Faithful irreducible representation

Groups G whose centre is cyclic (and only these) admit a faithful irreducible representation ρ: G→GLn(ℂ). In the table below the groups are sorted by the smallest dimension n and the Frobenius-Schur indicator + if ρ is orthogonal, - if ρ is symplectic, and nothing otherwise.

Jump to: 1,1+ (cyclic)  2+ (dihedral)  2- (dicyclic+3 more)  2  3+ (symmetries of platonic solids)  3 
4+  4-  4  5+  5  6+  6-  6  7+  7  8+  8-  8  9+  9  10+  10-  10  11  12+  12-  12  13  14+  14-  14  15+  15  16+  18+  20+ 

Dimension 1  (ρ=1,1+)

A group has a faithful 1-dimensional representation if and only if it is cyclic.

Orthogonal of dimension 2  (ρ=2+)

A group has a faithful 2-dimensional orthogonal irreducible representation if and only if it is dihedral.

Symplectic of dimension 2  (ρ=2-)

A group with a faithful 2-dimensional symplectic irreducible representation is either dicyclic (e.g. generalized quaternion) or one of the following groups (Klein 1876).

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
CSU2(𝔽3)Conformal special unitary group on 𝔽32; = Q8.S3 = 2O = <2,3,4>162-CSU(2,3)48,28

Groups of order 120

dρLabelID
SL2(𝔽5)Special linear group on 𝔽52; = C2.A5 = 2I = <2,3,5>242-SL(2,5)120,5

Complex of dimension 2  (ρ=2)

Groups of order 16

dρLabelID
M4(2)Modular maximal-cyclic group; = C83C282M4(2)16,6
SD16Semidihedral group; = Q8C2 = QD1682SD1616,8
C4○D4Pauli group = central product of C4 and D482C4oD416,13

Groups of order 18

dρLabelID
C3×S3Direct product of C3 and S3; = U2(𝔽2)62C3xS318,3

Groups of order 24

dρLabelID
C3⋊C8The semidirect product of C3 and C8 acting via C8/C4=C2242C3:C824,1
C4×S3Direct product of C4 and S3122C4xS324,5
C3⋊D4The semidirect product of C3 and D4 acting via D4/C22=C2122C3:D424,8
C3×D4Direct product of C3 and D4122C3xD424,10
C3×Q8Direct product of C3 and Q8242C3xQ824,11

Groups of order 30

dρLabelID
C5×S3Direct product of C5 and S3152C5xS330,1
C3×D5Direct product of C3 and D5152C3xD530,2

Groups of order 32

dρLabelID
C4≀C2Wreath product of C4 by C282C4wrC232,11
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2162C8.C432,15
M5(2)Modular maximal-cyclic group; = C163C2162M5(2)32,17
SD32Semidihedral group; = C162C2 = QD32162SD3232,19
C8○D4Central product of C8 and D4162C8oD432,38
C4○D8Central product of C4 and D8162C4oD832,42

Groups of order 36

dρLabelID
C3×Dic3Direct product of C3 and Dic3122C3xDic336,6
S3×C6Direct product of C6 and S3122S3xC636,12

Groups of order 40

dρLabelID
C52C8The semidirect product of C5 and C8 acting via C8/C4=C2402C5:2C840,1
C4×D5Direct product of C4 and D5202C4xD540,5
C5⋊D4The semidirect product of C5 and D4 acting via D4/C22=C2202C5:D440,8
C5×D4Direct product of C5 and D4202C5xD440,10
C5×Q8Direct product of C5 and Q8402C5xQ840,11

Groups of order 42

dρLabelID
S3×C7Direct product of C7 and S3212S3xC742,3
C3×D7Direct product of C3 and D7212C3xD742,4

Groups of order 48

dρLabelID
C3⋊C16The semidirect product of C3 and C16 acting via C16/C8=C2482C3:C1648,1
S3×C8Direct product of C8 and S3242S3xC848,4
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
C4.Dic3The non-split extension by C4 of Dic3 acting via Dic3/C6=C2242C4.Dic348,10
C3×M4(2)Direct product of C3 and M4(2)242C3xM4(2)48,24
C3×D8Direct product of C3 and D8242C3xD848,25
C3×SD16Direct product of C3 and SD16242C3xSD1648,26
C3×Q16Direct product of C3 and Q16482C3xQ1648,27
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32)82GL(2,3)48,29
C4.A4The central extension by C4 of A4162C4.A448,33
C4○D12Central product of C4 and D12242C4oD1248,37
C3×C4○D4Direct product of C3 and C4○D4242C3xC4oD448,47

Groups of order 50

dρLabelID
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)102C5xD550,3

Groups of order 54

dρLabelID
C3×D9Direct product of C3 and D9182C3xD954,3
S3×C9Direct product of C9 and S3182S3xC954,4

Groups of order 56

dρLabelID
C7⋊C8The semidirect product of C7 and C8 acting via C8/C4=C2562C7:C856,1
C4×D7Direct product of C4 and D7282C4xD756,4
C7⋊D4The semidirect product of C7 and D4 acting via D4/C22=C2282C7:D456,7
C7×D4Direct product of C7 and D4282C7xD456,9
C7×Q8Direct product of C7 and Q8562C7xQ856,10

Groups of order 60

dρLabelID
C5×Dic3Direct product of C5 and Dic3602C5xDic360,1
C3×Dic5Direct product of C3 and Dic5602C3xDic560,2
C6×D5Direct product of C6 and D5302C6xD560,10
S3×C10Direct product of C10 and S3302S3xC1060,11

Groups of order 64

dρLabelID
D4.C8The non-split extension by D4 of C8 acting via C8/C4=C2322D4.C864,31
D8.C41st non-split extension by D8 of C4 acting via C4/C2=C2322D8.C464,40
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2162C8.C864,45
C8.4Q83rd non-split extension by C8 of Q8 acting via Q8/C4=C2322C8.4Q864,49
M6(2)Modular maximal-cyclic group; = C323C2322M6(2)64,51
SD64Semidihedral group; = C322C2 = QD64322SD6464,53
C8○D8Central product of C8 and D8162C8oD864,124
D4○C16Central product of D4 and C16322D4oC1664,185
C4○D16Central product of C4 and D16322C4oD1664,189

Groups of order 66

dρLabelID
S3×C11Direct product of C11 and S3332S3xC1166,1
C3×D11Direct product of C3 and D11332C3xD1166,2

Groups of order 70

dρLabelID
C7×D5Direct product of C7 and D5352C7xD570,1
C5×D7Direct product of C5 and D7352C5xD770,2

Groups of order 72

dρLabelID
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
C4×D9Direct product of C4 and D9362C4xD972,5
C9⋊D4The semidirect product of C9 and D4 acting via D4/C22=C2362C9:D472,8
D4×C9Direct product of C9 and D4362D4xC972,10
Q8×C9Direct product of C9 and Q8722Q8xC972,11
C3×C3⋊C8Direct product of C3 and C3⋊C8242C3xC3:C872,12
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)242C3xSL(2,3)72,25
C3×Dic6Direct product of C3 and Dic6242C3xDic672,26
S3×C12Direct product of C12 and S3242S3xC1272,27
C3×D12Direct product of C3 and D12242C3xD1272,28
C3×C3⋊D4Direct product of C3 and C3⋊D4122C3xC3:D472,30

Groups of order 78

dρLabelID
S3×C13Direct product of C13 and S3392S3xC1378,3
C3×D13Direct product of C3 and D13392C3xD1378,4

Groups of order 80

dρLabelID
C52C16The semidirect product of C5 and C16 acting via C16/C8=C2802C5:2C1680,1
C8×D5Direct product of C8 and D5402C8xD580,4
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
C4.Dic5The non-split extension by C4 of Dic5 acting via Dic5/C10=C2402C4.Dic580,10
C5×M4(2)Direct product of C5 and M4(2)402C5xM4(2)80,24
C5×D8Direct product of C5 and D8402C5xD880,25
C5×SD16Direct product of C5 and SD16402C5xSD1680,26
C5×Q16Direct product of C5 and Q16802C5xQ1680,27
C4○D20Central product of C4 and D20402C4oD2080,38
C5×C4○D4Direct product of C5 and C4○D4402C5xC4oD480,48

Groups of order 84

dρLabelID
C7×Dic3Direct product of C7 and Dic3842C7xDic384,3
C3×Dic7Direct product of C3 and Dic7842C3xDic784,4
C6×D7Direct product of C6 and D7422C6xD784,12
S3×C14Direct product of C14 and S3422S3xC1484,13

Groups of order 88

dρLabelID
C11⋊C8The semidirect product of C11 and C8 acting via C8/C4=C2882C11:C888,1
C4×D11Direct product of C4 and D11442C4xD1188,4
C11⋊D4The semidirect product of C11 and D4 acting via D4/C22=C2442C11:D488,7
D4×C11Direct product of C11 and D4442D4xC1188,9
Q8×C11Direct product of C11 and Q8882Q8xC1188,10

Groups of order 90

dρLabelID
C5×D9Direct product of C5 and D9452C5xD990,1
C9×D5Direct product of C9 and D5452C9xD590,2
S3×C15Direct product of C15 and S3302S3xC1590,6
C3×D15Direct product of C3 and D15302C3xD1590,7

Groups of order 96

dρLabelID
C3⋊C32The semidirect product of C3 and C32 acting via C32/C16=C2962C3:C3296,1
S3×C16Direct product of C16 and S3482S3xC1696,4
D6.C8The non-split extension by D6 of C8 acting via C8/C4=C2482D6.C896,5
C48⋊C22nd semidirect product of C48 and C2 acting faithfully482C48:C296,7
C424S33rd semidirect product of C42 and S3 acting via S3/C3=C2242C4^2:4S396,12
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
C3×C4≀C2Direct product of C3 and C4≀C2242C3xC4wrC296,54
C3×C8.C4Direct product of C3 and C8.C4482C3xC8.C496,58
C3×M5(2)Direct product of C3 and M5(2)482C3xM5(2)96,60
C3×D16Direct product of C3 and D16482C3xD1696,61
C3×SD32Direct product of C3 and SD32482C3xSD3296,62
C3×Q32Direct product of C3 and Q32962C3xQ3296,63
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4242U(2,3)96,67
C8.A4The central extension by C8 of A4322C8.A496,74
C8○D12Central product of C8 and D12482C8oD1296,108
C4○D24Central product of C4 and D24482C4oD2496,111
C3×C8○D4Direct product of C3 and C8○D4482C3xC8oD496,178
C3×C4○D8Direct product of C3 and C4○D8482C3xC4oD896,182
C4.6S43rd central extension by C4 of S4162C4.6S496,192

Groups of order 98

dρLabelID
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)142C7xD798,3

Groups of order 100

dρLabelID
C5×Dic5Direct product of C5 and Dic5202C5xDic5100,6
D5×C10Direct product of C10 and D5202D5xC10100,14

Groups of order 102

dρLabelID
S3×C17Direct product of C17 and S3512S3xC17102,1
C3×D17Direct product of C3 and D17512C3xD17102,2

Groups of order 104

dρLabelID
C132C8The semidirect product of C13 and C8 acting via C8/C4=C21042C13:2C8104,1
C4×D13Direct product of C4 and D13522C4xD13104,5
C13⋊D4The semidirect product of C13 and D4 acting via D4/C22=C2522C13:D4104,8
D4×C13Direct product of C13 and D4522D4xC13104,10
Q8×C13Direct product of C13 and Q81042Q8xC13104,11

Groups of order 108

dρLabelID
C3×Dic9Direct product of C3 and Dic9362C3xDic9108,6
C9×Dic3Direct product of C9 and Dic3362C9xDic3108,7
C6×D9Direct product of C6 and D9362C6xD9108,23
S3×C18Direct product of C18 and S3362S3xC18108,24

Groups of order 110

dρLabelID
D5×C11Direct product of C11 and D5552D5xC11110,3
C5×D11Direct product of C5 and D11552C5xD11110,4

Groups of order 112

dρLabelID
C7⋊C16The semidirect product of C7 and C16 acting via C16/C8=C21122C7:C16112,1
C8×D7Direct product of C8 and D7562C8xD7112,3
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
C4.Dic7The non-split extension by C4 of Dic7 acting via Dic7/C14=C2562C4.Dic7112,9
C7×M4(2)Direct product of C7 and M4(2)562C7xM4(2)112,23
C7×D8Direct product of C7 and D8562C7xD8112,24
C7×SD16Direct product of C7 and SD16562C7xSD16112,25
C7×Q16Direct product of C7 and Q161122C7xQ16112,26
C4○D28Central product of C4 and D28562C4oD28112,30
C7×C4○D4Direct product of C7 and C4○D4562C7xC4oD4112,40

Groups of order 114

dρLabelID
S3×C19Direct product of C19 and S3572S3xC19114,3
C3×D19Direct product of C3 and D19572C3xD19114,4

Groups of order 120

dρLabelID
C5×C3⋊C8Direct product of C5 and C3⋊C81202C5xC3:C8120,1
C3×C52C8Direct product of C3 and C52C81202C3xC5:2C8120,2
C153C81st semidirect product of C15 and C8 acting via C8/C4=C21202C15:3C8120,3
C5×SL2(𝔽3)Direct product of C5 and SL2(𝔽3)402C5xSL(2,3)120,15
C3×Dic10Direct product of C3 and Dic101202C3xDic10120,16
D5×C12Direct product of C12 and D5602D5xC12120,17
C3×D20Direct product of C3 and D20602C3xD20120,18
C3×C5⋊D4Direct product of C3 and C5⋊D4602C3xC5:D4120,20
C5×Dic6Direct product of C5 and Dic61202C5xDic6120,21
S3×C20Direct product of C20 and S3602S3xC20120,22
C5×D12Direct product of C5 and D12602C5xD12120,23
C5×C3⋊D4Direct product of C5 and C3⋊D4602C5xC3:D4120,25
C4×D15Direct product of C4 and D15602C4xD15120,27
C157D41st semidirect product of C15 and D4 acting via D4/C22=C2602C15:7D4120,30
D4×C15Direct product of C15 and D4602D4xC15120,32
Q8×C15Direct product of C15 and Q81202Q8xC15120,33

Groups of order 126

dρLabelID
C7×D9Direct product of C7 and D9632C7xD9126,3
C9×D7Direct product of C9 and D7632C9xD7126,4
S3×C21Direct product of C21 and S3422S3xC21126,12
C3×D21Direct product of C3 and D21422C3xD21126,13

Groups of order 128

dρLabelID
C8≀C2Wreath product of C8 by C2162C8wrC2128,67
C16.3C81st non-split extension by C16 of C8 acting via C8/C4=C2322C16.3C8128,105
D4.C16The non-split extension by D4 of C16 acting via C16/C8=C2642D4.C16128,133
D16.C41st non-split extension by D16 of C4 acting via C4/C2=C2642D16.C4128,149
C8.C161st non-split extension by C8 of C16 acting via C16/C8=C2322C8.C16128,154
C32.C41st non-split extension by C32 of C4 acting via C4/C2=C2642C32.C4128,157
M7(2)Modular maximal-cyclic group; = C643C2642M7(2)128,160
SD128Semidihedral group; = C642C2 = QD128642SD128128,162
C16○D8Central product of C16 and D8322C16oD8128,902
C8○D16Central product of C8 and D16322C8oD16128,910
D4○C32Central product of D4 and C32642D4oC32128,990
C4○D32Central product of C4 and D32642C4oD32128,994

Groups of order 130

dρLabelID
D5×C13Direct product of C13 and D5652D5xC13130,1
C5×D13Direct product of C5 and D13652C5xD13130,2

Groups of order 132

dρLabelID
C11×Dic3Direct product of C11 and Dic31322C11xDic3132,1
C3×Dic11Direct product of C3 and Dic111322C3xDic11132,2
C6×D11Direct product of C6 and D11662C6xD11132,7
S3×C22Direct product of C22 and S3662S3xC22132,8

Groups of order 136

dρLabelID
C173C8The semidirect product of C17 and C8 acting via C8/C4=C21362C17:3C8136,1
C4×D17Direct product of C4 and D17682C4xD17136,5
C17⋊D4The semidirect product of C17 and D4 acting via D4/C22=C2682C17:D4136,8
D4×C17Direct product of C17 and D4682D4xC17136,10
Q8×C17Direct product of C17 and Q81362Q8xC17136,11

Groups of order 138

dρLabelID
S3×C23Direct product of C23 and S3692S3xC23138,1
C3×D23Direct product of C3 and D23692C3xD23138,2

Groups of order 140

dρLabelID
C7×Dic5Direct product of C7 and Dic51402C7xDic5140,1
C5×Dic7Direct product of C5 and Dic71402C5xDic7140,2
C10×D7Direct product of C10 and D7702C10xD7140,8
D5×C14Direct product of C14 and D5702D5xC14140,9

Groups of order 144

dρLabelID
C9⋊C16The semidirect product of C9 and C16 acting via C16/C8=C21442C9:C16144,1
C8×D9Direct product of C8 and D9722C8xD9144,5
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
C4.Dic9The non-split extension by C4 of Dic9 acting via Dic9/C18=C2722C4.Dic9144,10
C9×M4(2)Direct product of C9 and M4(2)722C9xM4(2)144,24
C9×D8Direct product of C9 and D8722C9xD8144,25
C9×SD16Direct product of C9 and SD16722C9xSD16144,26
C9×Q16Direct product of C9 and Q161442C9xQ16144,27
C3×C3⋊C16Direct product of C3 and C3⋊C16482C3xC3:C16144,28
Q8.C18The non-split extension by Q8 of C18 acting via C18/C6=C3722Q8.C18144,36
D365C2The semidirect product of D36 and C2 acting through Inn(D36)722D36:5C2144,40
C9×C4○D4Direct product of C9 and C4○D4722C9xC4oD4144,50
S3×C24Direct product of C24 and S3482S3xC24144,69
C3×C8⋊S3Direct product of C3 and C8⋊S3482C3xC8:S3144,70
C3×C24⋊C2Direct product of C3 and C24⋊C2482C3xC24:C2144,71
C3×D24Direct product of C3 and D24482C3xD24144,72
C3×Dic12Direct product of C3 and Dic12482C3xDic12144,73
C3×C4.Dic3Direct product of C3 and C4.Dic3242C3xC4.Dic3144,75
C3×CSU2(𝔽3)Direct product of C3 and CSU2(𝔽3)482C3xCSU(2,3)144,121
C3×GL2(𝔽3)Direct product of C3 and GL2(𝔽3)242C3xGL(2,3)144,122
C3×C4.A4Direct product of C3 and C4.A4482C3xC4.A4144,157
C3×C4○D12Direct product of C3 and C4○D12242C3xC4oD12144,161

Groups of order 150

dρLabelID
S3×C25Direct product of C25 and S3752S3xC25150,1
C3×D25Direct product of C3 and D25752C3xD25150,2
D5×C15Direct product of C15 and D5302D5xC15150,8
C5×D15Direct product of C5 and D15302C5xD15150,11

Groups of order 152

dρLabelID
C19⋊C8The semidirect product of C19 and C8 acting via C8/C4=C21522C19:C8152,1
C4×D19Direct product of C4 and D19762C4xD19152,4
C19⋊D4The semidirect product of C19 and D4 acting via D4/C22=C2762C19:D4152,7
D4×C19Direct product of C19 and D4762D4xC19152,9
Q8×C19Direct product of C19 and Q81522Q8xC19152,10

Groups of order 154

dρLabelID
C11×D7Direct product of C11 and D7772C11xD7154,1
C7×D11Direct product of C7 and D11772C7xD11154,2

Groups of order 156

dρLabelID
Dic3×C13Direct product of C13 and Dic31562Dic3xC13156,3
C3×Dic13Direct product of C3 and Dic131562C3xDic13156,4
C6×D13Direct product of C6 and D13782C6xD13156,15
S3×C26Direct product of C26 and S3782S3xC26156,16

Groups of order 160

dρLabelID
C52C32The semidirect product of C5 and C32 acting via C32/C16=C21602C5:2C32160,1
D5×C16Direct product of C16 and D5802D5xC16160,4
C80⋊C25th semidirect product of C80 and C2 acting faithfully802C80:C2160,5
C16⋊D52nd semidirect product of C16 and D5 acting via D5/C5=C2802C16:D5160,7
D204C41st semidirect product of D20 and C4 acting via C4/C2=C2402D20:4C4160,12
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
C5×C4≀C2Direct product of C5 and C4≀C2402C5xC4wrC2160,54
C5×C8.C4Direct product of C5 and C8.C4802C5xC8.C4160,58
C5×M5(2)Direct product of C5 and M5(2)802C5xM5(2)160,60
C5×D16Direct product of C5 and D16802C5xD16160,61
C5×SD32Direct product of C5 and SD32802C5xSD32160,62
C5×Q32Direct product of C5 and Q321602C5xQ32160,63
D20.3C4The non-split extension by D20 of C4 acting through Inn(D20)802D20.3C4160,122
D407C2The semidirect product of D40 and C2 acting through Inn(D40)802D40:7C2160,125
C5×C8○D4Direct product of C5 and C8○D4802C5xC8oD4160,192
C5×C4○D8Direct product of C5 and C4○D8802C5xC4oD8160,196

Groups of order 162

dρLabelID
C9×D9Direct product of C9 and D9182C9xD9162,3
C3×D27Direct product of C3 and D27542C3xD27162,7
S3×C27Direct product of C27 and S3542S3xC27162,8

Groups of order 168

dρLabelID
C7×C3⋊C8Direct product of C7 and C3⋊C81682C7xC3:C8168,3
C3×C7⋊C8Direct product of C3 and C7⋊C81682C3xC7:C8168,4
C21⋊C81st semidirect product of C21 and C8 acting via C8/C4=C21682C21:C8168,5
C7×SL2(𝔽3)Direct product of C7 and SL2(𝔽3)562C7xSL(2,3)168,22
C3×Dic14Direct product of C3 and Dic141682C3xDic14168,24
C12×D7Direct product of C12 and D7842C12xD7168,25
C3×D28Direct product of C3 and D28842C3xD28168,26
C3×C7⋊D4Direct product of C3 and C7⋊D4842C3xC7:D4168,28
C7×Dic6Direct product of C7 and Dic61682C7xDic6168,29
S3×C28Direct product of C28 and S3842S3xC28168,30
C7×D12Direct product of C7 and D12842C7xD12168,31
C7×C3⋊D4Direct product of C7 and C3⋊D4842C7xC3:D4168,33
C4×D21Direct product of C4 and D21842C4xD21168,35
C217D41st semidirect product of C21 and D4 acting via D4/C22=C2842C21:7D4168,38
D4×C21Direct product of C21 and D4842D4xC21168,40
Q8×C21Direct product of C21 and Q81682Q8xC21168,41

Groups of order 170

dρLabelID
D5×C17Direct product of C17 and D5852D5xC17170,1
C5×D17Direct product of C5 and D17852C5xD17170,2

Groups of order 174

dρLabelID
S3×C29Direct product of C29 and S3872S3xC29174,1
C3×D29Direct product of C3 and D29872C3xD29174,2

Groups of order 176

dρLabelID
C11⋊C16The semidirect product of C11 and C16 acting via C16/C8=C21762C11:C16176,1
C8×D11Direct product of C8 and D11882C8xD11176,3
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
C44.C41st non-split extension by C44 of C4 acting via C4/C2=C2882C44.C4176,9
C11×M4(2)Direct product of C11 and M4(2)882C11xM4(2)176,23
C11×D8Direct product of C11 and D8882C11xD8176,24
C11×SD16Direct product of C11 and SD16882C11xSD16176,25
C11×Q16Direct product of C11 and Q161762C11xQ16176,26
D445C2The semidirect product of D44 and C2 acting through Inn(D44)882D44:5C2176,30
C11×C4○D4Direct product of C11 and C4○D4882C11xC4oD4176,40

Groups of order 180

dρLabelID
C5×Dic9Direct product of C5 and Dic91802C5xDic9180,1
C9×Dic5Direct product of C9 and Dic51802C9xDic5180,2
D5×C18Direct product of C18 and D5902D5xC18180,9
C10×D9Direct product of C10 and D9902C10xD9180,10
Dic3×C15Direct product of C15 and Dic3602Dic3xC15180,14
C3×Dic15Direct product of C3 and Dic15602C3xDic15180,15
S3×C30Direct product of C30 and S3602S3xC30180,33
C6×D15Direct product of C6 and D15602C6xD15180,34

Groups of order 182

dρLabelID
C13×D7Direct product of C13 and D7912C13xD7182,1
C7×D13Direct product of C7 and D13912C7xD13182,2

Groups of order 184

dρLabelID
C23⋊C8The semidirect product of C23 and C8 acting via C8/C4=C21842C23:C8184,1
C4×D23Direct product of C4 and D23922C4xD23184,4
C23⋊D4The semidirect product of C23 and D4 acting via D4/C22=C2922C23:D4184,7
D4×C23Direct product of C23 and D4922D4xC23184,9
Q8×C23Direct product of C23 and Q81842Q8xC23184,10

Groups of order 186

dρLabelID
S3×C31Direct product of C31 and S3932S3xC31186,3
C3×D31Direct product of C3 and D31932C3xD31186,4

Groups of order 190

dρLabelID
D5×C19Direct product of C19 and D5952D5xC19190,1
C5×D19Direct product of C5 and D19952C5xD19190,2

Groups of order 192

dρLabelID
C3⋊C64The semidirect product of C3 and C64 acting via C64/C32=C21922C3:C64192,1
S3×C32Direct product of C32 and S3962S3xC32192,5
C96⋊C26th semidirect product of C96 and C2 acting faithfully962C96:C2192,6
C32⋊S32nd semidirect product of C32 and S3 acting via S3/C3=C2962C32:S3192,8
C24.1C81st non-split extension by C24 of C8 acting via C8/C4=C2482C24.1C8192,22
C3⋊M6(2)The semidirect product of C3 and M6(2) acting via M6(2)/C2×C16=C2962C3:M6(2)192,58
C48.C41st non-split extension by C48 of C4 acting via C4/C2=C2962C48.C4192,65
D12.C81st non-split extension by D12 of C8 acting via C8/C4=C2962D12.C8192,67
D24.1C41st non-split extension by D24 of C4 acting via C4/C2=C2962D24.1C4192,69
C3×D4.C8Direct product of C3 and D4.C8962C3xD4.C8192,156
C3×D8.C4Direct product of C3 and D8.C4962C3xD8.C4192,165
C3×C8.C8Direct product of C3 and C8.C8482C3xC8.C8192,170
C3×C8.4Q8Direct product of C3 and C8.4Q8962C3xC8.4Q8192,174
C3×M6(2)Direct product of C3 and M6(2)962C3xM6(2)192,176
C3×D32Direct product of C3 and D32962C3xD32192,177
C3×SD64Direct product of C3 and SD64962C3xSD64192,178
C3×Q64Direct product of C3 and Q641922C3xQ64192,179
C8.7S42nd central extension by C8 of S4642C8.7S4192,187
C16.A4The central extension by C16 of A4642C16.A4192,204
D2411C4The semidirect product of D24 and C4 acting through Inn(D24)482D24:11C4192,259
D12.4C8The non-split extension by D12 of C8 acting through Inn(D12)962D12.4C8192,460
D487C2The semidirect product of D48 and C2 acting through Inn(D48)962D48:7C2192,463
C3×C8○D8Direct product of C3 and C8○D8482C3xC8oD8192,876
C3×D4○C16Direct product of C3 and D4○C16962C3xD4oC16192,937
C3×C4○D16Direct product of C3 and C4○D16962C3xC4oD16192,941
CU2(𝔽3)Conformal unitary group on 𝔽32; = U2(𝔽3)7C2322CU(2,3)192,963

Groups of order 196

dρLabelID
C7×Dic7Direct product of C7 and Dic7282C7xDic7196,5
D7×C14Direct product of C14 and D7282D7xC14196,10

Groups of order 198

dρLabelID
C11×D9Direct product of C11 and D9992C11xD9198,1
C9×D11Direct product of C9 and D11992C9xD11198,2
S3×C33Direct product of C33 and S3662S3xC33198,6
C3×D33Direct product of C3 and D33662C3xD33198,7

Groups of order 200

dρLabelID
C252C8The semidirect product of C25 and C8 acting via C8/C4=C22002C25:2C8200,1
C4×D25Direct product of C4 and D251002C4xD25200,5
C25⋊D4The semidirect product of C25 and D4 acting via D4/C22=C21002C25:D4200,8
D4×C25Direct product of C25 and D41002D4xC25200,10
Q8×C25Direct product of C25 and Q82002Q8xC25200,11
C5×C52C8Direct product of C5 and C52C8402C5xC5:2C8200,15
C5×Dic10Direct product of C5 and Dic10402C5xDic10200,27
D5×C20Direct product of C20 and D5402D5xC20200,28
C5×D20Direct product of C5 and D20402C5xD20200,29
C5×C5⋊D4Direct product of C5 and C5⋊D4202C5xC5:D4200,31

Groups of order 204

dρLabelID
Dic3×C17Direct product of C17 and Dic32042Dic3xC17204,1
C3×Dic17Direct product of C3 and Dic172042C3xDic17204,2
C6×D17Direct product of C6 and D171022C6xD17204,9
S3×C34Direct product of C34 and S31022S3xC34204,10

Groups of order 208

dρLabelID
C132C16The semidirect product of C13 and C16 acting via C16/C8=C22082C13:2C16208,1
C8×D13Direct product of C8 and D131042C8xD13208,4
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
C52.4C41st non-split extension by C52 of C4 acting via C4/C2=C21042C52.4C4208,10
C13×M4(2)Direct product of C13 and M4(2)1042C13xM4(2)208,24
C13×D8Direct product of C13 and D81042C13xD8208,25
C13×SD16Direct product of C13 and SD161042C13xSD16208,26
C13×Q16Direct product of C13 and Q162082C13xQ16208,27
D525C2The semidirect product of D52 and C2 acting through Inn(D52)1042D52:5C2208,38
C13×C4○D4Direct product of C13 and C4○D41042C13xC4oD4208,48

Groups of order 210

dρLabelID
D7×C15Direct product of C15 and D71052D7xC15210,5
D5×C21Direct product of C21 and D51052D5xC21210,6
C3×D35Direct product of C3 and D351052C3xD35210,7
S3×C35Direct product of C35 and S31052S3xC35210,8
C5×D21Direct product of C5 and D211052C5xD21210,9
C7×D15Direct product of C7 and D151052C7xD15210,10

Groups of order 216

dρLabelID
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
C4×D27Direct product of C4 and D271082C4xD27216,5
C27⋊D4The semidirect product of C27 and D4 acting via D4/C22=C21082C27:D4216,8
D4×C27Direct product of C27 and D41082D4xC27216,10
Q8×C27Direct product of C27 and Q82162Q8xC27216,11
C3×C9⋊C8Direct product of C3 and C9⋊C8722C3xC9:C8216,12
C9×C3⋊C8Direct product of C9 and C3⋊C8722C9xC3:C8216,13
C9×SL2(𝔽3)Direct product of C9 and SL2(𝔽3)722C9xSL(2,3)216,38
C3×Dic18Direct product of C3 and Dic18722C3xDic18216,43
C9×Dic6Direct product of C9 and Dic6722C9xDic6216,44
C12×D9Direct product of C12 and D9722C12xD9216,45
C3×D36Direct product of C3 and D36722C3xD36216,46
S3×C36Direct product of C36 and S3722S3xC36216,47
C9×D12Direct product of C9 and D12722C9xD12216,48
C3×C9⋊D4Direct product of C3 and C9⋊D4362C3xC9:D4216,57
C9×C3⋊D4Direct product of C9 and C3⋊D4362C9xC3:D4216,58

Groups of order 220

dρLabelID
C11×Dic5Direct product of C11 and Dic52202C11xDic5220,3
C5×Dic11Direct product of C5 and Dic112202C5xDic11220,4
C10×D11Direct product of C10 and D111102C10xD11220,12
D5×C22Direct product of C22 and D51102D5xC22220,13

Groups of order 222

dρLabelID
S3×C37Direct product of C37 and S31112S3xC37222,3
C3×D37Direct product of C3 and D371112C3xD37222,4

Groups of order 224

dρLabelID
C7⋊C32The semidirect product of C7 and C32 acting via C32/C16=C22242C7:C32224,1
D7×C16Direct product of C16 and D71122D7xC16224,3
C16⋊D73rd semidirect product of C16 and D7 acting via D7/C7=C21122C16:D7224,4
C112⋊C22nd semidirect product of C112 and C2 acting faithfully1122C112:C2224,6
Dic14⋊C41st semidirect product of Dic14 and C4 acting via C4/C2=C2562Dic14:C4224,11
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
C7×C4≀C2Direct product of C7 and C4≀C2562C7xC4wrC2224,53
C7×C8.C4Direct product of C7 and C8.C41122C7xC8.C4224,57
C7×M5(2)Direct product of C7 and M5(2)1122C7xM5(2)224,59
C7×D16Direct product of C7 and D161122C7xD16224,60
C7×SD32Direct product of C7 and SD321122C7xSD32224,61
C7×Q32Direct product of C7 and Q322242C7xQ32224,62
D28.2C4The non-split extension by D28 of C4 acting through Inn(D28)1122D28.2C4224,96
D567C2The semidirect product of D56 and C2 acting through Inn(D56)1122D56:7C2224,99
C7×C8○D4Direct product of C7 and C8○D41122C7xC8oD4224,166
C7×C4○D8Direct product of C7 and C4○D81122C7xC4oD8224,170

Groups of order 228

dρLabelID
Dic3×C19Direct product of C19 and Dic32282Dic3xC19228,3
C3×Dic19Direct product of C3 and Dic192282C3xDic19228,4
C6×D19Direct product of C6 and D191142C6xD19228,12
S3×C38Direct product of C38 and S31142S3xC38228,13

Groups of order 230

dρLabelID
D5×C23Direct product of C23 and D51152D5xC23230,1
C5×D23Direct product of C5 and D231152C5xD23230,2

Groups of order 232

dρLabelID
C292C8The semidirect product of C29 and C8 acting via C8/C4=C22322C29:2C8232,1
C4×D29Direct product of C4 and D291162C4xD29232,5
C29⋊D4The semidirect product of C29 and D4 acting via D4/C22=C21162C29:D4232,8
D4×C29Direct product of C29 and D41162D4xC29232,10
Q8×C29Direct product of C29 and Q82322Q8xC29232,11

Groups of order 234

dρLabelID
C13×D9Direct product of C13 and D91172C13xD9234,3
C9×D13Direct product of C9 and D131172C9xD13234,4
S3×C39Direct product of C39 and S3782S3xC39234,12
C3×D39Direct product of C3 and D39782C3xD39234,13

Groups of order 238

dρLabelID
D7×C17Direct product of C17 and D71192D7xC17238,1
C7×D17Direct product of C7 and D171192C7xD17238,2

Groups of order 240

dρLabelID
C5×C3⋊C16Direct product of C5 and C3⋊C162402C5xC3:C16240,1
C3×C52C16Direct product of C3 and C52C162402C3xC5:2C16240,2
C153C161st semidirect product of C15 and C16 acting via C16/C8=C22402C15:3C16240,3
D5×C24Direct product of C24 and D51202D5xC24240,33
C3×C8⋊D5Direct product of C3 and C8⋊D51202C3xC8:D5240,34
C3×C40⋊C2Direct product of C3 and C40⋊C21202C3xC40:C2240,35
C3×D40Direct product of C3 and D401202C3xD40240,36
C3×Dic20Direct product of C3 and Dic202402C3xDic20240,37
C3×C4.Dic5Direct product of C3 and C4.Dic51202C3xC4.Dic5240,39
S3×C40Direct product of C40 and S31202S3xC40240,49
C5×C8⋊S3Direct product of C5 and C8⋊S31202C5xC8:S3240,50
C5×C24⋊C2Direct product of C5 and C24⋊C21202C5xC24:C2240,51
C5×D24Direct product of C5 and D241202C5xD24240,52
C5×Dic12Direct product of C5 and Dic122402C5xDic12240,53
C5×C4.Dic3Direct product of C5 and C4.Dic31202C5xC4.Dic3240,55
C8×D15Direct product of C8 and D151202C8xD15240,65
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
C60.7C41st non-split extension by C60 of C4 acting via C4/C2=C21202C60.7C4240,71
C15×M4(2)Direct product of C15 and M4(2)1202C15xM4(2)240,85
C15×D8Direct product of C15 and D81202C15xD8240,86
C15×SD16Direct product of C15 and SD161202C15xSD16240,87
C15×Q16Direct product of C15 and Q162402C15xQ16240,88
C4.A5The central extension by C4 of A5242C4.A5240,93
C5×CSU2(𝔽3)Direct product of C5 and CSU2(𝔽3)802C5xCSU(2,3)240,102
C5×GL2(𝔽3)Direct product of C5 and GL2(𝔽3)402C5xGL(2,3)240,103
C5×C4.A4Direct product of C5 and C4.A4802C5xC4.A4240,154
C3×C4○D20Direct product of C3 and C4○D201202C3xC4oD20240,158
C5×C4○D12Direct product of C5 and C4○D121202C5xC4oD12240,168
D6011C2The semidirect product of D60 and C2 acting through Inn(D60)1202D60:11C2240,178
C15×C4○D4Direct product of C15 and C4○D41202C15xC4oD4240,188

Groups of order 242

dρLabelID
C11×D11Direct product of C11 and D11; = AΣL1(𝔽121)222C11xD11242,3

Groups of order 246

dρLabelID
S3×C41Direct product of C41 and S31232S3xC41246,1
C3×D41Direct product of C3 and D411232C3xD41246,2

Groups of order 248

dρLabelID
C31⋊C8The semidirect product of C31 and C8 acting via C8/C4=C22482C31:C8248,1
C4×D31Direct product of C4 and D311242C4xD31248,4
C31⋊D4The semidirect product of C31 and D4 acting via D4/C22=C21242C31:D4248,7
D4×C31Direct product of C31 and D41242D4xC31248,9
Q8×C31Direct product of C31 and Q82482Q8xC31248,10

Groups of order 250

dρLabelID
C5×D25Direct product of C5 and D25502C5xD25250,3
D5×C25Direct product of C25 and D5502D5xC25250,4

Groups of order 252

dρLabelID
C7×Dic9Direct product of C7 and Dic92522C7xDic9252,3
C9×Dic7Direct product of C9 and Dic72522C9xDic7252,4
D7×C18Direct product of C18 and D71262D7xC18252,12
C14×D9Direct product of C14 and D91262C14xD9252,13
Dic3×C21Direct product of C21 and Dic3842Dic3xC21252,21
C3×Dic21Direct product of C3 and Dic21842C3xDic21252,22
S3×C42Direct product of C42 and S3842S3xC42252,42
C6×D21Direct product of C6 and D21842C6xD21252,43

Groups of order 258

dρLabelID
S3×C43Direct product of C43 and S31292S3xC43258,3
C3×D43Direct product of C3 and D431292C3xD43258,4

Groups of order 260

dρLabelID
C13×Dic5Direct product of C13 and Dic52602C13xDic5260,1
C5×Dic13Direct product of C5 and Dic132602C5xDic13260,2
C10×D13Direct product of C10 and D131302C10xD13260,12
D5×C26Direct product of C26 and D51302D5xC26260,13

Groups of order 264

dρLabelID
C11×C3⋊C8Direct product of C11 and C3⋊C82642C11xC3:C8264,1
C3×C11⋊C8Direct product of C3 and C11⋊C82642C3xC11:C8264,2
C33⋊C81st semidirect product of C33 and C8 acting via C8/C4=C22642C33:C8264,3
C11×SL2(𝔽3)Direct product of C11 and SL2(𝔽3)882C11xSL(2,3)264,12
C3×Dic22Direct product of C3 and Dic222642C3xDic22264,13
C12×D11Direct product of C12 and D111322C12xD11264,14
C3×D44Direct product of C3 and D441322C3xD44264,15
C3×C11⋊D4Direct product of C3 and C11⋊D41322C3xC11:D4264,17
C11×Dic6Direct product of C11 and Dic62642C11xDic6264,18
S3×C44Direct product of C44 and S31322S3xC44264,19
C11×D12Direct product of C11 and D121322C11xD12264,20
C11×C3⋊D4Direct product of C11 and C3⋊D41322C11xC3:D4264,22
C4×D33Direct product of C4 and D331322C4xD33264,24
C337D41st semidirect product of C33 and D4 acting via D4/C22=C21322C33:7D4264,27
D4×C33Direct product of C33 and D41322D4xC33264,29
Q8×C33Direct product of C33 and Q82642Q8xC33264,30

Groups of order 266

dρLabelID
D7×C19Direct product of C19 and D71332D7xC19266,1
C7×D19Direct product of C7 and D191332C7xD19266,2

Groups of order 270

dρLabelID
C5×D27Direct product of C5 and D271352C5xD27270,1
D5×C27Direct product of C27 and D51352D5xC27270,2
C15×D9Direct product of C15 and D9902C15xD9270,8
S3×C45Direct product of C45 and S3902S3xC45270,9
C3×D45Direct product of C3 and D45902C3xD45270,12
C9×D15Direct product of C9 and D15902C9xD15270,13

Groups of order 272

dρLabelID
C174C16The semidirect product of C17 and C16 acting via C16/C8=C22722C17:4C16272,1
C8×D17Direct product of C8 and D171362C8xD17272,4
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
C68.4C41st non-split extension by C68 of C4 acting via C4/C2=C21362C68.4C4272,10
M4(2)×C17Direct product of C17 and M4(2)1362M4(2)xC17272,24
D8×C17Direct product of C17 and D81362D8xC17272,25
SD16×C17Direct product of C17 and SD161362SD16xC17272,26
Q16×C17Direct product of C17 and Q162722Q16xC17272,27
D685C2The semidirect product of D68 and C2 acting through Inn(D68)1362D68:5C2272,39
C4○D4×C17Direct product of C17 and C4○D41362C4oD4xC17272,49

Groups of order 276

dρLabelID
Dic3×C23Direct product of C23 and Dic32762Dic3xC23276,1
C3×Dic23Direct product of C3 and Dic232762C3xDic23276,2
C6×D23Direct product of C6 and D231382C6xD23276,7
S3×C46Direct product of C46 and S31382S3xC46276,8

Groups of order 280

dρLabelID
C7×C52C8Direct product of C7 and C52C82802C7xC5:2C8280,1
C5×C7⋊C8Direct product of C5 and C7⋊C82802C5xC7:C8280,2
C353C81st semidirect product of C35 and C8 acting via C8/C4=C22802C35:3C8280,3
C5×Dic14Direct product of C5 and Dic142802C5xDic14280,14
D7×C20Direct product of C20 and D71402D7xC20280,15
C5×D28Direct product of C5 and D281402C5xD28280,16
C5×C7⋊D4Direct product of C5 and C7⋊D41402C5xC7:D4280,18
C7×Dic10Direct product of C7 and Dic102802C7xDic10280,19
D5×C28Direct product of C28 and D51402D5xC28280,20
C7×D20Direct product of C7 and D201402C7xD20280,21
C7×C5⋊D4Direct product of C7 and C5⋊D41402C7xC5:D4280,23
C4×D35Direct product of C4 and D351402C4xD35280,25
C357D41st semidirect product of C35 and D4 acting via D4/C22=C21402C35:7D4280,28
D4×C35Direct product of C35 and D41402D4xC35280,30
Q8×C35Direct product of C35 and Q82802Q8xC35280,31

Groups of order 282

dρLabelID
S3×C47Direct product of C47 and S31412S3xC47282,1
C3×D47Direct product of C3 and D471412C3xD47282,2

Groups of order 286

dρLabelID
C13×D11Direct product of C13 and D111432C13xD11286,1
C11×D13Direct product of C11 and D131432C11xD13286,2

Groups of order 288

dρLabelID
C9⋊C32The semidirect product of C9 and C32 acting via C32/C16=C22882C9:C32288,1
C16×D9Direct product of C16 and D91442C16xD9288,4
C16⋊D93rd semidirect product of C16 and D9 acting via D9/C9=C21442C16:D9288,5
C144⋊C22nd semidirect product of C144 and C2 acting faithfully1442C144:C2288,7
C424D93rd semidirect product of C42 and D9 acting via D9/C9=C2722C4^2:4D9288,12
C36.C81st non-split extension by C36 of C8 acting via C8/C4=C21442C36.C8288,19
C72.C41st non-split extension by C72 of C4 acting via C4/C2=C21442C72.C4288,20
C9×C4≀C2Direct product of C9 and C4≀C2722C9xC4wrC2288,54
C9×C8.C4Direct product of C9 and C8.C41442C9xC8.C4288,58
C9×M5(2)Direct product of C9 and M5(2)1442C9xM5(2)288,60
C9×D16Direct product of C9 and D161442C9xD16288,61
C9×SD32Direct product of C9 and SD321442C9xSD32288,62
C9×Q32Direct product of C9 and Q322882C9xQ32288,63
C3×C3⋊C32Direct product of C3 and C3⋊C32962C3xC3:C32288,64
Q8.C36The non-split extension by Q8 of C36 acting via C36/C12=C31442Q8.C36288,77
D36.2C4The non-split extension by D36 of C4 acting through Inn(D36)1442D36.2C4288,112
D727C2The semidirect product of D72 and C2 acting through Inn(D72)1442D72:7C2288,115
C9×C8○D4Direct product of C9 and C8○D41442C9xC8oD4288,181
C9×C4○D8Direct product of C9 and C4○D81442C9xC4oD8288,185
S3×C48Direct product of C48 and S3962S3xC48288,231
C3×D6.C8Direct product of C3 and D6.C8962C3xD6.C8288,232
C3×D48Direct product of C3 and D48962C3xD48288,233
C3×C48⋊C2Direct product of C3 and C48⋊C2962C3xC48:C2288,234
C3×Dic24Direct product of C3 and Dic24962C3xDic24288,235
C3×C424S3Direct product of C3 and C424S3242C3xC4^2:4S3288,239
C3×C12.C8Direct product of C3 and C12.C8482C3xC12.C8288,246
C3×C24.C4Direct product of C3 and C24.C4482C3xC24.C4288,253
C3×U2(𝔽3)Direct product of C3 and U2(𝔽3)722C3xU(2,3)288,400
C3×C8.A4Direct product of C3 and C8.A4962C3xC8.A4288,638
C3×C8○D12Direct product of C3 and C8○D12482C3xC8oD12288,672
C3×C4○D24Direct product of C3 and C4○D24482C3xC4oD24288,675
C3×C4.6S4Direct product of C3 and C4.6S4482C3xC4.6S4288,903

Groups of order 290

dρLabelID
D5×C29Direct product of C29 and D51452D5xC29290,1
C5×D29Direct product of C5 and D291452C5xD29290,2

Groups of order 294

dρLabelID
S3×C49Direct product of C49 and S31472S3xC49294,3
C3×D49Direct product of C3 and D491472C3xD49294,4
D7×C21Direct product of C21 and D7422D7xC21294,18
C7×D21Direct product of C7 and D21422C7xD21294,21

Groups of order 296

dρLabelID
C372C8The semidirect product of C37 and C8 acting via C8/C4=C22962C37:2C8296,1
C4×D37Direct product of C4 and D371482C4xD37296,5
C37⋊D4The semidirect product of C37 and D4 acting via D4/C22=C21482C37:D4296,8
D4×C37Direct product of C37 and D41482D4xC37296,10
Q8×C37Direct product of C37 and Q82962Q8xC37296,11

Groups of order 300

dρLabelID
Dic3×C25Direct product of C25 and Dic33002Dic3xC25300,1
C3×Dic25Direct product of C3 and Dic253002C3xDic25300,2
C6×D25Direct product of C6 and D251502C6xD25300,9
S3×C50Direct product of C50 and S31502S3xC50300,10
C15×Dic5Direct product of C15 and Dic5602C15xDic5300,16
C5×Dic15Direct product of C5 and Dic15602C5xDic15300,19
D5×C30Direct product of C30 and D5602D5xC30300,44
C10×D15Direct product of C10 and D15602C10xD15300,47

Groups of order 304

dρLabelID
C19⋊C16The semidirect product of C19 and C16 acting via C16/C8=C23042C19:C16304,1
C8×D19Direct product of C8 and D191522C8xD19304,3
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
C76.C41st non-split extension by C76 of C4 acting via C4/C2=C21522C76.C4304,9
M4(2)×C19Direct product of C19 and M4(2)1522M4(2)xC19304,23
D8×C19Direct product of C19 and D81522D8xC19304,24
SD16×C19Direct product of C19 and SD161522SD16xC19304,25
Q16×C19Direct product of C19 and Q163042Q16xC19304,26
D765C2The semidirect product of D76 and C2 acting through Inn(D76)1522D76:5C2304,30
C4○D4×C19Direct product of C19 and C4○D41522C4oD4xC19304,40

Groups of order 306

dρLabelID
C17×D9Direct product of C17 and D91532C17xD9306,1
C9×D17Direct product of C9 and D171532C9xD17306,2
S3×C51Direct product of C51 and S31022S3xC51306,6
C3×D51Direct product of C3 and D511022C3xD51306,7

Groups of order 308

dρLabelID
C11×Dic7Direct product of C11 and Dic73082C11xDic7308,1
C7×Dic11Direct product of C7 and Dic113082C7xDic11308,2
C14×D11Direct product of C14 and D111542C14xD11308,6
D7×C22Direct product of C22 and D71542D7xC22308,7

Groups of order 310

dρLabelID
D5×C31Direct product of C31 and D51552D5xC31310,3
C5×D31Direct product of C5 and D311552C5xD31310,4

Groups of order 312

dρLabelID
C13×C3⋊C8Direct product of C13 and C3⋊C83122C13xC3:C8312,3
C3×C132C8Direct product of C3 and C132C83122C3xC13:2C8312,4
C393C81st semidirect product of C39 and C8 acting via C8/C4=C23122C39:3C8312,5
C13×SL2(𝔽3)Direct product of C13 and SL2(𝔽3)1042C13xSL(2,3)312,25
C3×Dic26Direct product of C3 and Dic263122C3xDic26312,27
C12×D13Direct product of C12 and D131562C12xD13312,28
C3×D52Direct product of C3 and D521562C3xD52312,29
C3×C13⋊D4Direct product of C3 and C13⋊D41562C3xC13:D4312,31
C13×Dic6Direct product of C13 and Dic63122C13xDic6312,32
S3×C52Direct product of C52 and S31562S3xC52312,33
C13×D12Direct product of C13 and D121562C13xD12312,34
C13×C3⋊D4Direct product of C13 and C3⋊D41562C13xC3:D4312,36
C4×D39Direct product of C4 and D391562C4xD39312,38
C397D41st semidirect product of C39 and D4 acting via D4/C22=C21562C39:7D4312,41
D4×C39Direct product of C39 and D41562D4xC39312,43
Q8×C39Direct product of C39 and Q83122Q8xC39312,44

Groups of order 318

dρLabelID
S3×C53Direct product of C53 and S31592S3xC53318,1
C3×D53Direct product of C3 and D531592C3xD53318,2

Groups of order 320

dρLabelID
C52C64The semidirect product of C5 and C64 acting via C64/C32=C23202C5:2C64320,1
D5×C32Direct product of C32 and D51602D5xC32320,4
C32⋊D53rd semidirect product of C32 and D5 acting via D5/C5=C21602C32:D5320,5
C160⋊C22nd semidirect product of C160 and C2 acting faithfully1602C160:C2320,7
C40.7C81st non-split extension by C40 of C8 acting via C8/C4=C2802C40.7C8320,21
C80.9C44th non-split extension by C80 of C4 acting via C4/C2=C21602C80.9C4320,57
C80.6C41st non-split extension by C80 of C4 acting via C4/C2=C21602C80.6C4320,64
D20.3C81st non-split extension by D20 of C8 acting via C8/C4=C21602D20.3C8320,66
D40.3C41st non-split extension by D40 of C4 acting via C4/C2=C21602D40.3C4320,68
C5×D4.C8Direct product of C5 and D4.C81602C5xD4.C8320,155
C5×D8.C4Direct product of C5 and D8.C41602C5xD8.C4320,164
C5×C8.C8Direct product of C5 and C8.C8802C5xC8.C8320,169
C5×C8.4Q8Direct product of C5 and C8.4Q81602C5xC8.4Q8320,173
C5×M6(2)Direct product of C5 and M6(2)1602C5xM6(2)320,175
C5×D32Direct product of C5 and D321602C5xD32320,176
C5×SD64Direct product of C5 and SD641602C5xSD64320,177
C5×Q64Direct product of C5 and Q643202C5xQ64320,178
D4017C4The semidirect product of D40 and C4 acting through Inn(D40)802D40:17C4320,327
D20.6C8The non-split extension by D20 of C8 acting through Inn(D20)1602D20.6C8320,528
D807C2The semidirect product of D80 and C2 acting through Inn(D80)1602D80:7C2320,531
C5×C8○D8Direct product of C5 and C8○D8802C5xC8oD8320,944
C5×D4○C16Direct product of C5 and D4○C161602C5xD4oC16320,1005
C5×C4○D16Direct product of C5 and C4○D161602C5xC4oD16320,1009

Groups of order 322

dρLabelID
D7×C23Direct product of C23 and D71612D7xC23322,1
C7×D23Direct product of C7 and D231612C7xD23322,2

Groups of order 324

dρLabelID
C9×Dic9Direct product of C9 and Dic9362C9xDic9324,6
C3×Dic27Direct product of C3 and Dic271082C3xDic27324,10
Dic3×C27Direct product of C27 and Dic31082Dic3xC27324,11
D9×C18Direct product of C18 and D9362D9xC18324,61
C6×D27Direct product of C6 and D271082C6xD27324,65
S3×C54Direct product of C54 and S31082S3xC54324,66

Groups of order 328

dρLabelID
C413C8The semidirect product of C41 and C8 acting via C8/C4=C23282C41:3C8328,1
C4×D41Direct product of C4 and D411642C4xD41328,5
C41⋊D4The semidirect product of C41 and D4 acting via D4/C22=C21642C41:D4328,8
D4×C41Direct product of C41 and D41642D4xC41328,10
Q8×C41Direct product of C41 and Q83282Q8xC41328,11

Groups of order 330

dρLabelID
C15×D11Direct product of C15 and D111652C15xD11330,5
D5×C33Direct product of C33 and D51652D5xC33330,6
C3×D55Direct product of C3 and D551652C3xD55330,7
S3×C55Direct product of C55 and S31652S3xC55330,8
C5×D33Direct product of C5 and D331652C5xD33330,9
C11×D15Direct product of C11 and D151652C11xD15330,10

Groups of order 336

dρLabelID
C7×C3⋊C16Direct product of C7 and C3⋊C163362C7xC3:C16336,3
C3×C7⋊C16Direct product of C3 and C7⋊C163362C3xC7:C16336,4
C21⋊C161st semidirect product of C21 and C16 acting via C16/C8=C23362C21:C16336,5
D7×C24Direct product of C24 and D71682D7xC24336,58
C3×C8⋊D7Direct product of C3 and C8⋊D71682C3xC8:D7336,59
C3×C56⋊C2Direct product of C3 and C56⋊C21682C3xC56:C2336,60
C3×D56Direct product of C3 and D561682C3xD56336,61
C3×Dic28Direct product of C3 and Dic283362C3xDic28336,62
C3×C4.Dic7Direct product of C3 and C4.Dic71682C3xC4.Dic7336,64
S3×C56Direct product of C56 and S31682S3xC56336,74
C7×C8⋊S3Direct product of C7 and C8⋊S31682C7xC8:S3336,75
C7×C24⋊C2Direct product of C7 and C24⋊C21682C7xC24:C2336,76
C7×D24Direct product of C7 and D241682C7xD24336,77
C7×Dic12Direct product of C7 and Dic123362C7xDic12336,78
C7×C4.Dic3Direct product of C7 and C4.Dic31682C7xC4.Dic3336,80
C8×D21Direct product of C8 and D211682C8xD21336,90
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
C84.C41st non-split extension by C84 of C4 acting via C4/C2=C21682C84.C4336,96
M4(2)×C21Direct product of C21 and M4(2)1682M4(2)xC21336,110
D8×C21Direct product of C21 and D81682D8xC21336,111
SD16×C21Direct product of C21 and SD161682SD16xC21336,112
Q16×C21Direct product of C21 and Q163362Q16xC21336,113
C7×CSU2(𝔽3)Direct product of C7 and CSU2(𝔽3)1122C7xCSU(2,3)336,115
C7×GL2(𝔽3)Direct product of C7 and GL2(𝔽3)562C7xGL(2,3)336,116
C7×C4.A4Direct product of C7 and C4.A41122C7xC4.A4336,170
C3×C4○D28Direct product of C3 and C4○D281682C3xC4oD28336,177
C7×C4○D12Direct product of C7 and C4○D121682C7xC4oD12336,187
D8411C2The semidirect product of D84 and C2 acting through Inn(D84)1682D84:11C2336,197
C4○D4×C21Direct product of C21 and C4○D41682C4oD4xC21336,207

Groups of order 338

dρLabelID
C13×D13Direct product of C13 and D13; = AΣL1(𝔽169)262C13xD13338,3

Groups of order 340

dρLabelID
C17×Dic5Direct product of C17 and Dic53402C17xDic5340,1
C5×Dic17Direct product of C5 and Dic173402C5xDic17340,2
C10×D17Direct product of C10 and D171702C10xD17340,12
D5×C34Direct product of C34 and D51702D5xC34340,13

Groups of order 342

dρLabelID
D9×C19Direct product of C19 and D91712D9xC19342,3
C9×D19Direct product of C9 and D191712C9xD19342,4
S3×C57Direct product of C57 and S31142S3xC57342,14
C3×D57Direct product of C3 and D571142C3xD57342,15

Groups of order 344

dρLabelID
C43⋊C8The semidirect product of C43 and C8 acting via C8/C4=C23442C43:C8344,1
C4×D43Direct product of C4 and D431722C4xD43344,4
C43⋊D4The semidirect product of C43 and D4 acting via D4/C22=C21722C43:D4344,7
D4×C43Direct product of C43 and D41722D4xC43344,9
Q8×C43Direct product of C43 and Q83442Q8xC43344,10

Groups of order 348

dρLabelID
Dic3×C29Direct product of C29 and Dic33482Dic3xC29348,1
C3×Dic29Direct product of C3 and Dic293482C3xDic29348,2
C6×D29Direct product of C6 and D291742C6xD29348,9
S3×C58Direct product of C58 and S31742S3xC58348,10

Groups of order 350

dρLabelID
C7×D25Direct product of C7 and D251752C7xD25350,1
D7×C25Direct product of C25 and D71752D7xC25350,2
D5×C35Direct product of C35 and D5702D5xC35350,6
C5×D35Direct product of C5 and D35702C5xD35350,7

Groups of order 352

dρLabelID
C11⋊C32The semidirect product of C11 and C32 acting via C32/C16=C23522C11:C32352,1
C16×D11Direct product of C16 and D111762C16xD11352,3
D22.C8The non-split extension by D22 of C8 acting via C8/C4=C21762D22.C8352,4
C176⋊C22nd semidirect product of C176 and C2 acting faithfully1762C176:C2352,6
D441C41st semidirect product of D44 and C4 acting via C4/C2=C2882D44:1C4352,11
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
C11×C4≀C2Direct product of C11 and C4≀C2882C11xC4wrC2352,53
C11×C8.C4Direct product of C11 and C8.C41762C11xC8.C4352,57
C11×M5(2)Direct product of C11 and M5(2)1762C11xM5(2)352,59
C11×D16Direct product of C11 and D161762C11xD16352,60
C11×SD32Direct product of C11 and SD321762C11xSD32352,61
C11×Q32Direct product of C11 and Q323522C11xQ32352,62
D44.2C4The non-split extension by D44 of C4 acting through Inn(D44)1762D44.2C4352,96
D887C2The semidirect product of D88 and C2 acting through Inn(D88)1762D88:7C2352,99
C11×C8○D4Direct product of C11 and C8○D41762C11xC8oD4352,166
C11×C4○D8Direct product of C11 and C4○D81762C11xC4oD8352,170

Groups of order 354

dρLabelID
S3×C59Direct product of C59 and S31772S3xC59354,1
C3×D59Direct product of C3 and D591772C3xD59354,2

Groups of order 360

dρLabelID
C5×C9⋊C8Direct product of C5 and C9⋊C83602C5xC9:C8360,1
C9×C52C8Direct product of C9 and C52C83602C9xC5:2C8360,2
C453C81st semidirect product of C45 and C8 acting via C8/C4=C23602C45:3C8360,3
C5×Q8⋊C9Direct product of C5 and Q8⋊C93602C5xQ8:C9360,14
C9×Dic10Direct product of C9 and Dic103602C9xDic10360,15
D5×C36Direct product of C36 and D51802D5xC36360,16
C9×D20Direct product of C9 and D201802C9xD20360,17
C9×C5⋊D4Direct product of C9 and C5⋊D41802C9xC5:D4360,19
C5×Dic18Direct product of C5 and Dic183602C5xDic18360,20
D9×C20Direct product of C20 and D91802D9xC20360,21
C5×D36Direct product of C5 and D361802C5xD36360,22
C5×C9⋊D4Direct product of C5 and C9⋊D41802C5xC9:D4360,24
C4×D45Direct product of C4 and D451802C4xD45360,26
C457D41st semidirect product of C45 and D4 acting via D4/C22=C21802C45:7D4360,29
D4×C45Direct product of C45 and D41802D4xC45360,31
Q8×C45Direct product of C45 and Q83602Q8xC45360,32
C15×C3⋊C8Direct product of C15 and C3⋊C81202C15xC3:C8360,34
C3×C153C8Direct product of C3 and C153C81202C3xC15:3C8360,35
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
C15×Dic6Direct product of C15 and Dic61202C15xDic6360,95
S3×C60Direct product of C60 and S31202S3xC60360,96
C15×D12Direct product of C15 and D121202C15xD12360,97
C15×C3⋊D4Direct product of C15 and C3⋊D4602C15xC3:D4360,99
C3×Dic30Direct product of C3 and Dic301202C3xDic30360,100
C12×D15Direct product of C12 and D151202C12xD15360,101
C3×D60Direct product of C3 and D601202C3xD60360,102
C3×C157D4Direct product of C3 and C157D4602C3xC15:7D4360,104

Groups of order 364

dρLabelID
C13×Dic7Direct product of C13 and Dic73642C13xDic7364,1
C7×Dic13Direct product of C7 and Dic133642C7xDic13364,2
C14×D13Direct product of C14 and D131822C14xD13364,8
D7×C26Direct product of C26 and D71822D7xC26364,9

Groups of order 366

dρLabelID
S3×C61Direct product of C61 and S31832S3xC61366,3
C3×D61Direct product of C3 and D611832C3xD61366,4

Groups of order 368

dρLabelID
C23⋊C16The semidirect product of C23 and C16 acting via C16/C8=C23682C23:C16368,1
C8×D23Direct product of C8 and D231842C8xD23368,3
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
C92.C41st non-split extension by C92 of C4 acting via C4/C2=C21842C92.C4368,9
M4(2)×C23Direct product of C23 and M4(2)1842M4(2)xC23368,23
D8×C23Direct product of C23 and D81842D8xC23368,24
SD16×C23Direct product of C23 and SD161842SD16xC23368,25
Q16×C23Direct product of C23 and Q163682Q16xC23368,26
D925C2The semidirect product of D92 and C2 acting through Inn(D92)1842D92:5C2368,30
C4○D4×C23Direct product of C23 and C4○D41842C4oD4xC23368,40

Groups of order 370

dρLabelID
D5×C37Direct product of C37 and D51852D5xC37370,1
C5×D37Direct product of C5 and D371852C5xD37370,2

Groups of order 372

dρLabelID
Dic3×C31Direct product of C31 and Dic33722Dic3xC31372,3
C3×Dic31Direct product of C3 and Dic313722C3xDic31372,4
C6×D31Direct product of C6 and D311862C6xD31372,12
S3×C62Direct product of C62 and S31862S3xC62372,13

Groups of order 374

dρLabelID
C17×D11Direct product of C17 and D111872C17xD11374,1
C11×D17Direct product of C11 and D171872C11xD17374,2

Groups of order 376

dρLabelID
C47⋊C8The semidirect product of C47 and C8 acting via C8/C4=C23762C47:C8376,1
C4×D47Direct product of C4 and D471882C4xD47376,4
C47⋊D4The semidirect product of C47 and D4 acting via D4/C22=C21882C47:D4376,7
D4×C47Direct product of C47 and D41882D4xC47376,9
Q8×C47Direct product of C47 and Q83762Q8xC47376,10

