2×C5⋊S4Direct product of C2 and C5⋊S4306+C2xC5:S4240,197
C2×D5×A4Direct product of C2, D5 and A4306+C2xD5xA4240,198
C2×S3×F5Direct product of C2, S3 and F5; = Aut(D30) = Hol(C30)308+C2xS3xF5240,195
C3×C24⋊C5Direct product of C3 and C24⋊C5305C3xC2^4:C5240,199
C4×S3×D5Direct product of C4, S3 and D5604C4xS3xD5240,135
C3×D4×D5Direct product of C3, D4 and D5604C3xD4xD5240,159
C5×S3×D4Direct product of C5, S3 and D4604C5xS3xD4240,169
C4×C3⋊F5Direct product of C4 and C3⋊F5604C4xC3:F5240,120
C2×C6×F5Direct product of C2×C6 and F560C2xC6xF5240,200
A4×C2×C10Direct product of C2×C10 and A460A4xC2xC10240,203
D5×C3⋊D4Direct product of D5 and C3⋊D4604D5xC3:D4240,149
S3×C5⋊D4Direct product of S3 and C5⋊D4604S3xC5:D4240,150
C3×C4⋊F5Direct product of C3 and C4⋊F5604C3xC4:F5240,114
C5×A4⋊C4Direct product of C5 and A4⋊C4603C5xA4:C4240,104
C5×C42⋊C3Direct product of C5 and C42⋊C3603C5xC4^2:C3240,32
C22×S3×D5Direct product of C22, S3 and D560C2^2xS3xD5240,202
C22×C3⋊F5Direct product of C22 and C3⋊F560C2^2xC3:F5240,201
C5×C22⋊A4Direct product of C5 and C22⋊A460C5xC2^2:A4240,204
C3×C22⋊F5Direct product of C3 and C22⋊F5604C3xC2^2:F5240,117
C5×C4.A4Direct product of C5 and C4.A4802C5xC4.A4240,154
S3×C5⋊C8Direct product of S3 and C5⋊C81208-S3xC5:C8240,98
D5×C3⋊C8Direct product of D5 and C3⋊C81204D5xC3:C8240,7
C3×Q8×D5Direct product of C3, Q8 and D51204C3xQ8xD5240,161
C5×S3×Q8Direct product of C5, S3 and Q81204C5xS3xQ8240,171
S3×C2×C20Direct product of C2×C20 and S3120S3xC2xC20240,166
D5×C2×C12Direct product of C2×C12 and D5120D5xC2xC12240,156
C2×C4×D15Direct product of C2×C4 and D15120C2xC4xD15240,176
C6×C5⋊D4Direct product of C6 and C5⋊D4120C6xC5:D4240,164
C5×C8⋊S3Direct product of C5 and C8⋊S31202C5xC8:S3240,50
S3×C52C8Direct product of S3 and C52C81204S3xC5:2C8240,8
C3×D4⋊D5Direct product of C3 and D4⋊D51204C3xD4:D5240,44
C5×D6⋊C4Direct product of C5 and D6⋊C4120C5xD6:C4240,59
C5×D4⋊S3Direct product of C5 and D4⋊S31204C5xD4:S3240,60
C3×D5⋊C8Direct product of C3 and D5⋊C81204C3xD5:C8240,111
C3×C8⋊D5Direct product of C3 and C8⋊D51202C3xC8:D5240,34
C2×C15⋊D4Direct product of C2 and C15⋊D4120C2xC15:D4240,145
C2×C3⋊D20Direct product of C2 and C3⋊D20120C2xC3:D20240,146
C2×C5⋊D12Direct product of C2 and C5⋊D12120C2xC5:D12240,147
C10×C3⋊D4Direct product of C10 and C3⋊D4120C10xC3:D4240,174
C3×Q8⋊D5Direct product of C3 and Q8⋊D51204C3xQ8:D5240,46
C2×D5×Dic3Direct product of C2, D5 and Dic3120C2xD5xDic3240,139
C2×S3×Dic5Direct product of C2, S3 and Dic5120C2xS3xDic5240,142
C3×C40⋊C2Direct product of C3 and C40⋊C21202C3xC40:C2240,35
C5×C24⋊C2Direct product of C5 and C24⋊C21202C5xC24:C2240,51
D5×C22×C6Direct product of C22×C6 and D5120D5xC2^2xC6240,205
C3×C4.F5Direct product of C3 and C4.F51204C3xC4.F5240,112
C3×C4○D20Direct product of C3 and C4○D201202C3xC4oD20240,158
C5×C4○D12Direct product of C5 and C4○D121202C5xC4oD12240,168
C15×C4○D4Direct product of C15 and C4○D41202C15xC4oD4240,188
C2×C157D4Direct product of C2 and C157D4120C2xC15:7D4240,184
C3×D4.D5Direct product of C3 and D4.D51204C3xD4.D5240,45
C5×D4.S3Direct product of C5 and D4.S31204C5xD4.S3240,61
S3×C22×C10Direct product of C22×C10 and S3120S3xC2^2xC10240,206
C5×C6.D4Direct product of C5 and C6.D4120C5xC6.D4240,64
C3×D10⋊C4Direct product of C3 and D10⋊C4120C3xD10:C4240,43
C3×D42D5Direct product of C3 and D42D51204C3xD4:2D5240,160
C5×D42S3Direct product of C5 and D42S31204C5xD4:2S3240,170
C15×C22⋊C4Direct product of C15 and C22⋊C4120C15xC2^2:C4240,82
C2×D30.C2Direct product of C2 and D30.C2120C2xD30.C2240,144
C5×Q82S3Direct product of C5 and Q82S31204C5xQ8:2S3240,62
C3×Q82D5Direct product of C3 and Q82D51204C3xQ8:2D5240,162
C5×Q83S3Direct product of C5 and Q83S31204C5xQ8:3S3240,172
C3×C4.Dic5Direct product of C3 and C4.Dic51202C3xC4.Dic5240,39
C5×C4.Dic3Direct product of C5 and C4.Dic31202C5xC4.Dic3240,55
C3×C23.D5Direct product of C3 and C23.D5120C3xC2^3.D5240,48
C3×C22.F5Direct product of C3 and C22.F51204C3xC2^2.F5240,116
C6×C5⋊C8Direct product of C6 and C5⋊C8240C6xC5:C8240,115
C5×C3⋊C16Direct product of C5 and C3⋊C162402C5xC3:C16240,1
C3×C5⋊C16Direct product of C3 and C5⋊C162404C3xC5:C16240,5
C10×C3⋊C8Direct product of C10 and C3⋊C8240C10xC3:C8240,54
C15×C4⋊C4Direct product of C15 and C4⋊C4240C15xC4:C4240,83
C2×C15⋊Q8Direct product of C2 and C15⋊Q8240C2xC15:Q8240,148
C6×C52C8Direct product of C6 and C52C8240C6xC5:2C8240,38
C2×C15⋊C8Direct product of C2 and C15⋊C8240C2xC15:C8240,122
C2×C6×Dic5Direct product of C2×C6 and Dic5240C2xC6xDic5240,163
C3×C5⋊Q16Direct product of C3 and C5⋊Q162404C3xC5:Q16240,47
C5×C3⋊Q16Direct product of C5 and C3⋊Q162404C5xC3:Q16240,63
C3×C52C16Direct product of C3 and C52C162402C3xC5:2C16240,2
C2×C153C8Direct product of C2 and C153C8240C2xC15:3C8240,70
C3×C4⋊Dic5Direct product of C3 and C4⋊Dic5240C3xC4:Dic5240,42
C5×C4⋊Dic3Direct product of C5 and C4⋊Dic3240C5xC4:Dic3240,58
Dic3×C2×C10Direct product of C2×C10 and Dic3240Dic3xC2xC10240,173
C5×Dic3⋊C4Direct product of C5 and Dic3⋊C4240C5xDic3:C4240,57
C3×C10.D4Direct product of C3 and C10.D4240C3xC10.D4240,41

Groups of order 241

dρLabelID
C241Cyclic group2411C241241,1

Groups of order 242

dρLabelID
C242Cyclic group2421C242242,2
D121Dihedral group1212+D121242,1
C11⋊D11The semidirect product of C11 and D11 acting via D11/C11=C2121C11:D11242,4
C11×C22Abelian group of type [11,22]242C11xC22242,5
C11×D11Direct product of C11 and D11; = AΣL1(𝔽121)222C11xD11242,3

Groups of order 243

dρLabelID
C243Cyclic group2431C243243,1
3+ 1+4Extraspecial group; = He3He3279ES+(3,2)243,65
3- 1+4Extraspecial group; = He33- 1+2279ES-(3,2)243,66
C27○He3Central product of C27 and He3813C27oHe3243,50
C27⋊C9The semidirect product of C27 and C9 acting faithfully279C27:C9243,22
C32⋊He3The semidirect product of C32 and He3 acting via He3/C32=C327C3^2:He3243,37
C33⋊C91st semidirect product of C33 and C9 acting via C9/C3=C327C3^3:C9243,13
C92⋊C31st semidirect product of C92 and C3 acting faithfully273C9^2:C3243,25
C922C32nd semidirect product of C92 and C3 acting faithfully273C9^2:2C3243,26
He3⋊C323rd semidirect product of He3 and C32 acting via C32/C3=C3279He3:C3^2243,58
C33⋊C322nd semidirect product of C33 and C32 acting faithfully279C3^3:C3^2243,56
C81⋊C3The semidirect product of C81 and C3 acting faithfully813C81:C3243,24
C9⋊He3The semidirect product of C9 and He3 acting via He3/C32=C381C9:He3243,39
He3⋊C9The semidirect product of He3 and C9 acting via C9/C3=C381He3:C9243,17
C32⋊C27The semidirect product of C32 and C27 acting via C27/C9=C381C3^2:C27243,12
C923C33rd semidirect product of C92 and C3 acting faithfully81C9^2:3C3243,34
C927C37th semidirect product of C92 and C3 acting faithfully81C9^2:7C3243,43
C924C34th semidirect product of C92 and C3 acting faithfully81C9^2:4C3243,44
C925C35th semidirect product of C92 and C3 acting faithfully81C9^2:5C3243,45
C928C38th semidirect product of C92 and C3 acting faithfully81C9^2:8C3243,46
C929C39th semidirect product of C92 and C3 acting faithfully81C9^2:9C3243,47
3- 1+2⋊C9The semidirect product of 3- 1+2 and C9 acting via C9/C3=C381ES-(3,1):C9243,18
C9⋊3- 1+2The semidirect product of C9 and 3- 1+2 acting via 3- 1+2/C32=C381C9:ES-(3,1)243,41
C9⋊C27The semidirect product of C9 and C27 acting via C27/C9=C3243C9:C27243,21
C272C9The semidirect product of C27 and C9 acting via C9/C3=C3243C27:2C9243,11
C9.4He32nd central extension by C9 of He3273C9.4He3243,16
C9.He31st non-split extension by C9 of He3 acting via He3/C32=C3273C9.He3243,55
C9.2He32nd non-split extension by C9 of He3 acting via He3/C32=C3279C9.2He3243,60
C92.C32nd non-split extension by C92 of C3 acting faithfully273C9^2.C3243,27
C34.C33rd non-split extension by C34 of C3 acting faithfully27C3^4.C3243,38
C32.He34th non-split extension by C32 of He3 acting via He3/C32=C3279C3^2.He3243,28
C32.5He35th non-split extension by C32 of He3 acting via He3/C32=C3279C3^2.5He3243,29
C32.6He36th non-split extension by C32 of He3 acting via He3/C32=C3279C3^2.6He3243,30
He3.C324th non-split extension by He3 of C32 acting via C32/C3=C3279He3.C3^2243,57
C32.C339th non-split extension by C32 of C33 acting via C33/C32=C3279C3^2.C3^3243,59
C9.5He33rd central extension by C9 of He3813C9.5He3243,19
C9.6He34th central extension by C9 of He3813C9.6He3243,20
C32.24He31st central stem extension by C32 of He381C3^2.24He3243,3
C33.C322nd non-split extension by C33 of C32 acting faithfully81C3^3.C3^2243,4
C33.3C323rd non-split extension by C33 of C32 acting faithfully81C3^3.3C3^2243,5
C32.27He34th central stem extension by C32 of He381C3^2.27He3243,6
C32.28He35th central stem extension by C32 of He381C3^2.28He3243,7
C32.29He36th central stem extension by C32 of He381C3^2.29He3243,8
C33.7C327th non-split extension by C33 of C32 acting faithfully81C3^3.7C3^2243,9
C32.19He33rd central extension by C32 of He381C3^2.19He3243,14
C32.20He34th central extension by C32 of He381C3^2.20He3243,15
C32.23C334th central stem extension by C32 of C3381C3^2.23C3^3243,40
C33.31C3214th non-split extension by C33 of C32 acting via C32/C3=C381C3^3.31C3^2243,42
C3.C921st central stem extension by C3 of C92243C3.C9^2243,2
C35Elementary abelian group of type [3,3,3,3,3]243C3^5243,67
C9×C27Abelian group of type [9,27]243C9xC27243,10
C3×C81Abelian group of type [3,81]243C3xC81243,23
C3×C92Abelian group of type [3,9,9]243C3xC9^2243,31
C33×C9Abelian group of type [3,3,3,9]243C3^3xC9243,61
C32×C27Abelian group of type [3,3,27]243C3^2xC27243,48
C9×He3Direct product of C9 and He381C9xHe3243,35
C32×He3Direct product of C32 and He381C3^2xHe3243,62
C9×3- 1+2Direct product of C9 and 3- 1+281C9xES-(3,1)243,36
C32×3- 1+2Direct product of C32 and 3- 1+281C3^2xES-(3,1)243,63
C3×C3≀C3Direct product of C3 and C3≀C327C3xC3wrC3243,51
C3×C27⋊C3Direct product of C3 and C27⋊C381C3xC27:C3243,49
C3×C32⋊C9Direct product of C3 and C32⋊C981C3xC3^2:C9243,32
C3×C9○He3Direct product of C3 and C9○He381C3xC9oHe3243,64
C3×He3⋊C3Direct product of C3 and He3⋊C381C3xHe3:C3243,53
C3×He3.C3Direct product of C3 and He3.C381C3xHe3.C3243,52
C3×C3.He3Direct product of C3 and C3.He381C3xC3.He3243,54
C3×C9⋊C9Direct product of C3 and C9⋊C9243C3xC9:C9243,33

Groups of order 244

dρLabelID
C244Cyclic group2441C244244,2
D122Dihedral group; = C2×D611222+D122244,4
Dic61Dicyclic group; = C612C42442-Dic61244,1
C61⋊C4The semidirect product of C61 and C4 acting faithfully614+C61:C4244,3
C2×C122Abelian group of type [2,122]244C2xC122244,5

Groups of order 245

dρLabelID
C245Cyclic group2451C245245,1
C7×C35Abelian group of type [7,35]245C7xC35245,2

Groups of order 246

dρLabelID
C246Cyclic group2461C246246,4
D123Dihedral group1232+D123246,3
S3×C41Direct product of C41 and S31232S3xC41246,1
C3×D41Direct product of C3 and D411232C3xD41246,2

Groups of order 247

dρLabelID
C247Cyclic group2471C247247,1

Groups of order 248

dρLabelID
C248Cyclic group2481C248248,2
D124Dihedral group1242+D124248,5
Dic62Dicyclic group; = C31Q82482-Dic62248,3
C31⋊D4The semidirect product of C31 and D4 acting via D4/C22=C21242C31:D4248,7
C31⋊C8The semidirect product of C31 and C8 acting via C8/C4=C22482C31:C8248,1
C2×C124Abelian group of type [2,124]248C2xC124248,8
C22×C62Abelian group of type [2,2,62]248C2^2xC62248,12
C4×D31Direct product of C4 and D311242C4xD31248,4
D4×C31Direct product of C31 and D41242D4xC31248,9
C22×D31Direct product of C22 and D31124C2^2xD31248,11
Q8×C31Direct product of C31 and Q82482Q8xC31248,10
C2×Dic31Direct product of C2 and Dic31248C2xDic31248,6

Groups of order 249

dρLabelID
C249Cyclic group2491C249249,1

Groups of order 250

dρLabelID
C250Cyclic group2501C250250,2
D125Dihedral group1252+D125250,1
C25⋊C10The semidirect product of C25 and C10 acting faithfully2510+C25:C10250,6
C52⋊C10The semidirect product of C52 and C10 acting faithfully2510+C5^2:C10250,5
He5⋊C22nd semidirect product of He5 and C2 acting faithfully255He5:C2250,8
C25⋊D5The semidirect product of C25 and D5 acting via D5/C5=C2125C25:D5250,7
C53⋊C23rd semidirect product of C53 and C2 acting faithfully125C5^3:C2250,14
C5×C50Abelian group of type [5,50]250C5xC50250,9
C52×C10Abelian group of type [5,5,10]250C5^2xC10250,15
C5×D25Direct product of C5 and D25502C5xD25250,3
D5×C25Direct product of C25 and D5502D5xC25250,4
C2×He5Direct product of C2 and He5505C2xHe5250,10
D5×C52Direct product of C52 and D550D5xC5^2250,12
C2×5- 1+2Direct product of C2 and 5- 1+2505C2xES-(5,1)250,11
C5×C5⋊D5Direct product of C5 and C5⋊D550C5xC5:D5250,13

Groups of order 251

dρLabelID
C251Cyclic group2511C251251,1

Groups of order 252

dρLabelID
C252Cyclic group2521C252252,6
D126Dihedral group; = C2×D631262+D126252,14
Dic63Dicyclic group; = C9Dic72522-Dic63252,5
D21⋊S3The semidirect product of D21 and S3 acting via S3/C3=C2424D21:S3252,37
C32⋊Dic7The semidirect product of C32 and Dic7 acting via Dic7/C7=C4424C3^2:Dic7252,32
C7⋊C36The semidirect product of C7 and C36 acting via C36/C6=C62526C7:C36252,1
C3⋊Dic21The semidirect product of C3 and Dic21 acting via Dic21/C42=C2252C3:Dic21252,24
C6.F7The non-split extension by C6 of F7 acting via F7/C7⋊C3=C2846-C6.F7252,18
C21.A4The non-split extension by C21 of A4 acting via A4/C22=C31263C21.A4252,11
C3×C84Abelian group of type [3,84]252C3xC84252,25
C6×C42Abelian group of type [6,42]252C6xC42252,46
C2×C126Abelian group of type [2,126]252C2xC126252,15
S3×F7Direct product of S3 and F7; = Aut(D21) = Hol(C21)2112+S3xF7252,26
C6×F7Direct product of C6 and F7426C6xF7252,28
S3×D21Direct product of S3 and D21424+S3xD21252,36
D7×D9Direct product of D7 and D9634+D7xD9252,8
S3×C42Direct product of C42 and S3842S3xC42252,42
A4×C21Direct product of C21 and A4843A4xC21252,39
C6×D21Direct product of C6 and D21842C6xD21252,43
Dic3×C21Direct product of C21 and Dic3842Dic3xC21252,21
C3×Dic21Direct product of C3 and Dic21842C3xDic21252,22
D7×C18Direct product of C18 and D71262D7xC18252,12
C14×D9Direct product of C14 and D91262C14xD9252,13
C7×Dic9Direct product of C7 and Dic92522C7xDic9252,3
C9×Dic7Direct product of C9 and Dic72522C9xDic7252,4
C32×Dic7Direct product of C32 and Dic7252C3^2xDic7252,20
A4×C7⋊C3Direct product of A4 and C7⋊C3289A4xC7:C3252,27
S32×C7Direct product of C7, S3 and S3424S3^2xC7252,35
C3×S3×D7Direct product of C3, S3 and D7424C3xS3xD7252,33
C2×C3⋊F7Direct product of C2 and C3⋊F7426+C2xC3:F7252,30
C7×C32⋊C4Direct product of C7 and C32⋊C4424C7xC3^2:C4252,31
D7×C3⋊S3Direct product of D7 and C3⋊S363D7xC3:S3252,34
C3×C7⋊A4Direct product of C3 and C7⋊A4843C3xC7:A4252,40
C3×C7⋊C12Direct product of C3 and C7⋊C12846C3xC7:C12252,16
C12×C7⋊C3Direct product of C12 and C7⋊C3843C12xC7:C3252,19
Dic3×C7⋊C3Direct product of Dic3 and C7⋊C3846Dic3xC7:C3252,17
D7×C3×C6Direct product of C3×C6 and D7126D7xC3xC6252,41
C2×C7⋊C18Direct product of C2 and C7⋊C181266C2xC7:C18252,7
C14×C3⋊S3Direct product of C14 and C3⋊S3126C14xC3:S3252,44
C2×C3⋊D21Direct product of C2 and C3⋊D21126C2xC3:D21252,45
C7×C3.A4Direct product of C7 and C3.A41263C7xC3.A4252,10
C4×C7⋊C9Direct product of C4 and C7⋊C92523C4xC7:C9252,2
C22×C7⋊C9Direct product of C22 and C7⋊C9252C2^2xC7:C9252,9
C7×C3⋊Dic3Direct product of C7 and C3⋊Dic3252C7xC3:Dic3252,23
C2×S3×C7⋊C3Direct product of C2, S3 and C7⋊C3426C2xS3xC7:C3252,29
C2×C6×C7⋊C3Direct product of C2×C6 and C7⋊C384C2xC6xC7:C3252,38

Groups of order 253

dρLabelID
C253Cyclic group2531C253253,2
C23⋊C11The semidirect product of C23 and C11 acting faithfully2311C23:C11253,1

Groups of order 254

dρLabelID
C254Cyclic group2541C254254,2
D127Dihedral group1272+D127254,1

Groups of order 255

dρLabelID
C255Cyclic group2551C255255,1

Groups of order 257

dρLabelID
C257Cyclic group2571C257257,1

Groups of order 258

dρLabelID
C258Cyclic group2581C258258,6
D129Dihedral group1292+D129258,5
C43⋊C6The semidirect product of C43 and C6 acting faithfully436+C43:C6258,1
S3×C43Direct product of C43 and S31292S3xC43258,3
C3×D43Direct product of C3 and D431292C3xD43258,4
C2×C43⋊C3Direct product of C2 and C43⋊C3863C2xC43:C3258,2

Groups of order 259

dρLabelID
C259Cyclic group2591C259259,1

Groups of order 260

dρLabelID
C260Cyclic group2601C260260,4
D130Dihedral group; = C2×D651302+D130260,14
Dic65Dicyclic group; = C657C42602-Dic65260,3
C65⋊C43rd semidirect product of C65 and C4 acting faithfully654C65:C4260,6
C652C42nd semidirect product of C65 and C4 acting faithfully654+C65:2C4260,10
C133F5The semidirect product of C13 and F5 acting via F5/D5=C2654C13:3F5260,8
C13⋊F51st semidirect product of C13 and F5 acting via F5/C5=C4654+C13:F5260,9
C2×C130Abelian group of type [2,130]260C2xC130260,15
D5×D13Direct product of D5 and D13654+D5xD13260,11
C13×F5Direct product of C13 and F5654C13xF5260,7
D5×C26Direct product of C26 and D51302D5xC26260,13
C10×D13Direct product of C10 and D131302C10xD13260,12
C13×Dic5Direct product of C13 and Dic52602C13xDic5260,1
C5×Dic13Direct product of C5 and Dic132602C5xDic13260,2
C5×C13⋊C4Direct product of C5 and C13⋊C4654C5xC13:C4260,5

Groups of order 261

dρLabelID
C261Cyclic group2611C261261,1
C3×C87Abelian group of type [3,87]261C3xC87261,2

Groups of order 262

dρLabelID
C262Cyclic group2621C262262,2
D131Dihedral group1312+D131262,1

Groups of order 263

dρLabelID
C263Cyclic group2631C263263,1

Groups of order 264

dρLabelID
C264Cyclic group2641C264264,4
D132Dihedral group1322+D132264,25
Dic66Dicyclic group; = C332Q82642-Dic66264,23
C11⋊S4The semidirect product of C11 and S4 acting via S4/A4=C2446+C11:S4264,32
D33⋊C4The semidirect product of D33 and C4 acting via C4/C2=C21324+D33:C4264,7
C33⋊D41st semidirect product of C33 and D4 acting via D4/C2=C221324-C33:D4264,8
C3⋊D44The semidirect product of C3 and D44 acting via D44/D22=C21324+C3:D44264,9
C337D41st semidirect product of C33 and D4 acting via D4/C22=C21322C33:7D4264,27
C11⋊D12The semidirect product of C11 and D12 acting via D12/D6=C21324+C11:D12264,10
C33⋊Q8The semidirect product of C33 and Q8 acting via Q8/C2=C222644-C33:Q8264,11
C33⋊C81st semidirect product of C33 and C8 acting via C8/C4=C22642C33:C8264,3
C2×C132Abelian group of type [2,132]264C2xC132264,28
C22×C66Abelian group of type [2,2,66]264C2^2xC66264,39
C11×S4Direct product of C11 and S4443C11xS4264,31
A4×D11Direct product of A4 and D11446+A4xD11264,33
A4×C22Direct product of C22 and A4663A4xC22264,35
C11×SL2(𝔽3)Direct product of C11 and SL2(𝔽3)882C11xSL(2,3)264,12
S3×C44Direct product of C44 and S31322S3xC44264,19
C3×D44Direct product of C3 and D441322C3xD44264,15
C4×D33Direct product of C4 and D331322C4xD33264,24
D4×C33Direct product of C33 and D41322D4xC33264,29
C12×D11Direct product of C12 and D111322C12xD11264,14
C11×D12Direct product of C11 and D121322C11xD12264,20
Dic3×D11Direct product of Dic3 and D111324-Dic3xD11264,5
S3×Dic11Direct product of S3 and Dic111324-S3xDic11264,6
C22×D33Direct product of C22 and D33132C2^2xD33264,38
Q8×C33Direct product of C33 and Q82642Q8xC33264,30
C3×Dic22Direct product of C3 and Dic222642C3xDic22264,13
C6×Dic11Direct product of C6 and Dic11264C6xDic11264,16
C11×Dic6Direct product of C11 and Dic62642C11xDic6264,18
Dic3×C22Direct product of C22 and Dic3264Dic3xC22264,21
C2×Dic33Direct product of C2 and Dic33264C2xDic33264,26
C2×S3×D11Direct product of C2, S3 and D11664+C2xS3xD11264,34
S3×C2×C22Direct product of C2×C22 and S3132S3xC2xC22264,37
C2×C6×D11Direct product of C2×C6 and D11132C2xC6xD11264,36
C3×C11⋊D4Direct product of C3 and C11⋊D41322C3xC11:D4264,17
C11×C3⋊D4Direct product of C11 and C3⋊D41322C11xC3:D4264,22
C11×C3⋊C8Direct product of C11 and C3⋊C82642C11xC3:C8264,1
C3×C11⋊C8Direct product of C3 and C11⋊C82642C3xC11:C8264,2

Groups of order 265

dρLabelID
C265Cyclic group2651C265265,1

Groups of order 266

dρLabelID
C266Cyclic group2661C266266,4
D133Dihedral group1332+D133266,3
D7×C19Direct product of C19 and D71332D7xC19266,1
C7×D19Direct product of C7 and D191332C7xD19266,2

Groups of order 267

dρLabelID
C267Cyclic group2671C267267,1

Groups of order 268

dρLabelID
C268Cyclic group2681C268268,2
D134Dihedral group; = C2×D671342+D134268,3
Dic67Dicyclic group; = C67C42682-Dic67268,1
C2×C134Abelian group of type [2,134]268C2xC134268,4

Groups of order 269

dρLabelID
C269Cyclic group2691C269269,1

Groups of order 270

dρLabelID
C270Cyclic group2701C270270,4
D135Dihedral group1352+D135270,3
D45⋊C3The semidirect product of D45 and C3 acting faithfully456+D45:C3270,15
He3⋊D51st semidirect product of He3 and D5 acting via D5/C5=C2456+He3:D5270,14
C32⋊D152nd semidirect product of C32 and D15 acting via D15/C5=S3456C3^2:D15270,19
C3⋊D45The semidirect product of C3 and D45 acting via D45/C45=C2135C3:D45270,18
C33⋊D53rd semidirect product of C33 and D5 acting via D5/C5=C2135C3^3:D5270,29
C3×C90Abelian group of type [3,90]270C3xC90270,20
C32×C30Abelian group of type [3,3,30]270C3^2xC30270,30
D5×He3Direct product of D5 and He3456D5xHe3270,6
D5×3- 1+2Direct product of D5 and 3- 1+2456D5xES-(3,1)270,7
S3×C45Direct product of C45 and S3902S3xC45270,9
C15×D9Direct product of C15 and D9902C15xD9270,8
C3×D45Direct product of C3 and D45902C3xD45270,12
C9×D15Direct product of C9 and D15902C9xD15270,13
C10×He3Direct product of C10 and He3903C10xHe3270,21
C32×D15Direct product of C32 and D1590C3^2xD15270,25
C10×3- 1+2Direct product of C10 and 3- 1+2903C10xES-(3,1)270,22
C5×D27Direct product of C5 and D271352C5xD27270,1
D5×C27Direct product of C27 and D51352D5xC27270,2
D5×C33Direct product of C33 and D5135D5xC3^3270,23
C5×C9⋊C6Direct product of C5 and C9⋊C6456C5xC9:C6270,11
C5×C32⋊C6Direct product of C5 and C32⋊C6456C5xC3^2:C6270,10
C5×He3⋊C2Direct product of C5 and He3⋊C2453C5xHe3:C2270,17
S3×C3×C15Direct product of C3×C15 and S390S3xC3xC15270,24
C15×C3⋊S3Direct product of C15 and C3⋊S390C15xC3:S3270,26
C3×C3⋊D15Direct product of C3 and C3⋊D1590C3xC3:D15270,27
D5×C3×C9Direct product of C3×C9 and D5135D5xC3xC9270,5
C5×C9⋊S3Direct product of C5 and C9⋊S3135C5xC9:S3270,16
C5×C33⋊C2Direct product of C5 and C33⋊C2135C5xC3^3:C2270,28

Groups of order 271

dρLabelID
C271Cyclic group2711C271271,1

Groups of order 272

dρLabelID
C272Cyclic group2721C272272,2
D136Dihedral group1362+D136272,7
F17Frobenius group; = C17C16 = AGL1(𝔽17) = Aut(D17) = Hol(C17)1716+F17272,50
Dic68Dicyclic group; = C171Q162722-Dic68272,8
C68⋊C41st semidirect product of C68 and C4 acting faithfully684C68:C4272,32
D4⋊D17The semidirect product of D4 and D17 acting via D17/C17=C21364+D4:D17272,15
Q8⋊D17The semidirect product of Q8 and D17 acting via D17/C17=C21364+Q8:D17272,17
C8⋊D173rd semidirect product of C8 and D17 acting via D17/C17=C21362C8:D17272,5
C136⋊C22nd semidirect product of C136 and C2 acting faithfully1362C136:C2272,6
D34⋊C41st semidirect product of D34 and C4 acting via C4/C2=C2136D34:C4272,14
D685C2The semidirect product of D68 and C2 acting through Inn(D68)1362D68:5C2272,39
D42D17The semidirect product of D4 and D17 acting through Inn(D4)1364-D4:2D17272,41
D68⋊C24th semidirect product of D68 and C2 acting faithfully1364+D68:C2272,43
C17⋊M4(2)The semidirect product of C17 and M4(2) acting via M4(2)/C22=C41364-C17:M4(2)272,34
C683C41st semidirect product of C68 and C4 acting via C4/C2=C2272C68:3C4272,13
C174C16The semidirect product of C17 and C16 acting via C16/C8=C22722C17:4C16272,1
C173C16The semidirect product of C17 and C16 acting via C16/C4=C42724C17:3C16272,3
C17⋊Q16The semidirect product of C17 and Q16 acting via Q16/Q8=C22724-C17:Q16272,18
D17.D4The non-split extension by D17 of D4 acting via D4/C22=C2684+D17.D4272,35
D4.D17The non-split extension by D4 of D17 acting via D17/C17=C21364-D4.D17272,16
C68.4C41st non-split extension by C68 of C4 acting via C4/C2=C21362C68.4C4272,10
C68.C43rd non-split extension by C68 of C4 acting faithfully1364C68.C4272,29
C23.D17The non-split extension by C23 of D17 acting via D17/C17=C2136C2^3.D17272,19
D34.4C43rd non-split extension by D34 of C4 acting via C4/C2=C21364D34.4C4272,30
C34.C8The non-split extension by C34 of C8 acting faithfully2728-C34.C8272,28
C34.D41st non-split extension by C34 of D4 acting via D4/C22=C2272C34.D4272,12
C4×C68Abelian group of type [4,68]272C4xC68272,20
C2×C136Abelian group of type [2,136]272C2xC136272,23
C22×C68Abelian group of type [2,2,68]272C2^2xC68272,46
C23×C34Abelian group of type [2,2,2,34]272C2^3xC34272,54
D4×D17Direct product of D4 and D17684+D4xD17272,40
C8×D17Direct product of C8 and D171362C8xD17272,4
D8×C17Direct product of C17 and D81362D8xC17272,25
C2×D68Direct product of C2 and D68136C2xD68272,38
D4×C34Direct product of C34 and D4136D4xC34272,47
Q8×D17Direct product of Q8 and D171364-Q8xD17272,42
SD16×C17Direct product of C17 and SD161362SD16xC17272,26
C23×D17Direct product of C23 and D17136C2^3xD17272,53
M4(2)×C17Direct product of C17 and M4(2)1362M4(2)xC17272,24
Q8×C34Direct product of C34 and Q8272Q8xC34272,48
Q16×C17Direct product of C17 and Q162722Q16xC17272,27
C4×Dic17Direct product of C4 and Dic17272C4xDic17272,11
C2×Dic34Direct product of C2 and Dic34272C2xDic34272,36
C22×Dic17Direct product of C22 and Dic17272C2^2xDic17272,44
C2×C17⋊C8Direct product of C2 and C17⋊C8348+C2xC17:C8272,51
C4×C17⋊C4Direct product of C4 and C17⋊C4684C4xC17:C4272,31
C22×C17⋊C4Direct product of C22 and C17⋊C468C2^2xC17:C4272,52
C2×C4×D17Direct product of C2×C4 and D17136C2xC4xD17272,37
C2×C17⋊D4Direct product of C2 and C17⋊D4136C2xC17:D4272,45
C4○D4×C17Direct product of C17 and C4○D41362C4oD4xC17272,49
C22⋊C4×C17Direct product of C17 and C22⋊C4136C2^2:C4xC17272,21
C4⋊C4×C17Direct product of C17 and C4⋊C4272C4:C4xC17272,22
C2×C173C8Direct product of C2 and C173C8272C2xC17:3C8272,9
C2×C172C8Direct product of C2 and C172C8272C2xC17:2C8272,33

Groups of order 273

dρLabelID
C273Cyclic group2731C273273,5
C91⋊C33rd semidirect product of C91 and C3 acting faithfully913C91:C3273,3
C914C34th semidirect product of C91 and C3 acting faithfully913C91:4C3273,4
C13×C7⋊C3Direct product of C13 and C7⋊C3913C13xC7:C3273,1
C7×C13⋊C3Direct product of C7 and C13⋊C3913C7xC13:C3273,2

Groups of order 274

dρLabelID
C274Cyclic group2741C274274,2
D137Dihedral group1372+D137274,1

Groups of order 275

dρLabelID
C275Cyclic group2751C275275,2
C11⋊C25The semidirect product of C11 and C25 acting via C25/C5=C52755C11:C25275,1
C5×C55Abelian group of type [5,55]275C5xC55275,4
C5×C11⋊C5Direct product of C5 and C11⋊C5555C5xC11:C5275,3

Groups of order 276

dρLabelID
C276Cyclic group2761C276276,4
D138Dihedral group; = C2×D691382+D138276,9
Dic69Dicyclic group; = C691C42762-Dic69276,3
C2×C138Abelian group of type [2,138]276C2xC138276,10
S3×D23Direct product of S3 and D23694+S3xD23276,5
A4×C23Direct product of C23 and A4923A4xC23276,6
S3×C46Direct product of C46 and S31382S3xC46276,8
C6×D23Direct product of C6 and D231382C6xD23276,7
Dic3×C23Direct product of C23 and Dic32762Dic3xC23276,1
C3×Dic23Direct product of C3 and Dic232762C3xDic23276,2

Groups of order 277

dρLabelID
C277Cyclic group2771C277277,1

Groups of order 278

dρLabelID
C278Cyclic group2781C278278,2
D139Dihedral group1392+D139278,1

Groups of order 279

dρLabelID
C279Cyclic group2791C279279,2
C31⋊C9The semidirect product of C31 and C9 acting via C9/C3=C32793C31:C9279,1
C3×C93Abelian group of type [3,93]279C3xC93279,4
C3×C31⋊C3Direct product of C3 and C31⋊C3933C3xC31:C3279,3

Groups of order 280

dρLabelID
C280Cyclic group2801C280280,4
D140Dihedral group1402+D140280,26
Dic70Dicyclic group; = C352Q82802-Dic70280,24
C35⋊D41st semidirect product of C35 and D4 acting via D4/C2=C221404-C35:D4280,10
C5⋊D28The semidirect product of C5 and D28 acting via D28/D14=C21404+C5:D28280,11
C7⋊D20The semidirect product of C7 and D20 acting via D20/D10=C21404+C7:D20280,12
C357D41st semidirect product of C35 and D4 acting via D4/C22=C21402C35:7D4280,28
C35⋊Q8The semidirect product of C35 and Q8 acting via Q8/C2=C222804-C35:Q8280,13
C353C81st semidirect product of C35 and C8 acting via C8/C4=C22802C35:3C8280,3
C35⋊C81st semidirect product of C35 and C8 acting via C8/C2=C42804C35:C8280,6
D70.C2The non-split extension by D70 of C2 acting faithfully1404+D70.C2280,9
C2×C140Abelian group of type [2,140]280C2xC140280,29
C22×C70Abelian group of type [2,2,70]280C2^2xC70280,40
D7×F5Direct product of D7 and F5358+D7xF5280,32
C5×F8Direct product of C5 and F8407C5xF8280,33
C14×F5Direct product of C14 and F5704C14xF5280,34
D7×C20Direct product of C20 and D71402D7xC20280,15
C5×D28Direct product of C5 and D281402C5xD28280,16
D5×C28Direct product of C28 and D51402D5xC28280,20
C7×D20Direct product of C7 and D201402C7xD20280,21
C4×D35Direct product of C4 and D351402C4xD35280,25
D4×C35Direct product of C35 and D41402D4xC35280,30
D7×Dic5Direct product of D7 and Dic51404-D7xDic5280,7
D5×Dic7Direct product of D5 and Dic71404-D5xDic7280,8
C22×D35Direct product of C22 and D35140C2^2xD35280,39
Q8×C35Direct product of C35 and Q82802Q8xC35280,31
C5×Dic14Direct product of C5 and Dic142802C5xDic14280,14
C10×Dic7Direct product of C10 and Dic7280C10xDic7280,17
C7×Dic10Direct product of C7 and Dic102802C7xDic10280,19
C14×Dic5Direct product of C14 and Dic5280C14xDic5280,22
C2×Dic35Direct product of C2 and Dic35280C2xDic35280,27
C2×D5×D7Direct product of C2, D5 and D7704+C2xD5xD7280,36
C2×C7⋊F5Direct product of C2 and C7⋊F5704C2xC7:F5280,35
D7×C2×C10Direct product of C2×C10 and D7140D7xC2xC10280,37
D5×C2×C14Direct product of C2×C14 and D5140D5xC2xC14280,38
C5×C7⋊D4Direct product of C5 and C7⋊D41402C5xC7:D4280,18
C7×C5⋊D4Direct product of C7 and C5⋊D41402C7xC5:D4280,23
C5×C7⋊C8Direct product of C5 and C7⋊C82802C5xC7:C8280,2
C7×C5⋊C8Direct product of C7 and C5⋊C82804C7xC5:C8280,5
C7×C52C8Direct product of C7 and C52C82802C7xC5:2C8280,1

Groups of order 281

dρLabelID
C281Cyclic group2811C281281,1

Groups of order 282

dρLabelID
C282Cyclic group2821C282282,4
D141Dihedral group1412+D141282,3
S3×C47Direct product of C47 and S31412S3xC47282,1
C3×D47Direct product of C3 and D471412C3xD47282,2

Groups of order 283

dρLabelID
C283Cyclic group2831C283283,1

Groups of order 284

dρLabelID
C284Cyclic group2841C284284,2
D142Dihedral group; = C2×D711422+D142284,3
Dic71Dicyclic group; = C71C42842-Dic71284,1
C2×C142Abelian group of type [2,142]284C2xC142284,4

Groups of order 285

dρLabelID
C285Cyclic group2851C285285,2
C5×C19⋊C3Direct product of C5 and C19⋊C3953C5xC19:C3285,1

Groups of order 286

dρLabelID
C286Cyclic group2861C286286,4
D143Dihedral group1432+D143286,3
C13×D11Direct product of C13 and D111432C13xD11286,1
C11×D13Direct product of C11 and D131432C11xD13286,2

