Non-monomial groups

See monomial groups.

Groups of order 24

dρLabelID
SL2(𝔽3)Special linear group on 𝔽32; = Q8C3 = 2T = <2,3,3> = 1st non-monomial group82-SL(2,3)24,3

Groups of order 48

dρLabelID
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32) = 2O = <2,3,4>82GL(2,3)48,29
CSU2(𝔽3)Conformal special unitary group on 𝔽32; = Q8.S3162-CSU(2,3)48,28
C4.A4The central extension by C4 of A4162C4.A448,33
C2×SL2(𝔽3)Direct product of C2 and SL2(𝔽3)16C2xSL(2,3)48,32

Groups of order 60

dρLabelID
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simple53+A560,5

Groups of order 72

dρLabelID
Q8⋊C9The semidirect product of Q8 and C9 acting via C9/C3=C3722Q8:C972,3
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)242C3xSL(2,3)72,25

Groups of order 96

dρLabelID
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4242U(2,3)96,67
Q8⋊A41st semidirect product of Q8 and A4 acting via A4/C22=C3246-Q8:A496,203
Q8⋊Dic3The semidirect product of Q8 and Dic3 acting via Dic3/C2=S332Q8:Dic396,66
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3126+C2^3.3A496,3
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
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
C2×GL2(𝔽3)Direct product of C2 and GL2(𝔽3)16C2xGL(2,3)96,189
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
C2×C4.A4Direct product of C2 and C4.A432C2xC4.A496,200

Groups of order 108

dρLabelID
He3⋊C4The semidirect product of He3 and C4 acting faithfully183He3:C4108,15

Groups of order 120

dρLabelID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simple54+S5120,34
SL2(𝔽5)Special linear group on 𝔽52; = C2.A5 = 2I = <2,3,5>242-SL(2,5)120,5
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetries103+C2xA5120,35
C5×SL2(𝔽3)Direct product of C5 and SL2(𝔽3)402C5xSL(2,3)120,15

Groups of order 144

dρLabelID
Q8⋊D9The semidirect product of Q8 and D9 acting via D9/C3=S3724+Q8:D9144,32
C6.6S46th non-split extension by C6 of S4 acting via S4/A4=C2244+C6.6S4144,125
C6.5S45th non-split extension by C6 of S4 acting via S4/A4=C2484-C6.5S4144,124
Dic3.A4The non-split extension by Dic3 of A4 acting through Inn(Dic3)484+Dic3.A4144,127
Q8.C18The non-split extension by Q8 of C18 acting via C18/C6=C3722Q8.C18144,36
Q8.D9The non-split extension by Q8 of D9 acting via D9/C3=S31444-Q8.D9144,31
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
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
C3×C4.A4Direct product of C3 and C4.A4482C3xC4.A4144,157
C2×Q8⋊C9Direct product of C2 and Q8⋊C9144C2xQ8:C9144,35

Groups of order 160

dρLabelID
2- 1+4⋊C5The semidirect product of 2- 1+4 and C5 acting faithfully324-ES-(2,2):C5160,199

Groups of order 168

dρLabelID
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simple73GL(3,2)168,42
C14.A4The non-split extension by C14 of A4 acting via A4/C22=C3566C14.A4168,23
C7×SL2(𝔽3)Direct product of C7 and SL2(𝔽3)562C7xSL(2,3)168,22