Groups of order 378

dρLabelID
C7×D27Direct product of C7 and D271892C7xD27378,3
D7×C27Direct product of C27 and D71892D7xC27378,4
D9×C21Direct product of C21 and D91262D9xC21378,32
S3×C63Direct product of C63 and S31262S3xC63378,33
C3×D63Direct product of C3 and D631262C3xD63378,36
C9×D21Direct product of C9 and D211262C9xD21378,37

Groups of order 380

dρLabelID
C19×Dic5Direct product of C19 and Dic53802C19xDic5380,1
C5×Dic19Direct product of C5 and Dic193802C5xDic19380,2
C10×D19Direct product of C10 and D191902C10xD19380,8
D5×C38Direct product of C38 and D51902D5xC38380,9

Groups of order 390

dρLabelID
C15×D13Direct product of C15 and D131952C15xD13390,5
D5×C39Direct product of C39 and D51952D5xC39390,6
C3×D65Direct product of C3 and D651952C3xD65390,7
S3×C65Direct product of C65 and S31952S3xC65390,8
C5×D39Direct product of C5 and D391952C5xD39390,9
C13×D15Direct product of C13 and D151952C13xD15390,10

Groups of order 392

dρLabelID
C49⋊C8The semidirect product of C49 and C8 acting via C8/C4=C23922C49:C8392,1
C4×D49Direct product of C4 and D491962C4xD49392,4
C49⋊D4The semidirect product of C49 and D4 acting via D4/C22=C21962C49:D4392,7
D4×C49Direct product of C49 and D41962D4xC49392,9
Q8×C49Direct product of C49 and Q83922Q8xC49392,10
C7×C7⋊C8Direct product of C7 and C7⋊C8562C7xC7:C8392,14
C7×Dic14Direct product of C7 and Dic14562C7xDic14392,23
D7×C28Direct product of C28 and D7562D7xC28392,24
C7×D28Direct product of C7 and D28562C7xD28392,25
C7×C7⋊D4Direct product of C7 and C7⋊D4282C7xC7:D4392,27

Groups of order 396

dρLabelID
C11×Dic9Direct product of C11 and Dic93962C11xDic9396,1
C9×Dic11Direct product of C9 and Dic113962C9xDic11396,2
C18×D11Direct product of C18 and D111982C18xD11396,7
D9×C22Direct product of C22 and D91982D9xC22396,8
Dic3×C33Direct product of C33 and Dic31322Dic3xC33396,12
C3×Dic33Direct product of C3 and Dic331322C3xDic33396,13
S3×C66Direct product of C66 and S31322S3xC66396,26
C6×D33Direct product of C6 and D331322C6xD33396,27

Groups of order 400

dρLabelID
C252C16The semidirect product of C25 and C16 acting via C16/C8=C24002C25:2C16400,1
C8×D25Direct product of C8 and D252002C8xD25400,5
C8⋊D253rd semidirect product of C8 and D25 acting via D25/C25=C22002C8:D25400,6
C200⋊C22nd semidirect product of C200 and C2 acting faithfully2002C200:C2400,7
C4.Dic25The non-split extension by C4 of Dic25 acting via Dic25/C50=C22002C4.Dic25400,10
M4(2)×C25Direct product of C25 and M4(2)2002M4(2)xC25400,24
D8×C25Direct product of C25 and D82002D8xC25400,25
SD16×C25Direct product of C25 and SD162002SD16xC25400,26
Q16×C25Direct product of C25 and Q164002Q16xC25400,27
D1005C2The semidirect product of D100 and C2 acting through Inn(D100)2002D100:5C2400,38
C4○D4×C25Direct product of C25 and C4○D42002C4oD4xC25400,48
C5×C52C16Direct product of C5 and C52C16802C5xC5:2C16400,49
D5×C40Direct product of C40 and D5802D5xC40400,76
C5×C8⋊D5Direct product of C5 and C8⋊D5802C5xC8:D5400,77
C5×C40⋊C2Direct product of C5 and C40⋊C2802C5xC40:C2400,78
C5×D40Direct product of C5 and D40802C5xD40400,79
C5×Dic20Direct product of C5 and Dic20802C5xDic20400,80
C5×C4.Dic5Direct product of C5 and C4.Dic5402C5xC4.Dic5400,82
C5×C4○D20Direct product of C5 and C4○D20402C5xC4oD20400,184

Groups of order 402

dρLabelID
S3×C67Direct product of C67 and S32012S3xC67402,3
C3×D67Direct product of C3 and D672012C3xD67402,4

Groups of order 406

dρLabelID
D7×C29Direct product of C29 and D72032D7xC29406,3
C7×D29Direct product of C7 and D292032C7xD29406,4

Groups of order 408

dρLabelID
C17×C3⋊C8Direct product of C17 and C3⋊C84082C17xC3:C8408,1
C3×C173C8Direct product of C3 and C173C84082C3xC17:3C8408,2
C515C81st semidirect product of C51 and C8 acting via C8/C4=C24082C51:5C8408,3
C17×SL2(𝔽3)Direct product of C17 and SL2(𝔽3)1362C17xSL(2,3)408,14
C3×Dic34Direct product of C3 and Dic344082C3xDic34408,15
C12×D17Direct product of C12 and D172042C12xD17408,16
C3×D68Direct product of C3 and D682042C3xD68408,17
C3×C17⋊D4Direct product of C3 and C17⋊D42042C3xC17:D4408,19
C17×Dic6Direct product of C17 and Dic64082C17xDic6408,20
S3×C68Direct product of C68 and S32042S3xC68408,21
C17×D12Direct product of C17 and D122042C17xD12408,22
C17×C3⋊D4Direct product of C17 and C3⋊D42042C17xC3:D4408,24
C4×D51Direct product of C4 and D512042C4xD51408,26
C517D41st semidirect product of C51 and D4 acting via D4/C22=C22042C51:7D4408,29
D4×C51Direct product of C51 and D42042D4xC51408,31
Q8×C51Direct product of C51 and Q84082Q8xC51408,32

Groups of order 410

dρLabelID
D5×C41Direct product of C41 and D52052D5xC41410,3
C5×D41Direct product of C5 and D412052C5xD41410,4

Groups of order 414

dρLabelID
D9×C23Direct product of C23 and D92072D9xC23414,1
C9×D23Direct product of C9 and D232072C9xD23414,2
S3×C69Direct product of C69 and S31382S3xC69414,6
C3×D69Direct product of C3 and D691382C3xD69414,7

Groups of order 416

dρLabelID
C132C32The semidirect product of C13 and C32 acting via C32/C16=C24162C13:2C32416,1
C16×D13Direct product of C16 and D132082C16xD13416,4
C208⋊C24th semidirect product of C208 and C2 acting faithfully2082C208:C2416,5
C16⋊D132nd semidirect product of C16 and D13 acting via D13/C13=C22082C16:D13416,7
D524C41st semidirect product of D52 and C4 acting via C4/C2=C21042D52:4C4416,12
C52.4C81st non-split extension by C52 of C8 acting via C8/C4=C22082C52.4C8416,19
C104.6C41st non-split extension by C104 of C4 acting via C4/C2=C22082C104.6C4416,26
C13×C4≀C2Direct product of C13 and C4≀C21042C13xC4wrC2416,54
C13×C8.C4Direct product of C13 and C8.C42082C13xC8.C4416,58
C13×M5(2)Direct product of C13 and M5(2)2082C13xM5(2)416,60
C13×D16Direct product of C13 and D162082C13xD16416,61
C13×SD32Direct product of C13 and SD322082C13xSD32416,62
C13×Q32Direct product of C13 and Q324162C13xQ32416,63
D52.3C4The non-split extension by D52 of C4 acting through Inn(D52)2082D52.3C4416,122
D1047C2The semidirect product of D104 and C2 acting through Inn(D104)2082D104:7C2416,125
C13×C8○D4Direct product of C13 and C8○D42082C13xC8oD4416,192
C13×C4○D8Direct product of C13 and C4○D82082C13xC4oD8416,196

Groups of order 418

dρLabelID
C19×D11Direct product of C19 and D112092C19xD11418,1
C11×D19Direct product of C11 and D192092C11xD19418,2

Groups of order 420

dρLabelID
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
D7×C30Direct product of C30 and D72102D7xC30420,34
D5×C42Direct product of C42 and D52102D5xC42420,35
C6×D35Direct product of C6 and D352102C6xD35420,36
S3×C70Direct product of C70 and S32102S3xC70420,37
C10×D21Direct product of C10 and D212102C10xD21420,38
C14×D15Direct product of C14 and D152102C14xD15420,39

Groups of order 424

dρLabelID
C532C8The semidirect product of C53 and C8 acting via C8/C4=C24242C53:2C8424,1
C4×D53Direct product of C4 and D532122C4xD53424,5
C53⋊D4The semidirect product of C53 and D4 acting via D4/C22=C22122C53:D4424,8
D4×C53Direct product of C53 and D42122D4xC53424,10
Q8×C53Direct product of C53 and Q84242Q8xC53424,11

Groups of order 426

dρLabelID
S3×C71Direct product of C71 and S32132S3xC71426,1
C3×D71Direct product of C3 and D712132C3xD71426,2

Groups of order 430

dρLabelID
D5×C43Direct product of C43 and D52152D5xC43430,1
C5×D43Direct product of C5 and D432152C5xD43430,2

Groups of order 432

dρLabelID
C27⋊C16The semidirect product of C27 and C16 acting via C16/C8=C24322C27:C16432,1
C8×D27Direct product of C8 and D272162C8xD27432,5
C8⋊D273rd semidirect product of C8 and D27 acting via D27/C27=C22162C8:D27432,6
C216⋊C22nd semidirect product of C216 and C2 acting faithfully2162C216:C2432,7
C4.Dic27The non-split extension by C4 of Dic27 acting via Dic27/C54=C22162C4.Dic27432,10
M4(2)×C27Direct product of C27 and M4(2)2162M4(2)xC27432,24
D8×C27Direct product of C27 and D82162D8xC27432,25
SD16×C27Direct product of C27 and SD162162SD16xC27432,26
Q16×C27Direct product of C27 and Q164322Q16xC27432,27
C3×C9⋊C16Direct product of C3 and C9⋊C161442C3xC9:C16432,28
C9×C3⋊C16Direct product of C9 and C3⋊C161442C9xC3:C16432,29
Q8.C54The non-split extension by Q8 of C54 acting via C54/C18=C32162Q8.C54432,42
D1085C2The semidirect product of D108 and C2 acting through Inn(D108)2162D108:5C2432,46
C4○D4×C27Direct product of C27 and C4○D42162C4oD4xC27432,56
C3×Dic36Direct product of C3 and Dic361442C3xDic36432,104
D9×C24Direct product of C24 and D91442D9xC24432,105
C3×C8⋊D9Direct product of C3 and C8⋊D91442C3xC8:D9432,106
C3×C72⋊C2Direct product of C3 and C72⋊C21442C3xC72:C2432,107
C3×D72Direct product of C3 and D721442C3xD72432,108
S3×C72Direct product of C72 and S31442S3xC72432,109
C9×C8⋊S3Direct product of C9 and C8⋊S31442C9xC8:S3432,110
C9×C24⋊C2Direct product of C9 and C24⋊C21442C9xC24:C2432,111
C9×D24Direct product of C9 and D241442C9xD24432,112
C9×Dic12Direct product of C9 and Dic121442C9xDic12432,113
C3×C4.Dic9Direct product of C3 and C4.Dic9722C3xC4.Dic9432,125
C9×C4.Dic3Direct product of C9 and C4.Dic3722C9xC4.Dic3432,127
C9×CSU2(𝔽3)Direct product of C9 and CSU2(𝔽3)1442C9xCSU(2,3)432,240
C9×GL2(𝔽3)Direct product of C9 and GL2(𝔽3)722C9xGL(2,3)432,241
C9×C4.A4Direct product of C9 and C4.A41442C9xC4.A4432,329
C3×D365C2Direct product of C3 and D365C2722C3xD36:5C2432,344
C9×C4○D12Direct product of C9 and C4○D12722C9xC4oD12432,347

Groups of order 434

dρLabelID
D7×C31Direct product of C31 and D72172D7xC31434,1
C7×D31Direct product of C7 and D312172C7xD31434,2

Groups of order 438

dρLabelID
S3×C73Direct product of C73 and S32192S3xC73438,3
C3×D73Direct product of C3 and D732192C3xD73438,4

Groups of order 440

dρLabelID
C11×C52C8Direct product of C11 and C52C84402C11xC5:2C8440,3
C5×C11⋊C8Direct product of C5 and C11⋊C84402C5xC11:C8440,4
C553C81st semidirect product of C55 and C8 acting via C8/C4=C24402C55:3C8440,5
C5×Dic22Direct product of C5 and Dic224402C5xDic22440,24
C20×D11Direct product of C20 and D112202C20xD11440,25
C5×D44Direct product of C5 and D442202C5xD44440,26
C5×C11⋊D4Direct product of C5 and C11⋊D42202C5xC11:D4440,28
C11×Dic10Direct product of C11 and Dic104402C11xDic10440,29
D5×C44Direct product of C44 and D52202D5xC44440,30
C11×D20Direct product of C11 and D202202C11xD20440,31
C11×C5⋊D4Direct product of C11 and C5⋊D42202C11xC5:D4440,33
C4×D55Direct product of C4 and D552202C4xD55440,35
C557D41st semidirect product of C55 and D4 acting via D4/C22=C22202C55:7D4440,38
D4×C55Direct product of C55 and D42202D4xC55440,40
Q8×C55Direct product of C55 and Q84402Q8xC55440,41

Groups of order 442

dρLabelID
C17×D13Direct product of C17 and D132212C17xD13442,1
C13×D17Direct product of C13 and D172212C13xD17442,2

Groups of order 444

dρLabelID
Dic3×C37Direct product of C37 and Dic34442Dic3xC37444,3
C3×Dic37Direct product of C3 and Dic374442C3xDic37444,4
C6×D37Direct product of C6 and D372222C6xD37444,15
S3×C74Direct product of C74 and S32222S3xC74444,16

Groups of order 448

dρLabelID
C7⋊C64The semidirect product of C7 and C64 acting via C64/C32=C24482C7:C64448,1
D7×C32Direct product of C32 and D72242D7xC32448,3
C32⋊D73rd semidirect product of C32 and D7 acting via D7/C7=C22242C32:D7448,4
C224⋊C22nd semidirect product of C224 and C2 acting faithfully2242C224:C2448,6
C56.16Q86th non-split extension by C56 of Q8 acting via Q8/C4=C21122C56.16Q8448,20
C7⋊M6(2)The semidirect product of C7 and M6(2) acting via M6(2)/C2×C16=C22242C7:M6(2)448,56
C112.C41st non-split extension by C112 of C4 acting via C4/C2=C22242C112.C4448,63
D28.C81st non-split extension by D28 of C8 acting via C8/C4=C22242D28.C8448,65
D56.1C41st non-split extension by D56 of C4 acting via C4/C2=C22242D56.1C4448,67
C7×D4.C8Direct product of C7 and D4.C82242C7xD4.C8448,154
C7×D8.C4Direct product of C7 and D8.C42242C7xD8.C4448,163
C7×C8.C8Direct product of C7 and C8.C81122C7xC8.C8448,168
C7×C8.4Q8Direct product of C7 and C8.4Q82242C7xC8.4Q8448,172
C7×M6(2)Direct product of C7 and M6(2)2242C7xM6(2)448,174
C7×D32Direct product of C7 and D322242C7xD32448,175
C7×SD64Direct product of C7 and SD642242C7xSD64448,176
C7×Q64Direct product of C7 and Q644482C7xQ64448,177
D5611C4The semidirect product of D56 and C4 acting through Inn(D56)1122D56:11C4448,234
D28.4C8The non-split extension by D28 of C8 acting through Inn(D28)2242D28.4C8448,435
D1127C2The semidirect product of D112 and C2 acting through Inn(D112)2242D112:7C2448,438
C7×C8○D8Direct product of C7 and C8○D81122C7xC8oD8448,851
C7×D4○C16Direct product of C7 and D4○C162242C7xD4oC16448,912
C7×C4○D16Direct product of C7 and C4○D162242C7xC4oD16448,916

Groups of order 450

dρLabelID
D9×C25Direct product of C25 and D92252D9xC25450,1
C9×D25Direct product of C9 and D252252C9xD25450,2
S3×C75Direct product of C75 and S31502S3xC75450,6
C3×D75Direct product of C3 and D751502C3xD75450,7
D5×C45Direct product of C45 and D5902D5xC45450,14
C5×D45Direct product of C5 and D45902C5xD45450,17
C15×D15Direct product of C15 and D15302C15xD15450,29

Groups of order 456

dρLabelID
C19×C3⋊C8Direct product of C19 and C3⋊C84562C19xC3:C8456,3
C3×C19⋊C8Direct product of C3 and C19⋊C84562C3xC19:C8456,4
C57⋊C81st semidirect product of C57 and C8 acting via C8/C4=C24562C57:C8456,5
C19×SL2(𝔽3)Direct product of C19 and SL2(𝔽3)1522C19xSL(2,3)456,22
C3×Dic38Direct product of C3 and Dic384562C3xDic38456,24
C12×D19Direct product of C12 and D192282C12xD19456,25
C3×D76Direct product of C3 and D762282C3xD76456,26
C3×C19⋊D4Direct product of C3 and C19⋊D42282C3xC19:D4456,28
C19×Dic6Direct product of C19 and Dic64562C19xDic6456,29
S3×C76Direct product of C76 and S32282S3xC76456,30
C19×D12Direct product of C19 and D122282C19xD12456,31
C19×C3⋊D4Direct product of C19 and C3⋊D42282C19xC3:D4456,33
C4×D57Direct product of C4 and D572282C4xD57456,35
C577D41st semidirect product of C57 and D4 acting via D4/C22=C22282C57:7D4456,38
D4×C57Direct product of C57 and D42282D4xC57456,40
Q8×C57Direct product of C57 and Q84562Q8xC57456,41

Groups of order 460

dρLabelID
Dic5×C23Direct product of C23 and Dic54602Dic5xC23460,1
C5×Dic23Direct product of C5 and Dic234602C5xDic23460,2
C10×D23Direct product of C10 and D232302C10xD23460,8
D5×C46Direct product of C46 and D52302D5xC46460,9

Groups of order 462

dρLabelID
C21×D11Direct product of C21 and D112312C21xD11462,5
D7×C33Direct product of C33 and D72312D7xC33462,6
C3×D77Direct product of C3 and D772312C3xD77462,7
S3×C77Direct product of C77 and S32312S3xC77462,8
C7×D33Direct product of C7 and D332312C7xD33462,9
C11×D21Direct product of C11 and D212312C11xD21462,10

Groups of order 464

dρLabelID
C292C16The semidirect product of C29 and C16 acting via C16/C8=C24642C29:2C16464,1
C8×D29Direct product of C8 and D292322C8xD29464,4
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
C4.Dic29The non-split extension by C4 of Dic29 acting via Dic29/C58=C22322C4.Dic29464,10
M4(2)×C29Direct product of C29 and M4(2)2322M4(2)xC29464,24
D8×C29Direct product of C29 and D82322D8xC29464,25
SD16×C29Direct product of C29 and SD162322SD16xC29464,26
Q16×C29Direct product of C29 and Q164642Q16xC29464,27
D1165C2The semidirect product of D116 and C2 acting through Inn(D116)2322D116:5C2464,38
C4○D4×C29Direct product of C29 and C4○D42322C4oD4xC29464,48

Groups of order 468

dρLabelID
C13×Dic9Direct product of C13 and Dic94682C13xDic9468,3
C9×Dic13Direct product of C9 and Dic134682C9xDic13468,4
C18×D13Direct product of C18 and D132342C18xD13468,15
D9×C26Direct product of C26 and D92342D9xC26468,16
Dic3×C39Direct product of C39 and Dic31562Dic3xC39468,24
C3×Dic39Direct product of C3 and Dic391562C3xDic39468,25
S3×C78Direct product of C78 and S31562S3xC78468,51
C6×D39Direct product of C6 and D391562C6xD39468,52

Groups of order 470

dρLabelID
D5×C47Direct product of C47 and D52352D5xC47470,1
C5×D47Direct product of C5 and D472352C5xD47470,2

Groups of order 472

dρLabelID
C59⋊C8The semidirect product of C59 and C8 acting via C8/C4=C24722C59:C8472,1
C4×D59Direct product of C4 and D592362C4xD59472,4
C59⋊D4The semidirect product of C59 and D4 acting via D4/C22=C22362C59:D4472,7
D4×C59Direct product of C59 and D42362D4xC59472,9
Q8×C59Direct product of C59 and Q84722Q8xC59472,10

Groups of order 474

dρLabelID
S3×C79Direct product of C79 and S32372S3xC79474,3
C3×D79Direct product of C3 and D792372C3xD79474,4

Groups of order 476

dρLabelID
C17×Dic7Direct product of C17 and Dic74762C17xDic7476,1
C7×Dic17Direct product of C7 and Dic174762C7xDic17476,2
C14×D17Direct product of C14 and D172382C14xD17476,8
D7×C34Direct product of C34 and D72382D7xC34476,9

Groups of order 480

dρLabelID
C5×C3⋊C32Direct product of C5 and C3⋊C324802C5xC3:C32480,1
C3×C52C32Direct product of C3 and C52C324802C3xC5:2C32480,2
C153C321st semidirect product of C15 and C32 acting via C32/C16=C24802C15:3C32480,3
D5×C48Direct product of C48 and D52402D5xC48480,75
C3×C80⋊C2Direct product of C3 and C80⋊C22402C3xC80:C2480,76
C3×D80Direct product of C3 and D802402C3xD80480,77
C3×C16⋊D5Direct product of C3 and C16⋊D52402C3xC16:D5480,78
C3×Dic40Direct product of C3 and Dic404802C3xDic40480,79
C3×D204C4Direct product of C3 and D204C41202C3xD20:4C4480,83
C3×C20.4C8Direct product of C3 and C20.4C82402C3xC20.4C8480,90
C3×C40.6C4Direct product of C3 and C40.6C42402C3xC40.6C4480,97
S3×C80Direct product of C80 and S32402S3xC80480,116
C5×D6.C8Direct product of C5 and D6.C82402C5xD6.C8480,117
C5×D48Direct product of C5 and D482402C5xD48480,118
C5×C48⋊C2Direct product of C5 and C48⋊C22402C5xC48:C2480,119
C5×Dic24Direct product of C5 and Dic244802C5xDic24480,120
C5×C424S3Direct product of C5 and C424S31202C5xC4^2:4S3480,124
C5×C12.C8Direct product of C5 and C12.C82402C5xC12.C8480,131
C5×C24.C4Direct product of C5 and C24.C42402C5xC24.C4480,138
C16×D15Direct product of C16 and D152402C16xD15480,157
C80⋊S35th semidirect product of C80 and S3 acting via S3/C3=C22402C80:S3480,158
C48⋊D52nd semidirect product of C48 and D5 acting via D5/C5=C22402C48:D5480,160
D607C41st semidirect product of D60 and C4 acting via C4/C2=C21202D60:7C4480,165
C60.7C81st non-split extension by C60 of C8 acting via C8/C4=C22402C60.7C8480,172
C4.18D603rd central extension by C4 of D602402C4.18D60480,179
C15×C4≀C2Direct product of C15 and C4≀C21202C15xC4wrC2480,207
C15×C8.C4Direct product of C15 and C8.C42402C15xC8.C4480,211
C15×M5(2)Direct product of C15 and M5(2)2402C15xM5(2)480,213
C15×D16Direct product of C15 and D162402C15xD16480,214
C15×SD32Direct product of C15 and SD322402C15xSD32480,215
C15×Q32Direct product of C15 and Q324802C15xQ32480,216
C8.A5The central extension by C8 of A5482C8.A5480,221
C5×U2(𝔽3)Direct product of C5 and U2(𝔽3)1202C5xU(2,3)480,257
C5×C8.A4Direct product of C5 and C8.A41602C5xC8.A4480,660
C3×D20.3C4Direct product of C3 and D20.3C42402C3xD20.3C4480,694
C3×D407C2Direct product of C3 and D407C22402C3xD40:7C2480,697
C5×C8○D12Direct product of C5 and C8○D122402C5xC8oD12480,780
C5×C4○D24Direct product of C5 and C4○D242402C5xC4oD24480,783
D60.6C4The non-split extension by D60 of C4 acting through Inn(D60)2402D60.6C4480,866
C40.69D65th non-split extension by C40 of D6 acting via D6/C6=C22402C40.69D6480,869
C15×C8○D4Direct product of C15 and C8○D42402C15xC8oD4480,936
C15×C4○D8Direct product of C15 and C4○D82402C15xC4oD8480,940
C5×C4.6S4Direct product of C5 and C4.6S4802C5xC4.6S4480,1020

Groups of order 484

dρLabelID
C11×Dic11Direct product of C11 and Dic11442C11xDic11484,5
D11×C22Direct product of C22 and D11442D11xC22484,10

Groups of order 486

dρLabelID
C9×D27Direct product of C9 and D27542C9xD27486,13
D9×C27Direct product of C27 and D9542D9xC27486,14
C3×D81Direct product of C3 and D811622C3xD81486,32
S3×C81Direct product of C81 and S31622S3xC81486,33

Groups of order 488

dρLabelID
C612C8The semidirect product of C61 and C8 acting via C8/C4=C24882C61:2C8488,1
C4×D61Direct product of C4 and D612442C4xD61488,5
C61⋊D4The semidirect product of C61 and D4 acting via D4/C22=C22442C61:D4488,8
D4×C61Direct product of C61 and D42442D4xC61488,10
Q8×C61Direct product of C61 and Q84882Q8xC61488,11

Groups of order 490

dρLabelID
D5×C49Direct product of C49 and D52452D5xC49490,1
C5×D49Direct product of C5 and D492452C5xD49490,2
D7×C35Direct product of C35 and D7702D7xC35490,5
C7×D35Direct product of C7 and D35702C7xD35490,8

Groups of order 492

dρLabelID
Dic3×C41Direct product of C41 and Dic34922Dic3xC41492,1
C3×Dic41Direct product of C3 and Dic414922C3xDic41492,2
C6×D41Direct product of C6 and D412462C6xD41492,9
S3×C82Direct product of C82 and S32462S3xC82492,10

Groups of order 494

dρLabelID
C19×D13Direct product of C19 and D132472C19xD13494,1
C13×D19Direct product of C13 and D192472C13xD19494,2

Groups of order 496

dρLabelID
C31⋊C16The semidirect product of C31 and C16 acting via C16/C8=C24962C31:C16496,1
C8×D31Direct product of C8 and D312482C8xD31496,3
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
C4.Dic31The non-split extension by C4 of Dic31 acting via Dic31/C62=C22482C4.Dic31496,9
M4(2)×C31Direct product of C31 and M4(2)2482M4(2)xC31496,23
D8×C31Direct product of C31 and D82482D8xC31496,24
SD16×C31Direct product of C31 and SD162482SD16xC31496,25
Q16×C31Direct product of C31 and Q164962Q16xC31496,26
D1245C2The semidirect product of D124 and C2 acting through Inn(D124)2482D124:5C2496,30
C4○D4×C31Direct product of C31 and C4○D42482C4oD4xC31496,40

Groups of order 498

dρLabelID
S3×C83Direct product of C83 and S32492S3xC83498,1
C3×D83Direct product of C3 and D832492C3xD83498,2

Groups of order 500

dρLabelID
C5×Dic25Direct product of C5 and Dic251002C5xDic25500,6
Dic5×C25Direct product of C25 and Dic51002Dic5xC25500,7
C10×D25Direct product of C10 and D251002C10xD25500,28
D5×C50Direct product of C50 and D51002D5xC50500,29

Orthogonal of dimension 3  (ρ=3+)

Groups of order 12

dρLabelID
A4Alternating group on 4 letters; = PSL2(𝔽3) = L2(3) = tetrahedron rotations43+A412,3

Groups of order 24

dρLabelID
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotations43+S424,12
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)63+C2xA424,13

Groups of order 48

dρLabelID
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetries63+C2xS448,48

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 120

dρLabelID
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetries103+C2xA5120,35

Complex of dimension 3  (ρ=3)

Groups of order 21

dρLabelID
C7⋊C3The semidirect product of C7 and C3 acting faithfully73C7:C321,1

Groups of order 27

dρLabelID
He3Heisenberg group; = C32C3 = 3+ 1+293He327,3
3- 1+2Extraspecial group93ES-(3,1)27,4

Groups of order 36

dρLabelID
C3.A4The central extension by C3 of A4183C3.A436,3
C3×A4Direct product of C3 and A4123C3xA436,11

Groups of order 39

dρLabelID
C13⋊C3The semidirect product of C13 and C3 acting faithfully133C13:C339,1

Groups of order 42

dρLabelID
C2×C7⋊C3Direct product of C2 and C7⋊C3143C2xC7:C342,2

Groups of order 48

dρLabelID
C42⋊C3The semidirect product of C42 and C3 acting faithfully123C4^2:C348,3
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)123A4:C448,30
C4×A4Direct product of C4 and A4123C4xA448,31

Groups of order 54

dρLabelID
He3⋊C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)93He3:C254,8
C2×He3Direct product of C2 and He3183C2xHe354,10
C2×3- 1+2Direct product of C2 and 3- 1+2183C2xES-(3,1)54,11

Groups of order 57

dρLabelID
C19⋊C3The semidirect product of C19 and C3 acting faithfully193C19:C357,1

Groups of order 60

dρLabelID
C5×A4Direct product of C5 and A4203C5xA460,9

Groups of order 63

dρLabelID
C7⋊C9The semidirect product of C7 and C9 acting via C9/C3=C3633C7:C963,1
C3×C7⋊C3Direct product of C3 and C7⋊C3213C3xC7:C363,3

Groups of order 72

dρLabelID
C2×C3.A4Direct product of C2 and C3.A4183C2xC3.A472,16
C3×S4Direct product of C3 and S4123C3xS472,42
C6×A4Direct product of C6 and A4183C6xA472,47

Groups of order 75

dρLabelID
C52⋊C3The semidirect product of C52 and C3 acting faithfully153C5^2:C375,2

Groups of order 78

dρLabelID
C2×C13⋊C3Direct product of C2 and C13⋊C3263C2xC13:C378,2

Groups of order 81

dρLabelID
C27⋊C3The semidirect product of C27 and C3 acting faithfully273C27:C381,6
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)93C3wrC381,7
He3.C3The non-split extension by He3 of C3 acting faithfully273He3.C381,8
He3⋊C32nd semidirect product of He3 and C3 acting faithfully273He3:C381,9
C3.He34th central stem extension by C3 of He3273C3.He381,10
C9○He3Central product of C9 and He3273C9oHe381,14

Groups of order 84

dρLabelID
C4×C7⋊C3Direct product of C4 and C7⋊C3283C4xC7:C384,2
C7×A4Direct product of C7 and A4283C7xA484,10
C7⋊A4The semidirect product of C7 and A4 acting via A4/C22=C3283C7:A484,11

Groups of order 93

dρLabelID
C31⋊C3The semidirect product of C31 and C3 acting faithfully313C31:C393,1

Groups of order 96

dρLabelID
C42⋊S3The semidirect product of C42 and S3 acting faithfully123C4^2:S396,64
A4⋊C8The semidirect product of A4 and C8 acting via C8/C4=C2243A4:C896,65
C2×C42⋊C3Direct product of C2 and C42⋊C3123C2xC4^2:C396,68
C8×A4Direct product of C8 and A4243C8xA496,73
C4×S4Direct product of C4 and S4123C4xS496,186

Groups of order 105

dρLabelID
C5×C7⋊C3Direct product of C5 and C7⋊C3353C5xC7:C3105,1

Groups of order 108

dρLabelID
C9.A4The central extension by C9 of A4543C9.A4108,3
He33C42nd semidirect product of He3 and C4 acting via C4/C2=C2363He3:3C4108,11
C4×He3Direct product of C4 and He3363C4xHe3108,13
C4×3- 1+2Direct product of C4 and 3- 1+2363C4xES-(3,1)108,14
He3⋊C4The semidirect product of He3 and C4 acting faithfully183He3:C4108,15
C9×A4Direct product of C9 and A4363C9xA4108,18
C9⋊A4The semidirect product of C9 and A4 acting via A4/C22=C3363C9:A4108,19
C32.A4The non-split extension by C32 of A4 acting via A4/C22=C3183C3^2.A4108,21
C32⋊A4The semidirect product of C32 and A4 acting via A4/C22=C3183C3^2:A4108,22
C2×He3⋊C2Direct product of C2 and He3⋊C2183C2xHe3:C2108,28

Groups of order 111

dρLabelID
C37⋊C3The semidirect product of C37 and C3 acting faithfully373C37:C3111,1

Groups of order 114

dρLabelID
C2×C19⋊C3Direct product of C2 and C19⋊C3383C2xC19:C3114,2

Groups of order 117

dρLabelID
C13⋊C9The semidirect product of C13 and C9 acting via C9/C3=C31173C13:C9117,1
C3×C13⋊C3Direct product of C3 and C13⋊C3393C3xC13:C3117,3

Groups of order 120

dρLabelID
C5×S4Direct product of C5 and S4203C5xS4120,37
C10×A4Direct product of C10 and A4303C10xA4120,43

Groups of order 126

dρLabelID
C2×C7⋊C9Direct product of C2 and C7⋊C91263C2xC7:C9126,2
C6×C7⋊C3Direct product of C6 and C7⋊C3423C6xC7:C3126,10

Groups of order 129

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

Groups of order 132

dρLabelID
C11×A4Direct product of C11 and A4443C11xA4132,6

Groups of order 135

dρLabelID
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 144

dρLabelID
C42⋊C9The semidirect product of C42 and C9 acting via C9/C3=C3363C4^2:C9144,3
C4×C3.A4Direct product of C4 and C3.A4363C4xC3.A4144,34
C3×C42⋊C3Direct product of C3 and C42⋊C3363C3xC4^2:C3144,68
C3×A4⋊C4Direct product of C3 and A4⋊C4363C3xA4:C4144,123
C12×A4Direct product of C12 and A4363C12xA4144,155
C6×S4Direct product of C6 and S4183C6xS4144,188

Groups of order 147

dρLabelID
C49⋊C3The semidirect product of C49 and C3 acting faithfully493C49:C3147,1
C7×C7⋊C3Direct product of C7 and C7⋊C3213C7xC7:C3147,3
C723C33rd semidirect product of C72 and C3 acting faithfully213C7^2:3C3147,5

Groups of order 150

dρLabelID
C52⋊S3The semidirect product of C52 and S3 acting faithfully153C5^2:S3150,5
C2×C52⋊C3Direct product of C2 and C52⋊C3303C2xC5^2:C3150,7

Groups of order 156

dρLabelID
C4×C13⋊C3Direct product of C4 and C13⋊C3523C4xC13:C3156,2
A4×C13Direct product of C13 and A4523A4xC13156,13
C13⋊A4The semidirect product of C13 and A4 acting via A4/C22=C3523C13:A4156,14

Groups of order 162

dρLabelID
C3≀S3Wreath product of C3 by S393C3wrS3162,10
He3.C61st non-split extension by He3 of C6 acting faithfully273He3.C6162,12
He3.2C62nd non-split extension by He3 of C6 acting faithfully273He3.2C6162,14
C2×C27⋊C3Direct product of C2 and C27⋊C3543C2xC27:C3162,27
C2×C3≀C3Direct product of C2 and C3≀C3183C2xC3wrC3162,28
C2×He3.C3Direct product of C2 and He3.C3543C2xHe3.C3162,29
C2×He3⋊C3Direct product of C2 and He3⋊C3543C2xHe3:C3162,30
C2×C3.He3Direct product of C2 and C3.He3543C2xC3.He3162,31
He3.4C6The non-split extension by He3 of C6 acting via C6/C3=C2273He3.4C6162,44
C2×C9○He3Direct product of C2 and C9○He3543C2xC9oHe3162,50

Groups of order 168

dρLabelID
C8×C7⋊C3Direct product of C8 and C7⋊C3563C8xC7:C3168,2
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simple73GL(3,2)168,42
C7×S4Direct product of C7 and S4283C7xS4168,45
A4×C14Direct product of C14 and A4423A4xC14168,52
C2×C7⋊A4Direct product of C2 and C7⋊A4423C2xC7:A4168,53

Groups of order 171

dρLabelID
C192C9The semidirect product of C19 and C9 acting via C9/C3=C31713C19:2C9171,1
C3×C19⋊C3Direct product of C3 and C19⋊C3573C3xC19:C3171,4

Groups of order 180

dρLabelID
C5×C3.A4Direct product of C5 and C3.A4903C5xC3.A4180,8
C3×A5Direct product of C3 and A5; = GL2(𝔽4)153C3xA5180,19
A4×C15Direct product of C15 and A4603A4xC15180,31

Groups of order 183

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

Groups of order 186

dρLabelID
C2×C31⋊C3Direct product of C2 and C31⋊C3623C2xC31:C3186,2

Groups of order 189

dρLabelID
C7⋊C27The semidirect product of C7 and C27 acting via C27/C9=C31893C7:C27189,1
C9×C7⋊C3Direct product of C9 and C7⋊C3633C9xC7:C3189,3
C63⋊C32nd semidirect product of C63 and C3 acting faithfully633C63:C3189,4
C633C33rd semidirect product of C63 and C3 acting faithfully633C63:3C3189,5
C21.C325th non-split extension by C21 of C32 acting via C32/C3=C3633C21.C3^2189,7
C7⋊He3The semidirect product of C7 and He3 acting via He3/C32=C3633C7:He3189,8
C7×He3Direct product of C7 and He3633C7xHe3189,10
C7×3- 1+2Direct product of C7 and 3- 1+2633C7xES-(3,1)189,11

Groups of order 192

dρLabelID
C82⋊C3The semidirect product of C82 and C3 acting faithfully243C8^2:C3192,3
C23.9S43rd non-split extension by C23 of S4 acting via S4/C22=S3123C2^3.9S4192,182
A4⋊C16The semidirect product of A4 and C16 acting via C16/C8=C2483A4:C16192,186
C4×C42⋊C3Direct product of C4 and C42⋊C3123C4xC4^2:C3192,188
A4×C16Direct product of C16 and A4483A4xC16192,203
C2×C42⋊S3Direct product of C2 and C42⋊S3123C2xC4^2:S3192,944
C8×S4Direct product of C8 and S4243C8xS4192,958

Groups of order 195

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

Groups of order 201

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

Groups of order 204

dρLabelID
A4×C17Direct product of C17 and A4683A4xC17204,8

Groups of order 210

dρLabelID
C10×C7⋊C3Direct product of C10 and C7⋊C3703C10xC7:C3210,4

Groups of order 216

dρLabelID
He34C82nd semidirect product of He3 and C8 acting via C8/C4=C2723He3:4C8216,17
C8×He3Direct product of C8 and He3723C8xHe3216,19
C8×3- 1+2Direct product of C8 and 3- 1+2723C8xES-(3,1)216,20
C2×C9.A4Direct product of C2 and C9.A4543C2xC9.A4216,22
He32C8The semidirect product of He3 and C8 acting via C8/C2=C4723He3:2C8216,25
C4×He3⋊C2Direct product of C4 and He3⋊C2363C4xHe3:C2216,67
SU3(𝔽2)Special unitary group on 𝔽23; = He3Q8273SU(3,2)216,88
C9×S4Direct product of C9 and S4363C9xS4216,89
C32⋊S42nd semidirect product of C32 and S4 acting via S4/C22=S3183C3^2:S4216,95
C2×He3⋊C4Direct product of C2 and He3⋊C4363C2xHe3:C4216,100
A4×C18Direct product of C18 and A4543A4xC18216,103
C2×C9⋊A4Direct product of C2 and C9⋊A4543C2xC9:A4216,104
C2×C32.A4Direct product of C2 and C32.A4183C2xC3^2.A4216,106
C2×C32⋊A4Direct product of C2 and C32⋊A4183C2xC3^2:A4216,107

Groups of order 219

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

Groups of order 222

dρLabelID
C2×C37⋊C3Direct product of C2 and C37⋊C3743C2xC37:C3222,2

Groups of order 225

dρLabelID
C52⋊C9The semidirect product of C52 and C9 acting via C9/C3=C3453C5^2:C9225,3
C3×C52⋊C3Direct product of C3 and C52⋊C3453C3xC5^2:C3225,5

Groups of order 228

dρLabelID
C4×C19⋊C3Direct product of C4 and C19⋊C3763C4xC19:C3228,2
A4×C19Direct product of C19 and A4763A4xC19228,10
C19⋊A4The semidirect product of C19 and A4 acting via A4/C22=C3763C19:A4228,11

Groups of order 231

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

Groups of order 234

dρLabelID
C2×C13⋊C9Direct product of C2 and C13⋊C92343C2xC13:C9234,2
C6×C13⋊C3Direct product of C6 and C13⋊C3783C6xC13:C3234,10

Groups of order 237

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

Groups of order 240

dρLabelID
C5×C42⋊C3Direct product of C5 and C42⋊C3603C5xC4^2:C3240,32
C4×A5Direct product of C4 and A5203C4xA5240,92
C5×A4⋊C4Direct product of C5 and A4⋊C4603C5xA4:C4240,104
A4×C20Direct product of C20 and A4603A4xC20240,152
C10×S4Direct product of C10 and S4303C10xS4240,196

Groups of order 243

dρLabelID
C9.4He32nd central extension by C9 of He3273C9.4He3243,16
C9.5He33rd central extension by C9 of He3813C9.5He3243,19
C9.6He34th central extension by C9 of He3813C9.6He3243,20
C81⋊C3The semidirect product of C81 and C3 acting faithfully813C81:C3243,24
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
C92.C32nd non-split extension by C92 of C3 acting faithfully273C9^2.C3243,27
C27○He3Central product of C27 and He3813C27oHe3243,50
C9.He31st non-split extension by C9 of He3 acting via He3/C32=C3273C9.He3243,55

Groups of order 252

dρLabelID
C4×C7⋊C9Direct product of C4 and C7⋊C92523C4xC7:C9252,2
C7×C3.A4Direct product of C7 and C3.A41263C7xC3.A4252,10
C21.A4The non-split extension by C21 of A4 acting via A4/C22=C31263C21.A4252,11
C12×C7⋊C3Direct product of C12 and C7⋊C3843C12xC7:C3252,19
A4×C21Direct product of C21 and A4843A4xC21252,39
C3×C7⋊A4Direct product of C3 and C7⋊A4843C3xC7:A4252,40

Groups of order 258

dρLabelID
C2×C43⋊C3Direct product of C2 and C43⋊C3863C2xC43:C3258,2

Groups of order 264

dρLabelID
C11×S4Direct product of C11 and S4443C11xS4264,31
A4×C22Direct product of C22 and A4663A4xC22264,35

Groups of order 270

dρLabelID
C5×He3⋊C2Direct product of C5 and He3⋊C2453C5xHe3:C2270,17
C10×He3Direct product of C10 and He3903C10xHe3270,21
C10×3- 1+2Direct product of C10 and 3- 1+2903C10xES-(3,1)270,22

Groups of order 273

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

Groups of order 276

dρLabelID
A4×C23Direct product of C23 and A4923A4xC23276,6

Groups of order 279

dρLabelID
C31⋊C9The semidirect product of C31 and C9 acting via C9/C3=C32793C31:C9279,1
C3×C31⋊C3Direct product of C3 and C31⋊C3933C3xC31:C3279,3

Groups of order 285

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

Groups of order 288

dρLabelID
C2×C42⋊C9Direct product of C2 and C42⋊C9363C2xC4^2:C9288,71
C8×C3.A4Direct product of C8 and C3.A4723C8xC3.A4288,76
C3×C42⋊S3Direct product of C3 and C42⋊S3363C3xC4^2:S3288,397
C3×A4⋊C8Direct product of C3 and A4⋊C8723C3xA4:C8288,398
C6×C42⋊C3Direct product of C6 and C42⋊C3363C6xC4^2:C3288,632
A4×C24Direct product of C24 and A4723A4xC24288,637
C12×S4Direct product of C12 and S4363C12xS4288,897

Groups of order 291

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

Groups of order 294

dρLabelID
C2×C49⋊C3Direct product of C2 and C49⋊C3983C2xC49:C3294,2
C72⋊S3The semidirect product of C72 and S3 acting faithfully143C7^2:S3294,7
C14×C7⋊C3Direct product of C14 and C7⋊C3423C14xC7:C3294,15
C2×C723C3Direct product of C2 and C723C3423C2xC7^2:3C3294,17

Groups of order 297

dρLabelID
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 300

dρLabelID
A4×C25Direct product of C25 and A41003A4xC25300,8
C522Dic3The semidirect product of C52 and Dic3 acting via Dic3/C2=S3603C5^2:2Dic3300,13
C4×C52⋊C3Direct product of C4 and C52⋊C3603C4xC5^2:C3300,15
C5×A5Direct product of C5 and A5; = U2(𝔽4)253C5xA5300,22
C2×C52⋊S3Direct product of C2 and C52⋊S3303C2xC5^2:S3300,26
C52⋊A4The semidirect product of C52 and A4 acting via A4/C22=C3303C5^2:A4300,43

Groups of order 309

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

Groups of order 312

dρLabelID
C8×C13⋊C3Direct product of C8 and C13⋊C31043C8xC13:C3312,2
C13×S4Direct product of C13 and S4523C13xS4312,47
A4×C26Direct product of C26 and A4783A4xC26312,56
C2×C13⋊A4Direct product of C2 and C13⋊A4783C2xC13:A4312,57

Groups of order 315

dρLabelID
C5×C7⋊C9Direct product of C5 and C7⋊C93153C5xC7:C9315,1
C15×C7⋊C3Direct product of C15 and C7⋊C31053C15xC7:C3315,3

Groups of order 324

dρLabelID
C27.A4The central extension by C27 of A41623C27.A4324,3
He3⋊C12The semidirect product of He3 and C12 acting via C12/C2=C6363He3:C12324,13
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
C4×C27⋊C3Direct product of C4 and C27⋊C31083C4xC27:C3324,30
C4×C3≀C3Direct product of C4 and C3≀C3363C4xC3wrC3324,31
C4×He3.C3Direct product of C4 and He3.C31083C4xHe3.C3324,32
C4×He3⋊C3Direct product of C4 and He3⋊C31083C4xHe3:C3324,33
C4×C3.He3Direct product of C4 and C3.He31083C4xC3.He3324,34
A4×C27Direct product of C27 and A41083A4xC27324,42
C27⋊A4The semidirect product of C27 and A4 acting via A4/C22=C31083C27:A4324,43
C62.C92nd non-split extension by C62 of C9 acting via C9/C3=C3543C6^2.C9324,45
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
C332A41st semidirect product of C33 and A4 acting via A4/C22=C3183C3^3:2A4324,60
C2×C3≀S3Direct product of C2 and C3≀S3183C2xC3wrS3324,68
C2×He3.C6Direct product of C2 and He3.C6543C2xHe3.C6324,70
C2×He3.2C6Direct product of C2 and He3.2C6543C2xHe3.2C6324,72
He3.5C12The non-split extension by He3 of C12 acting via C12/C6=C21083He3.5C12324,102
C4×C9○He3Direct product of C4 and C9○He31083C4xC9oHe3324,108
He3.3C12The non-split extension by He3 of C12 acting via C12/C3=C4543He3.3C12324,111
C62.25C3216th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.25C3^2324,128
C2×He3.4C6Direct product of C2 and He3.4C6543C2xHe3.4C6324,148

Groups of order 327

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

Groups of order 333

dρLabelID
C372C9The semidirect product of C37 and C9 acting via C9/C3=C33333C37:2C9333,1
C3×C37⋊C3Direct product of C3 and C37⋊C31113C3xC37:C3333,4

Groups of order 336

dρLabelID
C16×C7⋊C3Direct product of C16 and C7⋊C31123C16xC7:C3336,2
C7×C42⋊C3Direct product of C7 and C42⋊C3843C7xC4^2:C3336,56
C42⋊(C7⋊C3)The semidirect product of C42 and C7⋊C3 acting via C7⋊C3/C7=C3843C4^2:(C7:C3)336,57
C7×A4⋊C4Direct product of C7 and A4⋊C4843C7xA4:C4336,117
A4×C28Direct product of C28 and A4843A4xC28336,168
C4×C7⋊A4Direct product of C4 and C7⋊A4843C4xC7:A4336,171
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)143C2xGL(3,2)336,209
C14×S4Direct product of C14 and S4423C14xS4336,214

Groups of order 342

dρLabelID
C2×C192C9Direct product of C2 and C192C93423C2xC19:2C9342,2
C6×C19⋊C3Direct product of C6 and C19⋊C31143C6xC19:C3342,12

Groups of order 348

dρLabelID
A4×C29Direct product of C29 and A41163A4xC29348,8

Groups of order 351

dρLabelID
C13⋊C27The semidirect product of C13 and C27 acting via C27/C9=C33513C13:C27351,1
C9×C13⋊C3Direct product of C9 and C13⋊C31173C9xC13:C3351,3
C117⋊C32nd semidirect product of C117 and C3 acting faithfully1173C117:C3351,4
C1173C33rd semidirect product of C117 and C3 acting faithfully1173C117:3C3351,5
C39.C325th non-split extension by C39 of C32 acting via C32/C3=C31173C39.C3^2351,7
C13⋊He3The semidirect product of C13 and He3 acting via He3/C32=C31173C13:He3351,8
C13×He3Direct product of C13 and He31173C13xHe3351,10
C13×3- 1+2Direct product of C13 and 3- 1+21173C13xES-(3,1)351,11

Groups of order 357

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

Groups of order 360

dρLabelID
C10×C3.A4Direct product of C10 and C3.A4903C10xC3.A4360,46
C6×A5Direct product of C6 and A5303C6xA5360,122
C15×S4Direct product of C15 and S4603C15xS4360,138
A4×C30Direct product of C30 and A4903A4xC30360,156

Groups of order 363

dρLabelID
C112⋊C3The semidirect product of C112 and C3 acting faithfully333C11^2:C3363,2

Groups of order 366

dρLabelID
C2×C61⋊C3Direct product of C2 and C61⋊C31223C2xC61:C3366,2

Groups of order 372

dρLabelID
C4×C31⋊C3Direct product of C4 and C31⋊C31243C4xC31:C3372,2
A4×C31Direct product of C31 and A41243A4xC31372,10
C31⋊A4The semidirect product of C31 and A4 acting via A4/C22=C31243C31:A4372,11

Groups of order 375

dρLabelID
C5×C52⋊C3Direct product of C5 and C52⋊C3; = AΣL1(𝔽125)153C5xC5^2:C3375,6

Groups of order 378

dρLabelID
C2×C7⋊C27Direct product of C2 and C7⋊C273783C2xC7:C27378,2
C18×C7⋊C3Direct product of C18 and C7⋊C31263C18xC7:C3378,23
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
C2×C7⋊He3Direct product of C2 and C7⋊He31263C2xC7:He3378,28
C7×He3⋊C2Direct product of C7 and He3⋊C2633C7xHe3:C2378,41
C14×He3Direct product of C14 and He31263C14xHe3378,45
C14×3- 1+2Direct product of C14 and 3- 1+21263C14xES-(3,1)378,46

Groups of order 381

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

Groups of order 387

dρLabelID
C43⋊C9The semidirect product of C43 and C9 acting via C9/C3=C33873C43:C9387,1
C3×C43⋊C3Direct product of C3 and C43⋊C31293C3xC43:C3387,3

Groups of order 390

dρLabelID
C10×C13⋊C3Direct product of C10 and C13⋊C31303C10xC13:C3390,4

Groups of order 396

dρLabelID
C11×C3.A4Direct product of C11 and C3.A41983C11xC3.A4396,6
A4×C33Direct product of C33 and A41323A4xC33396,24

Groups of order 399

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

Groups of order 402

dρLabelID
C2×C67⋊C3Direct product of C2 and C67⋊C31343C2xC67:C3402,2

Groups of order 405

dρLabelID
C5×C27⋊C3Direct product of C5 and C27⋊C31353C5xC27:C3405,6
C5×C3≀C3Direct product of C5 and C3≀C3453C5xC3wrC3405,7
C5×He3.C3Direct product of C5 and He3.C31353C5xHe3.C3405,8
C5×He3⋊C3Direct product of C5 and He3⋊C31353C5xHe3:C3405,9
C5×C3.He3Direct product of C5 and C3.He31353C5xC3.He3405,10
C5×C9○He3Direct product of C5 and C9○He31353C5xC9oHe3405,14

Groups of order 408

dρLabelID
C17×S4Direct product of C17 and S4683C17xS4408,36
A4×C34Direct product of C34 and A41023A4xC34408,42

Groups of order 417

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

Groups of order 420

dρLabelID
C20×C7⋊C3Direct product of C20 and C7⋊C31403C20xC7:C3420,4
C7×A5Direct product of C7 and A5353C7xA5420,13
A4×C35Direct product of C35 and A41403A4xC35420,32
C5×C7⋊A4Direct product of C5 and C7⋊A41403C5xC7:A4420,33

Groups of order 429

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

Groups of order 432

dρLabelID
C42⋊C27The semidirect product of C42 and C27 acting via C27/C9=C31083C4^2:C27432,3
He34C162nd semidirect product of He3 and C16 acting via C16/C8=C21443He3:4C16432,33
C16×He3Direct product of C16 and He31443C16xHe3432,35
C16×3- 1+2Direct product of C16 and 3- 1+21443C16xES-(3,1)432,36
C4×C9.A4Direct product of C4 and C9.A41083C4xC9.A4432,40
He32C16The semidirect product of He3 and C16 acting via C16/C4=C41443He3:2C16432,57
C9×C42⋊C3Direct product of C9 and C42⋊C31083C9xC4^2:C3432,99
C42⋊3- 1+2The semidirect product of C42 and 3- 1+2 acting via 3- 1+2/C9=C31083C4^2:ES-(3,1)432,100
C122.C32nd non-split extension by C122 of C3 acting faithfully363C12^2.C3432,102
C42⋊He3The semidirect product of C42 and He3 acting via He3/C32=C3363C4^2:He3432,103
C8×He3⋊C2Direct product of C8 and He3⋊C2723C8xHe3:C2432,173
C2.SU3(𝔽2)The central extension by C2 of SU3(𝔽2)723C2.SU(3,2)432,239
C9×A4⋊C4Direct product of C9 and A4⋊C41083C9xA4:C4432,242
C626Dic35th semidirect product of C62 and Dic3 acting via Dic3/C2=S3363C6^2:6Dic3432,260
He32(C2×C8)The semidirect product of He3 and C2×C8 acting via C2×C8/C4=C4723He3:2(C2xC8)432,273
C4×He3⋊C4Direct product of C4 and He3⋊C4723C4xHe3:C4432,275
A4×C36Direct product of C36 and A41083A4xC36432,325
C4×C9⋊A4Direct product of C4 and C9⋊A41083C4xC9:A4432,326
C4×C32.A4Direct product of C4 and C32.A4363C4xC3^2.A4432,332
C4×C32⋊A4Direct product of C4 and C32⋊A4363C4xC3^2:A4432,333
C2×SU3(𝔽2)Direct product of C2 and SU3(𝔽2)543C2xSU(3,2)432,531
C18×S4Direct product of C18 and S4543C18xS4432,532
C2×C32⋊S4Direct product of C2 and C32⋊S4183C2xC3^2:S4432,538

Groups of order 438

dρLabelID
C2×C73⋊C3Direct product of C2 and C73⋊C31463C2xC73:C3438,2

Groups of order 441

dρLabelID
C49⋊C9The semidirect product of C49 and C9 acting via C9/C3=C34413C49:C9441,1
C3×C49⋊C3Direct product of C3 and C49⋊C31473C3xC49:C3441,3
C7×C7⋊C9Direct product of C7 and C7⋊C9633C7xC7:C9441,5
C723C93rd semidirect product of C72 and C9 acting via C9/C3=C3633C7^2:3C9441,7
C7⋊C3×C21Direct product of C21 and C7⋊C3633C7:C3xC21441,10
C3×C723C3Direct product of C3 and C723C3633C3xC7^2:3C3441,12

Groups of order 444

dρLabelID
C4×C37⋊C3Direct product of C4 and C37⋊C31483C4xC37:C3444,2
A4×C37Direct product of C37 and A41483A4xC37444,13
C37⋊A4The semidirect product of C37 and A4 acting via A4/C22=C31483C37:A4444,14

Groups of order 450

dρLabelID
C2×C52⋊C9Direct product of C2 and C52⋊C9903C2xC5^2:C9450,13
C3×C52⋊S3Direct product of C3 and C52⋊S3453C3xC5^2:S3450,20
C6×C52⋊C3Direct product of C6 and C52⋊C3903C6xC5^2:C3450,25

Groups of order 453

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

Groups of order 456

dρLabelID
C8×C19⋊C3Direct product of C8 and C19⋊C31523C8xC19:C3456,2
C19×S4Direct product of C19 and S4763C19xS4456,42
A4×C38Direct product of C38 and A41143A4xC38456,49
C2×C19⋊A4Direct product of C2 and C19⋊A41143C2xC19:A4456,50

Groups of order 459

dρLabelID
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 462

dρLabelID
C7⋊C3×C22Direct product of C22 and C7⋊C31543C7:C3xC22462,4

Groups of order 465

dρLabelID
C5×C31⋊C3Direct product of C5 and C31⋊C31553C5xC31:C3465,3

Groups of order 468

dρLabelID
C4×C13⋊C9Direct product of C4 and C13⋊C94683C4xC13:C9468,2
C13×C3.A4Direct product of C13 and C3.A42343C13xC3.A4468,13
C39.A4The non-split extension by C39 of A4 acting via A4/C22=C32343C39.A4468,14
C12×C13⋊C3Direct product of C12 and C13⋊C31563C12xC13:C3468,22
A4×C39Direct product of C39 and A41563A4xC39468,48
C3×C13⋊A4Direct product of C3 and C13⋊A41563C3xC13:A4468,49

Groups of order 471

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

Groups of order 474

dρLabelID
C2×C79⋊C3Direct product of C2 and C79⋊C31583C2xC79:C3474,2

Groups of order 480

dρLabelID
C8×A5Direct product of C8 and A5403C8xA5480,220
C5×C42⋊S3Direct product of C5 and C42⋊S3603C5xC4^2:S3480,254
C5×A4⋊C8Direct product of C5 and A4⋊C81203C5xA4:C8480,255
C10×C42⋊C3Direct product of C10 and C42⋊C3603C10xC4^2:C3480,654
A4×C40Direct product of C40 and A41203A4xC40480,659
C20×S4Direct product of C20 and S4603C20xS4480,1014

Groups of order 483

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

Groups of order 486

dρLabelID
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
C922S32nd semidirect product of C92 and S3 acting faithfully273C9^2:2S3486,61
C2×C9.4He3Direct product of C2 and C9.4He3543C2xC9.4He3486,76
C2×C9.5He3Direct product of C2 and C9.5He31623C2xC9.5He3486,79
C2×C9.6He3Direct product of C2 and C9.6He31623C2xC9.6He3486,80
C2×C81⋊C3Direct product of C2 and C81⋊C31623C2xC81:C3486,84
C2×C92⋊C3Direct product of C2 and C92⋊C3543C2xC9^2:C3486,85
C2×C922C3Direct product of C2 and C922C3543C2xC9^2:2C3486,86
C2×C92.C3Direct product of C2 and C92.C3543C2xC9^2.C3486,87
C3≀S33C3The semidirect product of C3≀S3 and C3 acting through Inn(C3≀S3)273C3wrS3:3C3486,125
He3.5C18The non-split extension by He3 of C18 acting via C18/C9=C2813He3.5C18486,164
C2×C27○He3Direct product of C2 and C27○He31623C2xC27oHe3486,209
C2×C9.He3Direct product of C2 and C9.He3543C2xC9.He3486,214

Groups of order 489

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

Groups of order 492

dρLabelID
A4×C41Direct product of C41 and A41643A4xC41492,8

Orthogonal of dimension 4  (ρ=4+)

Groups of order 20

dρLabelID
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)54+F520,3

Groups of order 32

dρLabelID
C23⋊C4The semidirect product of C23 and C4 acting faithfully84+C2^3:C432,6
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C284+C4.D432,7
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)84+C8:C2^232,43
2+ 1+4Extraspecial group; = D4D484+ES+(2,2)32,49

Groups of order 36

dρLabelID
C32⋊C4The semidirect product of C32 and C4 acting faithfully64+C3^2:C436,9
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)64+S3^236,10

Groups of order 40

dρLabelID
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)104+C2xF540,12

Groups of order 48

dρLabelID
D4⋊S3The semidirect product of D4 and S3 acting via S3/C3=C2244+D4:S348,15
Q82S3The semidirect product of Q8 and S3 acting via S3/C3=C2244+Q8:2S348,17
S3×D4Direct product of S3 and D4; = Aut(D12) = Hol(C12)124+S3xD448,38
Q83S3The semidirect product of Q8 and S3 acting through Inn(Q8)244+Q8:3S348,41

Groups of order 52

dρLabelID
C13⋊C4The semidirect product of C13 and C4 acting faithfully134+C13:C452,3

Groups of order 60

dρLabelID
S3×D5Direct product of S3 and D5154+S3xD560,8

Groups of order 64

dρLabelID
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)84+C2wrC464,32
C42⋊C42nd semidirect product of C42 and C4 acting faithfully84+C4^2:C464,34
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfully164+M5(2):C264,42
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)84+D4:4D464,134
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)84+C2wrC2^264,138
D4.4D44th non-split extension by D4 of D4 acting via D4/C4=C2164+D4.4D464,153
C16⋊C22The semidirect product of C16 and C22 acting faithfully164+C16:C2^264,190
D4○D8Central product of D4 and D8164+D4oD864,257

Groups of order 68

dρLabelID
C17⋊C4The semidirect product of C17 and C4 acting faithfully174+C17:C468,3

Groups of order 72

dρLabelID
C6.D62nd non-split extension by C6 of D6 acting via D6/S3=C2124+C6.D672,21
C3⋊D12The semidirect product of C3 and D12 acting via D12/D6=C2124+C3:D1272,23
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)64+S3wrC272,40
C2×C32⋊C4Direct product of C2 and C32⋊C4124+C2xC3^2:C472,45
C2×S32Direct product of C2, S3 and S3124+C2xS3^272,46

Groups of order 80

dρLabelID
D4⋊D5The semidirect product of D4 and D5 acting via D5/C5=C2404+D4:D580,15
Q8⋊D5The semidirect product of Q8 and D5 acting via D5/C5=C2404+Q8:D580,17
C22⋊F5The semidirect product of C22 and F5 acting via F5/D5=C2204+C2^2:F580,34
D4×D5Direct product of D4 and D5204+D4xD580,39
Q82D5The semidirect product of Q8 and D5 acting through Inn(Q8)404+Q8:2D580,42

Groups of order 84

dρLabelID
S3×D7Direct product of S3 and D7214+S3xD784,8

Groups of order 96

dρLabelID
C12.46D43rd non-split extension by C12 of D4 acting via D4/C22=C2244+C12.46D496,30
C3⋊D16The semidirect product of C3 and D16 acting via D16/D8=C2484+C3:D1696,33
C8.6D63rd non-split extension by C8 of D6 acting via D6/S3=C2484+C8.6D696,35
C8⋊D61st semidirect product of C8 and D6 acting via D6/C3=C22244+C8:D696,115
S3×D8Direct product of S3 and D8244+S3xD896,117
Q83D62nd semidirect product of Q8 and D6 acting via D6/S3=C2244+Q8:3D696,121
D24⋊C25th semidirect product of D24 and C2 acting faithfully484+D24:C296,126
D4⋊D62nd semidirect product of D4 and D6 acting via D6/C6=C2244+D4:D696,156
C4.3S43rd non-split extension by C4 of S4 acting via S4/A4=C2164+C4.3S496,193
Q8.A4The non-split extension by Q8 of A4 acting through Inn(Q8)244+Q8.A496,201
C23⋊A42nd semidirect product of C23 and A4 acting faithfully84+C2^3:A496,204
D4○D12Central product of D4 and D12244+D4oD1296,216