Groups of order 287

dρLabelID
C287Cyclic group2871C287287,1

Groups of order 288

dρLabelID
C288Cyclic group2881C288288,2
D144Dihedral group1442+D144288,6
Dic72Dicyclic group; = C91Q322882-Dic72288,8
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)129+PSO+(4,3)288,1026
Ω4+ (𝔽3)Omega group of + type on 𝔽34; = SL2(𝔽3)A4244+Omega+(4,3)288,860
A4≀C2Wreath product of A4 by C286+A4wrC2288,1025
D6≀C2Wreath product of D6 by C2124+D6wrC2288,889
Dic3≀C2Wreath product of Dic3 by C2244-Dic3wrC2288,389
C22⋊F9The semidirect product of C22 and F9 acting via F9/C32⋊C4=C2248+C2^2:F9288,867
D12⋊D64th semidirect product of D12 and D6 acting via D6/C3=C22248+D12:D6288,574
D125D65th semidirect product of D12 and D6 acting via D6/C3=C22248+D12:5D6288,585
C628D45th semidirect product of C62 and D4 acting via D4/C2=C2224C6^2:8D4288,629
C62⋊D42nd semidirect product of C62 and D4 acting faithfully248+C6^2:D4288,890
D1218D62nd semidirect product of D12 and D6 acting via D6/C6=C2244+D12:18D6288,473
D1223D67th semidirect product of D12 and D6 acting via D6/C6=C2244D12:23D6288,954
D1227D63rd semidirect product of D12 and D6 acting through Inn(D12)244+D12:27D6288,956
D1213D67th semidirect product of D12 and D6 acting via D6/S3=C2248+D12:13D6288,962
C62⋊Q81st semidirect product of C62 and Q8 acting faithfully248+C6^2:Q8288,895
Dic6⋊D64th semidirect product of Dic6 and D6 acting via D6/C3=C22248+Dic6:D6288,578
D124Dic34th semidirect product of D12 and Dic3 acting via Dic3/C6=C2244D12:4Dic3288,216
Dic612D66th semidirect product of Dic6 and D6 acting via D6/S3=C2248+Dic6:12D6288,960
C32⋊2+ 1+4The semidirect product of C32 and 2+ 1+4 acting via 2+ 1+4/C23=C22244C3^2:ES+(2,2)288,978
C4⋊F9The semidirect product of C4 and F9 acting via F9/C32⋊C4=C2368C4:F9288,864
F9⋊C4The semidirect product of F9 and C4 acting via C4/C2=C2368F9:C4288,843
C42⋊D9The semidirect product of C42 and D9 acting via D9/C3=S3366+C4^2:D9288,67
C12⋊S41st semidirect product of C12 and S4 acting via S4/A4=C2366+C12:S4288,909
D6⋊S41st semidirect product of D6 and S4 acting via S4/A4=C2366D6:S4288,857
Dic3⋊S4The semidirect product of Dic3 and S4 acting via S4/A4=C2366Dic3:S4288,855
C22⋊D36The semidirect product of C22 and D36 acting via D36/C12=S3366+C2^2:D36288,334
A4⋊D12The semidirect product of A4 and D12 acting via D12/D6=C2366+A4:D12288,858
C24⋊D93rd semidirect product of C24 and D9 acting via D9/C3=S3366C2^4:D9288,836
C24⋊C181st semidirect product of C24 and C18 acting via C18/C3=C6366C2^4:C18288,73
C422C182nd semidirect product of C42 and C18 acting via C18/C3=C6366C4^2:2C18288,75
Dic32S4The semidirect product of Dic3 and S4 acting through Inn(Dic3)366Dic3:2S4288,854
C4⋊PSU3(𝔽2)The semidirect product of C4 and PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2368C4:PSU(3,2)288,893
PSU3(𝔽2)⋊C4The semidirect product of PSU3(𝔽2) and C4 acting via C4/C2=C2368PSU(3,2):C4288,842
C32⋊D16The semidirect product of C32 and D16 acting via D16/C4=D4488+C3^2:D16288,382
C3⋊D48The semidirect product of C3 and D48 acting via D48/D24=C2484+C3:D48288,194
C241D61st semidirect product of C24 and D6 acting via D6/C3=C22484+C24:1D6288,442
C249D69th semidirect product of C24 and D6 acting via D6/C3=C22484C24:9D6288,444
C244D64th semidirect product of C24 and D6 acting via D6/C3=C22484C24:4D6288,445
C246D66th semidirect product of C24 and D6 acting via D6/C3=C22484C24:6D6288,446
C32⋊SD32The semidirect product of C32 and SD32 acting via SD32/C4=D4488+C3^2:SD32288,383
D24⋊S32nd semidirect product of D24 and S3 acting via S3/C3=C2484D24:S3288,443
D245S35th semidirect product of D24 and S3 acting via S3/C3=C2484D24:5S3288,458
D6⋊D121st semidirect product of D6 and D12 acting via D12/C12=C248D6:D12288,554
D64D121st semidirect product of D6 and D12 acting via D12/D6=C248D6:4D12288,570
D65D122nd semidirect product of D6 and D12 acting via D12/D6=C248D6:5D12288,571
D129D63rd semidirect product of D12 and D6 acting via D6/S3=C2488-D12:9D6288,580
D126D66th semidirect product of D12 and D6 acting via D6/C3=C22488+D12:6D6288,587

Full list: Groups of order 288 (1045 groups)

Groups of order 289

dρLabelID
C289Cyclic group2891C289289,1
C172Elementary abelian group of type [17,17]289C17^2289,2

Groups of order 290

dρLabelID
C290Cyclic group2901C290290,4
D145Dihedral group1452+D145290,3
D5×C29Direct product of C29 and D51452D5xC29290,1
C5×D29Direct product of C5 and D291452C5xD29290,2

Groups of order 291

dρLabelID
C291Cyclic group2911C291291,2
C97⋊C3The semidirect product of C97 and C3 acting faithfully973C97:C3291,1

Groups of order 292

dρLabelID
C292Cyclic group2921C292292,2
D146Dihedral group; = C2×D731462+D146292,4
Dic73Dicyclic group; = C732C42922-Dic73292,1
C73⋊C4The semidirect product of C73 and C4 acting faithfully734+C73:C4292,3
C2×C146Abelian group of type [2,146]292C2xC146292,5

Groups of order 293

dρLabelID
C293Cyclic group2931C293293,1

Groups of order 294

dρLabelID
C294Cyclic group2941C294294,6
D147Dihedral group1472+D147294,5
C72⋊S3The semidirect product of C72 and S3 acting faithfully143C7^2:S3294,7
C74F72nd semidirect product of C7 and F7 acting via F7/D7=C3146C7:4F7294,12
C75F7The semidirect product of C7 and F7 acting via F7/C7⋊C3=C2216+C7:5F7294,10
C72⋊C67th semidirect product of C72 and C6 acting faithfully216+C7^2:C6294,14
C73F71st semidirect product of C7 and F7 acting via F7/D7=C3426C7:3F7294,11
C49⋊C6The semidirect product of C49 and C6 acting faithfully496+C49:C6294,1
C7⋊F71st semidirect product of C7 and F7 acting via F7/C7=C649C7:F7294,13
C7⋊D21The semidirect product of C7 and D21 acting via D21/C21=C2147C7:D21294,22
C7×C42Abelian group of type [7,42]294C7xC42294,23
C7×F7Direct product of C7 and F7426C7xF7294,8
D7×C21Direct product of C21 and D7422D7xC21294,18
C7×D21Direct product of C7 and D21422C7xD21294,21
S3×C49Direct product of C49 and S31472S3xC49294,3
C3×D49Direct product of C3 and D491472C3xD49294,4
S3×C72Direct product of C72 and S3147S3xC7^2294,20
D7×C7⋊C3Direct product of D7 and C7⋊C3426D7xC7:C3294,9
C14×C7⋊C3Direct product of C14 and C7⋊C3423C14xC7:C3294,15
C2×C723C3Direct product of C2 and C723C3423C2xC7^2:3C3294,17
C2×C49⋊C3Direct product of C2 and C49⋊C3983C2xC49:C3294,2
C2×C72⋊C3Direct product of C2 and C72⋊C398C2xC7^2:C3294,16
C3×C7⋊D7Direct product of C3 and C7⋊D7147C3xC7:D7294,19

Groups of order 295

dρLabelID
C295Cyclic group2951C295295,1

Groups of order 296

dρLabelID
C296Cyclic group2961C296296,2
D148Dihedral group1482+D148296,6
Dic74Dicyclic group; = C37Q82962-Dic74296,4
C37⋊D4The semidirect product of C37 and D4 acting via D4/C22=C21482C37:D4296,8
C37⋊C8The semidirect product of C37 and C8 acting via C8/C2=C42964-C37:C8296,3
C372C8The semidirect product of C37 and C8 acting via C8/C4=C22962C37:2C8296,1
C2×C148Abelian group of type [2,148]296C2xC148296,9
C22×C74Abelian group of type [2,2,74]296C2^2xC74296,14
C4×D37Direct product of C4 and D371482C4xD37296,5
D4×C37Direct product of C37 and D41482D4xC37296,10
C22×D37Direct product of C22 and D37148C2^2xD37296,13
Q8×C37Direct product of C37 and Q82962Q8xC37296,11
C2×Dic37Direct product of C2 and Dic37296C2xDic37296,7
C2×C37⋊C4Direct product of C2 and C37⋊C4744+C2xC37:C4296,12

Groups of order 297

dρLabelID
C297Cyclic group2971C297297,1
C3×C99Abelian group of type [3,99]297C3xC99297,2
C32×C33Abelian group of type [3,3,33]297C3^2xC33297,5
C11×He3Direct product of C11 and He3993C11xHe3297,3
C11×3- 1+2Direct product of C11 and 3- 1+2993C11xES-(3,1)297,4

Groups of order 298

dρLabelID
C298Cyclic group2981C298298,2
D149Dihedral group1492+D149298,1

Groups of order 299

dρLabelID
C299Cyclic group2991C299299,1

Groups of order 300

dρLabelID
C300Cyclic group3001C300300,4
D150Dihedral group; = C2×D751502+D150300,11
Dic75Dicyclic group; = C753C43002-Dic75300,3
C52⋊D6The semidirect product of C52 and D6 acting faithfully156+C5^2:D6300,25
C52⋊C12The semidirect product of C52 and C12 acting faithfully1512+C5^2:C12300,24
C52⋊Dic3The semidirect product of C52 and Dic3 acting faithfully1512+C5^2:Dic3300,23
C52⋊A4The semidirect product of C52 and A4 acting via A4/C22=C3303C5^2:A4300,43
D15⋊D5The semidirect product of D15 and D5 acting via D5/C5=C2304D15:D5300,40
C152F52nd semidirect product of C15 and F5 acting via F5/C5=C4304C15:2F5300,35
C522C12The semidirect product of C52 and C12 acting via C12/C2=C6606-C5^2:2C12300,14
C522Dic3The semidirect product of C52 and Dic3 acting via Dic3/C2=S3603C5^2:2Dic3300,13
C75⋊C41st semidirect product of C75 and C4 acting faithfully754C75:C4300,6
C15⋊F51st semidirect product of C15 and F5 acting via F5/C5=C475C15:F5300,34
D5.D15The non-split extension by D5 of D15 acting via D15/C15=C2604D5.D15300,33
C30.D53rd non-split extension by C30 of D5 acting via D5/C5=C2300C30.D5300,20
C5×C60Abelian group of type [5,60]300C5xC60300,21
C2×C150Abelian group of type [2,150]300C2xC150300,12
C10×C30Abelian group of type [10,30]300C10xC30300,49
C5×A5Direct product of C5 and A5; = U2(𝔽4)253C5xA5300,22
D5×D15Direct product of D5 and D15304+D5xD15300,39
D5×C30Direct product of C30 and D5602D5xC30300,44
C15×F5Direct product of C15 and F5604C15xF5300,28
C10×D15Direct product of C10 and D15602C10xD15300,47
C15×Dic5Direct product of C15 and Dic5602C15xDic5300,16
C5×Dic15Direct product of C5 and Dic15602C5xDic15300,19
S3×D25Direct product of S3 and D25754+S3xD25300,7
A4×C25Direct product of C25 and A41003A4xC25300,8
A4×C52Direct product of C52 and A4100A4xC5^2300,42
S3×C50Direct product of C50 and S31502S3xC50300,10
C6×D25Direct product of C6 and D251502C6xD25300,9
Dic3×C25Direct product of C25 and Dic33002Dic3xC25300,1
C3×Dic25Direct product of C3 and Dic253002C3xDic25300,2
Dic3×C52Direct product of C52 and Dic3300Dic3xC5^2300,18
C3×D52Direct product of C3, D5 and D5304C3xD5^2300,36
C5×S3×D5Direct product of C5, S3 and D5304C5xS3xD5300,37
C2×C52⋊S3Direct product of C2 and C52⋊S3303C2xC5^2:S3300,26
C2×C52⋊C6Direct product of C2 and C52⋊C6306+C2xC5^2:C6300,27
C3×C52⋊C4Direct product of C3 and C52⋊C4304C3xC5^2:C4300,31
C5×C3⋊F5Direct product of C5 and C3⋊F5604C5xC3:F5300,32
C4×C52⋊C3Direct product of C4 and C52⋊C3603C4xC5^2:C3300,15
C3×D5.D5Direct product of C3 and D5.D5604C3xD5.D5300,29
C22×C52⋊C3Direct product of C22 and C52⋊C360C2^2xC5^2:C3300,41
C3×C25⋊C4Direct product of C3 and C25⋊C4754C3xC25:C4300,5
S3×C5⋊D5Direct product of S3 and C5⋊D575S3xC5:D5300,38
C3×C5⋊F5Direct product of C3 and C5⋊F575C3xC5:F5300,30
S3×C5×C10Direct product of C5×C10 and S3150S3xC5xC10300,46
C6×C5⋊D5Direct product of C6 and C5⋊D5150C6xC5:D5300,45
C2×C5⋊D15Direct product of C2 and C5⋊D15150C2xC5:D15300,48
C3×C526C4Direct product of C3 and C526C4300C3xC5^2:6C4300,17

Groups of order 301

dρLabelID
C301Cyclic group3011C301301,2
C43⋊C7The semidirect product of C43 and C7 acting faithfully437C43:C7301,1

Groups of order 302

dρLabelID
C302Cyclic group3021C302302,2
D151Dihedral group1512+D151302,1

Groups of order 303

dρLabelID
C303Cyclic group3031C303303,1

Groups of order 304

dρLabelID
C304Cyclic group3041C304304,2
D152Dihedral group1522+D152304,6
Dic76Dicyclic group; = C191Q163042-Dic76304,7
D38⋊C4The semidirect product of D38 and C4 acting via C4/C2=C2152D38:C4304,13
D4⋊D19The semidirect product of D4 and D19 acting via D19/C19=C21524+D4:D19304,14
Q8⋊D19The semidirect product of Q8 and D19 acting via D19/C19=C21524+Q8:D19304,16
C8⋊D193rd semidirect product of C8 and D19 acting via D19/C19=C21522C8:D19304,4
C152⋊C22nd semidirect product of C152 and C2 acting faithfully1522C152:C2304,5
D765C2The semidirect product of D76 and C2 acting through Inn(D76)1522D76:5C2304,30
D42D19The semidirect product of D4 and D19 acting through Inn(D4)1524-D4:2D19304,32
D76⋊C24th semidirect product of D76 and C2 acting faithfully1524+D76:C2304,34
C19⋊C16The semidirect product of C19 and C16 acting via C16/C8=C23042C19:C16304,1
C76⋊C41st semidirect product of C76 and C4 acting via C4/C2=C2304C76:C4304,12
C19⋊Q16The semidirect product of C19 and Q16 acting via Q16/Q8=C23044-C19:Q16304,17
Dic19⋊C4The semidirect product of Dic19 and C4 acting via C4/C2=C2304Dic19:C4304,11
D4.D19The non-split extension by D4 of D19 acting via D19/C19=C21524-D4.D19304,15
C76.C41st non-split extension by C76 of C4 acting via C4/C2=C21522C76.C4304,9
C23.D19The non-split extension by C23 of D19 acting via D19/C19=C2152C2^3.D19304,18
C4×C76Abelian group of type [4,76]304C4xC76304,19
C2×C152Abelian group of type [2,152]304C2xC152304,22
C22×C76Abelian group of type [2,2,76]304C2^2xC76304,37
C23×C38Abelian group of type [2,2,2,38]304C2^3xC38304,42
D4×D19Direct product of D4 and D19764+D4xD19304,31
C8×D19Direct product of C8 and D191522C8xD19304,3
D8×C19Direct product of C19 and D81522D8xC19304,24
C2×D76Direct product of C2 and D76152C2xD76304,29
D4×C38Direct product of C38 and D4152D4xC38304,38
Q8×D19Direct product of Q8 and D191524-Q8xD19304,33
SD16×C19Direct product of C19 and SD161522SD16xC19304,25
C23×D19Direct product of C23 and D19152C2^3xD19304,41
M4(2)×C19Direct product of C19 and M4(2)1522M4(2)xC19304,23
Q8×C38Direct product of C38 and Q8304Q8xC38304,39
Q16×C19Direct product of C19 and Q163042Q16xC19304,26
C4×Dic19Direct product of C4 and Dic19304C4xDic19304,10
C2×Dic38Direct product of C2 and Dic38304C2xDic38304,27
C22×Dic19Direct product of C22 and Dic19304C2^2xDic19304,35
C2×C4×D19Direct product of C2×C4 and D19152C2xC4xD19304,28
C2×C19⋊D4Direct product of C2 and C19⋊D4152C2xC19:D4304,36
C4○D4×C19Direct product of C19 and C4○D41522C4oD4xC19304,40
C22⋊C4×C19Direct product of C19 and C22⋊C4152C2^2:C4xC19304,20
C2×C19⋊C8Direct product of C2 and C19⋊C8304C2xC19:C8304,8
C4⋊C4×C19Direct product of C19 and C4⋊C4304C4:C4xC19304,21

Groups of order 305

dρLabelID
C305Cyclic group3051C305305,2
C61⋊C5The semidirect product of C61 and C5 acting faithfully615C61:C5305,1

Groups of order 306

dρLabelID
C306Cyclic group3061C306306,4
D153Dihedral group1532+D153306,3
C3⋊D51The semidirect product of C3 and D51 acting via D51/C51=C2153C3:D51306,9
C3×C102Abelian group of type [3,102]306C3xC102306,10
S3×C51Direct product of C51 and S31022S3xC51306,6
C3×D51Direct product of C3 and D511022C3xD51306,7
C17×D9Direct product of C17 and D91532C17xD9306,1
C9×D17Direct product of C9 and D171532C9xD17306,2
C32×D17Direct product of C32 and D17153C3^2xD17306,5
C17×C3⋊S3Direct product of C17 and C3⋊S3153C17xC3:S3306,8

Groups of order 307

dρLabelID
C307Cyclic group3071C307307,1

Groups of order 308

dρLabelID
C308Cyclic group3081C308308,4
D154Dihedral group; = C2×D771542+D154308,8
Dic77Dicyclic group; = C771C43082-Dic77308,3
C2×C154Abelian group of type [2,154]308C2xC154308,9
D7×D11Direct product of D7 and D11774+D7xD11308,5
D7×C22Direct product of C22 and D71542D7xC22308,7
C14×D11Direct product of C14 and D111542C14xD11308,6
C11×Dic7Direct product of C11 and Dic73082C11xDic7308,1
C7×Dic11Direct product of C7 and Dic113082C7xDic11308,2

Groups of order 309

dρLabelID
C309Cyclic group3091C309309,2
C103⋊C3The semidirect product of C103 and C3 acting faithfully1033C103:C3309,1

Groups of order 310

dρLabelID
C310Cyclic group3101C310310,6
D155Dihedral group1552+D155310,5
C31⋊C10The semidirect product of C31 and C10 acting faithfully3110+C31:C10310,1
D5×C31Direct product of C31 and D51552D5xC31310,3
C5×D31Direct product of C5 and D311552C5xD31310,4
C2×C31⋊C5Direct product of C2 and C31⋊C5625C2xC31:C5310,2

Groups of order 311

dρLabelID
C311Cyclic group3111C311311,1

Groups of order 312

dρLabelID
C312Cyclic group3121C312312,6
D156Dihedral group1562+D156312,39
Dic78Dicyclic group; = C392Q83122-Dic78312,37
C13⋊S4The semidirect product of C13 and S4 acting via S4/A4=C2526+C13:S4312,48
D52⋊C3The semidirect product of D52 and C3 acting faithfully526+D52:C3312,10
D13⋊A4The semidirect product of D13 and A4 acting via A4/C22=C3526+D13:A4312,51
D26⋊C62nd semidirect product of D26 and C6 acting faithfully526D26:C6312,12
C13⋊C24The semidirect product of C13 and C24 acting via C24/C2=C1210412-C13:C24312,7
C132C24The semidirect product of C13 and C24 acting via C24/C4=C61046C13:2C24312,1
Dic26⋊C3The semidirect product of Dic26 and C3 acting faithfully1046-Dic26:C3312,8
C39⋊D41st semidirect product of C39 and D4 acting via D4/C2=C221564-C39:D4312,18
C3⋊D52The semidirect product of C3 and D52 acting via D52/D26=C21564+C3:D52312,19
C397D41st semidirect product of C39 and D4 acting via D4/C22=C21562C39:7D4312,41
C13⋊D12The semidirect product of C13 and D12 acting via D12/D6=C21564+C13:D12312,20
C39⋊Q8The semidirect product of C39 and Q8 acting via Q8/C2=C223124-C39:Q8312,21
C393C81st semidirect product of C39 and C8 acting via C8/C4=C23122C39:3C8312,5
C39⋊C81st semidirect product of C39 and C8 acting via C8/C2=C43124C39:C8312,14
C26.A4The non-split extension by C26 of A4 acting via A4/C22=C31046C26.A4312,26
D78.C2The non-split extension by D78 of C2 acting faithfully1564+D78.C2312,17
C2×C156Abelian group of type [2,156]312C2xC156312,42
C22×C78Abelian group of type [2,2,78]312C2^2xC78312,61
C2×F13Direct product of C2 and F13; = Aut(D26) = Hol(C26)2612+C2xF13312,45
C13×S4Direct product of C13 and S4523C13xS4312,47
A4×D13Direct product of A4 and D13526+A4xD13312,50
A4×C26Direct product of C26 and A4783A4xC26312,56
C13×SL2(𝔽3)Direct product of C13 and SL2(𝔽3)1042C13xSL(2,3)312,25
S3×C52Direct product of C52 and S31562S3xC52312,33
C3×D52Direct product of C3 and D521562C3xD52312,29
C4×D39Direct product of C4 and D391562C4xD39312,38
D4×C39Direct product of C39 and D41562D4xC39312,43
C12×D13Direct product of C12 and D131562C12xD13312,28
C13×D12Direct product of C13 and D121562C13xD12312,34
Dic3×D13Direct product of Dic3 and D131564-Dic3xD13312,15
S3×Dic13Direct product of S3 and Dic131564-S3xDic13312,16
C22×D39Direct product of C22 and D39156C2^2xD39312,60
Q8×C39Direct product of C39 and Q83122Q8xC39312,44
C3×Dic26Direct product of C3 and Dic263122C3xDic26312,27
C6×Dic13Direct product of C6 and Dic13312C6xDic13312,30
C13×Dic6Direct product of C13 and Dic63122C13xDic6312,32
Dic3×C26Direct product of C26 and Dic3312Dic3xC26312,35
C2×Dic39Direct product of C2 and Dic39312C2xDic39312,40
S3×C13⋊C4Direct product of S3 and C13⋊C4398+S3xC13:C4312,46
C4×C13⋊C6Direct product of C4 and C13⋊C6526C4xC13:C6312,9
D4×C13⋊C3Direct product of D4 and C13⋊C3526D4xC13:C3312,23
C22×C13⋊C6Direct product of C22 and C13⋊C652C2^2xC13:C6312,49
C6×C13⋊C4Direct product of C6 and C13⋊C4784C6xC13:C4312,52
C2×C13⋊A4Direct product of C2 and C13⋊A4783C2xC13:A4312,57
C2×S3×D13Direct product of C2, S3 and D13784+C2xS3xD13312,54
C2×C39⋊C4Direct product of C2 and C39⋊C4784C2xC39:C4312,53
C8×C13⋊C3Direct product of C8 and C13⋊C31043C8xC13:C3312,2
Q8×C13⋊C3Direct product of Q8 and C13⋊C31046Q8xC13:C3312,24
C2×C26.C6Direct product of C2 and C26.C6104C2xC26.C6312,11
C23×C13⋊C3Direct product of C23 and C13⋊C3104C2^3xC13:C3312,55
S3×C2×C26Direct product of C2×C26 and S3156S3xC2xC26312,59
C2×C6×D13Direct product of C2×C6 and D13156C2xC6xD13312,58
C3×C13⋊D4Direct product of C3 and C13⋊D41562C3xC13:D4312,31
C13×C3⋊D4Direct product of C13 and C3⋊D41562C13xC3:D4312,36
C13×C3⋊C8Direct product of C13 and C3⋊C83122C13xC3:C8312,3
C3×C13⋊C8Direct product of C3 and C13⋊C83124C3xC13:C8312,13
C3×C132C8Direct product of C3 and C132C83122C3xC13:2C8312,4
C2×C4×C13⋊C3Direct product of C2×C4 and C13⋊C3104C2xC4xC13:C3312,22

Groups of order 313

dρLabelID
C313Cyclic group3131C313313,1

Groups of order 314

dρLabelID
C314Cyclic group3141C314314,2
D157Dihedral group1572+D157314,1

Groups of order 315

dρLabelID
C315Cyclic group3151C315315,2
C3×C105Abelian group of type [3,105]315C3xC105315,4
C15×C7⋊C3Direct product of C15 and C7⋊C31053C15xC7:C3315,3
C5×C7⋊C9Direct product of C5 and C7⋊C93153C5xC7:C9315,1

Groups of order 316

dρLabelID
C316Cyclic group3161C316316,2
D158Dihedral group; = C2×D791582+D158316,3
Dic79Dicyclic group; = C79C43162-Dic79316,1
C2×C158Abelian group of type [2,158]316C2xC158316,4

Groups of order 317

dρLabelID
C317Cyclic group3171C317317,1

Groups of order 318

dρLabelID
C318Cyclic group3181C318318,4
D159Dihedral group1592+D159318,3
S3×C53Direct product of C53 and S31592S3xC53318,1
C3×D53Direct product of C3 and D531592C3xD53318,2

Groups of order 319

dρLabelID
C319Cyclic group3191C319319,1

Groups of order 320

dρLabelID
C320Cyclic group3201C320320,2
D160Dihedral group1602+D160320,6
Dic80Dicyclic group; = C51Q643202-Dic80320,8
C24⋊F5The semidirect product of C24 and F5 acting faithfully105+C2^4:F5320,1635
2- 1+4⋊D5The semidirect product of 2- 1+4 and D5 acting faithfully324ES-(2,2):D5320,1582
C23⋊D20The semidirect product of C23 and D20 acting via D20/C5=D4408+C2^3:D20320,368
D201D41st semidirect product of D20 and D4 acting via D4/C2=C22408+D20:1D4320,374
D44D203rd semidirect product of D4 and D20 acting via D20/D10=C2404+D4:4D20320,449
D205D45th semidirect product of D20 and D4 acting via D4/C2=C22404D20:5D4320,704
D40⋊C42nd semidirect product of D40 and C4 acting faithfully408+D40:C4320,1069
C42⋊F51st semidirect product of C42 and F5 acting via F5/C5=C4404+C4^2:F5320,191
C426F53rd semidirect product of C42 and F5 acting via F5/D5=C2404C4^2:6F5320,200
C242F51st semidirect product of C24 and F5 acting via F5/C5=C4404C2^4:2F5320,272
C244F51st semidirect product of C24 and F5 acting via F5/D5=C240C2^4:4F5320,1138
D2018D46th semidirect product of D20 and D4 acting via D4/C22=C2408+D20:18D4320,825
SD16⋊F51st semidirect product of SD16 and F5 acting via F5/D5=C2408SD16:F5320,1073
C242D101st semidirect product of C24 and D10 acting via D10/C5=C22404C2^4:2D10320,659
M4(2)⋊F52nd semidirect product of M4(2) and F5 acting via F5/D5=C2408M4(2):F5320,237
M4(2)⋊3F53rd semidirect product of M4(2) and F5 acting via F5/D5=C2408M4(2):3F5320,238
M4(2)⋊1F51st semidirect product of M4(2) and F5 acting via F5/D5=C2408M4(2):1F5320,1065
C242Dic51st semidirect product of C24 and Dic5 acting via Dic5/C5=C4404C2^4:2Dic5320,94
C423Dic53rd semidirect product of C42 and Dic5 acting via Dic5/C5=C4404C4^2:3Dic5320,103
2+ 1+4⋊D51st semidirect product of 2+ 1+4 and D5 acting via D5/C5=C2408+ES+(2,2):D5320,868
2+ 1+42D52nd semidirect product of 2+ 1+4 and D5 acting via D5/C5=C2408+ES+(2,2):2D5320,871
C80⋊C46th semidirect product of C80 and C4 acting faithfully804C80:C4320,70
C804C44th semidirect product of C80 and C4 acting faithfully804C80:4C4320,185
C805C45th semidirect product of C80 and C4 acting faithfully804C80:5C4320,186
C802C42nd semidirect product of C80 and C4 acting faithfully804C80:2C4320,187
C803C43rd semidirect product of C80 and C4 acting faithfully804C80:3C4320,188
D85F5The semidirect product of D8 and F5 acting through Inn(D8)808-D8:5F5320,1070
D8⋊F54th semidirect product of D8 and F5 acting via F5/D5=C2808-D8:F5320,1071
C167F53rd semidirect product of C16 and F5 acting via F5/D5=C2804C16:7F5320,182
C16⋊F53rd semidirect product of C16 and F5 acting via F5/C5=C4804C16:F5320,183
C164F54th semidirect product of C16 and F5 acting via F5/C5=C4804C16:4F5320,184
D408C42nd semidirect product of D40 and C4 acting via C4/C2=C2804D40:8C4320,76
D401C41st semidirect product of D40 and C4 acting faithfully808+D40:1C4320,245
D4⋊D201st semidirect product of D4 and D20 acting via D20/D10=C280D4:D20320,400
D80⋊C22nd semidirect product of D80 and C2 acting faithfully804+D80:C2320,535
D16⋊D52nd semidirect product of D16 and D5 acting via D5/C5=C2804D16:D5320,538
D20⋊D46th semidirect product of D20 and D4 acting via D4/C2=C2280D20:D4320,783
D8⋊D102nd semidirect product of D8 and D10 acting via D10/C10=C2804+D8:D10320,820
D45D201st semidirect product of D4 and D20 acting through Inn(D4)80D4:5D20320,1226
D85D105th semidirect product of D8 and D10 acting via D10/D5=C2808+D8:5D10320,1446
D86D106th semidirect product of D8 and D10 acting via D10/D5=C2808-D8:6D10320,1447
C16⋊D103rd semidirect product of C16 and D10 acting via D10/C5=C22804+C16:D10320,541
Q165F5The semidirect product of Q16 and F5 acting through Inn(Q16)808+Q16:5F5320,1078
Q16⋊F54th semidirect product of Q16 and F5 acting via F5/D5=C2808+Q16:F5320,1079
D5⋊M5(2)The semidirect product of D5 and M5(2) acting via M5(2)/C2×C8=C2804D5:M5(2)320,1053
C422F52nd semidirect product of C42 and F5 acting via F5/C5=C4804C4^2:2F5320,192
C423F53rd semidirect product of C42 and F5 acting via F5/C5=C4804C4^2:3F5320,201

Full list: Groups of order 320 (1640 groups)

Groups of order 321

dρLabelID
C321Cyclic group3211C321321,1

Groups of order 322

dρLabelID
C322Cyclic group3221C322322,4
D161Dihedral group1612+D161322,3
D7×C23Direct product of C23 and D71612D7xC23322,1
C7×D23Direct product of C7 and D231612C7xD23322,2

Groups of order 323

dρLabelID
C323Cyclic group3231C323323,1

Groups of order 324

dρLabelID
C324Cyclic group3241C324324,2
D162Dihedral group; = C2×D811622+D162324,4
Dic81Dicyclic group; = C81C43242-Dic81324,1
He3⋊D6The semidirect product of He3 and D6 acting faithfully96+He3:D6324,39
C33⋊A4The semidirect product of C33 and A4 acting faithfully94C3^3:A4324,160
C92⋊C4The semidirect product of C92 and C4 acting faithfully184+C9^2:C4324,35
C344C44th semidirect product of C34 and C4 acting faithfully18C3^4:4C4324,164
C32⋊D18The semidirect product of C32 and D18 acting via D18/C3=D61812+C3^2:D18324,37
He35D61st semidirect product of He3 and D6 acting via D6/C3=C221812+He3:5D6324,121
C332A41st semidirect product of C33 and A4 acting via A4/C22=C3183C3^3:2A4324,60
He34Dic3The semidirect product of He3 and Dic3 acting via Dic3/C3=C4186He3:4Dic3324,113
He36D62nd semidirect product of He3 and D6 acting via D6/C3=C2227He3:6D6324,124
C9⋊C36The semidirect product of C9 and C36 acting via C36/C6=C6366C9:C36324,9
He3⋊C12The semidirect product of He3 and C12 acting via C12/C2=C6363He3:C12324,13
C32⋊C36The semidirect product of C32 and C36 acting via C36/C6=C6366C3^2:C36324,7
C34⋊C43rd semidirect product of C34 and C4 acting faithfully36C3^4:C4324,163
He32A42nd semidirect product of He3 and A4 acting via A4/C22=C3369He3:2A4324,55
C33⋊C121st semidirect product of C33 and C12 acting via C12/C2=C6366-C3^3:C12324,14
C325D182nd semidirect product of C32 and D18 acting via D18/C9=C22364C3^2:5D18324,123
C3317D65th semidirect product of C33 and D6 acting via D6/C3=C2236C3^3:17D6324,170
He36Dic32nd semidirect product of He3 and Dic3 acting via Dic3/C6=C2366He3:6Dic3324,104
C322Dic92nd semidirect product of C32 and Dic9 acting via Dic9/C6=S3366C3^2:2Dic9324,20
C33⋊Dic32nd semidirect product of C33 and Dic3 acting via Dic3/C2=S3366-C3^3:Dic3324,22
C323Dic9The semidirect product of C32 and Dic9 acting via Dic9/C9=C4364C3^2:3Dic9324,112
He3⋊A41st semidirect product of He3 and A4 acting via A4/C22=C3549He3:A4324,54
C62⋊C91st semidirect product of C62 and C9 acting via C9/C3=C354C6^2:C9324,59
3- 1+2⋊A41st semidirect product of 3- 1+2 and A4 acting via A4/C22=C3549ES-(3,1):A4324,57
C27⋊A4The semidirect product of C27 and A4 acting via A4/C22=C31083C27:A4324,43
C27⋊C12The semidirect product of C27 and C12 acting via C12/C2=C61086-C27:C12324,12
C334C124th semidirect product of C33 and C12 acting via C12/C2=C6108C3^3:4C12324,98
He3⋊Dic33rd semidirect product of He3 and Dic3 acting via Dic3/C2=S31086-He3:Dic3324,24
C32⋊Dic91st semidirect product of C32 and Dic9 acting via Dic9/C6=S3108C3^2:Dic9324,8
C9⋊Dic9The semidirect product of C9 and Dic9 acting via Dic9/C18=C2324C9:Dic9324,19
C27⋊Dic3The semidirect product of C27 and Dic3 acting via Dic3/C6=C2324C27:Dic3324,21
C348C44th semidirect product of C34 and C4 acting via C4/C2=C2324C3^4:8C4324,158
C325Dic92nd semidirect product of C32 and Dic9 acting via Dic9/C18=C2324C3^2:5Dic9324,103
He3.D61st non-split extension by He3 of D6 acting faithfully276+He3.D6324,40
He3.2D62nd non-split extension by He3 of D6 acting faithfully276+He3.2D6324,41
He3.6D6The non-split extension by He3 of D6 acting via D6/C3=C22276+He3.6D6324,125
C62.6C326th non-split extension by C62 of C32 acting faithfully369C6^2.6C3^2324,58
He3.A4The non-split extension by He3 of A4 acting via A4/C22=C3549He3.A4324,53
He3.2A4The non-split extension by He3 of A4 acting through Inn(He3)549He3.2A4324,129
C62.C92nd non-split extension by C62 of C9 acting via C9/C3=C3543C6^2.C9324,45
He3.3C12The non-split extension by He3 of C12 acting via C12/C3=C4543He3.3C12324,111
C62.C324th non-split extension by C62 of C32 acting faithfully549C6^2.C3^2324,56
C62.9C329th non-split extension by C62 of C32 acting faithfully549C6^2.9C3^2324,132
C62.13C324th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.13C3^2324,49
C62.14C325th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.14C3^2324,50
C62.15C326th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.15C3^2324,51
C62.25C3216th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.25C3^2324,128
He3.C121st non-split extension by He3 of C12 acting via C12/C2=C61083He3.C12324,15
He3.2C122nd non-split extension by He3 of C12 acting via C12/C2=C61083He3.2C12324,17
He3.5C12The non-split extension by He3 of C12 acting via C12/C6=C21083He3.5C12324,102
He3.Dic31st non-split extension by He3 of Dic3 acting via Dic3/C2=S31086-He3.Dic3324,16
He3.2Dic32nd non-split extension by He3 of Dic3 acting via Dic3/C2=S31086-He3.2Dic3324,18
He3.3Dic33rd non-split extension by He3 of Dic3 acting via Dic3/C2=S31086-He3.3Dic3324,23
He3.4Dic3The non-split extension by He3 of Dic3 acting via Dic3/C6=C21086-He3.4Dic3324,101
C33.Dic34th non-split extension by C33 of Dic3 acting via Dic3/C2=S3108C3^3.Dic3324,100
C62.16C327th non-split extension by C62 of C32 acting via C32/C3=C3108C6^2.16C3^2324,52
3- 1+2.Dic3The non-split extension by 3- 1+2 of Dic3 acting via Dic3/C2=S31086-ES-(3,1).Dic3324,25
C27.A4The central extension by C27 of A41623C27.A4324,3
C62.11C322nd non-split extension by C62 of C32 acting via C32/C3=C3162C6^2.11C3^2324,47
C62.12C323rd non-split extension by C62 of C32 acting via C32/C3=C3162C6^2.12C3^2324,48
C182Abelian group of type [18,18]324C18^2324,81
C9×C36Abelian group of type [9,36]324C9xC36324,26
C6×C54Abelian group of type [6,54]324C6xC54324,84
C2×C162Abelian group of type [2,162]324C2xC162324,5
C3×C108Abelian group of type [3,108]324C3xC108324,29
C32×C36Abelian group of type [3,3,36]324C3^2xC36324,105
C33×C12Abelian group of type [3,3,3,12]324C3^3xC12324,159
C32×C62Abelian group of type [3,3,6,6]324C3^2xC6^2324,176
C3×C6×C18Abelian group of type [3,6,18]324C3xC6xC18324,151
D92Direct product of D9 and D9184+D9^2324,36
D9×C18Direct product of C18 and D9362D9xC18324,61
A4×He3Direct product of A4 and He3369A4xHe3324,130
C9×Dic9Direct product of C9 and Dic9362C9xDic9324,6
Dic3×He3Direct product of Dic3 and He3366Dic3xHe3324,93
A4×3- 1+2Direct product of A4 and 3- 1+2369A4xES-(3,1)324,131
Dic3×3- 1+2Direct product of Dic3 and 3- 1+2366Dic3xES-(3,1)324,95
S3×D27Direct product of S3 and D27544+S3xD27324,38
S3×C54Direct product of C54 and S31082S3xC54324,66
A4×C27Direct product of C27 and A41083A4xC27324,42
C6×D27Direct product of C6 and D271082C6xD27324,65
C12×He3Direct product of C12 and He3108C12xHe3324,106
A4×C33Direct product of C33 and A4108A4xC3^3324,171
C3×Dic27Direct product of C3 and Dic271082C3xDic27324,10
Dic3×C27Direct product of C27 and Dic31082Dic3xC27324,11
C32×Dic9Direct product of C32 and Dic9108C3^2xDic9324,90
Dic3×C33Direct product of C33 and Dic3108Dic3xC3^3324,155
C12×3- 1+2Direct product of C12 and 3- 1+2108C12xES-(3,1)324,107
C3×C33⋊C4Direct product of C3 and C33⋊C4; = AΣL1(𝔽81)124C3xC3^3:C4324,162
C3×C324D6Direct product of C3 and C324D6124C3xC3^2:4D6324,167
S3×C9⋊C6Direct product of S3 and C9⋊C61812+S3xC9:C6324,118
C2×C3≀S3Direct product of C2 and C3≀S3183C2xC3wrS3324,68
S3×C32⋊C6Direct product of S3 and C32⋊C61812+S3xC3^2:C6324,116
S3×He3⋊C2Direct product of S3 and He3⋊C2186S3xHe3:C2324,122
C3×C32⋊D6Direct product of C3 and C32⋊D6186C3xC3^2:D6324,117
C2×C33⋊C6Direct product of C2 and C33⋊C6186+C2xC3^3:C6324,69
C2×C33⋊S3Direct product of C2 and C33⋊S3186+C2xC3^3:S3324,77
S32×C9Direct product of C9, S3 and S3364S3^2xC9324,115
C3×S3×D9Direct product of C3, S3 and D9364C3xS3xD9324,114
C6×C9⋊C6Direct product of C6 and C9⋊C6366C6xC9:C6324,140
C4×C3≀C3Direct product of C4 and C3≀C3363C4xC3wrC3324,31
C2×C9⋊C18Direct product of C2 and C9⋊C18366C2xC9:C18324,64
C3×C9⋊C12Direct product of C3 and C9⋊C12366C3xC9:C12324,94
C2×S3×He3Direct product of C2, S3 and He3366C2xS3xHe3324,139
S32×C32Direct product of C32, S3 and S336S3^2xC3^2324,165
C9×C32⋊C4Direct product of C9 and C32⋊C4364C9xC3^2:C4324,109
C6×C32⋊C6Direct product of C6 and C32⋊C6366C6xC3^2:C6324,138
C22×C3≀C3Direct product of C22 and C3≀C336C2^2xC3wrC3324,86
C2×C32⋊C18Direct product of C2 and C32⋊C18366C2xC3^2:C18324,62
C3×C32⋊C12Direct product of C3 and C32⋊C12366C3xC3^2:C12324,92
C32×C32⋊C4Direct product of C32 and C32⋊C436C3^2xC3^2:C4324,161
C2×He35S3Direct product of C2 and He35S3366C2xHe3:5S3324,150
C2×C322D9Direct product of C2 and C322D9366C2xC3^2:2D9324,75
C32×C3⋊Dic3Direct product of C32 and C3⋊Dic336C3^2xC3:Dic3324,156
C2×S3×3- 1+2Direct product of C2, S3 and 3- 1+2366C2xS3xES-(3,1)324,141
S3×C9⋊S3Direct product of S3 and C9⋊S354S3xC9:S3324,120
D9×C3⋊S3Direct product of D9 and C3⋊S354D9xC3:S3324,119
C2×C27⋊C6Direct product of C2 and C27⋊C6546+C2xC27:C6324,67
C3×He3⋊C4Direct product of C3 and He3⋊C454C3xHe3:C4324,110
C3×C32⋊A4Direct product of C3 and C32⋊A454C3xC3^2:A4324,135
C6×He3⋊C2Direct product of C6 and He3⋊C254C6xHe3:C2324,145
S3×C33⋊C2Direct product of S3 and C33⋊C254S3xC3^3:C2324,168
C2×He3⋊S3Direct product of C2 and He3⋊S3546+C2xHe3:S3324,79
C2×C32⋊D9Direct product of C2 and C32⋊D954C2xC3^2:D9324,63
C3×C32.A4Direct product of C3 and C32.A454C3xC3^2.A4324,134
C2×He34S3Direct product of C2 and He34S354C2xHe3:4S3324,144
C2×He3.C6Direct product of C2 and He3.C6543C2xHe3.C6324,70
C2×He3.S3Direct product of C2 and He3.S3546+C2xHe3.S3324,71
C2×C33.S3Direct product of C2 and C33.S354C2xC3^3.S3324,146
C2×He3.2C6Direct product of C2 and He3.2C6543C2xHe3.2C6324,72
C2×He3.2S3Direct product of C2 and He3.2S3546+C2xHe3.2S3324,73
C2×He3.3S3Direct product of C2 and He3.3S3546+C2xHe3.3S3324,78
C2×He3.4S3Direct product of C2 and He3.4S3546+C2xHe3.4S3324,147
C2×He3.4C6Direct product of C2 and He3.4C6543C2xHe3.4C6324,148
C2×3- 1+2.S3Direct product of C2 and 3- 1+2.S3546+C2xES-(3,1).S3324,80
A4×C3×C9Direct product of C3×C9 and A4108A4xC3xC9324,126
D9×C3×C6Direct product of C3×C6 and D9108D9xC3xC6324,136
C6×C9⋊S3Direct product of C6 and C9⋊S3108C6xC9:S3324,142
C3×C9⋊A4Direct product of C3 and C9⋊A4108C3xC9:A4324,127
S3×C3×C18Direct product of C3×C18 and S3108S3xC3xC18324,137
C4×C27⋊C3Direct product of C4 and C27⋊C31083C4xC27:C3324,30
C2×C6×He3Direct product of C2×C6 and He3108C2xC6xHe3324,152
C18×C3⋊S3Direct product of C18 and C3⋊S3108C18xC3:S3324,143
S3×C32×C6Direct product of C32×C6 and S3108S3xC3^2xC6324,172
Dic3×C3×C9Direct product of C3×C9 and Dic3108Dic3xC3xC9324,91
C4×C32⋊C9Direct product of C4 and C32⋊C9108C4xC3^2:C9324,27
C4×C9○He3Direct product of C4 and C9○He31083C4xC9oHe3324,108
C3×C9⋊Dic3Direct product of C3 and C9⋊Dic3108C3xC9:Dic3324,96
C9×C3⋊Dic3Direct product of C9 and C3⋊Dic3108C9xC3:Dic3324,97
C6×C33⋊C2Direct product of C6 and C33⋊C2108C6xC3^3:C2324,174
C22×C27⋊C3Direct product of C22 and C27⋊C3108C2^2xC27:C3324,85
C4×He3⋊C3Direct product of C4 and He3⋊C31083C4xHe3:C3324,33
C3×He33C4Direct product of C3 and He33C4108C3xHe3:3C4324,99
C3×C335C4Direct product of C3 and C335C4108C3xC3^3:5C4324,157
C4×He3.C3Direct product of C4 and He3.C31083C4xHe3.C3324,32
C4×C3.He3Direct product of C4 and C3.He31083C4xC3.He3324,34
C22×C32⋊C9Direct product of C22 and C32⋊C9108C2^2xC3^2:C9324,82
C22×C9○He3Direct product of C22 and C9○He3108C2^2xC9oHe3324,154
C2×C6×3- 1+2Direct product of C2×C6 and 3- 1+2108C2xC6xES-(3,1)324,153
C22×He3⋊C3Direct product of C22 and He3⋊C3108C2^2xHe3:C3324,88
C22×He3.C3Direct product of C22 and He3.C3108C2^2xHe3.C3324,87
C22×C3.He3Direct product of C22 and C3.He3108C2^2xC3.He3324,89
C2×C9⋊D9Direct product of C2 and C9⋊D9162C2xC9:D9324,74
C2×C27⋊S3Direct product of C2 and C27⋊S3162C2xC27:S3324,76
C3×C9.A4Direct product of C3 and C9.A4162C3xC9.A4324,44
C9×C3.A4Direct product of C9 and C3.A4162C9xC3.A4324,46
C2×C34⋊C2Direct product of C2 and C34⋊C2162C2xC3^4:C2324,175
C32×C3.A4Direct product of C32 and C3.A4162C3^2xC3.A4324,133
C2×C324D9Direct product of C2 and C324D9162C2xC3^2:4D9324,149
C4×C9⋊C9Direct product of C4 and C9⋊C9324C4xC9:C9324,28
C22×C9⋊C9Direct product of C22 and C9⋊C9324C2^2xC9:C9324,83
C3⋊S32Direct product of C3⋊S3 and C3⋊S318C3:S3^2324,169
C3×S3×C3⋊S3Direct product of C3, S3 and C3⋊S336C3xS3xC3:S3324,166
C3⋊S3×C3×C6Direct product of C3×C6 and C3⋊S336C3:S3xC3xC6324,173