Groups of order 180

dρLabelID
C3×A5Direct product of C3 and A5; = GL2(𝔽4)153C3xA5180,19

Groups of order 192

dρLabelID
CU2(𝔽3)Conformal unitary group on 𝔽32; = U2(𝔽3)7C2322CU(2,3)192,963
Q8⋊S41st semidirect product of Q8 and S4 acting via S4/C22=S3246Q8:S4192,1490
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+44C62nd semidirect product of 2+ 1+4 and C6 acting via C6/C2=C3324ES+(2,2):4C6192,1504
GL2(𝔽3)⋊C223rd semidirect product of GL2(𝔽3) and C22 acting via C22/C2=C2324GL(2,3):C2^2192,1482
Q8⋊Dic6The semidirect product of Q8 and Dic6 acting via Dic6/C4=S364Q8:Dic6192,945
Q8⋊SL2(𝔽3)The semidirect product of Q8 and SL2(𝔽3) acting via SL2(𝔽3)/Q8=C364Q8:SL(2,3)192,1022
SL2(𝔽3)⋊Q82nd semidirect product of SL2(𝔽3) and Q8 acting via Q8/C4=C264SL(2,3):Q8192,950
SL2(𝔽3)⋊6D42nd semidirect product of SL2(𝔽3) and D4 acting through Inn(SL2(𝔽3))64SL(2,3):6D4192,1005
SL2(𝔽3)⋊3Q8The semidirect product of SL2(𝔽3) and Q8 acting through Inn(SL2(𝔽3))64SL(2,3):3Q8192,1006
CSU2(𝔽3)⋊C41st semidirect product of CSU2(𝔽3) and C4 acting via C4/C2=C264CSU(2,3):C4192,947
C232D4⋊C3The semidirect product of C232D4 and C3 acting faithfully126+C2^3:2D4:C3192,194
C4○D4⋊A41st semidirect product of C4○D4 and A4 acting via A4/C22=C3246C4oD4:A4192,1507
C424C4⋊C3The semidirect product of C424C4 and C3 acting faithfully246C4^2:4C4:C3192,190
(C2×Q8)⋊C12The semidirect product of C2×Q8 and C12 acting via C12/C2=C632(C2xQ8):C12192,998
C4○D4⋊C12The semidirect product of C4○D4 and C12 acting via C12/C2=C664C4oD4:C12192,999
C4.A4⋊C44th semidirect product of C4.A4 and C4 acting via C4/C2=C264C4.A4:C4192,983
C24.2A42nd non-split extension by C24 of A4 acting faithfully126+C2^4.2A4192,197
D4.4S41st non-split extension by D4 of S4 acting through Inn(D4)164D4.4S4192,1485
C24.7A47th non-split extension by C24 of A4 acting faithfully16C2^4.7A4192,1021
C23.SL2(𝔽3)1st non-split extension by C23 of SL2(𝔽3) acting via SL2(𝔽3)/C2=A4164C2^3.SL(2,3)192,4
Q8.5S43rd non-split extension by Q8 of S4 acting via S4/A4=C2244+Q8.5S4192,988
C23.7S41st non-split extension by C23 of S4 acting via S4/C22=S3246C2^3.7S4192,180
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3246+C2^3.8S4192,181
C24.A41st non-split extension by C24 of A4 acting faithfully246C2^4.A4192,195
C24.3A43rd non-split extension by C24 of A4 acting faithfully246C2^4.3A4192,198
D8.A4The non-split extension by D8 of A4 acting through Inn(D8)324-D8.A4192,1019
C8.5S45th non-split extension by C8 of S4 acting via S4/A4=C2324C8.5S4192,964
C8.4S44th non-split extension by C8 of S4 acting via S4/A4=C2324C8.4S4192,965
C8.3S43rd non-split extension by C8 of S4 acting via S4/A4=C2324+C8.3S4192,966
D4.S42nd non-split extension by D4 of S4 acting via S4/A4=C2324-D4.S4192,989
D4.3S43rd non-split extension by D4 of S4 acting via S4/A4=C2324D4.3S4192,990
D4.5S42nd non-split extension by D4 of S4 acting through Inn(D4)324-D4.5S4192,1486
SD16.A4The non-split extension by SD16 of A4 acting through Inn(SD16)324SD16.A4192,1018
Q8.6S41st non-split extension by Q8 of S4 acting through Inn(Q8)324Q8.6S4192,1483
Q8.7S42nd non-split extension by Q8 of S4 acting through Inn(Q8)324+Q8.7S4192,1484
Q8.2D122nd non-split extension by Q8 of D12 acting via D12/C4=S332Q8.2D12192,954
M4(2).A4The non-split extension by M4(2) of A4 acting through Inn(M4(2))324M4(2).A4192,1013
C23.14S41st non-split extension by C23 of S4 acting via S4/A4=C232C2^3.14S4192,978
C23.15S42nd non-split extension by C23 of S4 acting via S4/A4=C232C2^3.15S4192,979
C23.16S43rd non-split extension by C23 of S4 acting via S4/A4=C232C2^3.16S4192,980
Q16.A4The non-split extension by Q16 of A4 acting through Inn(Q16)484+Q16.A4192,1017
Q8.4S42nd non-split extension by Q8 of S4 acting via S4/A4=C2484Q8.4S4192,987
Q8.1S41st non-split extension by Q8 of S4 acting via S4/C22=S3486-Q8.1S4192,1489
C16.A4The central extension by C16 of A4642C16.A4192,204
C8.7S42nd central extension by C8 of S4642C8.7S4192,187
C8.S42nd non-split extension by C8 of S4 acting via S4/A4=C2644-C8.S4192,962
C2.U2(𝔽3)The central extension by C2 of U2(𝔽3)64C2.U(2,3)192,183
Q8.D121st non-split extension by Q8 of D12 acting via D12/C4=S364Q8.D12192,949
Q8.Dic61st non-split extension by Q8 of Dic6 acting via Dic6/C4=S364Q8.Dic6192,948
SL2(𝔽3).D42nd non-split extension by SL2(𝔽3) of D4 acting via D4/C22=C264SL(2,3).D4192,984
(C22×C4).A44th non-split extension by C22×C4 of A4 acting faithfully246-(C2^2xC4).A4192,196
C23.19(C2×A4)12nd non-split extension by C23 of C2×A4 acting via C2×A4/C23=C3246C2^3.19(C2xA4)192,199
(C2×C4).S415th non-split extension by C2×C4 of S4 acting via S4/A4=C264(C2xC4).S4192,985
C4×GL2(𝔽3)Direct product of C4 and GL2(𝔽3)32C4xGL(2,3)192,951
D4×SL2(𝔽3)Direct product of D4 and SL2(𝔽3)32D4xSL(2,3)192,1004
C22×GL2(𝔽3)Direct product of C22 and GL2(𝔽3)32C2^2xGL(2,3)192,1475
C2×U2(𝔽3)Direct product of C2 and U2(𝔽3)48C2xU(2,3)192,981
C8×SL2(𝔽3)Direct product of C8 and SL2(𝔽3)64C8xSL(2,3)192,200
Q8×SL2(𝔽3)Direct product of Q8 and SL2(𝔽3)64Q8xSL(2,3)192,1007
C4×CSU2(𝔽3)Direct product of C4 and CSU2(𝔽3)64C4xCSU(2,3)192,946
C23×SL2(𝔽3)Direct product of C23 and SL2(𝔽3)64C2^3xSL(2,3)192,1498
C22×CSU2(𝔽3)Direct product of C22 and CSU2(𝔽3)64C2^2xCSU(2,3)192,1474
C2×C23.3A4Direct product of C2 and C23.3A424C2xC2^3.3A4192,189
C2×D4.A4Direct product of C2 and D4.A432C2xD4.A4192,1503
C2×C4.6S4Direct product of C2 and C4.6S432C2xC4.6S4192,1480
C2×C4.3S4Direct product of C2 and C4.3S432C2xC4.3S4192,1481
C2×Q8.D6Direct product of C2 and Q8.D632C2xQ8.D6192,1476
C2×Q8⋊A4Direct product of C2 and Q8⋊A448C2xQ8:A4192,1506
C2×Q8.A4Direct product of C2 and Q8.A448C2xQ8.A4192,1502
C4×C4.A4Direct product of C4 and C4.A464C4xC4.A4192,997
C2×C8.A4Direct product of C2 and C8.A464C2xC8.A4192,1012
C2×C4.S4Direct product of C2 and C4.S464C2xC4.S4192,1479
C2×Q8⋊Dic3Direct product of C2 and Q8⋊Dic364C2xQ8:Dic3192,977
C22×C4.A4Direct product of C22 and C4.A464C2^2xC4.A4192,1500
C2×C4×SL2(𝔽3)Direct product of C2×C4 and SL2(𝔽3)64C2xC4xSL(2,3)192,996