Groups of order 100

dρLabelID
C25⋊C4The semidirect product of C25 and C4 acting faithfully254+C25:C4100,3
C52⋊C44th semidirect product of C52 and C4 acting faithfully104+C5^2:C4100,12
D52Direct product of D5 and D5104+D5^2100,13

Groups of order 104

dρLabelID
C2×C13⋊C4Direct product of C2 and C13⋊C4264+C2xC13:C4104,12

Groups of order 108

dρLabelID
S3×D9Direct product of S3 and D9184+S3xD9108,16

Groups of order 112

dρLabelID
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
D4×D7Direct product of D4 and D7284+D4xD7112,31
Q82D7The semidirect product of Q8 and D7 acting through Inn(Q8)564+Q8:2D7112,34

Groups of order 116

dρLabelID
C29⋊C4The semidirect product of C29 and C4 acting faithfully294+C29:C4116,3

Groups of order 120

dρLabelID
D30.C2The non-split extension by D30 of C2 acting faithfully604+D30.C2120,10
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
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simple54+S5120,34
C2×S3×D5Direct product of C2, S3 and D5304+C2xS3xD5120,42

Groups of order 128

dρLabelID
C8.24D81st non-split extension by C8 of D8 acting via D8/D4=C2164+C8.24D8128,89
C42.D41st non-split extension by C42 of D4 acting faithfully164+C4^2.D4128,134
C41D4⋊C42nd semidirect product of C41D4 and C4 acting faithfully164+C4:1D4:C4128,140
M6(2)⋊C26th semidirect product of M6(2) and C2 acting faithfully324+M6(2):C2128,151
Q16.10D43rd non-split extension by Q16 of D4 acting via D4/C22=C2324+Q16.10D4128,924
D4≀C2Wreath product of D4 by C284+D4wrC2128,928
D83D42nd semidirect product of D8 and D4 acting via D4/C4=C2164+D8:3D4128,945
D4.3D83rd non-split extension by D4 of D8 acting via D8/C8=C2324+D4.3D8128,953
C32⋊C22The semidirect product of C32 and C22 acting faithfully324+C32:C2^2128,995
D8○D8Central product of D8 and D8164+D8oD8128,2024
D4○D16Central product of D4 and D16324+D4oD16128,2147

Groups of order 132

dρLabelID
S3×D11Direct product of S3 and D11334+S3xD11132,5

Groups of order 136

dρLabelID
C2×C17⋊C4Direct product of C2 and C17⋊C4344+C2xC17:C4136,13

Groups of order 140

dρLabelID
D5×D7Direct product of D5 and D7354+D5xD7140,7

Groups of order 144

dρLabelID
D4⋊D9The semidirect product of D4 and D9 acting via D9/C9=C2724+D4:D9144,16
Q82D9The semidirect product of Q8 and D9 acting via D9/C9=C2724+Q8:2D9144,18
Q8⋊D9The semidirect product of Q8 and D9 acting via D9/C3=S3724+Q8:D9144,32
D4×D9Direct product of D4 and D9364+D4xD9144,41
Q83D9The semidirect product of Q8 and D9 acting through Inn(Q8)724+Q8:3D9144,44
C3⋊D24The semidirect product of C3 and D24 acting via D24/D12=C2244+C3:D24144,57
C325SD163rd semidirect product of C32 and SD16 acting via SD16/C4=C22244+C3^2:5SD16144,60
S32⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2124+S3^2:C4144,115
C6.6S46th non-split extension by C6 of S4 acting via S4/A4=C2244+C6.6S4144,125
Dic3.A4The non-split extension by Dic3 of A4 acting through Inn(Dic3)484+Dic3.A4144,127
C62⋊C41st semidirect product of C62 and C4 acting faithfully124+C6^2:C4144,136
D6.6D62nd non-split extension by D6 of D6 acting via D6/C6=C2244+D6.6D6144,142
S3×D12Direct product of S3 and D12244+S3xD12144,144
Dic3⋊D62nd semidirect product of Dic3 and D6 acting via D6/S3=C2; = Hol(Dic3)124+Dic3:D6144,154
C2×S3≀C2Direct product of C2 and S3≀C2124+C2xS3wrC2144,186

Groups of order 148

dρLabelID
C37⋊C4The semidirect product of C37 and C4 acting faithfully374+C37:C4148,3

Groups of order 156

dρLabelID
S3×D13Direct product of S3 and D13394+S3xD13156,11

Groups of order 160

dρLabelID
C20.46D43rd non-split extension by C20 of D4 acting via D4/C22=C2404+C20.46D4160,30
C5⋊D16The semidirect product of C5 and D16 acting via D16/D8=C2804+C5:D16160,33
C5⋊SD32The semidirect product of C5 and SD32 acting via SD32/Q16=C2804+C5:SD32160,35
D10.D41st non-split extension by D10 of D4 acting via D4/C2=C22404+D10.D4160,74
C8⋊D101st semidirect product of C8 and D10 acting via D10/C5=C22404+C8:D10160,129
D5×D8Direct product of D5 and D8404+D5xD8160,131
D40⋊C26th semidirect product of D40 and C2 acting faithfully404+D40:C2160,135
Q8.D105th non-split extension by Q8 of D10 acting via D10/D5=C2804+Q8.D10160,140
D4⋊D102nd semidirect product of D4 and D10 acting via D10/C10=C2404+D4:D10160,170
D48D104th semidirect product of D4 and D10 acting through Inn(D4)404+D4:8D10160,224

Groups of order 164

dρLabelID
C41⋊C4The semidirect product of C41 and C4 acting faithfully414+C41:C4164,3

Groups of order 168

dρLabelID
D21⋊C4The semidirect product of D21 and C4 acting via C4/C2=C2844+D21:C4168,14
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
C2×S3×D7Direct product of C2, S3 and D7424+C2xS3xD7168,50

Groups of order 176

dρLabelID
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
D4×D11Direct product of D4 and D11444+D4xD11176,31
D44⋊C24th semidirect product of D44 and C2 acting faithfully884+D44:C2176,34

Groups of order 180

dρLabelID
D5×D9Direct product of D5 and D9454+D5xD9180,7
C32⋊F5The semidirect product of C32 and F5 acting via F5/C5=C4304+C3^2:F5180,25
S3×D15Direct product of S3 and D15304+S3xD15180,29

Groups of order 192

dρLabelID
D24.C44th non-split extension by D24 of C4 acting via C4/C2=C2484+D24.C4192,54
M5(2)⋊S35th semidirect product of M5(2) and S3 acting via S3/C3=C2484+M5(2):S3192,75
C3⋊D32The semidirect product of C3 and D32 acting via D32/D16=C2964+C3:D32192,78
C3⋊SD64The semidirect product of C3 and SD64 acting via SD64/Q32=C2964+C3:SD64192,80
C2≀A4Wreath product of C2 by A484+C2wrA4192,201
Q85D123rd semidirect product of Q8 and D12 acting via D12/D6=C2244+Q8:5D12192,381
C24.19D419th non-split extension by C24 of D4 acting via D4/C2=C22484+C24.19D4192,456
C16⋊D61st semidirect product of C16 and D6 acting via D6/C3=C22484+C16:D6192,467
S3×D16Direct product of S3 and D16484+S3xD16192,469
D48⋊C26th semidirect product of D48 and C2 acting faithfully484+D48:C2192,473
D485C25th semidirect product of D48 and C2 acting faithfully964+D48:5C2192,478
Q8.9D124th non-split extension by Q8 of D12 acting via D12/C12=C2484+Q8.9D12192,701
Q16⋊D62nd semidirect product of Q16 and D6 acting via D6/C6=C2484+Q16:D6192,752
C8.3S43rd non-split extension by C8 of S4 acting via S4/A4=C2324+C8.3S4192,966
Q8.5S43rd non-split extension by Q8 of S4 acting via S4/A4=C2244+Q8.5S4192,988
Q16.A4The non-split extension by Q16 of A4 acting through Inn(Q16)484+Q16.A4192,1017
D4.12D122nd non-split extension by D4 of D12 acting through Inn(D4)484+D4.12D12192,1311
D815D64th semidirect product of D8 and D6 acting through Inn(D8)484+D8:15D6192,1328
Q8.7S42nd non-split extension by Q8 of S4 acting through Inn(Q8)324+Q8.7S4192,1484
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)84+C2^3:S4192,1493
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)84+Q8:2S4192,1494

Groups of order 196

dρLabelID
C72⋊C4The semidirect product of C72 and C4 acting faithfully144+C7^2:C4196,8
D72Direct product of D7 and D7144+D7^2196,9

Groups of order 200

dρLabelID
C2×C25⋊C4Direct product of C2 and C25⋊C4504+C2xC25:C4200,12
Dic52D5The semidirect product of Dic5 and D5 acting through Inn(Dic5)204+Dic5:2D5200,23
C5⋊D20The semidirect product of C5 and D20 acting via D20/D10=C2204+C5:D20200,25
D5≀C2Wreath product of D5 by C2104+D5wrC2200,43
C2×C52⋊C4Direct product of C2 and C52⋊C4204+C2xC5^2:C4200,48
C2×D52Direct product of C2, D5 and D5204+C2xD5^2200,49

Groups of order 204

dρLabelID
S3×D17Direct product of S3 and D17514+S3xD17204,7

Groups of order 208

dρLabelID
D4⋊D13The semidirect product of D4 and D13 acting via D13/C13=C21044+D4:D13208,15
Q8⋊D13The semidirect product of Q8 and D13 acting via D13/C13=C21044+Q8:D13208,17
D13.D4The non-split extension by D13 of D4 acting via D4/C22=C2524+D13.D4208,34
D4×D13Direct product of D4 and D13524+D4xD13208,39
D52⋊C24th semidirect product of D52 and C2 acting faithfully1044+D52:C2208,42

Groups of order 212

dρLabelID
C53⋊C4The semidirect product of C53 and C4 acting faithfully534+C53:C4212,3

Groups of order 216

dρLabelID
C18.D63rd non-split extension by C18 of D6 acting via D6/S3=C2364+C18.D6216,28
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
C2×S3×D9Direct product of C2, S3 and D9364+C2xS3xD9216,101

Groups of order 220

dρLabelID
D5×D11Direct product of D5 and D11554+D5xD11220,11

Groups of order 224

dρLabelID
C28.46D43rd non-split extension by C28 of D4 acting via D4/C22=C2564+C28.46D4224,29
C7⋊D16The semidirect product of C7 and D16 acting via D16/D8=C21124+C7:D16224,32
C7⋊SD32The semidirect product of C7 and SD32 acting via SD32/Q16=C21124+C7:SD32224,34
C8⋊D141st semidirect product of C8 and D14 acting via D14/C7=C22564+C8:D14224,103
D7×D8Direct product of D7 and D8564+D7xD8224,105
D56⋊C26th semidirect product of D56 and C2 acting faithfully564+D56:C2224,109
Q8.D145th non-split extension by Q8 of D14 acting via D14/D7=C21124+Q8.D14224,114
D4⋊D142nd semidirect product of D4 and D14 acting via D14/C14=C2564+D4:D14224,144
D48D144th semidirect product of D4 and D14 acting through Inn(D4)564+D4:8D14224,185

Groups of order 228

dρLabelID
S3×D19Direct product of S3 and D19574+S3xD19228,8

Groups of order 232

dρLabelID
C2×C29⋊C4Direct product of C2 and C29⋊C4584+C2xC29:C4232,12

Groups of order 240

dρLabelID
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
C15⋊SD164th semidirect product of C15 and SD16 acting via SD16/C4=C221204+C15:SD16240,19
Dic6⋊D51st semidirect product of Dic6 and D5 acting via D5/C5=C21204+Dic6:D5240,21
D4⋊D15The semidirect product of D4 and D15 acting via D15/C15=C21204+D4:D15240,76
Q82D15The semidirect product of Q8 and D15 acting via D15/C15=C21204+Q8:2D15240,78
Q8⋊D15The semidirect product of Q8 and D15 acting via D15/C5=S3404+Q8:D15240,106
Dic5.A4The non-split extension by Dic5 of A4 acting through Inn(Dic5)804+Dic5.A4240,108
D60⋊C26th semidirect product of D60 and C2 acting faithfully1204+D60:C2240,130
C12.28D107th non-split extension by C12 of D10 acting via D10/D5=C21204+C12.28D10240,134
D5×D12Direct product of D5 and D12604+D5xD12240,136
S3×D20Direct product of S3 and D20604+S3xD20240,137
D10⋊D64th semidirect product of D10 and D6 acting via D6/S3=C2604+D10:D6240,151
D4×D15Direct product of D4 and D15604+D4xD15240,179
Q83D15The semidirect product of Q8 and D15 acting through Inn(Q8)1204+Q8:3D15240,182
C2×S5Direct product of C2 and S5; = O3(𝔽5)104+C2xS5240,189

Groups of order 244

dρLabelID
C61⋊C4The semidirect product of C61 and C4 acting faithfully614+C61:C4244,3

Groups of order 252

dρLabelID
D7×D9Direct product of D7 and D9634+D7xD9252,8
S3×D21Direct product of S3 and D21424+S3xD21252,36

Groups of order 260

dρLabelID
C13⋊F51st semidirect product of C13 and F5 acting via F5/C5=C4654+C13:F5260,9
C652C42nd semidirect product of C65 and C4 acting faithfully654+C65:2C4260,10
D5×D13Direct product of D5 and D13654+D5xD13260,11

Groups of order 264

dρLabelID
D33⋊C4The semidirect product of D33 and C4 acting via C4/C2=C21324+D33:C4264,7
C3⋊D44The semidirect product of C3 and D44 acting via D44/D22=C21324+C3:D44264,9
C11⋊D12The semidirect product of C11 and D12 acting via D12/D6=C21324+C11:D12264,10
C2×S3×D11Direct product of C2, S3 and D11664+C2xS3xD11264,34

Groups of order 272

dρLabelID
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
D17.D4The non-split extension by D17 of D4 acting via D4/C22=C2684+D17.D4272,35
D4×D17Direct product of D4 and D17684+D4xD17272,40
D68⋊C24th semidirect product of D68 and C2 acting faithfully1364+D68:C2272,43

Groups of order 276

dρLabelID
S3×D23Direct product of S3 and D23694+S3xD23276,5

Groups of order 280

dρLabelID
D70.C2The non-split extension by D70 of C2 acting faithfully1404+D70.C2280,9
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
C2×D5×D7Direct product of C2, D5 and D7704+C2xD5xD7280,36

Groups of order 288

dρLabelID
C36.48D44th non-split extension by C36 of D4 acting via D4/C22=C2724+C36.48D4288,31
C9⋊D16The semidirect product of C9 and D16 acting via D16/D8=C21444+C9:D16288,33
C9⋊SD32The semidirect product of C9 and SD32 acting via SD32/Q16=C21444+C9:SD32288,35
C8⋊D181st semidirect product of C8 and D18 acting via D18/C9=C22724+C8:D18288,118
D8×D9Direct product of D8 and D9724+D8xD9288,120
D72⋊C26th semidirect product of D72 and C2 acting faithfully724+D72:C2288,124
D725C25th semidirect product of D72 and C2 acting faithfully1444+D72:5C2288,129
D4⋊D182nd semidirect product of D4 and D18 acting via D18/C18=C2724+D4:D18288,160
C3⋊D48The semidirect product of C3 and D48 acting via D48/D24=C2484+C3:D48288,194
C24.49D62nd non-split extension by C24 of D6 acting via D6/S3=C2484+C24.49D6288,197
C12.70D121st non-split extension by C12 of D12 acting via D12/D6=C2244+C12.70D12288,207
C12.4S44th non-split extension by C12 of S4 acting via S4/A4=C2724+C12.4S4288,340
D48D184th semidirect product of D4 and D18 acting through Inn(D4)724+D4:8D18288,363
C62.2D42nd non-split extension by C62 of D4 acting faithfully244+C6^2.2D4288,386
(C6×C12)⋊C41st semidirect product of C6×C12 and C4 acting faithfully244+(C6xC12):C4288,422
S3×D24Direct product of S3 and D24484+S3xD24288,441
C241D61st semidirect product of C24 and D6 acting via D6/C3=C22484+C24:1D6288,442
D6.3D123rd non-split extension by D6 of D12 acting via D12/C12=C2484+D6.3D12288,456
D1218D62nd semidirect product of D12 and D6 acting via D6/C6=C2244+D12:18D6288,473
Dic3.5S42nd non-split extension by Dic3 of S4 acting through Inn(Dic3)484+Dic3.5S4288,846
GL2(𝔽3)⋊S31st semidirect product of GL2(𝔽3) and S3 acting via S3/C3=C2484+GL(2,3):S3288,847
Ω4+ (𝔽3)Omega group of + type on 𝔽34; = SL2(𝔽3)A4244+Omega+(4,3)288,860
D6≀C2Wreath product of D6 by C2124+D6wrC2288,889
C12.7S47th non-split extension by C12 of S4 acting via S4/A4=C2484+C12.7S4288,915
Dic6.A4The non-split extension by Dic6 of A4 acting through Inn(Dic6)724+Dic6.A4288,924
D1227D63rd semidirect product of D12 and D6 acting through Inn(D12)244+D12:27D6288,956

Groups of order 292

dρLabelID
C73⋊C4The semidirect product of C73 and C4 acting faithfully734+C73:C4292,3

Groups of order 296

dρLabelID
C2×C37⋊C4Direct product of C2 and C37⋊C4744+C2xC37:C4296,12

Groups of order 300

dρLabelID
S3×D25Direct product of S3 and D25754+S3xD25300,7
D5×D15Direct product of D5 and D15304+D5xD15300,39

Groups of order 304

dρLabelID
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
D4×D19Direct product of D4 and D19764+D4xD19304,31
D76⋊C24th semidirect product of D76 and C2 acting faithfully1524+D76:C2304,34

Groups of order 308

dρLabelID
D7×D11Direct product of D7 and D11774+D7xD11308,5

Groups of order 312

dρLabelID
D78.C2The non-split extension by D78 of C2 acting faithfully1564+D78.C2312,17
C3⋊D52The semidirect product of C3 and D52 acting via D52/D26=C21564+C3:D52312,19
C13⋊D12The semidirect product of C13 and D12 acting via D12/D6=C21564+C13:D12312,20
C2×S3×D13Direct product of C2, S3 and D13784+C2xS3xD13312,54

Groups of order 320

dρLabelID
D40.6C44th non-split extension by D40 of C4 acting via C4/C2=C2804+D40.6C4320,53
D40.4C42nd non-split extension by D40 of C4 acting via C4/C2=C2804+D40.4C4320,74
C5⋊D32The semidirect product of C5 and D32 acting via D32/D16=C21604+C5:D32320,77
C5⋊SD64The semidirect product of C5 and SD64 acting via SD64/Q32=C21604+C5:SD64320,79
C42⋊F51st semidirect product of C42 and F5 acting via F5/C5=C4404+C4^2:F5320,191
D44D203rd semidirect product of D4 and D20 acting via D20/D10=C2404+D4:4D20320,449
C8.21D207th non-split extension by C8 of D20 acting via D20/D10=C2804+C8.21D20320,524
D80⋊C22nd semidirect product of D80 and C2 acting faithfully804+D80:C2320,535
D5×D16Direct product of D5 and D16804+D5xD16320,537
C16⋊D103rd semidirect product of C16 and D10 acting via D10/C5=C22804+C16:D10320,541
D805C25th semidirect product of D80 and C2 acting faithfully1604+D80:5C2320,546
D4.4D204th non-split extension by D4 of D20 acting via D20/C20=C2804+D4.4D20320,769
D8⋊D102nd semidirect product of D8 and D10 acting via D10/C10=C2804+D8:D10320,820
D4.12D202nd non-split extension by D4 of D20 acting through Inn(D4)804+D4.12D20320,1424
D815D104th semidirect product of D8 and D10 acting through Inn(D8)804+D8:15D10320,1441

Groups of order 324

dρLabelID
C92⋊C4The semidirect product of C92 and C4 acting faithfully184+C9^2:C4324,35
D92Direct product of D9 and D9184+D9^2324,36
S3×D27Direct product of S3 and D27544+S3xD27324,38

Groups of order 328

dρLabelID
C2×C41⋊C4Direct product of C2 and C41⋊C4824+C2xC41:C4328,13

Groups of order 336

dρLabelID
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
C21⋊SD164th semidirect product of C21 and SD16 acting via SD16/C4=C221684+C21:SD16336,35
Dic6⋊D71st semidirect product of Dic6 and D7 acting via D7/C7=C21684+Dic6:D7336,37
D4⋊D21The semidirect product of D4 and D21 acting via D21/C21=C21684+D4:D21336,101
Q82D21The semidirect product of Q8 and D21 acting via D21/C21=C21684+Q8:2D21336,103
Q8⋊D21The semidirect product of Q8 and D21 acting via D21/C7=S3564+Q8:D21336,119
Dic7.2A4The non-split extension by Dic7 of A4 acting through Inn(Dic7)1124+Dic7.2A4336,131
D84⋊C26th semidirect product of D84 and C2 acting faithfully1684+D84:C2336,142
D14.D63rd non-split extension by D14 of D6 acting via D6/C6=C21684+D14.D6336,146
D7×D12Direct product of D7 and D12844+D7xD12336,148
S3×D28Direct product of S3 and D28844+S3xD28336,149
D6⋊D144th semidirect product of D6 and D14 acting via D14/D7=C2844+D6:D14336,163
D4×D21Direct product of D4 and D21844+D4xD21336,198
Q83D21The semidirect product of Q8 and D21 acting through Inn(Q8)1684+Q8:3D21336,201

Groups of order 340

dρLabelID
C17⋊F51st semidirect product of C17 and F5 acting via F5/C5=C4854+C17:F5340,9
C852C42nd semidirect product of C85 and C4 acting faithfully854+C85:2C4340,10
D5×D17Direct product of D5 and D17854+D5xD17340,11

Groups of order 348

dρLabelID
S3×D29Direct product of S3 and D29874+S3xD29348,7

Groups of order 352

dρLabelID
C44.46D43rd non-split extension by C44 of D4 acting via D4/C22=C2884+C44.46D4352,29
C11⋊D16The semidirect product of C11 and D16 acting via D16/D8=C21764+C11:D16352,32
C8.6D223rd non-split extension by C8 of D22 acting via D22/D11=C21764+C8.6D22352,34
C8⋊D221st semidirect product of C8 and D22 acting via D22/C11=C22884+C8:D22352,103
D8×D11Direct product of D8 and D11884+D8xD11352,105
D88⋊C26th semidirect product of D88 and C2 acting faithfully884+D88:C2352,109
D885C25th semidirect product of D88 and C2 acting faithfully1764+D88:5C2352,114
Q8⋊D222nd semidirect product of Q8 and D22 acting via D22/C22=C2884+Q8:D22352,144
D48D224th semidirect product of D4 and D22 acting through Inn(D4)884+D4:8D22352,184

Groups of order 356

dρLabelID
C89⋊C4The semidirect product of C89 and C4 acting faithfully894+C89:C4356,3

Groups of order 360

dρLabelID
D90.C2The non-split extension by D90 of C2 acting faithfully1804+D90.C2360,9
C5⋊D36The semidirect product of C5 and D36 acting via D36/D18=C21804+C5:D36360,10
C9⋊D20The semidirect product of C9 and D20 acting via D20/D10=C21804+C9:D20360,13
C2×D5×D9Direct product of C2, D5 and D9904+C2xD5xD9360,45
C6.D303rd non-split extension by C6 of D30 acting via D30/D15=C2604+C6.D30360,79
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
C2×C32⋊F5Direct product of C2 and C32⋊F5604+C2xC3^2:F5360,150
C2×S3×D15Direct product of C2, S3 and D15604+C2xS3xD15360,154

Groups of order 364

dρLabelID
D7×D13Direct product of D7 and D13914+D7xD13364,7

Groups of order 368

dρLabelID
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
D4×D23Direct product of D4 and D23924+D4xD23368,31
D92⋊C24th semidirect product of D92 and C2 acting faithfully1844+D92:C2368,34

Groups of order 372

dρLabelID
S3×D31Direct product of S3 and D31934+S3xD31372,8

Groups of order 380

dρLabelID
D5×D19Direct product of D5 and D19954+D5xD19380,7

Groups of order 388

dρLabelID
C97⋊C4The semidirect product of C97 and C4 acting faithfully974+C97:C4388,3

Groups of order 392

dρLabelID
Dic72D7The semidirect product of Dic7 and D7 acting through Inn(Dic7)284+Dic7:2D7392,19
C7⋊D28The semidirect product of C7 and D28 acting via D28/D14=C2284+C7:D28392,21
D7≀C2Wreath product of D7 by C2144+D7wrC2392,37
C2×C72⋊C4Direct product of C2 and C72⋊C4284+C2xC7^2:C4392,40
C2×D72Direct product of C2, D7 and D7284+C2xD7^2392,41

Groups of order 396

dρLabelID
D9×D11Direct product of D9 and D11994+D9xD11396,5
S3×D33Direct product of S3 and D33664+S3xD33396,22

Groups of order 400

dρLabelID
D4⋊D25The semidirect product of D4 and D25 acting via D25/C25=C22004+D4:D25400,16
Q8⋊D25The semidirect product of Q8 and D25 acting via D25/C25=C22004+Q8:D25400,18
D25.D4The non-split extension by D25 of D4 acting via D4/C22=C21004+D25.D4400,34
D4×D25Direct product of D4 and D251004+D4xD25400,39
Q82D25The semidirect product of Q8 and D25 acting through Inn(Q8)2004+Q8:2D25400,42
C5⋊D40The semidirect product of C5 and D40 acting via D40/D20=C2404+C5:D40400,65
C524SD163rd semidirect product of C52 and SD16 acting via SD16/C4=C22404+C5^2:4SD16400,68
D52⋊C41st semidirect product of D52 and C4 acting via C4/C2=C2204+D5^2:C4400,129
C1024C44th semidirect product of C102 and C4 acting faithfully204+C10^2:4C4400,162
Dic105D5The semidirect product of Dic10 and D5 acting through Inn(Dic10)404+Dic10:5D5400,168
D5×D20Direct product of D5 and D20404+D5xD20400,170
D10⋊D103rd semidirect product of D10 and D10 acting via D10/D5=C2204+D10:D10400,180
C2×D5≀C2Direct product of C2 and D5≀C2204+C2xD5wrC2400,211

Groups of order 404

dρLabelID
C101⋊C4The semidirect product of C101 and C4 acting faithfully1014+C101:C4404,3

Groups of order 408

dρLabelID
D512C4The semidirect product of D51 and C4 acting via C4/C2=C22044+D51:2C4408,9
C3⋊D68The semidirect product of C3 and D68 acting via D68/D34=C22044+C3:D68408,11
C17⋊D12The semidirect product of C17 and D12 acting via D12/D6=C22044+C17:D12408,12
C2×S3×D17Direct product of C2, S3 and D171024+C2xS3xD17408,41

Groups of order 416

dρLabelID
C52.46D43rd non-split extension by C52 of D4 acting via D4/C22=C21044+C52.46D4416,30
C13⋊D16The semidirect product of C13 and D16 acting via D16/D8=C22084+C13:D16416,33
C8.6D263rd non-split extension by C8 of D26 acting via D26/D13=C22084+C8.6D26416,35
D26.D41st non-split extension by D26 of D4 acting via D4/C2=C221044+D26.D4416,74
C8⋊D261st semidirect product of C8 and D26 acting via D26/C13=C221044+C8:D26416,129
D8×D13Direct product of D8 and D131044+D8xD13416,131
Q8⋊D262nd semidirect product of Q8 and D26 acting via D26/D13=C21044+Q8:D26416,135
D104⋊C25th semidirect product of D104 and C2 acting faithfully2084+D104:C2416,140
D4⋊D262nd semidirect product of D4 and D26 acting via D26/C26=C21044+D4:D26416,170
D48D264th semidirect product of D4 and D26 acting through Inn(D4)1044+D4:8D26416,223

Groups of order 420

dρLabelID
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

Groups of order 424

dρLabelID
C2×C53⋊C4Direct product of C2 and C53⋊C41064+C2xC53:C4424,12

Groups of order 432

dρLabelID
D4⋊D27The semidirect product of D4 and D27 acting via D27/C27=C22164+D4:D27432,16
Q82D27The semidirect product of Q8 and D27 acting via D27/C27=C22164+Q8:2D27432,18
Q8⋊D27The semidirect product of Q8 and D27 acting via D27/C9=S32164+Q8:D27432,38
D4×D27Direct product of D4 and D271084+D4xD27432,47
Q83D27The semidirect product of Q8 and D27 acting through Inn(Q8)2164+Q8:3D27432,50
C6.D362nd non-split extension by C6 of D36 acting via D36/D18=C2724+C6.D36432,63
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
C18.D123rd non-split extension by C18 of D12 acting via D12/D6=C2724+C18.D12432,73
C18.6S46th non-split extension by C18 of S4 acting via S4/A4=C2724+C18.6S4432,253
Dic9.2A4The non-split extension by Dic9 of A4 acting through Inn(Dic9)1444+Dic9.2A4432,262
Dic65D9The semidirect product of Dic6 and D9 acting through Inn(Dic6)724+Dic6:5D9432,282
Dic9.D64th non-split extension by Dic9 of D6 acting via D6/S3=C2724+Dic9.D6432,289
S3×D36Direct product of S3 and D36724+S3xD36432,291
D9×D12Direct product of D9 and D12724+D9xD12432,292
D18⋊D64th semidirect product of D18 and D6 acting via D6/S3=C2364+D18:D6432,315

Groups of order 436

dρLabelID
C109⋊C4The semidirect product of C109 and C4 acting faithfully1094+C109:C4436,3

Groups of order 440

dρLabelID
D552C4The semidirect product of D55 and C4 acting via C4/C2=C22204+D55:2C4440,19
C5⋊D44The semidirect product of C5 and D44 acting via D44/D22=C22204+C5:D44440,21
C11⋊D20The semidirect product of C11 and D20 acting via D20/D10=C22204+C11:D20440,22
C2×D5×D11Direct product of C2, D5 and D111104+C2xD5xD11440,47

Groups of order 444

dρLabelID
S3×D37Direct product of S3 and D371114+S3xD37444,11

Groups of order 448

dρLabelID
D56.C44th non-split extension by D56 of C4 acting via C4/C2=C21124+D56.C4448,52
C28.3D83rd non-split extension by C28 of D8 acting via D8/C4=C221124+C28.3D8448,73
C7⋊D32The semidirect product of C7 and D32 acting via D32/D16=C22244+C7:D32448,76
C7⋊SD64The semidirect product of C7 and SD64 acting via SD64/Q32=C22244+C7:SD64448,78
D44D283rd semidirect product of D4 and D28 acting via D28/D14=C2564+D4:4D28448,356
C8.21D287th non-split extension by C8 of D28 acting via D28/D14=C21124+C8.21D28448,431
C16⋊D141st semidirect product of C16 and D14 acting via D14/C7=C221124+C16:D14448,442
D7×D16Direct product of D7 and D161124+D7xD16448,444
D112⋊C26th semidirect product of D112 and C2 acting faithfully1124+D112:C2448,448
Q323D7The semidirect product of Q32 and D7 acting through Inn(Q32)2244+Q32:3D7448,453
D4.4D284th non-split extension by D4 of D28 acting via D28/C28=C21124+D4.4D28448,676
Q16⋊D142nd semidirect product of Q16 and D14 acting via D14/C14=C21124+Q16:D14448,727
D4.12D282nd non-split extension by D4 of D28 acting through Inn(D4)1124+D4.12D28448,1205
D815D144th semidirect product of D8 and D14 acting through Inn(D8)1124+D8:15D14448,1222

Groups of order 452

dρLabelID
C113⋊C4The semidirect product of C113 and C4 acting faithfully1134+C113:C4452,3

Groups of order 456

dρLabelID
D57⋊C4The semidirect product of D57 and C4 acting via C4/C2=C22284+D57:C4456,14
C3⋊D76The semidirect product of C3 and D76 acting via D76/D38=C22284+C3:D76456,16
C19⋊D12The semidirect product of C19 and D12 acting via D12/D6=C22284+C19:D12456,17
C2×S3×D19Direct product of C2, S3 and D191144+C2xS3xD19456,47

Groups of order 460

dρLabelID
D5×D23Direct product of D5 and D231154+D5xD23460,7

Groups of order 464

dρLabelID
D4⋊D29The semidirect product of D4 and D29 acting via D29/C29=C22324+D4:D29464,15
Q8⋊D29The semidirect product of Q8 and D29 acting via D29/C29=C22324+Q8:D29464,17
D29.D4The non-split extension by D29 of D4 acting via D4/C22=C21164+D29.D4464,34
D4×D29Direct product of D4 and D291164+D4xD29464,39
Q82D29The semidirect product of Q8 and D29 acting through Inn(Q8)2324+Q8:2D29464,42

Groups of order 468

dρLabelID
D9×D13Direct product of D9 and D131174+D9xD13468,11
(C3×C39)⋊C41st semidirect product of C3×C39 and C4 acting faithfully784+(C3xC39):C4468,41
S3×D39Direct product of S3 and D39784+S3xD39468,45

Groups of order 476

dρLabelID
D7×D17Direct product of D7 and D171194+D7xD17476,7

Groups of order 480

dρLabelID
C3⋊D80The semidirect product of C3 and D80 acting via D80/D40=C22404+C3:D80480,14
C5⋊D48The semidirect product of C5 and D48 acting via D48/D24=C22404+C5:D48480,15
C24.D109th non-split extension by C24 of D10 acting via D10/C5=C222404+C24.D10480,19
Dic12⋊D51st semidirect product of Dic12 and D5 acting via D5/C5=C22404+Dic12:D5480,21
C60.29D429th non-split extension by C60 of D4 acting via D4/C2=C221204+C60.29D4480,36
M4(2)⋊D153rd semidirect product of M4(2) and D15 acting via D15/C15=C21204+M4(2):D15480,183
C157D161st semidirect product of C15 and D16 acting via D16/D8=C22404+C15:7D16480,186
C8.6D303rd non-split extension by C8 of D30 acting via D30/D15=C22404+C8.6D30480,188
D5×D24Direct product of D5 and D241204+D5xD24480,324
C24⋊D101st semidirect product of C24 and D10 acting via D10/C5=C221204+C24:D10480,325
S3×D40Direct product of S3 and D401204+S3xD40480,328
C401D61st semidirect product of C40 and D6 acting via D6/C3=C221204+C40:1D6480,329
D120⋊C212nd semidirect product of D120 and C2 acting faithfully2404+D120:C2480,347
D1205C25th semidirect product of D120 and C2 acting faithfully2404+D120:5C2480,351
D2019D62nd semidirect product of D20 and D6 acting via D6/C6=C21204+D20:19D6480,377
C60.38D438th non-split extension by C60 of D4 acting via D4/C2=C221204+C60.38D4480,381
C8⋊D301st semidirect product of C8 and D30 acting via D30/C15=C221204+C8:D30480,873
D8×D15Direct product of D8 and D151204+D8xD15480,875
Q83D302nd semidirect product of Q8 and D30 acting via D30/D15=C21204+Q8:3D30480,879
D1208C28th semidirect product of D120 and C2 acting faithfully2404+D120:8C2480,884
D4⋊D302nd semidirect product of D4 and D30 acting via D30/C30=C21204+D4:D30480,914
Q8.A5The non-split extension by Q8 of A5 acting through Inn(Q8)484+Q8.A5480,959
Dic5.7S42nd non-split extension by Dic5 of S4 acting through Inn(Dic5)804+Dic5.7S4480,969
GL2(𝔽3)⋊D51st semidirect product of GL2(𝔽3) and D5 acting via D5/C5=C2804+GL(2,3):D5480,970
C20.3S43rd non-split extension by C20 of S4 acting via S4/A4=C2804+C20.3S4480,1032
Dic10.A4The non-split extension by Dic10 of A4 acting through Inn(Dic10)1204+Dic10.A4480,1041
D2029D63rd semidirect product of D20 and D6 acting through Inn(D20)1204+D20:29D6480,1095
D48D304th semidirect product of D4 and D30 acting through Inn(D4)1204+D4:8D30480,1176

Groups of order 484

dρLabelID
C112⋊C4The semidirect product of C112 and C4 acting faithfully224+C11^2:C4484,8
D112Direct product of D11 and D11224+D11^2484,9

Groups of order 488

dρLabelID
C2×C61⋊C4Direct product of C2 and C61⋊C41224+C2xC61:C4488,12

Groups of order 492

dρLabelID
S3×D41Direct product of S3 and D411234+S3xD41492,7

Groups of order 496

dρLabelID
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
D4×D31Direct product of D4 and D311244+D4xD31496,31
Q82D31The semidirect product of Q8 and D31 acting through Inn(Q8)2484+Q8:2D31496,34

Groups of order 500

dρLabelID
C125⋊C4The semidirect product of C125 and C4 acting faithfully1254+C125:C4500,3
C252F52nd semidirect product of C25 and F5 acting via F5/C5=C4504+C25:2F5500,24
D5×D25Direct product of D5 and D25504+D5xD25500,26

Symplectic of dimension 4  (ρ=4-)

Groups of order 32

dρLabelID
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2164-C4.10D432,8
C8.C22The non-split extension by C8 of C22 acting faithfully164-C8.C2^232,44
2- 1+4Gamma matrices = Extraspecial group; = D4Q8164-ES-(2,2)32,50

Groups of order 40

dρLabelID
C5⋊C8The semidirect product of C5 and C8 acting via C8/C2=C4404-C5:C840,3

Groups of order 48

dρLabelID
D4.S3The non-split extension by D4 of S3 acting via S3/C3=C2244-D4.S348,16
C3⋊Q16The semidirect product of C3 and Q16 acting via Q16/Q8=C2484-C3:Q1648,18
D42S3The semidirect product of D4 and S3 acting through Inn(D4)244-D4:2S348,39
S3×Q8Direct product of S3 and Q8244-S3xQ848,40

Groups of order 64

dρLabelID
C42.3C43rd non-split extension by C42 of C4 acting faithfully164-C4^2.3C464,37
C8.17D44th non-split extension by C8 of D4 acting via D4/C22=C2324-C8.17D464,43
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2164-D4.10D464,137
D4.5D45th non-split extension by D4 of D4 acting via D4/C4=C2324-D4.5D464,154
Q32⋊C22nd semidirect product of Q32 and C2 acting faithfully324-Q32:C264,191
Q8○D8Central product of Q8 and D8324-Q8oD864,259

Groups of order 72

dρLabelID
C322C8The semidirect product of C32 and C8 acting via C8/C2=C4244-C3^2:2C872,19
S3×Dic3Direct product of S3 and Dic3244-S3xDic372,20
D6⋊S31st semidirect product of D6 and S3 acting via S3/C3=C2244-D6:S372,22
C322Q8The semidirect product of C32 and Q8 acting via Q8/C2=C22244-C3^2:2Q872,24

Groups of order 80

dρLabelID
D4.D5The non-split extension by D4 of D5 acting via D5/C5=C2404-D4.D580,16
C5⋊Q16The semidirect product of C5 and Q16 acting via Q16/Q8=C2804-C5:Q1680,18
C22.F5The non-split extension by C22 of F5 acting via F5/D5=C2404-C2^2.F580,33
D42D5The semidirect product of D4 and D5 acting through Inn(D4)404-D4:2D580,40
Q8×D5Direct product of Q8 and D5404-Q8xD580,41

Groups of order 96

dρLabelID
C12.47D44th non-split extension by C12 of D4 acting via D4/C22=C2484-C12.47D496,31
D8.S3The non-split extension by D8 of S3 acting via S3/C3=C2484-D8.S396,34
C3⋊Q32The semidirect product of C3 and Q32 acting via Q32/Q16=C2964-C3:Q3296,36
C8.D61st non-split extension by C8 of D6 acting via D6/C3=C22484-C8.D696,116
D83S3The semidirect product of D8 and S3 acting through Inn(D8)484-D8:3S396,119
D4.D64th non-split extension by D4 of D6 acting via D6/S3=C2484-D4.D696,122
S3×Q16Direct product of S3 and Q16484-S3xQ1696,124
Q8.14D64th non-split extension by Q8 of D6 acting via D6/C6=C2484-Q8.14D696,158
Q8.D62nd non-split extension by Q8 of D6 acting via D6/C2=S3164-Q8.D696,190
C4.S42nd non-split extension by C4 of S4 acting via S4/A4=C2324-C4.S496,191
D4.A4The non-split extension by D4 of A4 acting through Inn(D4)164-D4.A496,202
Q8○D12Central product of Q8 and D12484-Q8oD1296,217

Groups of order 104

dρLabelID
C13⋊C8The semidirect product of C13 and C8 acting via C8/C2=C41044-C13:C8104,3

Groups of order 112

dρLabelID
D4.D7The non-split extension by D4 of D7 acting via D7/C7=C2564-D4.D7112,15
C7⋊Q16The semidirect product of C7 and Q16 acting via Q16/Q8=C21124-C7:Q16112,17
D42D7The semidirect product of D4 and D7 acting through Inn(D4)564-D4:2D7112,32
Q8×D7Direct product of Q8 and D7564-Q8xD7112,33

Groups of order 120

dρLabelID
D5×Dic3Direct product of D5 and Dic3604-D5xDic3120,8
S3×Dic5Direct product of S3 and Dic5604-S3xDic5120,9
C15⋊D41st semidirect product of C15 and D4 acting via D4/C2=C22604-C15:D4120,11
C15⋊Q8The semidirect product of C15 and Q8 acting via Q8/C2=C221204-C15:Q8120,14

Groups of order 128

dρLabelID
C8.25D82nd non-split extension by C8 of D8 acting via D8/D4=C2324-C8.25D8128,90
C42.4D44th non-split extension by C42 of D4 acting faithfully164-C4^2.4D4128,137
(C2×Q8).D46th non-split extension by C2×Q8 of D4 acting faithfully324-(C2xQ8).D4128,143
C16.18D44th non-split extension by C16 of D4 acting via D4/C22=C2644-C16.18D4128,152
D8.12D44th non-split extension by D8 of D4 acting via D4/C22=C2644-D8.12D4128,927
Q8≀C2Wreath product of Q8 by C2164-Q8wrC2128,937
C8.5D85th non-split extension by C8 of D8 acting via D8/C4=C22324-C8.5D8128,946
D4.4D84th non-split extension by D4 of D8 acting via D8/C8=C2644-D4.4D8128,954
Q64⋊C22nd semidirect product of Q64 and C2 acting faithfully644-Q64:C2128,996
D8○Q16Central product of D8 and Q16324-D8oQ16128,2025
Q8○D16Central product of Q8 and D16644-Q8oD16128,2149

Groups of order 136

dρLabelID
C172C8The semidirect product of C17 and C8 acting via C8/C2=C41364-C17:2C8136,3

Groups of order 144

dρLabelID
D4.D9The non-split extension by D4 of D9 acting via D9/C9=C2724-D4.D9144,15
C9⋊Q16The semidirect product of C9 and Q16 acting via Q16/Q8=C21444-C9:Q16144,17
Q8.D9The non-split extension by Q8 of D9 acting via D9/C3=S31444-Q8.D9144,31
D42D9The semidirect product of D4 and D9 acting through Inn(D4)724-D4:2D9144,42
Q8×D9Direct product of Q8 and D9724-Q8xD9144,43
D12.S31st non-split extension by D12 of S3 acting via S3/C3=C2484-D12.S3144,59
C323Q162nd semidirect product of C32 and Q16 acting via Q16/C4=C22484-C3^2:3Q16144,62
C322SD16The semidirect product of C32 and SD16 acting via SD16/C2=D4244-C3^2:2SD16144,118
C32⋊Q16The semidirect product of C32 and Q16 acting via Q16/C2=D4484-C3^2:Q16144,119
C6.5S45th non-split extension by C6 of S4 acting via S4/A4=C2484-C6.5S4144,124
S3×SL2(𝔽3)Direct product of S3 and SL2(𝔽3); = SL2(ℤ/6ℤ)244-S3xSL(2,3)144,128
C62.C42nd non-split extension by C62 of C4 acting faithfully244-C6^2.C4144,135
S3×Dic6Direct product of S3 and Dic6484-S3xDic6144,137
D125S3The semidirect product of D12 and S3 acting through Inn(D12)484-D12:5S3144,138
D6.4D64th non-split extension by D6 of D6 acting via D6/S3=C2244-D6.4D6144,148

Groups of order 160

dρLabelID
C4.12D204th non-split extension by C4 of D20 acting via D20/D10=C2804-C4.12D20160,31
D8.D5The non-split extension by D8 of D5 acting via D5/C5=C2804-D8.D5160,34
C5⋊Q32The semidirect product of C5 and Q32 acting via Q32/Q16=C21604-C5:Q32160,36
Dic5.D41st non-split extension by Dic5 of D4 acting via D4/C2=C22804-Dic5.D4160,80
C8.D101st non-split extension by C8 of D10 acting via D10/C5=C22804-C8.D10160,130
D83D5The semidirect product of D8 and D5 acting through Inn(D8)804-D8:3D5160,133
SD16⋊D52nd semidirect product of SD16 and D5 acting via D5/C5=C2804-SD16:D5160,136
D5×Q16Direct product of D5 and Q16804-D5xQ16160,138
D4.9D104th non-split extension by D4 of D10 acting via D10/C10=C2804-D4.9D10160,172
2- 1+4⋊C5The semidirect product of 2- 1+4 and C5 acting faithfully324-ES-(2,2):C5160,199
D4.10D10The non-split extension by D4 of D10 acting through Inn(D4)804-D4.10D10160,225

Groups of order 168

dρLabelID
Dic3×D7Direct product of Dic3 and D7844-Dic3xD7168,12
S3×Dic7Direct product of S3 and Dic7844-S3xDic7168,13
C21⋊D41st semidirect product of C21 and D4 acting via D4/C2=C22844-C21:D4168,15
C21⋊Q8The semidirect product of C21 and Q8 acting via Q8/C2=C221684-C21:Q8168,18

Groups of order 176

dρLabelID
D4.D11The non-split extension by D4 of D11 acting via D11/C11=C2884-D4.D11176,15
C11⋊Q16The semidirect product of C11 and Q16 acting via Q16/Q8=C21764-C11:Q16176,17
D42D11The semidirect product of D4 and D11 acting through Inn(D4)884-D4:2D11176,32
Q8×D11Direct product of Q8 and D11884-Q8xD11176,33

Groups of order 192

dρLabelID
C24.8D48th non-split extension by C24 of D4 acting via D4/C2=C22964-C24.8D4192,55
C12.4D84th non-split extension by C12 of D8 acting via D8/C4=C22964-C12.4D8192,76
D16.S3The non-split extension by D16 of S3 acting via S3/C3=C2964-D16.S3192,79
C3⋊Q64The semidirect product of C3 and Q64 acting via Q64/Q32=C21924-C3:Q64192,81
Q8.14D124th non-split extension by Q8 of D12 acting via D12/D6=C2484-Q8.14D12192,385
C24.18D418th non-split extension by C24 of D4 acting via D4/C2=C22964-C24.18D4192,455
C16.D61st non-split extension by C16 of D6 acting via D6/C3=C22964-C16.D6192,468
D163S3The semidirect product of D16 and S3 acting through Inn(D16)964-D16:3S3192,471
SD32⋊S32nd semidirect product of SD32 and S3 acting via S3/C3=C2964-SD32:S3192,474
S3×Q32Direct product of S3 and Q32964-S3xQ32192,476
Q8.10D125th non-split extension by Q8 of D12 acting via D12/C12=C2964-Q8.10D12192,702
D8.9D64th non-split extension by D8 of D6 acting via D6/C6=C2964-D8.9D6192,754
C8.S42nd non-split extension by C8 of S4 acting via S4/A4=C2644-C8.S4192,962
D4.S42nd non-split extension by D4 of S4 acting via S4/A4=C2324-D4.S4192,989
D8.A4The non-split extension by D8 of A4 acting through Inn(D8)324-D8.A4192,1019
D4.13D123rd non-split extension by D4 of D12 acting through Inn(D4)964-D4.13D12192,1312
D8.10D6The non-split extension by D8 of D6 acting through Inn(D8)964-D8.10D6192,1330
D4.5S42nd non-split extension by D4 of S4 acting through Inn(D4)324-D4.5S4192,1486

Groups of order 200

dρLabelID
C25⋊C8The semidirect product of C25 and C8 acting via C8/C2=C42004-C25:C8200,3
C525C84th semidirect product of C52 and C8 acting via C8/C2=C4404-C5^2:5C8200,21
D5×Dic5Direct product of D5 and Dic5404-D5xDic5200,22
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

Groups of order 208

dρLabelID
D4.D13The non-split extension by D4 of D13 acting via D13/C13=C21044-D4.D13208,16
C13⋊Q16The semidirect product of C13 and Q16 acting via Q16/Q8=C22084-C13:Q16208,18
C13⋊M4(2)The semidirect product of C13 and M4(2) acting via M4(2)/C22=C41044-C13:M4(2)208,33
D42D13The semidirect product of D4 and D13 acting through Inn(D4)1044-D4:2D13208,40
Q8×D13Direct product of Q8 and D131044-Q8xD13208,41

Groups of order 216

dρLabelID
C9⋊Dic6The semidirect product of C9 and Dic6 acting via Dic6/Dic3=C2724-C9:Dic6216,26
Dic3×D9Direct product of Dic3 and D9724-Dic3xD9216,27
S3×Dic9Direct product of S3 and Dic9724-S3xDic9216,30
D6⋊D91st semidirect product of D6 and D9 acting via D9/C9=C2724-D6:D9216,31

Groups of order 224

dρLabelID
C4.12D284th non-split extension by C4 of D28 acting via D28/D14=C21124-C4.12D28224,30
D8.D7The non-split extension by D8 of D7 acting via D7/C7=C21124-D8.D7224,33
C7⋊Q32The semidirect product of C7 and Q32 acting via Q32/Q16=C22244-C7:Q32224,35
C8.D141st non-split extension by C8 of D14 acting via D14/C7=C221124-C8.D14224,104
D83D7The semidirect product of D8 and D7 acting through Inn(D8)1124-D8:3D7224,107
SD16⋊D72nd semidirect product of SD16 and D7 acting via D7/C7=C21124-SD16:D7224,110
D7×Q16Direct product of D7 and Q161124-D7xQ16224,112
D4.9D144th non-split extension by D4 of D14 acting via D14/C14=C21124-D4.9D14224,146
D4.10D14The non-split extension by D4 of D14 acting through Inn(D4)1124-D4.10D14224,186

Groups of order 232

dρLabelID
C29⋊C8The semidirect product of C29 and C8 acting via C8/C2=C42324-C29:C8232,3

Groups of order 240

dρLabelID
C6.D202nd non-split extension by C6 of D20 acting via D20/D10=C21204-C6.D20240,18
D12.D51st non-split extension by D12 of D5 acting via D5/C5=C21204-D12.D5240,20
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
D4.D15The non-split extension by D4 of D15 acting via D15/C15=C21204-D4.D15240,77
C157Q161st semidirect product of C15 and Q16 acting via Q16/Q8=C22404-C15:7Q16240,79
CSU2(𝔽5)Conformal special unitary group on 𝔽52; = C2.2S5484-CSU(2,5)240,89
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
D5×SL2(𝔽3)Direct product of D5 and SL2(𝔽3)404-D5xSL(2,3)240,109
D5×Dic6Direct product of D5 and Dic61204-D5xDic6240,125
D205S3The semidirect product of D20 and S3 acting through Inn(D20)1204-D20:5S3240,126
S3×Dic10Direct product of S3 and Dic101204-S3xDic10240,128
D125D5The semidirect product of D12 and D5 acting through Inn(D12)1204-D12:5D5240,133
C30.C2317th non-split extension by C30 of C23 acting via C23/C2=C221204-C30.C2^3240,141
D42D15The semidirect product of D4 and D15 acting through Inn(D4)1204-D4:2D15240,180
Q8×D15Direct product of Q8 and D151204-Q8xD15240,181

Groups of order 264

dρLabelID
Dic3×D11Direct product of Dic3 and D111324-Dic3xD11264,5
S3×Dic11Direct product of S3 and Dic111324-S3xDic11264,6
C33⋊D41st semidirect product of C33 and D4 acting via D4/C2=C221324-C33:D4264,8
C33⋊Q8The semidirect product of C33 and Q8 acting via Q8/C2=C222644-C33:Q8264,11

Groups of order 272

dρLabelID
D4.D17The non-split extension by D4 of D17 acting via D17/C17=C21364-D4.D17272,16
C17⋊Q16The semidirect product of C17 and Q16 acting via Q16/Q8=C22724-C17:Q16272,18
C17⋊M4(2)The semidirect product of C17 and M4(2) acting via M4(2)/C22=C41364-C17:M4(2)272,34
D42D17The semidirect product of D4 and D17 acting through Inn(D4)1364-D4:2D17272,41
Q8×D17Direct product of Q8 and D171364-Q8xD17272,42

Groups of order 280

dρLabelID
D7×Dic5Direct product of D7 and Dic51404-D7xDic5280,7
D5×Dic7Direct product of D5 and Dic71404-D5xDic7280,8
C35⋊D41st semidirect product of C35 and D4 acting via D4/C2=C221404-C35:D4280,10
C35⋊Q8The semidirect product of C35 and Q8 acting via Q8/C2=C222804-C35:Q8280,13

Groups of order 288

dρLabelID
C4.D363rd non-split extension by C4 of D36 acting via D36/D18=C21444-C4.D36288,30
D8.D9The non-split extension by D8 of D9 acting via D9/C9=C21444-D8.D9288,34
C9⋊Q32The semidirect product of C9 and Q32 acting via Q32/Q16=C22884-C9:Q32288,36
C8.D181st non-split extension by C8 of D18 acting via D18/C9=C221444-C8.D18288,119
D83D9The semidirect product of D8 and D9 acting through Inn(D8)1444-D8:3D9288,122
SD16⋊D92nd semidirect product of SD16 and D9 acting via D9/C9=C21444-SD16:D9288,125
Q16×D9Direct product of Q16 and D91444-Q16xD9288,127
D4.D183rd non-split extension by D4 of D18 acting via D18/C18=C21444-D4.D18288,159
C323SD322nd semidirect product of C32 and SD32 acting via SD32/C8=C22964-C3^2:3SD32288,196
C323Q322nd semidirect product of C32 and Q32 acting via Q32/C8=C22964-C3^2:3Q32288,199
C12.71D122nd non-split extension by C12 of D12 acting via D12/D6=C2484-C12.71D12288,209
C12.3S43rd non-split extension by C12 of S4 acting via S4/A4=C21444-C12.3S4288,338
D4.10D18The non-split extension by D4 of D18 acting through Inn(D4)1444-D4.10D18288,364
Dic3≀C2Wreath product of Dic3 by C2244-Dic3wrC2288,389
C3⋊Dic3.D49th non-split extension by C3⋊Dic3 of D4 acting via D4/C2=C22484-C3:Dic3.D4288,428
S3×Dic12Direct product of S3 and Dic12964-S3xDic12288,447
C24.3D63rd non-split extension by C24 of D6 acting via D6/C3=C22964-C24.3D6288,448
D247S3The semidirect product of D24 and S3 acting through Inn(D24)964-D24:7S3288,455
D12.29D64th non-split extension by D12 of D6 acting via D6/C6=C2484-D12.29D6288,479
S3×CSU2(𝔽3)Direct product of S3 and CSU2(𝔽3)484-S3xCSU(2,3)288,848
D6.S41st non-split extension by D6 of S4 acting via S4/A4=C2484-D6.S4288,849
C62.15D415th non-split extension by C62 of D4 acting faithfully484-C6^2.15D4288,887
C12.6S46th non-split extension by C12 of S4 acting via S4/A4=C2964-C12.6S4288,913
D12.A4The non-split extension by D12 of A4 acting through Inn(D12)484-D12.A4288,926
D12.34D6The non-split extension by D12 of D6 acting through Inn(D12)484-D12.34D6288,946

Groups of order 296

dρLabelID
C37⋊C8The semidirect product of C37 and C8 acting via C8/C2=C42964-C37:C8296,3

Groups of order 304

dρLabelID
D4.D19The non-split extension by D4 of D19 acting via D19/C19=C21524-D4.D19304,15
C19⋊Q16The semidirect product of C19 and Q16 acting via Q16/Q8=C23044-C19:Q16304,17
D42D19The semidirect product of D4 and D19 acting through Inn(D4)1524-D4:2D19304,32
Q8×D19Direct product of Q8 and D191524-Q8xD19304,33

Groups of order 312

dρLabelID
Dic3×D13Direct product of Dic3 and D131564-Dic3xD13312,15
S3×Dic13Direct product of S3 and Dic131564-S3xDic13312,16
C39⋊D41st semidirect product of C39 and D4 acting via D4/C2=C221564-C39:D4312,18
C39⋊Q8The semidirect product of C39 and Q8 acting via Q8/C2=C223124-C39:Q8312,21

Groups of order 320

dρLabelID
C40.8D48th non-split extension by C40 of D4 acting via D4/C2=C221604-C40.8D4320,54
C20.4D84th non-split extension by C20 of D8 acting via D8/C4=C221604-C20.4D8320,75
D16.D5The non-split extension by D16 of D5 acting via D5/C5=C21604-D16.D5320,78
C5⋊Q64The semidirect product of C5 and Q64 acting via Q64/Q32=C23204-C5:Q64320,80
C42.F51st non-split extension by C42 of F5 acting via F5/C5=C4804-C4^2.F5320,193
D4.9D204th non-split extension by D4 of D20 acting via D20/D10=C2804-D4.9D20320,453
C8.20D206th non-split extension by C8 of D20 acting via D20/D10=C21604-C8.20D20320,523
C16.D101st non-split extension by C16 of D10 acting via D10/C5=C221604-C16.D10320,536
D163D5The semidirect product of D16 and D5 acting through Inn(D16)1604-D16:3D5320,539
SD32⋊D52nd semidirect product of SD32 and D5 acting via D5/C5=C21604-SD32:D5320,542
D5×Q32Direct product of D5 and Q321604-D5xQ32320,544
D4.5D205th non-split extension by D4 of D20 acting via D20/C20=C21604-D4.5D20320,770
C40.31C2324th non-split extension by C40 of C23 acting via C23/C2=C221604-C40.31C2^3320,822
D4.13D203rd non-split extension by D4 of D20 acting through Inn(D4)1604-D4.13D20320,1425
D20.47D43rd non-split extension by D20 of D4 acting through Inn(D20)1604-D20.47D4320,1443
2- 1+4.D5The non-split extension by 2- 1+4 of D5 acting faithfully644-ES-(2,2).D5320,1581

Groups of order 328

dρLabelID
C412C8The semidirect product of C41 and C8 acting via C8/C2=C43284-C41:2C8328,3

Groups of order 336

dρLabelID
C6.D282nd non-split extension by C6 of D28 acting via D28/D14=C21684-C6.D28336,34
D12.D71st non-split extension by D12 of D7 acting via D7/C7=C21684-D12.D7336,36
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
D4.D21The non-split extension by D4 of D21 acting via D21/C21=C21684-D4.D21336,102
C217Q161st semidirect product of C21 and Q16 acting via Q16/Q8=C23364-C21:7Q16336,104
Q8.D21The non-split extension by Q8 of D21 acting via D21/C7=S31124-Q8.D21336,118
D7×SL2(𝔽3)Direct product of D7 and SL2(𝔽3)564-D7xSL(2,3)336,132
D7×Dic6Direct product of D7 and Dic61684-D7xDic6336,137
D285S3The semidirect product of D28 and S3 acting through Inn(D28)1684-D28:5S3336,138
S3×Dic14Direct product of S3 and Dic141684-S3xDic14336,140
D125D7The semidirect product of D12 and D7 acting through Inn(D12)1684-D12:5D7336,145
C42.C2317th non-split extension by C42 of C23 acting via C23/C2=C221684-C42.C2^3336,153
D42D21The semidirect product of D4 and D21 acting through Inn(D4)1684-D4:2D21336,199
Q8×D21Direct product of Q8 and D211684-Q8xD21336,200

Groups of order 352

dρLabelID
C44.47D44th non-split extension by C44 of D4 acting via D4/C22=C21764-C44.47D4352,30
D8.D11The non-split extension by D8 of D11 acting via D11/C11=C21764-D8.D11352,33
C11⋊Q32The semidirect product of C11 and Q32 acting via Q32/Q16=C23524-C11:Q32352,35
C8.D221st non-split extension by C8 of D22 acting via D22/C11=C221764-C8.D22352,104
D83D11The semidirect product of D8 and D11 acting through Inn(D8)1764-D8:3D11352,107
D4.D224th non-split extension by D4 of D22 acting via D22/D11=C21764-D4.D22352,110
Q16×D11Direct product of Q16 and D111764-Q16xD11352,112
D4.9D224th non-split extension by D4 of D22 acting via D22/C22=C21764-D4.9D22352,146
D4.10D22The non-split extension by D4 of D22 acting through Inn(D4)1764-D4.10D22352,185

Groups of order 360

dρLabelID
C45⋊Q8The semidirect product of C45 and Q8 acting via Q8/C2=C223604-C45:Q8360,7
D9×Dic5Direct product of D9 and Dic51804-D9xDic5360,8
D5×Dic9Direct product of D5 and Dic91804-D5xDic9360,11
C45⋊D42nd semidirect product of C45 and D4 acting via D4/C2=C221804-C45:D4360,12
(C3×C6).F5The non-split extension by C3×C6 of F5 acting via F5/C5=C41204-(C3xC6).F5360,57
Dic3×D15Direct product of Dic3 and D151204-Dic3xD15360,77
S3×Dic15Direct product of S3 and Dic151204-S3xDic15360,78
D6⋊D151st semidirect product of D6 and D15 acting via D15/C15=C21204-D6:D15360,80
C3⋊Dic30The semidirect product of C3 and Dic30 acting via Dic30/Dic15=C21204-C3:Dic30360,83

Groups of order 368

dρLabelID
D4.D23The non-split extension by D4 of D23 acting via D23/C23=C21844-D4.D23368,15
C23⋊Q16The semidirect product of C23 and Q16 acting via Q16/Q8=C23684-C23:Q16368,17
D42D23The semidirect product of D4 and D23 acting through Inn(D4)1844-D4:2D23368,32
Q8×D23Direct product of Q8 and D231844-Q8xD23368,33

Groups of order 392

dρLabelID
C722C8The semidirect product of C72 and C8 acting via C8/C2=C4564-C7^2:2C8392,17
D7×Dic7Direct product of D7 and Dic7564-D7xDic7392,18
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

Groups of order 400

dρLabelID
D4.D25The non-split extension by D4 of D25 acting via D25/C25=C22004-D4.D25400,15
C25⋊Q16The semidirect product of C25 and Q16 acting via Q16/Q8=C24004-C25:Q16400,17
C25⋊M4(2)The semidirect product of C25 and M4(2) acting via M4(2)/C22=C42004-C25:M4(2)400,33
D42D25The semidirect product of D4 and D25 acting through Inn(D4)2004-D4:2D25400,40
Q8×D25Direct product of Q8 and D252004-Q8xD25400,41
C523SD162nd semidirect product of C52 and SD16 acting via SD16/C4=C22804-C5^2:3SD16400,67
C523Q162nd semidirect product of C52 and Q16 acting via Q16/C4=C22804-C5^2:3Q16400,70
C52⋊SD16The semidirect product of C52 and SD16 acting via SD16/C2=D4404-C5^2:SD16400,132
C52⋊Q16The semidirect product of C52 and Q16 acting via Q16/C2=D4804-C5^2:Q16400,133
C5214M4(2)4th semidirect product of C52 and M4(2) acting via M4(2)/C22=C4404-C5^2:14M4(2)400,161
D5×Dic10Direct product of D5 and Dic10804-D5xDic10400,163
D205D5The semidirect product of D20 and D5 acting through Inn(D20)804-D20:5D5400,164
D10.4D104th non-split extension by D10 of D10 acting via D10/D5=C2404-D10.4D10400,174

Groups of order 408

dρLabelID
Dic3×D17Direct product of Dic3 and D172044-Dic3xD17408,7
S3×Dic17Direct product of S3 and Dic172044-S3xDic17408,8
C51⋊D41st semidirect product of C51 and D4 acting via D4/C2=C222044-C51:D4408,10
C51⋊Q8The semidirect product of C51 and Q8 acting via Q8/C2=C224084-C51:Q8408,13