Groups of order 325

dρLabelID
C325Cyclic group3251C325325,1
C5×C65Abelian group of type [5,65]325C5xC65325,2

Groups of order 326

dρLabelID
C326Cyclic group3261C326326,2
D163Dihedral group1632+D163326,1

Groups of order 327

dρLabelID
C327Cyclic group3271C327327,2
C109⋊C3The semidirect product of C109 and C3 acting faithfully1093C109:C3327,1

Groups of order 328

dρLabelID
C328Cyclic group3281C328328,2
D164Dihedral group1642+D164328,6
Dic82Dicyclic group; = C41Q83282-Dic82328,4
C41⋊C8The semidirect product of C41 and C8 acting faithfully418+C41:C8328,12
C41⋊D4The semidirect product of C41 and D4 acting via D4/C22=C21642C41:D4328,8
C413C8The semidirect product of C41 and C8 acting via C8/C4=C23282C41:3C8328,1
C412C8The semidirect product of C41 and C8 acting via C8/C2=C43284-C41:2C8328,3
C2×C164Abelian group of type [2,164]328C2xC164328,9
C22×C82Abelian group of type [2,2,82]328C2^2xC82328,15
C4×D41Direct product of C4 and D411642C4xD41328,5
D4×C41Direct product of C41 and D41642D4xC41328,10
C22×D41Direct product of C22 and D41164C2^2xD41328,14
Q8×C41Direct product of C41 and Q83282Q8xC41328,11
C2×Dic41Direct product of C2 and Dic41328C2xDic41328,7
C2×C41⋊C4Direct product of C2 and C41⋊C4824+C2xC41:C4328,13

Groups of order 329

dρLabelID
C329Cyclic group3291C329329,1

Groups of order 330

dρLabelID
C330Cyclic group3301C330330,12
D165Dihedral group1652+D165330,11
C3⋊F11The semidirect product of C3 and F11 acting via F11/C11⋊C5=C23310+C3:F11330,3
C3×F11Direct product of C3 and F113310C3xF11330,1
S3×C55Direct product of C55 and S31652S3xC55330,8
D5×C33Direct product of C33 and D51652D5xC33330,6
C3×D55Direct product of C3 and D551652C3xD55330,7
C5×D33Direct product of C5 and D331652C5xD33330,9
C15×D11Direct product of C15 and D111652C15xD11330,5
C11×D15Direct product of C11 and D151652C11xD15330,10
S3×C11⋊C5Direct product of S3 and C11⋊C53310S3xC11:C5330,2
C6×C11⋊C5Direct product of C6 and C11⋊C5665C6xC11:C5330,4

Groups of order 331

dρLabelID
C331Cyclic group3311C331331,1

Groups of order 332

dρLabelID
C332Cyclic group3321C332332,2
D166Dihedral group; = C2×D831662+D166332,3
Dic83Dicyclic group; = C83C43322-Dic83332,1
C2×C166Abelian group of type [2,166]332C2xC166332,4

Groups of order 333

dρLabelID
C333Cyclic group3331C333333,2
C37⋊C9The semidirect product of C37 and C9 acting faithfully379C37:C9333,3
C372C9The semidirect product of C37 and C9 acting via C9/C3=C33333C37:2C9333,1
C3×C111Abelian group of type [3,111]333C3xC111333,5
C3×C37⋊C3Direct product of C3 and C37⋊C31113C3xC37:C3333,4

Groups of order 334

dρLabelID
C334Cyclic group3341C334334,2
D167Dihedral group1672+D167334,1

Groups of order 335

dρLabelID
C335Cyclic group3351C335335,1

Groups of order 336

dρLabelID
C336Cyclic group3361C336336,6
D168Dihedral group1682+D168336,93
Dic84Dicyclic group; = C214Q163362-Dic84336,94
SL2(𝔽7)Special linear group on 𝔽72; = C2.GL3(𝔽2)164SL(2,7)336,114
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simple86+PGL(2,7)336,208
D56⋊C3The semidirect product of D56 and C3 acting faithfully566+D56:C3336,10
D4⋊F7The semidirect product of D4 and F7 acting via F7/C7⋊C3=C25612+D4:F7336,18
Q8⋊F7The semidirect product of Q8 and F7 acting via F7/D7=C35612-Q8:F7336,135
Q8⋊D21The semidirect product of Q8 and D21 acting via D21/C7=S3564+Q8:D21336,119
C8⋊F73rd semidirect product of C8 and F7 acting via F7/C7⋊C3=C2566C8:F7336,8
C56⋊C62nd semidirect product of C56 and C6 acting faithfully566C56:C6336,9
D14⋊C12The semidirect product of D14 and C12 acting via C12/C2=C656D14:C12336,17
D42F7The semidirect product of D4 and F7 acting through Inn(D4)5612-D4:2F7336,126
Q82F7The semidirect product of Q8 and F7 acting via F7/C7⋊C3=C25612+Q8:2F7336,20
Q83F7The semidirect product of Q8 and F7 acting through Inn(Q8)5612+Q8:3F7336,128
D286C62nd semidirect product of D28 and C6 acting via C6/C2=C3566D28:6C6336,124
C28⋊D62nd semidirect product of C28 and D6 acting via D6/C3=C22844C28:D6336,150
A4⋊Dic7The semidirect product of A4 and Dic7 acting via Dic7/C14=C2846-A4:Dic7336,120
Dic7⋊A4The semidirect product of Dic7 and A4 acting via A4/C22=C3846-Dic7:A4336,136
D6⋊D144th semidirect product of D6 and D14 acting via D14/D7=C2844+D6:D14336,163
C7⋊C48The semidirect product of C7 and C48 acting via C48/C8=C61126C7:C48336,1
C28⋊C121st semidirect product of C28 and C12 acting via C12/C2=C6112C28:C12336,16
Dic7⋊C12The semidirect product of Dic7 and C12 acting via C12/C2=C6112Dic7:C12336,15
D21⋊C8The semidirect product of D21 and C8 acting via C8/C4=C21684D21:C8336,25
D4⋊D21The semidirect product of D4 and D21 acting via D21/C21=C21684+D4:D21336,101
C21⋊D81st semidirect product of C21 and D8 acting via D8/C4=C221684C21:D8336,29
C3⋊D56The semidirect product of C3 and D56 acting via D56/D28=C21684+C3:D56336,30
C7⋊D24The semidirect product of C7 and D24 acting via D24/D12=C21684+C7:D24336,31
D21⋊Q8The semidirect product of D21 and Q8 acting via Q8/C4=C21684D21:Q8336,143
C56⋊S34th semidirect product of C56 and S3 acting via S3/C3=C21682C56:S3336,91
C8⋊D212nd semidirect product of C8 and D21 acting via D21/C21=C21682C8:D21336,92
D6⋊Dic7The semidirect product of D6 and Dic7 acting via Dic7/C14=C2168D6:Dic7336,43
D42⋊C42nd semidirect product of D42 and C4 acting via C4/C2=C2168D42:C4336,44
D285S3The semidirect product of D28 and S3 acting through Inn(D28)1684-D28:5S3336,138
D28⋊S33rd semidirect product of D28 and S3 acting via S3/C3=C21684D28:S3336,139
D12⋊D73rd semidirect product of D12 and D7 acting via D7/C7=C21684D12:D7336,141
D84⋊C26th semidirect product of D84 and C2 acting faithfully1684+D84:C2336,142
D125D7The semidirect product of D12 and D7 acting through Inn(D12)1684-D12:5D7336,145
D42D21The semidirect product of D4 and D21 acting through Inn(D4)1684-D4:2D21336,199
D14⋊Dic3The semidirect product of D14 and Dic3 acting via Dic3/C6=C2168D14:Dic3336,42
Q82D21The semidirect product of Q8 and D21 acting via D21/C21=C21684+Q8:2D21336,103
Q83D21The semidirect product of Q8 and D21 acting through Inn(Q8)1684+Q8:3D21336,201
C21⋊SD164th semidirect product of C21 and SD16 acting via SD16/C4=C221684+C21:SD16336,35
D8411C2The semidirect product of D84 and C2 acting through Inn(D84)1682D84:11C2336,197
Dic6⋊D71st semidirect product of Dic6 and D7 acting via D7/C7=C21684+Dic6:D7336,37
C84⋊C41st semidirect product of C84 and C4 acting via C4/C2=C2336C84:C4336,99
C21⋊C161st semidirect product of C21 and C16 acting via C16/C8=C23362C21:C16336,5
C21⋊Q161st semidirect product of C21 and Q16 acting via Q16/C4=C223364C21:Q16336,38
C217Q161st semidirect product of C21 and Q16 acting via Q16/Q8=C23364-C21:7Q16336,104
C3⋊Dic28The semidirect product of C3 and Dic28 acting via Dic28/Dic14=C23364-C3:Dic28336,39
C7⋊Dic12The semidirect product of C7 and Dic12 acting via Dic12/Dic6=C23364-C7:Dic12336,40
Dic21⋊C43rd semidirect product of Dic21 and C4 acting via C4/C2=C2336Dic21:C4336,46
C42⋊(C7⋊C3)The semidirect product of C42 and C7⋊C3 acting via C7⋊C3/C7=C3843C4^2:(C7:C3)336,57
C7⋊(C22⋊A4)The semidirect product of C7 and C22⋊A4 acting via C22⋊A4/C24=C384C7:(C2^2:A4)336,224
D4.F7The non-split extension by D4 of F7 acting via F7/C7⋊C3=C25612-D4.F7336,19
C28.C121st non-split extension by C28 of C12 acting via C12/C2=C6566C28.C12336,13
C23.2F7The non-split extension by C23 of F7 acting via F7/C7⋊C3=C256C2^3.2F7336,22
C8.F7The non-split extension by C8 of F7 acting via F7/C7⋊C3=C21126-C8.F7336,11
C28.A4The non-split extension by C28 of A4 acting via A4/C22=C31126C28.A4336,173
Q8.F7The non-split extension by Q8 of F7 acting via F7/D7=C311212+Q8.F7336,134
Q8.D21The non-split extension by Q8 of D21 acting via D21/C7=S31124-Q8.D21336,118
Q8.2F7The non-split extension by Q8 of F7 acting via F7/C7⋊C3=C211212-Q8.2F7336,21
Dic7.2A4The non-split extension by Dic7 of A4 acting through Inn(Dic7)1124+Dic7.2A4336,131
D4.D21The non-split extension by D4 of D21 acting via D21/C21=C21684-D4.D21336,102
C84.C41st non-split extension by C84 of C4 acting via C4/C2=C21682C84.C4336,96
C28.D63rd non-split extension by C28 of D6 acting via D6/C3=C221684C28.D6336,32
C42.D45th non-split extension by C42 of D4 acting via D4/C2=C221684C42.D4336,33
C6.D282nd non-split extension by C6 of D28 acting via D28/D14=C21684-C6.D28336,34
C2.D842nd central extension by C2 of D84168C2.D84336,100
D6.Dic7The non-split extension by D6 of Dic7 acting via Dic7/C14=C21684D6.Dic7336,27
D42.C43rd non-split extension by D42 of C4 acting via C4/C2=C21684D42.C4336,28
D12.D71st non-split extension by D12 of D7 acting via D7/C7=C21684-D12.D7336,36
D6.D143rd non-split extension by D6 of D14 acting via D14/C14=C21684D6.D14336,144
D14.D63rd non-split extension by D14 of D6 acting via D6/C6=C21684+D14.D6336,146
C28.32D611st non-split extension by C28 of D6 acting via D6/S3=C21684C28.32D6336,26
C42.38D47th non-split extension by C42 of D4 acting via D4/C22=C2168C42.38D4336,105
Dic7.D65th non-split extension by Dic7 of D6 acting via D6/S3=C21684Dic7.D6336,152
C42.C2317th non-split extension by C42 of C23 acting via C23/C2=C221684-C42.C2^3336,153
Dic3.D146th non-split extension by Dic3 of D14 acting via D14/D7=C21684Dic3.D14336,155
C42.Q81st non-split extension by C42 of Q8 acting via Q8/C2=C22336C42.Q8336,45
C42.4Q81st non-split extension by C42 of Q8 acting via Q8/C4=C2336C42.4Q8336,98
C14.Dic63rd non-split extension by C14 of Dic6 acting via Dic6/Dic3=C2336C14.Dic6336,47
C4×C84Abelian group of type [4,84]336C4xC84336,106
C2×C168Abelian group of type [2,168]336C2xC168336,109
C22×C84Abelian group of type [2,2,84]336C2^2xC84336,204
C23×C42Abelian group of type [2,2,2,42]336C2^3xC42336,228
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)143C2xGL(3,2)336,209
C2×AΓL1(𝔽8)Direct product of C2 and AΓL1(𝔽8)147+C2xAGammaL(1,8)336,210
S3×F8Direct product of S3 and F82414+S3xF8336,211
D7×S4Direct product of D7 and S4286+D7xS4336,212
D4×F7Direct product of D4 and F7; = Aut(D28) = Hol(C28)2812+D4xF7336,125
C6×F8Direct product of C6 and F8427C6xF8336,213
C14×S4Direct product of C14 and S4423C14xS4336,214
C8×F7Direct product of C8 and F7566C8xF7336,7
Q8×F7Direct product of Q8 and F75612-Q8xF7336,127
C23×F7Direct product of C23 and F756C2^3xF7336,216
C7×GL2(𝔽3)Direct product of C7 and GL2(𝔽3)562C7xGL(2,3)336,116
D7×SL2(𝔽3)Direct product of D7 and SL2(𝔽3)564-D7xSL(2,3)336,132
A4×C28Direct product of C28 and A4843A4xC28336,168
D7×D12Direct product of D7 and D12844+D7xD12336,148
S3×D28Direct product of S3 and D28844+S3xD28336,149
D4×D21Direct product of D4 and D21844+D4xD21336,198
A4×Dic7Direct product of A4 and Dic7846-A4xDic7336,133
C7×CSU2(𝔽3)Direct product of C7 and CSU2(𝔽3)1122C7xCSU(2,3)336,115
C14×SL2(𝔽3)Direct product of C14 and SL2(𝔽3)112C14xSL(2,3)336,169
S3×C56Direct product of C56 and S31682S3xC56336,74
D7×C24Direct product of C24 and D71682D7xC24336,58
C3×D56Direct product of C3 and D561682C3xD56336,61
C7×D24Direct product of C7 and D241682C7xD24336,77
C8×D21Direct product of C8 and D211682C8xD21336,90
D8×C21Direct product of C21 and D81682D8xC21336,111
C6×D28Direct product of C6 and D28168C6xD28336,176
C2×D84Direct product of C2 and D84168C2xD84336,196
D4×C42Direct product of C42 and D4168D4xC42336,205
Q8×D21Direct product of Q8 and D211684-Q8xD21336,200
C14×D12Direct product of C14 and D12168C14xD12336,186
D7×Dic6Direct product of D7 and Dic61684-D7xDic6336,137
SD16×C21Direct product of C21 and SD161682SD16xC21336,112
S3×Dic14Direct product of S3 and Dic141684-S3xDic14336,140
C23×D21Direct product of C23 and D21168C2^3xD21336,227
M4(2)×C21Direct product of C21 and M4(2)1682M4(2)xC21336,110
Q8×C42Direct product of C42 and Q8336Q8xC42336,206
Q16×C21Direct product of C21 and Q163362Q16xC21336,113
C3×Dic28Direct product of C3 and Dic283362C3xDic28336,62
C12×Dic7Direct product of C12 and Dic7336C12xDic7336,65
C7×Dic12Direct product of C7 and Dic123362C7xDic12336,78
Dic3×C28Direct product of C28 and Dic3336Dic3xC28336,81
C4×Dic21Direct product of C4 and Dic21336C4xDic21336,97
C6×Dic14Direct product of C6 and Dic14336C6xDic14336,174
C14×Dic6Direct product of C14 and Dic6336C14xDic6336,184
C2×Dic42Direct product of C2 and Dic42336C2xDic42336,194
Dic3×Dic7Direct product of Dic3 and Dic7336Dic3xDic7336,41
C22×Dic21Direct product of C22 and Dic21336C2^2xDic21336,202
C2×C7⋊S4Direct product of C2 and C7⋊S4426+C2xC7:S4336,215
C2×A4×D7Direct product of C2, A4 and D7426+C2xA4xD7336,217
C2×D7⋊A4Direct product of C2 and D7⋊A4426+C2xD7:A4336,218
D8×C7⋊C3Direct product of D8 and C7⋊C3566D8xC7:C3336,53
C2×C4×F7Direct product of C2×C4 and F756C2xC4xF7336,122
C2×C4⋊F7Direct product of C2 and C4⋊F756C2xC4:F7336,123
SD16×C7⋊C3Direct product of SD16 and C7⋊C3566SD16xC7:C3336,54
M4(2)×C7⋊C3Direct product of M4(2) and C7⋊C3566M4(2)xC7:C3336,52
C2×Dic7⋊C6Direct product of C2 and Dic7⋊C656C2xDic7:C6336,130
C4×C7⋊A4Direct product of C4 and C7⋊A4843C4xC7:A4336,171
C4×S3×D7Direct product of C4, S3 and D7844C4xS3xD7336,147
C3×D4×D7Direct product of C3, D4 and D7844C3xD4xD7336,178
S3×C7×D4Direct product of C7, S3 and D4844S3xC7xD4336,188
A4×C2×C14Direct product of C2×C14 and A484A4xC2xC14336,221
D7×C3⋊D4Direct product of D7 and C3⋊D4844D7xC3:D4336,161
S3×C7⋊D4Direct product of S3 and C7⋊D4844S3xC7:D4336,162
C7×A4⋊C4Direct product of C7 and A4⋊C4843C7xA4:C4336,117
C7×C42⋊C3Direct product of C7 and C42⋊C3843C7xC4^2:C3336,56
C22×C7⋊A4Direct product of C22 and C7⋊A484C2^2xC7:A4336,222
C22×S3×D7Direct product of C22, S3 and D784C2^2xS3xD7336,219
C7×C22⋊A4Direct product of C7 and C22⋊A484C7xC2^2:A4336,223
C16×C7⋊C3Direct product of C16 and C7⋊C31123C16xC7:C3336,2
C2×C7⋊C24Direct product of C2 and C7⋊C24112C2xC7:C24336,12
C4×C7⋊C12Direct product of C4 and C7⋊C12112C4xC7:C12336,14
Q16×C7⋊C3Direct product of Q16 and C7⋊C31126Q16xC7:C3336,55
C7×C4.A4Direct product of C7 and C4.A41122C7xC4.A4336,170
C42×C7⋊C3Direct product of C42 and C7⋊C3112C4^2xC7:C3336,48
C24×C7⋊C3Direct product of C24 and C7⋊C3112C2^4xC7:C3336,220
C2×C4.F7Direct product of C2 and C4.F7112C2xC4.F7336,121
C2×C14.A4Direct product of C2 and C14.A4112C2xC14.A4336,172
C22×C7⋊C12Direct product of C22 and C7⋊C12112C2^2xC7:C12336,129
S3×C7⋊C8Direct product of S3 and C7⋊C81684S3xC7:C8336,24
D7×C3⋊C8Direct product of D7 and C3⋊C81684D7xC3:C8336,23
C3×Q8×D7Direct product of C3, Q8 and D71684C3xQ8xD7336,180
S3×C7×Q8Direct product of C7, S3 and Q81684S3xC7xQ8336,190
S3×C2×C28Direct product of C2×C28 and S3168S3xC2xC28336,185
D7×C2×C12Direct product of C2×C12 and D7168D7xC2xC12336,175
C2×C4×D21Direct product of C2×C4 and D21168C2xC4xD21336,195
C6×C7⋊D4Direct product of C6 and C7⋊D4168C6xC7:D4336,183
C7×C8⋊S3Direct product of C7 and C8⋊S31682C7xC8:S3336,75
C3×D4⋊D7Direct product of C3 and D4⋊D71684C3xD4:D7336,69
C7×D6⋊C4Direct product of C7 and D6⋊C4168C7xD6:C4336,84
C7×D4⋊S3Direct product of C7 and D4⋊S31684C7xD4:S3336,85
C3×C8⋊D7Direct product of C3 and C8⋊D71682C3xC8:D7336,59
C2×C21⋊D4Direct product of C2 and C21⋊D4168C2xC21:D4336,157
C2×C3⋊D28Direct product of C2 and C3⋊D28168C2xC3:D28336,158
C2×C7⋊D12Direct product of C2 and C7⋊D12168C2xC7:D12336,159
C14×C3⋊D4Direct product of C14 and C3⋊D4168C14xC3:D4336,193
C3×Q8⋊D7Direct product of C3 and Q8⋊D71684C3xQ8:D7336,71
C2×Dic3×D7Direct product of C2, Dic3 and D7168C2xDic3xD7336,151
C2×S3×Dic7Direct product of C2, S3 and Dic7168C2xS3xDic7336,154
C3×C56⋊C2Direct product of C3 and C56⋊C21682C3xC56:C2336,60
C7×C24⋊C2Direct product of C7 and C24⋊C21682C7xC24:C2336,76
D7×C22×C6Direct product of C22×C6 and D7168D7xC2^2xC6336,225
C3×D14⋊C4Direct product of C3 and D14⋊C4168C3xD14:C4336,68
C2×D21⋊C4Direct product of C2 and D21⋊C4168C2xD21:C4336,156
C3×C4○D28Direct product of C3 and C4○D281682C3xC4oD28336,177
C7×C4○D12Direct product of C7 and C4○D121682C7xC4oD12336,187
C4○D4×C21Direct product of C21 and C4○D41682C4oD4xC21336,207
C2×C217D4Direct product of C2 and C217D4168C2xC21:7D4336,203
C3×D4.D7Direct product of C3 and D4.D71684C3xD4.D7336,70
C7×D4.S3Direct product of C7 and D4.S31684C7xD4.S3336,86
S3×C22×C14Direct product of C22×C14 and S3168S3xC2^2xC14336,226
C7×C6.D4Direct product of C7 and C6.D4168C7xC6.D4336,89
C3×D42D7Direct product of C3 and D42D71684C3xD4:2D7336,179
C7×D42S3Direct product of C7 and D42S31684C7xD4:2S3336,189
C22⋊C4×C21Direct product of C21 and C22⋊C4168C2^2:C4xC21336,107
C7×Q82S3Direct product of C7 and Q82S31684C7xQ8:2S3336,87
C3×Q82D7Direct product of C3 and Q82D71684C3xQ8:2D7336,181
C7×Q83S3Direct product of C7 and Q83S31684C7xQ8:3S3336,191
C3×C4.Dic7Direct product of C3 and C4.Dic71682C3xC4.Dic7336,64
C7×C4.Dic3Direct product of C7 and C4.Dic31682C7xC4.Dic3336,80
C3×C23.D7Direct product of C3 and C23.D7168C3xC2^3.D7336,73
C6×C7⋊C8Direct product of C6 and C7⋊C8336C6xC7:C8336,63
C7×C3⋊C16Direct product of C7 and C3⋊C163362C7xC3:C16336,3
C3×C7⋊C16Direct product of C3 and C7⋊C163362C3xC7:C16336,4
C14×C3⋊C8Direct product of C14 and C3⋊C8336C14xC3:C8336,79
C4⋊C4×C21Direct product of C21 and C4⋊C4336C4:C4xC21336,108
C2×C21⋊Q8Direct product of C2 and C21⋊Q8336C2xC21:Q8336,160
C2×C21⋊C8Direct product of C2 and C21⋊C8336C2xC21:C8336,95
C2×C6×Dic7Direct product of C2×C6 and Dic7336C2xC6xDic7336,182
C3×C7⋊Q16Direct product of C3 and C7⋊Q163364C3xC7:Q16336,72
C7×C3⋊Q16Direct product of C7 and C3⋊Q163364C7xC3:Q16336,88
C3×C4⋊Dic7Direct product of C3 and C4⋊Dic7336C3xC4:Dic7336,67
C7×C4⋊Dic3Direct product of C7 and C4⋊Dic3336C7xC4:Dic3336,83
Dic3×C2×C14Direct product of C2×C14 and Dic3336Dic3xC2xC14336,192
C3×Dic7⋊C4Direct product of C3 and Dic7⋊C4336C3xDic7:C4336,66
C7×Dic3⋊C4Direct product of C7 and Dic3⋊C4336C7xDic3:C4336,82
C2×D4×C7⋊C3Direct product of C2, D4 and C7⋊C356C2xD4xC7:C3336,165
C4○D4×C7⋊C3Direct product of C4○D4 and C7⋊C3566C4oD4xC7:C3336,167
C22⋊C4×C7⋊C3Direct product of C22⋊C4 and C7⋊C356C2^2:C4xC7:C3336,49
C2×C8×C7⋊C3Direct product of C2×C8 and C7⋊C3112C2xC8xC7:C3336,51
C4⋊C4×C7⋊C3Direct product of C4⋊C4 and C7⋊C3112C4:C4xC7:C3336,50
C2×Q8×C7⋊C3Direct product of C2, Q8 and C7⋊C3112C2xQ8xC7:C3336,166
C22×C4×C7⋊C3Direct product of C22×C4 and C7⋊C3112C2^2xC4xC7:C3336,164

Groups of order 337

dρLabelID
C337Cyclic group3371C337337,1

Groups of order 338

dρLabelID
C338Cyclic group3381C338338,2
D169Dihedral group1692+D169338,1
C13⋊D13The semidirect product of C13 and D13 acting via D13/C13=C2169C13:D13338,4
C13×C26Abelian group of type [13,26]338C13xC26338,5
C13×D13Direct product of C13 and D13; = AΣL1(𝔽169)262C13xD13338,3

Groups of order 339

dρLabelID
C339Cyclic group3391C339339,1

Groups of order 340

dρLabelID
C340Cyclic group3401C340340,4
D170Dihedral group; = C2×D851702+D170340,14
Dic85Dicyclic group; = C857C43402-Dic85340,3
C85⋊C43rd semidirect product of C85 and C4 acting faithfully854C85:C4340,6
C852C42nd semidirect product of C85 and C4 acting faithfully854+C85:2C4340,10
C173F5The semidirect product of C17 and F5 acting via F5/D5=C2854C17:3F5340,8
C17⋊F51st semidirect product of C17 and F5 acting via F5/C5=C4854+C17:F5340,9
C2×C170Abelian group of type [2,170]340C2xC170340,15
D5×D17Direct product of D5 and D17854+D5xD17340,11
C17×F5Direct product of C17 and F5854C17xF5340,7
D5×C34Direct product of C34 and D51702D5xC34340,13
C10×D17Direct product of C10 and D171702C10xD17340,12
C17×Dic5Direct product of C17 and Dic53402C17xDic5340,1
C5×Dic17Direct product of C5 and Dic173402C5xDic17340,2
C5×C17⋊C4Direct product of C5 and C17⋊C4854C5xC17:C4340,5

Groups of order 341

dρLabelID
C341Cyclic group3411C341341,1

Groups of order 342

dρLabelID
C342Cyclic group3421C342342,6
D171Dihedral group1712+D171342,5
F19Frobenius group; = C19C18 = AGL1(𝔽19) = Aut(D19) = Hol(C19)1918+F19342,7
D57⋊C3The semidirect product of D57 and C3 acting faithfully576+D57:C3342,11
C3⋊D57The semidirect product of C3 and D57 acting via D57/C57=C2171C3:D57342,17
C57.C6The non-split extension by C57 of C6 acting faithfully1716C57.C6342,1
C3×C114Abelian group of type [3,114]342C3xC114342,18
S3×C57Direct product of C57 and S31142S3xC57342,14
C3×D57Direct product of C3 and D571142C3xD57342,15
D9×C19Direct product of C19 and D91712D9xC19342,3
C9×D19Direct product of C9 and D191712C9xD19342,4
C32×D19Direct product of C32 and D19171C3^2xD19342,13
C2×C19⋊C9Direct product of C2 and C19⋊C9389C2xC19:C9342,8
C3×C19⋊C6Direct product of C3 and C19⋊C6576C3xC19:C6342,9
S3×C19⋊C3Direct product of S3 and C19⋊C3576S3xC19:C3342,10
C6×C19⋊C3Direct product of C6 and C19⋊C31143C6xC19:C3342,12
C3⋊S3×C19Direct product of C19 and C3⋊S3171C3:S3xC19342,16
C2×C192C9Direct product of C2 and C192C93423C2xC19:2C9342,2

Groups of order 343

dρLabelID
C343Cyclic group3431C343343,1
He7Heisenberg group; = C72C7 = 7+ 1+2497He7343,3
7- 1+2Extraspecial group497ES-(7,1)343,4
C73Elementary abelian group of type [7,7,7]343C7^3343,5
C7×C49Abelian group of type [7,49]343C7xC49343,2

Groups of order 344

dρLabelID
C344Cyclic group3441C344344,2
D172Dihedral group1722+D172344,5
Dic86Dicyclic group; = C43Q83442-Dic86344,3
C43⋊D4The semidirect product of C43 and D4 acting via D4/C22=C21722C43:D4344,7
C43⋊C8The semidirect product of C43 and C8 acting via C8/C4=C23442C43:C8344,1
C2×C172Abelian group of type [2,172]344C2xC172344,8
C22×C86Abelian group of type [2,2,86]344C2^2xC86344,12
C4×D43Direct product of C4 and D431722C4xD43344,4
D4×C43Direct product of C43 and D41722D4xC43344,9
C22×D43Direct product of C22 and D43172C2^2xD43344,11
Q8×C43Direct product of C43 and Q83442Q8xC43344,10
C2×Dic43Direct product of C2 and Dic43344C2xDic43344,6

Groups of order 345

dρLabelID
C345Cyclic group3451C345345,1

Groups of order 346

dρLabelID
C346Cyclic group3461C346346,2
D173Dihedral group1732+D173346,1

Groups of order 347

dρLabelID
C347Cyclic group3471C347347,1

Groups of order 348

dρLabelID
C348Cyclic group3481C348348,4
D174Dihedral group; = C2×D871742+D174348,11
Dic87Dicyclic group; = C873C43482-Dic87348,3
C87⋊C41st semidirect product of C87 and C4 acting faithfully874C87:C4348,6
C2×C174Abelian group of type [2,174]348C2xC174348,12
S3×D29Direct product of S3 and D29874+S3xD29348,7
A4×C29Direct product of C29 and A41163A4xC29348,8
S3×C58Direct product of C58 and S31742S3xC58348,10
C6×D29Direct product of C6 and D291742C6xD29348,9
Dic3×C29Direct product of C29 and Dic33482Dic3xC29348,1
C3×Dic29Direct product of C3 and Dic293482C3xDic29348,2
C3×C29⋊C4Direct product of C3 and C29⋊C4874C3xC29:C4348,5

Groups of order 349

dρLabelID
C349Cyclic group3491C349349,1

Groups of order 350

dρLabelID
C350Cyclic group3501C350350,4
D175Dihedral group1752+D175350,3
C5⋊D35The semidirect product of C5 and D35 acting via D35/C35=C2175C5:D35350,9
C5×C70Abelian group of type [5,70]350C5xC70350,10
D5×C35Direct product of C35 and D5702D5xC35350,6
C5×D35Direct product of C5 and D35702C5xD35350,7
C7×D25Direct product of C7 and D251752C7xD25350,1
D7×C25Direct product of C25 and D71752D7xC25350,2
D7×C52Direct product of C52 and D7175D7xC5^2350,5
C7×C5⋊D5Direct product of C7 and C5⋊D5175C7xC5:D5350,8

Groups of order 351

dρLabelID
C351Cyclic group3511C351351,2
C33⋊C13The semidirect product of C33 and C13 acting faithfully2713C3^3:C13351,12
C13⋊He3The semidirect product of C13 and He3 acting via He3/C32=C31173C13:He3351,8
C117⋊C32nd semidirect product of C117 and C3 acting faithfully1173C117:C3351,4
C1173C33rd semidirect product of C117 and C3 acting faithfully1173C117:3C3351,5
C13⋊C27The semidirect product of C13 and C27 acting via C27/C9=C33513C13:C27351,1
C39.C325th non-split extension by C39 of C32 acting via C32/C3=C31173C39.C3^2351,7
C3×C117Abelian group of type [3,117]351C3xC117351,9
C32×C39Abelian group of type [3,3,39]351C3^2xC39351,14
C13×He3Direct product of C13 and He31173C13xHe3351,10
C13×3- 1+2Direct product of C13 and 3- 1+21173C13xES-(3,1)351,11
C9×C13⋊C3Direct product of C9 and C13⋊C31173C9xC13:C3351,3
C32×C13⋊C3Direct product of C32 and C13⋊C3117C3^2xC13:C3351,13
C3×C13⋊C9Direct product of C3 and C13⋊C9351C3xC13:C9351,6