Groups of order 216

dρLabelID
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
He3⋊D4The semidirect product of He3 and D4 acting faithfully186+He3:D4216,87
He3⋊C8The semidirect product of He3 and C8 acting faithfully276+He3:C8216,86
Q8⋊He3The semidirect product of Q8 and He3 acting via He3/C32=C3726Q8:He3216,42
He32C8The semidirect product of He3 and C8 acting via C8/C2=C4723He3:2C8216,25
Q8⋊3- 1+2The semidirect product of Q8 and 3- 1+2 acting via 3- 1+2/C32=C3726Q8:ES-(3,1)216,41
Q8⋊C27The semidirect product of Q8 and C27 acting via C27/C9=C32162Q8:C27216,3
C18.A4The non-split extension by C18 of A4 acting via A4/C22=C3726C18.A4216,39
C9×SL2(𝔽3)Direct product of C9 and SL2(𝔽3)722C9xSL(2,3)216,38
C32×SL2(𝔽3)Direct product of C32 and SL2(𝔽3)72C3^2xSL(2,3)216,134
C2×He3⋊C4Direct product of C2 and He3⋊C4363C2xHe3:C4216,100
C3×Q8⋊C9Direct product of C3 and Q8⋊C9216C3xQ8:C9216,40

Groups of order 240

dρLabelID
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
Q8⋊D15The semidirect product of Q8 and D15 acting via D15/C5=S3404+Q8:D15240,106
C4.A5The central extension by C4 of A5242C4.A5240,93
C2.S52nd central stem extension by C2 of S5404-C2.S5240,90
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
C2×S5Direct product of C2 and S5; = O3(𝔽5)104+C2xS5240,189
C4×A5Direct product of C4 and A5203C4xA5240,92
C22×A5Direct product of C22 and A520C2^2xA5240,190
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
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
C5×C4.A4Direct product of C5 and C4.A4802C5xC4.A4240,154