Groups of order 416

dρLabelID
C4.12D524th non-split extension by C4 of D52 acting via D52/D26=C22084-C4.12D52416,31
D8.D13The non-split extension by D8 of D13 acting via D13/C13=C22084-D8.D13416,34
C13⋊Q32The semidirect product of C13 and Q32 acting via Q32/Q16=C24164-C13:Q32416,36
Dic13.D41st non-split extension by Dic13 of D4 acting via D4/C2=C222084-Dic13.D4416,80
C8.D261st non-split extension by C8 of D26 acting via D26/C13=C222084-C8.D26416,130
D83D13The semidirect product of D8 and D13 acting through Inn(D8)2084-D8:3D13416,133
D4.D264th non-split extension by D4 of D26 acting via D26/D13=C22084-D4.D26416,136
Q16×D13Direct product of Q16 and D132084-Q16xD13416,138
D4.9D264th non-split extension by D4 of D26 acting via D26/C26=C22084-D4.9D26416,172
D4.10D26The non-split extension by D4 of D26 acting through Inn(D4)2084-D4.10D26416,224

Groups of order 424

dρLabelID
C53⋊C8The semidirect product of C53 and C8 acting via C8/C2=C44244-C53:C8424,3

Groups of order 432

dρLabelID
D4.D27The non-split extension by D4 of D27 acting via D27/C27=C22164-D4.D27432,15
C27⋊Q16The semidirect product of C27 and Q16 acting via Q16/Q8=C24324-C27:Q16432,17
Q8.D27The non-split extension by Q8 of D27 acting via D27/C9=S34324-Q8.D27432,37
D42D27The semidirect product of D4 and D27 acting through Inn(D4)2164-D4:2D27432,48
Q8×D27Direct product of Q8 and D272164-Q8xD27432,49
D36.S31st non-split extension by D36 of S3 acting via S3/C3=C21444-D36.S3432,62
C3⋊Dic36The semidirect product of C3 and Dic36 acting via Dic36/Dic18=C21444-C3:Dic36432,65
C36.D612nd non-split extension by C36 of D6 acting via D6/C3=C221444-C36.D6432,71
C9⋊Dic12The semidirect product of C9 and Dic12 acting via Dic12/Dic6=C21444-C9:Dic12432,75
C18.5S45th non-split extension by C18 of S4 acting via S4/A4=C21444-C18.5S4432,252
D9×SL2(𝔽3)Direct product of D9 and SL2(𝔽3)724-D9xSL(2,3)432,264
D9×Dic6Direct product of D9 and Dic61444-D9xDic6432,280
S3×Dic18Direct product of S3 and Dic181444-S3xDic18432,284
D125D9The semidirect product of D12 and D9 acting through Inn(D12)1444-D12:5D9432,285
D365S3The semidirect product of D36 and S3 acting through Inn(D36)1444-D36:5S3432,288
D18.4D64th non-split extension by D18 of D6 acting via D6/S3=C2724-D18.4D6432,310

Groups of order 440

dρLabelID
Dic5×D11Direct product of Dic5 and D112204-Dic5xD11440,17
D5×Dic11Direct product of D5 and Dic112204-D5xDic11440,18
C55⋊D41st semidirect product of C55 and D4 acting via D4/C2=C222204-C55:D4440,20
C55⋊Q8The semidirect product of C55 and Q8 acting via Q8/C2=C224404-C55:Q8440,23

Groups of order 448

dρLabelID
C56.8D48th non-split extension by C56 of D4 acting via D4/C2=C222244-C56.8D4448,53
C28.4D84th non-split extension by C28 of D8 acting via D8/C4=C222244-C28.4D8448,74
D16.D7The non-split extension by D16 of D7 acting via D7/C7=C22244-D16.D7448,77
C7⋊Q64The semidirect product of C7 and Q64 acting via Q64/Q32=C24484-C7:Q64448,79
D4.9D284th non-split extension by D4 of D28 acting via D28/D14=C21124-D4.9D28448,360
C8.20D286th non-split extension by C8 of D28 acting via D28/D14=C22244-C8.20D28448,430
C16.D141st non-split extension by C16 of D14 acting via D14/C7=C222244-C16.D14448,443
D163D7The semidirect product of D16 and D7 acting through Inn(D16)2244-D16:3D7448,446
SD32⋊D72nd semidirect product of SD32 and D7 acting via D7/C7=C22244-SD32:D7448,449
D7×Q32Direct product of D7 and Q322244-D7xQ32448,451
D4.5D285th non-split extension by D4 of D28 acting via D28/C28=C22244-D4.5D28448,677
C56.31C2324th non-split extension by C56 of C23 acting via C23/C2=C222244-C56.31C2^3448,729
D4.13D283rd non-split extension by D4 of D28 acting through Inn(D4)2244-D4.13D28448,1206
D8.10D14The non-split extension by D8 of D14 acting through Inn(D8)2244-D8.10D14448,1224

Groups of order 456

dρLabelID
Dic3×D19Direct product of Dic3 and D192284-Dic3xD19456,12
S3×Dic19Direct product of S3 and Dic192284-S3xDic19456,13
C57⋊D41st semidirect product of C57 and D4 acting via D4/C2=C222284-C57:D4456,15
C57⋊Q8The semidirect product of C57 and Q8 acting via Q8/C2=C224564-C57:Q8456,18

Groups of order 464

dρLabelID
D4.D29The non-split extension by D4 of D29 acting via D29/C29=C22324-D4.D29464,16
C29⋊Q16The semidirect product of C29 and Q16 acting via Q16/Q8=C24644-C29:Q16464,18
C29⋊M4(2)The semidirect product of C29 and M4(2) acting via M4(2)/C22=C42324-C29:M4(2)464,33
D42D29The semidirect product of D4 and D29 acting through Inn(D4)2324-D4:2D29464,40
Q8×D29Direct product of Q8 and D292324-Q8xD29464,41

Groups of order 480

dρLabelID
D40.S31st non-split extension by D40 of S3 acting via S3/C3=C22404-D40.S3480,18
D24.D51st non-split extension by D24 of D5 acting via D5/C5=C22404-D24.D5480,20
C3⋊Dic40The semidirect product of C3 and Dic40 acting via Dic40/Dic20=C24804-C3:Dic40480,23
C5⋊Dic24The semidirect product of C5 and Dic24 acting via Dic24/Dic12=C24804-C5:Dic24480,24
C60.31D431st non-split extension by C60 of D4 acting via D4/C2=C222404-C60.31D4480,39
C4.D604th non-split extension by C4 of D60 acting via D60/D30=C22404-C4.D60480,184
D8.D15The non-split extension by D8 of D15 acting via D15/C15=C22404-D8.D15480,187
C157Q321st semidirect product of C15 and Q32 acting via Q32/Q16=C24804-C15:7Q32480,189
D5×Dic12Direct product of D5 and Dic122404-D5xDic12480,335
Dic60⋊C214th semidirect product of Dic60 and C2 acting faithfully2404-Dic60:C2480,336
S3×Dic20Direct product of S3 and Dic202404-S3xDic20480,338
D247D5The semidirect product of D24 and D5 acting through Inn(D24)2404-D24:7D5480,346
D407S3The semidirect product of D40 and S3 acting through Inn(D40)2404-D40:7S3480,349
C40.2D62nd non-split extension by C40 of D6 acting via D6/C3=C222404-C40.2D6480,350
C60.63D463rd non-split extension by C60 of D4 acting via D4/C2=C222404-C60.63D4480,389
D12.33D104th non-split extension by D12 of D10 acting via D10/C10=C22404-D12.33D10480,398
C8.D301st non-split extension by C8 of D30 acting via D30/C15=C222404-C8.D30480,874
D83D15The semidirect product of D8 and D15 acting through Inn(D8)2404-D8:3D15480,877
SD16⋊D152nd semidirect product of SD16 and D15 acting via D15/C15=C22404-SD16:D15480,880
Q16×D15Direct product of Q16 and D152404-Q16xD15480,882
D4.9D304th non-split extension by D4 of D30 acting via D30/C30=C22404-D4.9D30480,916
C22.S5The non-split extension by C22 of S5 acting via S5/A5=C2484-C2^2.S5480,953
D4.A5The non-split extension by D4 of A5 acting through Inn(D4)484-D4.A5480,957
D5×CSU2(𝔽3)Direct product of D5 and CSU2(𝔽3)804-D5xCSU(2,3)480,971
D10.1S41st non-split extension by D10 of S4 acting via S4/A4=C2804-D10.1S4480,972
C20.2S42nd non-split extension by C20 of S4 acting via S4/A4=C21604-C20.2S4480,1030
D20.A4The non-split extension by D20 of A4 acting through Inn(D20)804-D20.A4480,1043
D20.39D6The non-split extension by D20 of D6 acting through Inn(D20)2404-D20.39D6480,1077
D4.10D30The non-split extension by D4 of D30 acting through Inn(D4)2404-D4.10D30480,1177

Groups of order 488

dρLabelID
C61⋊C8The semidirect product of C61 and C8 acting via C8/C2=C44884-C61:C8488,3

Groups of order 496

dρLabelID
D4.D31The non-split extension by D4 of D31 acting via D31/C31=C22484-D4.D31496,15
C31⋊Q16The semidirect product of C31 and Q16 acting via Q16/Q8=C24964-C31:Q16496,17
D42D31The semidirect product of D4 and D31 acting through Inn(D4)2484-D4:2D31496,32
Q8×D31Direct product of Q8 and D312484-Q8xD31496,33

Complex of dimension 4  (ρ=4)

Groups of order 60

dρLabelID
C3×F5Direct product of C3 and F5154C3xF560,6
C3⋊F5The semidirect product of C3 and F5 acting via F5/D5=C2154C3:F560,7

Groups of order 64

dρLabelID
C4.9C421st central stem extension by C4 of C42164C4.9C4^264,18
C4.10C422nd central stem extension by C4 of C42164C4.10C4^264,19
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2164M4(2):4C464,25
C16⋊C42nd semidirect product of C16 and C4 acting faithfully164C16:C464,28
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4164C2^3.C864,30
C23.D42nd non-split extension by C23 of D4 acting faithfully164C2^3.D464,33
C423C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
C42.C42nd non-split extension by C42 of C4 acting faithfully164C4^2.C464,36
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22164C8.Q864,46
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22164C2^3.C2^364,91
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2164M4(2).8C2^264,94
C42⋊C221st semidirect product of C42 and C22 acting faithfully164C4^2:C2^264,102
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2164M4(2).C464,111
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2164C8.26D464,125
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
C23.7D47th non-split extension by C23 of D4 acting faithfully164C2^3.7D464,139
D4.3D43rd non-split extension by D4 of D4 acting via D4/C4=C2164D4.3D464,152
Q8○M4(2)Central product of Q8 and M4(2)164Q8oM4(2)64,249
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2164D8:C2^264,256
D4○SD16Central product of D4 and SD16164D4oSD1664,258
C2.C256th central stem extension by C2 of C25164C2.C2^564,266

Groups of order 80

dρLabelID
C5⋊C16The semidirect product of C5 and C16 acting via C16/C4=C4804C5:C1680,3
D5⋊C8The semidirect product of D5 and C8 acting via C8/C4=C2404D5:C880,28
C4.F5The non-split extension by C4 of F5 acting via F5/D5=C2404C4.F580,29
C4×F5Direct product of C4 and F5204C4xF580,30
C4⋊F5The semidirect product of C4 and F5 acting via F5/D5=C2204C4:F580,31

Groups of order 96

dρLabelID
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.6D696,13
C12.53D410th non-split extension by C12 of D4 acting via D4/C22=C2484C12.53D496,29
D12⋊C44th semidirect product of D12 and C4 acting via C4/C2=C2244D12:C496,32
C12.D48th non-split extension by C12 of D4 acting via D4/C2=C22244C12.D496,40
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.7D696,41
C12.10D410th non-split extension by C12 of D4 acting via D4/C2=C22484C12.10D496,43
Q83Dic32nd semidirect product of Q8 and Dic3 acting via Dic3/C6=C2244Q8:3Dic396,44
C3×C23⋊C4Direct product of C3 and C23⋊C4244C3xC2^3:C496,49
C3×C4.D4Direct product of C3 and C4.D4244C3xC4.D496,50
C3×C4.10D4Direct product of C3 and C4.10D4484C3xC4.10D496,51
S3×M4(2)Direct product of S3 and M4(2)244S3xM4(2)96,113
D12.C4The non-split extension by D12 of C4 acting via C4/C2=C2484D12.C496,114
D8⋊S32nd semidirect product of D8 and S3 acting via S3/C3=C2244D8:S396,118
S3×SD16Direct product of S3 and SD16244S3xSD1696,120
Q8.7D62nd non-split extension by Q8 of D6 acting via D6/S3=C2484Q8.7D696,123
Q16⋊S32nd semidirect product of Q16 and S3 acting via S3/C3=C2484Q16:S396,125
D126C224th semidirect product of D12 and C22 acting via C22/C2=C2244D12:6C2^296,139
Q8.11D61st non-split extension by Q8 of D6 acting via D6/C6=C2484Q8.11D696,149
D4.Dic3The non-split extension by D4 of Dic3 acting through Inn(D4)484D4.Dic396,155
Q8.13D63rd non-split extension by Q8 of D6 acting via D6/C6=C2484Q8.13D696,157
C3×C8⋊C22Direct product of C3 and C8⋊C22244C3xC8:C2^296,183
C3×C8.C22Direct product of C3 and C8.C22484C3xC8.C2^296,184
D46D62nd semidirect product of D4 and D6 acting through Inn(D4)244D4:6D696,211
Q8.15D61st non-split extension by Q8 of D6 acting through Inn(Q8)484Q8.15D696,214
S3×C4○D4Direct product of S3 and C4○D4244S3xC4oD496,215
C3×2+ 1+4Direct product of C3 and 2+ 1+4244C3xES+(2,2)96,224
C3×2- 1+4Direct product of C3 and 2- 1+4484C3xES-(2,2)96,225

Groups of order 100

dρLabelID
C5×F5Direct product of C5 and F5204C5xF5100,9
D5.D5The non-split extension by D5 of D5 acting via D5/C5=C2204D5.D5100,10

Groups of order 108

dρLabelID
C3×C32⋊C4Direct product of C3 and C32⋊C4124C3xC3^2:C4108,36
C33⋊C42nd semidirect product of C33 and C4 acting faithfully124C3^3:C4108,37
C3×S32Direct product of C3, S3 and S3124C3xS3^2108,38
C324D6The semidirect product of C32 and D6 acting via D6/C3=C22124C3^2:4D6108,40

Groups of order 120

dρLabelID
C3×C5⋊C8Direct product of C3 and C5⋊C81204C3xC5:C8120,6
C15⋊C81st semidirect product of C15 and C8 acting via C8/C2=C41204C15:C8120,7
C6×F5Direct product of C6 and F5304C6xF5120,40
C2×C3⋊F5Direct product of C2 and C3⋊F5304C2xC3:F5120,41

Groups of order 128

dρLabelID
C24.C82nd non-split extension by C24 of C8 acting via C8/C2=C4164C2^4.C8128,52
C23.1M4(2)1st non-split extension by C23 of M4(2) acting via M4(2)/C4=C4324C2^3.1M4(2)128,53
C42.C81st non-split extension by C42 of C8 acting via C8/C2=C4164C4^2.C8128,59
C22⋊C4.C8The non-split extension by C22⋊C4 of C8 acting via C8/C2=C4324C2^2:C4.C8128,60
C8.32D89th non-split extension by C8 of D8 acting via D8/D4=C2164C8.32D8128,68
C8.29D86th non-split extension by C8 of D8 acting via D8/D4=C2164C8.29D8128,91
C8.1Q161st non-split extension by C8 of Q16 acting via Q16/C4=C22324C8.1Q16128,98
C16.C81st non-split extension by C16 of C8 acting via C8/C2=C4324C16.C8128,101
M4(2).C82nd non-split extension by M4(2) of C8 acting via C8/C4=C2324M4(2).C8128,110
C23.9D82nd non-split extension by C23 of D8 acting via D8/C4=C22324C2^3.9D8128,116
C8.13C427th non-split extension by C8 of C42 acting via C42/C2×C4=C2324C8.13C4^2128,117
M5(2).C42nd non-split extension by M5(2) of C4 acting via C4/C2=C2324M5(2).C4128,120
C8.4C424th non-split extension by C8 of C42 acting via C42/C22=C22324C8.4C4^2128,121
C23.2C422nd non-split extension by C23 of C42 acting via C42/C4=C4324C2^3.2C4^2128,123
C23.3C423rd non-split extension by C23 of C42 acting via C42/C4=C4324C2^3.3C4^2128,124
(C22×C8)⋊C44th semidirect product of C22×C8 and C4 acting faithfully324(C2^2xC8):C4128,127
C32⋊C42nd semidirect product of C32 and C4 acting faithfully324C32:C4128,130
C23.C16The non-split extension by C23 of C16 acting via C16/C4=C4324C2^3.C16128,132
C42.2D42nd non-split extension by C42 of D4 acting faithfully164C4^2.2D4128,135
C42.3D43rd non-split extension by C42 of D4 acting faithfully164C4^2.3D4128,136
(C4×C8)⋊6C46th semidirect product of C4×C8 and C4 acting faithfully164(C4xC8):6C4128,141
(C4×C8).C46th non-split extension by C4×C8 of C4 acting faithfully164(C4xC8).C4128,142
(C4×C8)⋊C43rd semidirect product of C4×C8 and C4 acting faithfully324(C4xC8):C4128,146
D163C42nd semidirect product of D16 and C4 acting via C4/C2=C2324D16:3C4128,150
C8.Q162nd non-split extension by C8 of Q16 acting via Q16/C4=C22324C8.Q16128,158
C8.16C4210th non-split extension by C8 of C42 acting via C42/C2×C4=C2324C8.16C4^2128,479
C23.5C425th non-split extension by C23 of C42 acting via C42/C4=C4324C2^3.5C4^2128,489
2+ 1+4.2C4The non-split extension by 2+ 1+4 of C4 acting via C4/C2=C2324ES+(2,2).2C4128,523
2+ 1+44C43rd semidirect product of 2+ 1+4 and C4 acting via C4/C2=C2324ES+(2,2):4C4128,526
(C2×D4).24Q85th non-split extension by C2×D4 of Q8 acting via Q8/C4=C2324(C2xD4).24Q8128,544
(C2×C8).103D471st non-split extension by C2×C8 of D4 acting via D4/C2=C22324(C2xC8).103D4128,545
C8○D4⋊C41st semidirect product of C8○D4 and C4 acting via C4/C2=C2324C8oD4:C4128,546
(C2×C42)⋊C48th semidirect product of C2×C42 and C4 acting faithfully164(C2xC4^2):C4128,559
C8.(C4⋊C4)4th non-split extension by C8 of C4⋊C4 acting via C4⋊C4/C22=C22324C8.(C4:C4)128,565
C8⋊C417C412nd semidirect product of C8⋊C4 and C4 acting via C4/C2=C2164C8:C4:17C4128,573
M4(2).40D44th non-split extension by M4(2) of D4 acting via D4/C22=C2324M4(2).40D4128,590
M4(2).41D45th non-split extension by M4(2) of D4 acting via D4/C22=C2164M4(2).41D4128,593
(C2×D4).Q89th non-split extension by C2×D4 of Q8 acting via Q8/C2=C22324(C2xD4).Q8128,600
M4(2).44D48th non-split extension by M4(2) of D4 acting via D4/C22=C2324M4(2).44D4128,613
M4(2)⋊19D46th semidirect product of M4(2) and D4 acting via D4/C22=C2164M4(2):19D4128,616
(C2×C8)⋊D43rd semidirect product of C2×C8 and D4 acting faithfully164(C2xC8):D4128,623
C42.426D459th non-split extension by C42 of D4 acting via D4/C22=C2164C4^2.426D4128,638
C42.427D460th non-split extension by C42 of D4 acting via D4/C22=C2164C4^2.427D4128,664
M4(2).27D48th non-split extension by M4(2) of D4 acting via D4/C4=C2324M4(2).27D4128,685
M4(2).30D411st non-split extension by M4(2) of D4 acting via D4/C4=C2324M4(2).30D4128,708
C422D42nd semidirect product of C42 and D4 acting faithfully164C4^2:2D4128,742
(C2×C8).2D42nd non-split extension by C2×C8 of D4 acting faithfully324(C2xC8).2D4128,749
C42.8D48th non-split extension by C42 of D4 acting faithfully164C4^2.8D4128,763
C42.131D4113rd non-split extension by C42 of D4 acting via D4/C2=C22164C4^2.131D4128,782
C22⋊C4.7D45th non-split extension by C22⋊C4 of D4 acting via D4/C2=C22324C2^2:C4.7D4128,785
C42.9D49th non-split extension by C42 of D4 acting faithfully324C4^2.9D4128,812
C24.11Q810th non-split extension by C24 of Q8 acting via Q8/C2=C22164C2^4.11Q8128,823
C42.10D410th non-split extension by C42 of D4 acting faithfully324C4^2.10D4128,830
C42.32Q832nd non-split extension by C42 of Q8 acting via Q8/C2=C22164C4^2.32Q8128,834
C22⋊C4.Q81st non-split extension by C22⋊C4 of Q8 acting via Q8/C2=C22324C2^2:C4.Q8128,835
C8.23C424th central extension by C8 of C42324C8.23C4^2128,842
M5(2).19C226th non-split extension by M5(2) of C22 acting via C22/C2=C2324M5(2).19C2^2128,847
M5(2)⋊12C228th semidirect product of M5(2) and C22 acting via C22/C2=C2324M5(2):12C2^2128,849
C4○C2≀C4Central product of C4 and C2≀C4164C4oC2wrC4128,852
C4⋊Q829C424th semidirect product of C4⋊Q8 and C4 acting via C4/C2=C2164C4:Q8:29C4128,858
(C2×D4).135D497th non-split extension by C2×D4 of D4 acting via D4/C2=C22164(C2xD4).135D4128,864
C23.20SD1610th non-split extension by C23 of SD16 acting via SD16/C4=C22324C2^3.20SD16128,875
C23.13D86th non-split extension by C23 of D8 acting via D8/C4=C22324C2^3.13D8128,877
C23.21SD1611st non-split extension by C23 of SD16 acting via SD16/C4=C22324C2^3.21SD16128,880
M4(2).1C81st non-split extension by M4(2) of C8 acting via C8/C4=C2324M4(2).1C8128,885
M5(2)⋊3C43rd semidirect product of M5(2) and C4 acting via C4/C2=C2324M5(2):3C4128,887
M5(2).1C41st non-split extension by M5(2) of C4 acting via C4/C2=C2324M5(2).1C4128,893
C8.5M4(2)5th non-split extension by C8 of M4(2) acting via M4(2)/C4=C22164C8.5M4(2)128,897
C8.19M4(2)7th non-split extension by C8 of M4(2) acting via M4(2)/C2×C4=C2324C8.19M4(2)128,898
D8.C8The non-split extension by D8 of C8 acting via C8/C4=C2324D8.C8128,903
D165C44th semidirect product of D16 and C4 acting via C4/C2=C2324D16:5C4128,911
Q16.D42nd non-split extension by Q16 of D4 acting via D4/C2=C22324Q16.D4128,925
D8.3D43rd non-split extension by D8 of D4 acting via D4/C2=C22324D8.3D4128,926
C424D44th semidirect product of C42 and D4 acting faithfully164C4^2:4D4128,929
C42.13D413rd non-split extension by C42 of D4 acting faithfully164C4^2.13D4128,930
C42.17D417th non-split extension by C42 of D4 acting faithfully164C4^2.17D4128,936
C8.3D83rd non-split extension by C8 of D8 acting via D8/C4=C22324C8.3D8128,944
D4.5D85th non-split extension by D4 of D8 acting via D8/C8=C2324D4.5D8128,955
D83Q83rd semidirect product of D8 and Q8 acting via Q8/C4=C2164D8:3Q8128,962
D8.2Q82nd non-split extension by D8 of Q8 acting via Q8/C4=C2324D8.2Q8128,963
2- 1+45C44th semidirect product of 2- 1+4 and C4 acting via C4/C2=C2164ES-(2,2):5C4128,1633
M4(2).29C2311st non-split extension by M4(2) of C23 acting via C23/C22=C2324M4(2).29C2^3128,1648
C42.283C23144th non-split extension by C42 of C23 acting via C23/C2=C22324C4^2.283C2^3128,1687
M4(2).51D41st non-split extension by M4(2) of D4 acting through Inn(M4(2))164M4(2).51D4128,1688
M4(2)○D8Central product of M4(2) and D8324M4(2)oD8128,1689
C42.313C23174th non-split extension by C42 of C23 acting via C23/C2=C22164C4^2.313C2^3128,1750
C23.7C247th non-split extension by C23 of C24 acting via C24/C22=C22164C2^3.7C2^4128,1757
M4(2).10C2310th non-split extension by M4(2) of C23 acting via C23/C2=C22324M4(2).10C2^3128,1799
D8○SD16Central product of D8 and SD16324D8oSD16128,2022
D86D45th semidirect product of D8 and D4 acting via D4/C4=C2164D8:6D4128,2023
Q8○M5(2)Central product of Q8 and M5(2)324Q8oM5(2)128,2139
D16⋊C224th semidirect product of D16 and C22 acting via C22/C2=C2324D16:C2^2128,2146
D4○SD32Central product of D4 and SD32324D4oSD32128,2148
C4.22C254th central extension by C4 of C25324C4.22C2^5128,2305
C8.C246th non-split extension by C8 of C24 acting via C24/C22=C22324C8.C2^4128,2316

Groups of order 140

dρLabelID
C7×F5Direct product of C7 and F5354C7xF5140,5
C7⋊F5The semidirect product of C7 and F5 acting via F5/D5=C2354C7:F5140,6

Groups of order 144

dρLabelID
C322C16The semidirect product of C32 and C16 acting via C16/C4=C4484C3^2:2C16144,51
S3×C3⋊C8Direct product of S3 and C3⋊C8484S3xC3:C8144,52
C12.29D63rd non-split extension by C12 of D6 acting via D6/S3=C2244C12.29D6144,53
D6.Dic3The non-split extension by D6 of Dic3 acting via Dic3/C6=C2484D6.Dic3144,54
C12.31D65th non-split extension by C12 of D6 acting via D6/S3=C2244C12.31D6144,55
C322D81st semidirect product of C32 and D8 acting via D8/C4=C22484C3^2:2D8144,56
Dic6⋊S32nd semidirect product of Dic6 and S3 acting via S3/C3=C2484Dic6:S3144,58
C322Q161st semidirect product of C32 and Q16 acting via Q16/C4=C22484C3^2:2Q16144,61
C3×D4⋊S3Direct product of C3 and D4⋊S3244C3xD4:S3144,80
C3×D4.S3Direct product of C3 and D4.S3244C3xD4.S3144,81
C3×Q82S3Direct product of C3 and Q82S3484C3xQ8:2S3144,82
C3×C3⋊Q16Direct product of C3 and C3⋊Q16484C3xC3:Q16144,83
C3⋊S3.Q8The non-split extension by C3⋊S3 of Q8 acting via Q8/C2=C22244C3:S3.Q8144,116
C32⋊D8The semidirect product of C32 and D8 acting via D8/C2=D4244C3^2:D8144,117
C3⋊S33C82nd semidirect product of C3⋊S3 and C8 acting via C8/C4=C2244C3:S3:3C8144,130
C32⋊M4(2)The semidirect product of C32 and M4(2) acting via M4(2)/C4=C4244C3^2:M4(2)144,131
C4×C32⋊C4Direct product of C4 and C32⋊C4244C4xC3^2:C4144,132
C4⋊(C32⋊C4)The semidirect product of C4 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2244C4:(C3^2:C4)144,133
D12⋊S33rd semidirect product of D12 and S3 acting via S3/C3=C2244D12:S3144,139
Dic3.D62nd non-split extension by Dic3 of D6 acting via D6/S3=C2244Dic3.D6144,140
D6.D61st non-split extension by D6 of D6 acting via D6/C6=C2244D6.D6144,141
C4×S32Direct product of C4, S3 and S3244C4xS3^2144,143
D6⋊D62nd semidirect product of D6 and D6 acting via D6/S3=C2244D6:D6144,145
D6.3D63rd non-split extension by D6 of D6 acting via D6/S3=C2244D6.3D6144,147
S3×C3⋊D4Direct product of S3 and C3⋊D4244S3xC3:D4144,153
C3×S3×D4Direct product of C3, S3 and D4244C3xS3xD4144,162
C3×D42S3Direct product of C3 and D42S3244C3xD4:2S3144,163
C3×S3×Q8Direct product of C3, S3 and Q8484C3xS3xQ8144,164
C3×Q83S3Direct product of C3 and Q83S3484C3xQ8:3S3144,165

Groups of order 156

dρLabelID
C3×C13⋊C4Direct product of C3 and C13⋊C4394C3xC13:C4156,9
C39⋊C41st semidirect product of C39 and C4 acting faithfully394C39:C4156,10

Groups of order 160

dρLabelID
C5⋊C32The semidirect product of C5 and C32 acting via C32/C8=C41604C5:C32160,3
C23.1D101st non-split extension by C23 of D10 acting via D10/C5=C22404C2^3.1D10160,13
C20.53D410th non-split extension by C20 of D4 acting via D4/C22=C2804C20.53D4160,29
D207C44th semidirect product of D20 and C4 acting via C4/C2=C2404D20:7C4160,32
C20.D48th non-split extension by C20 of D4 acting via D4/C2=C22404C20.D4160,40
C23⋊Dic5The semidirect product of C23 and Dic5 acting via Dic5/C5=C4404C2^3:Dic5160,41
C20.10D410th non-split extension by C20 of D4 acting via D4/C2=C22804C20.10D4160,43
D42Dic52nd semidirect product of D4 and Dic5 acting via Dic5/C10=C2404D4:2Dic5160,44
C5×C23⋊C4Direct product of C5 and C23⋊C4404C5xC2^3:C4160,49
C5×C4.D4Direct product of C5 and C4.D4404C5xC4.D4160,50
C5×C4.10D4Direct product of C5 and C4.10D4804C5xC4.10D4160,51
D5⋊C16The semidirect product of D5 and C16 acting via C16/C8=C2804D5:C16160,64
C8.F53rd non-split extension by C8 of F5 acting via F5/D5=C2804C8.F5160,65
C8×F5Direct product of C8 and F5404C8xF5160,66
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
D5.D8The non-split extension by D5 of D8 acting via D8/C8=C2404D5.D8160,69
C40.C42nd non-split extension by C40 of C4 acting faithfully804C40.C4160,70
D10.Q82nd non-split extension by D10 of Q8 acting via Q8/C4=C2804D10.Q8160,71
C20.C81st non-split extension by C20 of C8 acting via C8/C2=C4804C20.C8160,73
C23⋊F5The semidirect product of C23 and F5 acting via F5/C5=C4404C2^3:F5160,86
C23.F5The non-split extension by C23 of F5 acting via F5/C5=C4404C2^3.F5160,88
D5×M4(2)Direct product of D5 and M4(2)404D5xM4(2)160,127
D20.2C4The non-split extension by D20 of C4 acting via C4/C2=C2804D20.2C4160,128
D8⋊D52nd semidirect product of D8 and D5 acting via D5/C5=C2404D8:D5160,132
D5×SD16Direct product of D5 and SD16404D5xSD16160,134
SD163D5The semidirect product of SD16 and D5 acting through Inn(SD16)804SD16:3D5160,137
Q16⋊D52nd semidirect product of Q16 and D5 acting via D5/C5=C2804Q16:D5160,139
D4.D101st non-split extension by D4 of D10 acting via D10/C10=C2404D4.D10160,153
C20.C2315th non-split extension by C20 of C23 acting via C23/C2=C22804C20.C2^3160,163
D4.Dic5The non-split extension by D4 of Dic5 acting through Inn(D4)804D4.Dic5160,169
D4.8D103rd non-split extension by D4 of D10 acting via D10/C10=C2804D4.8D10160,171
C5×C8⋊C22Direct product of C5 and C8⋊C22404C5xC8:C2^2160,197
C5×C8.C22Direct product of C5 and C8.C22804C5xC8.C2^2160,198
D5⋊M4(2)The semidirect product of D5 and M4(2) acting via M4(2)/C2×C4=C2404D5:M4(2)160,202
D10.C2311st non-split extension by D10 of C23 acting via C23/C22=C2404D10.C2^3160,205
D46D102nd semidirect product of D4 and D10 acting through Inn(D4)404D4:6D10160,219
Q8.10D101st non-split extension by Q8 of D10 acting through Inn(Q8)804Q8.10D10160,222
D5×C4○D4Direct product of D5 and C4○D4404D5xC4oD4160,223
C5×2+ 1+4Direct product of C5 and 2+ 1+4404C5xES+(2,2)160,232
C5×2- 1+4Direct product of C5 and 2- 1+4804C5xES-(2,2)160,233

Groups of order 180

dρLabelID
C9×F5Direct product of C9 and F5454C9xF5180,5
C9⋊F5The semidirect product of C9 and F5 acting via F5/D5=C2454C9:F5180,6
C3×C3⋊F5Direct product of C3 and C3⋊F5304C3xC3:F5180,21
C5×C32⋊C4Direct product of C5 and C32⋊C4304C5xC3^2:C4180,23
C32⋊Dic5The semidirect product of C32 and Dic5 acting via Dic5/C5=C4304C3^2:Dic5180,24
C3×S3×D5Direct product of C3, S3 and D5304C3xS3xD5180,26
C5×S32Direct product of C5, S3 and S3304C5xS3^2180,28
D15⋊S3The semidirect product of D15 and S3 acting via S3/C3=C2304D15:S3180,30

Groups of order 192

dρLabelID
C23.SL2(𝔽3)1st non-split extension by C23 of SL2(𝔽3) acting via SL2(𝔽3)/C2=A4164C2^3.SL(2,3)192,4
C12.15C428th non-split extension by C12 of C42 acting via C42/C2×C4=C2484C12.15C4^2192,25
C8.Dic61st non-split extension by C8 of Dic6 acting via Dic6/C6=C22484C8.Dic6192,46
D248C48th semidirect product of D24 and C4 acting via C4/C2=C2484D24:8C4192,47
C24.7Q87th non-split extension by C24 of Q8 acting via Q8/C2=C22964C24.7Q8192,52
C24.6Q86th non-split extension by C24 of Q8 acting via Q8/C2=C22484C24.6Q8192,53
Dic12.C43rd non-split extension by Dic12 of C4 acting via C4/C2=C2964Dic12.C4192,56
C24.97D420th non-split extension by C24 of D4 acting via D4/C22=C2484C24.97D4192,70
C48⋊C42nd semidirect product of C48 and C4 acting faithfully484C48:C4192,71
C24.Q81st non-split extension by C24 of Q8 acting via Q8/C2=C22484C24.Q8192,72
C8.25D1211st non-split extension by C8 of D12 acting via D12/D6=C2484C8.25D12192,73
Dic6.C82nd non-split extension by Dic6 of C8 acting via C8/C4=C2964Dic6.C8192,74
D242C42nd semidirect product of D24 and C4 acting via C4/C2=C2484D24:2C4192,77
C423Dic31st semidirect product of C42 and Dic3 acting via Dic3/C3=C4484C4^2:3Dic3192,90
(C2×C12).Q88th non-split extension by C2×C12 of Q8 acting via Q8/C2=C22484(C2xC12).Q8192,92
C245Dic31st semidirect product of C24 and Dic3 acting via Dic3/C3=C4244C2^4:5Dic3192,95
(C22×C12)⋊C42nd semidirect product of C22×C12 and C4 acting faithfully484(C2^2xC12):C4192,98
C424Dic32nd semidirect product of C42 and Dic3 acting via Dic3/C3=C4484C4^2:4Dic3192,100
C42.Dic32nd non-split extension by C42 of Dic3 acting via Dic3/C3=C4484C4^2.Dic3192,101
C425Dic33rd semidirect product of C42 and Dic3 acting via Dic3/C3=C4244C4^2:5Dic3192,104
C42.3Dic33rd non-split extension by C42 of Dic3 acting via Dic3/C3=C4484C4^2.3Dic3192,107
C24.D452nd non-split extension by C24 of D4 acting via D4/C2=C22484C24.D4192,112
(C2×C24)⋊C41st semidirect product of C2×C24 and C4 acting faithfully484(C2xC24):C4192,115
C12.20C4213rd non-split extension by C12 of C42 acting via C42/C2×C4=C2484C12.20C4^2192,116
M4(2)⋊4Dic34th semidirect product of M4(2) and Dic3 acting via Dic3/C6=C2484M4(2):4Dic3192,118
C12.21C4214th non-split extension by C12 of C42 acting via C42/C2×C4=C2484C12.21C4^2192,119
C24.99D422nd non-split extension by C24 of D4 acting via D4/C22=C2964C24.99D4192,120
D8.Dic32nd non-split extension by D8 of Dic3 acting via Dic3/C6=C2484D8.Dic3192,122
Q16.Dic32nd non-split extension by Q16 of Dic3 acting via Dic3/C6=C2964Q16.Dic3192,124
D82Dic32nd semidirect product of D8 and Dic3 acting via Dic3/C6=C2484D8:2Dic3192,125
C24.41D441st non-split extension by C24 of D4 acting via D4/C2=C22964C24.41D4192,126
C3×C4.9C42Direct product of C3 and C4.9C42484C3xC4.9C4^2192,143
C3×C4.10C42Direct product of C3 and C4.10C42484C3xC4.10C4^2192,144
C3×M4(2)⋊4C4Direct product of C3 and M4(2)⋊4C4484C3xM4(2):4C4192,150
C3×C16⋊C4Direct product of C3 and C16⋊C4484C3xC16:C4192,153
C3×C23.C8Direct product of C3 and C23.C8484C3xC2^3.C8192,155
C3×C2≀C4Direct product of C3 and C2≀C4244C3xC2wrC4192,157
C3×C23.D4Direct product of C3 and C23.D4484C3xC2^3.D4192,158
C3×C42⋊C4Direct product of C3 and C42⋊C4244C3xC4^2:C4192,159
C3×C423C4Direct product of C3 and C423C4484C3xC4^2:3C4192,160
C3×C42.C4Direct product of C3 and C42.C4484C3xC4^2.C4192,161
C3×C42.3C4Direct product of C3 and C42.3C4484C3xC4^2.3C4192,162
C3×D82C4Direct product of C3 and D82C4484C3xD8:2C4192,166
C3×M5(2)⋊C2Direct product of C3 and M5(2)⋊C2484C3xM5(2):C2192,167
C3×C8.17D4Direct product of C3 and C8.17D4964C3xC8.17D4192,168
C3×C8.Q8Direct product of C3 and C8.Q8484C3xC8.Q8192,171
2+ 1+4.C61st non-split extension by 2+ 1+4 of C6 acting faithfully164ES+(2,2).C6192,202
D244C44th semidirect product of D24 and C4 acting via C4/C2=C2484D24:4C4192,276
S3×C4≀C2Direct product of S3 and C4≀C2244S3xC4wrC2192,379
C423D61st semidirect product of C42 and D6 acting via D6/C3=C22484C4^2:3D6192,380
M4(2).22D65th non-split extension by M4(2) of D6 acting via D6/S3=C2484M4(2).22D6192,382
C42.196D616th non-split extension by C42 of D6 acting via D6/S3=C2484C4^2.196D6192,383
C425D63rd semidirect product of C42 and D6 acting via D6/C3=C22484C4^2:5D6192,384
D4.10D125th non-split extension by D4 of D12 acting via D12/D6=C2484D4.10D12192,386
S3×C8.C4Direct product of S3 and C8.C4484S3xC8.C4192,451
M4(2).25D68th non-split extension by M4(2) of D6 acting via D6/S3=C2484M4(2).25D6192,452
D2410C410th semidirect product of D24 and C4 acting via C4/C2=C2484D24:10C4192,453
D247C47th semidirect product of D24 and C4 acting via C4/C2=C2484D24:7C4192,454
C24.42D442nd non-split extension by C24 of D4 acting via D4/C2=C22484C24.42D4192,457
S3×M5(2)Direct product of S3 and M5(2)484S3xM5(2)192,465
C16.12D69th non-split extension by C16 of D6 acting via D6/S3=C2964C16.12D6192,466
D8⋊D62nd semidirect product of D8 and D6 acting via D6/S3=C2484D8:D6192,470
S3×SD32Direct product of S3 and SD32484S3xSD32192,472
D6.2D82nd non-split extension by D6 of D8 acting via D8/C8=C2964D6.2D8192,475
Q32⋊S32nd semidirect product of Q32 and S3 acting via S3/C3=C2964Q32:S3192,477
C426D64th semidirect product of C42 and D6 acting via D6/C3=C22484C4^2:6D6192,564
(C2×D12)⋊13C49th semidirect product of C2×D12 and C4 acting via C4/C2=C2484(C2xD12):13C4192,565
C246D61st semidirect product of C24 and D6 acting via D6/C3=C22244C2^4:6D6192,591
C22⋊C4⋊D64th semidirect product of C22⋊C4 and D6 acting via D6/C3=C22484C2^2:C4:D6192,612
C427D65th semidirect product of C42 and D6 acting via D6/C3=C22484C4^2:7D6192,620
D12.14D414th non-split extension by D12 of D4 acting via D4/C2=C22484D12.14D4192,621
C428D66th semidirect product of C42 and D6 acting via D6/C3=C22244C4^2:8D6192,636
D12.15D415th non-split extension by D12 of D4 acting via D4/C2=C22484D12.15D4192,654
C23.8Dic66th non-split extension by C23 of Dic6 acting via Dic6/C6=C22484C2^3.8Dic6192,683
C23.9Dic67th non-split extension by C23 of Dic6 acting via Dic6/C6=C22484C2^3.9Dic6192,684
M4(2).31D64th non-split extension by M4(2) of D6 acting via D6/C6=C2484M4(2).31D6192,691
M4(2)⋊24D68th semidirect product of M4(2) and D6 acting via D6/C6=C2484M4(2):24D6192,698
C24.78C2324th non-split extension by C24 of C23 acting via C23/C22=C2964C24.78C2^3192,699
Q8.8D123rd non-split extension by Q8 of D12 acting via D12/C12=C2484Q8.8D12192,700
C24.100D423rd non-split extension by C24 of D4 acting via D4/C22=C2484C24.100D4192,703
C24.54D454th non-split extension by C24 of D4 acting via D4/C2=C22484C24.54D4192,704
D8.D61st non-split extension by D8 of D6 acting via D6/C6=C2484D8.D6192,706
C24.23D423rd non-split extension by C24 of D4 acting via D4/C2=C22484C24.23D4192,719
C24.44D444th non-split extension by C24 of D4 acting via D4/C2=C22484C24.44D4192,736
C24.27C2320th non-split extension by C24 of C23 acting via C23/C2=C22964C24.27C2^3192,738
C24.29D429th non-split extension by C24 of D4 acting via D4/C2=C22964C24.29D4192,751
Q16.D63rd non-split extension by Q16 of D6 acting via D6/C6=C2964Q16.D6192,753
D85Dic3The semidirect product of D8 and Dic3 acting through Inn(D8)484D8:5Dic3192,755
D84Dic34th semidirect product of D8 and Dic3 acting via Dic3/C6=C2484D8:4Dic3192,756
(C6×D4)⋊9C45th semidirect product of C6×D4 and C4 acting via C4/C2=C2484(C6xD4):9C4192,795
(C6×D4).16C410th non-split extension by C6×D4 of C4 acting via C4/C2=C2484(C6xD4).16C4192,796
(C6×D4)⋊10C46th semidirect product of C6×D4 and C4 acting via C4/C2=C2484(C6xD4):10C4192,799
C3×C23.C23Direct product of C3 and C23.C23484C3xC2^3.C2^3192,843
C3×M4(2).8C22Direct product of C3 and M4(2).8C22484C3xM4(2).8C2^2192,846
C3×C42⋊C22Direct product of C3 and C42⋊C22484C3xC4^2:C2^2192,854
C3×M4(2).C4Direct product of C3 and M4(2).C4484C3xM4(2).C4192,863
C3×C8.26D4Direct product of C3 and C8.26D4484C3xC8.26D4192,877
C3×D44D4Direct product of C3 and D44D4244C3xD4:4D4192,886
C3×D4.8D4Direct product of C3 and D4.8D4484C3xD4.8D4192,887
C3×D4.9D4Direct product of C3 and D4.9D4484C3xD4.9D4192,888
C3×D4.10D4Direct product of C3 and D4.10D4484C3xD4.10D4192,889
C3×C2≀C22Direct product of C3 and C2≀C22244C3xC2wrC2^2192,890
C3×C23.7D4Direct product of C3 and C23.7D4484C3xC2^3.7D4192,891
C3×D4.3D4Direct product of C3 and D4.3D4484C3xD4.3D4192,904
C3×D4.4D4Direct product of C3 and D4.4D4484C3xD4.4D4192,905
C3×D4.5D4Direct product of C3 and D4.5D4964C3xD4.5D4192,906
C3×C16⋊C22Direct product of C3 and C16⋊C22484C3xC16:C2^2192,942
C3×Q32⋊C2Direct product of C3 and Q32⋊C2964C3xQ32:C2192,943
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
U2(𝔽3)⋊C26th semidirect product of U2(𝔽3) and C2 acting faithfully324U(2,3):C2192,982
Q8.4S42nd non-split extension by Q8 of S4 acting via S4/A4=C2484Q8.4S4192,987
D4.3S43rd non-split extension by D4 of S4 acting via S4/A4=C2324D4.3S4192,990
M4(2).A4The non-split extension by M4(2) of A4 acting through Inn(M4(2))324M4(2).A4192,1013
SD16.A4The non-split extension by SD16 of A4 acting through Inn(SD16)324SD16.A4192,1018
M4(2)⋊26D62nd semidirect product of M4(2) and D6 acting through Inn(M4(2))484M4(2):26D6192,1304
C24.9C232nd non-split extension by C24 of C23 acting via C23/C2=C22484C24.9C2^3192,1307
S3×C8○D4Direct product of S3 and C8○D4484S3xC8oD4192,1308
M4(2)⋊28D64th semidirect product of M4(2) and D6 acting through Inn(M4(2))484M4(2):28D6192,1309
D4.11D121st non-split extension by D4 of D12 acting through Inn(D4)484D4.11D12192,1310
D813D62nd semidirect product of D8 and D6 acting through Inn(D8)484D8:13D6192,1316
SD1613D62nd semidirect product of SD16 and D6 acting through Inn(SD16)484SD16:13D6192,1321
D12.30D413rd non-split extension by D12 of D4 acting via D4/C4=C2964D12.30D4192,1325
S3×C4○D8Direct product of S3 and C4○D8484S3xC4oD8192,1326
SD16⋊D63rd semidirect product of SD16 and D6 acting via D6/C6=C2484SD16:D6192,1327
D811D65th semidirect product of D8 and D6 acting via D6/C6=C2484D8:11D6192,1329
C12.76C2423rd non-split extension by C12 of C24 acting via C24/C23=C2484C12.76C2^4192,1378
C12.C2435th non-split extension by C12 of C24 acting via C24/C22=C22484C12.C2^4192,1381
C3×Q8○M4(2)Direct product of C3 and Q8○M4(2)484C3xQ8oM4(2)192,1457
C3×D8⋊C22Direct product of C3 and D8⋊C22484C3xD8:C2^2192,1464
C3×D4○D8Direct product of C3 and D4○D8484C3xD4oD8192,1465
C3×D4○SD16Direct product of C3 and D4○SD16484C3xD4oSD16192,1466
C3×Q8○D8Direct product of C3 and Q8○D8964C3xQ8oD8192,1467
GL2(𝔽3)⋊C223rd semidirect product of GL2(𝔽3) and C22 acting via C22/C2=C2324GL(2,3):C2^2192,1482
Q8.6S41st non-split extension by Q8 of S4 acting through Inn(Q8)324Q8.6S4192,1483
D4.4S41st non-split extension by D4 of S4 acting through Inn(D4)164D4.4S4192,1485
C23.S44th non-split extension by C23 of S4 acting faithfully164C2^3.S4192,1491
Q8.S42nd non-split extension by Q8 of S4 acting via S4/C22=S3164Q8.S4192,1492
2- 1+43C62nd semidirect product of 2- 1+4 and C6 acting via C6/C2=C3324ES-(2,2):3C6192,1504
2+ 1+4.3C6The non-split extension by 2+ 1+4 of C6 acting via C6/C2=C3164ES+(2,2).3C6192,1509
C6.C2514th non-split extension by C6 of C25 acting via C25/C24=C2484C6.C2^5192,1523
C3×C2.C25Direct product of C3 and C2.C25484C3xC2.C2^5192,1536

Groups of order 200

dρLabelID
C5×C5⋊C8Direct product of C5 and C5⋊C8404C5xC5:C8200,18
C523C82nd semidirect product of C52 and C8 acting via C8/C2=C4404C5^2:3C8200,19
C10×F5Direct product of C10 and F5404C10xF5200,45
C2×D5.D5Direct product of C2 and D5.D5404C2xD5.D5200,46

Groups of order 204

dρLabelID
C3×C17⋊C4Direct product of C3 and C17⋊C4514C3xC17:C4204,5
C51⋊C41st semidirect product of C51 and C4 acting faithfully514C51:C4204,6

Groups of order 208

dρLabelID
C13⋊C16The semidirect product of C13 and C16 acting via C16/C4=C42084C13:C16208,3
D13⋊C8The semidirect product of D13 and C8 acting via C8/C4=C21044D13:C8208,28
C52.C41st non-split extension by C52 of C4 acting faithfully1044C52.C4208,29
C4×C13⋊C4Direct product of C4 and C13⋊C4524C4xC13:C4208,30
C52⋊C41st semidirect product of C52 and C4 acting faithfully524C52:C4208,31

Groups of order 216

dρLabelID
C3×C322C8Direct product of C3 and C322C8244C3xC3^2:2C8216,117
C334C82nd semidirect product of C33 and C8 acting via C8/C2=C4244C3^3:4C8216,118
C3×S3×Dic3Direct product of C3, S3 and Dic3244C3xS3xDic3216,119
C3×C6.D6Direct product of C3 and C6.D6244C3xC6.D6216,120
C3×D6⋊S3Direct product of C3 and D6⋊S3244C3xD6:S3216,121
C3×C3⋊D12Direct product of C3 and C3⋊D12244C3xC3:D12216,122
C3×C322Q8Direct product of C3 and C322Q8244C3xC3^2:2Q8216,123
C339(C2×C4)6th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22244C3^3:9(C2xC4)216,131
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
C3×S3≀C2Direct product of C3 and S3≀C2124C3xS3wrC2216,157
C33⋊D42nd semidirect product of C33 and D4 acting faithfully124C3^3:D4216,158
C6×C32⋊C4Direct product of C6 and C32⋊C4244C6xC3^2:C4216,168
C2×C33⋊C4Direct product of C2 and C33⋊C4244C2xC3^3:C4216,169
S32×C6Direct product of C6, S3 and S3244S3^2xC6216,170
C2×C324D6Direct product of C2 and C324D6244C2xC3^2:4D6216,172

Groups of order 220

dρLabelID
C11×F5Direct product of C11 and F5554C11xF5220,9
C11⋊F5The semidirect product of C11 and F5 acting via F5/D5=C2554C11:F5220,10

Groups of order 224

dρLabelID
C23.1D141st non-split extension by C23 of D14 acting via D14/C7=C22564C2^3.1D14224,12
C28.53D410th non-split extension by C28 of D4 acting via D4/C22=C21124C28.53D4224,28
D284C44th semidirect product of D28 and C4 acting via C4/C2=C2564D28:4C4224,31
C28.D48th non-split extension by C28 of D4 acting via D4/C2=C22564C28.D4224,39
C23⋊Dic7The semidirect product of C23 and Dic7 acting via Dic7/C7=C4564C2^3:Dic7224,40
C28.10D410th non-split extension by C28 of D4 acting via D4/C2=C221124C28.10D4224,42
D42Dic72nd semidirect product of D4 and Dic7 acting via Dic7/C14=C2564D4:2Dic7224,43
C7×C23⋊C4Direct product of C7 and C23⋊C4564C7xC2^3:C4224,48
C7×C4.D4Direct product of C7 and C4.D4564C7xC4.D4224,49
C7×C4.10D4Direct product of C7 and C4.10D41124C7xC4.10D4224,50
D7×M4(2)Direct product of D7 and M4(2)564D7xM4(2)224,101
D28.C4The non-split extension by D28 of C4 acting via C4/C2=C21124D28.C4224,102
D8⋊D72nd semidirect product of D8 and D7 acting via D7/C7=C2564D8:D7224,106
D7×SD16Direct product of D7 and SD16564D7xSD16224,108
SD163D7The semidirect product of SD16 and D7 acting through Inn(SD16)1124SD16:3D7224,111
Q16⋊D72nd semidirect product of Q16 and D7 acting via D7/C7=C21124Q16:D7224,113
D4.D141st non-split extension by D4 of D14 acting via D14/C14=C2564D4.D14224,127
C28.C2315th non-split extension by C28 of C23 acting via C23/C2=C221124C28.C2^3224,137
Q8.Dic7The non-split extension by Q8 of Dic7 acting through Inn(Q8)1124Q8.Dic7224,143
D4.8D143rd non-split extension by D4 of D14 acting via D14/C14=C21124D4.8D14224,145
C7×C8⋊C22Direct product of C7 and C8⋊C22564C7xC8:C2^2224,171
C7×C8.C22Direct product of C7 and C8.C221124C7xC8.C2^2224,172
D46D142nd semidirect product of D4 and D14 acting through Inn(D4)564D4:6D14224,180
Q8.10D141st non-split extension by Q8 of D14 acting through Inn(Q8)1124Q8.10D14224,183
D7×C4○D4Direct product of D7 and C4○D4564D7xC4oD4224,184
C7×2+ 1+4Direct product of C7 and 2+ 1+4564C7xES+(2,2)224,193
C7×2- 1+4Direct product of C7 and 2- 1+41124C7xES-(2,2)224,194

Groups of order 240

dρLabelID
C3×C5⋊C16Direct product of C3 and C5⋊C162404C3xC5:C16240,5
C15⋊C161st semidirect product of C15 and C16 acting via C16/C4=C42404C15:C16240,6
D5×C3⋊C8Direct product of D5 and C3⋊C81204D5xC3:C8240,7
S3×C52C8Direct product of S3 and C52C81204S3xC5:2C8240,8
D152C8The semidirect product of D15 and C8 acting via C8/C4=C21204D15:2C8240,9
C20.32D611st non-split extension by C20 of D6 acting via D6/S3=C21204C20.32D6240,10
D6.Dic5The non-split extension by D6 of Dic5 acting via Dic5/C10=C21204D6.Dic5240,11
D30.5C43rd non-split extension by D30 of C4 acting via C4/C2=C21204D30.5C4240,12
C15⋊D81st semidirect product of C15 and D8 acting via D8/C4=C221204C15:D8240,13
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
C15⋊Q161st semidirect product of C15 and Q16 acting via Q16/C4=C222404C15:Q16240,22
C3×D4⋊D5Direct product of C3 and D4⋊D51204C3xD4:D5240,44
C3×D4.D5Direct product of C3 and D4.D51204C3xD4.D5240,45
C3×Q8⋊D5Direct product of C3 and Q8⋊D51204C3xQ8:D5240,46
C3×C5⋊Q16Direct product of C3 and C5⋊Q162404C3xC5:Q16240,47
C5×D4⋊S3Direct product of C5 and D4⋊S31204C5xD4:S3240,60
C5×D4.S3Direct product of C5 and D4.S31204C5xD4.S3240,61
C5×Q82S3Direct product of C5 and Q82S31204C5xQ8:2S3240,62
C5×C3⋊Q16Direct product of C5 and C3⋊Q162404C5xC3:Q16240,63
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2124A5:C4240,91
C3×D5⋊C8Direct product of C3 and D5⋊C81204C3xD5:C8240,111
C3×C4.F5Direct product of C3 and C4.F51204C3xC4.F5240,112
C12×F5Direct product of C12 and F5604C12xF5240,113
C3×C4⋊F5Direct product of C3 and C4⋊F5604C3xC4:F5240,114
C3×C22.F5Direct product of C3 and C22.F51204C3xC2^2.F5240,116
C3×C22⋊F5Direct product of C3 and C22⋊F5604C3xC2^2:F5240,117
C60.C43rd non-split extension by C60 of C4 acting faithfully1204C60.C4240,118
C12.F51st non-split extension by C12 of F5 acting via F5/D5=C21204C12.F5240,119
C4×C3⋊F5Direct product of C4 and C3⋊F5604C4xC3:F5240,120
C60⋊C41st semidirect product of C60 and C4 acting faithfully604C60:C4240,121
C158M4(2)1st semidirect product of C15 and M4(2) acting via M4(2)/C22=C41204C15:8M4(2)240,123
D10.D66th non-split extension by D10 of D6 acting via D6/C6=C2604D10.D6240,124
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
D15⋊Q8The semidirect product of D15 and Q8 acting via Q8/C4=C21204D15:Q8240,131
D6.D103rd non-split extension by D6 of D10 acting via D10/C10=C21204D6.D10240,132
C4×S3×D5Direct product of C4, S3 and D5604C4xS3xD5240,135
C20⋊D62nd semidirect product of C20 and D6 acting via D6/C3=C22604C20:D6240,138
Dic5.D65th non-split extension by Dic5 of D6 acting via D6/S3=C21204Dic5.D6240,140
Dic3.D106th non-split extension by Dic3 of D10 acting via D10/D5=C21204Dic3.D10240,143
D5×C3⋊D4Direct product of D5 and C3⋊D4604D5xC3:D4240,149
S3×C5⋊D4Direct product of S3 and C5⋊D4604S3xC5:D4240,150
C3×D4×D5Direct product of C3, D4 and D5604C3xD4xD5240,159
C3×D42D5Direct product of C3 and D42D51204C3xD4:2D5240,160
C3×Q8×D5Direct product of C3, Q8 and D51204C3xQ8xD5240,161
C3×Q82D5Direct product of C3 and Q82D51204C3xQ8:2D5240,162
C5×S3×D4Direct product of C5, S3 and D4604C5xS3xD4240,169
C5×D42S3Direct product of C5 and D42S31204C5xD4:2S3240,170
C5×S3×Q8Direct product of C5, S3 and Q81204C5xS3xQ8240,171
C5×Q83S3Direct product of C5 and Q83S31204C5xQ8:3S3240,172

Groups of order 252

dρLabelID
C7×C32⋊C4Direct product of C7 and C32⋊C4424C7xC3^2:C4252,31
C32⋊Dic7The semidirect product of C32 and Dic7 acting via Dic7/C7=C4424C3^2:Dic7252,32
C3×S3×D7Direct product of C3, S3 and D7424C3xS3xD7252,33
S32×C7Direct product of C7, S3 and S3424S3^2xC7252,35
D21⋊S3The semidirect product of D21 and S3 acting via S3/C3=C2424D21:S3252,37

Groups of order 260

dρLabelID
C5×C13⋊C4Direct product of C5 and C13⋊C4654C5xC13:C4260,5
C65⋊C43rd semidirect product of C65 and C4 acting faithfully654C65:C4260,6
C13×F5Direct product of C13 and F5654C13xF5260,7
C133F5The semidirect product of C13 and F5 acting via F5/D5=C2654C13:3F5260,8

Groups of order 272

dρLabelID
C173C16The semidirect product of C17 and C16 acting via C16/C4=C42724C17:3C16272,3
C68.C43rd non-split extension by C68 of C4 acting faithfully1364C68.C4272,29
D34.4C43rd non-split extension by D34 of C4 acting via C4/C2=C21364D34.4C4272,30
C4×C17⋊C4Direct product of C4 and C17⋊C4684C4xC17:C4272,31
C68⋊C41st semidirect product of C68 and C4 acting faithfully684C68:C4272,32

Groups of order 280

dρLabelID
C7×C5⋊C8Direct product of C7 and C5⋊C82804C7xC5:C8280,5
C35⋊C81st semidirect product of C35 and C8 acting via C8/C2=C42804C35:C8280,6
C14×F5Direct product of C14 and F5704C14xF5280,34
C2×C7⋊F5Direct product of C2 and C7⋊F5704C2xC7:F5280,35