Groups of order 352

dρLabelID
C352Cyclic group3521C352352,2
D176Dihedral group1762+D176352,5
Dic88Dicyclic group; = C111Q323522-Dic88352,7
C8⋊D221st semidirect product of C8 and D22 acting via D22/C11=C22884+C8:D22352,103
D441C41st semidirect product of D44 and C4 acting via C4/C2=C2882D44:1C4352,11
D444C44th semidirect product of D44 and C4 acting via C4/C2=C2884D44:4C4352,31
D4⋊D222nd semidirect product of D4 and D22 acting via D22/D11=C2884D4:D22352,106
D88⋊C26th semidirect product of D88 and C2 acting faithfully884+D88:C2352,109
D46D222nd semidirect product of D4 and D22 acting through Inn(D4)884D4:6D22352,179
D48D224th semidirect product of D4 and D22 acting through Inn(D4)884+D4:8D22352,184
Q8⋊D222nd semidirect product of Q8 and D22 acting via D22/C22=C2884+Q8:D22352,144
C22⋊D44The semidirect product of C22 and D44 acting via D44/D22=C288C2^2:D44352,77
C23⋊D221st semidirect product of C23 and D22 acting via D22/C11=C2288C2^3:D22352,132
C24⋊D111st semidirect product of C24 and D11 acting via D11/C11=C288C2^4:D11352,148
C23⋊Dic11The semidirect product of C23 and Dic11 acting via Dic11/C11=C4884C2^3:Dic11352,40
D446C224th semidirect product of D44 and C22 acting via C22/C2=C2884D44:6C2^2352,127
D22⋊C8The semidirect product of D22 and C8 acting via C8/C4=C2176D22:C8352,26
C4⋊D44The semidirect product of C4 and D44 acting via D44/C44=C2176C4:D44352,69
C42D44The semidirect product of C4 and D44 acting via D44/D22=C2176C4:2D44352,90
C447D41st semidirect product of C44 and D4 acting via D4/C22=C2176C44:7D4352,125
C442D42nd semidirect product of C44 and D4 acting via D4/C2=C22176C44:2D4352,133
C44⋊D43rd semidirect product of C44 and D4 acting via D4/C2=C22176C44:D4352,135
C11⋊D16The semidirect product of C11 and D16 acting via D16/D8=C21764+C11:D16352,32
C176⋊C22nd semidirect product of C176 and C2 acting faithfully1762C176:C2352,6
D22⋊D41st semidirect product of D22 and D4 acting via D4/C4=C2176D22:D4352,79
D44⋊C45th semidirect product of D44 and C4 acting via C4/C2=C2176D44:C4352,88
D887C2The semidirect product of D88 and C2 acting through Inn(D88)1762D88:7C2352,99
D83D11The semidirect product of D8 and D11 acting through Inn(D8)1764-D8:3D11352,107
D885C25th semidirect product of D88 and C2 acting faithfully1764+D88:5C2352,114
D22⋊Q81st semidirect product of D22 and Q8 acting via Q8/C4=C2176D22:Q8352,91
D222Q82nd semidirect product of D22 and Q8 acting via Q8/C4=C2176D22:2Q8352,92
D223Q83rd semidirect product of D22 and Q8 acting via Q8/C4=C2176D22:3Q8352,141
Q16⋊D112nd semidirect product of Q16 and D11 acting via D11/C11=C21764Q16:D11352,113
C42⋊D111st semidirect product of C42 and D11 acting via D11/C11=C2176C4^2:D11352,67
C422D112nd semidirect product of C42 and D11 acting via D11/C11=C2176C4^2:2D11352,71
D4⋊Dic111st semidirect product of D4 and Dic11 acting via Dic11/C22=C2176D4:Dic11352,38
Dic114D41st semidirect product of Dic11 and D4 acting through Inn(Dic11)176Dic11:4D4352,76
Dic11⋊D42nd semidirect product of Dic11 and D4 acting via D4/C22=C2176Dic11:D4352,134
C22⋊Dic22The semidirect product of C22 and Dic22 acting via Dic22/Dic11=C2176C2^2:Dic22352,73
C11⋊C32The semidirect product of C11 and C32 acting via C32/C16=C23522C11:C32352,1
C44⋊Q8The semidirect product of C44 and Q8 acting via Q8/C2=C22352C44:Q8352,83
C44⋊C81st semidirect product of C44 and C8 acting via C8/C4=C2352C44:C8352,10
C88⋊C44th semidirect product of C88 and C4 acting via C4/C2=C2352C88:C4352,21
C442Q81st semidirect product of C44 and Q8 acting via Q8/C4=C2352C44:2Q8352,64
C11⋊Q32The semidirect product of C11 and Q32 acting via Q32/Q16=C23524-C11:Q32352,35
Dic11⋊C8The semidirect product of Dic11 and C8 acting via C8/C4=C2352Dic11:C8352,20
Q8⋊Dic111st semidirect product of Q8 and Dic11 acting via Dic11/C22=C2352Q8:Dic11352,41
Dic22⋊C45th semidirect product of Dic22 and C4 acting via C4/C2=C2352Dic22:C4352,82
Dic11⋊Q82nd semidirect product of Dic11 and Q8 acting via Q8/C4=C2352Dic11:Q8352,139
C4⋊C47D111st semidirect product of C4⋊C4 and D11 acting through Inn(C4⋊C4)176C4:C4:7D11352,87
C4⋊C4⋊D116th semidirect product of C4⋊C4 and D11 acting via D11/C11=C2176C4:C4:D11352,93
C44.D48th non-split extension by C44 of D4 acting via D4/C2=C22884C44.D4352,39
C44.46D43rd non-split extension by C44 of D4 acting via D4/C22=C2884+C44.46D4352,29
C44.56D413rd non-split extension by C44 of D4 acting via D4/C22=C2884C44.56D4352,43
C22.2D441st non-split extension by C22 of D44 acting via D44/D22=C2884C2^2.2D44352,12
D22.C8The non-split extension by D22 of C8 acting via C8/C4=C21762D22.C8352,4
D8.D11The non-split extension by D8 of D11 acting via D11/C11=C21764-D8.D11352,33
D44.C4The non-split extension by D44 of C4 acting via C4/C2=C21764D44.C4352,102
C44.C81st non-split extension by C44 of C8 acting via C8/C4=C21762C44.C8352,18
C88.C41st non-split extension by C88 of C4 acting via C4/C2=C21762C88.C4352,25
C22.D82nd non-split extension by C22 of D8 acting via D8/D4=C2176C22.D8352,15
C2.D882nd central extension by C2 of D88176C2.D88352,27
C8.6D223rd non-split extension by C8 of D22 acting via D22/D11=C21764+C8.6D22352,34
C4.D445th non-split extension by C4 of D44 acting via D44/C44=C2176C4.D44352,70
C8.D221st non-split extension by C8 of D22 acting via D22/C11=C221764-C8.D22352,104
D22.D41st non-split extension by D22 of D4 acting via D4/C22=C2176D22.D4352,78
D22.5D42nd non-split extension by D22 of D4 acting via D4/C22=C2176D22.5D4352,89
D44.2C4The non-split extension by D44 of C4 acting through Inn(D44)1762D44.2C4352,96
D4.D224th non-split extension by D4 of D22 acting via D22/D11=C21764-D4.D22352,110
D4.8D223rd non-split extension by D4 of D22 acting via D22/C22=C21764D4.8D22352,145
D4.9D224th non-split extension by D4 of D22 acting via D22/C22=C21764-D4.9D22352,146
C44.53D410th non-split extension by C44 of D4 acting via D4/C22=C21764C44.53D4352,28
C44.47D44th non-split extension by C44 of D4 acting via D4/C22=C21764-C44.47D4352,30
C44.55D412nd non-split extension by C44 of D4 acting via D4/C22=C2176C44.55D4352,36
C44.10D410th non-split extension by C44 of D4 acting via D4/C2=C221764C44.10D4352,42
C44.48D45th non-split extension by C44 of D4 acting via D4/C22=C2176C44.48D4352,119
C44.17D417th non-split extension by C44 of D4 acting via D4/C2=C22176C44.17D4352,131
C44.23D423rd non-split extension by C44 of D4 acting via D4/C2=C22176C44.23D4352,142
Q8.Dic11The non-split extension by Q8 of Dic11 acting through Inn(Q8)1764Q8.Dic11352,143
Q8.D222nd non-split extension by Q8 of D22 acting via D22/D11=C21764Q8.D22352,111
D4.10D22The non-split extension by D4 of D22 acting through Inn(D4)1764-D4.10D22352,185
Q8.10D221st non-split extension by Q8 of D22 acting through Inn(Q8)1764Q8.10D22352,182
C23.D223rd non-split extension by C23 of D22 acting via D22/C11=C22176C2^3.D22352,74
C22.D443rd non-split extension by C22 of D44 acting via D44/D22=C2176C2^2.D44352,81
C44.C2315th non-split extension by C44 of C23 acting via C23/C2=C221764C44.C2^3352,137
Dic11.D41st non-split extension by Dic11 of D4 acting via D4/C4=C2176Dic11.D4352,80
C23.11D221st non-split extension by C23 of D22 acting via D22/D11=C2176C2^3.11D22352,72
C23.21D222nd non-split extension by C23 of D22 acting via D22/C22=C2176C2^3.21D22352,121
C23.23D224th non-split extension by C23 of D22 acting via D22/C22=C2176C2^3.23D22352,124
C23.18D228th non-split extension by C23 of D22 acting via D22/D11=C2176C2^3.18D22352,130
C44.Q81st non-split extension by C44 of Q8 acting via Q8/C2=C22352C44.Q8352,13
C44.4Q81st non-split extension by C44 of Q8 acting via Q8/C4=C2352C44.4Q8352,23
C44.5Q82nd non-split extension by C44 of Q8 acting via Q8/C4=C2352C44.5Q8352,24
C44.6Q83rd non-split extension by C44 of Q8 acting via Q8/C4=C2352C44.6Q8352,65
C44.3Q83rd non-split extension by C44 of Q8 acting via Q8/C2=C22352C44.3Q8352,85
C44.44D41st non-split extension by C44 of D4 acting via D4/C22=C2352C44.44D4352,22
Dic11.Q8The non-split extension by Dic11 of Q8 acting via Q8/C4=C2352Dic11.Q8352,84
C22.Q162nd non-split extension by C22 of Q16 acting via Q16/Q8=C2352C22.Q16352,16
C22.C425th non-split extension by C22 of C42 acting via C42/C2×C4=C2352C22.C4^2352,37
C4.Dic222nd non-split extension by C4 of Dic22 acting via Dic22/Dic11=C2352C4.Dic22352,14
C42.D111st non-split extension by C42 of D11 acting via D11/C11=C2352C4^2.D11352,9
C4×C88Abelian group of type [4,88]352C4xC88352,45
C2×C176Abelian group of type [2,176]352C2xC176352,58
C22×C88Abelian group of type [2,2,88]352C2^2xC88352,164
C23×C44Abelian group of type [2,2,2,44]352C2^3xC44352,188
C24×C22Abelian group of type [2,2,2,2,22]352C2^4xC22352,195
C2×C4×C44Abelian group of type [2,4,44]352C2xC4xC44352,149
D8×D11Direct product of D8 and D11884+D8xD11352,105
SD16×D11Direct product of SD16 and D11884SD16xD11352,108
M4(2)×D11Direct product of M4(2) and D11884M4(2)xD11352,101
C11×2+ 1+4Direct product of C11 and 2+ 1+4884C11xES+(2,2)352,192
C4×D44Direct product of C4 and D44176C4xD44352,68
C2×D88Direct product of C2 and D88176C2xD88352,98
D4×C44Direct product of C44 and D4176D4xC44352,153
D8×C22Direct product of C22 and D8176D8xC22352,167
C16×D11Direct product of C16 and D111762C16xD11352,3
C11×D16Direct product of C11 and D161762C11xD16352,60
Q16×D11Direct product of Q16 and D111764-Q16xD11352,112
C11×SD32Direct product of C11 and SD321762C11xSD32352,61
D4×Dic11Direct product of D4 and Dic11176D4xDic11352,129
SD16×C22Direct product of C22 and SD16176SD16xC22352,168
C42×D11Direct product of C42 and D11176C4^2xD11352,66
C22×D44Direct product of C22 and D44176C2^2xD44352,175
C24×D11Direct product of C24 and D11176C2^4xD11352,194
C11×M5(2)Direct product of C11 and M5(2)1762C11xM5(2)352,59
M4(2)×C22Direct product of C22 and M4(2)176M4(2)xC22352,165
C11×2- 1+4Direct product of C11 and 2- 1+41764C11xES-(2,2)352,193
Q8×C44Direct product of C44 and Q8352Q8xC44352,154
C11×Q32Direct product of C11 and Q323522C11xQ32352,62
Q16×C22Direct product of C22 and Q16352Q16xC22352,169
C8×Dic11Direct product of C8 and Dic11352C8xDic11352,19
C4×Dic22Direct product of C4 and Dic22352C4xDic22352,63
C2×Dic44Direct product of C2 and Dic44352C2xDic44352,100
Q8×Dic11Direct product of Q8 and Dic11352Q8xDic11352,140
C22×Dic22Direct product of C22 and Dic22352C2^2xDic22352,173
C23×Dic11Direct product of C23 and Dic11352C2^3xDic11352,186
C2×D4×D11Direct product of C2, D4 and D1188C2xD4xD11352,177
C11×C4≀C2Direct product of C11 and C4≀C2882C11xC4wrC2352,53
C4○D4×D11Direct product of C4○D4 and D11884C4oD4xD11352,183
C11×C23⋊C4Direct product of C11 and C23⋊C4884C11xC2^3:C4352,48
C11×C8⋊C22Direct product of C11 and C8⋊C22884C11xC8:C2^2352,171
C22⋊C4×D11Direct product of C22⋊C4 and D1188C2^2:C4xD11352,75
C11×C4.D4Direct product of C11 and C4.D4884C11xC4.D4352,49
C11×C22≀C2Direct product of C11 and C22≀C288C11xC2^2wrC2352,155
C2×C8×D11Direct product of C2×C8 and D11176C2xC8xD11352,94
D4×C2×C22Direct product of C2×C22 and D4176D4xC2xC22352,189
C2×Q8×D11Direct product of C2, Q8 and D11176C2xQ8xD11352,180
C4⋊C4×D11Direct product of C4⋊C4 and D11176C4:C4xD11352,86
C4×C11⋊D4Direct product of C4 and C11⋊D4176C4xC11:D4352,123
C2×C88⋊C2Direct product of C2 and C88⋊C2176C2xC88:C2352,95
C2×D22⋊C4Direct product of C2 and D22⋊C4176C2xD22:C4352,122
C2×D4⋊D11Direct product of C2 and D4⋊D11176C2xD4:D11352,126
C11×C8○D4Direct product of C11 and C8○D41762C11xC8oD4352,166
C11×C4○D8Direct product of C11 and C4○D81762C11xC4oD8352,170
C4○D4×C22Direct product of C22 and C4○D4176C4oD4xC22352,191
C2×C8⋊D11Direct product of C2 and C8⋊D11176C2xC8:D11352,97
C11×C4⋊D4Direct product of C11 and C4⋊D4176C11xC4:D4352,156
C2×Q8⋊D11Direct product of C2 and Q8⋊D11176C2xQ8:D11352,136
C22×C4×D11Direct product of C22×C4 and D11176C2^2xC4xD11352,174
C11×D4⋊C4Direct product of C11 and D4⋊C4176C11xD4:C4352,51
C11×C8.C4Direct product of C11 and C8.C41762C11xC8.C4352,57
C2×C44.C4Direct product of C2 and C44.C4176C2xC44.C4352,116
C2×D44⋊C2Direct product of C2 and D44⋊C2176C2xD44:C2352,181
C11×C41D4Direct product of C11 and C41D4176C11xC4:1D4352,162
C11×C22⋊C8Direct product of C11 and C22⋊C8176C11xC2^2:C8352,47
C22⋊C4×C22Direct product of C22 and C22⋊C4176C2^2:C4xC22352,150
C2×D4.D11Direct product of C2 and D4.D11176C2xD4.D11352,128
C22×C11⋊D4Direct product of C22 and C11⋊D4176C2^2xC11:D4352,187
C11×C22⋊Q8Direct product of C11 and C22⋊Q8176C11xC2^2:Q8352,157
C2×D445C2Direct product of C2 and D445C2176C2xD44:5C2352,176
C2×D42D11Direct product of C2 and D42D11176C2xD4:2D11352,178
C11×C42⋊C2Direct product of C11 and C42⋊C2176C11xC4^2:C2352,152
C11×C4.4D4Direct product of C11 and C4.4D4176C11xC4.4D4352,159
C11×C8.C22Direct product of C11 and C8.C221764C11xC8.C2^2352,172
C2×C23.D11Direct product of C2 and C23.D11176C2xC2^3.D11352,147
C11×C422C2Direct product of C11 and C422C2176C11xC4^2:2C2352,161
C11×C4.10D4Direct product of C11 and C4.10D41764C11xC4.10D4352,50
C11×C22.D4Direct product of C11 and C22.D4176C11xC2^2.D4352,158
C4×C11⋊C8Direct product of C4 and C11⋊C8352C4xC11:C8352,8
C11×C4⋊C8Direct product of C11 and C4⋊C8352C11xC4:C8352,54
C4⋊C4×C22Direct product of C22 and C4⋊C4352C4:C4xC22352,151
C2×C11⋊C16Direct product of C2 and C11⋊C16352C2xC11:C16352,17
Q8×C2×C22Direct product of C2×C22 and Q8352Q8xC2xC22352,190
C11×C4⋊Q8Direct product of C11 and C4⋊Q8352C11xC4:Q8352,163
C11×C8⋊C4Direct product of C11 and C8⋊C4352C11xC8:C4352,46
C2×C44⋊C4Direct product of C2 and C44⋊C4352C2xC44:C4352,120
C22×C11⋊C8Direct product of C22 and C11⋊C8352C2^2xC11:C8352,115
C2×C4×Dic11Direct product of C2×C4 and Dic11352C2xC4xDic11352,117
C2×C11⋊Q16Direct product of C2 and C11⋊Q16352C2xC11:Q16352,138
C11×Q8⋊C4Direct product of C11 and Q8⋊C4352C11xQ8:C4352,52
C11×C2.D8Direct product of C11 and C2.D8352C11xC2.D8352,56
C11×C4.Q8Direct product of C11 and C4.Q8352C11xC4.Q8352,55
C2×Dic11⋊C4Direct product of C2 and Dic11⋊C4352C2xDic11:C4352,118
C11×C2.C42Direct product of C11 and C2.C42352C11xC2.C4^2352,44
C11×C42.C2Direct product of C11 and C42.C2352C11xC4^2.C2352,160

Groups of order 353

dρLabelID
C353Cyclic group3531C353353,1

Groups of order 354

dρLabelID
C354Cyclic group3541C354354,4
D177Dihedral group1772+D177354,3
S3×C59Direct product of C59 and S31772S3xC59354,1
C3×D59Direct product of C3 and D591772C3xD59354,2

Groups of order 355

dρLabelID
C355Cyclic group3551C355355,2
C71⋊C5The semidirect product of C71 and C5 acting faithfully715C71:C5355,1

Groups of order 356

dρLabelID
C356Cyclic group3561C356356,2
D178Dihedral group; = C2×D891782+D178356,4
Dic89Dicyclic group; = C892C43562-Dic89356,1
C89⋊C4The semidirect product of C89 and C4 acting faithfully894+C89:C4356,3
C2×C178Abelian group of type [2,178]356C2xC178356,5

Groups of order 357

dρLabelID
C357Cyclic group3571C357357,2
C17×C7⋊C3Direct product of C17 and C7⋊C31193C17xC7:C3357,1

Groups of order 358

dρLabelID
C358Cyclic group3581C358358,2
D179Dihedral group1792+D179358,1

Groups of order 359

dρLabelID
C359Cyclic group3591C359359,1

Groups of order 360

dρLabelID
C360Cyclic group3601C360360,4
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simple65+A6360,118
D180Dihedral group1802+D180360,27
Dic90Dicyclic group; = C452Q83602-Dic90360,25
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5156GammaL(2,4)360,120
C32⋊D20The semidirect product of C32 and D20 acting via D20/C5=D4308+C3^2:D20360,134
C5⋊F9The semidirect product of C5 and F9 acting via F9/C3⋊S3=C4458C5:F9360,125
C52F9The semidirect product of C5 and F9 acting via F9/C32⋊C4=C2458C5:2F9360,124
C32⋊Dic10The semidirect product of C32 and Dic10 acting via Dic10/C5=Q8458C3^2:Dic10360,136
A4⋊D15The semidirect product of A4 and D15 acting via D15/C15=C2606+A4:D15360,141
C3⋊D60The semidirect product of C3 and D60 acting via D60/D30=C2604+C3:D60360,81
D62D152nd semidirect product of D6 and D15 acting via D15/C15=C2604+D6:2D15360,82
D30⋊S33rd semidirect product of D30 and S3 acting via S3/C3=C2604D30:S3360,86
Dic15⋊S33rd semidirect product of Dic15 and S3 acting via S3/C3=C2604Dic15:S3360,85
C22⋊D45The semidirect product of C22 and D45 acting via D45/C15=S3906+C2^2:D45360,41
D6⋊D151st semidirect product of D6 and D15 acting via D15/C15=C21204-D6:D15360,80
C323D202nd semidirect product of C32 and D20 acting via D20/C10=C221204C3^2:3D20360,87
C3⋊Dic30The semidirect product of C3 and Dic30 acting via Dic30/Dic15=C21204-C3:Dic30360,83
C323Dic102nd semidirect product of C32 and Dic10 acting via Dic10/C10=C221204C3^2:3Dic10360,88
C5⋊D36The semidirect product of C5 and D36 acting via D36/D18=C21804+C5:D36360,10
C45⋊D42nd semidirect product of C45 and D4 acting via D4/C2=C221804-C45:D4360,12
C9⋊D20The semidirect product of C9 and D20 acting via D20/D10=C21804+C9:D20360,13
C457D41st semidirect product of C45 and D4 acting via D4/C22=C21802C45:7D4360,29
C60⋊S31st semidirect product of C60 and S3 acting via S3/C3=C2180C60:S3360,112
C15⋊D121st semidirect product of C15 and D12 acting via D12/C6=C22180C15:D12360,70
C62⋊D53rd semidirect product of C62 and D5 acting via D5/C5=C2180C6^2:D5360,114
C327D202nd semidirect product of C32 and D20 acting via D20/D10=C2180C3^2:7D20360,69
C45⋊Q8The semidirect product of C45 and Q8 acting via Q8/C2=C223604-C45:Q8360,7
C453C81st semidirect product of C45 and C8 acting via C8/C4=C23602C45:3C8360,3
C45⋊C81st semidirect product of C45 and C8 acting via C8/C2=C43604C45:C8360,6
C15⋊Dic61st semidirect product of C15 and Dic6 acting via Dic6/C6=C22360C15:Dic6360,71
S32⋊D5The semidirect product of S32 and D5 acting via D5/C5=C2304S3^2:D5360,133
C3⋊F5⋊S3The semidirect product of C3⋊F5 and S3 acting via S3/C3=C2308+C3:F5:S3360,129
C32⋊F5⋊C2The semidirect product of C32⋊F5 and C2 acting faithfully308+C3^2:F5:C2360,131
(C3×C15)⋊9C86th semidirect product of C3×C15 and C8 acting via C8/C2=C41204(C3xC15):9C8360,56
C6.D303rd non-split extension by C6 of D30 acting via D30/D15=C2604+C6.D30360,79
D30.S3The non-split extension by D30 of S3 acting via S3/C3=C21204D30.S3360,84
D90.C2The non-split extension by D90 of C2 acting faithfully1804+D90.C2360,9
C30.D611st non-split extension by C30 of D6 acting via D6/C3=C22180C30.D6360,67
C30.12D612nd non-split extension by C30 of D6 acting via D6/C3=C22180C30.12D6360,68
C60.S36th non-split extension by C60 of S3 acting via S3/C3=C2360C60.S3360,37
C12.D153rd non-split extension by C12 of D15 acting via D15/C15=C2360C12.D15360,110
C30.Dic33rd non-split extension by C30 of Dic3 acting via Dic3/C3=C4360C30.Dic3360,54
(C3×C6).F5The non-split extension by C3×C6 of F5 acting via F5/C5=C41204-(C3xC6).F5360,57
C6×C60Abelian group of type [6,60]360C6xC60360,115
C2×C180Abelian group of type [2,180]360C2xC180360,30
C3×C120Abelian group of type [3,120]360C3xC120360,38
C22×C90Abelian group of type [2,2,90]360C2^2xC90360,50
C2×C6×C30Abelian group of type [2,6,30]360C2xC6xC30360,162
C3×S5Direct product of C3 and S5154C3xS5360,119
S3×A5Direct product of S3 and A5156+S3xA5360,121
C6×A5Direct product of C6 and A5303C6xA5360,122
D9×F5Direct product of D9 and F5458+D9xF5360,39
C5×F9Direct product of C5 and F9458C5xF9360,123
C5×PSU3(𝔽2)Direct product of C5 and PSU3(𝔽2)458C5xPSU(3,2)360,135
C15×S4Direct product of C15 and S4603C15xS4360,138
A4×D15Direct product of A4 and D15606+A4xD15360,144
C3×SL2(𝔽5)Direct product of C3 and SL2(𝔽5)722C3xSL(2,5)360,51
A4×C30Direct product of C30 and A4903A4xC30360,156
C18×F5Direct product of C18 and F5904C18xF5360,43
S3×C60Direct product of C60 and S31202S3xC60360,96
C3×D60Direct product of C3 and D601202C3xD60360,102
C15×D12Direct product of C15 and D121202C15xD12360,97
C12×D15Direct product of C12 and D151202C12xD15360,101
Dic3×D15Direct product of Dic3 and D151204-Dic3xD15360,77
S3×Dic15Direct product of S3 and Dic151204-S3xDic15360,78
C15×Dic6Direct product of C15 and Dic61202C15xDic6360,95
Dic3×C30Direct product of C30 and Dic3120Dic3xC30360,98
C3×Dic30Direct product of C3 and Dic301202C3xDic30360,100
C6×Dic15Direct product of C6 and Dic15120C6xDic15360,103
C15×SL2(𝔽3)Direct product of C15 and SL2(𝔽3)1202C15xSL(2,3)360,89
D5×C36Direct product of C36 and D51802D5xC36360,16
C9×D20Direct product of C9 and D201802C9xD20360,17
D9×C20Direct product of C20 and D91802D9xC20360,21
C5×D36Direct product of C5 and D361802C5xD36360,22
C4×D45Direct product of C4 and D451802C4xD45360,26
D4×C45Direct product of C45 and D41802D4xC45360,31
D9×Dic5Direct product of D9 and Dic51804-D9xDic5360,8
D5×Dic9Direct product of D5 and Dic91804-D5xDic9360,11
D5×C62Direct product of C62 and D5180D5xC6^2360,157
C22×D45Direct product of C22 and D45180C2^2xD45360,49
C32×D20Direct product of C32 and D20180C3^2xD20360,92
Q8×C45Direct product of C45 and Q83602Q8xC45360,32
C9×Dic10Direct product of C9 and Dic103602C9xDic10360,15
C18×Dic5Direct product of C18 and Dic5360C18xDic5360,18
C5×Dic18Direct product of C5 and Dic183602C5xDic18360,20
C10×Dic9Direct product of C10 and Dic9360C10xDic9360,23
C2×Dic45Direct product of C2 and Dic45360C2xDic45360,28
C32×Dic10Direct product of C32 and Dic10360C3^2xDic10360,90
S32×D5Direct product of S3, S3 and D5308+S3^2xD5360,137
S3×C3⋊F5Direct product of S3 and C3⋊F5308S3xC3:F5360,128
C3×S3×F5Direct product of C3, S3 and F5308C3xS3xF5360,126
C5×S3≀C2Direct product of C5 and S3≀C2304C5xS3wrC2360,132
D5×C32⋊C4Direct product of D5 and C32⋊C4308+D5xC3^2:C4360,130
C3⋊S3×F5Direct product of C3⋊S3 and F545C3:S3xF5360,127
C3×C5⋊S4Direct product of C3 and C5⋊S4606C3xC5:S4360,139
C5×S3×A4Direct product of C5, S3 and A4606C5xS3xA4360,143
C3×D5×A4Direct product of C3, D5 and A4606C3xD5xA4360,142
S3×C6×D5Direct product of C6, S3 and D5604S3xC6xD5360,151
C6×C3⋊F5Direct product of C6 and C3⋊F5604C6xC3:F5360,146
S32×C10Direct product of C10, S3 and S3604S3^2xC10360,153
C5×C3⋊S4Direct product of C5 and C3⋊S4606C5xC3:S4360,140
C2×S3×D15Direct product of C2, S3 and D15604+C2xS3xD15360,154
C3×C15⋊D4Direct product of C3 and C15⋊D4604C3xC15:D4360,61
C3×C3⋊D20Direct product of C3 and C3⋊D20604C3xC3:D20360,62
C15×C3⋊D4Direct product of C15 and C3⋊D4602C15xC3:D4360,99
C3×D5×Dic3Direct product of C3, D5 and Dic3604C3xD5xDic3360,58
C2×C32⋊F5Direct product of C2 and C32⋊F5604+C2xC3^2:F5360,150
C2×D15⋊S3Direct product of C2 and D15⋊S3604C2xD15:S3360,155
C5×C3⋊D12Direct product of C5 and C3⋊D12604C5xC3:D12360,75
C3×C157D4Direct product of C3 and C157D4602C3xC15:7D4360,104
C10×C32⋊C4Direct product of C10 and C32⋊C4604C10xC3^2:C4360,148
C5×C6.D6Direct product of C5 and C6.D6604C5xC6.D6360,73
C2×C32⋊Dic5Direct product of C2 and C32⋊Dic5604C2xC3^2:Dic5360,149
C2×D5×D9Direct product of C2, D5 and D9904+C2xD5xD9360,45
C2×C9⋊F5Direct product of C2 and C9⋊F5904C2xC9:F5360,44
C3×C6×F5Direct product of C3×C6 and F590C3xC6xF5360,145
C5×C3.S4Direct product of C5 and C3.S4906C5xC3.S4360,40
D5×C3.A4Direct product of D5 and C3.A4906D5xC3.A4360,42
C10×C3.A4Direct product of C10 and C3.A4903C10xC3.A4360,46
C2×C323F5Direct product of C2 and C323F590C2xC3^2:3F5360,147
C15×C3⋊C8Direct product of C15 and C3⋊C81202C15xC3:C8360,34
S3×C2×C30Direct product of C2×C30 and S3120S3xC2xC30360,158
C2×C6×D15Direct product of C2×C6 and D15120C2xC6xD15360,159
C3×C15⋊Q8Direct product of C3 and C15⋊Q81204C3xC15:Q8360,64
C3×C15⋊C8Direct product of C3 and C15⋊C81204C3xC15:C8360,53
C3×C5⋊D12Direct product of C3 and C5⋊D121204C3xC5:D12360,63
C3×S3×Dic5Direct product of C3, S3 and Dic51204C3xS3xDic5360,59
C5×S3×Dic3Direct product of C5, S3 and Dic31204C5xS3xDic3360,72
C3×C153C8Direct product of C3 and C153C81202C3xC15:3C8360,35
C5×D6⋊S3Direct product of C5 and D6⋊S31204C5xD6:S3360,74
C3×D30.C2Direct product of C3 and D30.C21204C3xD30.C2360,60
C5×C322C8Direct product of C5 and C322C81204C5xC3^2:2C8360,55
C5×C322Q8Direct product of C5 and C322Q81204C5xC3^2:2Q8360,76
D5×C2×C18Direct product of C2×C18 and D5180D5xC2xC18360,47
D9×C2×C10Direct product of C2×C10 and D9180D9xC2xC10360,48
D5×C3×C12Direct product of C3×C12 and D5180D5xC3xC12360,91
D4×C3×C15Direct product of C3×C15 and D4180D4xC3xC15360,116
C9×C5⋊D4Direct product of C9 and C5⋊D41802C9xC5:D4360,19
C5×C9⋊D4Direct product of C5 and C9⋊D41802C5xC9:D4360,24
C3⋊S3×C20Direct product of C20 and C3⋊S3180C3:S3xC20360,106
C4×C3⋊D15Direct product of C4 and C3⋊D15180C4xC3:D15360,111
C5×C12⋊S3Direct product of C5 and C12⋊S3180C5xC12:S3360,107
D5×C3⋊Dic3Direct product of D5 and C3⋊Dic3180D5xC3:Dic3360,65
C3⋊S3×Dic5Direct product of C3⋊S3 and Dic5180C3:S3xDic5360,66
C32×C5⋊D4Direct product of C32 and C5⋊D4180C3^2xC5:D4360,94
C22×C3⋊D15Direct product of C22 and C3⋊D15180C2^2xC3:D15360,161
C5×C327D4Direct product of C5 and C327D4180C5xC3^2:7D4360,109
C5×C9⋊C8Direct product of C5 and C9⋊C83602C5xC9:C8360,1
C9×C5⋊C8Direct product of C9 and C5⋊C83604C9xC5:C8360,5
C5×Q8⋊C9Direct product of C5 and Q8⋊C93602C5xQ8:C9360,14
Q8×C3×C15Direct product of C3×C15 and Q8360Q8xC3xC15360,117
C9×C52C8Direct product of C9 and C52C83602C9xC5:2C8360,2
C32×C5⋊C8Direct product of C32 and C5⋊C8360C3^2xC5:C8360,52
C3×C6×Dic5Direct product of C3×C6 and Dic5360C3xC6xDic5360,93
C10×C3⋊Dic3Direct product of C10 and C3⋊Dic3360C10xC3:Dic3360,108
C2×C3⋊Dic15Direct product of C2 and C3⋊Dic15360C2xC3:Dic15360,113
C32×C52C8Direct product of C32 and C52C8360C3^2xC5:2C8360,33
C5×C324C8Direct product of C5 and C324C8360C5xC3^2:4C8360,36
C5×C324Q8Direct product of C5 and C324Q8360C5xC3^2:4Q8360,105
C2×D5×C3⋊S3Direct product of C2, D5 and C3⋊S390C2xD5xC3:S3360,152
C3⋊S3×C2×C10Direct product of C2×C10 and C3⋊S3180C3:S3xC2xC10360,160

Groups of order 361

dρLabelID
C361Cyclic group3611C361361,1
C192Elementary abelian group of type [19,19]361C19^2361,2

Groups of order 362

dρLabelID
C362Cyclic group3621C362362,2
D181Dihedral group1812+D181362,1

Groups of order 363

dρLabelID
C363Cyclic group3631C363363,1
C112⋊C3The semidirect product of C112 and C3 acting faithfully333C11^2:C3363,2
C11×C33Abelian group of type [11,33]363C11xC33363,3

Groups of order 364

dρLabelID
C364Cyclic group3641C364364,4
D182Dihedral group; = C2×D911822+D182364,10
Dic91Dicyclic group; = C913C43642-Dic91364,3
C91⋊C41st semidirect product of C91 and C4 acting faithfully914C91:C4364,6
C2×C182Abelian group of type [2,182]364C2xC182364,11
D7×D13Direct product of D7 and D13914+D7xD13364,7
D7×C26Direct product of C26 and D71822D7xC26364,9
C14×D13Direct product of C14 and D131822C14xD13364,8
C13×Dic7Direct product of C13 and Dic73642C13xDic7364,1
C7×Dic13Direct product of C7 and Dic133642C7xDic13364,2
C7×C13⋊C4Direct product of C7 and C13⋊C4914C7xC13:C4364,5

Groups of order 365

dρLabelID
C365Cyclic group3651C365365,1

Groups of order 366

dρLabelID
C366Cyclic group3661C366366,6
D183Dihedral group1832+D183366,5
C61⋊C6The semidirect product of C61 and C6 acting faithfully616+C61:C6366,1
S3×C61Direct product of C61 and S31832S3xC61366,3
C3×D61Direct product of C3 and D611832C3xD61366,4
C2×C61⋊C3Direct product of C2 and C61⋊C31223C2xC61:C3366,2

Groups of order 367

dρLabelID
C367Cyclic group3671C367367,1

Groups of order 368

dρLabelID
C368Cyclic group3681C368368,2
D184Dihedral group1842+D184368,6
Dic92Dicyclic group; = C231Q163682-Dic92368,7
D46⋊C4The semidirect product of D46 and C4 acting via C4/C2=C2184D46:C4368,13
D4⋊D23The semidirect product of D4 and D23 acting via D23/C23=C21844+D4:D23368,14
Q8⋊D23The semidirect product of Q8 and D23 acting via D23/C23=C21844+Q8:D23368,16
C8⋊D233rd semidirect product of C8 and D23 acting via D23/C23=C21842C8:D23368,4
C184⋊C22nd semidirect product of C184 and C2 acting faithfully1842C184:C2368,5
D925C2The semidirect product of D92 and C2 acting through Inn(D92)1842D92:5C2368,30
D42D23The semidirect product of D4 and D23 acting through Inn(D4)1844-D4:2D23368,32
D92⋊C24th semidirect product of D92 and C2 acting faithfully1844+D92:C2368,34
C23⋊C16The semidirect product of C23 and C16 acting via C16/C8=C23682C23:C16368,1
C92⋊C41st semidirect product of C92 and C4 acting via C4/C2=C2368C92:C4368,12
C23⋊Q16The semidirect product of C23 and Q16 acting via Q16/Q8=C23684-C23:Q16368,17
Dic23⋊C4The semidirect product of Dic23 and C4 acting via C4/C2=C2368Dic23:C4368,11
D4.D23The non-split extension by D4 of D23 acting via D23/C23=C21844-D4.D23368,15
C92.C41st non-split extension by C92 of C4 acting via C4/C2=C21842C92.C4368,9
C23.D23The non-split extension by C23 of D23 acting via D23/C23=C2184C2^3.D23368,18
C4×C92Abelian group of type [4,92]368C4xC92368,19
C2×C184Abelian group of type [2,184]368C2xC184368,22
C22×C92Abelian group of type [2,2,92]368C2^2xC92368,37
C23×C46Abelian group of type [2,2,2,46]368C2^3xC46368,42
D4×D23Direct product of D4 and D23924+D4xD23368,31
C8×D23Direct product of C8 and D231842C8xD23368,3
D8×C23Direct product of C23 and D81842D8xC23368,24
C2×D92Direct product of C2 and D92184C2xD92368,29
D4×C46Direct product of C46 and D4184D4xC46368,38
Q8×D23Direct product of Q8 and D231844-Q8xD23368,33
SD16×C23Direct product of C23 and SD161842SD16xC23368,25
C23×D23Direct product of C23 and D23184C2^3xD23368,41
M4(2)×C23Direct product of C23 and M4(2)1842M4(2)xC23368,23
Q8×C46Direct product of C46 and Q8368Q8xC46368,39
Q16×C23Direct product of C23 and Q163682Q16xC23368,26
C4×Dic23Direct product of C4 and Dic23368C4xDic23368,10
C2×Dic46Direct product of C2 and Dic46368C2xDic46368,27
C22×Dic23Direct product of C22 and Dic23368C2^2xDic23368,35
C2×C4×D23Direct product of C2×C4 and D23184C2xC4xD23368,28
C2×C23⋊D4Direct product of C2 and C23⋊D4184C2xC23:D4368,36
C4○D4×C23Direct product of C23 and C4○D41842C4oD4xC23368,40
C22⋊C4×C23Direct product of C23 and C22⋊C4184C2^2:C4xC23368,20
C2×C23⋊C8Direct product of C2 and C23⋊C8368C2xC23:C8368,8
C4⋊C4×C23Direct product of C23 and C4⋊C4368C4:C4xC23368,21

Groups of order 369

dρLabelID
C369Cyclic group3691C369369,1
C3×C123Abelian group of type [3,123]369C3xC123369,2

Groups of order 370

dρLabelID
C370Cyclic group3701C370370,4
D185Dihedral group1852+D185370,3
D5×C37Direct product of C37 and D51852D5xC37370,1
C5×D37Direct product of C5 and D371852C5xD37370,2

Groups of order 371

dρLabelID
C371Cyclic group3711C371371,1

Groups of order 372

dρLabelID
C372Cyclic group3721C372372,6
D186Dihedral group; = C2×D931862+D186372,14
Dic93Dicyclic group; = C931C43722-Dic93372,5
C31⋊A4The semidirect product of C31 and A4 acting via A4/C22=C31243C31:A4372,11
C31⋊C12The semidirect product of C31 and C12 acting via C12/C2=C61246-C31:C12372,1
C2×C186Abelian group of type [2,186]372C2xC186372,15
S3×D31Direct product of S3 and D31934+S3xD31372,8
A4×C31Direct product of C31 and A41243A4xC31372,10
S3×C62Direct product of C62 and S31862S3xC62372,13
C6×D31Direct product of C6 and D311862C6xD31372,12
Dic3×C31Direct product of C31 and Dic33722Dic3xC31372,3
C3×Dic31Direct product of C3 and Dic313722C3xDic31372,4
C2×C31⋊C6Direct product of C2 and C31⋊C6626+C2xC31:C6372,7
C4×C31⋊C3Direct product of C4 and C31⋊C31243C4xC31:C3372,2
C22×C31⋊C3Direct product of C22 and C31⋊C3124C2^2xC31:C3372,9

Groups of order 373

dρLabelID
C373Cyclic group3731C373373,1

Groups of order 374

dρLabelID
C374Cyclic group3741C374374,4
D187Dihedral group1872+D187374,3
C17×D11Direct product of C17 and D111872C17xD11374,1
C11×D17Direct product of C11 and D171872C11xD17374,2