Groups of order 264

dρLabelID
C11×SL2(𝔽3)Direct product of C11 and SL2(𝔽3)882C11xSL(2,3)264,12

Groups of order 288

dρLabelID
Ω4+ (𝔽3)Omega group of + type on 𝔽34; = SL2(𝔽3)A4244+Omega+(4,3)288,860
GL2(𝔽3)⋊S31st semidirect product of GL2(𝔽3) and S3 acting via S3/C3=C2484+GL(2,3):S3288,847
C3⋊U2(𝔽3)The semidirect product of C3 and U2(𝔽3) acting via U2(𝔽3)/C4.A4=C2724C3:U(2,3)288,404
2+ 1+4⋊C91st semidirect product of 2+ 1+4 and C9 acting via C9/C3=C3724ES+(2,2):C9288,348
CSU2(𝔽3)⋊S31st semidirect product of CSU2(𝔽3) and S3 acting via S3/C3=C2964CSU(2,3):S3288,844
2- 1+4⋊C9The semidirect product of 2- 1+4 and C9 acting via C9/C3=C31444ES-(2,2):C9288,349
Q8⋊Dic9The semidirect product of Q8 and Dic9 acting via Dic9/C6=S3288Q8:Dic9288,69
C22⋊(Q8⋊C9)The semidirect product of C22 and Q8⋊C9 acting via Q8⋊C9/C3×Q8=C3726C2^2:(Q8:C9)288,350
D12.A4The non-split extension by D12 of A4 acting through Inn(D12)484-D12.A4288,926
C12.7S47th non-split extension by C12 of S4 acting via S4/A4=C2484+C12.7S4288,915
D6.S41st non-split extension by D6 of S4 acting via S4/A4=C2484-D6.S4288,849
D6.2S42nd non-split extension by D6 of S4 acting via S4/A4=C2484D6.2S4288,850
C12.14S414th non-split extension by C12 of S4 acting via S4/A4=C2484C12.14S4288,914
Dic3.4S41st non-split extension by Dic3 of S4 acting through Inn(Dic3)484Dic3.4S4288,845
Dic3.5S42nd non-split extension by Dic3 of S4 acting through Inn(Dic3)484+Dic3.5S4288,846
SL2(𝔽3).D62nd non-split extension by SL2(𝔽3) of D6 acting via D6/C6=C2484SL(2,3).D6288,912
SL2(𝔽3).11D61st non-split extension by SL2(𝔽3) of D6 acting through Inn(SL2(𝔽3))484SL(2,3).11D6288,923
C12.9S49th non-split extension by C12 of S4 acting via S4/A4=C2724C12.9S4288,70
C12.4S44th non-split extension by C12 of S4 acting via S4/A4=C2724+C12.4S4288,340
Dic6.A4The non-split extension by Dic6 of A4 acting through Inn(Dic6)724+Dic6.A4288,924
C12.6S46th non-split extension by C12 of S4 acting via S4/A4=C2964-C12.6S4288,913
C6.GL2(𝔽3)3rd non-split extension by C6 of GL2(𝔽3) acting via GL2(𝔽3)/SL2(𝔽3)=C296C6.GL(2,3)288,403
SL2(𝔽3).Dic3The non-split extension by SL2(𝔽3) of Dic3 acting through Inn(SL2(𝔽3))964SL(2,3).Dic3288,410
Q8.C36The non-split extension by Q8 of C36 acting via C36/C12=C31442Q8.C36288,77
C12.3S43rd non-split extension by C12 of S4 acting via S4/A4=C21444-C12.3S4288,338
C12.11S411st non-split extension by C12 of S4 acting via S4/A4=C21444C12.11S4288,339
Q8.D182nd non-split extension by Q8 of D18 acting via D18/C6=S31444Q8.D18288,337
C2.(C42⋊C9)The central stem extension by C2 of C42⋊C9366C2.(C4^2:C9)288,3
S3×GL2(𝔽3)Direct product of S3 and GL2(𝔽3); = GL2(ℤ/6ℤ)244S3xGL(2,3)288,851
A4×SL2(𝔽3)Direct product of A4 and SL2(𝔽3)246-A4xSL(2,3)288,859
C6×GL2(𝔽3)Direct product of C6 and GL2(𝔽3)48C6xGL(2,3)288,900
S3×CSU2(𝔽3)Direct product of S3 and CSU2(𝔽3)484-S3xCSU(2,3)288,848
C3×U2(𝔽3)Direct product of C3 and U2(𝔽3)722C3xU(2,3)288,400
C12×SL2(𝔽3)Direct product of C12 and SL2(𝔽3)96C12xSL(2,3)288,633
C6×CSU2(𝔽3)Direct product of C6 and CSU2(𝔽3)96C6xCSU(2,3)288,899
Dic3×SL2(𝔽3)Direct product of Dic3 and SL2(𝔽3)96Dic3xSL(2,3)288,409
C3×C23.3A4Direct product of C3 and C23.3A4366C3xC2^3.3A4288,230
S3×C4.A4Direct product of S3 and C4.A4484S3xC4.A4288,925
C3×D4.A4Direct product of C3 and D4.A4484C3xD4.A4288,985
C3×C4.6S4Direct product of C3 and C4.6S4482C3xC4.6S4288,903
C3×C4.3S4Direct product of C3 and C4.3S4484C3xC4.3S4288,904
C2×C6.6S4Direct product of C2 and C6.6S448C2xC6.6S4288,911
C3×Q8.D6Direct product of C3 and Q8.D6484C3xQ8.D6288,901
C2×S3×SL2(𝔽3)Direct product of C2, S3 and SL2(𝔽3)48C2xS3xSL(2,3)288,922
C3×Q8⋊A4Direct product of C3 and Q8⋊A4726C3xQ8:A4288,986
C3×Q8.A4Direct product of C3 and Q8.A4724C3xQ8.A4288,984
C3×C8.A4Direct product of C3 and C8.A4962C3xC8.A4288,638
C6×C4.A4Direct product of C6 and C4.A496C6xC4.A4288,983
C3×C4.S4Direct product of C3 and C4.S4964C3xC4.S4288,902
C2×C6.5S4Direct product of C2 and C6.5S496C2xC6.5S4288,910
C3×Q8⋊Dic3Direct product of C3 and Q8⋊Dic396C3xQ8:Dic3288,399
C2×C6×SL2(𝔽3)Direct product of C2×C6 and SL2(𝔽3)96C2xC6xSL(2,3)288,981
C2×Dic3.A4Direct product of C2 and Dic3.A496C2xDic3.A4288,921
C2×Q8⋊D9Direct product of C2 and Q8⋊D9144C2xQ8:D9288,336
C2×Q8.C18Direct product of C2 and Q8.C18144C2xQ8.C18288,347
C4×Q8⋊C9Direct product of C4 and Q8⋊C9288C4xQ8:C9288,72
C2×Q8.D9Direct product of C2 and Q8.D9288C2xQ8.D9288,335
C22×Q8⋊C9Direct product of C22 and Q8⋊C9288C2^2xQ8:C9288,345