Groups of order 288

dρLabelID
C22.D361st non-split extension by C22 of D36 acting via D36/D18=C2724C2^2.D36288,13
C36.53D49th non-split extension by C36 of D4 acting via D4/C22=C21444C36.53D4288,29
Dic18⋊C44th semidirect product of Dic18 and C4 acting via C4/C2=C2724Dic18:C4288,32
C36.D47th non-split extension by C36 of D4 acting via D4/C2=C22724C36.D4288,39
C232Dic9The semidirect product of C23 and Dic9 acting via Dic9/C9=C4724C2^3:2Dic9288,41
C36.9D49th non-split extension by C36 of D4 acting via D4/C2=C221444C36.9D4288,42
Q83Dic92nd semidirect product of Q8 and Dic9 acting via Dic9/C18=C2724Q8:3Dic9288,44
C9×C23⋊C4Direct product of C9 and C23⋊C4724C9xC2^3:C4288,49
C9×C4.D4Direct product of C9 and C4.D4724C9xC4.D4288,50
C9×C4.10D4Direct product of C9 and C4.10D41444C9xC4.10D4288,51
C12.9S49th non-split extension by C12 of S4 acting via S4/A4=C2724C12.9S4288,70
M4(2)×D9Direct product of M4(2) and D9724M4(2)xD9288,116
D36.C4The non-split extension by D36 of C4 acting via C4/C2=C21444D36.C4288,117
D8⋊D92nd semidirect product of D8 and D9 acting via D9/C9=C2724D8:D9288,121
SD16×D9Direct product of SD16 and D9724SD16xD9288,123
SD163D9The semidirect product of SD16 and D9 acting through Inn(SD16)1444SD16:3D9288,126
Q16⋊D92nd semidirect product of Q16 and D9 acting via D9/C9=C21444Q16:D9288,128
D366C224th semidirect product of D36 and C22 acting via C22/C2=C2724D36:6C2^2288,143
C36.C2316th non-split extension by C36 of C23 acting via C23/C2=C221444C36.C2^3288,153
D4.Dic9The non-split extension by D4 of Dic9 acting through Inn(D4)1444D4.Dic9288,158
D4.9D184th non-split extension by D4 of D18 acting via D18/C18=C21444D4.9D18288,161
C9×C8⋊C22Direct product of C9 and C8⋊C22724C9xC8:C2^2288,186
C9×C8.C22Direct product of C9 and C8.C221444C9xC8.C2^2288,187
C322C32The semidirect product of C32 and C32 acting via C32/C8=C4964C3^2:2C32288,188
S3×C3⋊C16Direct product of S3 and C3⋊C16964S3xC3:C16288,189
C24.60D613rd non-split extension by C24 of D6 acting via D6/S3=C2484C24.60D6288,190
C24.61D614th non-split extension by C24 of D6 acting via D6/S3=C2964C24.61D6288,191
C24.62D615th non-split extension by C24 of D6 acting via D6/S3=C2484C24.62D6288,192
C322D161st semidirect product of C32 and D16 acting via D16/C8=C22964C3^2:2D16288,193
D24.S32nd non-split extension by D24 of S3 acting via S3/C3=C2964D24.S3288,195
C322Q321st semidirect product of C32 and Q32 acting via Q32/C8=C22964C3^2:2Q32288,198
C12.D1213rd non-split extension by C12 of D12 acting via D12/C6=C22484C12.D12288,206
C12.14D1214th non-split extension by C12 of D12 acting via D12/C6=C22484C12.14D12288,208
D124Dic34th semidirect product of D12 and Dic3 acting via Dic3/C6=C2244D12:4Dic3288,216
D122Dic32nd semidirect product of D12 and Dic3 acting via Dic3/C6=C2484D12:2Dic3288,217
C12.80D1211st non-split extension by C12 of D12 acting via D12/D6=C2484C12.80D12288,218
C12.82D1213rd non-split extension by C12 of D12 acting via D12/D6=C2484C12.82D12288,225
C62.5Q82nd non-split extension by C62 of Q8 acting via Q8/C2=C22484C6^2.5Q8288,226
C62.31D415th non-split extension by C62 of D4 acting via D4/C2=C22244C6^2.31D4288,228
C62.32D416th non-split extension by C62 of D4 acting via D4/C2=C22244C6^2.32D4288,229
C3×C23.6D6Direct product of C3 and C23.6D6244C3xC2^3.6D6288,240
C3×C12.53D4Direct product of C3 and C12.53D4484C3xC12.53D4288,256
C3×C12.46D4Direct product of C3 and C12.46D4484C3xC12.46D4288,257
C3×C12.47D4Direct product of C3 and C12.47D4484C3xC12.47D4288,258
C3×D12⋊C4Direct product of C3 and D12⋊C4484C3xD12:C4288,259
C3×C3⋊D16Direct product of C3 and C3⋊D16484C3xC3:D16288,260
C3×D8.S3Direct product of C3 and D8.S3484C3xD8.S3288,261
C3×C8.6D6Direct product of C3 and C8.6D6964C3xC8.6D6288,262
C3×C3⋊Q32Direct product of C3 and C3⋊Q32964C3xC3:Q32288,263
C3×C12.D4Direct product of C3 and C12.D4244C3xC12.D4288,267
C3×C23.7D6Direct product of C3 and C23.7D6244C3xC2^3.7D6288,268
C3×C12.10D4Direct product of C3 and C12.10D4484C3xC12.10D4288,270
C3×Q83Dic3Direct product of C3 and Q83Dic3484C3xQ8:3Dic3288,271
Q8.D182nd non-split extension by Q8 of D18 acting via D18/C6=S31444Q8.D18288,337
C12.11S411st non-split extension by C12 of S4 acting via S4/A4=C21444C12.11S4288,339
2+ 1+4⋊C91st semidirect product of 2+ 1+4 and C9 acting via C9/C3=C3724ES+(2,2):C9288,348
2- 1+4⋊C9The semidirect product of 2- 1+4 and C9 acting via C9/C3=C31444ES-(2,2):C9288,349
2+ 1+42C92nd semidirect product of 2+ 1+4 and C9 acting via C9/C3=C3724ES+(2,2):2C9288,351
D46D182nd semidirect product of D4 and D18 acting through Inn(D4)724D4:6D18288,358
Q8.15D181st non-split extension by Q8 of D18 acting through Inn(Q8)1444Q8.15D18288,361
C4○D4×D9Direct product of C4○D4 and D9724C4oD4xD9288,362
C9×2+ 1+4Direct product of C9 and 2+ 1+4724C9xES+(2,2)288,371
C9×2- 1+4Direct product of C9 and 2- 1+41444C9xES-(2,2)288,372
S32⋊C8The semidirect product of S32 and C8 acting via C8/C4=C2244S3^2:C8288,374
C4.S3≀C21st non-split extension by C4 of S3≀C2 acting via S3≀C2/S32=C2244C4.S3wrC2288,375
(C3×C12).D42nd non-split extension by C3×C12 of D4 acting faithfully484(C3xC12).D4288,376
C3⋊S3.2D81st non-split extension by C3⋊S3 of D8 acting via D8/C4=C22244C3:S3.2D8288,377
C3⋊S3.2Q161st non-split extension by C3⋊S3 of Q16 acting via Q16/C4=C22484C3:S3.2Q16288,378
C32⋊C4≀C2The semidirect product of C32 and C4≀C2 acting via C4≀C2/C4=D4484C3^2:C4wrC2288,379
C32⋊C4⋊C82nd semidirect product of C32⋊C4 and C8 acting via C8/C4=C2484C3^2:C4:C8288,380
C4.19S3≀C24th central extension by C4 of S3≀C2484C4.19S3wrC2288,381
C3⋊U2(𝔽3)The semidirect product of C3 and U2(𝔽3) acting via U2(𝔽3)/C4.A4=C2724C3:U(2,3)288,404
SL2(𝔽3).Dic3The non-split extension by SL2(𝔽3) of Dic3 acting through Inn(SL2(𝔽3))964SL(2,3).Dic3288,410
C3⋊S33C162nd semidirect product of C3⋊S3 and C16 acting via C16/C8=C2484C3:S3:3C16288,412
C323M5(2)The semidirect product of C32 and M5(2) acting via M5(2)/C8=C4484C3^2:3M5(2)288,413
C8×C32⋊C4Direct product of C8 and C32⋊C4484C8xC3^2:C4288,414
(C3×C24)⋊C42nd semidirect product of C3×C24 and C4 acting faithfully484(C3xC24):C4288,415
C8⋊(C32⋊C4)2nd semidirect product of C8 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2484C8:(C3^2:C4)288,416
C3⋊S3.4D8The non-split extension by C3⋊S3 of D8 acting via D8/C8=C2484C3:S3.4D8288,417
(C3×C24).C44th non-split extension by C3×C24 of C4 acting faithfully484(C3xC24).C4288,418
C8.(C32⋊C4)1st non-split extension by C8 of C32⋊C4 acting via C32⋊C4/C3⋊S3=C2484C8.(C3^2:C4)288,419
C62.4C82nd non-split extension by C62 of C8 acting via C8/C2=C4484C6^2.4C8288,421
(C2×C62)⋊C44th semidirect product of C2×C62 and C4 acting faithfully244(C2xC6^2):C4288,434
(C2×C62).C45th non-split extension by C2×C62 of C4 acting faithfully244(C2xC6^2).C4288,436
S32×C8Direct product of C8, S3 and S3484S3^2xC8288,437
S3×C8⋊S3Direct product of S3 and C8⋊S3484S3xC8:S3288,438
C24⋊D614th semidirect product of C24 and D6 acting via D6/C3=C22484C24:D6288,439
S3×C24⋊C2Direct product of S3 and C24⋊C2484S3xC24:C2288,440
D24⋊S32nd semidirect product of D24 and S3 acting via S3/C3=C2484D24:S3288,443
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
Dic12⋊S32nd semidirect product of Dic12 and S3 acting via S3/C3=C2484Dic12:S3288,449
C24.23D623rd non-split extension by C24 of D6 acting via D6/C3=C22484C24.23D6288,450
C24.63D616th non-split extension by C24 of D6 acting via D6/S3=C2484C24.63D6288,451
C24.64D617th non-split extension by C24 of D6 acting via D6/S3=C2484C24.64D6288,452
C24.D646th non-split extension by C24 of D6 acting via D6/C3=C22484C24.D6288,453
D6.1D121st non-split extension by D6 of D12 acting via D12/C12=C2484D6.1D12288,454
D12.2D62nd non-split extension by D12 of D6 acting via D6/C3=C22484D12.2D6288,457
D245S35th semidirect product of D24 and S3 acting via S3/C3=C2484D24:5S3288,458
D12.4D64th non-split extension by D12 of D6 acting via D6/C3=C22484D12.4D6288,459
S3×C4.Dic3Direct product of S3 and C4.Dic3484S3xC4.Dic3288,461
D12.2Dic3The non-split extension by D12 of Dic3 acting through Inn(D12)484D12.2Dic3288,462
D12.Dic3The non-split extension by D12 of Dic3 acting via Dic3/C6=C2484D12.Dic3288,463
C3⋊C8.22D611st non-split extension by C3⋊C8 of D6 acting via D6/S3=C2484C3:C8.22D6288,465
C3⋊C820D69th semidirect product of C3⋊C8 and D6 acting via D6/S3=C2244C3:C8:20D6288,466
D12.30D65th non-split extension by D12 of D6 acting via D6/C6=C2484D12.30D6288,470
D1220D64th semidirect product of D12 and D6 acting via D6/C6=C2484D12:20D6288,471
D12.32D67th non-split extension by D12 of D6 acting via D6/C6=C2484D12.32D6288,475
D12.27D62nd non-split extension by D12 of D6 acting via D6/C6=C2484D12.27D6288,477
D12.28D63rd non-split extension by D12 of D6 acting via D6/C6=C2484D12.28D6288,478
Dic6.29D63rd non-split extension by Dic6 of D6 acting via D6/C6=C2484Dic6.29D6288,481
C3×S3×M4(2)Direct product of C3, S3 and M4(2)484C3xS3xM4(2)288,677
C3×D12.C4Direct product of C3 and D12.C4484C3xD12.C4288,678
C3×C8⋊D6Direct product of C3 and C8⋊D6484C3xC8:D6288,679
C3×C8.D6Direct product of C3 and C8.D6484C3xC8.D6288,680
C3×S3×D8Direct product of C3, S3 and D8484C3xS3xD8288,681
C3×D8⋊S3Direct product of C3 and D8⋊S3484C3xD8:S3288,682
C3×D83S3Direct product of C3 and D83S3484C3xD8:3S3288,683
C3×S3×SD16Direct product of C3, S3 and SD16484C3xS3xSD16288,684
C3×Q83D6Direct product of C3 and Q83D6484C3xQ8:3D6288,685
C3×D4.D6Direct product of C3 and D4.D6484C3xD4.D6288,686
C3×Q8.7D6Direct product of C3 and Q8.7D6484C3xQ8.7D6288,687
C3×S3×Q16Direct product of C3, S3 and Q16964C3xS3xQ16288,688
C3×Q16⋊S3Direct product of C3 and Q16⋊S3964C3xQ16:S3288,689
C3×D24⋊C2Direct product of C3 and D24⋊C2964C3xD24:C2288,690
C3×D126C22Direct product of C3 and D126C22244C3xD12:6C2^2288,703
C3×Q8.11D6Direct product of C3 and Q8.11D6484C3xQ8.11D6288,713
C3×D4.Dic3Direct product of C3 and D4.Dic3484C3xD4.Dic3288,719
C3×D4⋊D6Direct product of C3 and D4⋊D6484C3xD4:D6288,720
C3×Q8.13D6Direct product of C3 and Q8.13D6484C3xQ8.13D6288,721
C3×Q8.14D6Direct product of C3 and Q8.14D6484C3xQ8.14D6288,722
CSU2(𝔽3)⋊S31st semidirect product of CSU2(𝔽3) and S3 acting via S3/C3=C2964CSU(2,3):S3288,844
Dic3.4S41st non-split extension by Dic3 of S4 acting through Inn(Dic3)484Dic3.4S4288,845
D6.2S42nd non-split extension by D6 of S4 acting via S4/A4=C2484D6.2S4288,850
S3×GL2(𝔽3)Direct product of S3 and GL2(𝔽3); = GL2(ℤ/6ℤ)244S3xGL(2,3)288,851
S32⋊Q8The semidirect product of S32 and Q8 acting via Q8/C4=C2244S3^2:Q8288,868
C32⋊D85C2The semidirect product of C32⋊D8 and C2 acting through Inn(C32⋊D8)484C3^2:D8:5C2288,871
C32⋊D8⋊C23rd semidirect product of C32⋊D8 and C2 acting faithfully244C3^2:D8:C2288,872
C32⋊Q16⋊C21st semidirect product of C32⋊Q16 and C2 acting faithfully484C3^2:Q16:C2288,874
C4×S3≀C2Direct product of C4 and S3≀C2244C4xS3wrC2288,877
S32⋊D4The semidirect product of S32 and D4 acting via D4/C4=C2244S3^2:D4288,878
C62.9D49th non-split extension by C62 of D4 acting faithfully244C6^2.9D4288,881
C62.12D412nd non-split extension by C62 of D4 acting faithfully244C6^2.12D4288,884
C3×Q8.D6Direct product of C3 and Q8.D6484C3xQ8.D6288,901
C3×C4.S4Direct product of C3 and C4.S4964C3xC4.S4288,902
C3×C4.3S4Direct product of C3 and C4.3S4484C3xC4.3S4288,904
SL2(𝔽3).D62nd non-split extension by SL2(𝔽3) of D6 acting via D6/C6=C2484SL(2,3).D6288,912
C12.14S414th non-split extension by C12 of S4 acting via S4/A4=C2484C12.14S4288,914
SL2(𝔽3).11D61st non-split extension by SL2(𝔽3) of D6 acting through Inn(SL2(𝔽3))484SL(2,3).11D6288,923
S3×C4.A4Direct product of S3 and C4.A4484S3xC4.A4288,925
C3⋊S3⋊M4(2)2nd semidirect product of C3⋊S3 and M4(2) acting via M4(2)/C2×C4=C2244C3:S3:M4(2)288,931
(C6×C12)⋊5C45th semidirect product of C6×C12 and C4 acting faithfully244(C6xC12):5C4288,934
D12.33D68th non-split extension by D12 of D6 acting via D6/C6=C2484D12.33D6288,945
S3×C4○D12Direct product of S3 and C4○D12484S3xC4oD12288,953
D1223D67th semidirect product of D12 and D6 acting via D6/C6=C2244D12:23D6288,954
D1224D68th semidirect product of D12 and D6 acting via D6/C6=C2484D12:24D6288,955
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
C3×Q8.A4Direct product of C3 and Q8.A4724C3xQ8.A4288,984
C3×D4.A4Direct product of C3 and D4.A4484C3xD4.A4288,985
C3×C23⋊A4Direct product of C3 and C23⋊A4244C3xC2^3:A4288,987
C3×D46D6Direct product of C3 and D46D6244C3xD4:6D6288,994
C3×Q8.15D6Direct product of C3 and Q8.15D6484C3xQ8.15D6288,997
C3×S3×C4○D4Direct product of C3, S3 and C4○D4484C3xS3xC4oD4288,998
C3×D4○D12Direct product of C3 and D4○D12484C3xD4oD12288,999
C3×Q8○D12Direct product of C3 and Q8○D12484C3xQ8oD12288,1000

Groups of order 300

dρLabelID
C3×C25⋊C4Direct product of C3 and C25⋊C4754C3xC25:C4300,5
C75⋊C41st semidirect product of C75 and C4 acting faithfully754C75:C4300,6
C15×F5Direct product of C15 and F5604C15xF5300,28
C3×D5.D5Direct product of C3 and D5.D5604C3xD5.D5300,29
C3×C52⋊C4Direct product of C3 and C52⋊C4304C3xC5^2:C4300,31
C5×C3⋊F5Direct product of C5 and C3⋊F5604C5xC3:F5300,32
D5.D15The non-split extension by D5 of D15 acting via D15/C15=C2604D5.D15300,33
C152F52nd semidirect product of C15 and F5 acting via F5/C5=C4304C15:2F5300,35
C3×D52Direct product of C3, D5 and D5304C3xD5^2300,36
C5×S3×D5Direct product of C5, S3 and D5304C5xS3xD5300,37
D15⋊D5The semidirect product of D15 and D5 acting via D5/C5=C2304D15:D5300,40

Groups of order 312

dρLabelID
C3×C13⋊C8Direct product of C3 and C13⋊C83124C3xC13:C8312,13
C39⋊C81st semidirect product of C39 and C8 acting via C8/C2=C43124C39:C8312,14
C6×C13⋊C4Direct product of C6 and C13⋊C4784C6xC13:C4312,52
C2×C39⋊C4Direct product of C2 and C39⋊C4784C2xC39:C4312,53

Groups of order 320

dρLabelID
C5⋊C64The semidirect product of C5 and C64 acting via C64/C16=C43204C5:C64320,3
C20.45C428th non-split extension by C20 of C42 acting via C42/C2×C4=C2804C20.45C4^2320,24
C8.Dic101st non-split extension by C8 of Dic10 acting via Dic10/C10=C22804C8.Dic10320,45
D4014C48th semidirect product of D40 and C4 acting via C4/C2=C2804D40:14C4320,46
C40.7Q87th non-split extension by C40 of Q8 acting via Q8/C2=C221604C40.7Q8320,51
C40.6Q86th non-split extension by C40 of Q8 acting via Q8/C2=C22804C40.6Q8320,52
D40.5C43rd non-split extension by D40 of C4 acting via C4/C2=C21604D40.5C4320,55
C40.9Q89th non-split extension by C40 of Q8 acting via Q8/C2=C22804C40.9Q8320,69
C80⋊C46th semidirect product of C80 and C4 acting faithfully804C80:C4320,70
C40.Q81st non-split extension by C40 of Q8 acting via Q8/C2=C22804C40.Q8320,71
C8.25D2011st non-split extension by C8 of D20 acting via D20/D10=C2804C8.25D20320,72
D20.4C82nd non-split extension by D20 of C8 acting via C8/C4=C21604D20.4C8320,73
D408C42nd semidirect product of D40 and C4 acting via C4/C2=C2804D40:8C4320,76
C421Dic51st semidirect product of C42 and Dic5 acting via Dic5/C5=C4804C4^2:1Dic5320,89
C20.60(C4⋊C4)7th non-split extension by C20 of C4⋊C4 acting via C4⋊C4/C2×C4=C2804C20.60(C4:C4)320,91
C242Dic51st semidirect product of C24 and Dic5 acting via Dic5/C5=C4404C2^4:2Dic5320,94
(C22×C20)⋊C42nd semidirect product of C22×C20 and C4 acting faithfully804(C2^2xC20):C4320,97
C42⋊Dic52nd semidirect product of C42 and Dic5 acting via Dic5/C5=C4804C4^2:Dic5320,99
C42.Dic52nd non-split extension by C42 of Dic5 acting via Dic5/C5=C4804C4^2.Dic5320,100
C423Dic53rd semidirect product of C42 and Dic5 acting via Dic5/C5=C4404C4^2:3Dic5320,103
C42.3Dic53rd non-split extension by C42 of Dic5 acting via Dic5/C5=C4804C4^2.3Dic5320,106
C40.D448th non-split extension by C40 of D4 acting via D4/C2=C22804C40.D4320,111
(C2×C40)⋊C411st semidirect product of C2×C40 and C4 acting faithfully804(C2xC40):C4320,114
C23.9D202nd non-split extension by C23 of D20 acting via D20/C10=C22804C2^3.9D20320,115
M4(2)⋊4Dic54th semidirect product of M4(2) and Dic5 acting via Dic5/C10=C2804M4(2):4Dic5320,117
C20.51C4214th non-split extension by C20 of C42 acting via C42/C2×C4=C2804C20.51C4^2320,118
C40.92D415th non-split extension by C40 of D4 acting via D4/C22=C21604C40.92D4320,119
D8.Dic52nd non-split extension by D8 of Dic5 acting via Dic5/C10=C2804D8.Dic5320,121
Q16.Dic52nd non-split extension by Q16 of Dic5 acting via Dic5/C10=C21604Q16.Dic5320,123
D82Dic52nd semidirect product of D8 and Dic5 acting via Dic5/C10=C2804D8:2Dic5320,124
C20.58D812nd non-split extension by C20 of D8 acting via D8/D4=C21604C20.58D8320,125
C5×C4.9C42Direct product of C5 and C4.9C42804C5xC4.9C4^2320,142
C5×C4.10C42Direct product of C5 and C4.10C42804C5xC4.10C4^2320,143
C5×M4(2)⋊4C4Direct product of C5 and M4(2)⋊4C4804C5xM4(2):4C4320,149
C5×C16⋊C4Direct product of C5 and C16⋊C4804C5xC16:C4320,152
C5×C23.C8Direct product of C5 and C23.C8804C5xC2^3.C8320,154
C5×C2≀C4Direct product of C5 and C2≀C4404C5xC2wrC4320,156
C5×C23.D4Direct product of C5 and C23.D4804C5xC2^3.D4320,157
C5×C42⋊C4Direct product of C5 and C42⋊C4404C5xC4^2:C4320,158
C5×C423C4Direct product of C5 and C423C4804C5xC4^2:3C4320,159
C5×C42.C4Direct product of C5 and C42.C4804C5xC4^2.C4320,160
C5×C42.3C4Direct product of C5 and C42.3C4804C5xC4^2.3C4320,161
C5×D82C4Direct product of C5 and D82C4804C5xD8:2C4320,165
C5×M5(2)⋊C2Direct product of C5 and M5(2)⋊C2804C5xM5(2):C2320,166
C5×C8.17D4Direct product of C5 and C8.17D41604C5xC8.17D4320,167
C5×C8.Q8Direct product of C5 and C8.Q8804C5xC8.Q8320,170
D5⋊C32The semidirect product of D5 and C32 acting via C32/C16=C21604D5:C32320,179
C80.C45th non-split extension by C80 of C4 acting faithfully1604C80.C4320,180
C16×F5Direct product of C16 and F5804C16xF5320,181
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
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
C16.F51st non-split extension by C16 of F5 acting via F5/D5=C21604C16.F5320,189
C80.2C42nd non-split extension by C80 of C4 acting faithfully1604C80.2C4320,190
C422F52nd semidirect product of C42 and F5 acting via F5/C5=C4804C4^2:2F5320,192
C42.2F52nd non-split extension by C42 of F5 acting via F5/C5=C4804C4^2.2F5320,194
C42.3F53rd non-split extension by C42 of F5 acting via F5/C5=C4804C4^2.3F5320,198
C42.9F56th non-split extension by C42 of F5 acting via F5/D5=C2804C4^2.9F5320,199
C426F53rd semidirect product of C42 and F5 acting via F5/D5=C2404C4^2:6F5320,200
C423F53rd semidirect product of C42 and F5 acting via F5/C5=C4804C4^2:3F5320,201
C5⋊M6(2)The semidirect product of C5 and M6(2) acting via M6(2)/C2×C8=C41604C5:M6(2)320,215
C40.1C81st non-split extension by C40 of C8 acting via C8/C2=C4804C40.1C8320,227
C20.23C4216th non-split extension by C20 of C42 acting via C42/C4=C4804C20.23C4^2320,228
C20.10M4(2)4th non-split extension by C20 of M4(2) acting via M4(2)/C4=C4804C20.10M4(2)320,229
(C2×C8)⋊F51st semidirect product of C2×C8 and F5 acting via F5/C5=C4804(C2xC8):F5320,232
C20.24C4217th non-split extension by C20 of C42 acting via C42/C4=C4804C20.24C4^2320,233
C20.25C4218th non-split extension by C20 of C42 acting via C42/C4=C4804C20.25C4^2320,235
C20.29M4(2)4th non-split extension by C20 of M4(2) acting via M4(2)/C22=C4804C20.29M4(2)320,250
(C22×C4)⋊F51st semidirect product of C22×C4 and F5 acting via F5/C5=C4804(C2^2xC4):F5320,254
C242F51st semidirect product of C24 and F5 acting via F5/C5=C4404C2^4:2F5320,272
D4010C44th semidirect product of D40 and C4 acting via C4/C2=C2804D40:10C4320,344
D5×C4≀C2Direct product of D5 and C4≀C2404D5xC4wrC2320,447
C42⋊D101st semidirect product of C42 and D10 acting via D10/C5=C22804C4^2:D10320,448
M4(2).22D105th non-split extension by M4(2) of D10 acting via D10/D5=C2804M4(2).22D10320,450
C42.196D1016th non-split extension by C42 of D10 acting via D10/D5=C2804C4^2.196D10320,451
M4(2)⋊D104th semidirect product of M4(2) and D10 acting via D10/C5=C22804M4(2):D10320,452
D4.10D205th non-split extension by D4 of D20 acting via D20/D10=C2804D4.10D20320,454
D5×C8.C4Direct product of D5 and C8.C4804D5xC8.C4320,519
M4(2).25D108th non-split extension by M4(2) of D10 acting via D10/D5=C2804M4(2).25D10320,520
D4016C410th semidirect product of D40 and C4 acting via C4/C2=C2804D40:16C4320,521
D4013C47th semidirect product of D40 and C4 acting via C4/C2=C2804D40:13C4320,522
C8.24D2010th non-split extension by C8 of D20 acting via D20/D10=C2804C8.24D20320,525
D5×M5(2)Direct product of D5 and M5(2)804D5xM5(2)320,533
D20.5C83rd non-split extension by D20 of C8 acting via C8/C4=C21604D20.5C8320,534
D16⋊D52nd semidirect product of D16 and D5 acting via D5/C5=C2804D16:D5320,538
D5×SD32Direct product of D5 and SD32804D5xSD32320,540
SD323D5The semidirect product of SD32 and D5 acting through Inn(SD32)1604SD32:3D5320,543
Q32⋊D52nd semidirect product of Q32 and D5 acting via D5/C5=C21604Q32:D5320,545
C424D104th semidirect product of C42 and D10 acting via D10/C5=C22804C4^2:4D10320,632
(C2×D20)⋊25C410th semidirect product of C2×D20 and C4 acting via C4/C2=C2804(C2xD20):25C4320,633
C242D101st semidirect product of C24 and D10 acting via D10/C5=C22404C2^4:2D10320,659
C22⋊C4⋊D104th semidirect product of C22⋊C4 and D10 acting via D10/C5=C22804C2^2:C4:D10320,680
C425D105th semidirect product of C42 and D10 acting via D10/C5=C22804C4^2:5D10320,688
D20.14D414th non-split extension by D20 of D4 acting via D4/C2=C22804D20.14D4320,689
D205D45th semidirect product of D20 and D4 acting via D4/C2=C22404D20:5D4320,704
D20.15D415th non-split extension by D20 of D4 acting via D4/C2=C22804D20.15D4320,722
C23.Dic106th non-split extension by C23 of Dic10 acting via Dic10/C10=C22804C2^3.Dic10320,751
M4(2).Dic51st non-split extension by M4(2) of Dic5 acting via Dic5/C10=C2804M4(2).Dic5320,752
M4(2).31D104th non-split extension by M4(2) of D10 acting via D10/C10=C2804M4(2).31D10320,759
C23.20D2013rd non-split extension by C23 of D20 acting via D20/C10=C22804C2^3.20D20320,766
C40.70C2316th non-split extension by C40 of C23 acting via C23/C22=C21604C40.70C2^3320,767
D4.3D203rd non-split extension by D4 of D20 acting via D20/C20=C2804D4.3D20320,768
C40.93D416th non-split extension by C40 of D4 acting via D4/C22=C2804C40.93D4320,771
C40.50D450th non-split extension by C40 of D4 acting via D4/C2=C22804C40.50D4320,772
D8.D101st non-split extension by D8 of D10 acting via D10/C10=C2804D8.D10320,774
C40.23D423rd non-split extension by C40 of D4 acting via D4/C2=C22804C40.23D4320,787
C40.44D444th non-split extension by C40 of D4 acting via D4/C2=C22804C40.44D4320,804
Q16.D101st non-split extension by Q16 of D10 acting via D10/C10=C21604Q16.D10320,806
C40.29D429th non-split extension by C40 of D4 acting via D4/C2=C221604C40.29D4320,819
C40.30C2323rd non-split extension by C40 of C23 acting via C23/C2=C221604C40.30C2^3320,821
D85Dic5The semidirect product of D8 and Dic5 acting through Inn(D8)804D8:5Dic5320,823
D84Dic54th semidirect product of D8 and Dic5 acting via Dic5/C10=C2804D8:4Dic5320,824
(D4×C10)⋊21C45th semidirect product of D4×C10 and C4 acting via C4/C2=C2804(D4xC10):21C4320,863
(D4×C10).29C410th non-split extension by D4×C10 of C4 acting via C4/C2=C2804(D4xC10).29C4320,864
(D4×C10)⋊22C46th semidirect product of D4×C10 and C4 acting via C4/C2=C2804(D4xC10):22C4320,867
C5×C23.C23Direct product of C5 and C23.C23804C5xC2^3.C2^3320,911
C5×M4(2).8C22Direct product of C5 and M4(2).8C22804C5xM4(2).8C2^2320,914
C5×C42⋊C22Direct product of C5 and C42⋊C22804C5xC4^2:C2^2320,922
C5×M4(2).C4Direct product of C5 and M4(2).C4804C5xM4(2).C4320,931
C5×C8.26D4Direct product of C5 and C8.26D4804C5xC8.26D4320,945
C5×D44D4Direct product of C5 and D44D4404C5xD4:4D4320,954
C5×D4.8D4Direct product of C5 and D4.8D4804C5xD4.8D4320,955
C5×D4.9D4Direct product of C5 and D4.9D4804C5xD4.9D4320,956
C5×D4.10D4Direct product of C5 and D4.10D4804C5xD4.10D4320,957
C5×C2≀C22Direct product of C5 and C2≀C22404C5xC2wrC2^2320,958
C5×C23.7D4Direct product of C5 and C23.7D4804C5xC2^3.7D4320,959
C5×D4.3D4Direct product of C5 and D4.3D4804C5xD4.3D4320,972
C5×D4.4D4Direct product of C5 and D4.4D4804C5xD4.4D4320,973
C5×D4.5D4Direct product of C5 and D4.5D41604C5xD4.5D4320,974
C5×C16⋊C22Direct product of C5 and C16⋊C22804C5xC16:C2^2320,1010
C5×Q32⋊C2Direct product of C5 and Q32⋊C21604C5xQ32:C2320,1011
D5⋊M5(2)The semidirect product of D5 and M5(2) acting via M5(2)/C2×C8=C2804D5:M5(2)320,1053
C20.12C425th non-split extension by C20 of C42 acting via C42/C4=C4804C20.12C4^2320,1056
(C2×C8)⋊6F54th semidirect product of C2×C8 and F5 acting via F5/D5=C2804(C2xC8):6F5320,1059
(C8×D5).C46th non-split extension by C8×D5 of C4 acting via C4/C2=C2804(C8xD5).C4320,1062
C23⋊F55C2The semidirect product of C23⋊F5 and C2 acting through Inn(C23⋊F5)804C2^3:F5:5C2320,1083
(C4×D5).D454th non-split extension by C4×D5 of D4 acting via D4/C2=C22804(C4xD5).D4320,1099
C40.47C2340th non-split extension by C40 of C23 acting via C23/C2=C22804C40.47C2^3320,1417
C40.9C232nd non-split extension by C40 of C23 acting via C23/C2=C22804C40.9C2^3320,1420
D5×C8○D4Direct product of D5 and C8○D4804D5xC8oD4320,1421
C20.72C2419th non-split extension by C20 of C24 acting via C24/C23=C2804C20.72C2^4320,1422
D4.11D201st non-split extension by D4 of D20 acting through Inn(D4)804D4.11D20320,1423
D813D102nd semidirect product of D8 and D10 acting through Inn(D8)804D8:13D10320,1429
D20.29D412nd non-split extension by D20 of D4 acting via D4/C4=C2804D20.29D4320,1434
D20.30D413rd non-split extension by D20 of D4 acting via D4/C4=C21604D20.30D4320,1438
D5×C4○D8Direct product of D5 and C4○D8804D5xC4oD8320,1439
Q16⋊D104th semidirect product of Q16 and D10 acting via D10/C10=C2804Q16:D10320,1440
D811D105th semidirect product of D8 and D10 acting via D10/C10=C2804D8:11D10320,1442
C20.76C2423rd non-split extension by C20 of C24 acting via C24/C23=C2804C20.76C2^4320,1491
C20.C2435th non-split extension by C20 of C24 acting via C24/C22=C22804C20.C2^4320,1494
C5×Q8○M4(2)Direct product of C5 and Q8○M4(2)804C5xQ8oM4(2)320,1570
C5×D8⋊C22Direct product of C5 and D8⋊C22804C5xD8:C2^2320,1577
C5×D4○D8Direct product of C5 and D4○D8804C5xD4oD8320,1578
C5×D4○SD16Direct product of C5 and D4○SD16804C5xD4oSD16320,1579
C5×Q8○D8Direct product of C5 and Q8○D81604C5xQ8oD8320,1580
2- 1+4⋊D5The semidirect product of 2- 1+4 and D5 acting faithfully324ES-(2,2):D5320,1582
2- 1+4.C10The non-split extension by 2- 1+4 of C10 acting via C10/C2=C5644ES-(2,2).C10320,1586
C10.C2514th non-split extension by C10 of C25 acting via C25/C24=C2804C10.C2^5320,1621
C5×C2.C25Direct product of C5 and C2.C25804C5xC2.C2^5320,1634

Groups of order 324

dρLabelID
C9×C32⋊C4Direct product of C9 and C32⋊C4364C9xC3^2:C4324,109
C323Dic9The semidirect product of C32 and Dic9 acting via Dic9/C9=C4364C3^2:3Dic9324,112
C3×S3×D9Direct product of C3, S3 and D9364C3xS3xD9324,114
S32×C9Direct product of C9, S3 and S3364S3^2xC9324,115
C325D182nd semidirect product of C32 and D18 acting via D18/C9=C22364C3^2:5D18324,123
C33⋊A4The semidirect product of C33 and A4 acting faithfully94C3^3:A4324,160
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

Groups of order 336

dρLabelID
D7×C3⋊C8Direct product of D7 and C3⋊C81684D7xC3:C8336,23
S3×C7⋊C8Direct product of S3 and C7⋊C81684S3xC7:C8336,24
D21⋊C8The semidirect product of D21 and C8 acting via C8/C4=C21684D21:C8336,25
C28.32D611st non-split extension by C28 of D6 acting via D6/S3=C21684C28.32D6336,26
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
C21⋊D81st semidirect product of C21 and D8 acting via D8/C4=C221684C21:D8336,29
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
C21⋊Q161st semidirect product of C21 and Q16 acting via Q16/C4=C223364C21:Q16336,38
C3×D4⋊D7Direct product of C3 and D4⋊D71684C3xD4:D7336,69
C3×D4.D7Direct product of C3 and D4.D71684C3xD4.D7336,70
C3×Q8⋊D7Direct product of C3 and Q8⋊D71684C3xQ8:D7336,71
C3×C7⋊Q16Direct product of C3 and C7⋊Q163364C3xC7:Q16336,72
C7×D4⋊S3Direct product of C7 and D4⋊S31684C7xD4:S3336,85
C7×D4.S3Direct product of C7 and D4.S31684C7xD4.S3336,86
C7×Q82S3Direct product of C7 and Q82S31684C7xQ8:2S3336,87
C7×C3⋊Q16Direct product of C7 and C3⋊Q163364C7xC3:Q16336,88
SL2(𝔽7)Special linear group on 𝔽72; = C2.GL3(𝔽2)164SL(2,7)336,114
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
D21⋊Q8The semidirect product of D21 and Q8 acting via Q8/C4=C21684D21:Q8336,143
D6.D143rd non-split extension by D6 of D14 acting via D14/C14=C21684D6.D14336,144
C4×S3×D7Direct product of C4, S3 and D7844C4xS3xD7336,147
C28⋊D62nd semidirect product of C28 and D6 acting via D6/C3=C22844C28:D6336,150
Dic7.D65th non-split extension by Dic7 of D6 acting via D6/S3=C21684Dic7.D6336,152
Dic3.D146th non-split extension by Dic3 of D14 acting via D14/D7=C21684Dic3.D14336,155
D7×C3⋊D4Direct product of D7 and C3⋊D4844D7xC3:D4336,161
S3×C7⋊D4Direct product of S3 and C7⋊D4844S3xC7:D4336,162
C3×D4×D7Direct product of C3, D4 and D7844C3xD4xD7336,178
C3×D42D7Direct product of C3 and D42D71684C3xD4:2D7336,179
C3×Q8×D7Direct product of C3, Q8 and D71684C3xQ8xD7336,180
C3×Q82D7Direct product of C3 and Q82D71684C3xQ8:2D7336,181
S3×C7×D4Direct product of C7, S3 and D4844S3xC7xD4336,188
C7×D42S3Direct product of C7 and D42S31684C7xD4:2S3336,189
S3×C7×Q8Direct product of C7, S3 and Q81684S3xC7xQ8336,190
C7×Q83S3Direct product of C7 and Q83S31684C7xQ8:3S3336,191

Groups of order 340

dρLabelID
C5×C17⋊C4Direct product of C5 and C17⋊C4854C5xC17:C4340,5
C85⋊C43rd semidirect product of C85 and C4 acting faithfully854C85:C4340,6
C17×F5Direct product of C17 and F5854C17xF5340,7
C173F5The semidirect product of C17 and F5 acting via F5/D5=C2854C17:3F5340,8

Groups of order 348

dρLabelID
C3×C29⋊C4Direct product of C3 and C29⋊C4874C3xC29:C4348,5
C87⋊C41st semidirect product of C87 and C4 acting faithfully874C87:C4348,6

Groups of order 352

dρLabelID
C22.2D441st non-split extension by C22 of D44 acting via D44/D22=C2884C2^2.2D44352,12
C44.53D410th non-split extension by C44 of D4 acting via D4/C22=C21764C44.53D4352,28
D444C44th semidirect product of D44 and C4 acting via C4/C2=C2884D44:4C4352,31
C44.D48th non-split extension by C44 of D4 acting via D4/C2=C22884C44.D4352,39
C23⋊Dic11The semidirect product of C23 and Dic11 acting via Dic11/C11=C4884C2^3:Dic11352,40
C44.10D410th non-split extension by C44 of D4 acting via D4/C2=C221764C44.10D4352,42
C44.56D413rd non-split extension by C44 of D4 acting via D4/C22=C2884C44.56D4352,43
C11×C23⋊C4Direct product of C11 and C23⋊C4884C11xC2^3:C4352,48
C11×C4.D4Direct product of C11 and C4.D4884C11xC4.D4352,49
C11×C4.10D4Direct product of C11 and C4.10D41764C11xC4.10D4352,50
M4(2)×D11Direct product of M4(2) and D11884M4(2)xD11352,101
D44.C4The non-split extension by D44 of C4 acting via C4/C2=C21764D44.C4352,102
D4⋊D222nd semidirect product of D4 and D22 acting via D22/D11=C2884D4:D22352,106
SD16×D11Direct product of SD16 and D11884SD16xD11352,108
Q8.D222nd non-split extension by Q8 of D22 acting via D22/D11=C21764Q8.D22352,111
Q16⋊D112nd semidirect product of Q16 and D11 acting via D11/C11=C21764Q16:D11352,113
D446C224th semidirect product of D44 and C22 acting via C22/C2=C2884D44:6C2^2352,127
C44.C2315th non-split extension by C44 of C23 acting via C23/C2=C221764C44.C2^3352,137
Q8.Dic11The non-split extension by Q8 of Dic11 acting through Inn(Q8)1764Q8.Dic11352,143
D4.8D223rd non-split extension by D4 of D22 acting via D22/C22=C21764D4.8D22352,145
C11×C8⋊C22Direct product of C11 and C8⋊C22884C11xC8:C2^2352,171
C11×C8.C22Direct product of C11 and C8.C221764C11xC8.C2^2352,172
D46D222nd semidirect product of D4 and D22 acting through Inn(D4)884D4:6D22352,179
Q8.10D221st non-split extension by Q8 of D22 acting through Inn(Q8)1764Q8.10D22352,182
C4○D4×D11Direct product of C4○D4 and D11884C4oD4xD11352,183
C11×2+ 1+4Direct product of C11 and 2+ 1+4884C11xES+(2,2)352,192
C11×2- 1+4Direct product of C11 and 2- 1+41764C11xES-(2,2)352,193

Groups of order 360

dρLabelID
C9×C5⋊C8Direct product of C9 and C5⋊C83604C9xC5:C8360,5
C45⋊C81st semidirect product of C45 and C8 acting via C8/C2=C43604C45:C8360,6
C18×F5Direct product of C18 and F5904C18xF5360,43
C2×C9⋊F5Direct product of C2 and C9⋊F5904C2xC9:F5360,44
C3×C15⋊C8Direct product of C3 and C15⋊C81204C3xC15:C8360,53
C5×C322C8Direct product of C5 and C322C81204C5xC3^2:2C8360,55
(C3×C15)⋊9C86th semidirect product of C3×C15 and C8 acting via C8/C2=C41204(C3xC15):9C8360,56
C3×D5×Dic3Direct product of C3, D5 and Dic3604C3xD5xDic3360,58
C3×S3×Dic5Direct product of C3, S3 and Dic51204C3xS3xDic5360,59
C3×D30.C2Direct product of C3 and D30.C21204C3xD30.C2360,60
C3×C15⋊D4Direct product of C3 and C15⋊D4604C3xC15:D4360,61
C3×C3⋊D20Direct product of C3 and C3⋊D20604C3xC3:D20360,62
C3×C5⋊D12Direct product of C3 and C5⋊D121204C3xC5:D12360,63
C3×C15⋊Q8Direct product of C3 and C15⋊Q81204C3xC15:Q8360,64
C5×S3×Dic3Direct product of C5, S3 and Dic31204C5xS3xDic3360,72
C5×C6.D6Direct product of C5 and C6.D6604C5xC6.D6360,73
C5×D6⋊S3Direct product of C5 and D6⋊S31204C5xD6:S3360,74
C5×C3⋊D12Direct product of C5 and C3⋊D12604C5xC3:D12360,75
C5×C322Q8Direct product of C5 and C322Q81204C5xC3^2:2Q8360,76
D30.S3The non-split extension by D30 of S3 acting via S3/C3=C21204D30.S3360,84
Dic15⋊S33rd semidirect product of Dic15 and S3 acting via S3/C3=C2604Dic15:S3360,85
D30⋊S33rd semidirect product of D30 and S3 acting via S3/C3=C2604D30:S3360,86
C323D202nd semidirect product of C32 and D20 acting via D20/C10=C221204C3^2:3D20360,87
C323Dic102nd semidirect product of C32 and Dic10 acting via Dic10/C10=C221204C3^2:3Dic10360,88
C3×S5Direct product of C3 and S5154C3xS5360,119
C5×S3≀C2Direct product of C5 and S3≀C2304C5xS3wrC2360,132
S32⋊D5The semidirect product of S32 and D5 acting via D5/C5=C2304S3^2:D5360,133
C6×C3⋊F5Direct product of C6 and C3⋊F5604C6xC3:F5360,146
C10×C32⋊C4Direct product of C10 and C32⋊C4604C10xC3^2:C4360,148
C2×C32⋊Dic5Direct product of C2 and C32⋊Dic5604C2xC3^2:Dic5360,149
S3×C6×D5Direct product of C6, S3 and D5604S3xC6xD5360,151
S32×C10Direct product of C10, S3 and S3604S3^2xC10360,153
C2×D15⋊S3Direct product of C2 and D15⋊S3604C2xD15:S3360,155

Groups of order 364

dρLabelID
C7×C13⋊C4Direct product of C7 and C13⋊C4914C7xC13:C4364,5
C91⋊C41st semidirect product of C91 and C4 acting faithfully914C91:C4364,6

Groups of order 380

dρLabelID
C19×F5Direct product of C19 and F5954C19xF5380,5
C19⋊F5The semidirect product of C19 and F5 acting via F5/D5=C2954C19:F5380,6

Groups of order 396

dρLabelID
C11×C32⋊C4Direct product of C11 and C32⋊C4664C11xC3^2:C4396,17
C32⋊Dic11The semidirect product of C32 and Dic11 acting via Dic11/C11=C4664C3^2:Dic11396,18
C3×S3×D11Direct product of C3, S3 and D11664C3xS3xD11396,19
S32×C11Direct product of C11, S3 and S3664S3^2xC11396,21
D33⋊S3The semidirect product of D33 and S3 acting via S3/C3=C2664D33:S3396,23

Groups of order 400

dρLabelID
C25⋊C16The semidirect product of C25 and C16 acting via C16/C4=C44004C25:C16400,3
D25⋊C8The semidirect product of D25 and C8 acting via C8/C4=C22004D25:C8400,28
C100.C41st non-split extension by C100 of C4 acting faithfully2004C100.C4400,29
C4×C25⋊C4Direct product of C4 and C25⋊C41004C4xC25:C4400,30
C100⋊C41st semidirect product of C100 and C4 acting faithfully1004C100:C4400,31
C5×C5⋊C16Direct product of C5 and C5⋊C16804C5xC5:C16400,56
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
D5×C52C8Direct product of D5 and C52C8804D5xC5:2C8400,60
C20.29D103rd non-split extension by C20 of D10 acting via D10/D5=C2404C20.29D10400,61
C20.30D104th non-split extension by C20 of D10 acting via D10/D5=C2804C20.30D10400,62
C20.31D105th non-split extension by C20 of D10 acting via D10/D5=C2404C20.31D10400,63
C522D81st semidirect product of C52 and D8 acting via D8/C4=C22804C5^2:2D8400,64
D20.D52nd non-split extension by D20 of D5 acting via D5/C5=C2804D20.D5400,66
C522Q161st semidirect product of C52 and Q16 acting via Q16/C4=C22804C5^2:2Q16400,69
C5×D4⋊D5Direct product of C5 and D4⋊D5404C5xD4:D5400,87
C5×D4.D5Direct product of C5 and D4.D5404C5xD4.D5400,88
C5×Q8⋊D5Direct product of C5 and Q8⋊D5804C5xQ8:D5400,89
C5×C5⋊Q16Direct product of C5 and C5⋊Q16804C5xC5:Q16400,90
C2.D5≀C22nd central extension by C2 of D5≀C2204C2.D5wrC2400,130
C52⋊D8The semidirect product of C52 and D8 acting via D8/C2=D4404C5^2:D8400,131
C5×D5⋊C8Direct product of C5 and D5⋊C8804C5xD5:C8400,135
C5×C4.F5Direct product of C5 and C4.F5804C5xC4.F5400,136
C20×F5Direct product of C20 and F5804C20xF5400,137
C5×C4⋊F5Direct product of C5 and C4⋊F5804C5xC4:F5400,138
C5×C22.F5Direct product of C5 and C22.F5404C5xC2^2.F5400,140
C5×C22⋊F5Direct product of C5 and C22⋊F5404C5xC2^2:F5400,141
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
C4×D5.D5Direct product of C4 and D5.D5804C4xD5.D5400,144
C205F51st semidirect product of C20 and F5 acting via F5/D5=C2804C20:5F5400,145
C102.C44th non-split extension by C102 of C4 acting faithfully404C10^2.C4400,147
D10.D105th non-split extension by D10 of D10 acting via D10/C10=C2404D10.D10400,148
C20.11F511st non-split extension by C20 of F5 acting via F5/C5=C4404C20.11F5400,156
C528M4(2)4th semidirect product of C52 and M4(2) acting via M4(2)/C4=C4404C5^2:8M4(2)400,157
C4×C52⋊C4Direct product of C4 and C52⋊C4404C4xC5^2:C4400,158
C202F52nd semidirect product of C20 and F5 acting via F5/C5=C4404C20:2F5400,159
D20⋊D53rd semidirect product of D20 and D5 acting via D5/C5=C2404D20:D5400,165
Dic10⋊D54th semidirect product of Dic10 and D5 acting via D5/C5=C2404Dic10:D5400,166
D10.9D101st non-split extension by D10 of D10 acting via D10/C10=C2404D10.9D10400,167
C4×D52Direct product of C4, D5 and D5404C4xD5^2400,169
C20⋊D102nd semidirect product of C20 and D10 acting via D10/C5=C22404C20:D10400,171
Dic5.D103rd non-split extension by Dic5 of D10 acting via D10/D5=C2404Dic5.D10400,173
D5×C5⋊D4Direct product of D5 and C5⋊D4404D5xC5:D4400,179
C5×D4×D5Direct product of C5, D4 and D5404C5xD4xD5400,185
C5×D42D5Direct product of C5 and D42D5404C5xD4:2D5400,186
C5×Q8×D5Direct product of C5, Q8 and D5804C5xQ8xD5400,187
C5×Q82D5Direct product of C5 and Q82D5804C5xQ8:2D5400,188

Groups of order 408

dρLabelID
C3×C172C8Direct product of C3 and C172C84084C3xC17:2C8408,5
C513C81st semidirect product of C51 and C8 acting via C8/C2=C44084C51:3C8408,6
C6×C17⋊C4Direct product of C6 and C17⋊C41024C6xC17:C4408,39
C2×C51⋊C4Direct product of C2 and C51⋊C41024C2xC51:C4408,40

Groups of order 416

dρLabelID
C13⋊C32The semidirect product of C13 and C32 acting via C32/C8=C44164C13:C32416,3
C22.2D521st non-split extension by C22 of D52 acting via D52/D26=C21044C2^2.2D52416,13
C52.53D410th non-split extension by C52 of D4 acting via D4/C22=C22084C52.53D4416,29
D527C44th semidirect product of D52 and C4 acting via C4/C2=C21044D52:7C4416,32
C52.D48th non-split extension by C52 of D4 acting via D4/C2=C221044C52.D4416,40
C23⋊Dic13The semidirect product of C23 and Dic13 acting via Dic13/C13=C41044C2^3:Dic13416,41
C52.10D410th non-split extension by C52 of D4 acting via D4/C2=C222084C52.10D4416,43
C52.56D413rd non-split extension by C52 of D4 acting via D4/C22=C21044C52.56D4416,44
C13×C23⋊C4Direct product of C13 and C23⋊C41044C13xC2^3:C4416,49
C13×C4.D4Direct product of C13 and C4.D41044C13xC4.D4416,50
C13×C4.10D4Direct product of C13 and C4.10D42084C13xC4.10D4416,51
D13⋊C16The semidirect product of D13 and C16 acting via C16/C8=C22084D13:C16416,64
D26.C83rd non-split extension by D26 of C8 acting via C8/C4=C22084D26.C8416,65
C8×C13⋊C4Direct product of C8 and C13⋊C41044C8xC13:C4416,66
C104⋊C44th semidirect product of C104 and C4 acting faithfully1044C104:C4416,67
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
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
C52.C81st non-split extension by C52 of C8 acting via C8/C2=C42084C52.C8416,73
D26.4D44th non-split extension by D26 of D4 acting via D4/C2=C221044D26.4D4416,86
Dic13.4D44th non-split extension by Dic13 of D4 acting via D4/C2=C221044Dic13.4D4416,88
M4(2)×D13Direct product of M4(2) and D131044M4(2)xD13416,127
D52.2C4The non-split extension by D52 of C4 acting via C4/C2=C22084D52.2C4416,128
D8⋊D132nd semidirect product of D8 and D13 acting via D13/C13=C21044D8:D13416,132
SD16×D13Direct product of SD16 and D131044SD16xD13416,134
D26.6D42nd non-split extension by D26 of D4 acting via D4/C4=C22084D26.6D4416,137
Q16⋊D132nd semidirect product of Q16 and D13 acting via D13/C13=C22084Q16:D13416,139
D526C224th semidirect product of D52 and C22 acting via C22/C2=C21044D52:6C2^2416,153
Q8.D261st non-split extension by Q8 of D26 acting via D26/C26=C22084Q8.D26416,163
D4.Dic13The non-split extension by D4 of Dic13 acting through Inn(D4)2084D4.Dic13416,169
C52.C2318th non-split extension by C52 of C23 acting via C23/C2=C222084C52.C2^3416,171
C13×C8⋊C22Direct product of C13 and C8⋊C221044C13xC8:C2^2416,197
C13×C8.C22Direct product of C13 and C8.C222084C13xC8.C2^2416,198
D13⋊M4(2)The semidirect product of D13 and M4(2) acting via M4(2)/C2×C4=C21044D13:M4(2)416,201
D26.C2311st non-split extension by D26 of C23 acting via C23/C22=C21044D26.C2^3416,204
D46D262nd semidirect product of D4 and D26 acting through Inn(D4)1044D4:6D26416,218
Q8.10D261st non-split extension by Q8 of D26 acting through Inn(Q8)2084Q8.10D26416,221
C4○D4×D13Direct product of C4○D4 and D131044C4oD4xD13416,222
C13×2+ 1+4Direct product of C13 and 2+ 1+41044C13xES+(2,2)416,231
C13×2- 1+4Direct product of C13 and 2- 1+42084C13xES-(2,2)416,232

Groups of order 420

dρLabelID
F5×C21Direct product of C21 and F51054F5xC21420,20
C3×C7⋊F5Direct product of C3 and C7⋊F51054C3xC7:F5420,21
C7×C3⋊F5Direct product of C7 and C3⋊F51054C7xC3:F5420,22
C5⋊Dic21The semidirect product of C5 and Dic21 acting via Dic21/C21=C41054C5:Dic21420,23
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
D15⋊D7The semidirect product of D15 and D7 acting via D7/C7=C21054D15:D7420,30

Groups of order 432

dρLabelID
D9×C3⋊C8Direct product of D9 and C3⋊C81444D9xC3:C8432,58
C36.38D69th non-split extension by C36 of D6 acting via D6/S3=C2724C36.38D6432,59
C36.39D610th non-split extension by C36 of D6 acting via D6/S3=C21444C36.39D6432,60
C36.40D611st non-split extension by C36 of D6 acting via D6/S3=C2724C36.40D6432,61
S3×C9⋊C8Direct product of S3 and C9⋊C81444S3xC9:C8432,66
D6.Dic9The non-split extension by D6 of Dic9 acting via Dic9/C18=C21444D6.Dic9432,67
D36⋊S32nd semidirect product of D36 and S3 acting via S3/C3=C21444D36:S3432,68
D12.D92nd non-split extension by D12 of D9 acting via D9/C9=C21444D12.D9432,70
Dic6⋊D92nd semidirect product of Dic6 and D9 acting via D9/C9=C21444Dic6:D9432,72
C12.D1816th non-split extension by C12 of D18 acting via D18/C9=C221444C12.D18432,74
C3×D4.D9Direct product of C3 and D4.D9724C3xD4.D9432,148
C3×D4⋊D9Direct product of C3 and D4⋊D9724C3xD4:D9432,149
C9×D4⋊S3Direct product of C9 and D4⋊S3724C9xD4:S3432,150
C9×D4.S3Direct product of C9 and D4.S3724C9xD4.S3432,151
C3×C9⋊Q16Direct product of C3 and C9⋊Q161444C3xC9:Q16432,156
C3×Q82D9Direct product of C3 and Q82D91444C3xQ8:2D9432,157
C9×Q82S3Direct product of C9 and Q82S31444C9xQ8:2S3432,158
C9×C3⋊Q16Direct product of C9 and C3⋊Q161444C9xC3:Q16432,159
C3×Q8.D9Direct product of C3 and Q8.D91444C3xQ8.D9432,244
C3×Q8⋊D9Direct product of C3 and Q8⋊D91444C3xQ8:D9432,246
Q8⋊C93S3The semidirect product of Q8⋊C9 and S3 acting through Inn(Q8⋊C9)1444Q8:C9:3S3432,267
S3×Q8⋊C9Direct product of S3 and Q8⋊C91444S3xQ8:C9432,268
D18.D61st non-split extension by D18 of D6 acting via D6/S3=C2724D18.D6432,281
Dic18⋊S33rd semidirect product of Dic18 and S3 acting via S3/C3=C2724Dic18:S3432,283
D12⋊D93rd semidirect product of D12 and D9 acting via D9/C9=C2724D12:D9432,286
D6.D181st non-split extension by D6 of D18 acting via D18/C18=C2724D6.D18432,287
C4×S3×D9Direct product of C4, S3 and D9724C4xS3xD9432,290
C36⋊D62nd semidirect product of C36 and D6 acting via D6/C3=C22724C36:D6432,293
D18.3D63rd non-split extension by D18 of D6 acting via D6/S3=C2724D18.3D6432,305
Dic3.D185th non-split extension by Dic3 of D18 acting via D18/D9=C2724Dic3.D18432,309
S3×C9⋊D4Direct product of S3 and C9⋊D4724S3xC9:D4432,313
D9×C3⋊D4Direct product of D9 and C3⋊D4724D9xC3:D4432,314
C3×D4×D9Direct product of C3, D4 and D9724C3xD4xD9432,356
C3×D42D9Direct product of C3 and D42D9724C3xD4:2D9432,357
S3×D4×C9Direct product of C9, S3 and D4724S3xD4xC9432,358
C9×D42S3Direct product of C9 and D42S3724C9xD4:2S3432,359
C3×Q8×D9Direct product of C3, Q8 and D91444C3xQ8xD9432,364
C3×Q83D9Direct product of C3 and Q83D91444C3xQ8:3D9432,365
S3×Q8×C9Direct product of C9, S3 and Q81444S3xQ8xC9432,366
C9×Q83S3Direct product of C9 and Q83S31444C9xQ8:3S3432,367
C3×C322C16Direct product of C3 and C322C16484C3xC3^2:2C16432,412
C334C162nd semidirect product of C33 and C16 acting via C16/C4=C4484C3^3:4C16432,413
C3×S3×C3⋊C8Direct product of C3, S3 and C3⋊C8484C3xS3xC3:C8432,414
C3×C12.29D6Direct product of C3 and C12.29D6484C3xC12.29D6432,415
C3×D6.Dic3Direct product of C3 and D6.Dic3484C3xD6.Dic3432,416
C3×C12.31D6Direct product of C3 and C12.31D6484C3xC12.31D6432,417
C3×C322D8Direct product of C3 and C322D8484C3xC3^2:2D8432,418
C3×C3⋊D24Direct product of C3 and C3⋊D24484C3xC3:D24432,419
C3×Dic6⋊S3Direct product of C3 and Dic6⋊S3484C3xDic6:S3432,420
C3×D12.S3Direct product of C3 and D12.S3484C3xD12.S3432,421
C3×C325SD16Direct product of C3 and C325SD16484C3xC3^2:5SD16432,422
C3×C322Q16Direct product of C3 and C322Q16484C3xC3^2:2Q16432,423
C3×C323Q16Direct product of C3 and C323Q16484C3xC3^2:3Q16432,424
C12.93S3213rd non-split extension by C12 of S32 acting via S32/C3⋊S3=C2484C12.93S3^2432,455
C3310M4(2)6th semidirect product of C33 and M4(2) acting via M4(2)/C4=C22484C3^3:10M4(2)432,456
C339D86th semidirect product of C33 and D8 acting via D8/C4=C22484C3^3:9D8432,457
C3318SD1610th semidirect product of C33 and SD16 acting via SD16/C4=C22484C3^3:18SD16432,458
C339Q166th semidirect product of C33 and Q16 acting via Q16/C4=C22484C3^3:9Q16432,459
C3×S32⋊C4Direct product of C3 and S32⋊C4244C3xS3^2:C4432,574
C3×C3⋊S3.Q8Direct product of C3 and C3⋊S3.Q8484C3xC3:S3.Q8432,575
C3×C32⋊D8Direct product of C3 and C32⋊D8244C3xC3^2:D8432,576
C3×C322SD16Direct product of C3 and C322SD16244C3xC3^2:2SD16432,577
C3×C32⋊Q16Direct product of C3 and C32⋊Q16484C3xC3^2:Q16432,578
C3⋊S3.2D121st non-split extension by C3⋊S3 of D12 acting via D12/C6=C22244C3:S3.2D12432,579
S32⋊Dic3The semidirect product of S32 and Dic3 acting via Dic3/C6=C2244S3^2:Dic3432,580
C33⋊C4⋊C42nd semidirect product of C33⋊C4 and C4 acting via C4/C2=C2484C3^3:C4:C4432,581
C33⋊D82nd semidirect product of C33 and D8 acting via D8/C2=D4244C3^3:D8432,582
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
C33⋊Q162nd semidirect product of C33 and Q16 acting via Q16/C2=D4484C3^3:Q16432,585
C3×C6.5S4Direct product of C3 and C6.5S4484C3xC6.5S4432,616
C3×C6.6S4Direct product of C3 and C6.6S4484C3xC6.6S4432,617
C3×Dic3.A4Direct product of C3 and Dic3.A4484C3xDic3.A4432,622
C3×S3×SL2(𝔽3)Direct product of C3, S3 and SL2(𝔽3)484C3xS3xSL(2,3)432,623
C3×C3⋊S33C8Direct product of C3 and C3⋊S33C8484C3xC3:S3:3C8432,628
C3×C32⋊M4(2)Direct product of C3 and C32⋊M4(2)484C3xC3^2:M4(2)432,629
C12×C32⋊C4Direct product of C12 and C32⋊C4484C12xC3^2:C4432,630
C3×C4⋊(C32⋊C4)Direct product of C3 and C4⋊(C32⋊C4)484C3xC4:(C3^2:C4)432,631
C3×C62.C4Direct product of C3 and C62.C4244C3xC6^2.C4432,633
C3×C62⋊C4Direct product of C3 and C62⋊C4244C3xC6^2:C4432,634
C337(C2×C8)2nd semidirect product of C33 and C2×C8 acting via C2×C8/C4=C4484C3^3:7(C2xC8)432,635
C334M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C4=C4484C3^3:4M4(2)432,636
C4×C33⋊C4Direct product of C4 and C33⋊C4484C4xC3^3:C4432,637
C339(C4⋊C4)2nd semidirect product of C33 and C4⋊C4 acting via C4⋊C4/C4=C4484C3^3:9(C4:C4)432,638
C3312M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C22=C4244C3^3:12M4(2)432,640
C6211Dic31st semidirect product of C62 and Dic3 acting via Dic3/C3=C4244C6^2:11Dic3432,641
C3×S3×Dic6Direct product of C3, S3 and Dic6484C3xS3xDic6432,642
C3×D125S3Direct product of C3 and D125S3484C3xD12:5S3432,643
C3×D12⋊S3Direct product of C3 and D12⋊S3484C3xD12:S3432,644
C3×Dic3.D6Direct product of C3 and Dic3.D6484C3xDic3.D6432,645
C3×D6.D6Direct product of C3 and D6.D6484C3xD6.D6432,646
C3×D6.6D6Direct product of C3 and D6.6D6484C3xD6.6D6432,647
S32×C12Direct product of C12, S3 and S3484S3^2xC12432,648
C3×S3×D12Direct product of C3, S3 and D12484C3xS3xD12432,649
C3×D6⋊D6Direct product of C3 and D6⋊D6484C3xD6:D6432,650
C3×D6.3D6Direct product of C3 and D6.3D6244C3xD6.3D6432,652
C3×D6.4D6Direct product of C3 and D6.4D6244C3xD6.4D6432,653
C3×S3×C3⋊D4Direct product of C3, S3 and C3⋊D4244C3xS3xC3:D4432,658
C3×Dic3⋊D6Direct product of C3 and Dic3⋊D6244C3xDic3:D6432,659
C3⋊S34Dic6The semidirect product of C3⋊S3 and Dic6 acting via Dic6/C12=C2484C3:S3:4Dic6432,687
C12⋊S312S36th semidirect product of C12⋊S3 and S3 acting via S3/C3=C2484C12:S3:12S3432,688
C12.95S3215th non-split extension by C12 of S32 acting via S32/C3⋊S3=C2484C12.95S3^2432,689
C4×C324D6Direct product of C4 and C324D6484C4xC3^2:4D6432,690
C123S323rd semidirect product of C12 and S32 acting via S32/C32=C22484C12:3S3^2432,691
C62.96D644th non-split extension by C62 of D6 acting via D6/C3=C22244C6^2.96D6432,693
C6224D65th semidirect product of C62 and D6 acting via D6/C3=C22244C6^2:24D6432,696
C6×S3≀C2Direct product of C6 and S3≀C2244C6xS3wrC2432,754
C2×C33⋊D4Direct product of C2 and C33⋊D4244C2xC3^3:D4432,755

Groups of order 440

dρLabelID
C11×C5⋊C8Direct product of C11 and C5⋊C84404C11xC5:C8440,15
C55⋊C81st semidirect product of C55 and C8 acting via C8/C2=C44404C55:C8440,16
F5×C22Direct product of C22 and F51104F5xC22440,45
C2×C11⋊F5Direct product of C2 and C11⋊F51104C2xC11:F5440,46

Groups of order 444

dρLabelID
C3×C37⋊C4Direct product of C3 and C37⋊C41114C3xC37:C4444,9
C37⋊Dic3The semidirect product of C37 and Dic3 acting via Dic3/C3=C41114C37:Dic3444,10