Groups of order 375

dρLabelID
C375Cyclic group3751C375375,1
He5⋊C3The semidirect product of He5 and C3 acting faithfully755He5:C3375,2
C5×C75Abelian group of type [5,75]375C5xC75375,3
C52×C15Abelian group of type [5,5,15]375C5^2xC15375,7
C3×He5Direct product of C3 and He5755C3xHe5375,4
C3×5- 1+2Direct product of C3 and 5- 1+2755C3xES-(5,1)375,5
C5×C52⋊C3Direct product of C5 and C52⋊C3; = AΣL1(𝔽125)153C5xC5^2:C3375,6

Groups of order 376

dρLabelID
C376Cyclic group3761C376376,2
D188Dihedral group1882+D188376,5
Dic94Dicyclic group; = C47Q83762-Dic94376,3
C47⋊D4The semidirect product of C47 and D4 acting via D4/C22=C21882C47:D4376,7
C47⋊C8The semidirect product of C47 and C8 acting via C8/C4=C23762C47:C8376,1
C2×C188Abelian group of type [2,188]376C2xC188376,8
C22×C94Abelian group of type [2,2,94]376C2^2xC94376,12
C4×D47Direct product of C4 and D471882C4xD47376,4
D4×C47Direct product of C47 and D41882D4xC47376,9
C22×D47Direct product of C22 and D47188C2^2xD47376,11
Q8×C47Direct product of C47 and Q83762Q8xC47376,10
C2×Dic47Direct product of C2 and Dic47376C2xDic47376,6

Groups of order 377

dρLabelID
C377Cyclic group3771C377377,1

Groups of order 378

dρLabelID
C378Cyclic group3781C378378,6
D189Dihedral group1892+D189378,5
D7⋊He3The semidirect product of D7 and He3 acting via He3/C32=C3636D7:He3378,12
C93F71st semidirect product of C9 and F7 acting via F7/D7=C3636C9:3F7378,8
C94F72nd semidirect product of C9 and F7 acting via F7/D7=C3636C9:4F7378,9
C9⋊F71st semidirect product of C9 and F7 acting via F7/C7=C6636+C9:F7378,18
C92F72nd semidirect product of C9 and F7 acting via F7/C7=C6636+C9:2F7378,19
C95F7The semidirect product of C9 and F7 acting via F7/C7⋊C3=C2636+C9:5F7378,20
C63⋊C65th semidirect product of C63 and C6 acting faithfully636C63:C6378,13
C636C66th semidirect product of C63 and C6 acting faithfully636C63:6C6378,14
C32⋊F7The semidirect product of C32 and F7 acting via F7/C7=C6636+C3^2:F7378,22
He3⋊D71st semidirect product of He3 and D7 acting via D7/C7=C2636+He3:D7378,38
D63⋊C31st semidirect product of D63 and C3 acting faithfully636+D63:C3378,39
C324F72nd semidirect product of C32 and F7 acting via F7/C7⋊C3=C263C3^2:4F7378,51
C32⋊D212nd semidirect product of C32 and D21 acting via D21/C7=S3636C3^2:D21378,43
D21⋊C9The semidirect product of D21 and C9 acting via C9/C3=C31266D21:C9378,21
C7⋊C54The semidirect product of C7 and C54 acting via C54/C9=C61896C7:C54378,1
C3⋊D63The semidirect product of C3 and D63 acting via D63/C63=C2189C3:D63378,42
C33⋊D73rd semidirect product of C33 and D7 acting via D7/C7=C2189C3^3:D7378,59
C7⋊He3⋊C23rd semidirect product of C7⋊He3 and C2 acting faithfully636C7:He3:C2378,17
C32.F7The non-split extension by C32 of F7 acting via F7/D7=C3636C3^2.F7378,11
C3×C126Abelian group of type [3,126]378C3xC126378,44
C32×C42Abelian group of type [3,3,42]378C3^2xC42378,60
C9×F7Direct product of C9 and F7636C9xF7378,7
D7×He3Direct product of D7 and He3636D7xHe3378,30
C32×F7Direct product of C32 and F763C3^2xF7378,47
D7×3- 1+2Direct product of D7 and 3- 1+2636D7xES-(3,1)378,31
S3×C63Direct product of C63 and S31262S3xC63378,33
D9×C21Direct product of C21 and D91262D9xC21378,32
C3×D63Direct product of C3 and D631262C3xD63378,36
C9×D21Direct product of C9 and D211262C9xD21378,37
C14×He3Direct product of C14 and He31263C14xHe3378,45
C32×D21Direct product of C32 and D21126C3^2xD21378,55
C14×3- 1+2Direct product of C14 and 3- 1+21263C14xES-(3,1)378,46
C7×D27Direct product of C7 and D271892C7xD27378,3
D7×C27Direct product of C27 and D71892D7xC27378,4
D7×C33Direct product of C33 and D7189D7xC3^3378,53
C3×C3⋊F7Direct product of C3 and C3⋊F7426C3xC3:F7378,49
D9×C7⋊C3Direct product of D9 and C7⋊C3636D9xC7:C3378,15
C7×C9⋊C6Direct product of C7 and C9⋊C6636C7xC9:C6378,35
C7×C32⋊C6Direct product of C7 and C32⋊C6636C7xC3^2:C6378,34
C7×He3⋊C2Direct product of C7 and He3⋊C2633C7xHe3:C2378,41
S3×C7⋊C9Direct product of S3 and C7⋊C91266S3xC7:C9378,16
C18×C7⋊C3Direct product of C18 and C7⋊C31263C18xC7:C3378,23
S3×C3×C21Direct product of C3×C21 and S3126S3xC3xC21378,54
C2×C7⋊He3Direct product of C2 and C7⋊He31263C2xC7:He3378,28
C3⋊S3×C21Direct product of C21 and C3⋊S3126C3:S3xC21378,56
C3×C3⋊D21Direct product of C3 and C3⋊D21126C3xC3:D21378,57
C2×C63⋊C3Direct product of C2 and C63⋊C31263C2xC63:C3378,24
C2×C633C3Direct product of C2 and C633C31263C2xC63:3C3378,25
C2×C21.C32Direct product of C2 and C21.C321263C2xC21.C3^2378,27
D7×C3×C9Direct product of C3×C9 and D7189D7xC3xC9378,29
C3×C7⋊C18Direct product of C3 and C7⋊C18189C3xC7:C18378,10
C7×C9⋊S3Direct product of C7 and C9⋊S3189C7xC9:S3378,40
C7×C33⋊C2Direct product of C7 and C33⋊C2189C7xC3^3:C2378,58
C6×C7⋊C9Direct product of C6 and C7⋊C9378C6xC7:C9378,26
C2×C7⋊C27Direct product of C2 and C7⋊C273783C2xC7:C27378,2
C3×S3×C7⋊C3Direct product of C3, S3 and C7⋊C3426C3xS3xC7:C3378,48
C3⋊S3×C7⋊C3Direct product of C3⋊S3 and C7⋊C363C3:S3xC7:C3378,50
C3×C6×C7⋊C3Direct product of C3×C6 and C7⋊C3126C3xC6xC7:C3378,52

Groups of order 379

dρLabelID
C379Cyclic group3791C379379,1

Groups of order 380

dρLabelID
C380Cyclic group3801C380380,4
D190Dihedral group; = C2×D951902+D190380,10
Dic95Dicyclic group; = C953C43802-Dic95380,3
C19⋊F5The semidirect product of C19 and F5 acting via F5/D5=C2954C19:F5380,6
C2×C190Abelian group of type [2,190]380C2xC190380,11
D5×D19Direct product of D5 and D19954+D5xD19380,7
C19×F5Direct product of C19 and F5954C19xF5380,5
D5×C38Direct product of C38 and D51902D5xC38380,9
C10×D19Direct product of C10 and D191902C10xD19380,8
C19×Dic5Direct product of C19 and Dic53802C19xDic5380,1
C5×Dic19Direct product of C5 and Dic193802C5xDic19380,2

Groups of order 381

dρLabelID
C381Cyclic group3811C381381,2
C127⋊C3The semidirect product of C127 and C3 acting faithfully1273C127:C3381,1

Groups of order 382

dρLabelID
C382Cyclic group3821C382382,2
D191Dihedral group1912+D191382,1

Groups of order 383

dρLabelID
C383Cyclic group3831C383383,1

Groups of order 385

dρLabelID
C385Cyclic group3851C385385,2
C7×C11⋊C5Direct product of C7 and C11⋊C5775C7xC11:C5385,1

Groups of order 386

dρLabelID
C386Cyclic group3861C386386,2
D193Dihedral group1932+D193386,1

Groups of order 387

dρLabelID
C387Cyclic group3871C387387,2
C43⋊C9The semidirect product of C43 and C9 acting via C9/C3=C33873C43:C9387,1
C3×C129Abelian group of type [3,129]387C3xC129387,4
C3×C43⋊C3Direct product of C3 and C43⋊C31293C3xC43:C3387,3

Groups of order 388

dρLabelID
C388Cyclic group3881C388388,2
D194Dihedral group; = C2×D971942+D194388,4
Dic97Dicyclic group; = C972C43882-Dic97388,1
C97⋊C4The semidirect product of C97 and C4 acting faithfully974+C97:C4388,3
C2×C194Abelian group of type [2,194]388C2xC194388,5

Groups of order 389

dρLabelID
C389Cyclic group3891C389389,1

Groups of order 390

dρLabelID
C390Cyclic group3901C390390,12
D195Dihedral group1952+D195390,11
D65⋊C3The semidirect product of D65 and C3 acting faithfully656+D65:C3390,3
S3×C65Direct product of C65 and S31952S3xC65390,8
D5×C39Direct product of C39 and D51952D5xC39390,6
C3×D65Direct product of C3 and D651952C3xD65390,7
C5×D39Direct product of C5 and D391952C5xD39390,9
C15×D13Direct product of C15 and D131952C15xD13390,5
C13×D15Direct product of C13 and D151952C13xD15390,10
C5×C13⋊C6Direct product of C5 and C13⋊C6656C5xC13:C6390,1
D5×C13⋊C3Direct product of D5 and C13⋊C3656D5xC13:C3390,2
C10×C13⋊C3Direct product of C10 and C13⋊C31303C10xC13:C3390,4

Groups of order 391

dρLabelID
C391Cyclic group3911C391391,1

Groups of order 392

dρLabelID
C392Cyclic group3921C392392,2
D196Dihedral group1962+D196392,5
Dic98Dicyclic group; = C49Q83922-Dic98392,3
D7≀C2Wreath product of D7 by C2144+D7wrC2392,37
C72⋊C8The semidirect product of C72 and C8 acting faithfully288+C7^2:C8392,36
C72⋊Q8The semidirect product of C72 and Q8 acting faithfully288+C7^2:Q8392,38
C7⋊D28The semidirect product of C7 and D28 acting via D28/D14=C2284+C7:D28392,21
Dic72D7The semidirect product of Dic7 and D7 acting through Inn(Dic7)284+Dic7:2D7392,19
C722C8The semidirect product of C72 and C8 acting via C8/C2=C4564-C7^2:2C8392,17
C722D41st semidirect product of C72 and D4 acting via D4/C2=C22564-C7^2:2D4392,20
C722Q8The semidirect product of C72 and Q8 acting via Q8/C2=C22564-C7^2:2Q8392,22
C49⋊D4The semidirect product of C49 and D4 acting via D4/C22=C21962C49:D4392,7
C28⋊D71st semidirect product of C28 and D7 acting via D7/C7=C2196C28:D7392,30
C727D42nd semidirect product of C72 and D4 acting via D4/C22=C2196C7^2:7D4392,32
C49⋊C8The semidirect product of C49 and C8 acting via C8/C4=C23922C49:C8392,1
C724C82nd semidirect product of C72 and C8 acting via C8/C4=C2392C7^2:4C8392,15
C724Q82nd semidirect product of C72 and Q8 acting via Q8/C4=C2392C7^2:4Q8392,28
C7.F8The central extension by C7 of F8987C7.F8392,11
C7×C56Abelian group of type [7,56]392C7xC56392,16
C2×C196Abelian group of type [2,196]392C2xC196392,8
C14×C28Abelian group of type [14,28]392C14xC28392,33
C22×C98Abelian group of type [2,2,98]392C2^2xC98392,13
C2×C142Abelian group of type [2,14,14]392C2xC14^2392,44
C7×F8Direct product of C7 and F8567C7xF8392,39
D7×C28Direct product of C28 and D7562D7xC28392,24
C7×D28Direct product of C7 and D28562C7xD28392,25
D7×Dic7Direct product of D7 and Dic7564-D7xDic7392,18
C7×Dic14Direct product of C7 and Dic14562C7xDic14392,23
C14×Dic7Direct product of C14 and Dic756C14xDic7392,26
C4×D49Direct product of C4 and D491962C4xD49392,4
D4×C49Direct product of C49 and D41962D4xC49392,9
D4×C72Direct product of C72 and D4196D4xC7^2392,34
C22×D49Direct product of C22 and D49196C2^2xD49392,12
Q8×C49Direct product of C49 and Q83922Q8xC49392,10
Q8×C72Direct product of C72 and Q8392Q8xC7^2392,35
C2×Dic49Direct product of C2 and Dic49392C2xDic49392,6
C2×D72Direct product of C2, D7 and D7284+C2xD7^2392,41
C7×C7⋊D4Direct product of C7 and C7⋊D4282C7xC7:D4392,27
C2×C72⋊C4Direct product of C2 and C72⋊C4284+C2xC7^2:C4392,40
C7×C7⋊C8Direct product of C7 and C7⋊C8562C7xC7:C8392,14
D7×C2×C14Direct product of C2×C14 and D756D7xC2xC14392,42
C4×C7⋊D7Direct product of C4 and C7⋊D7196C4xC7:D7392,29
C22×C7⋊D7Direct product of C22 and C7⋊D7196C2^2xC7:D7392,43
C2×C7⋊Dic7Direct product of C2 and C7⋊Dic7392C2xC7:Dic7392,31

Groups of order 393

dρLabelID
C393Cyclic group3931C393393,1

Groups of order 394

dρLabelID
C394Cyclic group3941C394394,2
D197Dihedral group1972+D197394,1

Groups of order 395

dρLabelID
C395Cyclic group3951C395395,1

Groups of order 396

dρLabelID
C396Cyclic group3961C396396,4
D198Dihedral group; = C2×D991982+D198396,9
Dic99Dicyclic group; = C991C43962-Dic99396,3
D33⋊S3The semidirect product of D33 and S3 acting via S3/C3=C2664D33:S3396,23
C32⋊Dic11The semidirect product of C32 and Dic11 acting via Dic11/C11=C4664C3^2:Dic11396,18
C3⋊Dic33The semidirect product of C3 and Dic33 acting via Dic33/C66=C2396C3:Dic33396,15
C6×C66Abelian group of type [6,66]396C6xC66396,30
C2×C198Abelian group of type [2,198]396C2xC198396,10
C3×C132Abelian group of type [3,132]396C3xC132396,16
S3×D33Direct product of S3 and D33664+S3xD33396,22
D9×D11Direct product of D9 and D11994+D9xD11396,5
S3×C66Direct product of C66 and S31322S3xC66396,26
A4×C33Direct product of C33 and A41323A4xC33396,24
C6×D33Direct product of C6 and D331322C6xD33396,27
Dic3×C33Direct product of C33 and Dic31322Dic3xC33396,12
C3×Dic33Direct product of C3 and Dic331322C3xDic33396,13
D9×C22Direct product of C22 and D91982D9xC22396,8
C18×D11Direct product of C18 and D111982C18xD11396,7
C11×Dic9Direct product of C11 and Dic93962C11xDic9396,1
C9×Dic11Direct product of C9 and Dic113962C9xDic11396,2
C32×Dic11Direct product of C32 and Dic11396C3^2xDic11396,11
S32×C11Direct product of C11, S3 and S3664S3^2xC11396,21
C3×S3×D11Direct product of C3, S3 and D11664C3xS3xD11396,19
C11×C32⋊C4Direct product of C11 and C32⋊C4664C11xC3^2:C4396,17
C3⋊S3×D11Direct product of C3⋊S3 and D1199C3:S3xD11396,20
C3×C6×D11Direct product of C3×C6 and D11198C3xC6xD11396,25
C3⋊S3×C22Direct product of C22 and C3⋊S3198C3:S3xC22396,28
C2×C3⋊D33Direct product of C2 and C3⋊D33198C2xC3:D33396,29
C11×C3.A4Direct product of C11 and C3.A41983C11xC3.A4396,6
C11×C3⋊Dic3Direct product of C11 and C3⋊Dic3396C11xC3:Dic3396,14

Groups of order 397

dρLabelID
C397Cyclic group3971C397397,1

Groups of order 398

dρLabelID
C398Cyclic group3981C398398,2
D199Dihedral group1992+D199398,1

Groups of order 399

dρLabelID
C399Cyclic group3991C399399,5
C133⋊C33rd semidirect product of C133 and C3 acting faithfully1333C133:C3399,3
C1334C34th semidirect product of C133 and C3 acting faithfully1333C133:4C3399,4
C19×C7⋊C3Direct product of C19 and C7⋊C31333C19xC7:C3399,1
C7×C19⋊C3Direct product of C7 and C19⋊C31333C7xC19:C3399,2

Groups of order 400

dρLabelID
C400Cyclic group4001C400400,2
D200Dihedral group2002+D200400,8
Dic100Dicyclic group; = C251Q164002-Dic100400,4
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfully108+C5^2:M4(2)400,206
D10⋊F52nd semidirect product of D10 and F5 acting via F5/D5=C2208+D10:F5400,125
D10⋊D103rd semidirect product of D10 and D10 acting via D10/D5=C2204+D10:D10400,180
C1024C44th semidirect product of C102 and C4 acting faithfully204+C10^2:4C4400,162
Dic5⋊F53rd semidirect product of Dic5 and F5 acting via F5/D5=C2208+Dic5:F5400,126
C523C422nd semidirect product of C52 and C42 acting via C42/C2=C2×C4208+C5^2:3C4^2400,124
C52⋊D8The semidirect product of C52 and D8 acting via D8/C2=D4404C5^2:D8400,131
C5⋊D40The semidirect product of C5 and D40 acting via D40/D20=C2404+C5:D40400,65
C202F52nd semidirect product of C20 and F5 acting via F5/C5=C4404C20:2F5400,159
C52⋊SD16The semidirect product of C52 and SD16 acting via SD16/C2=D4404-C5^2:SD16400,132
D20⋊D53rd semidirect product of D20 and D5 acting via D5/C5=C2404D20:D5400,165
C20⋊D102nd semidirect product of C20 and D10 acting via D10/C5=C22404C20:D10400,171
C524SD163rd semidirect product of C52 and SD16 acting via SD16/C4=C22404+C5^2:4SD16400,68
Dic10⋊D54th semidirect product of Dic10 and D5 acting via D5/C5=C2404Dic10:D5400,166
Dic105D5The semidirect product of Dic10 and D5 acting through Inn(Dic10)404+Dic10:5D5400,168
C528M4(2)4th semidirect product of C52 and M4(2) acting via M4(2)/C4=C4404C5^2:8M4(2)400,157
C5214M4(2)4th semidirect product of C52 and M4(2) acting via M4(2)/C22=C4404-C5^2:14M4(2)400,161
C24⋊C25The semidirect product of C24 and C25 acting via C25/C5=C5505C2^4:C25400,52
C52⋊C16The semidirect product of C52 and C16 acting via C16/C2=C8808-C5^2:C16400,116
C52⋊Q16The semidirect product of C52 and Q16 acting via Q16/C2=D4804-C5^2:Q16400,133
C205F51st semidirect product of C20 and F5 acting via F5/D5=C2804C20:5F5400,145
C522D81st semidirect product of C52 and D8 acting via D8/C4=C22804C5^2:2D8400,64
D205D5The semidirect product of D20 and D5 acting through Inn(D20)804-D20:5D5400,164
C523C162nd semidirect product of C52 and C16 acting via C16/C4=C4804C5^2:3C16400,57
C525C164th semidirect product of C52 and C16 acting via C16/C4=C4804C5^2:5C16400,59
C522Q161st semidirect product of C52 and Q16 acting via Q16/C4=C22804C5^2:2Q16400,69
C523Q162nd semidirect product of C52 and Q16 acting via Q16/C4=C22804-C5^2:3Q16400,70
C523SD162nd semidirect product of C52 and SD16 acting via SD16/C4=C22804-C5^2:3SD16400,67
D10⋊Dic51st semidirect product of D10 and Dic5 acting via Dic5/C10=C280D10:Dic5400,72
C524M4(2)3rd semidirect product of C52 and M4(2) acting via M4(2)/C2=C2×C4808-C5^2:4M4(2)400,128
Dic5⋊Dic51st semidirect product of Dic5 and Dic5 acting via Dic5/C10=C280Dic5:Dic5400,74
C20⋊F51st semidirect product of C20 and F5 acting via F5/C5=C4100C20:F5400,152
C100⋊C41st semidirect product of C100 and C4 acting faithfully1004C100:C4400,31
C102⋊C43rd semidirect product of C102 and C4 acting faithfully100C10^2:C4400,155
D4⋊D25The semidirect product of D4 and D25 acting via D25/C25=C22004+D4:D25400,16
D25⋊C8The semidirect product of D25 and C8 acting via C8/C4=C22004D25:C8400,28
Q8⋊D25The semidirect product of Q8 and D25 acting via D25/C25=C22004+Q8:D25400,18
C8⋊D253rd semidirect product of C8 and D25 acting via D25/C25=C22002C8:D25400,6
C40⋊D54th semidirect product of C40 and D5 acting via D5/C5=C2200C40:D5400,93
C402D52nd semidirect product of C40 and D5 acting via D5/C5=C2200C40:2D5400,94
C200⋊C22nd semidirect product of C200 and C2 acting faithfully2002C200:C2400,7
C525D82nd semidirect product of C52 and D8 acting via D8/C8=C2200C5^2:5D8400,95
C527D82nd semidirect product of C52 and D8 acting via D8/D4=C2200C5^2:7D8400,103
D50⋊C41st semidirect product of D50 and C4 acting via C4/C2=C2200D50:C4400,14
D42D25The semidirect product of D4 and D25 acting through Inn(D4)2004-D4:2D25400,40
Q82D25The semidirect product of Q8 and D25 acting through Inn(Q8)2004+Q8:2D25400,42
D1005C2The semidirect product of D100 and C2 acting through Inn(D100)2002D100:5C2400,38
C25⋊M4(2)The semidirect product of C25 and M4(2) acting via M4(2)/C22=C42004-C25:M4(2)400,33
C528SD162nd semidirect product of C52 and SD16 acting via SD16/D4=C2200C5^2:8SD16400,104
C10211C43rd semidirect product of C102 and C4 acting via C4/C2=C2200C10^2:11C4400,107
C5210SD162nd semidirect product of C52 and SD16 acting via SD16/Q8=C2200C5^2:10SD16400,105
C527M4(2)3rd semidirect product of C52 and M4(2) acting via M4(2)/C4=C4200C5^2:7M4(2)400,150
C5213M4(2)3rd semidirect product of C52 and M4(2) acting via M4(2)/C22=C4200C5^2:13M4(2)400,154
C25⋊C16The semidirect product of C25 and C16 acting via C16/C4=C44004C25:C16400,3
C252C16The semidirect product of C25 and C16 acting via C16/C8=C24002C25:2C16400,1
C4⋊Dic25The semidirect product of C4 and Dic25 acting via Dic25/C50=C2400C4:Dic25400,13
C25⋊Q16The semidirect product of C25 and Q16 acting via Q16/Q8=C24004-C25:Q16400,17
C527C162nd semidirect product of C52 and C16 acting via C16/C8=C2400C5^2:7C16400,50
C524C163rd semidirect product of C52 and C16 acting via C16/C4=C4400C5^2:4C16400,58
C527Q162nd semidirect product of C52 and Q16 acting via Q16/Q8=C2400C5^2:7Q16400,106
C203Dic51st semidirect product of C20 and Dic5 acting via Dic5/C10=C2400C20:3Dic5400,101
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfully108+D5wrC2:C2400,207
D52⋊C41st semidirect product of D52 and C4 acting via C4/C2=C2204+D5^2:C4400,129
D5.D20The non-split extension by D5 of D20 acting via D20/D10=C2408+D5.D20400,118
C20.11F511st non-split extension by C20 of F5 acting via F5/C5=C4404C20.11F5400,156
D10.9D101st non-split extension by D10 of D10 acting via D10/C10=C2404D10.9D10400,167
D10.4D104th non-split extension by D10 of D10 acting via D10/D5=C2404-D10.4D10400,174
C20.29D103rd non-split extension by C20 of D10 acting via D10/D5=C2404C20.29D10400,61
C20.31D105th non-split extension by C20 of D10 acting via D10/D5=C2404C20.31D10400,63
C10.D206th non-split extension by C10 of D20 acting via D20/D10=C240C10.D20400,73
C102.C44th non-split extension by C102 of C4 acting faithfully404C10^2.C4400,147
Dic5.4F5The non-split extension by Dic5 of F5 acting through Inn(Dic5)408+Dic5.4F5400,121
Dic5.F51st non-split extension by Dic5 of F5 acting via F5/D5=C2408+Dic5.F5400,123
D10.D105th non-split extension by D10 of D10 acting via D10/C10=C2404D10.D10400,148
Dic5.D103rd non-split extension by Dic5 of D10 acting via D10/D5=C2404Dic5.D10400,173
D20.D52nd non-split extension by D20 of D5 acting via D5/C5=C2804D20.D5400,66
D10.F51st non-split extension by D10 of F5 acting via F5/D5=C2808-D10.F5400,122
D10.2F52nd non-split extension by D10 of F5 acting via F5/D5=C2808-D10.2F5400,127
C20.14F53rd non-split extension by C20 of F5 acting via F5/D5=C2804C20.14F5400,142
C20.12F51st non-split extension by C20 of F5 acting via F5/D5=C2804C20.12F5400,143
C20.30D104th non-split extension by C20 of D10 acting via D10/D5=C2804C20.30D10400,62
D5.Dic10The non-split extension by D5 of Dic10 acting via Dic10/Dic5=C2808-D5.Dic10400,119
C10.Dic102nd non-split extension by C10 of Dic10 acting via Dic10/Dic5=C280C10.Dic10400,75
D25.D4The non-split extension by D25 of D4 acting via D4/C22=C21004+D25.D4400,34
D4.D25The non-split extension by D4 of D25 acting via D25/C25=C22004-D4.D25400,15
C4.Dic25The non-split extension by C4 of Dic25 acting via Dic25/C50=C22002C4.Dic25400,10
C23.D25The non-split extension by C23 of D25 acting via D25/C25=C2200C2^3.D25400,19
C100.C41st non-split extension by C100 of C4 acting faithfully2004C100.C4400,29
C20.F510th non-split extension by C20 of F5 acting via F5/C5=C4200C20.F5400,149
C20.59D1020th non-split extension by C20 of D10 acting via D10/C10=C2200C20.59D10400,98
C10.11D2011st non-split extension by C10 of D20 acting via D20/C20=C2200C10.11D20400,102
C20.50D1011st non-split extension by C20 of D10 acting via D10/C10=C2200C20.50D10400,194
C20.D1024th non-split extension by C20 of D10 acting via D10/C5=C22200C20.D10400,196
C20.26D1026th non-split extension by C20 of D10 acting via D10/C5=C22200C20.26D10400,198
C50.D41st non-split extension by C50 of D4 acting via D4/C22=C2400C50.D4400,12
C40.D53rd non-split extension by C40 of D5 acting via D5/C5=C2400C40.D5400,96
C102.22C228th non-split extension by C102 of C22 acting via C22/C2=C2400C10^2.22C2^2400,100
(C5×C10).Q8The non-split extension by C5×C10 of Q8 acting faithfully208+(C5xC10).Q8400,134
C2.D5≀C22nd central extension by C2 of D5≀C2204C2.D5wrC2400,130
C202Abelian group of type [20,20]400C20^2400,108
C5×C80Abelian group of type [5,80]400C5xC80400,51
C4×C100Abelian group of type [4,100]400C4xC100400,20
C2×C200Abelian group of type [2,200]400C2xC200400,23
C10×C40Abelian group of type [10,40]400C10xC40400,111
C23×C50Abelian group of type [2,2,2,50]400C2^3xC50400,55
C22×C100Abelian group of type [2,2,100]400C2^2xC100400,45
C22×C102Abelian group of type [2,2,10,10]400C2^2xC10^2400,221
C2×C10×C20Abelian group of type [2,10,20]400C2xC10xC20400,201
F52Direct product of F5 and F5; = Hol(F5)2016+F5^2400,205
D5×D20Direct product of D5 and D20404+D5xD20400,170
D5×C40Direct product of C40 and D5802D5xC40400,76
C5×D40Direct product of C5 and D40802C5xD40400,79
C20×F5Direct product of C20 and F5804C20xF5400,137
C10×D20Direct product of C10 and D2080C10xD20400,183
Dic52Direct product of Dic5 and Dic580Dic5^2400,71
Dic5×F5Direct product of Dic5 and F5808-Dic5xF5400,117
C5×Dic20Direct product of C5 and Dic20802C5xDic20400,80
Dic5×C20Direct product of C20 and Dic580Dic5xC20400,83
D5×Dic10Direct product of D5 and Dic10804-D5xDic10400,163
C10×Dic10Direct product of C10 and Dic1080C10xDic10400,181
D4×D25Direct product of D4 and D251004+D4xD25400,39
C8×D25Direct product of C8 and D252002C8xD25400,5
D8×C25Direct product of C25 and D82002D8xC25400,25
D4×C50Direct product of C50 and D4200D4xC50400,46
Q8×D25Direct product of Q8 and D252004-Q8xD25400,41
C2×D100Direct product of C2 and D100200C2xD100400,37
D8×C52Direct product of C52 and D8200D8xC5^2400,113
SD16×C25Direct product of C25 and SD162002SD16xC25400,26
C23×D25Direct product of C23 and D25200C2^3xD25400,54
M4(2)×C25Direct product of C25 and M4(2)2002M4(2)xC25400,24
SD16×C52Direct product of C52 and SD16200SD16xC5^2400,114
M4(2)×C52Direct product of C52 and M4(2)200M4(2)xC5^2400,112
Q8×C50Direct product of C50 and Q8400Q8xC50400,47
Q16×C25Direct product of C25 and Q164002Q16xC25400,27
C4×Dic25Direct product of C4 and Dic25400C4xDic25400,11
C2×Dic50Direct product of C2 and Dic50400C2xDic50400,35
Q16×C52Direct product of C52 and Q16400Q16xC5^2400,115
C22×Dic25Direct product of C22 and Dic25400C2^2xDic25400,43
C2×D5≀C2Direct product of C2 and D5≀C2204+C2xD5wrC2400,211
C2×D5⋊F5Direct product of C2 and D5⋊F5208+C2xD5:F5400,210
C2×C52⋊C8Direct product of C2 and C52⋊C8208+C2xC5^2:C8400,208
C2×C52⋊Q8Direct product of C2 and C52⋊Q8208+C2xC5^2:Q8400,212
C4×D52Direct product of C4, D5 and D5404C4xD5^2400,169
C5×D4×D5Direct product of C5, D4 and D5404C5xD4xD5400,185
C2×D5×F5Direct product of C2, D5 and F5408+C2xD5xF5400,209
D5×C5⋊D4Direct product of D5 and C5⋊D4404D5xC5:D4400,179
C5×D4⋊D5Direct product of C5 and D4⋊D5404C5xD4:D5400,87
C10×C5⋊D4Direct product of C10 and C5⋊D440C10xC5:D4400,190
C22×D52Direct product of C22, D5 and D540C2^2xD5^2400,218
C5×C4○D20Direct product of C5 and C4○D20402C5xC4oD20400,184
C2×C5⋊D20Direct product of C2 and C5⋊D2040C2xC5:D20400,177
C5×D4.D5Direct product of C5 and D4.D5404C5xD4.D5400,88
C4×C52⋊C4Direct product of C4 and C52⋊C4404C4xC5^2:C4400,158
C5×C22⋊F5Direct product of C5 and C22⋊F5404C5xC2^2:F5400,141
C5×D42D5Direct product of C5 and D42D5404C5xD4:2D5400,186
C5×C4.Dic5Direct product of C5 and C4.Dic5402C5xC4.Dic5400,82
C5×C23.D5Direct product of C5 and C23.D540C5xC2^3.D5400,91
C5×C22.F5Direct product of C5 and C22.F5404C5xC2^2.F5400,140
C22×C52⋊C4Direct product of C22 and C52⋊C440C2^2xC5^2:C4400,217
C2×Dic52D5Direct product of C2 and Dic52D540C2xDic5:2D5400,175
C5×C24⋊C5Direct product of C5 and C24⋊C5505C5xC2^4:C5400,213
D5×C5⋊C8Direct product of D5 and C5⋊C8808-D5xC5:C8400,120
C5×C5⋊C16Direct product of C5 and C5⋊C16804C5xC5:C16400,56
C10×C5⋊C8Direct product of C10 and C5⋊C880C10xC5:C8400,139
C5×Q8×D5Direct product of C5, Q8 and D5804C5xQ8xD5400,187
D5×C2×C20Direct product of C2×C20 and D580D5xC2xC20400,182
C5×C4⋊F5Direct product of C5 and C4⋊F5804C5xC4:F5400,138
F5×C2×C10Direct product of C2×C10 and F580F5xC2xC10400,214
C5×D5⋊C8Direct product of C5 and D5⋊C8804C5xD5:C8400,135
C5×C8⋊D5Direct product of C5 and C8⋊D5802C5xC8:D5400,77
D5×C52C8Direct product of D5 and C52C8804D5xC5:2C8400,60
C5×Q8⋊D5Direct product of C5 and Q8⋊D5804C5xQ8:D5400,89
C2×D5×Dic5Direct product of C2, D5 and Dic580C2xD5xDic5400,172
C5×C40⋊C2Direct product of C5 and C40⋊C2802C5xC40:C2400,78
C5×C5⋊Q16Direct product of C5 and C5⋊Q16804C5xC5:Q16400,90
C5×C52C16Direct product of C5 and C52C16802C5xC5:2C16400,49
C10×C52C8Direct product of C10 and C52C880C10xC5:2C8400,81
C5×C4.F5Direct product of C5 and C4.F5804C5xC4.F5400,136
C4×D5.D5Direct product of C4 and D5.D5804C4xD5.D5400,144
C5×C4⋊Dic5Direct product of C5 and C4⋊Dic580C5xC4:Dic5400,85
Dic5×C2×C10Direct product of C2×C10 and Dic580Dic5xC2xC10400,189
D5×C22×C10Direct product of C22×C10 and D580D5xC2^2xC10400,219
C5×D10⋊C4Direct product of C5 and D10⋊C480C5xD10:C4400,86
C2×C523C8Direct product of C2 and C523C880C2xC5^2:3C8400,146
C2×C525C8Direct product of C2 and C525C880C2xC5^2:5C8400,160
C5×Q82D5Direct product of C5 and Q82D5804C5xQ8:2D5400,188
C5×C10.D4Direct product of C5 and C10.D480C5xC10.D4400,84
C2×C522D4Direct product of C2 and C522D480C2xC5^2:2D4400,176
C2×C522Q8Direct product of C2 and C522Q880C2xC5^2:2Q8400,178
C22×D5.D5Direct product of C22 and D5.D580C2^2xD5.D5400,215
C4×C25⋊C4Direct product of C4 and C25⋊C41004C4xC25:C4400,30
D4×C5⋊D5Direct product of D4 and C5⋊D5100D4xC5:D5400,195
C4×C5⋊F5Direct product of C4 and C5⋊F5100C4xC5:F5400,151
C22×C25⋊C4Direct product of C22 and C25⋊C4100C2^2xC25:C4400,53
C22×C5⋊F5Direct product of C22 and C5⋊F5100C2^2xC5:F5400,216
C8×C5⋊D5Direct product of C8 and C5⋊D5200C8xC5:D5400,92
C2×C4×D25Direct product of C2×C4 and D25200C2xC4xD25400,36
D4×C5×C10Direct product of C5×C10 and D4200D4xC5xC10400,202
Q8×C5⋊D5Direct product of Q8 and C5⋊D5200Q8xC5:D5400,197
C2×C25⋊D4Direct product of C2 and C25⋊D4200C2xC25:D4400,44
C4○D4×C25Direct product of C25 and C4○D42002C4oD4xC25400,48
C2×C20⋊D5Direct product of C2 and C20⋊D5200C2xC20:D5400,193
C23×C5⋊D5Direct product of C23 and C5⋊D5200C2^3xC5:D5400,220
C22⋊C4×C25Direct product of C25 and C22⋊C4200C2^2:C4xC25400,21
C4○D4×C52Direct product of C52 and C4○D4200C4oD4xC5^2400,204
C2×C527D4Direct product of C2 and C527D4200C2xC5^2:7D4400,200
C22⋊C4×C52Direct product of C52 and C22⋊C4200C2^2:C4xC5^2400,109
C2×C25⋊C8Direct product of C2 and C25⋊C8400C2xC25:C8400,32
C4⋊C4×C25Direct product of C25 and C4⋊C4400C4:C4xC25400,22
Q8×C5×C10Direct product of C5×C10 and Q8400Q8xC5xC10400,203
C2×C252C8Direct product of C2 and C252C8400C2xC25:2C8400,9
C4⋊C4×C52Direct product of C52 and C4⋊C4400C4:C4xC5^2400,110
C2×C527C8Direct product of C2 and C527C8400C2xC5^2:7C8400,97
C4×C526C4Direct product of C4 and C526C4400C4xC5^2:6C4400,99
C2×C524C8Direct product of C2 and C524C8400C2xC5^2:4C8400,153
C2×C524Q8Direct product of C2 and C524Q8400C2xC5^2:4Q8400,191
C22×C526C4Direct product of C22 and C526C4400C2^2xC5^2:6C4400,199
C2×C4×C5⋊D5Direct product of C2×C4 and C5⋊D5200C2xC4xC5:D5400,192

Groups of order 401

dρLabelID
C401Cyclic group4011C401401,1

Groups of order 402

dρLabelID
C402Cyclic group4021C402402,6
D201Dihedral group2012+D201402,5
C67⋊C6The semidirect product of C67 and C6 acting faithfully676+C67:C6402,1
S3×C67Direct product of C67 and S32012S3xC67402,3
C3×D67Direct product of C3 and D672012C3xD67402,4
C2×C67⋊C3Direct product of C2 and C67⋊C31343C2xC67:C3402,2

Groups of order 403

dρLabelID
C403Cyclic group4031C403403,1

Groups of order 404

dρLabelID
C404Cyclic group4041C404404,2
D202Dihedral group; = C2×D1012022+D202404,4
Dic101Dicyclic group; = C1012C44042-Dic101404,1
C101⋊C4The semidirect product of C101 and C4 acting faithfully1014+C101:C4404,3
C2×C202Abelian group of type [2,202]404C2xC202404,5

Groups of order 405

dρLabelID
C405Cyclic group4051C405405,1
C34⋊C5The semidirect product of C34 and C5 acting faithfully155C3^4:C5405,15
C9×C45Abelian group of type [9,45]405C9xC45405,2
C3×C135Abelian group of type [3,135]405C3xC135405,5
C32×C45Abelian group of type [3,3,45]405C3^2xC45405,11
C33×C15Abelian group of type [3,3,3,15]405C3^3xC15405,16
C15×He3Direct product of C15 and He3135C15xHe3405,12
C15×3- 1+2Direct product of C15 and 3- 1+2135C15xES-(3,1)405,13
C5×C3≀C3Direct product of C5 and C3≀C3453C5xC3wrC3405,7
C5×C27⋊C3Direct product of C5 and C27⋊C31353C5xC27:C3405,6
C5×C32⋊C9Direct product of C5 and C32⋊C9135C5xC3^2:C9405,3
C5×C9○He3Direct product of C5 and C9○He31353C5xC9oHe3405,14
C5×He3⋊C3Direct product of C5 and He3⋊C31353C5xHe3:C3405,9
C5×He3.C3Direct product of C5 and He3.C31353C5xHe3.C3405,8
C5×C3.He3Direct product of C5 and C3.He31353C5xC3.He3405,10
C5×C9⋊C9Direct product of C5 and C9⋊C9405C5xC9:C9405,4

Groups of order 406

dρLabelID
C406Cyclic group4061C406406,6
D203Dihedral group2032+D203406,5
C29⋊C14The semidirect product of C29 and C14 acting faithfully2914+C29:C14406,1
D7×C29Direct product of C29 and D72032D7xC29406,3
C7×D29Direct product of C7 and D292032C7xD29406,4
C2×C29⋊C7Direct product of C2 and C29⋊C7587C2xC29:C7406,2