Groups of order 300

dρLabelID
C5×A5Direct product of C5 and A5; = U2(𝔽4)253C5xA5300,22

Groups of order 312

dρLabelID
C26.A4The non-split extension by C26 of A4 acting via A4/C22=C31046C26.A4312,26
C13×SL2(𝔽3)Direct product of C13 and SL2(𝔽3)1042C13xSL(2,3)312,25

Groups of order 320

dρLabelID
2- 1+4⋊D5The semidirect product of 2- 1+4 and D5 acting faithfully324ES-(2,2):D5320,1582
C22.58C24⋊C5The semidirect product of C22.58C24 and C5 acting faithfully64C2^2.58C2^4:C5320,1012
2- 1+4.D5The non-split extension by 2- 1+4 of D5 acting faithfully644-ES-(2,2).D5320,1581
2- 1+4.C10The non-split extension by 2- 1+4 of C10 acting via C10/C2=C5644ES-(2,2).C10320,1586
C2×2- 1+4⋊C5Direct product of C2 and 2- 1+4⋊C564C2xES-(2,2):C5320,1585

Groups of order 324

dρLabelID
He34Dic3The semidirect product of He3 and Dic3 acting via Dic3/C3=C4186He3:4Dic3324,113
He3.3C12The non-split extension by He3 of C12 acting via C12/C3=C4543He3.3C12324,111
C3×He3⋊C4Direct product of C3 and He3⋊C454C3xHe3:C4324,110

Groups of order 336

dρLabelID
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
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
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
Dic7.2A4The non-split extension by Dic7 of A4 acting through Inn(Dic7)1124+Dic7.2A4336,131
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)143C2xGL(3,2)336,209
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
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
C7×C4.A4Direct product of C7 and C4.A41122C7xC4.A4336,170
C2×C14.A4Direct product of C2 and C14.A4112C2xC14.A4336,172

Groups of order 360

dρLabelID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simple65+A6360,118
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5156GammaL(2,4)360,120
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
C3×SL2(𝔽5)Direct product of C3 and SL2(𝔽5)722C3xSL(2,5)360,51
C15×SL2(𝔽3)Direct product of C15 and SL2(𝔽3)1202C15xSL(2,3)360,89
C5×Q8⋊C9Direct product of C5 and Q8⋊C93602C5xQ8:C9360,14

Groups of order 375

dρLabelID
He5⋊C3The semidirect product of He5 and C3 acting faithfully755He5:C3375,2