Groups of order 448

dρLabelID
C28.15C428th non-split extension by C28 of C42 acting via C42/C2×C4=C21124C28.15C4^2448,23
C56.Q85th non-split extension by C56 of Q8 acting via Q8/C2=C221124C56.Q8448,44
D568C48th semidirect product of D56 and C4 acting via C4/C2=C21124D56:8C4448,45
C8.7Dic144th non-split extension by C8 of Dic14 acting via Dic14/Dic7=C22244C8.7Dic14448,50
C8.Dic142nd non-split extension by C8 of Dic14 acting via Dic14/C14=C221124C8.Dic14448,51
Dic28.C43rd non-split extension by Dic28 of C4 acting via C4/C2=C22244Dic28.C4448,54
C56.9Q89th non-split extension by C56 of Q8 acting via Q8/C2=C221124C56.9Q8448,68
C112⋊C42nd semidirect product of C112 and C4 acting faithfully1124C112:C4448,69
C16⋊Dic71st semidirect product of C16 and Dic7 acting via Dic7/C7=C41124C16:Dic7448,70
M5(2)⋊D73rd semidirect product of M5(2) and D7 acting via D7/C7=C21124M5(2):D7448,71
Dic14.C82nd non-split extension by Dic14 of C8 acting via C8/C4=C22244Dic14.C8448,72
D562C42nd semidirect product of D56 and C4 acting via C4/C2=C21124D56:2C4448,75
C42⋊Dic71st semidirect product of C42 and Dic7 acting via Dic7/C7=C41124C4^2:Dic7448,88
(C2×C28).Q88th non-split extension by C2×C28 of Q8 acting via Q8/C2=C221124(C2xC28).Q8448,90
C24⋊Dic71st semidirect product of C24 and Dic7 acting via Dic7/C7=C4564C2^4:Dic7448,93
(C22×C28)⋊C42nd semidirect product of C22×C28 and C4 acting faithfully1124(C2^2xC28):C4448,96
C422Dic72nd semidirect product of C42 and Dic7 acting via Dic7/C7=C41124C4^2:2Dic7448,98
C42.Dic72nd non-split extension by C42 of Dic7 acting via Dic7/C7=C41124C4^2.Dic7448,99
C423Dic73rd semidirect product of C42 and Dic7 acting via Dic7/C7=C4564C4^2:3Dic7448,102
C42.3Dic73rd non-split extension by C42 of Dic7 acting via Dic7/C7=C41124C4^2.3Dic7448,105
C56.D448th non-split extension by C56 of D4 acting via D4/C2=C221124C56.D4448,110
(C2×C56)⋊C41st semidirect product of C2×C56 and C4 acting faithfully1124(C2xC56):C4448,113
C23.9D282nd non-split extension by C23 of D28 acting via D28/C14=C221124C2^3.9D28448,114
M4(2)⋊4Dic74th semidirect product of M4(2) and Dic7 acting via Dic7/C14=C21124M4(2):4Dic7448,116
C28.21C4214th non-split extension by C28 of C42 acting via C42/C2×C4=C21124C28.21C4^2448,117
C56.92D415th non-split extension by C56 of D4 acting via D4/C22=C22244C56.92D4448,118
D8.Dic72nd non-split extension by D8 of Dic7 acting via Dic7/C14=C21124D8.Dic7448,120
Q16.Dic72nd non-split extension by Q16 of Dic7 acting via Dic7/C14=C22244Q16.Dic7448,122
D82Dic72nd semidirect product of D8 and Dic7 acting via Dic7/C14=C21124D8:2Dic7448,123
C28.58D812nd non-split extension by C28 of D8 acting via D8/D4=C22244C28.58D8448,124
C7×C4.9C42Direct product of C7 and C4.9C421124C7xC4.9C4^2448,141
C7×C4.10C42Direct product of C7 and C4.10C421124C7xC4.10C4^2448,142
C7×M4(2)⋊4C4Direct product of C7 and M4(2)⋊4C41124C7xM4(2):4C4448,148
C7×C16⋊C4Direct product of C7 and C16⋊C41124C7xC16:C4448,151
C7×C23.C8Direct product of C7 and C23.C81124C7xC2^3.C8448,153
C7×C2≀C4Direct product of C7 and C2≀C4564C7xC2wrC4448,155
C7×C23.D4Direct product of C7 and C23.D41124C7xC2^3.D4448,156
C7×C42⋊C4Direct product of C7 and C42⋊C4564C7xC4^2:C4448,157
C7×C423C4Direct product of C7 and C423C41124C7xC4^2:3C4448,158
C7×C42.C4Direct product of C7 and C42.C41124C7xC4^2.C4448,159
C7×C42.3C4Direct product of C7 and C42.3C41124C7xC4^2.3C4448,160
C7×D82C4Direct product of C7 and D82C41124C7xD8:2C4448,164
C7×M5(2)⋊C2Direct product of C7 and M5(2)⋊C21124C7xM5(2):C2448,165
C7×C8.17D4Direct product of C7 and C8.17D42244C7xC8.17D4448,166
C7×C8.Q8Direct product of C7 and C8.Q81124C7xC8.Q8448,169
D564C44th semidirect product of D56 and C4 acting via C4/C2=C21124D56:4C4448,251
D7×C4≀C2Direct product of D7 and C4≀C2564D7xC4wrC2448,354
C42⋊D141st semidirect product of C42 and D14 acting via D14/C7=C221124C4^2:D14448,355
M4(2).22D145th non-split extension by M4(2) of D14 acting via D14/D7=C21124M4(2).22D14448,357
C42.196D1416th non-split extension by C42 of D14 acting via D14/D7=C21124C4^2.196D14448,358
M4(2)⋊D144th semidirect product of M4(2) and D14 acting via D14/C7=C221124M4(2):D14448,359
D4.10D285th non-split extension by D4 of D28 acting via D28/D14=C21124D4.10D28448,361
D7×C8.C4Direct product of D7 and C8.C41124D7xC8.C4448,426
M4(2).25D148th non-split extension by M4(2) of D14 acting via D14/D7=C21124M4(2).25D14448,427
D5610C410th semidirect product of D56 and C4 acting via C4/C2=C21124D56:10C4448,428
D567C47th semidirect product of D56 and C4 acting via C4/C2=C21124D56:7C4448,429
C8.24D2810th non-split extension by C8 of D28 acting via D28/D14=C21124C8.24D28448,432
D7×M5(2)Direct product of D7 and M5(2)1124D7xM5(2)448,440
C16.12D149th non-split extension by C16 of D14 acting via D14/D7=C22244C16.12D14448,441
D8⋊D142nd semidirect product of D8 and D14 acting via D14/D7=C21124D8:D14448,445
D7×SD32Direct product of D7 and SD321124D7xSD32448,447
SD323D7The semidirect product of SD32 and D7 acting through Inn(SD32)2244SD32:3D7448,450
Q32⋊D72nd semidirect product of Q32 and D7 acting via D7/C7=C22244Q32:D7448,452
C424D144th semidirect product of C42 and D14 acting via D14/C7=C221124C4^2:4D14448,539
(C2×D28)⋊13C49th semidirect product of C2×D28 and C4 acting via C4/C2=C21124(C2xD28):13C4448,540
C24⋊D141st semidirect product of C24 and D14 acting via D14/C7=C22564C2^4:D14448,566
C22⋊C4⋊D144th semidirect product of C22⋊C4 and D14 acting via D14/C7=C221124C2^2:C4:D14448,587
C425D145th semidirect product of C42 and D14 acting via D14/C7=C221124C4^2:5D14448,595
D28.14D414th non-split extension by D28 of D4 acting via D4/C2=C221124D28.14D4448,596
D285D45th semidirect product of D28 and D4 acting via D4/C2=C22564D28:5D4448,611
D28.15D415th non-split extension by D28 of D4 acting via D4/C2=C221124D28.15D4448,629
C23.Dic146th non-split extension by C23 of Dic14 acting via Dic14/C14=C221124C2^3.Dic14448,658
M4(2).Dic71st non-split extension by M4(2) of Dic7 acting via Dic7/C14=C21124M4(2).Dic7448,659
M4(2).31D144th non-split extension by M4(2) of D14 acting via D14/C14=C21124M4(2).31D14448,666
C23.20D2813rd non-split extension by C23 of D28 acting via D28/C14=C221124C2^3.20D28448,673
C56.70C2316th non-split extension by C56 of C23 acting via C23/C22=C22244C56.70C2^3448,674
D4.3D283rd non-split extension by D4 of D28 acting via D28/C28=C21124D4.3D28448,675
C56.93D416th non-split extension by C56 of D4 acting via D4/C22=C21124C56.93D4448,678
C56.50D450th non-split extension by C56 of D4 acting via D4/C2=C221124C56.50D4448,679
D8.D141st non-split extension by D8 of D14 acting via D14/C14=C21124D8.D14448,681
C56.23D423rd non-split extension by C56 of D4 acting via D4/C2=C221124C56.23D4448,694
C56.44D444th non-split extension by C56 of D4 acting via D4/C2=C221124C56.44D4448,711
Q16.D141st non-split extension by Q16 of D14 acting via D14/C14=C22244Q16.D14448,713
C56.29D429th non-split extension by C56 of D4 acting via D4/C2=C222244C56.29D4448,726
C56.30C2323rd non-split extension by C56 of C23 acting via C23/C2=C222244C56.30C2^3448,728
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
(D4×C14)⋊9C45th semidirect product of D4×C14 and C4 acting via C4/C2=C21124(D4xC14):9C4448,770
(D4×C14).16C410th non-split extension by D4×C14 of C4 acting via C4/C2=C21124(D4xC14).16C4448,771
(D4×C14)⋊10C46th semidirect product of D4×C14 and C4 acting via C4/C2=C21124(D4xC14):10C4448,774
C7×C23.C23Direct product of C7 and C23.C231124C7xC2^3.C2^3448,818
C7×M4(2).8C22Direct product of C7 and M4(2).8C221124C7xM4(2).8C2^2448,821
C7×C42⋊C22Direct product of C7 and C42⋊C221124C7xC4^2:C2^2448,829
C7×M4(2).C4Direct product of C7 and M4(2).C41124C7xM4(2).C4448,838
C7×C8.26D4Direct product of C7 and C8.26D41124C7xC8.26D4448,852
C7×D44D4Direct product of C7 and D44D4564C7xD4:4D4448,861
C7×D4.8D4Direct product of C7 and D4.8D41124C7xD4.8D4448,862
C7×D4.9D4Direct product of C7 and D4.9D41124C7xD4.9D4448,863
C7×D4.10D4Direct product of C7 and D4.10D41124C7xD4.10D4448,864
C7×C2≀C22Direct product of C7 and C2≀C22564C7xC2wrC2^2448,865
C7×C23.7D4Direct product of C7 and C23.7D41124C7xC2^3.7D4448,866
C7×D4.3D4Direct product of C7 and D4.3D41124C7xD4.3D4448,879
C7×D4.4D4Direct product of C7 and D4.4D41124C7xD4.4D4448,880
C7×D4.5D4Direct product of C7 and D4.5D42244C7xD4.5D4448,881
C7×C16⋊C22Direct product of C7 and C16⋊C221124C7xC16:C2^2448,917
C7×Q32⋊C2Direct product of C7 and Q32⋊C22244C7xQ32:C2448,918
C28.70C2417th non-split extension by C28 of C24 acting via C24/C23=C21124C28.70C2^4448,1198
C56.9C232nd non-split extension by C56 of C23 acting via C23/C2=C221124C56.9C2^3448,1201
D7×C8○D4Direct product of D7 and C8○D41124D7xC8oD4448,1202
C56.49C2342nd non-split extension by C56 of C23 acting via C23/C2=C221124C56.49C2^3448,1203
D4.11D281st non-split extension by D4 of D28 acting through Inn(D4)1124D4.11D28448,1204
D813D142nd semidirect product of D8 and D14 acting through Inn(D8)1124D8:13D14448,1210
D28.29D412nd non-split extension by D28 of D4 acting via D4/C4=C21124D28.29D4448,1215
D28.30D413rd non-split extension by D28 of D4 acting via D4/C4=C22244D28.30D4448,1219
D7×C4○D8Direct product of D7 and C4○D81124D7xC4oD8448,1220
D810D144th semidirect product of D8 and D14 acting via D14/C14=C21124D8:10D14448,1221
D811D145th semidirect product of D8 and D14 acting via D14/C14=C21124D8:11D14448,1223
C28.76C2423rd non-split extension by C28 of C24 acting via C24/C23=C21124C28.76C2^4448,1272
C28.C2435th non-split extension by C28 of C24 acting via C24/C22=C221124C28.C2^4448,1275
C7×Q8○M4(2)Direct product of C7 and Q8○M4(2)1124C7xQ8oM4(2)448,1351
C7×D8⋊C22Direct product of C7 and D8⋊C221124C7xD8:C2^2448,1358
C7×D4○D8Direct product of C7 and D4○D81124C7xD4oD8448,1359
C7×D4○SD16Direct product of C7 and D4○SD161124C7xD4oSD16448,1360
C7×Q8○D8Direct product of C7 and Q8○D82244C7xQ8oD8448,1361
C14.C2514th non-split extension by C14 of C25 acting via C25/C24=C21124C14.C2^5448,1378
C7×C2.C25Direct product of C7 and C2.C251124C7xC2.C2^5448,1391

Groups of order 460

dρLabelID
F5×C23Direct product of C23 and F51154F5xC23460,5
C23⋊F5The semidirect product of C23 and F5 acting via F5/D5=C21154C23:F5460,6

Groups of order 464

dρLabelID
C29⋊C16The semidirect product of C29 and C16 acting via C16/C4=C44644C29:C16464,3
D29⋊C8The semidirect product of D29 and C8 acting via C8/C4=C22324D29:C8464,28
C116.C41st non-split extension by C116 of C4 acting faithfully2324C116.C4464,29
C4×C29⋊C4Direct product of C4 and C29⋊C41164C4xC29:C4464,30
C116⋊C41st semidirect product of C116 and C4 acting faithfully1164C116:C4464,31

Groups of order 468

dρLabelID
C9×C13⋊C4Direct product of C9 and C13⋊C41174C9xC13:C4468,9
C13⋊Dic9The semidirect product of C13 and Dic9 acting via Dic9/C9=C41174C13:Dic9468,10
C3×C39⋊C4Direct product of C3 and C39⋊C4784C3xC39:C4468,37
C13×C32⋊C4Direct product of C13 and C32⋊C4784C13xC3^2:C4468,39
C32⋊Dic13The semidirect product of C32 and Dic13 acting via Dic13/C13=C4784C3^2:Dic13468,40
C3×S3×D13Direct product of C3, S3 and D13784C3xS3xD13468,42
S32×C13Direct product of C13, S3 and S3784S3^2xC13468,44
D39⋊S3The semidirect product of D39 and S3 acting via S3/C3=C2784D39:S3468,46

Groups of order 476

dρLabelID
C7×C17⋊C4Direct product of C7 and C17⋊C41194C7xC17:C4476,5
C17⋊Dic7The semidirect product of C17 and Dic7 acting via Dic7/C7=C41194C17:Dic7476,6

Groups of order 480

dρLabelID
C3×C5⋊C32Direct product of C3 and C5⋊C324804C3xC5:C32480,5
C15⋊C321st semidirect product of C15 and C32 acting via C32/C8=C44804C15:C32480,6
D5×C3⋊C16Direct product of D5 and C3⋊C162404D5xC3:C16480,7
S3×C52C16Direct product of S3 and C52C162404S3xC5:2C16480,8
D152C16The semidirect product of D15 and C16 acting via C16/C8=C22404D15:2C16480,9
C40.51D612nd non-split extension by C40 of D6 acting via D6/S3=C22404C40.51D6480,10
C40.52D613rd non-split extension by C40 of D6 acting via D6/S3=C22404C40.52D6480,11
D30.5C83rd non-split extension by D30 of C8 acting via C8/C4=C22404D30.5C8480,12
C15⋊D161st semidirect product of C15 and D16 acting via D16/C8=C222404C15:D16480,13
C40.D66th non-split extension by C40 of D6 acting via D6/C3=C222404C40.D6480,16
C15⋊SD322nd semidirect product of C15 and SD32 acting via SD32/C8=C222404C15:SD32480,17
C15⋊Q321st semidirect product of C15 and Q32 acting via Q32/C8=C224804C15:Q32480,22
C60.28D428th non-split extension by C60 of D4 acting via D4/C2=C221204C60.28D4480,34
C20.5D125th non-split extension by C20 of D12 acting via D12/C6=C221204C20.5D12480,35
C12.6D206th non-split extension by C12 of D20 acting via D20/C10=C222404C12.6D20480,37
C60.54D454th non-split extension by C60 of D4 acting via D4/C2=C222404C60.54D4480,38
C60.96D496th non-split extension by C60 of D4 acting via D4/C2=C221204C60.96D4480,52
C60.97D497th non-split extension by C60 of D4 acting via D4/C2=C221204C60.97D4480,53
C60.98D498th non-split extension by C60 of D4 acting via D4/C2=C221204C60.98D4480,54
C60.99D499th non-split extension by C60 of D4 acting via D4/C2=C221204C60.99D4480,55
D6013C47th semidirect product of D60 and C4 acting via C4/C2=C21204D60:13C4480,56
D6016C410th semidirect product of D60 and C4 acting via C4/C2=C21204D60:16C4480,57
C60.105D4105th non-split extension by C60 of D4 acting via D4/C2=C222404C60.105D4480,67
C60.D4106th non-split extension by C60 of D4 acting via D4/C2=C222404C60.D4480,68
C12.59D2013rd non-split extension by C12 of D20 acting via D20/D10=C22404C12.59D20480,69
(C2×C6).D202nd non-split extension by C2×C6 of D20 acting via D20/C10=C221204(C2xC6).D20480,71
C158(C23⋊C4)2nd semidirect product of C15 and C23⋊C4 acting via C23⋊C4/C23=C221204C15:8(C2^3:C4)480,72
C159(C23⋊C4)3rd semidirect product of C15 and C23⋊C4 acting via C23⋊C4/C23=C221204C15:9(C2^3:C4)480,73
C3×C23.1D10Direct product of C3 and C23.1D101204C3xC2^3.1D10480,84
C3×C20.53D4Direct product of C3 and C20.53D42404C3xC20.53D4480,100
C3×C20.46D4Direct product of C3 and C20.46D41204C3xC20.46D4480,101
C3×C4.12D20Direct product of C3 and C4.12D202404C3xC4.12D20480,102
C3×D207C4Direct product of C3 and D207C41204C3xD20:7C4480,103
C3×C5⋊D16Direct product of C3 and C5⋊D162404C3xC5:D16480,104
C3×D8.D5Direct product of C3 and D8.D52404C3xD8.D5480,105
C3×C5⋊SD32Direct product of C3 and C5⋊SD322404C3xC5:SD32480,106
C3×C5⋊Q32Direct product of C3 and C5⋊Q324804C3xC5:Q32480,107
C3×C20.D4Direct product of C3 and C20.D41204C3xC20.D4480,111
C3×C23⋊Dic5Direct product of C3 and C23⋊Dic51204C3xC2^3:Dic5480,112
C3×C20.10D4Direct product of C3 and C20.10D42404C3xC20.10D4480,114
C3×D42Dic5Direct product of C3 and D42Dic51204C3xD4:2Dic5480,115
C5×C23.6D6Direct product of C5 and C23.6D61204C5xC2^3.6D6480,125
C5×C12.53D4Direct product of C5 and C12.53D42404C5xC12.53D4480,141
C5×C12.46D4Direct product of C5 and C12.46D41204C5xC12.46D4480,142
C5×C12.47D4Direct product of C5 and C12.47D42404C5xC12.47D4480,143
C5×D12⋊C4Direct product of C5 and D12⋊C41204C5xD12:C4480,144
C5×C3⋊D16Direct product of C5 and C3⋊D162404C5xC3:D16480,145
C5×D8.S3Direct product of C5 and D8.S32404C5xD8.S3480,146
C5×C8.6D6Direct product of C5 and C8.6D62404C5xC8.6D6480,147
C5×C3⋊Q32Direct product of C5 and C3⋊Q324804C5xC3:Q32480,148
C5×C12.D4Direct product of C5 and C12.D41204C5xC12.D4480,152
C5×C23.7D6Direct product of C5 and C23.7D61204C5xC2^3.7D6480,153
C5×C12.10D4Direct product of C5 and C12.10D42404C5xC12.10D4480,155
C5×Q83Dic3Direct product of C5 and Q83Dic31204C5xQ8:3Dic3480,156
C23.6D301st non-split extension by C23 of D30 acting via D30/C15=C221204C2^3.6D30480,166
C60.210D410th non-split extension by C60 of D4 acting via D4/C22=C22404C60.210D4480,182
D6010C44th semidirect product of D60 and C4 acting via C4/C2=C21204D60:10C4480,185
C60.8D48th non-split extension by C60 of D4 acting via D4/C2=C221204C60.8D4480,193
C23.7D302nd non-split extension by C23 of D30 acting via D30/C15=C221204C2^3.7D30480,194
C60.10D410th non-split extension by C60 of D4 acting via D4/C2=C222404C60.10D4480,196
Q83Dic152nd semidirect product of Q8 and Dic15 acting via Dic15/C30=C21204Q8:3Dic15480,197
C15×C23⋊C4Direct product of C15 and C23⋊C41204C15xC2^3:C4480,202
C15×C4.D4Direct product of C15 and C4.D41204C15xC4.D4480,203
C15×C4.10D4Direct product of C15 and C4.10D42404C15xC4.10D4480,204
A5⋊C8The semidirect product of A5 and C8 acting via C8/C4=C2404A5:C8480,217
GL2(𝔽5)General linear group on 𝔽52; = SL2(𝔽5)1C4 = Aut(C52)244GL(2,5)480,218
C52U2(𝔽3)The semidirect product of C5 and U2(𝔽3) acting via U2(𝔽3)/C4.A4=C21204C5:2U(2,3)480,261
SL2(𝔽3).Dic5The non-split extension by SL2(𝔽3) of Dic5 acting through Inn(SL2(𝔽3))1604SL(2,3).Dic5480,267
C3×D5⋊C16Direct product of C3 and D5⋊C162404C3xD5:C16480,269
C3×C8.F5Direct product of C3 and C8.F52404C3xC8.F5480,270
F5×C24Direct product of C24 and F51204F5xC24480,271
C3×C8⋊F5Direct product of C3 and C8⋊F51204C3xC8:F5480,272
C3×C40⋊C4Direct product of C3 and C40⋊C41204C3xC40:C4480,273
C3×D5.D8Direct product of C3 and D5.D81204C3xD5.D8480,274
C3×C40.C4Direct product of C3 and C40.C42404C3xC40.C4480,275
C3×D10.Q8Direct product of C3 and D10.Q82404C3xD10.Q8480,276
C3×C20.C8Direct product of C3 and C20.C82404C3xC20.C8480,278
C3×D10.D4Direct product of C3 and D10.D41204C3xD10.D4480,279
C3×Dic5.D4Direct product of C3 and Dic5.D42404C3xDic5.D4480,285
C3×C23⋊F5Direct product of C3 and C23⋊F51204C3xC2^3:F5480,291
C3×C23.F5Direct product of C3 and C23.F51204C3xC2^3.F5480,293
C24.F55th non-split extension by C24 of F5 acting via F5/D5=C22404C24.F5480,294
C120.C46th non-split extension by C120 of C4 acting faithfully2404C120.C4480,295
C8×C3⋊F5Direct product of C8 and C3⋊F51204C8xC3:F5480,296
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
D5.D24The non-split extension by D5 of D24 acting via D24/C24=C21204D5.D24480,299
C40.Dic32nd non-split extension by C40 of Dic3 acting via Dic3/C3=C42404C40.Dic3480,300
C24.1F51st non-split extension by C24 of F5 acting via F5/D5=C22404C24.1F5480,301
C60.C81st non-split extension by C60 of C8 acting via C8/C2=C42404C60.C8480,303
(C2×C60)⋊C42nd semidirect product of C2×C60 and C4 acting faithfully1204(C2xC60):C4480,304
(C2×C60).C42nd non-split extension by C2×C60 of C4 acting faithfully2404(C2xC60).C4480,310
C3⋊(C23⋊F5)The semidirect product of C3 and C23⋊F5 acting via C23⋊F5/C2×C5⋊D4=C21204C3:(C2^3:F5)480,316
C5⋊(C12.D4)The semidirect product of C5 and C12.D4 acting via C12.D4/C22×C6=C41204C5:(C12.D4)480,318
S3×C8×D5Direct product of C8, S3 and D51204S3xC8xD5480,319
D5×C8⋊S3Direct product of D5 and C8⋊S31204D5xC8:S3480,320
S3×C8⋊D5Direct product of S3 and C8⋊D51204S3xC8:D5480,321
C40⋊D617th semidirect product of C40 and D6 acting via D6/C3=C221204C40:D6480,322
D5×C24⋊C2Direct product of D5 and C24⋊C21204D5xC24:C2480,323
D24⋊D52nd semidirect product of D24 and D5 acting via D5/C5=C21204D24:D5480,326
S3×C40⋊C2Direct product of S3 and C40⋊C21204S3xC40:C2480,327
D40⋊S32nd semidirect product of D40 and S3 acting via S3/C3=C21204D40:S3480,330
C4014D614th semidirect product of C40 and D6 acting via D6/C3=C221204C40:14D6480,331
C405D65th semidirect product of C40 and D6 acting via D6/C3=C221204C40:5D6480,332
D246D56th semidirect product of D24 and D5 acting via D5/C5=C21204D24:6D5480,333
C408D68th semidirect product of C40 and D6 acting via D6/C3=C221204C40:8D6480,334
C24.2D102nd non-split extension by C24 of D10 acting via D10/C5=C222404C24.2D10480,337
Dic20⋊S32nd semidirect product of Dic20 and S3 acting via S3/C3=C22404Dic20:S3480,339
Dic10.D61st non-split extension by Dic10 of D6 acting via D6/C3=C222404Dic10.D6480,340
C40.54D615th non-split extension by C40 of D6 acting via D6/S3=C22404C40.54D6480,341
C40.34D634th non-split extension by C40 of D6 acting via D6/C3=C222404C40.34D6480,342
C40.55D616th non-split extension by C40 of D6 acting via D6/S3=C22404C40.55D6480,343
C40.35D635th non-split extension by C40 of D6 acting via D6/C3=C222404C40.35D6480,344
C40.31D631st non-split extension by C40 of D6 acting via D6/C3=C222404C40.31D6480,345
D6.1D201st non-split extension by D6 of D20 acting via D20/C20=C22404D6.1D20480,348
Dic6.D102nd non-split extension by Dic6 of D10 acting via D10/C5=C222404Dic6.D10480,352
D405S35th semidirect product of D40 and S3 acting via S3/C3=C22404D40:5S3480,353
D30.3D43rd non-split extension by D30 of D4 acting via D4/C2=C222404D30.3D4480,354
D245D55th semidirect product of D24 and D5 acting via D5/C5=C22404D24:5D5480,355
D30.4D44th non-split extension by D30 of D4 acting via D4/C2=C222404D30.4D4480,356
D5×C4.Dic3Direct product of D5 and C4.Dic31204D5xC4.Dic3480,358
D20.3Dic3The non-split extension by D20 of Dic3 acting through Inn(D20)2404D20.3Dic3480,359
D20.2Dic3The non-split extension by D20 of Dic3 acting via Dic3/C6=C22404D20.2Dic3480,360
D12.2Dic5The non-split extension by D12 of Dic5 acting through Inn(D12)2404D12.2Dic5480,362
S3×C4.Dic5Direct product of S3 and C4.Dic51204S3xC4.Dic5480,363
D12.Dic5The non-split extension by D12 of Dic5 acting via Dic5/C10=C22404D12.Dic5480,364
D60.5C43rd non-split extension by D60 of C4 acting via C4/C2=C22404D60.5C4480,366
D60.4C42nd non-split extension by D60 of C4 acting via C4/C2=C22404D60.4C4480,367
D154M4(2)The semidirect product of D15 and M4(2) acting via M4(2)/C2×C4=C21204D15:4M4(2)480,368
D20.34D65th non-split extension by D20 of D6 acting via D6/C6=C22404D20.34D6480,373
C60.36D436th non-split extension by C60 of D4 acting via D4/C2=C221204C60.36D4480,374
D2021D64th semidirect product of D20 and D6 acting via D6/C6=C21204D20:21D6480,375
C20.60D1214th non-split extension by C20 of D12 acting via D12/D6=C22404C20.60D12480,379
D6036C2217th semidirect product of D60 and C22 acting via C22/C2=C21204D60:36C2^2480,380
D20.37D68th non-split extension by D20 of D6 acting via D6/C6=C22404D20.37D6480,383
D12.37D108th non-split extension by D12 of D10 acting via D10/C10=C22404D12.37D10480,385
D20.31D62nd non-split extension by D20 of D6 acting via D6/C6=C22404D20.31D6480,387
D6030C2211st semidirect product of D60 and C22 acting via C22/C2=C21204D60:30C2^2480,388
C12.D2017th non-split extension by C12 of D20 acting via D20/C10=C222404C12.D20480,391
C20.D1218th non-split extension by C20 of D12 acting via D12/C6=C222404C20.D12480,397
C3×D5×M4(2)Direct product of C3, D5 and M4(2)1204C3xD5xM4(2)480,699
C3×D20.2C4Direct product of C3 and D20.2C42404C3xD20.2C4480,700
C3×C8⋊D10Direct product of C3 and C8⋊D101204C3xC8:D10480,701
C3×C8.D10Direct product of C3 and C8.D102404C3xC8.D10480,702
C3×D5×D8Direct product of C3, D5 and D81204C3xD5xD8480,703
C3×D8⋊D5Direct product of C3 and D8⋊D51204C3xD8:D5480,704
C3×D83D5Direct product of C3 and D83D52404C3xD8:3D5480,705
C3×D5×SD16Direct product of C3, D5 and SD161204C3xD5xSD16480,706
C3×D40⋊C2Direct product of C3 and D40⋊C21204C3xD40:C2480,707
C3×SD16⋊D5Direct product of C3 and SD16⋊D52404C3xSD16:D5480,708
C3×SD163D5Direct product of C3 and SD163D52404C3xSD16:3D5480,709
C3×D5×Q16Direct product of C3, D5 and Q162404C3xD5xQ16480,710
C3×Q16⋊D5Direct product of C3 and Q16⋊D52404C3xQ16:D5480,711
C3×Q8.D10Direct product of C3 and Q8.D102404C3xQ8.D10480,712
C3×D4.D10Direct product of C3 and D4.D101204C3xD4.D10480,725
C3×C20.C23Direct product of C3 and C20.C232404C3xC20.C2^3480,735
C3×D4.Dic5Direct product of C3 and D4.Dic52404C3xD4.Dic5480,741
C3×D4⋊D10Direct product of C3 and D4⋊D101204C3xD4:D10480,742
C3×D4.8D10Direct product of C3 and D4.8D102404C3xD4.8D10480,743
C3×D4.9D10Direct product of C3 and D4.9D102404C3xD4.9D10480,744
C5×S3×M4(2)Direct product of C5, S3 and M4(2)1204C5xS3xM4(2)480,785
C5×D12.C4Direct product of C5 and D12.C42404C5xD12.C4480,786
C5×C8⋊D6Direct product of C5 and C8⋊D61204C5xC8:D6480,787
C5×C8.D6Direct product of C5 and C8.D62404C5xC8.D6480,788
C5×S3×D8Direct product of C5, S3 and D81204C5xS3xD8480,789
C5×D8⋊S3Direct product of C5 and D8⋊S31204C5xD8:S3480,790
C5×D83S3Direct product of C5 and D83S32404C5xD8:3S3480,791
C5×S3×SD16Direct product of C5, S3 and SD161204C5xS3xSD16480,792
C5×Q83D6Direct product of C5 and Q83D61204C5xQ8:3D6480,793
C5×D4.D6Direct product of C5 and D4.D62404C5xD4.D6480,794
C5×Q8.7D6Direct product of C5 and Q8.7D62404C5xQ8.7D6480,795
C5×S3×Q16Direct product of C5, S3 and Q162404C5xS3xQ16480,796
C5×Q16⋊S3Direct product of C5 and Q16⋊S32404C5xQ16:S3480,797
C5×D24⋊C2Direct product of C5 and D24⋊C22404C5xD24:C2480,798
C5×D126C22Direct product of C5 and D126C221204C5xD12:6C2^2480,811
C5×Q8.11D6Direct product of C5 and Q8.11D62404C5xQ8.11D6480,821
C5×D4.Dic3Direct product of C5 and D4.Dic32404C5xD4.Dic3480,827
C5×D4⋊D6Direct product of C5 and D4⋊D61204C5xD4:D6480,828
C5×Q8.13D6Direct product of C5 and Q8.13D62404C5xQ8.13D6480,829
C5×Q8.14D6Direct product of C5 and Q8.14D62404C5xQ8.14D6480,830
M4(2)×D15Direct product of M4(2) and D151204M4(2)xD15480,871
D60.3C41st non-split extension by D60 of C4 acting via C4/C2=C22404D60.3C4480,872
D8⋊D152nd semidirect product of D8 and D15 acting via D15/C15=C21204D8:D15480,876
SD16×D15Direct product of SD16 and D151204SD16xD15480,878
D4.5D305th non-split extension by D4 of D30 acting via D30/D15=C22404D4.5D30480,881
Q16⋊D152nd semidirect product of Q16 and D15 acting via D15/C15=C22404Q16:D15480,883
D4.D301st non-split extension by D4 of D30 acting via D30/C30=C21204D4.D30480,897
Q8.11D301st non-split extension by Q8 of D30 acting via D30/C30=C22404Q8.11D30480,907
D4.Dic15The non-split extension by D4 of Dic15 acting through Inn(D4)2404D4.Dic15480,913
D4.8D303rd non-split extension by D4 of D30 acting via D30/C30=C22404D4.8D30480,915
C15×C8⋊C22Direct product of C15 and C8⋊C221204C15xC8:C2^2480,941
C15×C8.C22Direct product of C15 and C8.C222404C15xC8.C2^2480,942
C4×S5Direct product of C4 and S5; = CO3(𝔽5)204C4xS5480,943
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
C4.3S53rd non-split extension by C4 of S5 acting via S5/A5=C2404C4.3S5480,948
CSU2(𝔽3)⋊D51st semidirect product of CSU2(𝔽3) and D5 acting via D5/C5=C21604CSU(2,3):D5480,967
Dic5.6S41st non-split extension by Dic5 of S4 acting through Inn(Dic5)804Dic5.6S4480,968
D10.2S42nd non-split extension by D10 of S4 acting via S4/A4=C2804D10.2S4480,973
D5×GL2(𝔽3)Direct product of D5 and GL2(𝔽3)404D5xGL(2,3)480,974
C5×Q8.D6Direct product of C5 and Q8.D6804C5xQ8.D6480,1018
C5×C4.S4Direct product of C5 and C4.S41604C5xC4.S4480,1019
C5×C4.3S4Direct product of C5 and C4.3S4804C5xC4.3S4480,1021
Q8.D302nd non-split extension by Q8 of D30 acting via D30/C10=S3804Q8.D30480,1029
C20.6S46th non-split extension by C20 of S4 acting via S4/A4=C2804C20.6S4480,1031
SL2(𝔽3).11D101st non-split extension by SL2(𝔽3) of D10 acting through Inn(SL2(𝔽3))804SL(2,3).11D10480,1040
D5×C4.A4Direct product of D5 and C4.A4804D5xC4.A4480,1042
C3×2- 1+4⋊C5Direct product of C3 and 2- 1+4⋊C5964C3xES-(2,2):C5480,1046
C3×D5⋊M4(2)Direct product of C3 and D5⋊M4(2)1204C3xD5:M4(2)480,1049
C3×D10.C23Direct product of C3 and D10.C231204C3xD10.C2^3480,1052
C60.59(C2×C4)13rd non-split extension by C60 of C2×C4 acting via C2×C4/C2=C41204C60.59(C2xC4)480,1062
(C2×C12)⋊6F54th semidirect product of C2×C12 and F5 acting via F5/D5=C21204(C2xC12):6F5480,1065
D20.38D69th non-split extension by D20 of D6 acting via D6/C6=C22404D20.38D6480,1076
C30.C248th non-split extension by C30 of C24 acting via C24/C22=C222404C30.C2^4480,1080
D5×C4○D12Direct product of D5 and C4○D121204D5xC4oD12480,1090
S3×C4○D20Direct product of S3 and C4○D201204S3xC4oD20480,1091
D2024D67th semidirect product of D20 and D6 acting via D6/C6=C21204D20:24D6480,1092
D2025D68th semidirect product of D20 and D6 acting via D6/C6=C21204D20:25D6480,1093
D2026D69th semidirect product of D20 and D6 acting via D6/C6=C21204D20:26D6480,1094
C15⋊2+ 1+4The semidirect product of C15 and 2+ 1+4 acting via 2+ 1+4/C23=C221204C15:ES+(2,2)480,1125
C5×Q8.A4Direct product of C5 and Q8.A41204C5xQ8.A4480,1131
C5×D4.A4Direct product of C5 and D4.A4804C5xD4.A4480,1132
C5×C23⋊A4Direct product of C5 and C23⋊A4404C5xC2^3:A4480,1134
C3×D46D10Direct product of C3 and D46D101204C3xD4:6D10480,1141
C3×Q8.10D10Direct product of C3 and Q8.10D102404C3xQ8.10D10480,1144
C3×D5×C4○D4Direct product of C3, D5 and C4○D41204C3xD5xC4oD4480,1145
C3×D48D10Direct product of C3 and D48D101204C3xD4:8D10480,1146
C3×D4.10D10Direct product of C3 and D4.10D102404C3xD4.10D10480,1147
C5×D46D6Direct product of C5 and D46D61204C5xD4:6D6480,1156
C5×Q8.15D6Direct product of C5 and Q8.15D62404C5xQ8.15D6480,1159
C5×S3×C4○D4Direct product of C5, S3 and C4○D41204C5xS3xC4oD4480,1160
C5×D4○D12Direct product of C5 and D4○D121204C5xD4oD12480,1161
C5×Q8○D12Direct product of C5 and Q8○D122404C5xQ8oD12480,1162
D46D302nd semidirect product of D4 and D30 acting through Inn(D4)1204D4:6D30480,1171
Q8.15D301st non-split extension by Q8 of D30 acting through Inn(Q8)2404Q8.15D30480,1174
C4○D4×D15Direct product of C4○D4 and D151204C4oD4xD15480,1175
C15×2+ 1+4Direct product of C15 and 2+ 1+41204C15xES+(2,2)480,1184
C15×2- 1+4Direct product of C15 and 2- 1+42404C15xES-(2,2)480,1185

Groups of order 492

dρLabelID
C3×C41⋊C4Direct product of C3 and C41⋊C41234C3xC41:C4492,5
C41⋊Dic3The semidirect product of C41 and Dic3 acting via Dic3/C3=C41234C41:Dic3492,6

Groups of order 500

dρLabelID
F5×C25Direct product of C25 and F51004F5xC25500,15
C5×C25⋊C4Direct product of C5 and C25⋊C41004C5xC25:C4500,16
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
C5×D5.D5Direct product of C5 and D5.D5204C5xD5.D5500,42
C5×C52⋊C4Direct product of C5 and C52⋊C4204C5xC5^2:C4500,44
C536C46th semidirect product of C53 and C4 acting faithfully204C5^3:6C4500,46
C5×D52Direct product of C5, D5 and D5204C5xD5^2500,50
C525D102nd semidirect product of C52 and D10 acting via D10/C5=C22204C5^2:5D10500,52

Orthogonal of dimension 5  (ρ=5+)

Groups of order 80

dρLabelID
C24⋊C5The semidirect product of C24 and C5 acting faithfully105+C2^4:C580,49

Groups of order 160

dρLabelID
C24⋊D5The semidirect product of C24 and D5 acting faithfully105+C2^4:D5160,234
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)105+C2xC2^4:C5160,235

Groups of order 320

dρLabelID
C24⋊F5The semidirect product of C24 and F5 acting faithfully105+C2^4:F5320,1635
C2×C24⋊D5Direct product of C2 and C24⋊D5105+C2xC2^4:D5320,1636

Groups of order 360

dρLabelID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simple65+A6360,118

Complex of dimension 5  (ρ=5)

Groups of order 55

dρLabelID
C11⋊C5The semidirect product of C11 and C5 acting faithfully115C11:C555,1

Groups of order 110

dρLabelID
C2×C11⋊C5Direct product of C2 and C11⋊C5225C2xC11:C5110,2

Groups of order 125

dρLabelID
He5Heisenberg group; = C52C5 = 5+ 1+2255He5125,3
5- 1+2Extraspecial group255ES-(5,1)125,4

Groups of order 155

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

Groups of order 165

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

Groups of order 205

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

Groups of order 220

dρLabelID
C4×C11⋊C5Direct product of C4 and C11⋊C5445C4xC11:C5220,2

Groups of order 240

dρLabelID
C3×C24⋊C5Direct product of C3 and C24⋊C5305C3xC2^4:C5240,199

Groups of order 250

dρLabelID
He5⋊C22nd semidirect product of He5 and C2 acting faithfully255He5:C2250,8
C2×He5Direct product of C2 and He5505C2xHe5250,10
C2×5- 1+2Direct product of C2 and 5- 1+2505C2xES-(5,1)250,11

Groups of order 275

dρLabelID
C11⋊C25The semidirect product of C11 and C25 acting via C25/C5=C52755C11:C25275,1
C5×C11⋊C5Direct product of C5 and C11⋊C5555C5xC11:C5275,3

Groups of order 305

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

Groups of order 310

dρLabelID
C2×C31⋊C5Direct product of C2 and C31⋊C5625C2xC31:C5310,2

Groups of order 320

dρLabelID
C25.D5The non-split extension by C25 of D5 acting faithfully205C2^5.D5320,1583
C4×C24⋊C5Direct product of C4 and C24⋊C5205C4xC2^4:C5320,1584

Groups of order 330

dρLabelID
C6×C11⋊C5Direct product of C6 and C11⋊C5665C6xC11:C5330,4

Groups of order 355

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

Groups of order 375

dρLabelID
He5⋊C3The semidirect product of He5 and C3 acting faithfully755He5:C3375,2
C3×He5Direct product of C3 and He5755C3xHe5375,4
C3×5- 1+2Direct product of C3 and 5- 1+2755C3xES-(5,1)375,5

Groups of order 385

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

Groups of order 400

dρLabelID
C24⋊C25The semidirect product of C24 and C25 acting via C25/C5=C5505C2^4:C25400,52
C5×C24⋊C5Direct product of C5 and C24⋊C5505C5xC2^4:C5400,213

Groups of order 405

dρLabelID
C34⋊C5The semidirect product of C34 and C5 acting faithfully155C3^4:C5405,15

Groups of order 410

dρLabelID
C2×C41⋊C5Direct product of C2 and C41⋊C5825C2xC41:C5410,2

Groups of order 440

dρLabelID
C8×C11⋊C5Direct product of C8 and C11⋊C5885C8xC11:C5440,2

Groups of order 465

dρLabelID
C3×C31⋊C5Direct product of C3 and C31⋊C5935C3xC31:C5465,2

Groups of order 480

dρLabelID
C3×C24⋊D5Direct product of C3 and C24⋊D5305C3xC2^4:D5480,1194
C6×C24⋊C5Direct product of C6 and C24⋊C5305C6xC2^4:C5480,1204

Groups of order 495

dρLabelID
C9×C11⋊C5Direct product of C9 and C11⋊C5995C9xC11:C5495,1

Groups of order 500

dρLabelID
He56C42nd semidirect product of He5 and C4 acting via C4/C2=C21005He5:6C4500,11
C4×He5Direct product of C4 and He51005C4xHe5500,13
C4×5- 1+2Direct product of C4 and 5- 1+21005C4xES-(5,1)500,14
He54C44th semidirect product of He5 and C4 acting faithfully; = Aut(5- 1+2)255He5:4C4500,25
C2×He5⋊C2Direct product of C2 and He5⋊C2505C2xHe5:C2500,33

Orthogonal of dimension 6  (ρ=6+)

Groups of order 42

dρLabelID
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)76+F742,1

Groups of order 54

dρLabelID
C32⋊C6The semidirect product of C32 and C6 acting faithfully96+C3^2:C654,5
C9⋊C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)96+C9:C654,6

Groups of order 72

dρLabelID
C3.S4The non-split extension by C3 of S4 acting via S4/A4=C2186+C3.S472,15
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2126+C3:S472,43
S3×A4Direct product of S3 and A4126+S3xA472,44

Groups of order 78

dρLabelID
C13⋊C6The semidirect product of C13 and C6 acting faithfully136+C13:C678,1

Groups of order 84

dρLabelID
C2×F7Direct product of C2 and F7; = Aut(D14) = Hol(C14)146+C2xF784,7

Groups of order 96

dρLabelID
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3126+C2^3.3A496,3
C24⋊C61st semidirect product of C24 and C6 acting faithfully86+C2^4:C696,70
C23.A42nd non-split extension by C23 of A4 acting faithfully126+C2^3.A496,72
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2126+C4:S496,187
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)126+A4:D496,195
D4×A4Direct product of D4 and A4126+D4xA496,197
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S386+C2^2:S496,227

Groups of order 108

dρLabelID
C32⋊D6The semidirect product of C32 and D6 acting faithfully96+C3^2:D6108,17
C2×C32⋊C6Direct product of C2 and C32⋊C6186+C2xC3^2:C6108,25
C2×C9⋊C6Direct product of C2 and C9⋊C6; = Aut(D18) = Hol(C18)186+C2xC9:C6108,26

Groups of order 114

dρLabelID
C19⋊C6The semidirect product of C19 and C6 acting faithfully196+C19:C6114,1

Groups of order 120

dρLabelID
C5⋊S4The semidirect product of C5 and S4 acting via S4/A4=C2206+C5:S4120,38
D5×A4Direct product of D5 and A4206+D5xA4120,39

Groups of order 126

dρLabelID
C3⋊F7The semidirect product of C3 and F7 acting via F7/C7⋊C3=C2216+C3:F7126,9

Groups of order 144

dρLabelID
C2×C3.S4Direct product of C2 and C3.S4186+C2xC3.S4144,109
S3×S4Direct product of S3 and S4; = Hol(C2×C6)126+S3xS4144,183
C2×C3⋊S4Direct product of C2 and C3⋊S4186+C2xC3:S4144,189
C2×S3×A4Direct product of C2, S3 and A4186+C2xS3xA4144,190

Groups of order 150

dρLabelID
C52⋊C6The semidirect product of C52 and C6 acting faithfully156+C5^2:C6150,6

Groups of order 156

dρLabelID
C2×C13⋊C6Direct product of C2 and C13⋊C6266+C2xC13:C6156,8

Groups of order 162

dρLabelID
C27⋊C6The semidirect product of C27 and C6 acting faithfully276+C27:C6162,9
C33⋊C61st semidirect product of C33 and C6 acting faithfully96+C3^3:C6162,11
He3.S31st non-split extension by He3 of S3 acting faithfully276+He3.S3162,13
He3.2S32nd non-split extension by He3 of S3 acting faithfully276+He3.2S3162,15
C33⋊S32nd semidirect product of C33 and S3 acting faithfully96+C3^3:S3162,19
He3.3S33rd non-split extension by He3 of S3 acting faithfully276+He3.3S3162,20
He3⋊S33rd semidirect product of He3 and S3 acting faithfully276+He3:S3162,21
3- 1+2.S3The non-split extension by 3- 1+2 of S3 acting faithfully276+ES-(3,1).S3162,22
He3.4S3The non-split extension by He3 of S3 acting via S3/C3=C2276+He3.4S3162,43

Groups of order 168

dρLabelID
C4⋊F7The semidirect product of C4 and F7 acting via F7/C7⋊C3=C2286+C4:F7168,9
C7⋊S4The semidirect product of C7 and S4 acting via S4/A4=C2286+C7:S4168,46
A4×D7Direct product of A4 and D7286+A4xD7168,48
D7⋊A4The semidirect product of D7 and A4 acting via A4/C22=C3286+D7:A4168,49

Groups of order 186

dρLabelID
C31⋊C6The semidirect product of C31 and C6 acting faithfully316+C31:C6186,1

Groups of order 192

dρLabelID
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3246+C2^3.8S4192,181
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6126+C2^4:C12192,191
C232D4⋊C3The semidirect product of C232D4 and C3 acting faithfully126+C2^3:2D4:C3192,194
C24.2A42nd non-split extension by C24 of A4 acting faithfully126+C2^4.2A4192,197
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
A4⋊D8The semidirect product of A4 and D8 acting via D8/C8=C2246+A4:D8192,961
D4⋊S4The semidirect product of D4 and S4 acting via S4/A4=C2246+D4:S4192,974
C2×C24⋊C6Direct product of C2 and C24⋊C6126+C2xC2^4:C6192,1000
C2×C23.A4Direct product of C2 and C23.A4126+C2xC2^3.A4192,1002
A4×D8Direct product of A4 and D8246+A4xD8192,1014
D4×S4Direct product of D4 and S4126+D4xS4192,1472
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3126+C2^4:4Dic3192,1495
C2×C22⋊S4Direct product of C2 and C22⋊S4126+C2xC2^2:S4192,1538

Groups of order 210

dρLabelID
C5⋊F7The semidirect product of C5 and F7 acting via F7/C7⋊C3=C2356+C5:F7210,3

Groups of order 216

dρLabelID
C9.S4The non-split extension by C9 of S4 acting via S4/A4=C2546+C9.S4216,21
He32D41st semidirect product of He3 and D4 acting via D4/C2=C22366+He3:2D4216,35
He34D41st semidirect product of He3 and D4 acting via D4/C4=C2366+He3:4D4216,51
D36⋊C3The semidirect product of D36 and C3 acting faithfully366+D36:C3216,54
He3⋊C8The semidirect product of He3 and C8 acting faithfully276+He3:C8216,86
He3⋊D4The semidirect product of He3 and D4 acting faithfully186+He3:D4216,87
C32.S4The non-split extension by C32 of S4 acting via S4/C22=S3186+C3^2.S4216,90
C62⋊S34th semidirect product of C62 and S3 acting faithfully186+C6^2:S3216,92
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
A4×D9Direct product of A4 and D9366+A4xD9216,97
C62⋊C63rd semidirect product of C62 and C6 acting faithfully186+C6^2:C6216,99
C2×C32⋊D6Direct product of C2 and C32⋊D6186+C2xC3^2:D6216,102

Groups of order 222

dρLabelID
C37⋊C6The semidirect product of C37 and C6 acting faithfully376+C37:C6222,1

Groups of order 228

dρLabelID
C2×C19⋊C6Direct product of C2 and C19⋊C6386+C2xC19:C6228,7

Groups of order 234

dρLabelID
D39⋊C3The semidirect product of D39 and C3 acting faithfully396+D39:C3234,9

Groups of order 240

dρLabelID
D5×S4Direct product of D5 and S4206+D5xS4240,194
C2×C5⋊S4Direct product of C2 and C5⋊S4306+C2xC5:S4240,197
C2×D5×A4Direct product of C2, D5 and A4306+C2xD5xA4240,198

Groups of order 252

dρLabelID
C2×C3⋊F7Direct product of C2 and C3⋊F7426+C2xC3:F7252,30

Groups of order 258

dρLabelID
C43⋊C6The semidirect product of C43 and C6 acting faithfully436+C43:C6258,1

Groups of order 264

dρLabelID
C11⋊S4The semidirect product of C11 and S4 acting via S4/A4=C2446+C11:S4264,32
A4×D11Direct product of A4 and D11446+A4xD11264,33

Groups of order 270

dρLabelID
He3⋊D51st semidirect product of He3 and D5 acting via D5/C5=C2456+He3:D5270,14
D45⋊C3The semidirect product of D45 and C3 acting faithfully456+D45:C3270,15

Groups of order 288

dρLabelID
C42⋊D9The semidirect product of C42 and D9 acting via D9/C3=S3366+C4^2:D9288,67
C22⋊D36The semidirect product of C22 and D36 acting via D36/C12=S3366+C2^2:D36288,334
(C4×C12)⋊S31st semidirect product of C4×C12 and S3 acting faithfully366+(C4xC12):S3288,401
(C4×C12)⋊C63rd semidirect product of C4×C12 and C6 acting faithfully366+(C4xC12):C6288,405
A4⋊D12The semidirect product of A4 and D12 acting via D12/D6=C2366+A4:D12288,858
C12⋊S41st semidirect product of C12 and S4 acting via S4/A4=C2366+C12:S4288,909
A4×D12Direct product of A4 and D12366+A4xD12288,920
A4≀C2Wreath product of A4 by C286+A4wrC2288,1025
C2×S3×S4Direct product of C2, S3 and S4; = Aut(S3×SL2(𝔽3))186+C2xS3xS4288,1028

Groups of order 294

dρLabelID
C49⋊C6The semidirect product of C49 and C6 acting faithfully496+C49:C6294,1
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

Groups of order 300

dρLabelID
C52⋊D6The semidirect product of C52 and D6 acting faithfully156+C5^2:D6300,25
C2×C52⋊C6Direct product of C2 and C52⋊C6306+C2xC5^2:C6300,27

Groups of order 312

dρLabelID
D52⋊C3The semidirect product of D52 and C3 acting faithfully526+D52:C3312,10
C13⋊S4The semidirect product of C13 and S4 acting via S4/A4=C2526+C13:S4312,48
A4×D13Direct product of A4 and D13526+A4xD13312,50
D13⋊A4The semidirect product of D13 and A4 acting via A4/C22=C3526+D13:A4312,51

Groups of order 324

dρLabelID
He3⋊D6The semidirect product of He3 and D6 acting faithfully96+He3:D6324,39
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
C2×C27⋊C6Direct product of C2 and C27⋊C6546+C2xC27:C6324,67
C2×C33⋊C6Direct product of C2 and C33⋊C6186+C2xC3^3:C6324,69
C2×He3.S3Direct product of C2 and He3.S3546+C2xHe3.S3324,71
C2×He3.2S3Direct product of C2 and He3.2S3546+C2xHe3.2S3324,73
C2×C33⋊S3Direct product of C2 and C33⋊S3186+C2xC3^3:S3324,77
C2×He3.3S3Direct product of C2 and He3.3S3546+C2xHe3.3S3324,78
C2×He3⋊S3Direct product of C2 and He3⋊S3546+C2xHe3:S3324,79
C2×3- 1+2.S3Direct product of C2 and 3- 1+2.S3546+C2xES-(3,1).S3324,80
He3.6D6The non-split extension by He3 of D6 acting via D6/C3=C22276+He3.6D6324,125
C2×He3.4S3Direct product of C2 and He3.4S3546+C2xHe3.4S3324,147

Groups of order 336

dρLabelID
D56⋊C3The semidirect product of D56 and C3 acting faithfully566+D56:C3336,10
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simple86+PGL(2,7)336,208
D7×S4Direct product of D7 and S4286+D7xS4336,212
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

Groups of order 342

dρLabelID
D57⋊C3The semidirect product of D57 and C3 acting faithfully576+D57:C3342,11

Groups of order 360

dρLabelID
C22⋊D45The semidirect product of C22 and D45 acting via D45/C15=S3906+C2^2:D45360,41
S3×A5Direct product of S3 and A5156+S3xA5360,121
A4⋊D15The semidirect product of A4 and D15 acting via D15/C15=C2606+A4:D15360,141
A4×D15Direct product of A4 and D15606+A4xD15360,144

Groups of order 366

dρLabelID
C61⋊C6The semidirect product of C61 and C6 acting faithfully616+C61:C6366,1

Groups of order 372

dρLabelID
C2×C31⋊C6Direct product of C2 and C31⋊C6626+C2xC31:C6372,7

Groups of order 378

dρLabelID
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
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

Groups of order 390

dρLabelID
D65⋊C3The semidirect product of D65 and C3 acting faithfully656+D65:C3390,3

Groups of order 402

dρLabelID
C67⋊C6The semidirect product of C67 and C6 acting faithfully676+C67:C6402,1

Groups of order 408

dρLabelID
C17⋊S4The semidirect product of C17 and S4 acting via S4/A4=C2686+C17:S4408,37
A4×D17Direct product of A4 and D17686+A4xD17408,38

Groups of order 420

dρLabelID
C2×C5⋊F7Direct product of C2 and C5⋊F7706+C2xC5:F7420,19

Groups of order 432

dρLabelID
He32D81st semidirect product of He3 and D8 acting via D8/C4=C22726+He3:2D8432,79
He34D81st semidirect product of He3 and D8 acting via D8/C8=C2726+He3:4D8432,118
D72⋊C3The semidirect product of D72 and C3 acting faithfully726+D72:C3432,123
C2×C9.S4Direct product of C2 and C9.S4546+C2xC9.S4432,224
He3⋊D8The semidirect product of He3 and D8 acting via D8/C2=D4726+He3:D8432,235
C12.86S326th non-split extension by C12 of S32 acting via S32/C3⋊S3=C2366+C12.86S3^2432,302
He3⋊SD16The semidirect product of He3 and SD16 acting faithfully276+He3:SD16432,520
D9×S4Direct product of D9 and S4366+D9xS4432,521
C625D65th semidirect product of C62 and D6 acting faithfully186+C6^2:5D6432,523
C2×He3⋊C8Direct product of C2 and He3⋊C8546+C2xHe3:C8432,529
C2×He3⋊D4Direct product of C2 and He3⋊D4366+C2xHe3:D4432,530
C2×C32.S4Direct product of C2 and C32.S4186+C2xC3^2.S4432,533
C2×C62⋊S3Direct product of C2 and C62⋊S3186+C2xC6^2:S3432,535
C2×C9⋊S4Direct product of C2 and C9⋊S4546+C2xC9:S4432,536
C2×D9⋊A4Direct product of C2 and D9⋊A4546+C2xD9:A4432,539
C2×A4×D9Direct product of C2, A4 and D9546+C2xA4xD9432,540
C2×C62⋊C6Direct product of C2 and C62⋊C6186+C2xC6^2:C6432,542

Groups of order 438

dρLabelID
C73⋊C6The semidirect product of C73 and C6 acting faithfully736+C73:C6438,1

Groups of order 444

dρLabelID
C2×C37⋊C6Direct product of C2 and C37⋊C6746+C2xC37:C6444,8

Groups of order 450

dρLabelID
C52⋊D9The semidirect product of C52 and D9 acting via D9/C3=S3456+C5^2:D9450,11
C52⋊(C3⋊S3)The semidirect product of C52 and C3⋊S3 acting via C3⋊S3/C3=S3456+C5^2:(C3:S3)450,21
C5⋊D15⋊C3The semidirect product of C5⋊D15 and C3 acting faithfully456+C5:D15:C3450,24

Groups of order 456

dρLabelID
D76⋊C3The semidirect product of D76 and C3 acting faithfully766+D76:C3456,9
C19⋊S4The semidirect product of C19 and S4 acting via S4/A4=C2766+C19:S4456,43
A4×D19Direct product of A4 and D19766+A4xD19456,45
D19⋊A4The semidirect product of D19 and A4 acting via A4/C22=C3766+D19:A4456,46

Groups of order 462

dρLabelID
C11⋊F7The semidirect product of C11 and F7 acting via F7/C7⋊C3=C2776+C11:F7462,3

Groups of order 468

dρLabelID
C2×D39⋊C3Direct product of C2 and D39⋊C3786+C2xD39:C3468,35

Groups of order 474

dρLabelID
C79⋊C6The semidirect product of C79 and C6 acting faithfully796+C79:C6474,1

Groups of order 480

dρLabelID
C42⋊D15The semidirect product of C42 and D15 acting via D15/C5=S3606+C4^2:D15480,258
C204D4⋊C3The semidirect product of C204D4 and C3 acting faithfully606+C20:4D4:C3480,262
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2206+C2^2:S5480,951
D4×A5Direct product of D4 and A5206+D4xA5480,956
A4⋊D20The semidirect product of A4 and D20 acting via D20/D10=C2606+A4:D20480,981
C20⋊S41st semidirect product of C20 and S4 acting via S4/A4=C2606+C20:S4480,1026
A4×D20Direct product of A4 and D20606+A4xD20480,1037
C2×D5×S4Direct product of C2, D5 and S4306+C2xD5xS4480,1193

Groups of order 486

dρLabelID
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
C81⋊C6The semidirect product of C81 and C6 acting faithfully816+C81:C6486,34
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
C92.S32nd non-split extension by C92 of S3 acting faithfully276+C9^2.S3486,38
C33.D93rd non-split extension by C33 of D9 acting via D9/C3=S3276+C3^3.D9486,55
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
C3≀C3.S3The non-split extension by C3≀C3 of S3 acting via S3/C3=C2276+C3wrC3.S3486,175
C3≀C3⋊S32nd semidirect product of C3≀C3 and S3 acting via S3/C3=C2276+C3wrC3:S3486,189

Symplectic of dimension 6  (ρ=6-)

Groups of order 84

dρLabelID
C7⋊C12The semidirect product of C7 and C12 acting via C12/C2=C6286-C7:C1284,1

Groups of order 96

dρLabelID
A4⋊Q8The semidirect product of A4 and Q8 acting via Q8/C4=C2246-A4:Q896,185
Q8×A4Direct product of Q8 and A4246-Q8xA496,199
Q8⋊A41st semidirect product of Q8 and A4 acting via A4/C22=C3246-Q8:A496,203

Groups of order 108

dρLabelID
C32⋊C12The semidirect product of C32 and C12 acting via C12/C2=C6366-C3^2:C12108,8
C9⋊C12The semidirect product of C9 and C12 acting via C12/C2=C6366-C9:C12108,9

Groups of order 144

dρLabelID
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
Dic3×A4Direct product of Dic3 and A4366-Dic3xA4144,129

Groups of order 156

dρLabelID
C26.C6The non-split extension by C26 of C6 acting faithfully526-C26.C6156,1

Groups of order 168

dρLabelID
C4.F7The non-split extension by C4 of F7 acting via F7/C7⋊C3=C2566-C4.F7168,7

Groups of order 192

dρLabelID
C422C122nd semidirect product of C42 and C12 acting via C12/C2=C6246-C4^2:2C12192,193
(C22×C4).A44th non-split extension by C22×C4 of A4 acting faithfully246-(C2^2xC4).A4192,196
A4⋊Q16The semidirect product of A4 and Q16 acting via Q16/C8=C2486-A4:Q16192,957
A42Q16The semidirect product of A4 and Q16 acting via Q16/Q8=C2486-A4:2Q16192,975
A4×Q16Direct product of A4 and Q16486-A4xQ16192,1016
Q8×S4Direct product of Q8 and S4246-Q8xS4192,1477
Q8.1S41st non-split extension by Q8 of S4 acting via S4/C22=S3486-Q8.1S4192,1489

Groups of order 216

dρLabelID
He32Q8The semidirect product of He3 and Q8 acting via Q8/C2=C22726-He3:2Q8216,33
He3⋊(C2×C4)2nd semidirect product of He3 and C2×C4 acting via C2×C4/C2=C22366-He3:(C2xC4)216,36
He33Q81st semidirect product of He3 and Q8 acting via Q8/C4=C2726-He3:3Q8216,49
C36.C61st non-split extension by C36 of C6 acting faithfully726-C36.C6216,52

Groups of order 228

dρLabelID
C19⋊C12The semidirect product of C19 and C12 acting via C12/C2=C6766-C19:C12228,1

Groups of order 240

dρLabelID
A4⋊Dic5The semidirect product of A4 and Dic5 acting via Dic5/C10=C2606-A4:Dic5240,107
A4×Dic5Direct product of A4 and Dic5606-A4xDic5240,110

Groups of order 252

dρLabelID
C6.F7The non-split extension by C6 of F7 acting via F7/C7⋊C3=C2846-C6.F7252,18

Groups of order 288

dρLabelID
C12.1S41st non-split extension by C12 of S4 acting via S4/A4=C2726-C12.1S4288,332
Dic3.S43rd non-split extension by Dic3 of S4 acting via S4/A4=C2726-Dic3.S4288,852
Dic3×S4Direct product of Dic3 and S4366-Dic3xS4288,853
A4×SL2(𝔽3)Direct product of A4 and SL2(𝔽3)246-A4xSL(2,3)288,859
A4⋊Dic6The semidirect product of A4 and Dic6 acting via Dic6/C12=C2726-A4:Dic6288,907
A4×Dic6Direct product of A4 and Dic6726-A4xDic6288,918

Groups of order 300

dρLabelID
C522C12The semidirect product of C52 and C12 acting via C12/C2=C6606-C5^2:2C12300,14

Groups of order 312

dρLabelID
Dic26⋊C3The semidirect product of Dic26 and C3 acting faithfully1046-Dic26:C3312,8

Groups of order 324

dρLabelID
C27⋊C12The semidirect product of C27 and C12 acting via C12/C2=C61086-C27:C12324,12
C33⋊C121st semidirect product of C33 and C12 acting via C12/C2=C6366-C3^3:C12324,14
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
C33⋊Dic32nd semidirect product of C33 and Dic3 acting via Dic3/C2=S3366-C3^3:Dic3324,22
He3.3Dic33rd non-split extension by He3 of Dic3 acting via Dic3/C2=S31086-He3.3Dic3324,23
He3⋊Dic33rd semidirect product of He3 and Dic3 acting via Dic3/C2=S31086-He3:Dic3324,24
3- 1+2.Dic3The non-split extension by 3- 1+2 of Dic3 acting via Dic3/C2=S31086-ES-(3,1).Dic3324,25
He3.4Dic3The non-split extension by He3 of Dic3 acting via Dic3/C6=C21086-He3.4Dic3324,101