Groups of order 407

dρLabelID
C407Cyclic group4071C407407,1

Groups of order 408

dρLabelID
C408Cyclic group4081C408408,4
D204Dihedral group2042+D204408,27
Dic102Dicyclic group; = C512Q84082-Dic102408,25
C51⋊C81st semidirect product of C51 and C8 acting faithfully518C51:C8408,34
C17⋊S4The semidirect product of C17 and S4 acting via S4/A4=C2686+C17:S4408,37
C51⋊D41st semidirect product of C51 and D4 acting via D4/C2=C222044-C51:D4408,10
C3⋊D68The semidirect product of C3 and D68 acting via D68/D34=C22044+C3:D68408,11
C517D41st semidirect product of C51 and D4 acting via D4/C22=C22042C51:7D4408,29
C17⋊D12The semidirect product of C17 and D12 acting via D12/D6=C22044+C17:D12408,12
D512C4The semidirect product of D51 and C4 acting via C4/C2=C22044+D51:2C4408,9
C51⋊Q8The semidirect product of C51 and Q8 acting via Q8/C2=C224084-C51:Q8408,13
C515C81st semidirect product of C51 and C8 acting via C8/C4=C24082C51:5C8408,3
C513C81st semidirect product of C51 and C8 acting via C8/C2=C44084C51:3C8408,6
C2×C204Abelian group of type [2,204]408C2xC204408,30
C22×C102Abelian group of type [2,2,102]408C2^2xC102408,46
C17×S4Direct product of C17 and S4683C17xS4408,36
A4×D17Direct product of A4 and D17686+A4xD17408,38
A4×C34Direct product of C34 and A41023A4xC34408,42
C17×SL2(𝔽3)Direct product of C17 and SL2(𝔽3)1362C17xSL(2,3)408,14
S3×C68Direct product of C68 and S32042S3xC68408,21
C3×D68Direct product of C3 and D682042C3xD68408,17
C4×D51Direct product of C4 and D512042C4xD51408,26
D4×C51Direct product of C51 and D42042D4xC51408,31
C12×D17Direct product of C12 and D172042C12xD17408,16
C17×D12Direct product of C17 and D122042C17xD12408,22
Dic3×D17Direct product of Dic3 and D172044-Dic3xD17408,7
S3×Dic17Direct product of S3 and Dic172044-S3xDic17408,8
C22×D51Direct product of C22 and D51204C2^2xD51408,45
Q8×C51Direct product of C51 and Q84082Q8xC51408,32
C3×Dic34Direct product of C3 and Dic344082C3xDic34408,15
C6×Dic17Direct product of C6 and Dic17408C6xDic17408,18
C17×Dic6Direct product of C17 and Dic64082C17xDic6408,20
Dic3×C34Direct product of C34 and Dic3408Dic3xC34408,23
C2×Dic51Direct product of C2 and Dic51408C2xDic51408,28
C3×C17⋊C8Direct product of C3 and C17⋊C8518C3xC17:C8408,33
S3×C17⋊C4Direct product of S3 and C17⋊C4518+S3xC17:C4408,35
C6×C17⋊C4Direct product of C6 and C17⋊C41024C6xC17:C4408,39
C2×S3×D17Direct product of C2, S3 and D171024+C2xS3xD17408,41
C2×C51⋊C4Direct product of C2 and C51⋊C41024C2xC51:C4408,40
S3×C2×C34Direct product of C2×C34 and S3204S3xC2xC34408,44
C2×C6×D17Direct product of C2×C6 and D17204C2xC6xD17408,43
C3×C17⋊D4Direct product of C3 and C17⋊D42042C3xC17:D4408,19
C17×C3⋊D4Direct product of C17 and C3⋊D42042C17xC3:D4408,24
C17×C3⋊C8Direct product of C17 and C3⋊C84082C17xC3:C8408,1
C3×C173C8Direct product of C3 and C173C84082C3xC17:3C8408,2
C3×C172C8Direct product of C3 and C172C84084C3xC17:2C8408,5

Groups of order 409

dρLabelID
C409Cyclic group4091C409409,1

Groups of order 410

dρLabelID
C410Cyclic group4101C410410,6
D205Dihedral group2052+D205410,5
C41⋊C10The semidirect product of C41 and C10 acting faithfully4110+C41:C10410,1
D5×C41Direct product of C41 and D52052D5xC41410,3
C5×D41Direct product of C5 and D412052C5xD41410,4
C2×C41⋊C5Direct product of C2 and C41⋊C5825C2xC41:C5410,2

Groups of order 411

dρLabelID
C411Cyclic group4111C411411,1

Groups of order 412

dρLabelID
C412Cyclic group4121C412412,2
D206Dihedral group; = C2×D1032062+D206412,3
Dic103Dicyclic group; = C103C44122-Dic103412,1
C2×C206Abelian group of type [2,206]412C2xC206412,4

Groups of order 413

dρLabelID
C413Cyclic group4131C413413,1

Groups of order 414

dρLabelID
C414Cyclic group4141C414414,4
D207Dihedral group2072+D207414,3
C3⋊D69The semidirect product of C3 and D69 acting via D69/C69=C2207C3:D69414,9
C3×C138Abelian group of type [3,138]414C3xC138414,10
S3×C69Direct product of C69 and S31382S3xC69414,6
C3×D69Direct product of C3 and D691382C3xD69414,7
D9×C23Direct product of C23 and D92072D9xC23414,1
C9×D23Direct product of C9 and D232072C9xD23414,2
C32×D23Direct product of C32 and D23207C3^2xD23414,5
C3⋊S3×C23Direct product of C23 and C3⋊S3207C3:S3xC23414,8

Groups of order 415

dρLabelID
C415Cyclic group4151C415415,1

Groups of order 416

dρLabelID
C416Cyclic group4161C416416,2
D208Dihedral group2082+D208416,6
Dic104Dicyclic group; = C131Q324162-Dic104416,8
C8⋊D261st semidirect product of C8 and D26 acting via D26/C13=C221044+C8:D26416,129
C104⋊C44th semidirect product of C104 and C4 acting faithfully1044C104:C4416,67
D524C41st semidirect product of D52 and C4 acting via C4/C2=C21042D52:4C4416,12
D527C44th semidirect product of D52 and C4 acting via C4/C2=C21044D52:7C4416,32
D521C41st semidirect product of D52 and C4 acting faithfully1048+D52:1C4416,82
D52⋊C42nd semidirect product of D52 and C4 acting faithfully1048+D52:C4416,85
D8⋊D132nd semidirect product of D8 and D13 acting via D13/C13=C21044D8:D13416,132
D4⋊D262nd semidirect product of D4 and D26 acting via D26/C26=C21044+D4:D26416,170
D46D262nd semidirect product of D4 and D26 acting through Inn(D4)1044D4:6D26416,218
D48D264th semidirect product of D4 and D26 acting through Inn(D4)1044+D4:8D26416,223
Q8⋊D262nd semidirect product of Q8 and D26 acting via D26/D13=C21044+Q8:D26416,135
D13⋊M4(2)The semidirect product of D13 and M4(2) acting via M4(2)/C2×C4=C21044D13:M4(2)416,201
C22⋊D52The semidirect product of C22 and D52 acting via D52/D26=C2104C2^2:D52416,103
C23⋊D261st semidirect product of C23 and D26 acting via D26/C13=C22104C2^3:D26416,158
C24⋊D131st semidirect product of C24 and D13 acting via D13/C13=C2104C2^4:D13416,174
C23⋊Dic13The semidirect product of C23 and Dic13 acting via Dic13/C13=C41044C2^3:Dic13416,41
Dic26⋊C41st semidirect product of Dic26 and C4 acting faithfully1048-Dic26:C4416,83
D526C224th semidirect product of D52 and C22 acting via C22/C2=C21044D52:6C2^2416,153
D13⋊C16The semidirect product of D13 and C16 acting via C16/C8=C22084D13:C16416,64
C4⋊D52The semidirect product of C4 and D52 acting via D52/C52=C2208C4:D52416,95
C42D52The semidirect product of C4 and D52 acting via D52/D26=C2208C4:2D52416,116
C527D41st semidirect product of C52 and D4 acting via D4/C22=C2208C52:7D4416,151
C522D42nd semidirect product of C52 and D4 acting via D4/C2=C22208C52:2D4416,159
C52⋊D43rd semidirect product of C52 and D4 acting via D4/C2=C22208C52:D4416,161
C13⋊D16The semidirect product of C13 and D16 acting via D16/D8=C22084+C13:D16416,33
C208⋊C24th semidirect product of C208 and C2 acting faithfully2082C208:C2416,5
D526C43rd semidirect product of D52 and C4 acting via C4/C2=C2208D52:6C4416,16
D261C81st semidirect product of D26 and C8 acting via C8/C4=C2208D26:1C8416,27
D525C42nd semidirect product of D52 and C4 acting via C4/C2=C2208D52:5C4416,28
D26⋊C82nd semidirect product of D26 and C8 acting via C8/C4=C2208D26:C8416,78
D26⋊D41st semidirect product of D26 and D4 acting via D4/C4=C2208D26:D4416,105
D528C45th semidirect product of D52 and C4 acting via C4/C2=C2208D52:8C4416,114
D83D13The semidirect product of D8 and D13 acting through Inn(D8)2084-D8:3D13416,133
C16⋊D132nd semidirect product of C16 and D13 acting via D13/C13=C22082C16:D13416,7
D26⋊Q81st semidirect product of D26 and Q8 acting via Q8/C4=C2208D26:Q8416,117
D262Q82nd semidirect product of D26 and Q8 acting via Q8/C4=C2208D26:2Q8416,118
D263Q83rd semidirect product of D26 and Q8 acting via Q8/C4=C2208D26:3Q8416,167
D1047C2The semidirect product of D104 and C2 acting through Inn(D104)2082D104:7C2416,125
D104⋊C25th semidirect product of D104 and C2 acting faithfully2084+D104:C2416,140
Q16⋊D132nd semidirect product of Q16 and D13 acting via D13/C13=C22084Q16:D13416,139
C42⋊D131st semidirect product of C42 and D13 acting via D13/C13=C2208C4^2:D13416,93
C422D132nd semidirect product of C42 and D13 acting via D13/C13=C2208C4^2:2D13416,97
D4⋊Dic131st semidirect product of D4 and Dic13 acting via Dic13/C26=C2208D4:Dic13416,39
Dic134D41st semidirect product of Dic13 and D4 acting through Inn(Dic13)208Dic13:4D4416,102
Dic13⋊D42nd semidirect product of Dic13 and D4 acting via D4/C22=C2208Dic13:D4416,160
C22⋊Dic26The semidirect product of C22 and Dic26 acting via Dic26/Dic13=C2208C2^2:Dic26416,99
C13⋊C32The semidirect product of C13 and C32 acting via C32/C8=C44164C13:C32416,3
C52⋊Q8The semidirect product of C52 and Q8 acting via Q8/C2=C22416C52:Q8416,109
C523C81st semidirect product of C52 and C8 acting via C8/C4=C2416C52:3C8416,11
C52⋊C81st semidirect product of C52 and C8 acting via C8/C2=C4416C52:C8416,76
C132C32The semidirect product of C13 and C32 acting via C32/C16=C24162C13:2C32416,1
C522Q81st semidirect product of C52 and Q8 acting via Q8/C4=C2416C52:2Q8416,90
C1048C44th semidirect product of C104 and C4 acting via C4/C2=C2416C104:8C4416,22
C1046C42nd semidirect product of C104 and C4 acting via C4/C2=C2416C104:6C4416,24
C1045C41st semidirect product of C104 and C4 acting via C4/C2=C2416C104:5C4416,25
C13⋊Q32The semidirect product of C13 and Q32 acting via Q32/Q16=C24164-C13:Q32416,36
Q8⋊Dic131st semidirect product of Q8 and Dic13 acting via Dic13/C26=C2416Q8:Dic13416,42
Dic13⋊C83rd semidirect product of Dic13 and C8 acting via C8/C4=C2416Dic13:C8416,79
Dic133Q8The semidirect product of Dic13 and Q8 acting through Inn(Dic13)416Dic13:3Q8416,108
Dic13⋊Q82nd semidirect product of Dic13 and Q8 acting via Q8/C4=C2416Dic13:Q8416,165
C4⋊C47D131st semidirect product of C4⋊C4 and D13 acting through Inn(C4⋊C4)208C4:C4:7D13416,113
C4⋊C4⋊D136th semidirect product of C4⋊C4 and D13 acting via D13/C13=C2208C4:C4:D13416,119
C52.D48th non-split extension by C52 of D4 acting via D4/C2=C221044C52.D4416,40
D26.8D44th non-split extension by D26 of D4 acting via D4/C4=C21044D26.8D4416,68
D13.D8The non-split extension by D13 of D8 acting via D8/C8=C21044D13.D8416,69
D26.D41st non-split extension by D26 of D4 acting via D4/C2=C221044+D26.D4416,74
D26.4D44th non-split extension by D26 of D4 acting via D4/C2=C221044D26.4D4416,86
C52.46D43rd non-split extension by C52 of D4 acting via D4/C22=C21044+C52.46D4416,30
C52.56D413rd non-split extension by C52 of D4 acting via D4/C22=C21044C52.56D4416,44
D26.Q83rd non-split extension by D26 of Q8 acting via Q8/C4=C2104D26.Q8416,81
D13.Q16The non-split extension by D13 of Q16 acting via Q16/Q8=C21048-D13.Q16416,84
C22.2D521st non-split extension by C22 of D52 acting via D52/D26=C21044C2^2.2D52416,13
Dic13.4D44th non-split extension by Dic13 of D4 acting via D4/C2=C221044Dic13.4D4416,88
D26.C2311st non-split extension by D26 of C23 acting via C23/C22=C21044D26.C2^3416,204
D8.D13The non-split extension by D8 of D13 acting via D13/C13=C22084-D8.D13416,34
D52.C4The non-split extension by D52 of C4 acting faithfully2088+D52.C4416,207
C52.4C81st non-split extension by C52 of C8 acting via C8/C4=C22082C52.4C8416,19
C52.C81st non-split extension by C52 of C8 acting via C8/C2=C42084C52.C8416,73
C8.6D263rd non-split extension by C8 of D26 acting via D26/D13=C22084+C8.6D26416,35
C4.D525th non-split extension by C4 of D52 acting via D52/C52=C2208C4.D52416,96
C8.D261st non-split extension by C8 of D26 acting via D26/C13=C222084-C8.D26416,130
C104.6C41st non-split extension by C104 of C4 acting via C4/C2=C22082C104.6C4416,26
C104.C42nd non-split extension by C104 of C4 acting faithfully2084C104.C4416,70
C104.1C41st non-split extension by C104 of C4 acting faithfully2084C104.1C4416,71
D26.C83rd non-split extension by D26 of C8 acting via C8/C4=C22084D26.C8416,65
D52.3C4The non-split extension by D52 of C4 acting through Inn(D52)2082D52.3C4416,122
D52.2C4The non-split extension by D52 of C4 acting via C4/C2=C22084D52.2C4416,128
D4.D264th non-split extension by D4 of D26 acting via D26/D13=C22084-D4.D26416,136
D26.6D42nd non-split extension by D26 of D4 acting via D4/C4=C22084D26.6D4416,137
D4.9D264th non-split extension by D4 of D26 acting via D26/C26=C22084-D4.9D26416,172
C52.53D410th non-split extension by C52 of D4 acting via D4/C22=C22084C52.53D4416,29
C4.12D524th non-split extension by C4 of D52 acting via D52/D26=C22084-C4.12D52416,31
C52.55D412nd non-split extension by C52 of D4 acting via D4/C22=C2208C52.55D4416,37
C52.10D410th non-split extension by C52 of D4 acting via D4/C2=C222084C52.10D4416,43
C52.48D45th non-split extension by C52 of D4 acting via D4/C22=C2208C52.48D4416,145
C52.17D417th non-split extension by C52 of D4 acting via D4/C2=C22208C52.17D4416,157
C52.23D423rd non-split extension by C52 of D4 acting via D4/C2=C22208C52.23D4416,168
D4.Dic13The non-split extension by D4 of Dic13 acting through Inn(D4)2084D4.Dic13416,169
Dic26.C4The non-split extension by Dic26 of C4 acting faithfully2088-Dic26.C4416,205
Q8.D261st non-split extension by Q8 of D26 acting via D26/C26=C22084Q8.D26416,163
D26.12D41st non-split extension by D26 of D4 acting via D4/C22=C2208D26.12D4416,104
D26.13D42nd non-split extension by D26 of D4 acting via D4/C22=C2208D26.13D4416,115
D4.10D26The non-split extension by D4 of D26 acting through Inn(D4)2084-D4.10D26416,224
Q8.10D261st non-split extension by Q8 of D26 acting through Inn(Q8)2084Q8.10D26416,221
C23.D263rd non-split extension by C23 of D26 acting via D26/C13=C22208C2^3.D26416,100
C23.6D266th non-split extension by C23 of D26 acting via D26/C13=C22208C2^3.6D26416,106
C22.D523rd non-split extension by C22 of D52 acting via D52/D26=C2208C2^2.D52416,107
C52.C2318th non-split extension by C52 of C23 acting via C23/C2=C222084C52.C2^3416,171
Dic13.D41st non-split extension by Dic13 of D4 acting via D4/C2=C222084-Dic13.D4416,80
C23.11D261st non-split extension by C23 of D26 acting via D26/D13=C2208C2^3.11D26416,98
C23.21D262nd non-split extension by C23 of D26 acting via D26/C26=C2208C2^3.21D26416,147
C23.23D264th non-split extension by C23 of D26 acting via D26/C26=C2208C2^3.23D26416,150
C23.18D268th non-split extension by C23 of D26 acting via D26/D13=C2208C2^3.18D26416,156
C26.M4(2)2nd non-split extension by C26 of M4(2) acting via M4(2)/C22=C4208C26.M4(2)416,87
C26.D81st non-split extension by C26 of D8 acting via D8/D4=C2416C26.D8416,14
C52.Q82nd non-split extension by C52 of Q8 acting via Q8/C2=C22416C52.Q8416,15
C52.8Q85th non-split extension by C52 of Q8 acting via Q8/C4=C2416C52.8Q8416,21
C52.6Q83rd non-split extension by C52 of Q8 acting via Q8/C4=C2416C52.6Q8416,91
C52.44D41st non-split extension by C52 of D4 acting via D4/C22=C2416C52.44D4416,23
C26.Q162nd non-split extension by C26 of Q16 acting via Q16/Q8=C2416C26.Q16416,17
C26.7C422nd non-split extension by C26 of C42 acting via C42/C2×C4=C2416C26.7C4^2416,10
C26.C424th non-split extension by C26 of C42 acting via C42/C4=C4416C26.C4^2416,77
C4.Dic263rd non-split extension by C4 of Dic26 acting via Dic26/Dic13=C2416C4.Dic26416,111
C26.10C425th non-split extension by C26 of C42 acting via C42/C2×C4=C2416C26.10C4^2416,38
Dic13.Q81st non-split extension by Dic13 of Q8 acting via Q8/C4=C2416Dic13.Q8416,110
C4×C104Abelian group of type [4,104]416C4xC104416,46
C2×C208Abelian group of type [2,208]416C2xC208416,59
C23×C52Abelian group of type [2,2,2,52]416C2^3xC52416,227
C24×C26Abelian group of type [2,2,2,2,26]416C2^4xC26416,235
C22×C104Abelian group of type [2,2,104]416C2^2xC104416,190
C2×C4×C52Abelian group of type [2,4,52]416C2xC4xC52416,175
D8×D13Direct product of D8 and D131044+D8xD13416,131
SD16×D13Direct product of SD16 and D131044SD16xD13416,134
M4(2)×D13Direct product of M4(2) and D131044M4(2)xD13416,127
C13×2+ 1+4Direct product of C13 and 2+ 1+41044C13xES+(2,2)416,231
C4×D52Direct product of C4 and D52208C4xD52416,94
D4×C52Direct product of C52 and D4208D4xC52416,179
D8×C26Direct product of C26 and D8208D8xC26416,193
C16×D13Direct product of C16 and D132082C16xD13416,4
C13×D16Direct product of C13 and D162082C13xD16416,61
C2×D104Direct product of C2 and D104208C2xD104416,124
Q16×D13Direct product of Q16 and D132084-Q16xD13416,138
C13×SD32Direct product of C13 and SD322082C13xSD32416,62
D4×Dic13Direct product of D4 and Dic13208D4xDic13416,155
SD16×C26Direct product of C26 and SD16208SD16xC26416,194
C42×D13Direct product of C42 and D13208C4^2xD13416,92
C22×D52Direct product of C22 and D52208C2^2xD52416,214
C24×D13Direct product of C24 and D13208C2^4xD13416,234
C13×M5(2)Direct product of C13 and M5(2)2082C13xM5(2)416,60
M4(2)×C26Direct product of C26 and M4(2)208M4(2)xC26416,191
C13×2- 1+4Direct product of C13 and 2- 1+42084C13xES-(2,2)416,232
Q8×C52Direct product of C52 and Q8416Q8xC52416,180
C13×Q32Direct product of C13 and Q324162C13xQ32416,63
Q16×C26Direct product of C26 and Q16416Q16xC26416,195
C8×Dic13Direct product of C8 and Dic13416C8xDic13416,20
C4×Dic26Direct product of C4 and Dic26416C4xDic26416,89
C2×Dic52Direct product of C2 and Dic52416C2xDic52416,126
Q8×Dic13Direct product of Q8 and Dic13416Q8xDic13416,166
C22×Dic26Direct product of C22 and Dic26416C2^2xDic26416,212
C23×Dic13Direct product of C23 and Dic13416C2^3xDic13416,225
D4×C13⋊C4Direct product of D4 and C13⋊C4528+D4xC13:C4416,206
C8×C13⋊C4Direct product of C8 and C13⋊C41044C8xC13:C4416,66
C2×D4×D13Direct product of C2, D4 and D13104C2xD4xD13416,216
Q8×C13⋊C4Direct product of Q8 and C13⋊C41048-Q8xC13:C4416,208
C13×C4≀C2Direct product of C13 and C4≀C21042C13xC4wrC2416,54
C2×C52⋊C4Direct product of C2 and C52⋊C4104C2xC52:C4416,203
C4○D4×D13Direct product of C4○D4 and D131044C4oD4xD13416,222
C23×C13⋊C4Direct product of C23 and C13⋊C4104C2^3xC13:C4416,233
C13×C23⋊C4Direct product of C13 and C23⋊C41044C13xC2^3:C4416,49
C13×C8⋊C22Direct product of C13 and C8⋊C221044C13xC8:C2^2416,197
C22⋊C4×D13Direct product of C22⋊C4 and D13104C2^2:C4xD13416,101
C13×C4.D4Direct product of C13 and C4.D41044C13xC4.D4416,50
C13×C22≀C2Direct product of C13 and C22≀C2104C13xC2^2wrC2416,181
C2×D13.D4Direct product of C2 and D13.D4104C2xD13.D4416,211
C2×C8×D13Direct product of C2×C8 and D13208C2xC8xD13416,120
D4×C2×C26Direct product of C2×C26 and D4208D4xC2xC26416,228
C2×Q8×D13Direct product of C2, Q8 and D13208C2xQ8xD13416,219
C4⋊C4×D13Direct product of C4⋊C4 and D13208C4:C4xD13416,112
C4×C13⋊D4Direct product of C4 and C13⋊D4208C4xC13:D4416,149
C2×D4⋊D13Direct product of C2 and D4⋊D13208C2xD4:D13416,152
C2×D13⋊C8Direct product of C2 and D13⋊C8208C2xD13:C8416,199
C13×C8○D4Direct product of C13 and C8○D42082C13xC8oD4416,192
C13×C4○D8Direct product of C13 and C4○D82082C13xC4oD8416,196
C4○D4×C26Direct product of C26 and C4○D4208C4oD4xC26416,230
C2×C8⋊D13Direct product of C2 and C8⋊D13208C2xC8:D13416,121
C13×C4⋊D4Direct product of C13 and C4⋊D4208C13xC4:D4416,182
C2×Q8⋊D13Direct product of C2 and Q8⋊D13208C2xQ8:D13416,162
C2×C104⋊C2Direct product of C2 and C104⋊C2208C2xC104:C2416,123
C22×C4×D13Direct product of C22×C4 and D13208C2^2xC4xD13416,213
C13×D4⋊C4Direct product of C13 and D4⋊C4208C13xD4:C4416,52
C13×C8.C4Direct product of C13 and C8.C42082C13xC8.C4416,58
C2×D26⋊C4Direct product of C2 and D26⋊C4208C2xD26:C4416,148
C2×C52.C4Direct product of C2 and C52.C4208C2xC52.C4416,200
C2×D52⋊C2Direct product of C2 and D52⋊C2208C2xD52:C2416,220
C13×C41D4Direct product of C13 and C41D4208C13xC4:1D4416,188
C13×C22⋊C8Direct product of C13 and C22⋊C8208C13xC2^2:C8416,48
C22⋊C4×C26Direct product of C26 and C22⋊C4208C2^2:C4xC26416,176
C2×D4.D13Direct product of C2 and D4.D13208C2xD4.D13416,154
C22×C13⋊D4Direct product of C22 and C13⋊D4208C2^2xC13:D4416,226
C13×C22⋊Q8Direct product of C13 and C22⋊Q8208C13xC2^2:Q8416,183
C2×C52.4C4Direct product of C2 and C52.4C4208C2xC52.4C4416,142
C2×D525C2Direct product of C2 and D525C2208C2xD52:5C2416,215
C2×D42D13Direct product of C2 and D42D13208C2xD4:2D13416,217
C13×C42⋊C2Direct product of C13 and C42⋊C2208C13xC4^2:C2416,178
C13×C4.4D4Direct product of C13 and C4.4D4208C13xC4.4D4416,185
C13×C8.C22Direct product of C13 and C8.C222084C13xC8.C2^2416,198
C2×C13⋊M4(2)Direct product of C2 and C13⋊M4(2)208C2xC13:M4(2)416,210
C2×C23.D13Direct product of C2 and C23.D13208C2xC2^3.D13416,173
C13×C422C2Direct product of C13 and C422C2208C13xC4^2:2C2416,187
C13×C4.10D4Direct product of C13 and C4.10D42084C13xC4.10D4416,51
C13×C22.D4Direct product of C13 and C22.D4208C13xC2^2.D4416,184
C4×C13⋊C8Direct product of C4 and C13⋊C8416C4xC13:C8416,75
C13×C4⋊C8Direct product of C13 and C4⋊C8416C13xC4:C8416,55
C4⋊C4×C26Direct product of C26 and C4⋊C4416C4:C4xC26416,177
C2×C13⋊C16Direct product of C2 and C13⋊C16416C2xC13:C16416,72
Q8×C2×C26Direct product of C2×C26 and Q8416Q8xC2xC26416,229
C13×C4⋊Q8Direct product of C13 and C4⋊Q8416C13xC4:Q8416,189
C13×C8⋊C4Direct product of C13 and C8⋊C4416C13xC8:C4416,47
C4×C132C8Direct product of C4 and C132C8416C4xC13:2C8416,9
C22×C13⋊C8Direct product of C22 and C13⋊C8416C2^2xC13:C8416,209
C2×C4×Dic13Direct product of C2×C4 and Dic13416C2xC4xDic13416,143
C2×C523C4Direct product of C2 and C523C4416C2xC52:3C4416,146
C2×C13⋊Q16Direct product of C2 and C13⋊Q16416C2xC13:Q16416,164
C2×C132C16Direct product of C2 and C132C16416C2xC13:2C16416,18
C13×Q8⋊C4Direct product of C13 and Q8⋊C4416C13xQ8:C4416,53
C13×C2.D8Direct product of C13 and C2.D8416C13xC2.D8416,57
C2×C26.D4Direct product of C2 and C26.D4416C2xC26.D4416,144
C13×C4.Q8Direct product of C13 and C4.Q8416C13xC4.Q8416,56
C22×C132C8Direct product of C22 and C132C8416C2^2xC13:2C8416,141
C13×C2.C42Direct product of C13 and C2.C42416C13xC2.C4^2416,45
C13×C42.C2Direct product of C13 and C42.C2416C13xC4^2.C2416,186
C2×C4×C13⋊C4Direct product of C2×C4 and C13⋊C4104C2xC4xC13:C4416,202

Groups of order 417

dρLabelID
C417Cyclic group4171C417417,2
C139⋊C3The semidirect product of C139 and C3 acting faithfully1393C139:C3417,1

Groups of order 418

dρLabelID
C418Cyclic group4181C418418,4
D209Dihedral group2092+D209418,3
C19×D11Direct product of C19 and D112092C19xD11418,1
C11×D19Direct product of C11 and D192092C11xD19418,2

Groups of order 419

dρLabelID
C419Cyclic group4191C419419,1

Groups of order 420

dρLabelID
C420Cyclic group4201C420420,12
D210Dihedral group; = C2×D1052102+D210420,40
Dic105Dicyclic group; = C3Dic354202-Dic105420,11
C35⋊C121st semidirect product of C35 and C12 acting faithfully3512C35:C12420,15
D15⋊D7The semidirect product of D15 and D7 acting via D7/C7=C21054D15:D7420,30
C5⋊Dic21The semidirect product of C5 and Dic21 acting via Dic21/C21=C41054C5:Dic21420,23
C353C121st semidirect product of C35 and C12 acting via C12/C2=C61406-C35:3C12420,3
C2×C210Abelian group of type [2,210]420C2xC210420,41
C7×A5Direct product of C7 and A5353C7xA5420,13
D5×F7Direct product of D5 and F73512+D5xF7420,16
C10×F7Direct product of C10 and F7706C10xF7420,17
D7×D15Direct product of D7 and D151054+D7xD15420,26
D5×D21Direct product of D5 and D211054+D5xD21420,28
S3×D35Direct product of S3 and D351054+S3xD35420,29
F5×C21Direct product of C21 and F51054F5xC21420,20
A4×C35Direct product of C35 and A41403A4xC35420,32
S3×C70Direct product of C70 and S32102S3xC70420,37
D7×C30Direct product of C30 and D72102D7xC30420,34
D5×C42Direct product of C42 and D52102D5xC42420,35
C6×D35Direct product of C6 and D352102C6xD35420,36
C10×D21Direct product of C10 and D212102C10xD21420,38
C14×D15Direct product of C14 and D152102C14xD15420,39
C15×Dic7Direct product of C15 and Dic74202C15xDic7420,5
Dic5×C21Direct product of C21 and Dic54202Dic5xC21420,6
C3×Dic35Direct product of C3 and Dic354202C3xDic35420,7
Dic3×C35Direct product of C35 and Dic34202Dic3xC35420,8
C5×Dic21Direct product of C5 and Dic214202C5xDic21420,9
C7×Dic15Direct product of C7 and Dic154202C7xDic15420,10
F5×C7⋊C3Direct product of F5 and C7⋊C33512F5xC7:C3420,14
C2×C5⋊F7Direct product of C2 and C5⋊F7706+C2xC5:F7420,19
C3×D5×D7Direct product of C3, D5 and D71054C3xD5xD7420,24
C5×S3×D7Direct product of C5, S3 and D71054C5xS3xD7420,25
S3×C7×D5Direct product of C7, S3 and D51054S3xC7xD5420,27
C3×C7⋊F5Direct product of C3 and C7⋊F51054C3xC7:F5420,21
C7×C3⋊F5Direct product of C7 and C3⋊F51054C7xC3:F5420,22
C5×C7⋊A4Direct product of C5 and C7⋊A41403C5xC7:A4420,33
C5×C7⋊C12Direct product of C5 and C7⋊C121406C5xC7:C12420,1
C20×C7⋊C3Direct product of C20 and C7⋊C31403C20xC7:C3420,4
Dic5×C7⋊C3Direct product of Dic5 and C7⋊C31406Dic5xC7:C3420,2
C2×D5×C7⋊C3Direct product of C2, D5 and C7⋊C3706C2xD5xC7:C3420,18
C2×C10×C7⋊C3Direct product of C2×C10 and C7⋊C3140C2xC10xC7:C3420,31

Groups of order 421

dρLabelID
C421Cyclic group4211C421421,1

Groups of order 422

dρLabelID
C422Cyclic group4221C422422,2
D211Dihedral group2112+D211422,1

Groups of order 423

dρLabelID
C423Cyclic group4231C423423,1
C3×C141Abelian group of type [3,141]423C3xC141423,2

Groups of order 424

dρLabelID
C424Cyclic group4241C424424,2
D212Dihedral group2122+D212424,6
Dic106Dicyclic group; = C53Q84242-Dic106424,4
C53⋊D4The semidirect product of C53 and D4 acting via D4/C22=C22122C53:D4424,8
C53⋊C8The semidirect product of C53 and C8 acting via C8/C2=C44244-C53:C8424,3
C532C8The semidirect product of C53 and C8 acting via C8/C4=C24242C53:2C8424,1
C2×C212Abelian group of type [2,212]424C2xC212424,9
C22×C106Abelian group of type [2,2,106]424C2^2xC106424,14
C4×D53Direct product of C4 and D532122C4xD53424,5
D4×C53Direct product of C53 and D42122D4xC53424,10
C22×D53Direct product of C22 and D53212C2^2xD53424,13
Q8×C53Direct product of C53 and Q84242Q8xC53424,11
C2×Dic53Direct product of C2 and Dic53424C2xDic53424,7
C2×C53⋊C4Direct product of C2 and C53⋊C41064+C2xC53:C4424,12

Groups of order 425

dρLabelID
C425Cyclic group4251C425425,1
C5×C85Abelian group of type [5,85]425C5xC85425,2

Groups of order 426

dρLabelID
C426Cyclic group4261C426426,4
D213Dihedral group2132+D213426,3
S3×C71Direct product of C71 and S32132S3xC71426,1
C3×D71Direct product of C3 and D712132C3xD71426,2

Groups of order 427

dρLabelID
C427Cyclic group4271C427427,1

Groups of order 428

dρLabelID
C428Cyclic group4281C428428,2
D214Dihedral group; = C2×D1072142+D214428,3
Dic107Dicyclic group; = C107C44282-Dic107428,1
C2×C214Abelian group of type [2,214]428C2xC214428,4

Groups of order 429

dρLabelID
C429Cyclic group4291C429429,2
C11×C13⋊C3Direct product of C11 and C13⋊C31433C11xC13:C3429,1

Groups of order 430

dρLabelID
C430Cyclic group4301C430430,4
D215Dihedral group2152+D215430,3
D5×C43Direct product of C43 and D52152D5xC43430,1
C5×D43Direct product of C5 and D432152C5xD43430,2

Groups of order 431

dρLabelID
C431Cyclic group4311C431431,1

Groups of order 432

dρLabelID
C432Cyclic group4321C432432,2
D216Dihedral group2162+D216432,8
Dic108Dicyclic group; = C271Q164322-Dic108432,4
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)98+AGL(2,3)432,734
C625D65th semidirect product of C62 and D6 acting faithfully186+C6^2:5D6432,523
F9⋊S3The semidirect product of F9 and S3 acting via S3/C3=C22416+F9:S3432,740
C33⋊D82nd semidirect product of C33 and D8 acting via D8/C2=D4244C3^3:D8432,582
C62⋊Dic3The semidirect product of C62 and Dic3 acting faithfully2412+C6^2:Dic3432,743
C322D24The semidirect product of C32 and D24 acting via D24/C6=D4248+C3^2:2D24432,588
C6224D65th semidirect product of C62 and D6 acting via D6/C3=C22244C6^2:24D6432,696
C6210D610th semidirect product of C62 and D6 acting faithfully2412+C6^2:10D6432,748
C336SD162nd semidirect product of C33 and SD16 acting via SD16/C2=D4244C3^3:6SD16432,583
C337SD163rd semidirect product of C33 and SD16 acting via SD16/C2=D4244C3^3:7SD16432,584
C338SD164th semidirect product of C33 and SD16 acting via SD16/C2=D4248+C3^3:8SD16432,589
C33⋊SD162nd semidirect product of C33 and SD16 acting faithfully248C3^3:SD16432,738
C333SD163rd semidirect product of C33 and SD16 acting faithfully2416+C3^3:3SD16432,739
C332M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C2=C2×C4248+C3^3:2M4(2)432,573
C6211Dic31st semidirect product of C62 and Dic3 acting via Dic3/C3=C4244C6^2:11Dic3432,641
C3312M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C22=C4244C3^3:12M4(2)432,640
He3⋊SD16The semidirect product of He3 and SD16 acting faithfully276+He3:SD16432,520
C42⋊He3The semidirect product of C42 and He3 acting via He3/C32=C3363C4^2:He3432,103
C24⋊He3The semidirect product of C24 and He3 acting via He3/C3=C32369C2^4:He3432,526
D18⋊D64th semidirect product of D18 and D6 acting via D6/S3=C2364+D18:D6432,315
C62⋊A42nd semidirect product of C62 and A4 acting via A4/C22=C336C6^2:A4432,555
C62⋊D61st semidirect product of C62 and D6 acting faithfully3612+C6^2:D6432,323
C622D62nd semidirect product of C62 and D6 acting faithfully366C6^2:2D6432,324
C624C123rd semidirect product of C62 and C12 acting via C12/C2=C6366-C6^2:4C12432,272
C6223D64th semidirect product of C62 and D6 acting via D6/C3=C2236C6^2:23D6432,686
C625Dic34th semidirect product of C62 and Dic3 acting via Dic3/C2=S3366-C6^2:5Dic3432,251
C626Dic35th semidirect product of C62 and Dic3 acting via Dic3/C2=S3363C6^2:6Dic3432,260
C2423- 1+22nd semidirect product of C24 and 3- 1+2 acting via 3- 1+2/C3=C32369C2^4:2ES-(3,1)432,528
C339D86th semidirect product of C33 and D8 acting via D8/C4=C22484C3^3:9D8432,457
C334C162nd semidirect product of C33 and C16 acting via C16/C4=C4484C3^3:4C16432,413
C339Q166th semidirect product of C33 and Q16 acting via Q16/C4=C22484C3^3:9Q16432,459
C33⋊Q162nd semidirect product of C33 and Q16 acting via Q16/C2=D4484C3^3:Q16432,585
C333Q163rd semidirect product of C33 and Q16 acting via Q16/C2=D4488-C3^3:3Q16432,590
C336C423rd semidirect product of C33 and C42 acting via C42/C22=C2248C3^3:6C4^2432,460
C3318SD1610th semidirect product of C33 and SD16 acting via SD16/C4=C22484C3^3:18SD16432,458
C33⋊M4(2)1st semidirect product of C33 and M4(2) acting via M4(2)/C2=C2×C4488-C3^3:M4(2)432,572
C334M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C4=C4484C3^3:4M4(2)432,636
C3310M4(2)6th semidirect product of C33 and M4(2) acting via M4(2)/C4=C22484C3^3:10M4(2)432,456
C24⋊3- 1+21st semidirect product of C24 and 3- 1+2 acting via 3- 1+2/C3=C32549C2^4:ES-(3,1)432,527
He3⋊D8The semidirect product of He3 and D8 acting via D8/C2=D4726+He3:D8432,235
D72⋊C3The semidirect product of D72 and C3 acting faithfully726+D72:C3432,123
C72⋊C64th semidirect product of C72 and C6 acting faithfully726C72:C6432,121
C722C62nd semidirect product of C72 and C6 acting faithfully726C72:2C6432,122
D18⋊C12The semidirect product of D18 and C12 acting via C12/C2=C672D18:C12432,147
C3⋊D72The semidirect product of C3 and D72 acting via D72/D36=C2724+C3:D72432,64
C9⋊D24The semidirect product of C9 and D24 acting via D24/D12=C2724+C9:D24432,69
C36⋊D62nd semidirect product of C36 and D6 acting via D6/C3=C22724C36:D6432,293

Full list: Groups of order 432 (775 groups)

Groups of order 433

dρLabelID
C433Cyclic group4331C433433,1

Groups of order 434

dρLabelID
C434Cyclic group4341C434434,4
D217Dihedral group2172+D217434,3
D7×C31Direct product of C31 and D72172D7xC31434,1
C7×D31Direct product of C7 and D312172C7xD31434,2

Groups of order 435

dρLabelID
C435Cyclic group4351C435435,1

Groups of order 436

dρLabelID
C436Cyclic group4361C436436,2
D218Dihedral group; = C2×D1092182+D218436,4
Dic109Dicyclic group; = C1092C44362-Dic109436,1
C109⋊C4The semidirect product of C109 and C4 acting faithfully1094+C109:C4436,3
C2×C218Abelian group of type [2,218]436C2xC218436,5

Groups of order 437

dρLabelID
C437Cyclic group4371C437437,1

Groups of order 438

dρLabelID
C438Cyclic group4381C438438,6
D219Dihedral group2192+D219438,5
C73⋊C6The semidirect product of C73 and C6 acting faithfully736+C73:C6438,1
S3×C73Direct product of C73 and S32192S3xC73438,3
C3×D73Direct product of C3 and D732192C3xD73438,4
C2×C73⋊C3Direct product of C2 and C73⋊C31463C2xC73:C3438,2