Groups of order 408

dρLabelID
C17×SL2(𝔽3)Direct product of C17 and SL2(𝔽3)1362C17xSL(2,3)408,14

Groups of order 420

dρLabelID
C7×A5Direct product of C7 and A5353C7xA5420,13

Groups of order 432

dρLabelID
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)98+AGL(2,3)432,734
He3⋊SD16The semidirect product of He3 and SD16 acting faithfully276+He3:SD16432,520
He3⋊D8The semidirect product of He3 and D8 acting via D8/C2=D4726+He3:D8432,235
He32SD16The semidirect product of He3 and SD16 acting via SD16/C2=D4726He3:2SD16432,234
He31M4(2)The semidirect product of He3 and M4(2) acting via M4(2)/C4=C4726He3:1M4(2)432,274
He34M4(2)The semidirect product of He3 and M4(2) acting via M4(2)/C22=C4726He3:4M4(2)432,278
C322GL2(𝔽3)1st semidirect product of C32 and GL2(𝔽3) acting via GL2(𝔽3)/Q8=S37212+C3^2:2GL(2,3)432,248
C323GL2(𝔽3)2nd semidirect product of C32 and GL2(𝔽3) acting via GL2(𝔽3)/Q8=S3726C3^2:3GL(2,3)432,258
C325GL2(𝔽3)2nd semidirect product of C32 and GL2(𝔽3) acting via GL2(𝔽3)/SL2(𝔽3)=C272C3^2:5GL(2,3)432,620
He3⋊C16The semidirect product of He3 and C16 acting via C16/C2=C81446He3:C16432,233
He3⋊Q16The semidirect product of He3 and Q16 acting via Q16/C2=D41446-He3:Q16432,236
He32C16The semidirect product of He3 and C16 acting via C16/C4=C41443He3:2C16432,57
C32⋊CSU2(𝔽3)1st semidirect product of C32 and CSU2(𝔽3) acting via CSU2(𝔽3)/Q8=S314412-C3^2:CSU(2,3)432,247
C322CSU2(𝔽3)2nd semidirect product of C32 and CSU2(𝔽3) acting via CSU2(𝔽3)/Q8=S31446C3^2:2CSU(2,3)432,257
C324CSU2(𝔽3)2nd semidirect product of C32 and CSU2(𝔽3) acting via CSU2(𝔽3)/SL2(𝔽3)=C2144C3^2:4CSU(2,3)432,619
Q8⋊D27The semidirect product of Q8 and D27 acting via D27/C9=S32164+Q8:D27432,38
C32⋊D6⋊C4The semidirect product of C32⋊D6 and C4 acting via C4/C2=C2366C3^2:D6:C4432,238
C22⋊(He3⋊C4)The semidirect product of C22 and He3⋊C4 acting via He3⋊C4/He3⋊C2=C2366C2^2:(He3:C4)432,279
C4○D4⋊He3The semidirect product of C4○D4 and He3 acting via He3/C32=C3726C4oD4:He3432,339
C4⋊(He3⋊C4)The semidirect product of C4 and He3⋊C4 acting via He3⋊C4/He3⋊C2=C2726C4:(He3:C4)432,276
Q8⋊C94C63rd semidirect product of Q8⋊C9 and C6 acting via C6/C2=C3726Q8:C9:4C6432,338
Q8⋊He3⋊C24th semidirect product of Q8⋊He3 and C2 acting faithfully7212-Q8:He3:C2432,270
He32(C2×C8)The semidirect product of He3 and C2×C8 acting via C2×C8/C4=C4723He3:2(C2xC8)432,273
Q8⋊C93S3The semidirect product of Q8⋊C9 and S3 acting through Inn(Q8⋊C9)1444Q8:C9:3S3432,267
D18.A4The non-split extension by D18 of A4 acting via A4/C22=C37212-D18.A4432,263
C18.6S46th non-split extension by C18 of S4 acting via S4/A4=C2724+C18.6S4432,253
C2.SU3(𝔽2)The central extension by C2 of SU3(𝔽2)723C2.SU(3,2)432,239
C32.GL2(𝔽3)The non-split extension by C32 of GL2(𝔽3) acting via GL2(𝔽3)/Q8=S37212+C3^2.GL(2,3)432,245
C36.A4The non-split extension by C36 of A4 acting via A4/C22=C31446C36.A4432,330
C18.5S45th non-split extension by C18 of S4 acting via S4/A4=C21444-C18.5S4432,252