Groups of order 336

dρLabelID
C8.F7The non-split extension by C8 of F7 acting via F7/C7⋊C3=C21126-C8.F7336,11
A4⋊Dic7The semidirect product of A4 and Dic7 acting via Dic7/C14=C2846-A4:Dic7336,120
A4×Dic7Direct product of A4 and Dic7846-A4xDic7336,133
Dic7⋊A4The semidirect product of Dic7 and A4 acting via A4/C22=C3846-Dic7:A4336,136

Groups of order 372

dρLabelID
C31⋊C12The semidirect product of C31 and C12 acting via C12/C2=C61246-C31:C12372,1

Groups of order 420

dρLabelID
C353C121st semidirect product of C35 and C12 acting via C12/C2=C61406-C35:3C12420,3

Groups of order 432

dρLabelID
C18.S43rd non-split extension by C18 of S4 acting via S4/A4=C21086-C18.S4432,39
He32Q161st semidirect product of He3 and Q16 acting via Q16/C4=C221446-He3:2Q16432,80
He34Q161st semidirect product of He3 and Q16 acting via Q16/C8=C21446-He3:4Q16432,114
C72.C61st non-split extension by C72 of C6 acting faithfully1446-C72.C6432,119
He3⋊Q16The semidirect product of He3 and Q16 acting via Q16/C2=D41446-He3:Q16432,236
C6.S3≀C24th non-split extension by C6 of S3≀C2 acting via S3≀C2/C32⋊C4=C2726-C6.S3wrC2432,237
C62.Dic38th non-split extension by C62 of Dic3 acting via Dic3/C2=S3366-C6^2.Dic3432,249
C625Dic34th semidirect product of C62 and Dic3 acting via Dic3/C2=S3366-C6^2:5Dic3432,251
A4⋊Dic9The semidirect product of A4 and Dic9 acting via Dic9/C18=C21086-A4:Dic9432,254
Dic9⋊A4The semidirect product of Dic9 and A4 acting via A4/C22=C31086-Dic9:A4432,265
A4×Dic9Direct product of A4 and Dic91086-A4xDic9432,266
C624C123rd semidirect product of C62 and C12 acting via C12/C2=C6366-C6^2:4C12432,272
C12.85S325th non-split extension by C12 of S32 acting via S32/C3⋊S3=C2726-C12.85S3^2432,298

Groups of order 444

dρLabelID
C74.C6The non-split extension by C74 of C6 acting faithfully1486-C74.C6444,1

Groups of order 456

dρLabelID
Dic38⋊C3The semidirect product of Dic38 and C3 acting faithfully1526-Dic38:C3456,7

Groups of order 468

dρLabelID
C393C121st semidirect product of C39 and C12 acting via C12/C2=C61566-C39:3C12468,21

Groups of order 480

dρLabelID
Q8×A5Direct product of Q8 and A5406-Q8xA5480,958
A4⋊Dic10The semidirect product of A4 and Dic10 acting via Dic10/Dic5=C21206-A4:Dic10480,975
Dic5×S4Direct product of Dic5 and S4606-Dic5xS4480,976
C20.1S41st non-split extension by C20 of S4 acting via S4/A4=C21206-C20.1S4480,1024
A4×Dic10Direct product of A4 and Dic101206-A4xDic10480,1035

Complex of dimension 6  (ρ=6)

Groups of order 96

dρLabelID
C42⋊C61st semidirect product of C42 and C6 acting faithfully166C4^2:C696,71

Groups of order 126

dρLabelID
C7⋊C18The semidirect product of C7 and C18 acting via C18/C3=C6636C7:C18126,1
C3×F7Direct product of C3 and F7216C3xF7126,7
S3×C7⋊C3Direct product of S3 and C7⋊C3216S3xC7:C3126,8

Groups of order 162

dρLabelID
C32⋊C18The semidirect product of C32 and C18 acting via C18/C3=C6186C3^2:C18162,4
C9⋊C18The semidirect product of C9 and C18 acting via C18/C3=C6186C9:C18162,6
C322D92nd semidirect product of C32 and D9 acting via D9/C3=S3186C3^2:2D9162,17
C3×C32⋊C6Direct product of C3 and C32⋊C6186C3xC3^2:C6162,34
S3×He3Direct product of S3 and He3186S3xHe3162,35
C3×C9⋊C6Direct product of C3 and C9⋊C6186C3xC9:C6162,36
S3×3- 1+2Direct product of S3 and 3- 1+2186S3xES-(3,1)162,37
He35S32nd semidirect product of He3 and S3 acting via S3/C3=C2186He3:5S3162,46

Groups of order 168

dρLabelID
C7⋊C24The semidirect product of C7 and C24 acting via C24/C4=C6566C7:C24168,1
C4×F7Direct product of C4 and F7286C4xF7168,8
Dic7⋊C6The semidirect product of Dic7 and C6 acting faithfully286Dic7:C6168,11
D4×C7⋊C3Direct product of D4 and C7⋊C3286D4xC7:C3168,20
Q8×C7⋊C3Direct product of Q8 and C7⋊C3566Q8xC7:C3168,21
C14.A4The non-split extension by C14 of A4 acting via A4/C22=C3566C14.A4168,23

Groups of order 192

dρLabelID
C23.7S41st non-split extension by C23 of S4 acting via S4/C22=S3246C2^3.7S4192,180
C424C4⋊C3The semidirect product of C424C4 and C3 acting faithfully246C4^2:4C4:C3192,190
C42⋊C121st semidirect product of C42 and C12 acting via C12/C2=C6246C4^2:C12192,192
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
C23.19(C2×A4)12nd non-split extension by C23 of C2×A4 acting via C2×A4/C23=C3246C2^3.19(C2xA4)192,199
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⋊M4(2)The semidirect product of A4 and M4(2) acting via M4(2)/C2×C4=C2246A4:M4(2)192,968
A4⋊SD16The semidirect product of A4 and SD16 acting via SD16/D4=C2246A4:SD16192,973
Q83S4The semidirect product of Q8 and S4 acting via S4/A4=C2246Q8:3S4192,976
C2×C42⋊C6Direct product of C2 and C42⋊C6246C2xC4^2:C6192,1001
A4×M4(2)Direct product of A4 and M4(2)246A4xM4(2)192,1011
A4×SD16Direct product of A4 and SD16246A4xSD16192,1015
C24.10D69th non-split extension by C24 of D6 acting via D6/C2=S3246C2^4.10D6192,1471
D42S4The semidirect product of D4 and S4 acting through Inn(D4)246D4:2S4192,1473
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
A4×C4○D4Direct product of A4 and C4○D4246A4xC4oD4192,1501
C4○D4⋊A41st semidirect product of C4○D4 and A4 acting via A4/C22=C3246C4oD4:A4192,1507

Groups of order 210

dρLabelID
C5×F7Direct product of C5 and F7356C5xF7210,1
D5×C7⋊C3Direct product of D5 and C7⋊C3356D5xC7:C3210,2

Groups of order 216

dρLabelID
He33C81st semidirect product of He3 and C8 acting via C8/C4=C2726He3:3C8216,14
C9⋊C24The semidirect product of C9 and C24 acting via C24/C4=C6726C9:C24216,15
C6.S322nd non-split extension by C6 of S32 acting via S32/C3⋊S3=C2366C6.S3^2216,34
He33D42nd semidirect product of He3 and D4 acting via D4/C2=C22366He3:3D4216,37
C18.A4The non-split extension by C18 of A4 acting via A4/C22=C3726C18.A4216,39
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⋊He3The semidirect product of Q8 and He3 acting via He3/C32=C3726Q8:He3216,42
C4×C32⋊C6Direct product of C4 and C32⋊C6366C4xC3^2:C6216,50
C4×C9⋊C6Direct product of C4 and C9⋊C6366C4xC9:C6216,53
He36D41st semidirect product of He3 and D4 acting via D4/C22=C2366He3:6D4216,60
Dic9⋊C6The semidirect product of Dic9 and C6 acting faithfully366Dic9:C6216,62
He34Q82nd semidirect product of He3 and Q8 acting via Q8/C4=C2726He3:4Q8216,66
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
D4×He3Direct product of D4 and He3366D4xHe3216,77
D4×3- 1+2Direct product of D4 and 3- 1+2366D4xES-(3,1)216,78
Q8×He3Direct product of Q8 and He3726Q8xHe3216,80
Q8×3- 1+2Direct product of Q8 and 3- 1+2726Q8xES-(3,1)216,81
C3×C3.S4Direct product of C3 and C3.S4366C3xC3.S4216,91
S3×C3.A4Direct product of S3 and C3.A4366S3xC3.A4216,98
C3×C3⋊S4Direct product of C3 and C3⋊S4246C3xC3:S4216,164
C3×S3×A4Direct product of C3, S3 and A4246C3xS3xA4216,166

Groups of order 234

dρLabelID
C13⋊C18The semidirect product of C13 and C18 acting via C18/C3=C61176C13:C18234,1
C3×C13⋊C6Direct product of C3 and C13⋊C6396C3xC13:C6234,7
S3×C13⋊C3Direct product of S3 and C13⋊C3396S3xC13:C3234,8

Groups of order 252

dρLabelID
C7⋊C36The semidirect product of C7 and C36 acting via C36/C6=C62526C7:C36252,1
C2×C7⋊C18Direct product of C2 and C7⋊C181266C2xC7:C18252,7
C3×C7⋊C12Direct product of C3 and C7⋊C12846C3xC7:C12252,16
Dic3×C7⋊C3Direct product of Dic3 and C7⋊C3846Dic3xC7:C3252,17
C6×F7Direct product of C6 and F7426C6xF7252,28
C2×S3×C7⋊C3Direct product of C2, S3 and C7⋊C3426C2xS3xC7:C3252,29

Groups of order 270

dρLabelID
D5×He3Direct product of D5 and He3456D5xHe3270,6
D5×3- 1+2Direct product of D5 and 3- 1+2456D5xES-(3,1)270,7
C5×C32⋊C6Direct product of C5 and C32⋊C6456C5xC3^2:C6270,10
C5×C9⋊C6Direct product of C5 and C9⋊C6456C5xC9:C6270,11
C32⋊D152nd semidirect product of C32 and D15 acting via D15/C5=S3456C3^2:D15270,19

Groups of order 288

dρLabelID
C2.(C42⋊C9)The central stem extension by C2 of C42⋊C9366C2.(C4^2:C9)288,3
C12.S48th non-split extension by C12 of S4 acting via S4/A4=C2726C12.S4288,68
C24⋊C181st semidirect product of C24 and C18 acting via C18/C3=C6366C2^4:C18288,73
C42⋊C181st semidirect product of C42 and C18 acting via C18/C3=C6726C4^2:C18288,74
C422C182nd semidirect product of C42 and C18 acting via C18/C3=C6366C4^2:2C18288,75
C3×C23.3A4Direct product of C3 and C23.3A4366C3xC2^3.3A4288,230
C4×C3.S4Direct product of C4 and C3.S4366C4xC3.S4288,333
C23.D185th non-split extension by C23 of D18 acting via D18/C6=S3366C2^3.D18288,342
D4×C3.A4Direct product of D4 and C3.A4366D4xC3.A4288,344
Q8×C3.A4Direct product of Q8 and C3.A4726Q8xC3.A4288,346
C22⋊(Q8⋊C9)The semidirect product of C22 and Q8⋊C9 acting via Q8⋊C9/C3×Q8=C3726C2^2:(Q8:C9)288,350
C12.12S412nd non-split extension by C12 of S4 acting via S4/A4=C2726C12.12S4288,402
C42⋊C3⋊S31st semidirect product of C42⋊C3 and S3 acting via S3/C3=C2486C4^2:C3:S3288,406
S3×C42⋊C3Direct product of S3 and C42⋊C3366S3xC4^2:C3288,407
A4×C3⋊C8Direct product of A4 and C3⋊C8726A4xC3:C8288,408
(C22×S3)⋊A4The semidirect product of C22×S3 and A4 acting faithfully246(C2^2xS3):A4288,411
C3×C24⋊C6Direct product of C3 and C24⋊C6246C3xC2^4:C6288,634
C3×C42⋊C6Direct product of C3 and C42⋊C6486C3xC4^2:C6288,635
C3×C23.A4Direct product of C3 and C23.A4366C3xC2^3.A4288,636
C24⋊D93rd semidirect product of C24 and D9 acting via D9/C3=S3366C2^4:D9288,836
Dic32S4The semidirect product of Dic3 and S4 acting through Inn(Dic3)366Dic3:2S4288,854
Dic3⋊S4The semidirect product of Dic3 and S4 acting via S4/A4=C2366Dic3:S4288,855
S3×A4⋊C4Direct product of S3 and A4⋊C4366S3xA4:C4288,856
D6⋊S41st semidirect product of D6 and S4 acting via S4/A4=C2366D6:S4288,857
C3×A4⋊Q8Direct product of C3 and A4⋊Q8726C3xA4:Q8288,896
C3×C4⋊S4Direct product of C3 and C4⋊S4366C3xC4:S4288,898
C3×A4⋊D4Direct product of C3 and A4⋊D4366C3xA4:D4288,906
C4×C3⋊S4Direct product of C4 and C3⋊S4366C4xC3:S4288,908
(C2×C6)⋊4S42nd semidirect product of C2×C6 and S4 acting via S4/A4=C2366(C2xC6):4S4288,917
C4×S3×A4Direct product of C4, S3 and A4366C4xS3xA4288,919
A4×C3⋊D4Direct product of A4 and C3⋊D4366A4xC3:D4288,928
C3×D4×A4Direct product of C3, D4 and A4366C3xD4xA4288,980
C3×Q8×A4Direct product of C3, Q8 and A4726C3xQ8xA4288,982
C3×Q8⋊A4Direct product of C3 and Q8⋊A4726C3xQ8:A4288,986
C3×C22⋊S4Direct product of C3 and C22⋊S4246C3xC2^2:S4288,1035
(C2×C6)⋊S42nd semidirect product of C2×C6 and S4 acting via S4/C22=S3246(C2xC6):S4288,1036

Groups of order 294

dρLabelID
C7×F7Direct product of C7 and F7426C7xF7294,8
D7×C7⋊C3Direct product of D7 and C7⋊C3426D7xC7:C3294,9
C73F71st semidirect product of C7 and F7 acting via F7/D7=C3426C7:3F7294,11
C74F72nd semidirect product of C7 and F7 acting via F7/D7=C3146C7:4F7294,12

Groups of order 312

dρLabelID
C132C24The semidirect product of C13 and C24 acting via C24/C4=C61046C13:2C24312,1
C4×C13⋊C6Direct product of C4 and C13⋊C6526C4xC13:C6312,9
D26⋊C62nd semidirect product of D26 and C6 acting faithfully526D26:C6312,12
D4×C13⋊C3Direct product of D4 and C13⋊C3526D4xC13:C3312,23
Q8×C13⋊C3Direct product of Q8 and C13⋊C31046Q8xC13:C3312,24
C26.A4The non-split extension by C26 of A4 acting via A4/C22=C31046C26.A4312,26

Groups of order 324

dρLabelID
C32⋊C36The semidirect product of C32 and C36 acting via C36/C6=C6366C3^2:C36324,7
C9⋊C36The semidirect product of C9 and C36 acting via C36/C6=C6366C9:C36324,9
C322Dic92nd semidirect product of C32 and Dic9 acting via Dic9/C6=S3366C3^2:2Dic9324,20
C2×C32⋊C18Direct product of C2 and C32⋊C18366C2xC3^2:C18324,62
C2×C9⋊C18Direct product of C2 and C9⋊C18366C2xC9:C18324,64
C2×C322D9Direct product of C2 and C322D9366C2xC3^2:2D9324,75
C3×C32⋊C12Direct product of C3 and C32⋊C12366C3xC3^2:C12324,92
Dic3×He3Direct product of Dic3 and He3366Dic3xHe3324,93
C3×C9⋊C12Direct product of C3 and C9⋊C12366C3xC9:C12324,94
Dic3×3- 1+2Direct product of Dic3 and 3- 1+2366Dic3xES-(3,1)324,95
He36Dic32nd semidirect product of He3 and Dic3 acting via Dic3/C6=C2366He3:6Dic3324,104
He34Dic3The semidirect product of He3 and Dic3 acting via Dic3/C3=C4186He3:4Dic3324,113
C3×C32⋊D6Direct product of C3 and C32⋊D6186C3xC3^2:D6324,117
S3×He3⋊C2Direct product of S3 and He3⋊C2186S3xHe3:C2324,122
C6×C32⋊C6Direct product of C6 and C32⋊C6366C6xC3^2:C6324,138
C2×S3×He3Direct product of C2, S3 and He3366C2xS3xHe3324,139
C6×C9⋊C6Direct product of C6 and C9⋊C6366C6xC9:C6324,140
C2×S3×3- 1+2Direct product of C2, S3 and 3- 1+2366C2xS3xES-(3,1)324,141
C2×He35S3Direct product of C2 and He35S3366C2xHe3:5S3324,150

Groups of order 336

dρLabelID
C7⋊C48The semidirect product of C7 and C48 acting via C48/C8=C61126C7:C48336,1
C8×F7Direct product of C8 and F7566C8xF7336,7
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
C28.C121st non-split extension by C28 of C12 acting via C12/C2=C6566C28.C12336,13
M4(2)×C7⋊C3Direct product of M4(2) and C7⋊C3566M4(2)xC7:C3336,52
D8×C7⋊C3Direct product of D8 and C7⋊C3566D8xC7:C3336,53
SD16×C7⋊C3Direct product of SD16 and C7⋊C3566SD16xC7:C3336,54
Q16×C7⋊C3Direct product of Q16 and C7⋊C31126Q16xC7:C3336,55
D286C62nd semidirect product of D28 and C6 acting via C6/C2=C3566D28:6C6336,124
C4○D4×C7⋊C3Direct product of C4○D4 and C7⋊C3566C4oD4xC7:C3336,167
C28.A4The non-split extension by C28 of A4 acting via A4/C22=C31126C28.A4336,173

Groups of order 342

dρLabelID
C57.C6The non-split extension by C57 of C6 acting faithfully1716C57.C6342,1
C3×C19⋊C6Direct product of C3 and C19⋊C6576C3xC19:C6342,9
S3×C19⋊C3Direct product of S3 and C19⋊C3576S3xC19:C3342,10

Groups of order 360

dρLabelID
C5×C3.S4Direct product of C5 and C3.S4906C5xC3.S4360,40
D5×C3.A4Direct product of D5 and C3.A4906D5xC3.A4360,42
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5156GammaL(2,4)360,120
C3×C5⋊S4Direct product of C3 and C5⋊S4606C3xC5:S4360,139
C5×C3⋊S4Direct product of C5 and C3⋊S4606C5xC3:S4360,140
C3×D5×A4Direct product of C3, D5 and A4606C3xD5xA4360,142
C5×S3×A4Direct product of C5, S3 and A4606C5xS3xA4360,143

Groups of order 378

dρLabelID
C7⋊C54The semidirect product of C7 and C54 acting via C54/C9=C61896C7:C54378,1
C9×F7Direct product of C9 and F7636C9xF7378,7
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
C32.F7The non-split extension by C32 of F7 acting via F7/D7=C3636C3^2.F7378,11
D7⋊He3The semidirect product of D7 and He3 acting via He3/C32=C3636D7:He3378,12
C63⋊C65th semidirect product of C63 and C6 acting faithfully636C63:C6378,13
C636C66th semidirect product of C63 and C6 acting faithfully636C63:6C6378,14
D9×C7⋊C3Direct product of D9 and C7⋊C3636D9xC7:C3378,15
S3×C7⋊C9Direct product of S3 and C7⋊C91266S3xC7:C9378,16
C7⋊He3⋊C23rd semidirect product of C7⋊He3 and C2 acting faithfully636C7:He3:C2378,17
D21⋊C9The semidirect product of D21 and C9 acting via C9/C3=C31266D21:C9378,21
D7×He3Direct product of D7 and He3636D7xHe3378,30
D7×3- 1+2Direct product of D7 and 3- 1+2636D7xES-(3,1)378,31
C7×C32⋊C6Direct product of C7 and C32⋊C6636C7xC3^2:C6378,34
C7×C9⋊C6Direct product of C7 and C9⋊C6636C7xC9:C6378,35
C32⋊D212nd semidirect product of C32 and D21 acting via D21/C7=S3636C3^2:D21378,43
C3×S3×C7⋊C3Direct product of C3, S3 and C7⋊C3426C3xS3xC7:C3378,48
C3×C3⋊F7Direct product of C3 and C3⋊F7426C3xC3:F7378,49

Groups of order 390

dρLabelID
C5×C13⋊C6Direct product of C5 and C13⋊C6656C5xC13:C6390,1
D5×C13⋊C3Direct product of D5 and C13⋊C3656D5xC13:C3390,2

Groups of order 420

dρLabelID
C5×C7⋊C12Direct product of C5 and C7⋊C121406C5xC7:C12420,1
Dic5×C7⋊C3Direct product of Dic5 and C7⋊C31406Dic5xC7:C3420,2
C10×F7Direct product of C10 and F7706C10xF7420,17
C2×D5×C7⋊C3Direct product of C2, D5 and C7⋊C3706C2xD5xC7:C3420,18

Groups of order 432

dρLabelID
He33C161st semidirect product of He3 and C16 acting via C16/C8=C21446He3:3C16432,30
C9⋊C48The semidirect product of C9 and C48 acting via C48/C8=C61446C9:C48432,31
C32⋊C6⋊C8The semidirect product of C32⋊C6 and C8 acting via C8/C4=C2726C3^2:C6:C8432,76
He3⋊M4(2)1st semidirect product of He3 and M4(2) acting via M4(2)/C4=C22726He3:M4(2)432,77
He33SD161st semidirect product of He3 and SD16 acting via SD16/C4=C22726He3:3SD16432,78
C12.89S329th non-split extension by C12 of S32 acting via S32/C3⋊S3=C2726C12.89S3^2432,81
He33M4(2)2nd semidirect product of He3 and M4(2) acting via M4(2)/C4=C22726He3:3M4(2)432,82
C8×C32⋊C6Direct product of C8 and C32⋊C6726C8xC3^2:C6432,115
He35M4(2)1st semidirect product of He3 and M4(2) acting via M4(2)/C8=C2726He3:5M4(2)432,116
He36SD161st semidirect product of He3 and SD16 acting via SD16/C8=C2726He3:6SD16432,117
C8×C9⋊C6Direct product of C8 and C9⋊C6726C8xC9:C6432,120
C72⋊C64th semidirect product of C72 and C6 acting faithfully726C72:C6432,121
C722C62nd semidirect product of C72 and C6 acting faithfully726C72:2C6432,122
He37M4(2)1st semidirect product of He3 and M4(2) acting via M4(2)/C2×C4=C2726He3:7M4(2)432,137
C36.C121st non-split extension by C36 of C12 acting via C12/C2=C6726C36.C12432,143
He36M4(2)2nd semidirect product of He3 and M4(2) acting via M4(2)/C8=C2726He3:6M4(2)432,174
He37SD162nd semidirect product of He3 and SD16 acting via SD16/C8=C2726He3:7SD16432,175
He35D82nd semidirect product of He3 and D8 acting via D8/C8=C2726He3:5D8432,176
He35Q162nd semidirect product of He3 and Q16 acting via Q16/C8=C21446He3:5Q16432,177
He38M4(2)2nd semidirect product of He3 and M4(2) acting via M4(2)/C2×C4=C2726He3:8M4(2)432,185
He37D82nd semidirect product of He3 and D8 acting via D8/D4=C2726He3:7D8432,192
He39SD162nd semidirect product of He3 and SD16 acting via SD16/D4=C2726He3:9SD16432,193
He311SD162nd semidirect product of He3 and SD16 acting via SD16/Q8=C2726He3:11SD16432,196
He37Q162nd semidirect product of He3 and Q16 acting via Q16/Q8=C21446He3:7Q16432,197
M4(2)×He3Direct product of M4(2) and He3726M4(2)xHe3432,213
M4(2)×3- 1+2Direct product of M4(2) and 3- 1+2726M4(2)xES-(3,1)432,214
D8×He3Direct product of D8 and He3726D8xHe3432,216
D8×3- 1+2Direct product of D8 and 3- 1+2726D8xES-(3,1)432,217
SD16×He3Direct product of SD16 and He3726SD16xHe3432,219
SD16×3- 1+2Direct product of SD16 and 3- 1+2726SD16xES-(3,1)432,220
Q16×He3Direct product of Q16 and He31446Q16xHe3432,222
Q16×3- 1+2Direct product of Q16 and 3- 1+21446Q16xES-(3,1)432,223
He3⋊C16The semidirect product of He3 and C16 acting via C16/C2=C81446He3:C16432,233
He32SD16The semidirect product of He3 and SD16 acting via SD16/C2=D4726He3:2SD16432,234
C32⋊D6⋊C4The semidirect product of C32⋊D6 and C4 acting via C4/C2=C2366C3^2:D6:C4432,238
C3×C6.S4Direct product of C3 and C6.S4366C3xC6.S4432,250
C322CSU2(𝔽3)2nd semidirect product of C32 and CSU2(𝔽3) acting via CSU2(𝔽3)/Q8=S31446C3^2:2CSU(2,3)432,257
C323GL2(𝔽3)2nd semidirect product of C32 and GL2(𝔽3) acting via GL2(𝔽3)/Q8=S3726C3^2:3GL(2,3)432,258
Dic3×C3.A4Direct product of Dic3 and C3.A4366Dic3xC3.A4432,271
He31M4(2)The semidirect product of He3 and M4(2) acting via M4(2)/C4=C4726He3:1M4(2)432,274
C4⋊(He3⋊C4)The semidirect product of C4 and He3⋊C4 acting via He3⋊C4/He3⋊C2=C2726C4:(He3:C4)432,276
He34M4(2)The semidirect product of He3 and M4(2) acting via M4(2)/C22=C4726He3:4M4(2)432,278
C22⋊(He3⋊C4)The semidirect product of C22 and He3⋊C4 acting via He3⋊C4/He3⋊C2=C2366C2^2:(He3:C4)432,279
C12.84S324th non-split extension by C12 of S32 acting via S32/C3⋊S3=C2726C12.84S3^2432,296
C12.91S3211st non-split extension by C12 of S32 acting via S32/C3⋊S3=C2726C12.91S3^2432,297
C4×C32⋊D6Direct product of C4 and C32⋊D6366C4xC3^2:D6432,300
C62.9D69th non-split extension by C62 of D6 acting faithfully726C6^2.9D6432,319
C622D62nd semidirect product of C62 and D6 acting faithfully366C6^2:2D6432,324
C36.A4The non-split extension by C36 of A4 acting via A4/C22=C31446C36.A4432,330
Q8⋊C94C63rd semidirect product of Q8⋊C9 and C6 acting via C6/C2=C3726Q8:C9:4C6432,338
C4○D4⋊He3The semidirect product of C4○D4 and He3 acting via He3/C32=C3726C4oD4:He3432,339
C62.36D619th non-split extension by C62 of D6 acting via D6/C2=S3726C6^2.36D6432,351
D366C62nd semidirect product of D36 and C6 acting via C6/C2=C3726D36:6C6432,355
C62.47D630th non-split extension by C62 of D6 acting via D6/C2=S3726C6^2.47D6432,387
D4×He3⋊C2Direct product of D4 and He3⋊C2366D4xHe3:C2432,390
C62.16D616th non-split extension by C62 of D6 acting faithfully726C6^2.16D6432,391
Q8×He3⋊C2Direct product of Q8 and He3⋊C2726Q8xHe3:C2432,394
He35D4⋊C26th semidirect product of He35D4 and C2 acting faithfully726He3:5D4:C2432,395
C4○D4×He3Direct product of C4○D4 and He3726C4oD4xHe3432,410
C4○D4×3- 1+2Direct product of C4○D4 and 3- 1+2726C4oD4xES-(3,1)432,411
C6×C3.S4Direct product of C6 and C3.S4366C6xC3.S4432,534
C2×S3×C3.A4Direct product of C2, S3 and C3.A4366C2xS3xC3.A4432,541
C3×C6.7S4Direct product of C3 and C6.7S4366C3xC6.7S4432,618
C3×Dic3×A4Direct product of C3, Dic3 and A4366C3xDic3xA4432,624
C3×S3×S4Direct product of C3, S3 and S4246C3xS3xS4432,745
C6×C3⋊S4Direct product of C6 and C3⋊S4366C6xC3:S4432,761
S3×C6×A4Direct product of C6, S3 and A4366S3xC6xA4432,763

Groups of order 450

dρLabelID
C52⋊C18The semidirect product of C52 and C18 acting via C18/C3=C6456C5^2:C18450,12
C3×C52⋊C6Direct product of C3 and C52⋊C6456C3xC5^2:C6450,22
S3×C52⋊C3Direct product of S3 and C52⋊C3456S3xC5^2:C3450,23

Groups of order 456

dρLabelID
C19⋊C24The semidirect product of C19 and C24 acting via C24/C4=C61526C19:C24456,1
C4×C19⋊C6Direct product of C4 and C19⋊C6766C4xC19:C6456,8
D38⋊C62nd semidirect product of D38 and C6 acting faithfully766D38:C6456,11
D4×C19⋊C3Direct product of D4 and C19⋊C3766D4xC19:C3456,20
Q8×C19⋊C3Direct product of Q8 and C19⋊C31526Q8xC19:C3456,21
C38.A4The non-split extension by C38 of A4 acting via A4/C22=C31526C38.A4456,23

Groups of order 462

dρLabelID
C7⋊C3×D11Direct product of C7⋊C3 and D11776C7:C3xD11462,1
C11×F7Direct product of C11 and F7776C11xF7462,2

Groups of order 468

dρLabelID
C132C36The semidirect product of C13 and C36 acting via C36/C6=C64686C13:2C36468,1
C2×C13⋊C18Direct product of C2 and C13⋊C182346C2xC13:C18468,8
C3×C26.C6Direct product of C3 and C26.C61566C3xC26.C6468,19
Dic3×C13⋊C3Direct product of Dic3 and C13⋊C31566Dic3xC13:C3468,20
C6×C13⋊C6Direct product of C6 and C13⋊C6786C6xC13:C6468,33
C2×S3×C13⋊C3Direct product of C2, S3 and C13⋊C3786C2xS3xC13:C3468,34

Groups of order 480

dρLabelID
C5×C23.3A4Direct product of C5 and C23.3A4606C5xC2^3.3A4480,74
C20.S44th non-split extension by C20 of S4 acting via S4/A4=C21206C20.S4480,259
(C4×C20)⋊C61st semidirect product of C4×C20 and C6 acting faithfully806(C4xC20):C6480,263
D5×C42⋊C3Direct product of D5 and C42⋊C3606D5xC4^2:C3480,264
A4×C52C8Direct product of A4 and C52C81206A4xC5:2C8480,265
(C22×D5)⋊A4The semidirect product of C22×D5 and A4 acting faithfully406(C2^2xD5):A4480,268
C5×C24⋊C6Direct product of C5 and C24⋊C6406C5xC2^4:C6480,656
C5×C42⋊C6Direct product of C5 and C42⋊C6806C5xC4^2:C6480,657
C5×C23.A4Direct product of C5 and C23.A4606C5xC2^3.A4480,658
C4⋊S5The semidirect product of C4 and S5 acting via S5/A5=C2206C4:S5480,944
A5⋊Q8The semidirect product of A5 and Q8 acting via Q8/C4=C2246A5:Q8480,945
Dic52S4The semidirect product of Dic5 and S4 acting through Inn(Dic5)606Dic5:2S4480,977
Dic5⋊S4The semidirect product of Dic5 and S4 acting via S4/A4=C2606Dic5:S4480,978
D5×A4⋊C4Direct product of D5 and A4⋊C4606D5xA4:C4480,979
D10⋊S41st semidirect product of D10 and S4 acting via S4/A4=C2606D10:S4480,980
C5×A4⋊Q8Direct product of C5 and A4⋊Q81206C5xA4:Q8480,1013
C5×C4⋊S4Direct product of C5 and C4⋊S4606C5xC4:S4480,1015
C5×A4⋊D4Direct product of C5 and A4⋊D4606C5xA4:D4480,1023
C4×C5⋊S4Direct product of C4 and C5⋊S4606C4xC5:S4480,1025
C242D151st semidirect product of C24 and D15 acting via D15/C5=S3606C2^4:2D15480,1034
C4×D5×A4Direct product of C4, D5 and A4606C4xD5xA4480,1036
A4×C5⋊D4Direct product of A4 and C5⋊D4606A4xC5:D4480,1045
C5×D4×A4Direct product of C5, D4 and A4606C5xD4xA4480,1127
C5×Q8×A4Direct product of C5, Q8 and A41206C5xQ8xA4480,1129
C5×Q8⋊A4Direct product of C5 and Q8⋊A41206C5xQ8:A4480,1133
C5×C22⋊S4Direct product of C5 and C22⋊S4406C5xC2^2:S4480,1200
C244D153rd semidirect product of C24 and D15 acting via D15/C5=S3406C2^4:4D15480,1201

Groups of order 486

dρLabelID
C3.C3≀S31st non-split extension by C3 of C3≀S3 acting via C3≀S3/C3≀C3=C2546C3.C3wrS3486,4
C32⋊C9.S31st non-split extension by C32⋊C9 of S3 acting faithfully186C3^2:C9.S3486,5
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
C3.3C3≀S33rd non-split extension by C3 of C3≀S3 acting via C3≀S3/C3≀C3=C2546C3.3C3wrS3486,8
(C3×He3).C62nd non-split extension by C3×He3 of C6 acting faithfully546(C3xHe3).C6486,9
C32⋊C9.C62nd non-split extension by C32⋊C9 of C6 acting faithfully546C3^2:C9.C6486,10
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
C273C18The semidirect product of C27 and C18 acting via C18/C3=C6546C27:3C18486,15
C32⋊C54The semidirect product of C32 and C54 acting via C54/C9=C6546C3^2:C54486,16
C331C181st semidirect product of C33 and C18 acting via C18/C3=C6186C3^3:1C18486,18
C331D91st semidirect product of C33 and D9 acting via D9/C3=S3186C3^3:1D9486,19
(C3×C9)⋊C182nd semidirect product of C3×C9 and C18 acting via C18/C3=C6546(C3xC9):C18486,20
(C3×C9)⋊D92nd semidirect product of C3×C9 and D9 acting via D9/C3=S3546(C3xC9):D9486,21
C9⋊S33C93rd semidirect product of C9⋊S3 and C9 acting via C9/C3=C3546C9:S3:3C9486,22
(C3×C9)⋊3D93rd semidirect product of C3×C9 and D9 acting via D9/C3=S3546(C3xC9):3D9486,23
C9⋊C54The semidirect product of C9 and C54 acting via C54/C9=C6546C9:C54486,30
C322D272nd semidirect product of C32 and D27 acting via D27/C9=S3546C3^2:2D27486,51
C9×C32⋊C6Direct product of C9 and C32⋊C6546C9xC3^2:C6486,98
D9×He3Direct product of D9 and He3546D9xHe3486,99
C9×C9⋊C6Direct product of C9 and C9⋊C6546C9xC9:C6486,100
D9×3- 1+2Direct product of D9 and 3- 1+2546D9xES-(3,1)486,101
C34⋊C61st semidirect product of C34 and C6 acting faithfully186C3^4:C6486,102
C34.C64th non-split extension by C34 of C6 acting faithfully186C3^4.C6486,104
D9⋊He3The semidirect product of D9 and He3 acting via He3/C32=C3546D9:He3486,106
C9⋊He3⋊C23rd semidirect product of C9⋊He3 and C2 acting faithfully546C9:He3:C2486,107
D9⋊3- 1+2The semidirect product of D9 and 3- 1+2 acting via 3- 1+2/C32=C3546D9:ES-(3,1)486,108
C927C67th semidirect product of C92 and C6 acting faithfully546C9^2:7C6486,109
C928C68th semidirect product of C92 and C6 acting faithfully186C9^2:8C6486,110
C3×C27⋊C6Direct product of C3 and C27⋊C6546C3xC27:C6486,113
S3×C27⋊C3Direct product of S3 and C27⋊C3546S3xC27:C3486,114
C3×C33⋊C6Direct product of C3 and C33⋊C6186C3xC3^3:C6486,116
S3×C3≀C3Direct product of S3 and C3≀C3186S3xC3wrC3486,117
C3×He3.S3Direct product of C3 and He3.S3546C3xHe3.S3486,119
S3×He3.C3Direct product of S3 and He3.C3546S3xHe3.C3486,120
C3×He3.2S3Direct product of C3 and He3.2S3546C3xHe3.2S3486,122
S3×He3⋊C3Direct product of S3 and He3⋊C3546S3xHe3:C3486,123
S3×C3.He3Direct product of S3 and C3.He3546S3xC3.He3486,124
C923S33rd semidirect product of C92 and S3 acting faithfully546C9^2:3S3486,139
C924S34th semidirect product of C92 and S3 acting faithfully546C9^2:4S3486,140
C343S33rd semidirect product of C34 and S3 acting faithfully186C3^4:3S3486,145
C34.7S37th non-split extension by C34 of S3 acting faithfully186C3^4.7S3486,147
(C32×C9)⋊S314th semidirect product of C32×C9 and S3 acting faithfully546(C3^2xC9):S3486,149
(C32×C9)⋊8S38th semidirect product of C32×C9 and S3 acting faithfully546(C3^2xC9):8S3486,150
C9⋊C92S32nd semidirect product of C9⋊C9 and S3 acting faithfully546C9:C9:2S3486,152
C926S36th semidirect product of C92 and S3 acting faithfully186C9^2:6S3486,153
C925S35th semidirect product of C92 and S3 acting faithfully546C9^2:5S3486,156
C3×C33⋊S3Direct product of C3 and C33⋊S3186C3xC3^3:S3486,165
C345S35th semidirect product of C34 and S3 acting faithfully186C3^4:5S3486,166
C3×He3.3S3Direct product of C3 and He3.3S3546C3xHe3.3S3486,168
He3.C3⋊S35th semidirect product of He3.C3 and S3 acting via S3/C3=C2546He3.C3:S3486,169
C3×He3⋊S3Direct product of C3 and He3⋊S3546C3xHe3:S3486,171
He3⋊C32S31st semidirect product of He3⋊C3 and S3 acting via S3/C3=C2546He3:C3:2S3486,172
C3×3- 1+2.S3Direct product of C3 and 3- 1+2.S3546C3xES-(3,1).S3486,174
He34D92nd semidirect product of He3 and D9 acting via D9/C9=C2546He3:4D9486,182
S3×C9○He3Direct product of S3 and C9○He3546S3xC9oHe3486,226
C3×He3.4S3Direct product of C3 and He3.4S3546C3xHe3.4S3486,234
C9○He34S32nd semidirect product of C9○He3 and S3 acting via S3/C3=C2546C9oHe3:4S3486,246

Orthogonal of dimension 7  (ρ=7+)

Groups of order 56

dρLabelID
F8Frobenius group; = C23C7 = AGL1(𝔽8)87+F856,11

Groups of order 112

dρLabelID
C2×F8Direct product of C2 and F8147+C2xF8112,41

Groups of order 168

dρLabelID
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)87+AGammaL(1,8)168,43

Groups of order 336

dρLabelID
C2×AΓL1(𝔽8)Direct product of C2 and AΓL1(𝔽8)147+C2xAGammaL(1,8)336,210

Groups of order 448

dρLabelID
C23⋊F82nd semidirect product of C23 and F8 acting via F8/C23=C7147+C2^3:F8448,1394

Complex of dimension 7  (ρ=7)

Groups of order 168

dρLabelID
C3×F8Direct product of C3 and F8247C3xF8168,44

Groups of order 203

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

Groups of order 224

dρLabelID
C4×F8Direct product of C4 and F8287C4xF8224,173

Groups of order 280

dρLabelID
C5×F8Direct product of C5 and F8407C5xF8280,33

Groups of order 301

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

Groups of order 336

dρLabelID
C6×F8Direct product of C6 and F8427C6xF8336,213

Groups of order 343

dρLabelID
He7Heisenberg group; = C72C7 = 7+ 1+2497He7343,3
7- 1+2Extraspecial group497ES-(7,1)343,4

Groups of order 392

dρLabelID
C7.F8The central extension by C7 of F8987C7.F8392,11
C7×F8Direct product of C7 and F8567C7xF8392,39

Groups of order 406

dρLabelID
C2×C29⋊C7Direct product of C2 and C29⋊C7587C2xC29:C7406,2

Groups of order 448

dρLabelID
C43⋊C7The semidirect product of C43 and C7 acting faithfully287C4^3:C7448,178
C8×F8Direct product of C8 and F8567C8xF8448,919

Groups of order 497

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

Orthogonal of dimension 8  (ρ=8+)

Groups of order 72

dρLabelID
F9Frobenius group; = C32C8 = AGL1(𝔽9)98+F972,39
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M998+PSU(3,2)72,41

Groups of order 120

dρLabelID
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)158+S3xF5120,36

Groups of order 128

dρLabelID
C23.D81st non-split extension by C23 of D8 acting via D8/C2=D4168+C2^3.D8128,71
C23.SD161st non-split extension by C23 of SD16 acting via SD16/C2=D4168+C2^3.SD16128,73
C4.C4≀C29th non-split extension by C4 of C4≀C2 acting via C4≀C2/C42=C2168+C4.C4wrC2128,87
C8⋊C4⋊C41st semidirect product of C8⋊C4 and C4 acting faithfully168+C8:C4:C4128,138
C8⋊C45C45th semidirect product of C8⋊C4 and C4 acting faithfully168+C8:C4:5C4128,144
C4○D4.D43rd non-split extension by C4○D4 of D4 acting via D4/C2=C22168+C4oD4.D4128,527
C24.C231st non-split extension by C24 of C23 acting faithfully168+C2^4.C2^3128,560
C24.6(C2×C4)6th non-split extension by C24 of C2×C4 acting faithfully168+C2^4.6(C2xC4)128,561
M4(2).47D411st non-split extension by M4(2) of D4 acting via D4/C22=C2168+M4(2).47D4128,635
C42.5D45th non-split extension by C42 of D4 acting faithfully168+C4^2.5D4128,636
(C2×C8)⋊4D44th semidirect product of C2×C8 and D4 acting faithfully168+(C2xC8):4D4128,642
C42⋊D41st semidirect product of C42 and D4 acting faithfully168+C4^2:D4128,643
C24.28D428th non-split extension by C24 of D4 acting faithfully168+C2^4.28D4128,645
M4(2)⋊21D48th semidirect product of M4(2) and D4 acting via D4/C22=C2168+M4(2):21D4128,646
M4(2)⋊5D45th semidirect product of M4(2) and D4 acting via D4/C2=C22168+M4(2):5D4128,740
C24⋊Q8The semidirect product of C24 and Q8 acting faithfully168+C2^4:Q8128,764
M4(2).8D48th non-split extension by M4(2) of D4 acting via D4/C2=C22168+M4(2).8D4128,780
C24.Q8The non-split extension by C24 of Q8 acting faithfully168+C2^4.Q8128,801
(C2×C8).D45th non-split extension by C2×C8 of D4 acting faithfully168+(C2xC8).D4128,813
C24.4C234th non-split extension by C24 of C23 acting faithfully168+C2^4.4C2^3128,836
C24.36D436th non-split extension by C24 of D4 acting faithfully168+C2^4.36D4128,853
C2≀C4⋊C26th semidirect product of C2≀C4 and C2 acting faithfully168+C2wrC4:C2128,854
C24.39D439th non-split extension by C24 of D4 acting faithfully168+C2^4.39D4128,859
C4.4D4⋊C46th semidirect product of C4.4D4 and C4 acting faithfully168+C4.4D4:C4128,860
C41D4.C45th non-split extension by C41D4 of C4 acting faithfully168+C4:1D4.C4128,866
D16⋊C4The semidirect product of D16 and C4 acting faithfully; = Aut(D16) = Hol(C16)168+D16:C4128,913
D8⋊D4The semidirect product of D8 and D4 acting via D4/C2=C22168+D8:D4128,922
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
C42.15D415th non-split extension by C42 of D4 acting faithfully168+C4^2.15D4128,934
M5(2).C228th non-split extension by M5(2) of C22 acting faithfully168+M5(2).C2^2128,970
C23.C243rd non-split extension by C23 of C24 acting via C24/C22=C22168+C2^3.C2^4128,1615
M4(2).24C236th non-split extension by M4(2) of C23 acting via C23/C22=C2168+M4(2).24C2^3128,1620
M4(2)⋊C233rd semidirect product of M4(2) and C23 acting via C23/C2=C22168+M4(2):C2^3128,1751
C42.12C2312nd non-split extension by C42 of C23 acting faithfully168+C4^2.12C2^3128,1753
C24⋊C232nd semidirect product of C24 and C23 acting faithfully168+C2^4:C2^3128,1758
C23.9C249th non-split extension by C23 of C24 acting via C24/C22=C22168+C2^3.9C2^4128,1759
M4(2).37D41st non-split extension by M4(2) of D4 acting via D4/C22=C2168+M4(2).37D4128,1800
D811D45th semidirect product of D8 and D4 acting via D4/C22=C2168+D8:11D4128,2020
D8⋊C236th semidirect product of D8 and C23 acting via C23/C22=C2168+D8:C2^3128,2317
2+ 1+6Extraspecial group; = D42+ 1+4168+ES+(2,3)128,2326

Groups of order 136

dρLabelID
C17⋊C8The semidirect product of C17 and C8 acting faithfully178+C17:C8136,12

Groups of order 144

dρLabelID
C2.PSU3(𝔽2)The central extension by C2 of PSU3(𝔽2)248+C2.PSU(3,2)144,120
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)98+AGammaL(1,9)144,182
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

Groups of order 160

dρLabelID
D20⋊C41st semidirect product of D20 and C4 acting faithfully408+D20:C4160,82
Q82F52nd semidirect product of Q8 and F5 acting via F5/D5=C2408+Q8:2F5160,85
D4×F5Direct product of D4 and F5; = Aut(D20) = Hol(C20)208+D4xF5160,207
Q8.F5The non-split extension by Q8 of F5 acting through Inn(Q8)808+Q8.F5160,208

Groups of order 192

dρLabelID
C3⋊C2≀C4The semidirect product of C3 and C2≀C4 acting via C2≀C4/C23⋊C4=C2248+C3:C2wrC4192,30
C23.2D122nd non-split extension by C23 of D12 acting via D12/C3=D4248+C2^3.2D12192,33
C23.3D123rd non-split extension by C23 of D12 acting via D12/C3=D4248+C2^3.3D12192,34
(C2×C4).D123rd non-split extension by C2×C4 of D12 acting via D12/C3=D4488+(C2xC4).D12192,36
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4248+C2^3:D12192,300
S3×C23⋊C4Direct product of S3 and C23⋊C4248+S3xC2^3:C4192,302
S3×C4.D4Direct product of S3 and C4.D4248+S3xC4.D4192,303
D121D41st semidirect product of D12 and D4 acting via D4/C2=C22248+D12:1D4192,306
D12.3D43rd non-split extension by D12 of D4 acting via D4/C2=C22488+D12.3D4192,308
M4(2).21D64th non-split extension by M4(2) of D6 acting via D6/S3=C2488+M4(2).21D6192,310
D12.5D45th non-split extension by D12 of D4 acting via D4/C2=C22488+D12.5D4192,312
D12.6D46th non-split extension by D12 of D4 acting via D4/C2=C22488+D12.6D4192,313
D1218D46th semidirect product of D12 and D4 acting via D4/C22=C2248+D12:18D4192,757
M4(2).D612nd non-split extension by M4(2) of D6 acting via D6/C3=C22488+M4(2).D6192,758
D12.39D49th non-split extension by D12 of D4 acting via D4/C22=C2488+D12.39D4192,761
M4(2).15D615th non-split extension by M4(2) of D6 acting via D6/C3=C22488+M4(2).15D6192,762
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
2- 1+44S31st semidirect product of 2- 1+4 and S3 acting via S3/C3=C2488+ES-(2,2):4S3192,804
S3×C8⋊C22Direct product of S3 and C8⋊C22; = Aut(D24) = Hol(C24)248+S3xC8:C2^2192,1331
D85D65th semidirect product of D8 and D6 acting via D6/S3=C2488+D8:5D6192,1333
D24⋊C223rd semidirect product of D24 and C22 acting faithfully488+D24:C2^2192,1336
C24.C236th non-split extension by C24 of C23 acting faithfully488+C24.C2^3192,1337
D12.32C2313rd non-split extension by D12 of C23 acting via C23/C22=C2488+D12.32C2^3192,1394
D12.34C2315th non-split extension by D12 of C23 acting via C23/C22=C2488+D12.34C2^3192,1396
S3×2+ 1+4Direct product of S3 and 2+ 1+4248+S3xES+(2,2)192,1524
D12.39C2320th non-split extension by D12 of C23 acting via C23/C22=C2488+D12.39C2^3192,1527

Groups of order 200

dρLabelID
C52⋊C8The semidirect product of C52 and C8 acting faithfully108+C5^2:C8200,40
D5×F5Direct product of D5 and F5208+D5xF5200,41
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)108+D5:F5200,42
C52⋊Q8The semidirect product of C52 and Q8 acting faithfully108+C5^2:Q8200,44

Groups of order 216

dρLabelID
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C398+ASL(2,3)216,153
S3×C32⋊C4Direct product of S3 and C32⋊C4128+S3xC3^2:C4216,156
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4128+C3^2:2D12216,159
S33Direct product of S3, S3 and S3; = Hol(C3×S3)128+S3^3216,162

Groups of order 240

dρLabelID
D6⋊F5The semidirect product of D6 and F5 acting via F5/D5=C2608+D6:F5240,96
D15⋊C8The semidirect product of D15 and C8 acting via C8/C2=C41208+D15:C8240,99
Dic3.F5The non-split extension by Dic3 of F5 acting via F5/D5=C21208+Dic3.F5240,101
C2×S3×F5Direct product of C2, S3 and F5; = Aut(D30) = Hol(C30)308+C2xS3xF5240,195

Groups of order 272

dρLabelID
C2×C17⋊C8Direct product of C2 and C17⋊C8348+C2xC17:C8272,51

Groups of order 280

dρLabelID
D7×F5Direct product of D7 and F5358+D7xF5280,32

Groups of order 288

dρLabelID
C32⋊D16The semidirect product of C32 and D16 acting via D16/C4=D4488+C3^2:D16288,382
C32⋊SD32The semidirect product of C32 and SD32 acting via SD32/C4=D4488+C3^2:SD32288,383
C3⋊S3.5D8The non-split extension by C3⋊S3 of D8 acting via D8/D4=C2248+C3:S3.5D8288,430
C327C4≀C2The semidirect product of C32 and C4≀C2 acting via C4≀C2/Q8=C4488+C3^2:7C4wrC2288,433
S3×D4⋊S3Direct product of S3 and D4⋊S3488+S3xD4:S3288,572
Dic63D63rd semidirect product of Dic6 and D6 acting via D6/C3=C22488+Dic6:3D6288,573
D12⋊D64th semidirect product of D12 and D6 acting via D6/C3=C22248+D12:D6288,574
Dic6⋊D64th semidirect product of Dic6 and D6 acting via D6/C3=C22248+Dic6:D6288,578
D12.7D67th non-split extension by D12 of D6 acting via D6/C3=C22488+D12.7D6288,582
Dic6.20D67th non-split extension by Dic6 of D6 acting via D6/S3=C2488+Dic6.20D6288,583
D125D65th semidirect product of D12 and D6 acting via D6/C3=C22248+D12:5D6288,585
S3×Q82S3Direct product of S3 and Q82S3488+S3xQ8:2S3288,586
D126D66th semidirect product of D12 and D6 acting via D6/C3=C22488+D12:6D6288,587
D12.10D610th non-split extension by D12 of D6 acting via D6/C3=C22488+D12.10D6288,589
Dic6.10D610th non-split extension by Dic6 of D6 acting via D6/C3=C22488+Dic6.10D6288,593
Dic6.22D69th non-split extension by Dic6 of D6 acting via D6/S3=C2488+Dic6.22D6288,596
D12.13D613rd non-split extension by D12 of D6 acting via D6/C3=C22488+D12.13D6288,597
D12.14D614th non-split extension by D12 of D6 acting via D6/C3=C22488+D12.14D6288,598
C2.AΓL1(𝔽9)1st central extension by C2 of AΓL1(𝔽9)248+C2.AGammaL(1,9)288,841
C22⋊F9The semidirect product of C22 and F9 acting via F9/C32⋊C4=C2248+C2^2:F9288,867
C4.4S3≀C24th non-split extension by C4 of S3≀C2 acting via S3≀C2/C32⋊C4=C2248+C4.4S3wrC2288,869
C3⋊S3⋊D8The semidirect product of C3⋊S3 and D8 acting via D8/C4=C22248+C3:S3:D8288,873
C3⋊S32SD16The semidirect product of C3⋊S3 and SD16 acting via SD16/C4=C22248+C3:S3:2SD16288,875
C4⋊S3≀C2The semidirect product of C4 and S3≀C2 acting via S3≀C2/C32⋊C4=C2248+C4:S3wrC2288,879
C62⋊D42nd semidirect product of C62 and D4 acting faithfully248+C6^2:D4288,890
C62⋊Q81st semidirect product of C62 and Q8 acting faithfully248+C6^2:Q8288,895
D4×C32⋊C4Direct product of D4 and C32⋊C4248+D4xC3^2:C4288,936
C12⋊S3.C4The non-split extension by C12⋊S3 of C4 acting faithfully488+C12:S3.C4288,937
S32×D4Direct product of S3, S3 and D4248+S3^2xD4288,958
Dic612D66th semidirect product of Dic6 and D6 acting via D6/S3=C2248+Dic6:12D6288,960
D1213D67th semidirect product of D12 and D6 acting via D6/S3=C2248+D12:13D6288,962
Dic6.26D613rd non-split extension by Dic6 of D6 acting via D6/S3=C2488+Dic6.26D6288,964
S3×Q83S3Direct product of S3 and Q83S3488+S3xQ8:3S3288,966
D1216D610th semidirect product of D12 and D6 acting via D6/S3=C2488+D12:16D6288,968
C2×AΓL1(𝔽9)Direct product of C2 and AΓL1(𝔽9)188+C2xAGammaL(1,9)288,1027

Groups of order 312

dρLabelID
S3×C13⋊C4Direct product of S3 and C13⋊C4398+S3xC13:C4312,46

Groups of order 320

dρLabelID
C53C2≀C4The semidirect product of C5 and C2≀C4 acting via C2≀C4/C23⋊C4=C2408+C5:3C2wrC4320,29
C23.2D202nd non-split extension by C23 of D20 acting via D20/C5=D4408+C2^3.2D20320,32
C23.3D203rd non-split extension by C23 of D20 acting via D20/C5=D4408+C2^3.3D20320,33
(C2×C4).D203rd non-split extension by C2×C4 of D20 acting via D20/C5=D4808+(C2xC4).D20320,35
C5⋊C2≀C4The semidirect product of C5 and C2≀C4 acting via C2≀C4/C22⋊C4=C4408+C5:C2wrC4320,202
(C22×F5)⋊C4The semidirect product of C22×F5 and C4 acting faithfully408+(C2^2xF5):C4320,204
D5.D16The non-split extension by D5 of D16 acting via D16/D8=C2808+D5.D16320,242
D40.C41st non-split extension by D40 of C4 acting faithfully808+D40.C4320,244
D401C41st semidirect product of D40 and C4 acting faithfully808+D40:1C4320,245
Q16.F51st non-split extension by Q16 of F5 acting via F5/D5=C21608+Q16.F5320,247
(C2×D4)⋊F52nd semidirect product of C2×D4 and F5 acting via F5/C5=C4408+(C2xD4):F5320,260
(C2×Q8)⋊F52nd semidirect product of C2×Q8 and F5 acting via F5/C5=C4808+(C2xQ8):F5320,266
C23⋊D20The semidirect product of C23 and D20 acting via D20/C5=D4408+C2^3:D20320,368
D5×C23⋊C4Direct product of D5 and C23⋊C4408+D5xC2^3:C4320,370
D5×C4.D4Direct product of D5 and C4.D4408+D5xC4.D4320,371
D201D41st semidirect product of D20 and D4 acting via D4/C2=C22408+D20:1D4320,374
D20.3D43rd non-split extension by D20 of D4 acting via D4/C2=C22808+D20.3D4320,376
M4(2).21D104th non-split extension by M4(2) of D10 acting via D10/D5=C2808+M4(2).21D10320,378
D20.5D45th non-split extension by D20 of D4 acting via D4/C2=C22808+D20.5D4320,380
D20.6D46th non-split extension by D20 of D4 acting via D4/C2=C22808+D20.6D4320,381
D2018D46th semidirect product of D20 and D4 acting via D4/C22=C2408+D20:18D4320,825
M4(2).D1012nd non-split extension by M4(2) of D10 acting via D10/C5=C22808+M4(2).D10320,826
D20.39D49th non-split extension by D20 of D4 acting via D4/C22=C2808+D20.39D4320,829
M4(2).15D1015th non-split extension by M4(2) of D10 acting via D10/C5=C22808+M4(2).15D10320,830
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
2- 1+42D51st semidirect product of 2- 1+4 and D5 acting via D5/C5=C2808+ES-(2,2):2D5320,872
D8×F5Direct product of D8 and F5408+D8xF5320,1068
D40⋊C42nd semidirect product of D40 and C4 acting faithfully408+D40:C4320,1069
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
(D4×C10)⋊C46th semidirect product of D4×C10 and C4 acting faithfully408+(D4xC10):C4320,1105
(C2×D4)⋊7F55th semidirect product of C2×D4 and F5 acting via F5/D5=C2408+(C2xD4):7F5320,1108
D5⋊(C4.D4)The semidirect product of D5 and C4.D4 acting via C4.D4/C2×D4=C2408+D5:(C4.D4)320,1116
(C2×Q8)⋊6F54th semidirect product of C2×Q8 and F5 acting via F5/D5=C2808+(C2xQ8):6F5320,1122
(C2×Q8)⋊7F55th semidirect product of C2×Q8 and F5 acting via F5/D5=C2808+(C2xQ8):7F5320,1123
D5×C8⋊C22Direct product of D5 and C8⋊C22408+D5xC8:C2^2320,1444
D85D105th semidirect product of D8 and D10 acting via D10/D5=C2808+D8:5D10320,1446
D40⋊C223rd semidirect product of D40 and C22 acting faithfully808+D40:C2^2320,1449
C40.C236th non-split extension by C40 of C23 acting faithfully808+C40.C2^3320,1450
D20.32C2313rd non-split extension by D20 of C23 acting via C23/C22=C2808+D20.32C2^3320,1507
D20.34C2315th non-split extension by D20 of C23 acting via C23/C22=C2808+D20.34C2^3320,1509
D10.C2415th non-split extension by D10 of C24 acting via C24/C23=C2408+D10.C2^4320,1596
Dic5.20C2420th non-split extension by Dic5 of C24 acting via C24/C23=C2808+Dic5.20C2^4320,1598
D5×2+ 1+4Direct product of D5 and 2+ 1+4408+D5xES+(2,2)320,1622
D20.39C2320th non-split extension by D20 of C23 acting via C23/C22=C2808+D20.39C2^3320,1625

Groups of order 328

dρLabelID
C41⋊C8The semidirect product of C41 and C8 acting faithfully418+C41:C8328,12

Groups of order 360

dρLabelID
D9×F5Direct product of D9 and F5458+D9xF5360,39
C3⋊F5⋊S3The semidirect product of C3⋊F5 and S3 acting via S3/C3=C2308+C3:F5:S3360,129
D5×C32⋊C4Direct product of D5 and C32⋊C4308+D5xC3^2:C4360,130
C32⋊F5⋊C2The semidirect product of C32⋊F5 and C2 acting faithfully308+C3^2:F5:C2360,131
C32⋊D20The semidirect product of C32 and D20 acting via D20/C5=D4308+C3^2:D20360,134
S32×D5Direct product of S3, S3 and D5308+S3^2xD5360,137

Groups of order 392

dρLabelID
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

Groups of order 400

dρLabelID
D5.D20The non-split extension by D5 of D20 acting via D20/D10=C2408+D5.D20400,118
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
C523C422nd semidirect product of C52 and C42 acting via C42/C2=C2×C4208+C5^2:3C4^2400,124
D10⋊F52nd semidirect product of D10 and F5 acting via F5/D5=C2208+D10:F5400,125
Dic5⋊F53rd semidirect product of Dic5 and F5 acting via F5/D5=C2208+Dic5:F5400,126
(C5×C10).Q8The non-split extension by C5×C10 of Q8 acting faithfully208+(C5xC10).Q8400,134
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfully108+C5^2:M4(2)400,206
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfully108+D5wrC2:C2400,207
C2×C52⋊C8Direct product of C2 and C52⋊C8208+C2xC5^2:C8400,208
C2×D5×F5Direct product of C2, D5 and F5408+C2xD5xF5400,209
C2×D5⋊F5Direct product of C2 and D5⋊F5208+C2xD5:F5400,210
C2×C52⋊Q8Direct product of C2 and C52⋊Q8208+C2xC5^2:Q8400,212

Groups of order 408

dρLabelID
S3×C17⋊C4Direct product of S3 and C17⋊C4518+S3xC17:C4408,35

Groups of order 416

dρLabelID
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
D4×C13⋊C4Direct product of D4 and C13⋊C4528+D4xC13:C4416,206
D52.C4The non-split extension by D52 of C4 acting faithfully2088+D52.C4416,207

Groups of order 432

dρLabelID
D6⋊(C32⋊C4)The semidirect product of D6 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2248+D6:(C3^2:C4)432,568
C335(C2×C8)2nd semidirect product of C33 and C2×C8 acting via C2×C8/C2=C2×C4248+C3^3:5(C2xC8)432,571
C332M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C2=C2×C4248+C3^3:2M4(2)432,573
(C3×C6).8D121st non-split extension by C3×C6 of D12 acting via D12/C3=D4248+(C3xC6).8D12432,586
C322D24The semidirect product of C32 and D24 acting via D24/C6=D4248+C3^2:2D24432,588
C338SD164th semidirect product of C33 and SD16 acting via SD16/C2=D4248+C3^3:8SD16432,589
S3×C6.D6Direct product of S3 and C6.D6248+S3xC6.D6432,595
S3×C3⋊D12Direct product of S3 and C3⋊D12248+S3xC3:D12432,598
D64S321st semidirect product of D6 and S32 acting via S32/C3⋊S3=C2248+D6:4S3^2432,599
(S3×C6)⋊D61st semidirect product of S3×C6 and D6 acting via D6/C3=C22248+(S3xC6):D6432,601
C3⋊S34D12The semidirect product of C3⋊S3 and D12 acting via D12/D6=C2248+C3:S3:4D12432,602
C336(C2×Q8)3rd semidirect product of C33 and C2×Q8 acting via C2×Q8/C2=C23248+C3^3:6(C2xQ8)432,605
(S3×C6).D69th non-split extension by S3×C6 of D6 acting via D6/C3=C22248+(S3xC6).D6432,606
D6.3S323rd non-split extension by D6 of S32 acting via S32/C3×S3=C2248+D6.3S3^2432,609
Dic3.S324th non-split extension by Dic3 of S32 acting via S32/C3×S3=C2248+Dic3.S3^2432,612
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)98+AGL(2,3)432,734
C2×ASL2(𝔽3)Direct product of C2 and ASL2(𝔽3)188+C2xASL(2,3)432,735
S3×S3≀C2Direct product of S3 and S3≀C2128+S3xS3wrC2432,741
C2×S3×C32⋊C4Direct product of C2, S3 and C32⋊C4248+C2xS3xC3^2:C4432,753
C2×C322D12Direct product of C2 and C322D12248+C2xC3^2:2D12432,756
C2×S33Direct product of C2, S3, S3 and S3248+C2xS3^3432,759