Groups of order 439

dρLabelID
C439Cyclic group4391C439439,1

Groups of order 440

dρLabelID
C440Cyclic group4401C440440,6
D220Dihedral group2202+D220440,36
Dic110Dicyclic group; = C552Q84402-Dic110440,34
D44⋊C5The semidirect product of D44 and C5 acting faithfully4410+D44:C5440,9
C22⋊F11The semidirect product of C22 and F11 acting via F11/C11⋊C5=C24410C2^2:F11440,11
C11⋊C40The semidirect product of C11 and C40 acting via C40/C4=C108810C11:C40440,1
C55⋊D41st semidirect product of C55 and D4 acting via D4/C2=C222204-C55:D4440,20
C5⋊D44The semidirect product of C5 and D44 acting via D44/D22=C22204+C5:D44440,21
C557D41st semidirect product of C55 and D4 acting via D4/C22=C22202C55:7D4440,38
C11⋊D20The semidirect product of C11 and D20 acting via D20/D10=C22204+C11:D20440,22
D552C4The semidirect product of D55 and C4 acting via C4/C2=C22204+D55:2C4440,19
C55⋊Q8The semidirect product of C55 and Q8 acting via Q8/C2=C224404-C55:Q8440,23
C553C81st semidirect product of C55 and C8 acting via C8/C4=C24402C55:3C8440,5
C55⋊C81st semidirect product of C55 and C8 acting via C8/C2=C44404C55:C8440,16
C4.F11The non-split extension by C4 of F11 acting via F11/C11⋊C5=C28810-C4.F11440,7
C2×C220Abelian group of type [2,220]440C2xC220440,39
C22×C110Abelian group of type [2,2,110]440C2^2xC110440,51
C4×F11Direct product of C4 and F114410C4xF11440,8
C22×F11Direct product of C22 and F1144C2^2xF11440,42
F5×D11Direct product of F5 and D11558+F5xD11440,43
F5×C22Direct product of C22 and F51104F5xC22440,45
C5×D44Direct product of C5 and D442202C5xD44440,26
D5×C44Direct product of C44 and D52202D5xC44440,30
C4×D55Direct product of C4 and D552202C4xD55440,35
D4×C55Direct product of C55 and D42202D4xC55440,40
C20×D11Direct product of C20 and D112202C20xD11440,25
C11×D20Direct product of C11 and D202202C11xD20440,31
Dic5×D11Direct product of Dic5 and D112204-Dic5xD11440,17
D5×Dic11Direct product of D5 and Dic112204-D5xDic11440,18
C22×D55Direct product of C22 and D55220C2^2xD55440,50
Q8×C55Direct product of C55 and Q84402Q8xC55440,41
C5×Dic22Direct product of C5 and Dic224402C5xDic22440,24
Dic5×C22Direct product of C22 and Dic5440Dic5xC22440,32
C2×Dic55Direct product of C2 and Dic55440C2xDic55440,37
C10×Dic11Direct product of C10 and Dic11440C10xDic11440,27
C11×Dic10Direct product of C11 and Dic104402C11xDic10440,29
D4×C11⋊C5Direct product of D4 and C11⋊C54410D4xC11:C5440,13
C8×C11⋊C5Direct product of C8 and C11⋊C5885C8xC11:C5440,2
Q8×C11⋊C5Direct product of Q8 and C11⋊C58810Q8xC11:C5440,14
C2×C11⋊C20Direct product of C2 and C11⋊C2088C2xC11:C20440,10
C23×C11⋊C5Direct product of C23 and C11⋊C588C2^3xC11:C5440,44
C2×D5×D11Direct product of C2, D5 and D111104+C2xD5xD11440,47
C2×C11⋊F5Direct product of C2 and C11⋊F51104C2xC11:F5440,46
D5×C2×C22Direct product of C2×C22 and D5220D5xC2xC22440,49
C2×C10×D11Direct product of C2×C10 and D11220C2xC10xD11440,48
C5×C11⋊D4Direct product of C5 and C11⋊D42202C5xC11:D4440,28
C11×C5⋊D4Direct product of C11 and C5⋊D42202C11xC5:D4440,33
C5×C11⋊C8Direct product of C5 and C11⋊C84402C5xC11:C8440,4
C11×C5⋊C8Direct product of C11 and C5⋊C84404C11xC5:C8440,15
C11×C52C8Direct product of C11 and C52C84402C11xC5:2C8440,3
C2×C4×C11⋊C5Direct product of C2×C4 and C11⋊C588C2xC4xC11:C5440,12

Groups of order 441

dρLabelID
C441Cyclic group4411C441441,2
C723C93rd semidirect product of C72 and C9 acting via C9/C3=C3633C7^2:3C9441,7
C49⋊C9The semidirect product of C49 and C9 acting via C9/C3=C34413C49:C9441,1
C72⋊C92nd semidirect product of C72 and C9 acting via C9/C3=C3441C7^2:C9441,6
C212Abelian group of type [21,21]441C21^2441,13
C7×C63Abelian group of type [7,63]441C7xC63441,8
C3×C147Abelian group of type [3,147]441C3xC147441,4
C7×C7⋊C9Direct product of C7 and C7⋊C9633C7xC7:C9441,5
C7⋊C3×C21Direct product of C21 and C7⋊C3633C7:C3xC21441,10
C3×C723C3Direct product of C3 and C723C3633C3xC7^2:3C3441,12
C3×C49⋊C3Direct product of C3 and C49⋊C31473C3xC49:C3441,3
C3×C72⋊C3Direct product of C3 and C72⋊C3147C3xC7^2:C3441,11
C7⋊C32Direct product of C7⋊C3 and C7⋊C3219C7:C3^2441,9

Groups of order 442

dρLabelID
C442Cyclic group4421C442442,4
D221Dihedral group2212+D221442,3
C17×D13Direct product of C17 and D132212C17xD13442,1
C13×D17Direct product of C13 and D172212C13xD17442,2

Groups of order 443

dρLabelID
C443Cyclic group4431C443443,1

Groups of order 444

dρLabelID
C444Cyclic group4441C444444,6
D222Dihedral group; = C2×D1112222+D222444,17
Dic111Dicyclic group; = C3Dic374442-Dic111444,5
C37⋊C12The semidirect product of C37 and C12 acting faithfully3712+C37:C12444,7
C37⋊Dic3The semidirect product of C37 and Dic3 acting via Dic3/C3=C41114C37:Dic3444,10
C37⋊A4The semidirect product of C37 and A4 acting via A4/C22=C31483C37:A4444,14
C74.C6The non-split extension by C74 of C6 acting faithfully1486-C74.C6444,1
C2×C222Abelian group of type [2,222]444C2xC222444,18
S3×D37Direct product of S3 and D371114+S3xD37444,11
A4×C37Direct product of C37 and A41483A4xC37444,13
S3×C74Direct product of C74 and S32222S3xC74444,16
C6×D37Direct product of C6 and D372222C6xD37444,15
Dic3×C37Direct product of C37 and Dic34442Dic3xC37444,3
C3×Dic37Direct product of C3 and Dic374442C3xDic37444,4
C2×C37⋊C6Direct product of C2 and C37⋊C6746+C2xC37:C6444,8
C3×C37⋊C4Direct product of C3 and C37⋊C41114C3xC37:C4444,9
C4×C37⋊C3Direct product of C4 and C37⋊C31483C4xC37:C3444,2
C22×C37⋊C3Direct product of C22 and C37⋊C3148C2^2xC37:C3444,12

Groups of order 445

dρLabelID
C445Cyclic group4451C445445,1

Groups of order 446

dρLabelID
C446Cyclic group4461C446446,2
D223Dihedral group2232+D223446,1

Groups of order 447

dρLabelID
C447Cyclic group4471C447447,1

Groups of order 448

dρLabelID
C448Cyclic group4481C448448,2
D224Dihedral group2242+D224448,5
Dic112Dicyclic group; = C71Q644482-Dic112448,7
C23⋊F82nd semidirect product of C23 and F8 acting via F8/C23=C7147+C2^3:F8448,1394
C43⋊C7The semidirect product of C43 and C7 acting faithfully287C4^3:C7448,178
C26⋊C72nd semidirect product of C26 and C7 acting faithfully28C2^6:C7448,1393
C23⋊D28The semidirect product of C23 and D28 acting via D28/C7=D4568+C2^3:D28448,275
D281D41st semidirect product of D28 and D4 acting via D4/C2=C22568+D28:1D4448,281
D44D283rd semidirect product of D4 and D28 acting via D28/D14=C2564+D4:4D28448,356
D285D45th semidirect product of D28 and D4 acting via D4/C2=C22564D28:5D4448,611
D2818D46th semidirect product of D28 and D4 acting via D4/C22=C2568+D28:18D4448,732
C24⋊D141st semidirect product of C24 and D14 acting via D14/C7=C22564C2^4:D14448,566
C24⋊Dic71st semidirect product of C24 and Dic7 acting via Dic7/C7=C4564C2^4:Dic7448,93
C423Dic73rd semidirect product of C42 and Dic7 acting via Dic7/C7=C4564C4^2:3Dic7448,102
2+ 1+4⋊D71st semidirect product of 2+ 1+4 and D7 acting via D7/C7=C2568+ES+(2,2):D7448,775
2+ 1+42D72nd semidirect product of 2+ 1+4 and D7 acting via D7/C7=C2568+ES+(2,2):2D7448,778
C112⋊C42nd semidirect product of C112 and C4 acting faithfully1124C112:C4448,69
D568C48th semidirect product of D56 and C4 acting via C4/C2=C21124D56:8C4448,45
D562C42nd semidirect product of D56 and C4 acting via C4/C2=C21124D56:2C4448,75
D564C44th semidirect product of D56 and C4 acting via C4/C2=C21124D56:4C4448,251
D4⋊D281st semidirect product of D4 and D28 acting via D28/D14=C2112D4:D28448,307
D567C47th semidirect product of D56 and C4 acting via C4/C2=C21124D56:7C4448,429
D8⋊D142nd semidirect product of D8 and D14 acting via D14/D7=C21124D8:D14448,445
D28⋊D46th semidirect product of D28 and D4 acting via D4/C2=C22112D28:D4448,690
D45D281st semidirect product of D4 and D28 acting through Inn(D4)112D4:5D28448,1007
D85D145th semidirect product of D8 and D14 acting via D14/D7=C21128+D8:5D14448,1227
D86D146th semidirect product of D8 and D14 acting via D14/D7=C21128-D8:6D14448,1228
C16⋊D141st semidirect product of C16 and D14 acting via D14/C7=C221124+C16:D14448,442
D5611C4The semidirect product of D56 and C4 acting through Inn(D56)1122D56:11C4448,234
D2813D41st semidirect product of D28 and D4 acting via D4/C22=C2112D28:13D4448,266
D5610C410th semidirect product of D56 and C4 acting via C4/C2=C21124D56:10C4448,428
D112⋊C26th semidirect product of D112 and C2 acting faithfully1124+D112:C2448,448
D2816D44th semidirect product of D28 and D4 acting via D4/C22=C2112D28:16D4448,570
D2823D41st semidirect product of D28 and D4 acting through Inn(D28)112D28:23D4448,1003
D2819D47th semidirect product of D28 and D4 acting via D4/C22=C2112D28:19D4448,1062
D2820D48th semidirect product of D28 and D4 acting via D4/C22=C2112D28:20D4448,1065
D2821D49th semidirect product of D28 and D4 acting via D4/C22=C2112D28:21D4448,1083
D2810D43rd semidirect product of D28 and D4 acting via D4/C4=C2112D28:10D4448,1129
D2811D44th semidirect product of D28 and D4 acting via D4/C4=C2112D28:11D4448,1170
D813D142nd semidirect product of D8 and D14 acting through Inn(D8)1124D8:13D14448,1210
D810D144th semidirect product of D8 and D14 acting via D14/C14=C21124D8:10D14448,1221
D815D144th semidirect product of D8 and D14 acting through Inn(D8)1124+D8:15D14448,1222
D811D145th semidirect product of D8 and D14 acting via D14/C14=C21124D8:11D14448,1223
Q16⋊D142nd semidirect product of Q16 and D14 acting via D14/C14=C21124+Q16:D14448,727
D82Dic72nd semidirect product of D8 and Dic7 acting via Dic7/C14=C21124D8:2Dic7448,123
D85Dic7The semidirect product of D8 and Dic7 acting through Inn(D8)1124D8:5Dic7448,730
D84Dic74th semidirect product of D8 and Dic7 acting via Dic7/C14=C21124D8:4Dic7448,731
C16⋊Dic71st semidirect product of C16 and Dic7 acting via Dic7/C7=C41124C16:Dic7448,70
C42⋊D141st semidirect product of C42 and D14 acting via D14/C7=C221124C4^2:D14448,355
C424D144th semidirect product of C42 and D14 acting via D14/C7=C221124C4^2:4D14448,539

Full list: Groups of order 448 (1396 groups)

Groups of order 449

dρLabelID
C449Cyclic group4491C449449,1

Groups of order 450

dρLabelID
C450Cyclic group4501C450450,4
D225Dihedral group2252+D225450,3
C52⋊D9The semidirect product of C52 and D9 acting via D9/C3=S3456+C5^2:D9450,11
C52⋊C18The semidirect product of C52 and C18 acting via C18/C3=C6456C5^2:C18450,12
C3⋊D75The semidirect product of C3 and D75 acting via D75/C75=C2225C3:D75450,9
C5⋊D45The semidirect product of C5 and D45 acting via D45/C45=C2225C5:D45450,18
C15⋊D151st semidirect product of C15 and D15 acting via D15/C15=C2225C15:D15450,33
C5⋊D15⋊C3The semidirect product of C5⋊D15 and C3 acting faithfully456+C5:D15:C3450,24
C52⋊(C3⋊S3)The semidirect product of C52 and C3⋊S3 acting via C3⋊S3/C3=S3456+C5^2:(C3:S3)450,21
C5×C90Abelian group of type [5,90]450C5xC90450,19
C3×C150Abelian group of type [3,150]450C3xC150450,10
C15×C30Abelian group of type [15,30]450C15xC30450,34
C15×D15Direct product of C15 and D15302C15xD15450,29
D5×C45Direct product of C45 and D5902D5xC45450,14
C5×D45Direct product of C5 and D45902C5xD45450,17
S3×C75Direct product of C75 and S31502S3xC75450,6
C3×D75Direct product of C3 and D751502C3xD75450,7
D9×C25Direct product of C25 and D92252D9xC25450,1
C9×D25Direct product of C9 and D252252C9xD25450,2
D9×C52Direct product of C52 and D9225D9xC5^2450,16
C32×D25Direct product of C32 and D25225C3^2xD25450,5
C3×C52⋊S3Direct product of C3 and C52⋊S3453C3xC5^2:S3450,20
C3×C52⋊C6Direct product of C3 and C52⋊C6456C3xC5^2:C6450,22
S3×C52⋊C3Direct product of S3 and C52⋊C3456S3xC5^2:C3450,23
D5×C3×C15Direct product of C3×C15 and D590D5xC3xC15450,26
C5×C3⋊D15Direct product of C5 and C3⋊D1590C5xC3:D15450,32
C2×C52⋊C9Direct product of C2 and C52⋊C9903C2xC5^2:C9450,13
C6×C52⋊C3Direct product of C6 and C52⋊C3903C6xC5^2:C3450,25
S3×C5×C15Direct product of C5×C15 and S3150S3xC5xC15450,28
C3×C5⋊D15Direct product of C3 and C5⋊D15150C3xC5:D15450,30
C9×C5⋊D5Direct product of C9 and C5⋊D5225C9xC5:D5450,15
C3⋊S3×C25Direct product of C25 and C3⋊S3225C3:S3xC25450,8
C3⋊S3×C52Direct product of C52 and C3⋊S3225C3:S3xC5^2450,31
C32×C5⋊D5Direct product of C32 and C5⋊D5225C3^2xC5:D5450,27

Groups of order 451

dρLabelID
C451Cyclic group4511C451451,1

Groups of order 452

dρLabelID
C452Cyclic group4521C452452,2
D226Dihedral group; = C2×D1132262+D226452,4
Dic113Dicyclic group; = C1132C44522-Dic113452,1
C113⋊C4The semidirect product of C113 and C4 acting faithfully1134+C113:C4452,3
C2×C226Abelian group of type [2,226]452C2xC226452,5

Groups of order 453

dρLabelID
C453Cyclic group4531C453453,2
C151⋊C3The semidirect product of C151 and C3 acting faithfully1513C151:C3453,1

Groups of order 454

dρLabelID
C454Cyclic group4541C454454,2
D227Dihedral group2272+D227454,1

Groups of order 455

dρLabelID
C455Cyclic group4551C455455,1

Groups of order 456

dρLabelID
C456Cyclic group4561C456456,6
D228Dihedral group2282+D228456,36
Dic114Dicyclic group; = C572Q84562-Dic114456,34
C19⋊S4The semidirect product of C19 and S4 acting via S4/A4=C2766+C19:S4456,43
D76⋊C3The semidirect product of D76 and C3 acting faithfully766+D76:C3456,9
D19⋊A4The semidirect product of D19 and A4 acting via A4/C22=C3766+D19:A4456,46
D38⋊C62nd semidirect product of D38 and C6 acting faithfully766D38:C6456,11
C19⋊C24The semidirect product of C19 and C24 acting via C24/C4=C61526C19:C24456,1
Dic38⋊C3The semidirect product of Dic38 and C3 acting faithfully1526-Dic38:C3456,7
D57⋊C4The semidirect product of D57 and C4 acting via C4/C2=C22284+D57:C4456,14
C57⋊D41st semidirect product of C57 and D4 acting via D4/C2=C222284-C57:D4456,15
C3⋊D76The semidirect product of C3 and D76 acting via D76/D38=C22284+C3:D76456,16
C577D41st semidirect product of C57 and D4 acting via D4/C22=C22282C57:7D4456,38
C19⋊D12The semidirect product of C19 and D12 acting via D12/D6=C22284+C19:D12456,17
C57⋊Q8The semidirect product of C57 and Q8 acting via Q8/C2=C224564-C57:Q8456,18
C57⋊C81st semidirect product of C57 and C8 acting via C8/C4=C24562C57:C8456,5
C38.A4The non-split extension by C38 of A4 acting via A4/C22=C31526C38.A4456,23
C2×C228Abelian group of type [2,228]456C2xC228456,39
C22×C114Abelian group of type [2,2,114]456C2^2xC114456,54
C19×S4Direct product of C19 and S4763C19xS4456,42
A4×D19Direct product of A4 and D19766+A4xD19456,45
A4×C38Direct product of C38 and A41143A4xC38456,49
C19×SL2(𝔽3)Direct product of C19 and SL2(𝔽3)1522C19xSL(2,3)456,22
S3×C76Direct product of C76 and S32282S3xC76456,30
C3×D76Direct product of C3 and D762282C3xD76456,26
C4×D57Direct product of C4 and D572282C4xD57456,35
D4×C57Direct product of C57 and D42282D4xC57456,40
C12×D19Direct product of C12 and D192282C12xD19456,25
C19×D12Direct product of C19 and D122282C19xD12456,31
Dic3×D19Direct product of Dic3 and D192284-Dic3xD19456,12
S3×Dic19Direct product of S3 and Dic192284-S3xDic19456,13
C22×D57Direct product of C22 and D57228C2^2xD57456,53
Q8×C57Direct product of C57 and Q84562Q8xC57456,41
C3×Dic38Direct product of C3 and Dic384562C3xDic38456,24
C6×Dic19Direct product of C6 and Dic19456C6xDic19456,27
C19×Dic6Direct product of C19 and Dic64562C19xDic6456,29
Dic3×C38Direct product of C38 and Dic3456Dic3xC38456,32
C2×Dic57Direct product of C2 and Dic57456C2xDic57456,37
C4×C19⋊C6Direct product of C4 and C19⋊C6766C4xC19:C6456,8
D4×C19⋊C3Direct product of D4 and C19⋊C3766D4xC19:C3456,20
C22×C19⋊C6Direct product of C22 and C19⋊C676C2^2xC19:C6456,44
C2×C19⋊A4Direct product of C2 and C19⋊A41143C2xC19:A4456,50
C2×S3×D19Direct product of C2, S3 and D191144+C2xS3xD19456,47
C8×C19⋊C3Direct product of C8 and C19⋊C31523C8xC19:C3456,2
Q8×C19⋊C3Direct product of Q8 and C19⋊C31526Q8xC19:C3456,21
C2×C19⋊C12Direct product of C2 and C19⋊C12152C2xC19:C12456,10
C23×C19⋊C3Direct product of C23 and C19⋊C3152C2^3xC19:C3456,48
S3×C2×C38Direct product of C2×C38 and S3228S3xC2xC38456,52
C2×C6×D19Direct product of C2×C6 and D19228C2xC6xD19456,51
C3×C19⋊D4Direct product of C3 and C19⋊D42282C3xC19:D4456,28
C19×C3⋊D4Direct product of C19 and C3⋊D42282C19xC3:D4456,33
C19×C3⋊C8Direct product of C19 and C3⋊C84562C19xC3:C8456,3
C3×C19⋊C8Direct product of C3 and C19⋊C84562C3xC19:C8456,4
C2×C4×C19⋊C3Direct product of C2×C4 and C19⋊C3152C2xC4xC19:C3456,19

Groups of order 457

dρLabelID
C457Cyclic group4571C457457,1

Groups of order 458

dρLabelID
C458Cyclic group4581C458458,2
D229Dihedral group2292+D229458,1

Groups of order 459

dρLabelID
C459Cyclic group4591C459459,1
C3×C153Abelian group of type [3,153]459C3xC153459,2
C32×C51Abelian group of type [3,3,51]459C3^2xC51459,5
C17×He3Direct product of C17 and He31533C17xHe3459,3
C17×3- 1+2Direct product of C17 and 3- 1+21533C17xES-(3,1)459,4

Groups of order 460

dρLabelID
C460Cyclic group4601C460460,4
D230Dihedral group; = C2×D1152302+D230460,10
Dic115Dicyclic group; = C23Dic54602-Dic115460,3
C23⋊F5The semidirect product of C23 and F5 acting via F5/D5=C21154C23:F5460,6
C2×C230Abelian group of type [2,230]460C2xC230460,11
D5×D23Direct product of D5 and D231154+D5xD23460,7
F5×C23Direct product of C23 and F51154F5xC23460,5
D5×C46Direct product of C46 and D52302D5xC46460,9
C10×D23Direct product of C10 and D232302C10xD23460,8
Dic5×C23Direct product of C23 and Dic54602Dic5xC23460,1
C5×Dic23Direct product of C5 and Dic234602C5xDic23460,2

Groups of order 461

dρLabelID
C461Cyclic group4611C461461,1

Groups of order 462

dρLabelID
C462Cyclic group4621C462462,12
D231Dihedral group2312+D231462,11
C11⋊F7The semidirect product of C11 and F7 acting via F7/C7⋊C3=C2776+C11:F7462,3
C11×F7Direct product of C11 and F7776C11xF7462,2
S3×C77Direct product of C77 and S32312S3xC77462,8
D7×C33Direct product of C33 and D72312D7xC33462,6
C3×D77Direct product of C3 and D772312C3xD77462,7
C7×D33Direct product of C7 and D332312C7xD33462,9
C21×D11Direct product of C21 and D112312C21xD11462,5
C11×D21Direct product of C11 and D212312C11xD21462,10
C7⋊C3×D11Direct product of C7⋊C3 and D11776C7:C3xD11462,1
C7⋊C3×C22Direct product of C22 and C7⋊C31543C7:C3xC22462,4

Groups of order 463

dρLabelID
C463Cyclic group4631C463463,1

Groups of order 464

dρLabelID
C464Cyclic group4641C464464,2
D232Dihedral group2322+D232464,7
Dic116Dicyclic group; = C291Q164642-Dic116464,8
C116⋊C41st semidirect product of C116 and C4 acting faithfully1164C116:C4464,31
D4⋊D29The semidirect product of D4 and D29 acting via D29/C29=C22324+D4:D29464,15
D29⋊C8The semidirect product of D29 and C8 acting via C8/C4=C22324D29:C8464,28
Q8⋊D29The semidirect product of Q8 and D29 acting via D29/C29=C22324+Q8:D29464,17
C8⋊D293rd semidirect product of C8 and D29 acting via D29/C29=C22322C8:D29464,5
C232⋊C22nd semidirect product of C232 and C2 acting faithfully2322C232:C2464,6
D58⋊C41st semidirect product of D58 and C4 acting via C4/C2=C2232D58:C4464,14
D42D29The semidirect product of D4 and D29 acting through Inn(D4)2324-D4:2D29464,40
Q82D29The semidirect product of Q8 and D29 acting through Inn(Q8)2324+Q8:2D29464,42
D1165C2The semidirect product of D116 and C2 acting through Inn(D116)2322D116:5C2464,38
C29⋊M4(2)The semidirect product of C29 and M4(2) acting via M4(2)/C22=C42324-C29:M4(2)464,33
C29⋊C16The semidirect product of C29 and C16 acting via C16/C4=C44644C29:C16464,3
C292C16The semidirect product of C29 and C16 acting via C16/C8=C24642C29:2C16464,1
C4⋊Dic29The semidirect product of C4 and Dic29 acting via Dic29/C58=C2464C4:Dic29464,13
C29⋊Q16The semidirect product of C29 and Q16 acting via Q16/Q8=C24644-C29:Q16464,18
D29.D4The non-split extension by D29 of D4 acting via D4/C22=C21164+D29.D4464,34
D4.D29The non-split extension by D4 of D29 acting via D29/C29=C22324-D4.D29464,16
C4.Dic29The non-split extension by C4 of Dic29 acting via Dic29/C58=C22322C4.Dic29464,10
C23.D29The non-split extension by C23 of D29 acting via D29/C29=C2232C2^3.D29464,19
C116.C41st non-split extension by C116 of C4 acting faithfully2324C116.C4464,29
C58.D41st non-split extension by C58 of D4 acting via D4/C22=C2464C58.D4464,12
C4×C116Abelian group of type [4,116]464C4xC116464,20
C2×C232Abelian group of type [2,232]464C2xC232464,23
C23×C58Abelian group of type [2,2,2,58]464C2^3xC58464,51
C22×C116Abelian group of type [2,2,116]464C2^2xC116464,45
D4×D29Direct product of D4 and D291164+D4xD29464,39
C8×D29Direct product of C8 and D292322C8xD29464,4
D8×C29Direct product of C29 and D82322D8xC29464,25
D4×C58Direct product of C58 and D4232D4xC58464,46
Q8×D29Direct product of Q8 and D292324-Q8xD29464,41
C2×D116Direct product of C2 and D116232C2xD116464,37
SD16×C29Direct product of C29 and SD162322SD16xC29464,26
C23×D29Direct product of C23 and D29232C2^3xD29464,50
M4(2)×C29Direct product of C29 and M4(2)2322M4(2)xC29464,24
Q8×C58Direct product of C58 and Q8464Q8xC58464,47
Q16×C29Direct product of C29 and Q164642Q16xC29464,27
C4×Dic29Direct product of C4 and Dic29464C4xDic29464,11
C2×Dic58Direct product of C2 and Dic58464C2xDic58464,35
C22×Dic29Direct product of C22 and Dic29464C2^2xDic29464,43
C4×C29⋊C4Direct product of C4 and C29⋊C41164C4xC29:C4464,30
C22×C29⋊C4Direct product of C22 and C29⋊C4116C2^2xC29:C4464,49
C2×C4×D29Direct product of C2×C4 and D29232C2xC4xD29464,36
C2×C29⋊D4Direct product of C2 and C29⋊D4232C2xC29:D4464,44
C4○D4×C29Direct product of C29 and C4○D42322C4oD4xC29464,48
C22⋊C4×C29Direct product of C29 and C22⋊C4232C2^2:C4xC29464,21
C2×C29⋊C8Direct product of C2 and C29⋊C8464C2xC29:C8464,32
C4⋊C4×C29Direct product of C29 and C4⋊C4464C4:C4xC29464,22
C2×C292C8Direct product of C2 and C292C8464C2xC29:2C8464,9

Groups of order 465

dρLabelID
C465Cyclic group4651C465465,4
C31⋊C15The semidirect product of C31 and C15 acting faithfully3115C31:C15465,1
C3×C31⋊C5Direct product of C3 and C31⋊C5935C3xC31:C5465,2
C5×C31⋊C3Direct product of C5 and C31⋊C31553C5xC31:C3465,3

Groups of order 466

dρLabelID
C466Cyclic group4661C466466,2
D233Dihedral group2332+D233466,1

Groups of order 467

dρLabelID
C467Cyclic group4671C467467,1

Groups of order 468

dρLabelID
C468Cyclic group4681C468468,6
D234Dihedral group; = C2×D1172342+D234468,17
Dic117Dicyclic group; = C9Dic134682-Dic117468,5
C3⋊F13The semidirect product of C3 and F13 acting via F13/C13⋊C6=C23912C3:F13468,30
D39⋊S3The semidirect product of D39 and S3 acting via S3/C3=C2784D39:S3468,46
C32⋊Dic13The semidirect product of C32 and Dic13 acting via Dic13/C13=C4784C3^2:Dic13468,40
C13⋊C36The semidirect product of C13 and C36 acting via C36/C3=C1211712C13:C36468,7
C13⋊Dic9The semidirect product of C13 and Dic9 acting via Dic9/C9=C41174C13:Dic9468,10
C39⋊Dic31st semidirect product of C39 and Dic3 acting via Dic3/C3=C4117C39:Dic3468,38
C393C121st semidirect product of C39 and C12 acting via C12/C2=C61566-C39:3C12468,21
C132C36The semidirect product of C13 and C36 acting via C36/C6=C64686C13:2C36468,1
C3⋊Dic39The semidirect product of C3 and Dic39 acting via Dic39/C78=C2468C3:Dic39468,27
(C3×C39)⋊C41st semidirect product of C3×C39 and C4 acting faithfully784+(C3xC39):C4468,41
C39.A4The non-split extension by C39 of A4 acting via A4/C22=C32343C39.A4468,14
C6×C78Abelian group of type [6,78]468C6xC78468,55
C2×C234Abelian group of type [2,234]468C2xC234468,18
C3×C156Abelian group of type [3,156]468C3xC156468,28
C3×F13Direct product of C3 and F133912C3xF13468,29
S3×D39Direct product of S3 and D39784+S3xD39468,45
D9×D13Direct product of D9 and D131174+D9xD13468,11
S3×C78Direct product of C78 and S31562S3xC78468,51
A4×C39Direct product of C39 and A41563A4xC39468,48
C6×D39Direct product of C6 and D391562C6xD39468,52
Dic3×C39Direct product of C39 and Dic31562Dic3xC39468,24
C3×Dic39Direct product of C3 and Dic391562C3xDic39468,25
D9×C26Direct product of C26 and D92342D9xC26468,16
C18×D13Direct product of C18 and D132342C18xD13468,15
C13×Dic9Direct product of C13 and Dic94682C13xDic9468,3
C9×Dic13Direct product of C9 and Dic134682C9xDic13468,4
C32×Dic13Direct product of C32 and Dic13468C3^2xDic13468,23
S3×C13⋊C6Direct product of S3 and C13⋊C63912+S3xC13:C6468,31
A4×C13⋊C3Direct product of A4 and C13⋊C3529A4xC13:C3468,32
S32×C13Direct product of C13, S3 and S3784S3^2xC13468,44
C6×C13⋊C6Direct product of C6 and C13⋊C6786C6xC13:C6468,33
C3×S3×D13Direct product of C3, S3 and D13784C3xS3xD13468,42
C3×C39⋊C4Direct product of C3 and C39⋊C4784C3xC39:C4468,37
C2×D39⋊C3Direct product of C2 and D39⋊C3786+C2xD39:C3468,35
C13×C32⋊C4Direct product of C13 and C32⋊C4784C13xC3^2:C4468,39
C9×C13⋊C4Direct product of C9 and C13⋊C41174C9xC13:C4468,9
C3⋊S3×D13Direct product of C3⋊S3 and D13117C3:S3xD13468,43
C32×C13⋊C4Direct product of C32 and C13⋊C4117C3^2xC13:C4468,36
C3×C13⋊A4Direct product of C3 and C13⋊A41563C3xC13:A4468,49
C12×C13⋊C3Direct product of C12 and C13⋊C31563C12xC13:C3468,22
C3×C26.C6Direct product of C3 and C26.C61566C3xC26.C6468,19
Dic3×C13⋊C3Direct product of Dic3 and C13⋊C31566Dic3xC13:C3468,20
C3×C6×D13Direct product of C3×C6 and D13234C3xC6xD13468,50
C2×C13⋊C18Direct product of C2 and C13⋊C182346C2xC13:C18468,8
C3⋊S3×C26Direct product of C26 and C3⋊S3234C3:S3xC26468,53
C2×C3⋊D39Direct product of C2 and C3⋊D39234C2xC3:D39468,54
C13×C3.A4Direct product of C13 and C3.A42343C13xC3.A4468,13
C4×C13⋊C9Direct product of C4 and C13⋊C94683C4xC13:C9468,2
C22×C13⋊C9Direct product of C22 and C13⋊C9468C2^2xC13:C9468,12
C13×C3⋊Dic3Direct product of C13 and C3⋊Dic3468C13xC3:Dic3468,26
C2×S3×C13⋊C3Direct product of C2, S3 and C13⋊C3786C2xS3xC13:C3468,34
C2×C6×C13⋊C3Direct product of C2×C6 and C13⋊C3156C2xC6xC13:C3468,47

Groups of order 469

dρLabelID
C469Cyclic group4691C469469,1

Groups of order 470

dρLabelID
C470Cyclic group4701C470470,4
D235Dihedral group2352+D235470,3
D5×C47Direct product of C47 and D52352D5xC47470,1
C5×D47Direct product of C5 and D472352C5xD47470,2

Groups of order 471

dρLabelID
C471Cyclic group4711C471471,2
C157⋊C3The semidirect product of C157 and C3 acting faithfully1573C157:C3471,1

Groups of order 472

dρLabelID
C472Cyclic group4721C472472,2
D236Dihedral group2362+D236472,5
Dic118Dicyclic group; = C59Q84722-Dic118472,3
C59⋊D4The semidirect product of C59 and D4 acting via D4/C22=C22362C59:D4472,7
C59⋊C8The semidirect product of C59 and C8 acting via C8/C4=C24722C59:C8472,1
C2×C236Abelian group of type [2,236]472C2xC236472,8
C22×C118Abelian group of type [2,2,118]472C2^2xC118472,12
C4×D59Direct product of C4 and D592362C4xD59472,4
D4×C59Direct product of C59 and D42362D4xC59472,9
C22×D59Direct product of C22 and D59236C2^2xD59472,11
Q8×C59Direct product of C59 and Q84722Q8xC59472,10
C2×Dic59Direct product of C2 and Dic59472C2xDic59472,6

Groups of order 473

dρLabelID
C473Cyclic group4731C473473,1

Groups of order 474

dρLabelID
C474Cyclic group4741C474474,6
D237Dihedral group2372+D237474,5
C79⋊C6The semidirect product of C79 and C6 acting faithfully796+C79:C6474,1
S3×C79Direct product of C79 and S32372S3xC79474,3
C3×D79Direct product of C3 and D792372C3xD79474,4
C2×C79⋊C3Direct product of C2 and C79⋊C31583C2xC79:C3474,2

Groups of order 475

dρLabelID
C475Cyclic group4751C475475,1
C5×C95Abelian group of type [5,95]475C5xC95475,2

Groups of order 476

dρLabelID
C476Cyclic group4761C476476,4
D238Dihedral group; = C2×D1192382+D238476,10
Dic119Dicyclic group; = C7Dic174762-Dic119476,3
C17⋊Dic7The semidirect product of C17 and Dic7 acting via Dic7/C7=C41194C17:Dic7476,6
C2×C238Abelian group of type [2,238]476C2xC238476,11
D7×D17Direct product of D7 and D171194+D7xD17476,7
D7×C34Direct product of C34 and D72382D7xC34476,9
C14×D17Direct product of C14 and D172382C14xD17476,8
C17×Dic7Direct product of C17 and Dic74762C17xDic7476,1
C7×Dic17Direct product of C7 and Dic174762C7xDic17476,2
C7×C17⋊C4Direct product of C7 and C17⋊C41194C7xC17:C4476,5

Groups of order 477

dρLabelID
C477Cyclic group4771C477477,1
C3×C159Abelian group of type [3,159]477C3xC159477,2

Groups of order 478

dρLabelID
C478Cyclic group4781C478478,2
D239Dihedral group2392+D239478,1

Groups of order 479

dρLabelID
C479Cyclic group4791C479479,1

Groups of order 480

dρLabelID
C480Cyclic group4801C480480,4
D240Dihedral group2402+D240480,159
Dic120Dicyclic group; = C154Q324802-Dic120480,161
GL2(𝔽5)General linear group on 𝔽52; = SL2(𝔽5)1C4 = Aut(C52)244GL(2,5)480,218
F16⋊C2The semidirect product of F16 and C2 acting faithfully1615+F16:C2480,1188
C4⋊S5The semidirect product of C4 and S5 acting via S5/A5=C2206C4:S5480,944
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2206+C2^2:S5480,951
A5⋊Q8The semidirect product of A5 and Q8 acting via Q8/C4=C2246A5:Q8480,945
C24⋊D15The semidirect product of C24 and D15 acting via D15/C3=D53010+C2^4:D15480,1195
A5⋊C8The semidirect product of A5 and C8 acting via C8/C4=C2404A5:C8480,217
C244D153rd semidirect product of C24 and D15 acting via D15/C5=S3406C2^4:4D15480,1201
C20⋊S41st semidirect product of C20 and S4 acting via S4/A4=C2606+C20:S4480,1026
Dic5⋊S4The semidirect product of Dic5 and S4 acting via S4/A4=C2606Dic5:S4480,978
C42⋊D15The semidirect product of C42 and D15 acting via D15/C5=S3606+C4^2:D15480,258
D10⋊S41st semidirect product of D10 and S4 acting via S4/A4=C2606D10:S4480,980
A4⋊D20The semidirect product of A4 and D20 acting via D20/D10=C2606+A4:D20480,981
D603C43rd semidirect product of D60 and C4 acting faithfully608+D60:3C4480,997
Dic52S4The semidirect product of Dic5 and S4 acting through Inn(Dic5)606Dic5:2S4480,977
C242D151st semidirect product of C24 and D15 acting via D15/C5=S3606C2^4:2D15480,1034
GL2(𝔽3)⋊D51st semidirect product of GL2(𝔽3) and D5 acting via D5/C5=C2804+GL(2,3):D5480,970
C401D61st semidirect product of C40 and D6 acting via D6/C3=C221204+C40:1D6480,329
C405D65th semidirect product of C40 and D6 acting via D6/C3=C221204C40:5D6480,332
C408D68th semidirect product of C40 and D6 acting via D6/C3=C221204C40:8D6480,334
C8⋊D301st semidirect product of C8 and D30 acting via D30/C15=C221204+C8:D30480,873
C5⋊U2(𝔽3)The semidirect product of C5 and U2(𝔽3) acting via U2(𝔽3)/SL2(𝔽3)=C41208+C5:U(2,3)480,961
C24⋊F55th semidirect product of C24 and F5 acting via F5/D5=C21204C24:F5480,297
C120⋊C42nd semidirect product of C120 and C4 acting faithfully1204C120:C4480,298
D607C41st semidirect product of D60 and C4 acting via C4/C2=C21202D60:7C4480,165
D60⋊C41st semidirect product of D60 and C4 acting faithfully1208+D60:C4480,227
D602C42nd semidirect product of D60 and C4 acting faithfully1208+D60:2C4480,233
D605C45th semidirect product of D60 and C4 acting faithfully1208+D60:5C4480,234
D24⋊D52nd semidirect product of D24 and D5 acting via D5/C5=C21204D24:D5480,326
D40⋊S32nd semidirect product of D40 and S3 acting via S3/C3=C21204D40:S3480,330
D246D56th semidirect product of D24 and D5 acting via D5/C5=C21204D24:6D5480,333
D64D201st semidirect product of D6 and D20 acting via D20/D10=C2120D6:4D20480,550
D304D44th semidirect product of D30 and D4 acting via D4/C2=C22120D30:4D4480,551
D305D45th semidirect product of D30 and D4 acting via D4/C2=C22120D30:5D4480,552
D15⋊D8The semidirect product of D15 and D8 acting via D8/D4=C21208+D15:D8480,557
D20⋊D66th semidirect product of D20 and D6 acting via D6/C3=C221208+D20:D6480,578
D308D48th semidirect product of D30 and D4 acting via D4/C2=C22120D30:8D4480,653
D8⋊D152nd semidirect product of D8 and D15 acting via D15/C15=C21204D8:D15480,876
D4⋊D302nd semidirect product of D4 and D30 acting via D30/C30=C21204+D4:D30480,914
D46D302nd semidirect product of D4 and D30 acting through Inn(D4)1204D4:6D30480,1171
D48D304th semidirect product of D4 and D30 acting through Inn(D4)1204+D4:8D30480,1176
C40⋊D617th semidirect product of C40 and D6 acting via D6/C3=C221204C40:D6480,322
C24⋊D101st semidirect product of C24 and D10 acting via D10/C5=C221204+C24:D10480,325
C4014D614th semidirect product of C40 and D6 acting via D6/C3=C221204C40:14D6480,331
D12⋊F51st semidirect product of D12 and F5 acting via F5/D5=C21208+D12:F5480,228
D124F54th semidirect product of D12 and F5 acting via F5/D5=C21208-D12:4F5480,231
D122F52nd semidirect product of D12 and F5 acting via F5/D5=C21208-D12:2F5480,232