Dic9.A4The non-split extension by Dic9 of A4 acting via A4/C22=C314412+Dic9.A4432,261
Dic9.2A4The non-split extension by Dic9 of A4 acting through Inn(Dic9)1444+Dic9.2A4432,262
C32.CSU2(𝔽3)The non-split extension by C32 of CSU2(𝔽3) acting via CSU2(𝔽3)/Q8=S314412-C3^2.CSU(2,3)432,243
Q8.C54The non-split extension by Q8 of C54 acting via C54/C18=C32162Q8.C54432,42
C32.3GL2(𝔽3)2nd non-split extension by C32 of GL2(𝔽3) acting via GL2(𝔽3)/SL2(𝔽3)=C2216C3^2.3GL(2,3)432,256
Q8.D27The non-split extension by Q8 of D27 acting via D27/C9=S34324-Q8.D27432,37
C32.3CSU2(𝔽3)2nd non-split extension by C32 of CSU2(𝔽3) acting via CSU2(𝔽3)/SL2(𝔽3)=C2432C3^2.3CSU(2,3)432,255
C6.S3≀C24th non-split extension by C6 of S3≀C2 acting via S3≀C2/C32⋊C4=C2726-C6.S3wrC2432,237
C6.(S3×A4)7th non-split extension by C6 of S3×A4 acting via S3×A4/C3×A4=C27212+C6.(S3xA4)432,269
C3⋊Dic3.2A4The non-split extension by C3⋊Dic3 of A4 acting through Inn(C3⋊Dic3)144C3:Dic3.2A4432,625
C2×ASL2(𝔽3)Direct product of C2 and ASL2(𝔽3)188+C2xASL(2,3)432,735
C2×SU3(𝔽2)Direct product of C2 and SU3(𝔽2)543C2xSU(3,2)432,531
C9×GL2(𝔽3)Direct product of C9 and GL2(𝔽3)722C9xGL(2,3)432,241
D9×SL2(𝔽3)Direct product of D9 and SL2(𝔽3)724-D9xSL(2,3)432,264
C32×GL2(𝔽3)Direct product of C32 and GL2(𝔽3)72C3^2xGL(2,3)432,614
C9×CSU2(𝔽3)Direct product of C9 and CSU2(𝔽3)1442C9xCSU(2,3)432,240
C18×SL2(𝔽3)Direct product of C18 and SL2(𝔽3)144C18xSL(2,3)432,327
C32×CSU2(𝔽3)Direct product of C32 and CSU2(𝔽3)144C3^2xCSU(2,3)432,613
C2×He3⋊D4Direct product of C2 and He3⋊D4366+C2xHe3:D4432,530
C3×C6.5S4Direct product of C3 and C6.5S4484C3xC6.5S4432,616
C3×C6.6S4Direct product of C3 and C6.6S4484C3xC6.6S4432,617
C3×S3×SL2(𝔽3)Direct product of C3, S3 and SL2(𝔽3)484C3xS3xSL(2,3)432,623
C3×Dic3.A4Direct product of C3 and Dic3.A4484C3xDic3.A4432,622
C2×He3⋊C8Direct product of C2 and He3⋊C8546+C2xHe3:C8432,529
C4×He3⋊C4Direct product of C4 and He3⋊C4723C4xHe3:C4432,275
C22×He3⋊C4Direct product of C22 and He3⋊C472C2^2xHe3:C4432,543
C3⋊S3×SL2(𝔽3)Direct product of C3⋊S3 and SL2(𝔽3)72C3:S3xSL(2,3)432,626
S3×Q8⋊C9Direct product of S3 and Q8⋊C91444S3xQ8:C9432,268
C9×C4.A4Direct product of C9 and C4.A41442C9xC4.A4432,329
C3×Q8⋊D9Direct product of C3 and Q8⋊D91444C3xQ8:D9432,246
C2×Q8⋊He3Direct product of C2 and Q8⋊He3144C2xQ8:He3432,336
C2×C18.A4Direct product of C2 and C18.A4144C2xC18.A4432,328
C3×Q8.D9Direct product of C3 and Q8.D91444C3xQ8.D9432,244
C2×He32C8Direct product of C2 and He32C8144C2xHe3:2C8432,277
C32×C4.A4Direct product of C32 and C4.A4144C3^2xC4.A4432,699
C3×C6×SL2(𝔽3)Direct product of C3×C6 and SL2(𝔽3)144C3xC6xSL(2,3)432,698
C2×Q8⋊3- 1+2Direct product of C2 and Q8⋊3- 1+2144C2xQ8:ES-(3,1)432,335
C3×Q8.C18Direct product of C3 and Q8.C18216C3xQ8.C18432,337
C6×Q8⋊C9Direct product of C6 and Q8⋊C9432C6xQ8:C9432,334
C2×Q8⋊C27Direct product of C2 and Q8⋊C27432C2xQ8:C27432,41