Full list: Groups of order 480 (1213 groups)

Groups of order 481

dρLabelID
C481Cyclic group4811C481481,1

Groups of order 482

dρLabelID
C482Cyclic group4821C482482,2
D241Dihedral group2412+D241482,1

Groups of order 483

dρLabelID
C483Cyclic group4831C483483,2
C7⋊C3×C23Direct product of C23 and C7⋊C31613C7:C3xC23483,1

Groups of order 484

dρLabelID
C484Cyclic group4841C484484,2
D242Dihedral group; = C2×D1212422+D242484,3
Dic121Dicyclic group; = C121C44842-Dic121484,1
C112⋊C4The semidirect product of C112 and C4 acting faithfully224+C11^2:C4484,8
C11⋊Dic11The semidirect product of C11 and Dic11 acting via Dic11/C22=C2484C11:Dic11484,6
C222Abelian group of type [22,22]484C22^2484,12
C2×C242Abelian group of type [2,242]484C2xC242484,4
C11×C44Abelian group of type [11,44]484C11xC44484,7
D112Direct product of D11 and D11224+D11^2484,9
D11×C22Direct product of C22 and D11442D11xC22484,10
C11×Dic11Direct product of C11 and Dic11442C11xDic11484,5
C2×C11⋊D11Direct product of C2 and C11⋊D11242C2xC11:D11484,11

Groups of order 485

dρLabelID
C485Cyclic group4851C485485,1

Groups of order 486

dρLabelID
C486Cyclic group4861C486486,2
D243Dihedral group2432+D243486,1
C34⋊C61st semidirect product of C34 and C6 acting faithfully186C3^4:C6486,102
C928C68th semidirect product of C92 and C6 acting faithfully186C9^2:8C6486,110
C343S33rd semidirect product of C34 and S3 acting faithfully186C3^4:3S3486,145
C926S36th semidirect product of C92 and S3 acting faithfully186C9^2:6S3486,153
C345S35th semidirect product of C34 and S3 acting faithfully186C3^4:5S3486,166
C331D91st semidirect product of C33 and D9 acting via D9/C3=S3186C3^3:1D9486,19
C331C181st semidirect product of C33 and C18 acting via C18/C3=C6186C3^3:1C18486,18
C27⋊C18The semidirect product of C27 and C18 acting faithfully; = Aut(D27) = Hol(C27)2718+C27:C18486,31
C92⋊C61st semidirect product of C92 and C6 acting faithfully276+C9^2:C6486,35
C92⋊S31st semidirect product of C92 and S3 acting faithfully276+C9^2:S3486,36
C922C62nd semidirect product of C92 and C6 acting faithfully276+C9^2:2C6486,37
C922S32nd semidirect product of C92 and S3 acting faithfully273C9^2:2S3486,61
C34⋊S31st semidirect product of C34 and S3 acting faithfully27C3^4:S3486,103
C344C64th semidirect product of C34 and C6 acting faithfully27C3^4:4C6486,146
C345C65th semidirect product of C34 and C6 acting faithfully27C3^4:5C6486,167
C346S36th semidirect product of C34 and S3 acting faithfully27C3^4:6S3486,183
C347S37th semidirect product of C34 and S3 acting faithfully27C3^4:7S3486,185
C332D92nd semidirect product of C33 and D9 acting via D9/C3=S327C3^3:2D9486,52
3+ 1+4⋊C21st semidirect product of 3+ 1+4 and C2 acting faithfully2718+ES+(3,2):C2486,236
3+ 1+42C22nd semidirect product of 3+ 1+4 and C2 acting faithfully279ES+(3,2):2C2486,237
3- 1+4⋊C21st semidirect product of 3- 1+4 and C2 acting faithfully2718+ES-(3,2):C2486,238
3- 1+42C22nd semidirect product of 3- 1+4 and C2 acting faithfully279ES-(3,2):2C2486,239
3+ 1+43C23rd semidirect product of 3+ 1+4 and C2 acting faithfully279ES+(3,2):3C2486,249
C9⋊C54The semidirect product of C9 and C54 acting via C54/C9=C6546C9:C54486,30
D9⋊He3The semidirect product of D9 and He3 acting via He3/C32=C3546D9:He3486,106
C32⋊C54The semidirect product of C32 and C54 acting via C54/C9=C6546C3^2:C54486,16
C273C18The semidirect product of C27 and C18 acting via C18/C3=C6546C27:3C18486,15
He34D92nd semidirect product of He3 and D9 acting via D9/C9=C2546He3:4D9486,182
C927C67th semidirect product of C92 and C6 acting faithfully546C9^2:7C6486,109
C923S33rd semidirect product of C92 and S3 acting faithfully546C9^2:3S3486,139
C924S34th semidirect product of C92 and S3 acting faithfully546C9^2:4S3486,140
C925S35th semidirect product of C92 and S3 acting faithfully546C9^2:5S3486,156
C336D96th semidirect product of C33 and D9 acting via D9/C3=S354C3^3:6D9486,181
C33⋊C184th semidirect product of C33 and C18 acting via C18/C3=C654C3^3:C18486,136
C3413S313rd semidirect product of C34 and S3 acting faithfully54C3^4:13S3486,248
C322D272nd semidirect product of C32 and D27 acting via D27/C9=S3546C3^2:2D27486,51
D9⋊3- 1+2The semidirect product of D9 and 3- 1+2 acting via 3- 1+2/C32=C3546D9:ES-(3,1)486,108
C81⋊C6The semidirect product of C81 and C6 acting faithfully816+C81:C6486,34
He3⋊C18The semidirect product of He3 and C18 acting via C18/C3=C681He3:C18486,24
He3⋊D91st semidirect product of He3 and D9 acting via D9/C3=S381He3:D9486,25
He32D92nd semidirect product of He3 and D9 acting via D9/C3=S381He3:2D9486,56
He33D91st semidirect product of He3 and D9 acting via D9/C9=C281He3:3D9486,142
C923C63rd semidirect product of C92 and C6 acting faithfully81C9^2:3C6486,141
C929C69th semidirect product of C92 and C6 acting faithfully81C9^2:9C6486,144
C924C64th semidirect product of C92 and C6 acting faithfully81C9^2:4C6486,155
C925C65th semidirect product of C92 and C6 acting faithfully81C9^2:5C6486,157
C33⋊D95th semidirect product of C33 and D9 acting via D9/C3=S381C3^3:D9486,137
C9210C610th semidirect product of C92 and C6 acting faithfully81C9^2:10C6486,154
C9211C611st semidirect product of C92 and C6 acting faithfully81C9^2:11C6486,158
C9212C612nd semidirect product of C92 and C6 acting faithfully81C9^2:12C6486,159
C3410C610th semidirect product of C34 and C6 acting faithfully81C3^4:10C6486,242
C32⋊D271st semidirect product of C32 and D27 acting via D27/C9=S381C3^2:D27486,17
3- 1+2⋊D9The semidirect product of 3- 1+2 and D9 acting via D9/C3=S381ES-(3,1):D9486,57
C81⋊S3The semidirect product of C81 and S3 acting via S3/C3=C2243C81:S3486,60
C9⋊D27The semidirect product of C9 and D27 acting via D27/C27=C2243C9:D27486,50
C35⋊C25th semidirect product of C35 and C2 acting faithfully243C3^5:C2486,260
C928S32nd semidirect product of C92 and S3 acting via S3/C3=C2243C9^2:8S3486,180
C339D93rd semidirect product of C33 and D9 acting via D9/C9=C2243C3^3:9D9486,247
C324D272nd semidirect product of C32 and D27 acting via D27/C27=C2243C3^2:4D27486,184
C32⋊C9⋊C61st semidirect product of C32⋊C9 and C6 acting faithfully186C3^2:C9:C6486,6
C32⋊C9⋊S31st semidirect product of C32⋊C9 and S3 acting faithfully186C3^2:C9:S3486,7
C9⋊C9⋊S31st semidirect product of C9⋊C9 and S3 acting faithfully2718+C9:C9:S3486,41
C3≀C3⋊C62nd semidirect product of C3≀C3 and C6 acting faithfully279C3wrC3:C6486,126
C3≀S33C3The semidirect product of C3≀S3 and C3 acting through Inn(C3≀S3)273C3wrS3:3C3486,125
C3≀C3⋊S32nd semidirect product of C3≀C3 and S3 acting via S3/C3=C2276+C3wrC3:S3486,189
C3.He3⋊C6The semidirect product of C3.He3 and C6 acting faithfully2718+C3.He3:C6486,179
C9⋊S3⋊C322nd semidirect product of C9⋊S3 and C32 acting faithfully2718+C9:S3:C3^2486,129
(C3×He3)⋊C68th semidirect product of C3×He3 and C6 acting faithfully2718+(C3xHe3):C6486,127
He3⋊(C3×S3)4th semidirect product of He3 and C3×S3 acting via C3×S3/C3=S32718+He3:(C3xS3)486,178
C33⋊(C3×S3)4th semidirect product of C33 and C3×S3 acting faithfully2718+C3^3:(C3xS3)486,176
He3.C3⋊C63rd semidirect product of He3.C3 and C6 acting faithfully279He3.C3:C6486,128
He3.C32C62nd semidirect product of He3.C3 and C6 acting faithfully2718+He3.C3:2C6486,177
C9⋊(S3×C9)The semidirect product of C9 and S3×C9 acting via S3×C9/C32=C654C9:(S3xC9)486,138
C9⋊S3⋊C91st semidirect product of C9⋊S3 and C9 acting via C9/C3=C354C9:S3:C9486,3
C9⋊S33C93rd semidirect product of C9⋊S3 and C9 acting via C9/C3=C3546C9:S3:3C9486,22
C9⋊C92S32nd semidirect product of C9⋊C9 and S3 acting faithfully546C9:C9:2S3486,152
(C3×C9)⋊D92nd semidirect product of C3×C9 and D9 acting via D9/C3=S3546(C3xC9):D9486,21
(C3×C9)⋊3D93rd semidirect product of C3×C9 and D9 acting via D9/C3=S3546(C3xC9):3D9486,23
C9⋊He3⋊C23rd semidirect product of C9⋊He3 and C2 acting faithfully546C9:He3:C2486,107
(C3×C9)⋊C182nd semidirect product of C3×C9 and C18 acting via C18/C3=C6546(C3xC9):C18486,20
C9○He34S32nd semidirect product of C9○He3 and S3 acting via S3/C3=C2546C9oHe3:4S3486,246
(C32×C9)⋊8S38th semidirect product of C32×C9 and S3 acting faithfully546(C3^2xC9):8S3486,150
He3⋊C32S31st semidirect product of He3⋊C3 and S3 acting via S3/C3=C2546He3:C3:2S3486,172
(C32×C9)⋊S314th semidirect product of C32×C9 and S3 acting faithfully546(C3^2xC9):S3486,149
He3.C3⋊S35th semidirect product of He3.C3 and S3 acting via S3/C3=C2546He3.C3:S3486,169
(C3×C9)⋊5D95th semidirect product of C3×C9 and D9 acting via D9/C3=S381(C3xC9):5D9486,53
(C3×C9)⋊6D96th semidirect product of C3×C9 and D9 acting via D9/C3=S381(C3xC9):6D9486,54
C9⋊He32C22nd semidirect product of C9⋊He3 and C2 acting faithfully81C9:He3:2C2486,148
C32⋊C96S36th semidirect product of C32⋊C9 and S3 acting faithfully81C3^2:C9:6S3486,46
C3⋊(He3⋊S3)The semidirect product of C3 and He3⋊S3 acting via He3⋊S3/He3⋊C3=C281C3:(He3:S3)486,187
C9○He33S31st semidirect product of C9○He3 and S3 acting via S3/C3=C281C9oHe3:3S3486,245
(C3×He3)⋊S32nd semidirect product of C3×He3 and S3 acting faithfully81(C3xHe3):S3486,43
He3⋊C33S32nd semidirect product of He3⋊C3 and S3 acting via S3/C3=C281He3:C3:3S3486,173
(C32×C9)⋊C612nd semidirect product of C32×C9 and C6 acting faithfully81(C3^2xC9):C6486,151
C324D9⋊C35th semidirect product of C324D9 and C3 acting faithfully81C3^2:4D9:C3486,170
C34.C64th non-split extension by C34 of C6 acting faithfully186C3^4.C6486,104
C34.7S37th non-split extension by C34 of S3 acting faithfully186C3^4.7S3486,147
C92.S32nd non-split extension by C92 of S3 acting faithfully276+C9^2.S3486,38
C34.S34th non-split extension by C34 of S3 acting faithfully27C3^4.S3486,105
C33.D93rd non-split extension by C33 of D9 acting via D9/C3=S3276+C3^3.D9486,55
He3.D91st non-split extension by He3 of D9 acting via D9/C3=S3816+He3.D9486,27
He3.2D92nd non-split extension by He3 of D9 acting via D9/C3=S3816+He3.2D9486,29
He3.3D93rd non-split extension by He3 of D9 acting via D9/C3=S3816+He3.3D9486,58
He3.4D94th non-split extension by He3 of D9 acting via D9/C3=S3816+He3.4D9486,59
He3.5D9The non-split extension by He3 of D9 acting via D9/C9=C2816+He3.5D9486,163
C33.5D95th non-split extension by C33 of D9 acting via D9/C3=S381C3^3.5D9486,162
He3.C181st non-split extension by He3 of C18 acting via C18/C3=C6813He3.C18486,26
He3.2C182nd non-split extension by He3 of C18 acting via C18/C3=C6813He3.2C18486,28
He3.5C18The non-split extension by He3 of C18 acting via C18/C9=C2813He3.5C18486,164
C34.11S311st non-split extension by C34 of S3 acting faithfully81C3^4.11S3486,244
C32⋊C9.S31st non-split extension by C32⋊C9 of S3 acting faithfully186C3^2:C9.S3486,5
C3≀C3.C6The non-split extension by C3≀C3 of C6 acting faithfully279C3wrC3.C6486,132
C3≀C3.S3The non-split extension by C3≀C3 of S3 acting via S3/C3=C2276+C3wrC3.S3486,175
C9⋊C9.S32nd non-split extension by C9⋊C9 of S3 acting faithfully2718+C9:C9.S3486,39
C9⋊C9.3S33rd non-split extension by C9⋊C9 of S3 acting faithfully2718+C9:C9.3S3486,40
He3.(C3×C6)6th non-split extension by He3 of C3×C6 acting via C3×C6/C3=C6279He3.(C3xC6)486,130
He3.(C3×S3)5th non-split extension by He3 of C3×S3 acting via C3×S3/C3=S32718+He3.(C3xS3)486,131
C3.C3≀S31st non-split extension by C3 of C3≀S3 acting via C3≀S3/C3≀C3=C2546C3.C3wrS3486,4
C3.3C3≀S33rd non-split extension by C3 of C3≀S3 acting via C3≀S3/C3≀C3=C2546C3.3C3wrS3486,8
C32⋊C9.C62nd non-split extension by C32⋊C9 of C6 acting faithfully546C3^2:C9.C6486,10
(C3×He3).C62nd non-split extension by C3×He3 of C6 acting faithfully546(C3xHe3).C6486,9
C33.(C3×S3)8th non-split extension by C33 of C3×S3 acting faithfully546C3^3.(C3xS3)486,11
C322D9.C33rd non-split extension by C322D9 of C3 acting faithfully546C3^2:2D9.C3486,12
(C3×He3).S34th non-split extension by C3×He3 of S3 acting faithfully81(C3xHe3).S3486,44
C32⋊C9.10S310th non-split extension by C32⋊C9 of S3 acting faithfully81C3^2:C9.10S3486,49
He3.(C3⋊S3)4th non-split extension by He3 of C3⋊S3 acting via C3⋊S3/C3=S381He3.(C3:S3)486,186
C33.(C3⋊S3)3rd non-split extension by C33 of C3⋊S3 acting faithfully81C3^3.(C3:S3)486,45
(C32×C9).S316th non-split extension by C32×C9 of S3 acting faithfully81(C3^2xC9).S3486,188
C3.(He3⋊S3)3rd non-split extension by C3 of He3⋊S3 acting via He3⋊S3/He3⋊C3=C281C3.(He3:S3)486,48
C3.(C33⋊S3)5th non-split extension by C3 of C33⋊S3 acting via C33⋊S3/C3≀C3=C281C3.(C3^3:S3)486,47
C3.2(C9⋊D9)The central stem extension by C3 of C9⋊D9162C3.2(C9:D9)486,42
C9×C54Abelian group of type [9,54]486C9xC54486,70
C3×C162Abelian group of type [3,162]486C3xC162486,83
C34×C6Abelian group of type [3,3,3,3,6]486C3^4xC6486,261
C32×C54Abelian group of type [3,3,54]486C3^2xC54486,207
C33×C18Abelian group of type [3,3,3,18]486C3^3xC18486,250
C3×C9×C18Abelian group of type [3,9,18]486C3xC9xC18486,190
C9×D27Direct product of C9 and D27542C9xD27486,13
D9×C27Direct product of C27 and D9542D9xC27486,14
D9×He3Direct product of D9 and He3546D9xHe3486,99
D9×3- 1+2Direct product of D9 and 3- 1+2546D9xES-(3,1)486,101
C2×3+ 1+4Direct product of C2 and 3+ 1+4549C2xES+(3,2)486,254
C2×3- 1+4Direct product of C2 and 3- 1+4549C2xES-(3,2)486,255
S3×C81Direct product of C81 and S31622S3xC81486,33
C3×D81Direct product of C3 and D811622C3xD81486,32
S3×C92Direct product of C92 and S3162S3xC9^2486,92
C18×He3Direct product of C18 and He3162C18xHe3486,194
S3×C34Direct product of C34 and S3162S3xC3^4486,256
D9×C33Direct product of C33 and D9162D9xC3^3486,220
C32×D27Direct product of C32 and D27162C3^2xD27486,111
C18×3- 1+2Direct product of C18 and 3- 1+2162C18xES-(3,1)486,195
S3×C3≀C3Direct product of S3 and C3≀C3186S3xC3wrC3486,117
C3×C33⋊C6Direct product of C3 and C33⋊C6186C3xC3^3:C6486,116
C3×C33⋊S3Direct product of C3 and C33⋊S3186C3xC3^3:S3486,165
C3×C3≀S3Direct product of C3 and C3≀S327C3xC3wrS3486,115
D9×C3×C9Direct product of C3×C9 and D954D9xC3xC9486,91
C9×C9⋊C6Direct product of C9 and C9⋊C6546C9xC9:C6486,100
C9×C9⋊S3Direct product of C9 and C9⋊S354C9xC9:S3486,133
C6×C3≀C3Direct product of C6 and C3≀C354C6xC3wrC3486,210
C2×C27⋊C9Direct product of C2 and C27⋊C9549C2xC27:C9486,82
C3×C9⋊C18Direct product of C3 and C9⋊C1854C3xC9:C18486,96
C3×C27⋊C6Direct product of C3 and C27⋊C6546C3xC27:C6486,113
C3×S3×He3Direct product of C3, S3 and He354C3xS3xHe3486,223
S3×C27⋊C3Direct product of S3 and C27⋊C3546S3xC27:C3486,114
C3⋊S3×He3Direct product of C3⋊S3 and He354C3:S3xHe3486,231
S3×C32⋊C9Direct product of S3 and C32⋊C954S3xC3^2:C9486,95
C9×C32⋊C6Direct product of C9 and C32⋊C6546C9xC3^2:C6486,98
C32×C9⋊C6Direct product of C32 and C9⋊C654C3^2xC9:C6486,224
C32×C9⋊S3Direct product of C32 and C9⋊S354C3^2xC9:S3486,227
C3⋊S3×C33Direct product of C33 and C3⋊S354C3:S3xC3^3486,257
S3×C9○He3Direct product of S3 and C9○He3546S3xC9oHe3486,226
C3×C32⋊C18Direct product of C3 and C32⋊C1854C3xC3^2:C18486,93
S3×He3⋊C3Direct product of S3 and He3⋊C3546S3xHe3:C3486,123
C3×He3⋊S3Direct product of C3 and He3⋊S3546C3xHe3:S3486,171
C2×C33⋊C9Direct product of C2 and C33⋊C954C2xC3^3:C9486,73
C2×C92⋊C3Direct product of C2 and C92⋊C3543C2xC9^2:C3486,85
S3×He3.C3Direct product of S3 and He3.C3546S3xHe3.C3486,120
C3×C32⋊D9Direct product of C3 and C32⋊D954C3xC3^2:D9486,94
C2×C32⋊He3Direct product of C2 and C32⋊He354C2xC3^2:He3486,196
S3×C3.He3Direct product of S3 and C3.He3546S3xC3.He3486,124
C2×C9.He3Direct product of C2 and C9.He3543C2xC9.He3486,214
C3×He34S3Direct product of C3 and He34S354C3xHe3:4S3486,229
C3×He35S3Direct product of C3 and He35S354C3xHe3:5S3486,243
C2×C922C3Direct product of C2 and C922C3543C2xC9^2:2C3486,86
C3×C322D9Direct product of C3 and C322D954C3xC3^2:2D9486,135
C32×C32⋊C6Direct product of C32 and C32⋊C654C3^2xC3^2:C6486,222
C3×He3.S3Direct product of C3 and He3.S3546C3xHe3.S3486,119
C2×C9.4He3Direct product of C2 and C9.4He3543C2xC9.4He3486,76
C2×C92.C3Direct product of C2 and C92.C3543C2xC9^2.C3486,87
C2×C34.C3Direct product of C2 and C34.C354C2xC3^4.C3486,197
C2×C9.2He3Direct product of C2 and C9.2He3549C2xC9.2He3486,219
C3×C33.S3Direct product of C3 and C33.S354C3xC3^3.S3486,232
C32×C33⋊C2Direct product of C32 and C33⋊C254C3^2xC3^3:C2486,258
C3×S3×3- 1+2Direct product of C3, S3 and 3- 1+254C3xS3xES-(3,1)486,225
C3×He3.2S3Direct product of C3 and He3.2S3546C3xHe3.2S3486,122
C3×He3.3S3Direct product of C3 and He3.3S3546C3xHe3.3S3486,168
C3×He3.4S3Direct product of C3 and He3.4S3546C3xHe3.4S3486,234
C2×He3⋊C32Direct product of C2 and He3⋊C32549C2xHe3:C3^2486,217
C2×C33⋊C32Direct product of C2 and C33⋊C32549C2xC3^3:C3^2486,215
C3⋊S3×3- 1+2Direct product of C3⋊S3 and 3- 1+254C3:S3xES-(3,1)486,233
C2×C32.He3Direct product of C2 and C32.He3549C2xC3^2.He3486,88
C2×He3.C32Direct product of C2 and He3.C32549C2xHe3.C3^2486,216
C2×C32.5He3Direct product of C2 and C32.5He3549C2xC3^2.5He3486,89
C2×C32.6He3Direct product of C2 and C32.6He3549C2xC3^2.6He3486,90
C2×C32.C33Direct product of C2 and C32.C33549C2xC3^2.C3^3486,218
C3×3- 1+2.S3Direct product of C3 and 3- 1+2.S3546C3xES-(3,1).S3486,174
C9×He3⋊C2Direct product of C9 and He3⋊C281C9xHe3:C2486,143
C3×He3.C6Direct product of C3 and He3.C681C3xHe3.C6486,118
C32×He3⋊C2Direct product of C32 and He3⋊C281C3^2xHe3:C2486,230
C3×He3.2C6Direct product of C3 and He3.2C681C3xHe3.2C6486,121
C3×He3.4C6Direct product of C3 and He3.4C681C3xHe3.4C6486,235
S3×C9⋊C9Direct product of S3 and C9⋊C9162S3xC9:C9486,97
S3×C3×C27Direct product of C3×C27 and S3162S3xC3xC27486,112
C3×C9⋊D9Direct product of C3 and C9⋊D9162C3xC9:D9486,134
C2×C81⋊C3Direct product of C2 and C81⋊C31623C2xC81:C3486,84
C6×C27⋊C3Direct product of C6 and C27⋊C3162C6xC27:C3486,208
C3×C6×He3Direct product of C3×C6 and He3162C3xC6xHe3486,251
C3×C27⋊S3Direct product of C3 and C27⋊S3162C3xC27:S3486,160
C3⋊S3×C27Direct product of C27 and C3⋊S3162C3:S3xC27486,161
C2×C9⋊He3Direct product of C2 and C9⋊He3162C2xC9:He3486,198
S3×C32×C9Direct product of C32×C9 and S3162S3xC3^2xC9486,221
C2×He3⋊C9Direct product of C2 and He3⋊C9162C2xHe3:C9486,77
C6×C32⋊C9Direct product of C6 and C32⋊C9162C6xC3^2:C9486,191
C6×C9○He3Direct product of C6 and C9○He3162C6xC9oHe3486,253
C9×C33⋊C2Direct product of C9 and C33⋊C2162C9xC3^3:C2486,241
C3×C34⋊C2Direct product of C3 and C34⋊C2162C3xC3^4:C2486,259
C2×C32⋊C27Direct product of C2 and C32⋊C27162C2xC3^2:C27486,72
C2×C27○He3Direct product of C2 and C27○He31623C2xC27oHe3486,209
C6×He3⋊C3Direct product of C6 and He3⋊C3162C6xHe3:C3486,212
C6×He3.C3Direct product of C6 and He3.C3162C6xHe3.C3486,211
C6×C3.He3Direct product of C6 and C3.He3162C6xC3.He3486,213
C2×C923C3Direct product of C2 and C923C3162C2xC9^2:3C3486,193
C2×C927C3Direct product of C2 and C927C3162C2xC9^2:7C3486,202
C2×C924C3Direct product of C2 and C924C3162C2xC9^2:4C3486,203
C2×C925C3Direct product of C2 and C925C3162C2xC9^2:5C3486,204
C2×C928C3Direct product of C2 and C928C3162C2xC9^2:8C3486,205
C2×C929C3Direct product of C2 and C929C3162C2xC9^2:9C3486,206
C3×C324D9Direct product of C3 and C324D9162C3xC3^2:4D9486,240
C2×C9.5He3Direct product of C2 and C9.5He31623C2xC9.5He3486,79
C2×C9.6He3Direct product of C2 and C9.6He31623C2xC9.6He3486,80
C3×C6×3- 1+2Direct product of C3×C6 and 3- 1+2162C3xC6xES-(3,1)486,252
C2×3- 1+2⋊C9Direct product of C2 and 3- 1+2⋊C9162C2xES-(3,1):C9486,78
C2×C33.C32Direct product of C2 and C33.C32162C2xC3^3.C3^2486,64
C2×C9⋊3- 1+2Direct product of C2 and C9⋊3- 1+2162C2xC9:ES-(3,1)486,200
C2×C32.24He3Direct product of C2 and C32.24He3162C2xC3^2.24He3486,63
C2×C33.3C32Direct product of C2 and C33.3C32162C2xC3^3.3C3^2486,65
C2×C32.27He3Direct product of C2 and C32.27He3162C2xC3^2.27He3486,66
C2×C32.28He3Direct product of C2 and C32.28He3162C2xC3^2.28He3486,67
C2×C32.29He3Direct product of C2 and C32.29He3162C2xC3^2.29He3486,68
C2×C33.7C32Direct product of C2 and C33.7C32162C2xC3^3.7C3^2486,69
C2×C32.19He3Direct product of C2 and C32.19He3162C2xC3^2.19He3486,74
C2×C32.20He3Direct product of C2 and C32.20He3162C2xC3^2.20He3486,75
C2×C32.23C33Direct product of C2 and C32.23C33162C2xC3^2.23C3^3486,199
C2×C33.31C32Direct product of C2 and C33.31C32162C2xC3^3.31C3^2486,201
C6×C9⋊C9Direct product of C6 and C9⋊C9486C6xC9:C9486,192
C2×C9⋊C27Direct product of C2 and C9⋊C27486C2xC9:C27486,81
C2×C272C9Direct product of C2 and C272C9486C2xC27:2C9486,71
C2×C3.C92Direct product of C2 and C3.C92486C2xC3.C9^2486,62
C3⋊S3×C3×C9Direct product of C3×C9 and C3⋊S354C3:S3xC3xC9486,228

Groups of order 487

dρLabelID
C487Cyclic group4871C487487,1

Groups of order 488

dρLabelID
C488Cyclic group4881C488488,2
D244Dihedral group2442+D244488,6
Dic122Dicyclic group; = C61Q84882-Dic122488,4
C61⋊D4The semidirect product of C61 and D4 acting via D4/C22=C22442C61:D4488,8
C61⋊C8The semidirect product of C61 and C8 acting via C8/C2=C44884-C61:C8488,3
C612C8The semidirect product of C61 and C8 acting via C8/C4=C24882C61:2C8488,1
C2×C244Abelian group of type [2,244]488C2xC244488,9
C22×C122Abelian group of type [2,2,122]488C2^2xC122488,14
C4×D61Direct product of C4 and D612442C4xD61488,5
D4×C61Direct product of C61 and D42442D4xC61488,10
C22×D61Direct product of C22 and D61244C2^2xD61488,13
Q8×C61Direct product of C61 and Q84882Q8xC61488,11
C2×Dic61Direct product of C2 and Dic61488C2xDic61488,7
C2×C61⋊C4Direct product of C2 and C61⋊C41224+C2xC61:C4488,12

Groups of order 489

dρLabelID
C489Cyclic group4891C489489,2
C163⋊C3The semidirect product of C163 and C3 acting faithfully1633C163:C3489,1

Groups of order 490

dρLabelID
C490Cyclic group4901C490490,4
D245Dihedral group2452+D245490,3
C7⋊D35The semidirect product of C7 and D35 acting via D35/C35=C2245C7:D35490,9
C7×C70Abelian group of type [7,70]490C7xC70490,10
D7×C35Direct product of C35 and D7702D7xC35490,5
C7×D35Direct product of C7 and D35702C7xD35490,8
D5×C49Direct product of C49 and D52452D5xC49490,1
C5×D49Direct product of C5 and D492452C5xD49490,2
D5×C72Direct product of C72 and D5245D5xC7^2490,7
C5×C7⋊D7Direct product of C5 and C7⋊D7245C5xC7:D7490,6

Groups of order 491

dρLabelID
C491Cyclic group4911C491491,1

Groups of order 492

dρLabelID
C492Cyclic group4921C492492,4
D246Dihedral group; = C2×D1232462+D246492,11
Dic123Dicyclic group; = C3Dic414922-Dic123492,3
C41⋊Dic3The semidirect product of C41 and Dic3 acting via Dic3/C3=C41234C41:Dic3492,6
C2×C246Abelian group of type [2,246]492C2xC246492,12
S3×D41Direct product of S3 and D411234+S3xD41492,7
A4×C41Direct product of C41 and A41643A4xC41492,8
S3×C82Direct product of C82 and S32462S3xC82492,10
C6×D41Direct product of C6 and D412462C6xD41492,9
Dic3×C41Direct product of C41 and Dic34922Dic3xC41492,1
C3×Dic41Direct product of C3 and Dic414922C3xDic41492,2
C3×C41⋊C4Direct product of C3 and C41⋊C41234C3xC41:C4492,5

Groups of order 493

dρLabelID
C493Cyclic group4931C493493,1

Groups of order 494

dρLabelID
C494Cyclic group4941C494494,4
D247Dihedral group2472+D247494,3
C19×D13Direct product of C19 and D132472C19xD13494,1
C13×D19Direct product of C13 and D192472C13xD19494,2

Groups of order 495

dρLabelID
C495Cyclic group4951C495495,2
C3×C165Abelian group of type [3,165]495C3xC165495,4
C9×C11⋊C5Direct product of C9 and C11⋊C5995C9xC11:C5495,1
C32×C11⋊C5Direct product of C32 and C11⋊C599C3^2xC11:C5495,3

Groups of order 496

dρLabelID
C496Cyclic group4961C496496,2
D248Dihedral group2482+D248496,6
Dic124Dicyclic group; = C311Q164962-Dic124496,7
D62⋊C4The semidirect product of D62 and C4 acting via C4/C2=C2248D62:C4496,13
D4⋊D31The semidirect product of D4 and D31 acting via D31/C31=C22484+D4:D31496,14
Q8⋊D31The semidirect product of Q8 and D31 acting via D31/C31=C22484+Q8:D31496,16
C8⋊D313rd semidirect product of C8 and D31 acting via D31/C31=C22482C8:D31496,4
C248⋊C22nd semidirect product of C248 and C2 acting faithfully2482C248:C2496,5
D42D31The semidirect product of D4 and D31 acting through Inn(D4)2484-D4:2D31496,32
Q82D31The semidirect product of Q8 and D31 acting through Inn(Q8)2484+Q8:2D31496,34
D1245C2The semidirect product of D124 and C2 acting through Inn(D124)2482D124:5C2496,30
C31⋊C16The semidirect product of C31 and C16 acting via C16/C8=C24962C31:C16496,1
C4⋊Dic31The semidirect product of C4 and Dic31 acting via Dic31/C62=C2496C4:Dic31496,12
C31⋊Q16The semidirect product of C31 and Q16 acting via Q16/Q8=C24964-C31:Q16496,17
Dic31⋊C4The semidirect product of Dic31 and C4 acting via C4/C2=C2496Dic31:C4496,11
D4.D31The non-split extension by D4 of D31 acting via D31/C31=C22484-D4.D31496,15
C4.Dic31The non-split extension by C4 of Dic31 acting via Dic31/C62=C22482C4.Dic31496,9
C23.D31The non-split extension by C23 of D31 acting via D31/C31=C2248C2^3.D31496,18
C4×C124Abelian group of type [4,124]496C4xC124496,19
C2×C248Abelian group of type [2,248]496C2xC248496,22
C23×C62Abelian group of type [2,2,2,62]496C2^3xC62496,42
C22×C124Abelian group of type [2,2,124]496C2^2xC124496,37
D4×D31Direct product of D4 and D311244+D4xD31496,31
C8×D31Direct product of C8 and D312482C8xD31496,3
D8×C31Direct product of C31 and D82482D8xC31496,24
D4×C62Direct product of C62 and D4248D4xC62496,38
Q8×D31Direct product of Q8 and D312484-Q8xD31496,33
C2×D124Direct product of C2 and D124248C2xD124496,29
SD16×C31Direct product of C31 and SD162482SD16xC31496,25
C23×D31Direct product of C23 and D31248C2^3xD31496,41
M4(2)×C31Direct product of C31 and M4(2)2482M4(2)xC31496,23
Q8×C62Direct product of C62 and Q8496Q8xC62496,39
Q16×C31Direct product of C31 and Q164962Q16xC31496,26
C4×Dic31Direct product of C4 and Dic31496C4xDic31496,10
C2×Dic62Direct product of C2 and Dic62496C2xDic62496,27
C22×Dic31Direct product of C22 and Dic31496C2^2xDic31496,35
C2×C4×D31Direct product of C2×C4 and D31248C2xC4xD31496,28
C2×C31⋊D4Direct product of C2 and C31⋊D4248C2xC31:D4496,36
C4○D4×C31Direct product of C31 and C4○D42482C4oD4xC31496,40
C22⋊C4×C31Direct product of C31 and C22⋊C4248C2^2:C4xC31496,20
C2×C31⋊C8Direct product of C2 and C31⋊C8496C2xC31:C8496,8
C4⋊C4×C31Direct product of C31 and C4⋊C4496C4:C4xC31496,21

Groups of order 497

dρLabelID
C497Cyclic group4971C497497,2
C71⋊C7The semidirect product of C71 and C7 acting faithfully717C71:C7497,1

Groups of order 498

dρLabelID
C498Cyclic group4981C498498,4
D249Dihedral group2492+D249498,3
S3×C83Direct product of C83 and S32492S3xC83498,1
C3×D83Direct product of C3 and D832492C3xD83498,2

Groups of order 499

dρLabelID
C499Cyclic group4991C499499,1

Groups of order 500

dρLabelID
C500Cyclic group5001C500500,2
D250Dihedral group; = C2×D1252502+D250500,4
Dic125Dicyclic group; = C1252C45002-Dic125500,1
C536C46th semidirect product of C53 and C4 acting faithfully204C5^3:6C4500,46
C525D102nd semidirect product of C52 and D10 acting via D10/C5=C22204C5^2:5D10500,52
C25⋊C20The semidirect product of C25 and C20 acting faithfully; = Aut(D25) = Hol(C25)2520+C25:C20500,18
C52⋊C20The semidirect product of C52 and C20 acting faithfully2520+C5^2:C20500,17
He5⋊C42nd semidirect product of He5 and C4 acting faithfully2520+He5:C4500,21
He54C44th semidirect product of He5 and C4 acting faithfully; = Aut(5- 1+2)255He5:4C4500,25
C52⋊D10The semidirect product of C52 and D10 acting faithfully2510+C5^2:D10500,27
C52⋊F53rd semidirect product of C52 and F5 acting faithfully2510+C5^2:F5500,23
C252F52nd semidirect product of C25 and F5 acting via F5/C5=C4504+C25:2F5500,24
C539C49th semidirect product of C53 and C4 acting faithfully50C5^3:9C4500,49
He55C41st semidirect product of He5 and C4 acting via C4/C2=C210010-He5:5C4500,8
He56C42nd semidirect product of He5 and C4 acting via C4/C2=C21005He5:6C4500,11
C53⋊C45th semidirect product of C53 and C4 acting faithfully100C5^3:C4500,45
C537C47th semidirect product of C53 and C4 acting faithfully100C5^3:7C4500,47
C125⋊C4The semidirect product of C125 and C4 acting faithfully1254+C125:C4500,3
C25⋊F51st semidirect product of C25 and F5 acting via F5/C5=C4125C25:F5500,22
C538C48th semidirect product of C53 and C4 acting faithfully125C5^3:8C4500,48
C5312C43rd semidirect product of C53 and C4 acting via C4/C2=C2500C5^3:12C4500,39
C50.C10The non-split extension by C50 of C10 acting faithfully10010-C50.C10500,9
D5.D25The non-split extension by D5 of D25 acting via D25/C25=C21004D5.D25500,19
D25.D5The non-split extension by D25 of D5 acting via D5/C5=C21004D25.D5500,20
C50.D53rd non-split extension by C50 of D5 acting via D5/C5=C2500C50.D5500,10
C2×C250Abelian group of type [2,250]500C2xC250500,5
C5×C100Abelian group of type [5,100]500C5xC100500,12
C10×C50Abelian group of type [10,50]500C10xC50500,34
C52×C20Abelian group of type [5,5,20]500C5^2xC20500,40
C5×C102Abelian group of type [5,10,10]500C5xC10^2500,56
D5×D25Direct product of D5 and D25504+D5xD25500,26
D5×C50Direct product of C50 and D51002D5xC50500,29
C4×He5Direct product of C4 and He51005C4xHe5500,13
F5×C25Direct product of C25 and F51004F5xC25500,15
C10×D25Direct product of C10 and D251002C10xD25500,28
F5×C52Direct product of C52 and F5100F5xC5^2500,41
C5×Dic25Direct product of C5 and Dic251002C5xDic25500,6
Dic5×C25Direct product of C25 and Dic51002Dic5xC25500,7
C22×He5Direct product of C22 and He5100C2^2xHe5500,35
Dic5×C52Direct product of C52 and Dic5100Dic5xC5^2500,37
C4×5- 1+2Direct product of C4 and 5- 1+21005C4xES-(5,1)500,14
C22×5- 1+2Direct product of C22 and 5- 1+2100C2^2xES-(5,1)500,36
C5×D52Direct product of C5, D5 and D5204C5xD5^2500,50
C5×D5.D5Direct product of C5 and D5.D5204C5xD5.D5500,42
C5×C52⋊C4Direct product of C5 and C52⋊C4204C5xC5^2:C4500,44
D5×C5⋊D5Direct product of D5 and C5⋊D550D5xC5:D5500,51
C2×C25⋊C10Direct product of C2 and C25⋊C105010+C2xC25:C10500,31
C2×He5⋊C2Direct product of C2 and He5⋊C2505C2xHe5:C2500,33
C2×C52⋊C10Direct product of C2 and C52⋊C105010+C2xC5^2:C10500,30
C5×C25⋊C4Direct product of C5 and C25⋊C41004C5xC25:C4500,16
D5×C5×C10Direct product of C5×C10 and D5100D5xC5xC10500,53
C10×C5⋊D5Direct product of C10 and C5⋊D5100C10xC5:D5500,54
C5×C5⋊F5Direct product of C5 and C5⋊F5100C5xC5:F5500,43
C5×C526C4Direct product of C5 and C526C4100C5xC5^2:6C4500,38
C2×C25⋊D5Direct product of C2 and C25⋊D5250C2xC25:D5500,32
C2×C53⋊C2Direct product of C2 and C53⋊C2250C2xC5^3:C2500,55
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