Groups of order 456

dρLabelID
C38.A4The non-split extension by C38 of A4 acting via A4/C22=C31526C38.A4456,23
C19×SL2(𝔽3)Direct product of C19 and SL2(𝔽3)1522C19xSL(2,3)456,22

Groups of order 480

dρLabelID
GL2(𝔽5)General linear group on 𝔽52; = SL2(𝔽5)1C4 = Aut(C52)244GL(2,5)480,218
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
A5⋊C8The semidirect product of A5 and C8 acting via C8/C4=C2404A5:C8480,217
GL2(𝔽3)⋊D51st semidirect product of GL2(𝔽3) and D5 acting via D5/C5=C2804+GL(2,3):D5480,970
C5⋊U2(𝔽3)The semidirect product of C5 and U2(𝔽3) acting via U2(𝔽3)/SL2(𝔽3)=C41208+C5:U(2,3)480,961
C52U2(𝔽3)The semidirect product of C5 and U2(𝔽3) acting via U2(𝔽3)/C4.A4=C21204C5:2U(2,3)480,261
Q8⋊Dic15The semidirect product of Q8 and Dic15 acting via Dic15/C10=S3160Q8:Dic15480,260
CSU2(𝔽3)⋊D51st semidirect product of CSU2(𝔽3) and D5 acting via D5/C5=C21604CSU(2,3):D5480,967
C4.3S53rd non-split extension by C4 of S5 acting via S5/A5=C2404C4.3S5480,948
D10.S43rd non-split extension by D10 of S4 acting via S4/A4=C2408-D10.S4480,962
C8.A5The central extension by C8 of A5482C8.A5480,221
D4.A5The non-split extension by D4 of A5 acting through Inn(D4)484-D4.A5480,957
Q8.A5The non-split extension by Q8 of A5 acting through Inn(Q8)484+Q8.A5480,959
C4.6S53rd central extension by C4 of S5484C4.6S5480,946
C4.S52nd non-split extension by C4 of S5 acting via S5/A5=C2484C4.S5480,947
C22.S5The non-split extension by C22 of S5 acting via S5/A5=C2484-C2^2.S5480,953
D20.A4The non-split extension by D20 of A4 acting through Inn(D20)804-D20.A4480,1043
C20.6S46th non-split extension by C20 of S4 acting via S4/A4=C2804C20.6S4480,1031
C20.3S43rd non-split extension by C20 of S4 acting via S4/A4=C2804+C20.3S4480,1032
D10.1S41st non-split extension by D10 of S4 acting via S4/A4=C2804-D10.1S4480,972
D10.2S42nd non-split extension by D10 of S4 acting via S4/A4=C2804D10.2S4480,973
Q8.D302nd non-split extension by Q8 of D30 acting via D30/C10=S3804Q8.D30480,1029
Dic5.6S41st non-split extension by Dic5 of S4 acting through Inn(Dic5)804Dic5.6S4480,968
Dic5.7S42nd non-split extension by Dic5 of S4 acting through Inn(Dic5)804+Dic5.7S4480,969
SL2(𝔽3).11D101st non-split extension by SL2(𝔽3) of D10 acting through Inn(SL2(𝔽3))804SL(2,3).11D10480,1040
C22.2S51st central extension by C22 of S596C2^2.2S5480,219
Dic10.A4The non-split extension by Dic10 of A4 acting through Inn(Dic10)1204+Dic10.A4480,1041
C20.2S42nd non-split extension by C20 of S4 acting via S4/A4=C21604-C20.2S4480,1030
SL2(𝔽3).F5The non-split extension by SL2(𝔽3) of F5 acting through Inn(SL2(𝔽3))1608+SL(2,3).F5480,964
SL2(𝔽3).Dic5The non-split extension by SL2(𝔽3) of Dic5 acting through Inn(SL2(𝔽3))1604SL(2,3).Dic5480,267
C4×S5Direct product of C4 and S5; = CO3(𝔽5)204C4xS5480,943
D4×A5Direct product of D4 and A5206+D4xA5480,956
C22×S5Direct product of C22 and S520C2^2xS5480,1186
C8×A5Direct product of C8 and A5403C8xA5480,220
Q8×A5Direct product of Q8 and A5406-Q8xA5480,958
C23×A5Direct product of C23 and A540C2^3xA5480,1187
F5×SL2(𝔽3)Direct product of F5 and SL2(𝔽3)408-F5xSL(2,3)480,965
D5×GL2(𝔽3)Direct product of D5 and GL2(𝔽3)404D5xGL(2,3)480,974
D5×CSU2(𝔽3)Direct product of D5 and CSU2(𝔽3)804-D5xCSU(2,3)480,971
C10×GL2(𝔽3)Direct product of C10 and GL2(𝔽3)80C10xGL(2,3)480,1017
C4×SL2(𝔽5)Direct product of C4 and SL2(𝔽5)96C4xSL(2,5)480,222
C2×CSU2(𝔽5)Direct product of C2 and CSU2(𝔽5)96C2xCSU(2,5)480,949
C22×SL2(𝔽5)Direct product of C22 and SL2(𝔽5)96C2^2xSL(2,5)480,960
C5×U2(𝔽3)Direct product of C5 and U2(𝔽3)1202C5xU(2,3)480,257
C20×SL2(𝔽3)Direct product of C20 and SL2(𝔽3)160C20xSL(2,3)480,655
C10×CSU2(𝔽3)Direct product of C10 and CSU2(𝔽3)160C10xCSU(2,3)480,1016
Dic5×SL2(𝔽3)Direct product of Dic5 and SL2(𝔽3)160Dic5xSL(2,3)480,266
C2×A5⋊C4Direct product of C2 and A5⋊C424C2xA5:C4480,952
C2×C4×A5Direct product of C2×C4 and A540C2xC4xA5480,954
C2×C4.A5Direct product of C2 and C4.A548C2xC4.A5480,955
C5×C23.3A4Direct product of C5 and C23.3A4606C5xC2^3.3A4480,74
D5×C4.A4Direct product of D5 and C4.A4804D5xC4.A4480,1042
C2×C2.S5Direct product of C2 and C2.S580C2xC2.S5480,950
C2×Q8⋊D15Direct product of C2 and Q8⋊D1580C2xQ8:D15480,1028
C5×D4.A4Direct product of C5 and D4.A4804C5xD4.A4480,1132
C5×C4.6S4Direct product of C5 and C4.6S4802C5xC4.6S4480,1020
C5×C4.3S4Direct product of C5 and C4.3S4804C5xC4.3S4480,1021
C5×Q8.D6Direct product of C5 and Q8.D6804C5xQ8.D6480,1018
C2×D5×SL2(𝔽3)Direct product of C2, D5 and SL2(𝔽3)80C2xD5xSL(2,3)480,1039
C3×2- 1+4⋊C5Direct product of C3 and 2- 1+4⋊C5964C3xES-(2,2):C5480,1046
C5×Q8⋊A4Direct product of C5 and Q8⋊A41206C5xQ8:A4480,1133
C5×Q8.A4Direct product of C5 and Q8.A41204C5xQ8.A4480,1131
C5×C8.A4Direct product of C5 and C8.A41602C5xC8.A4480,660
C10×C4.A4Direct product of C10 and C4.A4160C10xC4.A4480,1130
C5×C4.S4Direct product of C5 and C4.S41604C5xC4.S4480,1019
C5×Q8⋊Dic3Direct product of C5 and Q8⋊Dic3160C5xQ8:Dic3480,256
C2×Q8.D15Direct product of C2 and Q8.D15160C2xQ8.D15480,1027
C2×Dic5.A4Direct product of C2 and Dic5.A4160C2xDic5.A4480,1038
C2×C10×SL2(𝔽3)Direct product of C2×C10 and SL2(𝔽3)160C2xC10xSL(2,3)480,1128
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