Groups of order 440

dρLabelID
F5×D11Direct product of F5 and D11558+F5xD11440,43

Groups of order 448

dρLabelID
C7⋊C2≀C4The semidirect product of C7 and C2≀C4 acting via C2≀C4/C23⋊C4=C2568+C7:C2wrC4448,28
C23.2D282nd non-split extension by C23 of D28 acting via D28/C7=D4568+C2^3.2D28448,31
C23.3D283rd non-split extension by C23 of D28 acting via D28/C7=D4568+C2^3.3D28448,32
(C2×C4).D283rd non-split extension by C2×C4 of D28 acting via D28/C7=D41128+(C2xC4).D28448,34
C23⋊D28The semidirect product of C23 and D28 acting via D28/C7=D4568+C2^3:D28448,275
D7×C23⋊C4Direct product of D7 and C23⋊C4568+D7xC2^3:C4448,277
D7×C4.D4Direct product of D7 and C4.D4568+D7xC4.D4448,278
D281D41st semidirect product of D28 and D4 acting via D4/C2=C22568+D28:1D4448,281
D28.3D43rd non-split extension by D28 of D4 acting via D4/C2=C221128+D28.3D4448,283
M4(2).21D144th non-split extension by M4(2) of D14 acting via D14/D7=C21128+M4(2).21D14448,285
D28.5D45th non-split extension by D28 of D4 acting via D4/C2=C221128+D28.5D4448,287
D28.6D46th non-split extension by D28 of D4 acting via D4/C2=C221128+D28.6D4448,288
D2818D46th semidirect product of D28 and D4 acting via D4/C22=C2568+D28:18D4448,732
M4(2).D1412nd non-split extension by M4(2) of D14 acting via D14/C7=C221128+M4(2).D14448,733
D28.39D49th non-split extension by D28 of D4 acting via D4/C22=C21128+D28.39D4448,736
M4(2).15D1415th non-split extension by M4(2) of D14 acting via D14/C7=C221128+M4(2).15D14448,737
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
2- 1+4⋊D71st semidirect product of 2- 1+4 and D7 acting via D7/C7=C21128+ES-(2,2):D7448,779
D7×C8⋊C22Direct product of D7 and C8⋊C22568+D7xC8:C2^2448,1225
D85D145th semidirect product of D8 and D14 acting via D14/D7=C21128+D8:5D14448,1227
D56⋊C223rd semidirect product of D56 and C22 acting faithfully1128+D56:C2^2448,1230
C56.C236th non-split extension by C56 of C23 acting faithfully1128+C56.C2^3448,1231
D28.32C2313rd non-split extension by D28 of C23 acting via C23/C22=C21128+D28.32C2^3448,1288
D28.34C2315th non-split extension by D28 of C23 acting via C23/C22=C21128+D28.34C2^3448,1290
D7×2+ 1+4Direct product of D7 and 2+ 1+4568+D7xES+(2,2)448,1379
D28.39C2320th non-split extension by D28 of C23 acting via C23/C22=C21128+D28.39C2^3448,1382

Groups of order 480

dρLabelID
D60⋊C41st semidirect product of D60 and C4 acting faithfully1208+D60:C4480,227
D12⋊F51st semidirect product of D12 and F5 acting via F5/D5=C21208+D12:F5480,228
D602C42nd semidirect product of D60 and C4 acting faithfully1208+D60:2C4480,233
D605C45th semidirect product of D60 and C4 acting faithfully1208+D60:5C4480,234
D10.4D124th non-split extension by D10 of D12 acting via D12/C6=C221208+D10.4D12480,249
Dic5.D123rd non-split extension by Dic5 of D12 acting via D12/C6=C221208+Dic5.D12480,250
D5×D4⋊S3Direct product of D5 and D4⋊S31208+D5xD4:S3480,553
Dic103D63rd semidirect product of Dic10 and D6 acting via D6/C3=C221208+Dic10:3D6480,554
S3×D4⋊D5Direct product of S3 and D4⋊D51208+S3xD4:D5480,555
D60.C222nd non-split extension by D60 of C22 acting faithfully1208+D60.C2^2480,556
D15⋊D8The semidirect product of D15 and D8 acting via D8/D4=C21208+D15:D8480,557
Dic10⋊D64th semidirect product of Dic10 and D6 acting via D6/C3=C221208+Dic10:D6480,563
D20.9D69th non-split extension by D20 of D6 acting via D6/C3=C221208+D20.9D6480,567
C60.16C2316th non-split extension by C60 of C23 acting faithfully2408+C60.16C2^3480,568
C60.19C2319th non-split extension by C60 of C23 acting faithfully2408+C60.19C2^3480,571
D12.9D109th non-split extension by D12 of D10 acting via D10/C5=C221208+D12.9D10480,572
Dic6⋊D105th semidirect product of Dic6 and D10 acting via D10/C5=C221208+Dic6:D10480,574
D125D105th semidirect product of D12 and D10 acting via D10/C5=C221208+D12:5D10480,576
D5×Q82S3Direct product of D5 and Q82S31208+D5xQ8:2S3480,577
D20⋊D66th semidirect product of D20 and D6 acting via D6/C3=C221208+D20:D6480,578
S3×Q8⋊D5Direct product of S3 and Q8⋊D51208+S3xQ8:D5480,579
D12⋊D106th semidirect product of D12 and D10 acting via D10/C5=C221208+D12:D10480,580
D60⋊C226th semidirect product of D60 and C22 acting faithfully1208+D60:C2^2480,582
C60.C2336th non-split extension by C60 of C23 acting faithfully2408+C60.C2^3480,588
C60.39C2339th non-split extension by C60 of C23 acting faithfully2408+C60.39C2^3480,591
D20.D615th non-split extension by D20 of D6 acting via D6/C3=C222408+D20.D6480,592
Dic10.27D610th non-split extension by Dic10 of D6 acting via D6/S3=C22408+Dic10.27D6480,595
C60.44C2344th non-split extension by C60 of C23 acting faithfully2408+C60.44C2^3480,596
D20.16D616th non-split extension by D20 of D6 acting via D6/C3=C222408+D20.16D6480,597
D12.D1016th non-split extension by D12 of D10 acting via D10/C5=C222408+D12.D10480,599
C5⋊U2(𝔽3)The semidirect product of C5 and U2(𝔽3) acting via U2(𝔽3)/SL2(𝔽3)=C41208+C5:U(2,3)480,961
SL2(𝔽3).F5The non-split extension by SL2(𝔽3) of F5 acting through Inn(SL2(𝔽3))1608+SL(2,3).F5480,964
D60.C42nd non-split extension by D60 of C4 acting faithfully2408+D60.C4480,990
Dic6.F5The non-split extension by Dic6 of F5 acting via F5/D5=C22408+Dic6.F5480,992
F5×D12Direct product of F5 and D12608+F5xD12480,995
D603C43rd semidirect product of D60 and C4 acting faithfully608+D60:3C4480,997
D152M4(2)The semidirect product of D15 and M4(2) acting via M4(2)/C22=C41208+D15:2M4(2)480,1007
S3×C22⋊F5Direct product of S3 and C22⋊F5608+S3xC2^2:F5480,1011
S3×D4×D5Direct product of S3, D4 and D5608+S3xD4xD5480,1097
D30.C2313rd non-split extension by D30 of C23 acting via C23/C2=C221208+D30.C2^3480,1100
D2014D68th semidirect product of D20 and D6 acting via D6/S3=C21208+D20:14D6480,1102
D1214D108th semidirect product of D12 and D10 acting via D10/D5=C21208+D12:14D10480,1103
C30.33C2433rd non-split extension by C30 of C24 acting via C24/C22=C222408+C30.33C2^4480,1105
D5×Q83S3Direct product of D5 and Q83S31208+D5xQ8:3S3480,1108
S3×Q82D5Direct product of S3 and Q82D51208+S3xQ8:2D5480,1109
D2017D611st semidirect product of D20 and D6 acting via D6/S3=C21208+D20:17D6480,1111

Symplectic of dimension 8  (ρ=8-)

Groups of order 128

dρLabelID
C23.2D82nd non-split extension by C23 of D8 acting via D8/C2=D4328-C2^3.2D8128,72
C23.2SD162nd non-split extension by C23 of SD16 acting via SD16/C2=D4328-C2^3.2SD16128,74
C42.(C2×C4)2nd non-split extension by C42 of C2×C4 acting faithfully328-C4^2.(C2xC4)128,88
(C2×D4).D44th non-split extension by C2×D4 of D4 acting faithfully328-(C2xD4).D4128,139
C8⋊C4.C43rd non-split extension by C8⋊C4 of C4 acting faithfully328-C8:C4.C4128,145
(C22×Q8)⋊C46th semidirect product of C22×Q8 and C4 acting faithfully328-(C2^2xQ8):C4128,528
(C2×Q8).211D419th non-split extension by C2×Q8 of D4 acting via D4/C22=C2328-(C2xQ8).211D4128,562
M4(2).46D410th non-split extension by M4(2) of D4 acting via D4/C22=C2328-M4(2).46D4128,634
C42.6D46th non-split extension by C42 of D4 acting faithfully328-C4^2.6D4128,637
C4.(C4×D4)5th non-split extension by C4 of C4×D4 acting via C4×D4/C42=C2328-C4.(C4xD4)128,641
C42.7D47th non-split extension by C42 of D4 acting faithfully328-C4^2.7D4128,644
M4(2).50D414th non-split extension by M4(2) of D4 acting via D4/C22=C2328-M4(2).50D4128,647
M4(2).D43rd non-split extension by M4(2) of D4 acting via D4/C2=C22328-M4(2).D4128,741
M4(2).9D49th non-split extension by M4(2) of D4 acting via D4/C2=C22328-M4(2).9D4128,781
M4(2).15D415th non-split extension by M4(2) of D4 acting via D4/C2=C22328-M4(2).15D4128,802
(C2×C8).6D46th non-split extension by C2×C8 of D4 acting faithfully328-(C2xC8).6D4128,814
C23.(C2×D4)6th non-split extension by C23 of C2×D4 acting via C2×D4/C2=D4328-C2^3.(C2xD4)128,855
C4⋊Q8⋊C45th semidirect product of C4⋊Q8 and C4 acting faithfully328-C4:Q8:C4128,861
C4⋊Q8.C45th non-split extension by C4⋊Q8 of C4 acting faithfully328-C4:Q8.C4128,865
(C2×D4).137D499th non-split extension by C2×D4 of D4 acting via D4/C2=C22328-(C2xD4).137D4128,867
Q32⋊C4The semidirect product of Q32 and C4 acting faithfully328-Q32:C4128,912
D8.D41st non-split extension by D8 of D4 acting via D4/C2=C22328-D8.D4128,923
C42.14D414th non-split extension by C42 of D4 acting faithfully328-C4^2.14D4128,933
C42.16D416th non-split extension by C42 of D4 acting faithfully328-C4^2.16D4128,935
C23.10SD1610th non-split extension by C23 of SD16 acting via SD16/C2=D4328-C2^3.10SD16128,971
C23.4C244th non-split extension by C23 of C24 acting via C24/C22=C22328-C2^3.4C2^4128,1616
M4(2).25C237th non-split extension by M4(2) of C23 acting via C23/C22=C2328-M4(2).25C2^3128,1621
M4(2).C234th non-split extension by M4(2) of C23 acting via C23/C2=C22328-M4(2).C2^3128,1752
C42.13C2313rd non-split extension by C42 of C23 acting faithfully328-C4^2.13C2^3128,1754
C23.10C2410th non-split extension by C23 of C24 acting via C24/C22=C22328-C2^3.10C2^4128,1760
M4(2).38D42nd non-split extension by M4(2) of D4 acting via D4/C22=C2328-M4(2).38D4128,1801
D8.13D45th non-split extension by D8 of D4 acting via D4/C22=C2328-D8.13D4128,2021
C4.C2513rd non-split extension by C4 of C25 acting via C25/C24=C2328-C4.C2^5128,2318
2- 1+6Extraspecial group; = D42- 1+4328-ES-(2,3)128,2327

Groups of order 144

dρLabelID
C2.F9The central extension by C2 of F9488-C2.F9144,114

Groups of order 160

dρLabelID
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
D4.F5The non-split extension by D4 of F5 acting through Inn(D4)808-D4.F5160,206
Q8×F5Direct product of Q8 and F5408-Q8xF5160,209

Groups of order 192

dρLabelID
(C2×D4).D62nd non-split extension by C2×D4 of D6 acting via D6/C3=C22488-(C2xD4).D6192,31
C23.D121st non-split extension by C23 of D12 acting via D12/C3=D4488-C2^3.D12192,32
C23.4D124th non-split extension by C23 of D12 acting via D12/C3=D4488-C2^3.4D12192,35
(C2×C12).D416th non-split extension by C2×C12 of D4 acting faithfully488-(C2xC12).D4192,37
C23⋊C45S3The semidirect product of C23⋊C4 and S3 acting through Inn(C23⋊C4)488-C2^3:C4:5S3192,299
C23.5D125th non-split extension by C23 of D12 acting via D12/C3=D4488-C2^3.5D12192,301
M4(2).19D62nd non-split extension by M4(2) of D6 acting via D6/S3=C2488-M4(2).19D6192,304
M4(2)⋊D61st semidirect product of M4(2) and D6 acting via D6/C3=C22488-M4(2):D6192,305
D12.2D42nd non-split extension by D12 of D4 acting via D4/C2=C22488-D12.2D4192,307
S3×C4.10D4Direct product of S3 and C4.10D4488-S3xC4.10D4192,309
D12.4D44th non-split extension by D12 of D4 acting via D4/C2=C22488-D12.4D4192,311
D12.7D47th non-split extension by D12 of D4 acting via D4/C2=C22968-D12.7D4192,314
M4(2).13D613rd non-split extension by M4(2) of D6 acting via D6/C3=C22488-M4(2).13D6192,759
D12.38D48th non-split extension by D12 of D4 acting via D4/C22=C2488-D12.38D4192,760
M4(2).16D616th non-split extension by M4(2) of D6 acting via D6/C3=C22968-M4(2).16D6192,763
D12.40D410th non-split extension by D12 of D4 acting via D4/C22=C2488-D12.40D4192,764
2+ 1+4.4S31st non-split extension by 2+ 1+4 of S3 acting via S3/C3=C2488-ES+(2,2).4S3192,801
2+ 1+4.5S32nd non-split extension by 2+ 1+4 of S3 acting via S3/C3=C2488-ES+(2,2).5S3192,802
2- 1+4.2S3The non-split extension by 2- 1+4 of S3 acting via S3/C3=C2488-ES-(2,2).2S3192,805
D84D64th semidirect product of D8 and D6 acting via D6/S3=C2488-D8:4D6192,1332
D86D66th semidirect product of D8 and D6 acting via D6/S3=C2488-D8:6D6192,1334
S3×C8.C22Direct product of S3 and C8.C22488-S3xC8.C2^2192,1335
SD16.D6The non-split extension by SD16 of D6 acting via D6/S3=C2968-SD16.D6192,1338
D12.33C2314th non-split extension by D12 of C23 acting via C23/C22=C2488-D12.33C2^3192,1395
D12.35C2316th non-split extension by D12 of C23 acting via C23/C22=C2968-D12.35C2^3192,1397
D6.C249th non-split extension by D6 of C24 acting via C24/C23=C2488-D6.C2^4192,1525
S3×2- 1+4Direct product of S3 and 2- 1+4488-S3xES-(2,2)192,1526

Groups of order 240

dρLabelID
Dic3×F5Direct product of Dic3 and F5608-Dic3xF5240,95
Dic3⋊F5The semidirect product of Dic3 and F5 acting via F5/D5=C2608-Dic3:F5240,97
S3×C5⋊C8Direct product of S3 and C5⋊C81208-S3xC5:C8240,98
D6.F5The non-split extension by D6 of F5 acting via F5/D5=C21208-D6.F5240,100

Groups of order 272

dρLabelID
C34.C8The non-split extension by C34 of C8 acting faithfully2728-C34.C8272,28

Groups of order 288

dρLabelID
C32⋊Q32The semidirect product of C32 and Q32 acting via Q32/C4=D4968-C3^2:Q32288,384
C62.2Q82nd non-split extension by C62 of Q8 acting faithfully488-C6^2.2Q8288,396
C326C4≀C2The semidirect product of C32 and C4≀C2 acting via C4≀C2/D4=C4488-C3^2:6C4wrC2288,431
C3⋊S3.5Q16The non-split extension by C3⋊S3 of Q16 acting via Q16/Q8=C2488-C3:S3.5Q16288,432
D12.D65th non-split extension by D12 of D6 acting via D6/C3=C22488-D12.D6288,575
S3×D4.S3Direct product of S3 and D4.S3488-S3xD4.S3288,576
Dic6.19D66th non-split extension by Dic6 of D6 acting via D6/S3=C2488-Dic6.19D6288,577
Dic6.D65th non-split extension by Dic6 of D6 acting via D6/C3=C22488-Dic6.D6288,579
D129D63rd semidirect product of D12 and D6 acting via D6/S3=C2488-D12:9D6288,580
D12.22D67th non-split extension by D12 of D6 acting via D6/S3=C2488-D12.22D6288,581
D12.8D68th non-split extension by D12 of D6 acting via D6/C3=C22488-D12.8D6288,584
D12.9D69th non-split extension by D12 of D6 acting via D6/C3=C22488-D12.9D6288,588
S3×C3⋊Q16Direct product of S3 and C3⋊Q16968-S3xC3:Q16288,590
D12.11D611st non-split extension by D12 of D6 acting via D6/C3=C22968-D12.11D6288,591
Dic6.9D69th non-split extension by Dic6 of D6 acting via D6/C3=C22488-Dic6.9D6288,592
D12.24D69th non-split extension by D12 of D6 acting via D6/S3=C2968-D12.24D6288,594
D12.12D612nd non-split extension by D12 of D6 acting via D6/C3=C22968-D12.12D6288,595
D12.15D615th non-split extension by D12 of D6 acting via D6/C3=C22488-D12.15D6288,599
C22.F9The non-split extension by C22 of F9 acting via F9/C32⋊C4=C2488-C2^2.F9288,866
C32⋊C4⋊Q81st semidirect product of C32⋊C4 and Q8 acting via Q8/C4=C2488-C3^2:C4:Q8288,870
C3⋊S3⋊Q16The semidirect product of C3⋊S3 and Q16 acting via Q16/C4=C22488-C3:S3:Q16288,876
C62.13D413rd non-split extension by C62 of D4 acting faithfully488-C6^2.13D4288,885
C62.(C2×C4)The non-split extension by C62 of C2×C4 acting faithfully488-C6^2.(C2xC4)288,935
Q8×C32⋊C4Direct product of Q8 and C32⋊C4488-Q8xC3^2:C4288,938
Dic6.24D611st non-split extension by Dic6 of D6 acting via D6/S3=C2488-Dic6.24D6288,957
S3×D42S3Direct product of S3 and D42S3488-S3xD4:2S3288,959
D1212D66th semidirect product of D12 and D6 acting via D6/S3=C2488-D12:12D6288,961
D12.25D610th non-split extension by D12 of D6 acting via D6/S3=C2488-D12.25D6288,963
S32×Q8Direct product of S3, S3 and Q8488-S3^2xQ8288,965
D1215D69th semidirect product of D12 and D6 acting via D6/S3=C2488-D12:15D6288,967

Groups of order 320

dρLabelID
(C2×C20).D42nd non-split extension by C2×C20 of D4 acting faithfully808-(C2xC20).D4320,30
C23.D201st non-split extension by C23 of D20 acting via D20/C5=D4808-C2^3.D20320,31
C23.4D204th non-split extension by C23 of D20 acting via D20/C5=D4808-C2^3.4D20320,34
(C2×Q8).D102nd non-split extension by C2×Q8 of D10 acting via D10/C5=C22808-(C2xQ8).D10320,36
C22⋊C4⋊F52nd semidirect product of C22⋊C4 and F5 acting via F5/C5=C4808-C2^2:C4:F5320,203
C22⋊C4.F51st non-split extension by C22⋊C4 of F5 acting via F5/D5=C2808-C2^2:C4.F5320,205
D10.D82nd non-split extension by D10 of D8 acting via D8/C4=C22808-D10.D8320,241
D8.F51st non-split extension by D8 of F5 acting via F5/D5=C21608-D8.F5320,243
D5.Q32The non-split extension by D5 of Q32 acting via Q32/Q16=C2808-D5.Q32320,246
Dic20.C41st non-split extension by Dic20 of C4 acting faithfully1608-Dic20.C4320,248
(D4×C10).C42nd non-split extension by D4×C10 of C4 acting faithfully808-(D4xC10).C4320,261
(Q8×C10).C42nd non-split extension by Q8×C10 of C4 acting faithfully808-(Q8xC10).C4320,267
C23⋊C45D5The semidirect product of C23⋊C4 and D5 acting through Inn(C23⋊C4)808-C2^3:C4:5D5320,367
C23.5D205th non-split extension by C23 of D20 acting via D20/C5=D4808-C2^3.5D20320,369
M4(2).19D102nd non-split extension by M4(2) of D10 acting via D10/D5=C2808-M4(2).19D10320,372
D20.1D41st non-split extension by D20 of D4 acting via D4/C2=C22808-D20.1D4320,373
D20.2D42nd non-split extension by D20 of D4 acting via D4/C2=C22808-D20.2D4320,375
D5×C4.10D4Direct product of D5 and C4.10D4808-D5xC4.10D4320,377
D20.4D44th non-split extension by D20 of D4 acting via D4/C2=C22808-D20.4D4320,379
D20.7D47th non-split extension by D20 of D4 acting via D4/C2=C221608-D20.7D4320,382
M4(2).13D1013rd non-split extension by M4(2) of D10 acting via D10/C5=C22808-M4(2).13D10320,827
D20.38D48th non-split extension by D20 of D4 acting via D4/C22=C2808-D20.38D4320,828
M4(2).16D1016th non-split extension by M4(2) of D10 acting via D10/C5=C221608-M4(2).16D10320,831
D20.40D410th non-split extension by D20 of D4 acting via D4/C22=C2808-D20.40D4320,832
2+ 1+4.D51st non-split extension by 2+ 1+4 of D5 acting via D5/C5=C2808-ES+(2,2).D5320,869
2+ 1+4.2D52nd non-split extension by 2+ 1+4 of D5 acting via D5/C5=C2808-ES+(2,2).2D5320,870
2- 1+4.2D5The non-split extension by 2- 1+4 of D5 acting via D5/C5=C2808-ES-(2,2).2D5320,873
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
Q16×F5Direct product of Q16 and F5808-Q16xF5320,1076
Dic20⋊C43rd semidirect product of Dic20 and C4 acting faithfully808-Dic20:C4320,1077
(C2×D4)⋊6F54th semidirect product of C2×D4 and F5 acting via F5/D5=C2808-(C2xD4):6F5320,1107
(C2×D4)⋊8F56th semidirect product of C2×D4 and F5 acting via F5/D5=C2808-(C2xD4):8F5320,1109
(C2×D4).9F56th non-split extension by C2×D4 of F5 acting via F5/D5=C2808-(C2xD4).9F5320,1115
(C2×Q8)⋊4F52nd semidirect product of C2×Q8 and F5 acting via F5/D5=C2808-(C2xQ8):4F5320,1120
(C2×Q8).7F54th non-split extension by C2×Q8 of F5 acting via F5/D5=C2808-(C2xQ8).7F5320,1127
SD16⋊D102nd semidirect product of SD16 and D10 acting via D10/D5=C2808-SD16:D10320,1445
D86D106th semidirect product of D8 and D10 acting via D10/D5=C2808-D8:6D10320,1447
D5×C8.C22Direct product of D5 and C8.C22808-D5xC8.C2^2320,1448
D20.44D414th non-split extension by D20 of D4 acting via D4/C22=C21608-D20.44D4320,1451
D20.33C2314th non-split extension by D20 of C23 acting via C23/C22=C2808-D20.33C2^3320,1508
D20.35C2316th non-split extension by D20 of C23 acting via C23/C22=C21608-D20.35C2^3320,1510
Dic5.C2418th non-split extension by Dic5 of C24 acting via C24/C23=C2808-Dic5.C2^4320,1594
D5.2- 1+4The non-split extension by D5 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2808-D5.ES-(2,2)320,1600
D20.37C2318th non-split extension by D20 of C23 acting via C23/C22=C2808-D20.37C2^3320,1623
D5×2- 1+4Direct product of D5 and 2- 1+4808-D5xES-(2,2)320,1624

Groups of order 400

dρLabelID
C52⋊C16The semidirect product of C52 and C16 acting via C16/C2=C8808-C5^2:C16400,116
Dic5×F5Direct product of Dic5 and F5808-Dic5xF5400,117
D5.Dic10The non-split extension by D5 of Dic10 acting via Dic10/Dic5=C2808-D5.Dic10400,119
D5×C5⋊C8Direct product of D5 and C5⋊C8808-D5xC5:C8400,120
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
C524M4(2)3rd semidirect product of C52 and M4(2) acting via M4(2)/C2=C2×C4808-C5^2:4M4(2)400,128

Groups of order 416

dρLabelID
Dic26⋊C41st semidirect product of Dic26 and C4 acting faithfully1048-Dic26:C4416,83
D13.Q16The non-split extension by D13 of Q16 acting via Q16/Q8=C21048-D13.Q16416,84
Dic26.C4The non-split extension by Dic26 of C4 acting faithfully2088-Dic26.C4416,205
Q8×C13⋊C4Direct product of Q8 and C13⋊C41048-Q8xC13:C4416,208

Groups of order 432

dρLabelID
Dic3×C32⋊C4Direct product of Dic3 and C32⋊C4488-Dic3xC3^2:C4432,567
C33⋊(C4⋊C4)The semidirect product of C33 and C4⋊C4 acting via C4⋊C4/C2=C2×C4488-C3^3:(C4:C4)432,569
S3×C322C8Direct product of S3 and C322C8488-S3xC3^2:2C8432,570
C33⋊M4(2)1st semidirect product of C33 and M4(2) acting via M4(2)/C2=C2×C4488-C3^3:M4(2)432,572
(C3×C6).9D122nd non-split extension by C3×C6 of D12 acting via D12/C3=D4488-(C3xC6).9D12432,587
C333Q163rd semidirect product of C33 and Q16 acting via Q16/C2=D4488-C3^3:3Q16432,590
S32×Dic3Direct product of S3, S3 and Dic3488-S3^2xDic3432,594
Dic36S322nd semidirect product of Dic3 and S32 acting through Inn(Dic3)488-Dic3:6S3^2432,596
S3×D6⋊S3Direct product of S3 and D6⋊S3488-S3xD6:S3432,597
D6⋊S323rd semidirect product of D6 and S32 acting via S32/C3×S3=C2488-D6:S3^2432,600
S3×C322Q8Direct product of S3 and C322Q8488-S3xC3^2:2Q8432,603
C335(C2×Q8)2nd semidirect product of C33 and C2×Q8 acting via C2×Q8/C2=C23488-C3^3:5(C2xQ8)432,604
D6.S322nd non-split extension by D6 of S32 acting via S32/C3×S3=C2488-D6.S3^2432,607
D6.4S321st non-split extension by D6 of S32 acting via S32/C3⋊S3=C2488-D6.4S3^2432,608
D6⋊S3⋊S35th semidirect product of D6⋊S3 and S3 acting via S3/C3=C2488-D6:S3:S3432,610
D6.6S323rd non-split extension by D6 of S32 acting via S32/C3⋊S3=C2488-D6.6S3^2432,611

Groups of order 448

dρLabelID
(C2×C28).D42nd non-split extension by C2×C28 of D4 acting faithfully1128-(C2xC28).D4448,29
C23.D281st non-split extension by C23 of D28 acting via D28/C7=D41128-C2^3.D28448,30
C23.4D284th non-split extension by C23 of D28 acting via D28/C7=D41128-C2^3.4D28448,33
(C2×Q8).D142nd non-split extension by C2×Q8 of D14 acting via D14/C7=C221128-(C2xQ8).D14448,35
C23⋊C45D7The semidirect product of C23⋊C4 and D7 acting through Inn(C23⋊C4)1128-C2^3:C4:5D7448,274
C23.5D285th non-split extension by C23 of D28 acting via D28/C7=D41128-C2^3.5D28448,276
M4(2).19D142nd non-split extension by M4(2) of D14 acting via D14/D7=C21128-M4(2).19D14448,279
D28.1D41st non-split extension by D28 of D4 acting via D4/C2=C221128-D28.1D4448,280
D28.2D42nd non-split extension by D28 of D4 acting via D4/C2=C221128-D28.2D4448,282
D7×C4.10D4Direct product of D7 and C4.10D41128-D7xC4.10D4448,284
D28.4D44th non-split extension by D28 of D4 acting via D4/C2=C221128-D28.4D4448,286
D28.7D47th non-split extension by D28 of D4 acting via D4/C2=C222248-D28.7D4448,289
M4(2).13D1413rd non-split extension by M4(2) of D14 acting via D14/C7=C221128-M4(2).13D14448,734
D28.38D48th non-split extension by D28 of D4 acting via D4/C22=C21128-D28.38D4448,735
M4(2).16D1416th non-split extension by M4(2) of D14 acting via D14/C7=C222248-M4(2).16D14448,738
D28.40D410th non-split extension by D28 of D4 acting via D4/C22=C21128-D28.40D4448,739
2+ 1+4.D71st non-split extension by 2+ 1+4 of D7 acting via D7/C7=C21128-ES+(2,2).D7448,776
2+ 1+4.2D72nd non-split extension by 2+ 1+4 of D7 acting via D7/C7=C21128-ES+(2,2).2D7448,777
2- 1+4.D7The non-split extension by 2- 1+4 of D7 acting via D7/C7=C21128-ES-(2,2).D7448,780
SD16⋊D142nd semidirect product of SD16 and D14 acting via D14/D7=C21128-SD16:D14448,1226
D86D146th semidirect product of D8 and D14 acting via D14/D7=C21128-D8:6D14448,1228
D7×C8.C22Direct product of D7 and C8.C221128-D7xC8.C2^2448,1229
D28.44D414th non-split extension by D28 of D4 acting via D4/C22=C22248-D28.44D4448,1232
D28.33C2314th non-split extension by D28 of C23 acting via C23/C22=C21128-D28.33C2^3448,1289
D28.35C2316th non-split extension by D28 of C23 acting via C23/C22=C22248-D28.35C2^3448,1291
D14.C249th non-split extension by D14 of C24 acting via C24/C23=C21128-D14.C2^4448,1380
D7×2- 1+4Direct product of D7 and 2- 1+41128-D7xES-(2,2)448,1381

Groups of order 480

dρLabelID
Dic6⋊F53rd semidirect product of Dic6 and F5 acting via F5/D5=C21208-Dic6:F5480,229
Dic30⋊C44th semidirect product of Dic30 and C4 acting faithfully1208-Dic30:C4480,230
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
D10.D123rd non-split extension by D10 of D12 acting via D12/C6=C221208-D10.D12480,248
Dic5.4D124th non-split extension by Dic5 of D12 acting via D12/C6=C222408-Dic5.4D12480,251
D30.8D48th non-split extension by D30 of D4 acting via D4/C2=C221208-D30.8D4480,558
D5×D4.S3Direct product of D5 and D4.S31208-D5xD4.S3480,559
C60.8C238th non-split extension by C60 of C23 acting faithfully2408-C60.8C2^3480,560
S3×D4.D5Direct product of S3 and D4.D51208-S3xD4.D5480,561
C60.10C2310th non-split extension by C60 of C23 acting faithfully2408-C60.10C2^3480,562
D30.9D49th non-split extension by D30 of D4 acting via D4/C2=C222408-D30.9D4480,564
D1210D104th semidirect product of D12 and D10 acting via D10/D5=C21208-D12:10D10480,565
D12.24D107th non-split extension by D12 of D10 acting via D10/D5=C22408-D12.24D10480,566
D20.24D67th non-split extension by D20 of D6 acting via D6/S3=C22408-D20.24D6480,569
D2010D64th semidirect product of D20 and D6 acting via D6/S3=C21208-D20:10D6480,570
D20.10D610th non-split extension by D20 of D6 acting via D6/C3=C222408-D20.10D6480,573
D30.11D411st non-split extension by D30 of D4 acting via D4/C2=C222408-D30.11D4480,575
D15⋊SD16The semidirect product of D15 and SD16 acting via SD16/Q8=C21208-D15:SD16480,581
D5×C3⋊Q16Direct product of D5 and C3⋊Q162408-D5xC3:Q16480,583
D20.13D613rd non-split extension by D20 of D6 acting via D6/C3=C222408-D20.13D6480,584
S3×C5⋊Q16Direct product of S3 and C5⋊Q162408-S3xC5:Q16480,585
Dic10.26D69th non-split extension by Dic10 of D6 acting via D6/S3=C22408-Dic10.26D6480,586
D15⋊Q16The semidirect product of D15 and Q16 acting via Q16/Q8=C22408-D15:Q16480,587
D12.27D1010th non-split extension by D12 of D10 acting via D10/D5=C22408-D12.27D10480,589
D20.14D614th non-split extension by D20 of D6 acting via D6/C3=C222408-D20.14D6480,590
D20.27D610th non-split extension by D20 of D6 acting via D6/S3=C22408-D20.27D6480,593
D20.28D611st non-split extension by D20 of D6 acting via D6/S3=C22408-D20.28D6480,594
D20.17D617th non-split extension by D20 of D6 acting via D6/C3=C222408-D20.17D6480,598
D30.44D417th non-split extension by D30 of D4 acting via D4/C22=C22408-D30.44D4480,600
D10.S43rd non-split extension by D10 of S4 acting via S4/A4=C2408-D10.S4480,962
F5×SL2(𝔽3)Direct product of F5 and SL2(𝔽3)408-F5xSL(2,3)480,965
F5×Dic6Direct product of F5 and Dic61208-F5xDic6480,982
Dic65F55th semidirect product of Dic6 and F5 acting via F5/D5=C21208-Dic6:5F5480,984
D12.2F5The non-split extension by D12 of F5 acting through Inn(D12)2408-D12.2F5480,987
D12.F5The non-split extension by D12 of F5 acting via F5/D5=C22408-D12.F5480,989
C22⋊F5.S3The non-split extension by C22⋊F5 of S3 acting through Inn(C22⋊F5)1208-C2^2:F5.S3480,999
S3×C22.F5Direct product of S3 and C22.F51208-S3xC2^2.F5480,1004
C15⋊2- 1+4The semidirect product of C15 and 2- 1+4 acting via 2- 1+4/D4=C222408-C15:ES-(2,2)480,1096
D5×D42S3Direct product of D5 and D42S31208-D5xD4:2S3480,1098
S3×D42D5Direct product of S3 and D42D51208-S3xD4:2D5480,1099
D2013D67th semidirect product of D20 and D6 acting via D6/S3=C21208-D20:13D6480,1101
D20.29D612nd non-split extension by D20 of D6 acting via D6/S3=C22408-D20.29D6480,1104
D12.29D1012nd non-split extension by D12 of D10 acting via D10/D5=C22408-D12.29D10480,1106
S3×Q8×D5Direct product of S3, Q8 and D51208-S3xQ8xD5480,1107
D2016D610th semidirect product of D20 and D6 acting via D6/S3=C21208-D20:16D6480,1110

Complex of dimension 8  (ρ=8)

Groups of order 216

dρLabelID
C3×F9Direct product of C3 and F9248C3xF9216,154
C3⋊F9The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2248C3:F9216,155
C3×PSU3(𝔽2)Direct product of C3 and PSU3(𝔽2)248C3xPSU(3,2)216,160
C33⋊Q82nd semidirect product of C33 and Q8 acting faithfully248C3^3:Q8216,161

Groups of order 288

dρLabelID
C32⋊C32The semidirect product of C32 and C32 acting via C32/C4=C8968C3^2:C32288,373
C4.4PSU3(𝔽2)The central extension by C4 of PSU3(𝔽2)488C4.4PSU(3,2)288,392
C4.PSU3(𝔽2)1st non-split extension by C4 of PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2488C4.PSU(3,2)288,393
C4.2PSU3(𝔽2)2nd non-split extension by C4 of PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2488C4.2PSU(3,2)288,394
PSU3(𝔽2)⋊C4The semidirect product of PSU3(𝔽2) and C4 acting via C4/C2=C2368PSU(3,2):C4288,842
F9⋊C4The semidirect product of F9 and C4 acting via C4/C2=C2368F9:C4288,843
C4.3F92nd central extension by C4 of F9488C4.3F9288,861
C4.F9The non-split extension by C4 of F9 acting via F9/C32⋊C4=C2488C4.F9288,862
C4×F9Direct product of C4 and F9368C4xF9288,863
C4⋊F9The semidirect product of C4 and F9 acting via F9/C32⋊C4=C2368C4:F9288,864
C4.3PSU3(𝔽2)3rd non-split extension by C4 of PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2488C4.3PSU(3,2)288,891
C4×PSU3(𝔽2)Direct product of C4 and PSU3(𝔽2)368C4xPSU(3,2)288,892
C4⋊PSU3(𝔽2)The semidirect product of C4 and PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2368C4:PSU(3,2)288,893

Groups of order 320

dρLabelID
D20.C81st non-split extension by D20 of C8 acting via C8/C2=C41608D20.C8320,236
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).F53rd non-split extension by M4(2) of F5 acting via F5/D5=C2808M4(2).F5320,239
M4(2)⋊4F54th semidirect product of M4(2) and F5 acting via F5/D5=C2808M4(2):4F5320,240
D4.(C5⋊C8)The non-split extension by D4 of C5⋊C8 acting via C5⋊C8/Dic5=C21608D4.(C5:C8)320,270
Dic10.C82nd non-split extension by Dic10 of C8 acting via C8/C2=C41608Dic10.C8320,1063
M4(2)×F5Direct product of M4(2) and F5408M4(2)xF5320,1064
M4(2)⋊1F51st semidirect product of M4(2) and F5 acting via F5/D5=C2408M4(2):1F5320,1065
M4(2)⋊5F5The semidirect product of M4(2) and F5 acting through Inn(M4(2))808M4(2):5F5320,1066
M4(2).1F51st non-split extension by M4(2) of F5 acting via F5/D5=C2808M4(2).1F5320,1067
SD16×F5Direct product of SD16 and F5408SD16xF5320,1072
SD16⋊F51st semidirect product of SD16 and F5 acting via F5/D5=C2408SD16:F5320,1073
SD163F5The semidirect product of SD16 and F5 acting through Inn(SD16)808SD16:3F5320,1074
SD162F52nd semidirect product of SD16 and F5 acting via F5/D5=C2808SD16:2F5320,1075
C5⋊C16.C22The non-split extension by C5⋊C16 of C22 acting via C22/C2=C21608C5:C16.C2^2320,1129
D5⋊C4≀C2The semidirect product of D5 and C4≀C2 acting via C4≀C2/C4○D4=C2408D5:C4wrC2320,1130
C4○D4⋊F52nd semidirect product of C4○D4 and F5 acting via F5/D5=C2408C4oD4:F5320,1131
C4○D20⋊C43rd semidirect product of C4○D20 and C4 acting faithfully808C4oD20:C4320,1132
D4⋊F5⋊C26th semidirect product of D4⋊F5 and C2 acting faithfully808D4:F5:C2320,1133
Dic5.21C2421st non-split extension by Dic5 of C24 acting via C24/C23=C2808Dic5.21C2^4320,1601
Dic5.22C2422nd non-split extension by Dic5 of C24 acting via C24/C23=C2808Dic5.22C2^4320,1602
C4○D4×F5Direct product of C4○D4 and F5408C4oD4xF5320,1603
D5.2+ 1+4The non-split extension by D5 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2408D5.ES+(2,2)320,1604

Groups of order 360

dρLabelID
C5×F9Direct product of C5 and F9458C5xF9360,123
C52F9The semidirect product of C5 and F9 acting via F9/C32⋊C4=C2458C5:2F9360,124
C5⋊F9The semidirect product of C5 and F9 acting via F9/C3⋊S3=C4458C5:F9360,125
C3×S3×F5Direct product of C3, S3 and F5308C3xS3xF5360,126
S3×C3⋊F5Direct product of S3 and C3⋊F5308S3xC3:F5360,128
C5×PSU3(𝔽2)Direct product of C5 and PSU3(𝔽2)458C5xPSU(3,2)360,135
C32⋊Dic10The semidirect product of C32 and Dic10 acting via Dic10/C5=Q8458C3^2:Dic10360,136

Groups of order 408

dρLabelID
C3×C17⋊C8Direct product of C3 and C17⋊C8518C3xC17:C8408,33
C51⋊C81st semidirect product of C51 and C8 acting faithfully518C51:C8408,34

Groups of order 432

dρLabelID
C3×C2.F9Direct product of C3 and C2.F9488C3xC2.F9432,565
C6.F93rd non-split extension by C6 of F9 acting via F9/C32⋊C4=C2488C6.F9432,566
C3×C2.PSU3(𝔽2)Direct product of C3 and C2.PSU3(𝔽2)488C3xC2.PSU(3,2)432,591
C6.PSU3(𝔽2)1st non-split extension by C6 of PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2488C6.PSU(3,2)432,592
C6.2PSU3(𝔽2)2nd non-split extension by C6 of PSU3(𝔽2) acting via PSU3(𝔽2)/C32⋊C4=C2488C6.2PSU(3,2)432,593
C3×AΓL1(𝔽9)Direct product of C3 and AΓL1(𝔽9)248C3xAGammaL(1,9)432,737
C33⋊SD162nd semidirect product of C33 and SD16 acting faithfully248C3^3:SD16432,738
C6×F9Direct product of C6 and F9488C6xF9432,751
C2×C3⋊F9Direct product of C2 and C3⋊F9488C2xC3:F9432,752
C6×PSU3(𝔽2)Direct product of C6 and PSU3(𝔽2)488C6xPSU(3,2)432,757
C2×C33⋊Q8Direct product of C2 and C33⋊Q8488C2xC3^3:Q8432,758

Groups of order 480

dρLabelID
F5×C3⋊C8Direct product of F5 and C3⋊C81208F5xC3:C8480,223
C30.C422nd non-split extension by C30 of C42 acting via C42/C2=C2×C41208C30.C4^2480,224
C30.3C423rd non-split extension by C30 of C42 acting via C42/C2=C2×C41208C30.3C4^2480,225
C30.4C424th non-split extension by C30 of C42 acting via C42/C2=C2×C41208C30.4C4^2480,226
Dic5.Dic63rd non-split extension by Dic5 of Dic6 acting via Dic6/Dic3=C21208Dic5.Dic6480,235
Dic5.4Dic64th non-split extension by Dic5 of Dic6 acting via Dic6/Dic3=C21208Dic5.4Dic6480,236
D10.Dic61st non-split extension by D10 of Dic6 acting via Dic6/Dic3=C22408D10.Dic6480,237
D10.2Dic62nd non-split extension by D10 of Dic6 acting via Dic6/Dic3=C22408D10.2Dic6480,238
S3×C5⋊C16Direct product of S3 and C5⋊C162408S3xC5:C16480,239
D15⋊C16The semidirect product of D15 and C16 acting via C16/C4=C42408D15:C16480,240
C15⋊M5(2)1st semidirect product of C15 and M5(2) acting via M5(2)/C4=C2×C42408C15:M5(2)480,241
D30.C82nd non-split extension by D30 of C8 acting via C8/C2=C42408D30.C8480,242
C3×D20⋊C4Direct product of C3 and D20⋊C41208C3xD20:C4480,287
C3×D4⋊F5Direct product of C3 and D4⋊F51208C3xD4:F5480,288
C3×Q8⋊F5Direct product of C3 and Q8⋊F51208C3xQ8:F5480,289
C3×Q82F5Direct product of C3 and Q82F51208C3xQ8:2F5480,290
D20⋊Dic31st semidirect product of D20 and Dic3 acting via Dic3/C3=C41208D20:Dic3480,312
Dic10⋊Dic31st semidirect product of Dic10 and Dic3 acting via Dic3/C3=C41208Dic10:Dic3480,313
Dic102Dic32nd semidirect product of Dic10 and Dic3 acting via Dic3/C3=C41208Dic10:2Dic3480,314
D202Dic32nd semidirect product of D20 and Dic3 acting via Dic3/C3=C41208D20:2Dic3480,315
C4⋊F53S3The semidirect product of C4⋊F5 and S3 acting through Inn(C4⋊F5)1208C4:F5:3S3480,983
(C4×S3)⋊F53rd semidirect product of C4×S3 and F5 acting via F5/D5=C21208(C4xS3):F5480,985
S3×D5⋊C8Direct product of S3 and D5⋊C81208S3xD5:C8480,986
S3×C4.F5Direct product of S3 and C4.F51208S3xC4.F5480,988
D15⋊M4(2)The semidirect product of D15 and M4(2) acting via M4(2)/C4=C41208D15:M4(2)480,991
C5⋊C8⋊D61st semidirect product of C5⋊C8 and D6 acting via D6/C6=C21208C5:C8:D6480,993
C4×S3×F5Direct product of C4, S3 and F5608C4xS3xF5480,994
S3×C4⋊F5Direct product of S3 and C4⋊F5608S3xC4:F5480,996
C5⋊C8.D63rd non-split extension by C5⋊C8 of D6 acting via D6/C6=C22408C5:C8.D6480,1003
D15⋊C8⋊C25th semidirect product of D15⋊C8 and C2 acting faithfully2408D15:C8:C2480,1005
F5×C3⋊D4Direct product of F5 and C3⋊D4608F5xC3:D4480,1010
C3⋊D4⋊F5The semidirect product of C3⋊D4 and F5 acting via F5/D5=C2608C3:D4:F5480,1012
C3×D4.F5Direct product of C3 and D4.F52408C3xD4.F5480,1053
C3×D4×F5Direct product of C3, D4 and F5608C3xD4xF5480,1054
C3×Q8.F5Direct product of C3 and Q8.F52408C3xQ8.F5480,1055
C3×Q8×F5Direct product of C3, Q8 and F51208C3xQ8xF5480,1056
Dic10.Dic3The non-split extension by Dic10 of Dic3 acting via Dic3/C3=C42408Dic10.Dic3480,1066
D4×C3⋊F5Direct product of D4 and C3⋊F5608D4xC3:F5480,1067
D20.Dic3The non-split extension by D20 of Dic3 acting via Dic3/C3=C42408D20.Dic3480,1068
Q8×C3⋊F5Direct product of Q8 and C3⋊F51208Q8xC3:F5480,1069

Orthogonal of dimension 9  (ρ=9+)

Groups of order 144

dρLabelID
A42Direct product of A4 and A4; = PΩ+4(𝔽3)129+A4^2144,184

Groups of order 288

dρLabelID
A4×S4Direct product of A4 and S4169+A4xS4288,1024
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)129+PSO+(4,3)288,1026
C2×A42Direct product of C2, A4 and A4189+C2xA4^2288,1029

Complex of dimension 9  (ρ=9)

Groups of order 171

dρLabelID
C19⋊C9The semidirect product of C19 and C9 acting faithfully199C19:C9171,3

Groups of order 243

dρLabelID
C27⋊C9The semidirect product of C27 and C9 acting faithfully279C27:C9243,22
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
C33⋊C322nd semidirect product of C33 and C32 acting faithfully279C3^3:C3^2243,56
He3.C324th non-split extension by He3 of C32 acting via C32/C3=C3279He3.C3^2243,57
He3⋊C323rd semidirect product of He3 and C32 acting via C32/C3=C3279He3:C3^2243,58
C32.C339th non-split extension by C32 of C33 acting via C33/C32=C3279C3^2.C3^3243,59
C9.2He32nd non-split extension by C9 of He3 acting via He3/C32=C3279C9.2He3243,60
3+ 1+4Extraspecial group; = He3He3279ES+(3,2)243,65
3- 1+4Extraspecial group; = He33- 1+2279ES-(3,2)243,66

Groups of order 252

dρLabelID
A4×C7⋊C3Direct product of A4 and C7⋊C3289A4xC7:C3252,27

Groups of order 324

dρLabelID
He3.A4The non-split extension by He3 of A4 acting via A4/C22=C3549He3.A4324,53
He3⋊A41st semidirect product of He3 and A4 acting via A4/C22=C3549He3:A4324,54
He32A42nd semidirect product of He3 and A4 acting via A4/C22=C3369He3:2A4324,55
C62.C324th non-split extension by C62 of C32 acting faithfully549C6^2.C3^2324,56
3- 1+2⋊A41st semidirect product of 3- 1+2 and A4 acting via A4/C22=C3549ES-(3,1):A4324,57
C62.6C326th non-split extension by C62 of C32 acting faithfully369C6^2.6C3^2324,58
He3.2A4The non-split extension by He3 of A4 acting through Inn(He3)549He3.2A4324,129
A4×He3Direct product of A4 and He3369A4xHe3324,130
A4×3- 1+2Direct product of A4 and 3- 1+2369A4xES-(3,1)324,131
C62.9C329th non-split extension by C62 of C32 acting faithfully549C6^2.9C3^2324,132

Groups of order 333

dρLabelID
C37⋊C9The semidirect product of C37 and C9 acting faithfully379C37:C9333,3

Groups of order 342

dρLabelID
C2×C19⋊C9Direct product of C2 and C19⋊C9389C2xC19:C9342,8

Groups of order 432

dρLabelID
A4×C3.A4Direct product of A4 and C3.A4549A4xC3.A4432,524
C3.A422nd central extension by C3 of A42369C3.A4^2432,525
C24⋊He3The semidirect product of C24 and He3 acting via He3/C3=C32369C2^4:He3432,526
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
C2423- 1+22nd semidirect product of C24 and 3- 1+2 acting via 3- 1+2/C3=C32369C2^4:2ES-(3,1)432,528
C3×A42Direct product of C3, A4 and A4369C3xA4^2432,750

Groups of order 441

dρLabelID
C7⋊C32Direct product of C7⋊C3 and C7⋊C3219C7:C3^2441,9

Groups of order 468

dρLabelID
A4×C13⋊C3Direct product of A4 and C13⋊C3529A4xC13:C3468,32

Groups of order 486

dρLabelID
C2×C27⋊C9Direct product of C2 and C27⋊C9549C2xC27:C9486,82
C2×C32.He3Direct product of C2 and C32.He3549C2xC3^2.He3486,88
C2×C32.5He3Direct product of C2 and C32.5He3549C2xC3^2.5He3486,89
C2×C32.6He3Direct product of C2 and C32.6He3549C2xC3^2.6He3486,90
C3≀C3⋊C62nd semidirect product of C3≀C3 and C6 acting faithfully279C3wrC3:C6486,126
He3.C3⋊C63rd semidirect product of He3.C3 and C6 acting faithfully279He3.C3:C6486,128
He3.(C3×C6)6th non-split extension by He3 of C3×C6 acting via C3×C6/C3=C6279He3.(C3xC6)486,130
C3≀C3.C6The non-split extension by C3≀C3 of C6 acting faithfully279C3wrC3.C6486,132
C2×C33⋊C32Direct product of C2 and C33⋊C32549C2xC3^3:C3^2486,215
C2×He3.C32Direct product of C2 and He3.C32549C2xHe3.C3^2486,216
C2×He3⋊C32Direct product of C2 and He3⋊C32549C2xHe3:C3^2486,217
C2×C32.C33Direct product of C2 and C32.C33549C2xC3^2.C3^3486,218
C2×C9.2He3Direct product of C2 and C9.2He3549C2xC9.2He3486,219
3+ 1+42C22nd semidirect product of 3+ 1+4 and C2 acting faithfully279ES+(3,2):2C2486,237
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
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

Orthogonal of dimension 10  (ρ=10+)

Groups of order 110

dρLabelID
F11Frobenius group; = C11C10 = AGL1(𝔽11) = Aut(D11) = Hol(C11)1110+F11110,1

Groups of order 220

dρLabelID
C2×F11Direct product of C2 and F11; = Aut(D22) = Hol(C22)2210+C2xF11220,7

Groups of order 250

dρLabelID
C52⋊C10The semidirect product of C52 and C10 acting faithfully2510+C5^2:C10250,5
C25⋊C10The semidirect product of C25 and C10 acting faithfully2510+C25:C10250,6

Groups of order 310

dρLabelID
C31⋊C10The semidirect product of C31 and C10 acting faithfully3110+C31:C10310,1

Groups of order 330

dρLabelID
C3⋊F11The semidirect product of C3 and F11 acting via F11/C11⋊C5=C23310+C3:F11330,3

Groups of order 410

dρLabelID
C41⋊C10The semidirect product of C41 and C10 acting faithfully4110+C41:C10410,1

Groups of order 440

dρLabelID
D44⋊C5The semidirect product of D44 and C5 acting faithfully4410+D44:C5440,9

Groups of order 480

dρLabelID
C24⋊D15The semidirect product of C24 and D15 acting via D15/C3=D53010+C2^4:D15480,1195
S3×C24⋊C5Direct product of S3 and C24⋊C53010+S3xC2^4:C5480,1196

Groups of order 500

dρLabelID
C52⋊F53rd semidirect product of C52 and F5 acting faithfully2510+C5^2:F5500,23
C52⋊D10The semidirect product of C52 and D10 acting faithfully2510+C5^2:D10500,27
C2×C52⋊C10Direct product of C2 and C52⋊C105010+C2xC5^2:C10500,30
C2×C25⋊C10Direct product of C2 and C25⋊C105010+C2xC25:C10500,31

Symplectic of dimension 10  (ρ=10-)

Groups of order 220

dρLabelID
C11⋊C20The semidirect product of C11 and C20 acting via C20/C2=C104410-C11:C20220,1

Groups of order 440

dρLabelID
C4.F11The non-split extension by C4 of F11 acting via F11/C11⋊C5=C28810-C4.F11440,7

Groups of order 500

dρLabelID
He55C41st semidirect product of He5 and C4 acting via C4/C2=C210010-He5:5C4500,8
C50.C10The non-split extension by C50 of C10 acting faithfully10010-C50.C10500,9

Complex of dimension 10  (ρ=10)

Groups of order 330

dρLabelID
C3×F11Direct product of C3 and F113310C3xF11330,1
S3×C11⋊C5Direct product of S3 and C11⋊C53310S3xC11:C5330,2

Groups of order 440

dρLabelID
C11⋊C40The semidirect product of C11 and C40 acting via C40/C4=C108810C11:C40440,1
C4×F11Direct product of C4 and F114410C4xF11440,8
C22⋊F11The semidirect product of C22 and F11 acting via F11/C11⋊C5=C24410C2^2:F11440,11
D4×C11⋊C5Direct product of D4 and C11⋊C54410D4xC11:C5440,13
Q8×C11⋊C5Direct product of Q8 and C11⋊C58810Q8xC11:C5440,14

Complex of dimension 11  (ρ=11)

Groups of order 253

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

Orthogonal of dimension 12  (ρ=12+)

Groups of order 156

dρLabelID
F13Frobenius group; = C13C12 = AGL1(𝔽13) = Aut(D13) = Hol(C13)1312+F13156,7

Groups of order 192

dρLabelID
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
C24.6A46th non-split extension by C24 of A4 acting faithfully1612+C2^4.6A4192,1008
C24⋊A43rd semidirect product of C24 and A4 acting faithfully1612+C2^4:A4192,1009
C42⋊A4The semidirect product of C42 and A4 acting faithfully1612+C4^2:A4192,1023

Groups of order 240

dρLabelID
A4⋊F5The semidirect product of A4 and F5 acting via F5/D5=C22012+A4:F5240,192
A4×F5Direct product of A4 and F52012+A4xF5240,193

Groups of order 252

dρLabelID
S3×F7Direct product of S3 and F7; = Aut(D21) = Hol(C21)2112+S3xF7252,26

Groups of order 300

dρLabelID
C52⋊Dic3The semidirect product of C52 and Dic3 acting faithfully1512+C5^2:Dic3300,23
C52⋊C12The semidirect product of C52 and C12 acting faithfully1512+C5^2:C12300,24

Groups of order 312

dρLabelID
C2×F13Direct product of C2 and F13; = Aut(D26) = Hol(C26)2612+C2xF13312,45

Groups of order 324

dρLabelID
C32⋊D18The semidirect product of C32 and D18 acting via D18/C3=D61812+C3^2:D18324,37
S3×C32⋊C6Direct product of S3 and C32⋊C61812+S3xC3^2:C6324,116
S3×C9⋊C6Direct product of S3 and C9⋊C61812+S3xC9:C6324,118
He35D61st semidirect product of He3 and D6 acting via D6/C3=C221812+He3:5D6324,121

Groups of order 336

dρLabelID
D4⋊F7The semidirect product of D4 and F7 acting via F7/C7⋊C3=C25612+D4:F7336,18
Q82F7The semidirect product of Q8 and F7 acting via F7/C7⋊C3=C25612+Q8:2F7336,20
D4×F7Direct product of D4 and F7; = Aut(D28) = Hol(C28)2812+D4xF7336,125
Q83F7The semidirect product of Q8 and F7 acting through Inn(Q8)5612+Q8:3F7336,128
Q8.F7The non-split extension by Q8 of F7 acting via F7/D7=C311212+Q8.F7336,134

Groups of order 420

dρLabelID
D5×F7Direct product of D5 and F73512+D5xF7420,16

Groups of order 432

dρLabelID
He33D82nd semidirect product of He3 and D8 acting via D8/C4=C227212+He3:3D8432,83
He35SD163rd semidirect product of He3 and SD16 acting via SD16/C4=C227212+He3:5SD16432,85
He36D81st semidirect product of He3 and D8 acting via D8/D4=C27212+He3:6D8432,153
D36⋊C61st semidirect product of D36 and C6 acting faithfully7212+D36:C6432,155
He310SD161st semidirect product of He3 and SD16 acting via SD16/Q8=C27212+He3:10SD16432,161
D36.C61st non-split extension by D36 of C6 acting faithfully7212+D36.C6432,163
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
C322GL2(𝔽3)1st semidirect product of C32 and GL2(𝔽3) acting via GL2(𝔽3)/Q8=S37212+C3^2:2GL(2,3)432,248
Dic9.A4The non-split extension by Dic9 of A4 acting via A4/C22=C314412+Dic9.A4432,261
C6.(S3×A4)7th non-split extension by C6 of S3×A4 acting via S3×A4/C3×A4=C27212+C6.(S3xA4)432,269
C12⋊S3⋊S33rd semidirect product of C12⋊S3 and S3 acting faithfully7212+C12:S3:S3432,295
C3⋊S3⋊D12The semidirect product of C3⋊S3 and D12 acting via D12/C4=S33612+C3:S3:D12432,301
C62⋊D61st semidirect product of C62 and D6 acting faithfully3612+C6^2:D6432,323
D4×C32⋊C6Direct product of D4 and C32⋊C63612+D4xC3^2:C6432,360
D4×C9⋊C6Direct product of D4 and C9⋊C6; = Aut(D36) = Hol(C36)3612+D4xC9:C6432,362
(Q8×He3)⋊C24th semidirect product of Q8×He3 and C2 acting faithfully7212+(Q8xHe3):C2432,369
D363C63rd semidirect product of D36 and C6 acting faithfully7212+D36:3C6432,371
S3×C3.S4Direct product of S3 and C3.S43612+S3xC3.S4432,522
C62⋊Dic3The semidirect product of C62 and Dic3 acting faithfully2412+C6^2:Dic3432,743
A4×C32⋊C4Direct product of A4 and C32⋊C42412+A4xC3^2:C4432,744
S3×C3⋊S4Direct product of S3 and C3⋊S42412+S3xC3:S4432,747
C6210D610th semidirect product of C62 and D6 acting faithfully2412+C6^2:10D6432,748
S32×A4Direct product of S3, S3 and A42412+S3^2xA4432,749

Groups of order 444

dρLabelID
C37⋊C12The semidirect product of C37 and C12 acting faithfully3712+C37:C12444,7

Groups of order 468

dρLabelID
S3×C13⋊C6Direct product of S3 and C13⋊C63912+S3xC13:C6468,31

Groups of order 480

dρLabelID
F5×S4Direct product of F5 and S4; = Hol(C2×C10)2012+F5xS4480,1189
C2×A4⋊F5Direct product of C2 and A4⋊F53012+C2xA4:F5480,1191
C2×A4×F5Direct product of C2, A4 and F53012+C2xA4xF5480,1192

Symplectic of dimension 12  (ρ=12-)

Groups of order 192

dρLabelID
C42.A4The non-split extension by C42 of A4 acting faithfully4812-C4^2.A4192,1025

Groups of order 312

dρLabelID
C13⋊C24The semidirect product of C13 and C24 acting via C24/C2=C1210412-C13:C24312,7

Groups of order 336

dρLabelID
D4.F7The non-split extension by D4 of F7 acting via F7/C7⋊C3=C25612-D4.F7336,19
Q8.2F7The non-split extension by Q8 of F7 acting via F7/C7⋊C3=C211212-Q8.2F7336,21
D42F7The semidirect product of D4 and F7 acting through Inn(D4)5612-D4:2F7336,126
Q8×F7Direct product of Q8 and F75612-Q8xF7336,127
Q8⋊F7The semidirect product of Q8 and F7 acting via F7/D7=C35612-Q8:F7336,135

Groups of order 432

dρLabelID
He34SD162nd semidirect product of He3 and SD16 acting via SD16/C4=C227212-He3:4SD16432,84
He33Q162nd semidirect product of He3 and Q16 acting via Q16/C4=C2214412-He3:3Q16432,86
He38SD161st semidirect product of He3 and SD16 acting via SD16/D4=C27212-He3:8SD16432,152
Dic18⋊C61st semidirect product of Dic18 and C6 acting faithfully7212-Dic18:C6432,154
He36Q161st semidirect product of He3 and Q16 acting via Q16/Q8=C214412-He3:6Q16432,160
Dic18.C61st non-split extension by Dic18 of C6 acting faithfully14412-Dic18.C6432,162
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
C32⋊CSU2(𝔽3)1st semidirect product of C32 and CSU2(𝔽3) acting via CSU2(𝔽3)/Q8=S314412-C3^2:CSU(2,3)432,247
D18.A4The non-split extension by D18 of A4 acting via A4/C22=C37212-D18.A4432,263
Q8⋊He3⋊C24th semidirect product of Q8⋊He3 and C2 acting faithfully7212-Q8:He3:C2432,270
C3⋊S3⋊Dic6The semidirect product of C3⋊S3 and Dic6 acting via Dic6/C4=S37212-C3:S3:Dic6432,294
C12.S3223rd non-split extension by C12 of S32 acting via S32/C32=C227212-C12.S3^2432,299
C62.8D68th non-split extension by C62 of D6 acting faithfully7212-C6^2.8D6432,318
C62.13D613rd non-split extension by C62 of D6 acting faithfully7212-C6^2.13D6432,361
Dic182C62nd semidirect product of Dic18 and C6 acting faithfully7212-Dic18:2C6432,363
Q8×C32⋊C6Direct product of Q8 and C32⋊C67212-Q8xC3^2:C6432,368
Q8×C9⋊C6Direct product of Q8 and C9⋊C67212-Q8xC9:C6432,370

Groups of order 480

dρLabelID
Dic5.S45th non-split extension by Dic5 of S4 acting via S4/A4=C212012-Dic5.S4480,963
A4×C5⋊C8Direct product of A4 and C5⋊C812012-A4xC5:C8480,966

Complex of dimension 12  (ρ=12)

Groups of order 420

dρLabelID
F5×C7⋊C3Direct product of F5 and C7⋊C33512F5xC7:C3420,14
C35⋊C121st semidirect product of C35 and C12 acting faithfully3512C35:C12420,15

Groups of order 468

dρLabelID
C13⋊C36The semidirect product of C13 and C36 acting via C36/C3=C1211712C13:C36468,7
C3×F13Direct product of C3 and F133912C3xF13468,29
C3⋊F13The semidirect product of C3 and F13 acting via F13/C13⋊C6=C23912C3:F13468,30

Complex of dimension 13  (ρ=13)

Groups of order 351

dρLabelID
C33⋊C13The semidirect product of C33 and C13 acting faithfully2713C3^3:C13351,12

Orthogonal of dimension 14  (ρ=14+)

Groups of order 336

dρLabelID
S3×F8Direct product of S3 and F82414+S3xF8336,211

Groups of order 406

dρLabelID
C29⋊C14The semidirect product of C29 and C14 acting faithfully2914+C29:C14406,1

Groups of order 448

dρLabelID
D4×F8Direct product of D4 and F82814+D4xF8448,1363

Symplectic of dimension 14  (ρ=14-)

Groups of order 448

dρLabelID
Q8×F8Direct product of Q8 and F85614-Q8xF8448,1364

Complex of dimension 14  (ρ=14)

Groups of order 448

dρLabelID
C23.F82nd non-split extension by C23 of F8 acting via F8/C23=C75614C2^3.F8448,179

Orthogonal of dimension 15  (ρ=15+)

Groups of order 240

dρLabelID
F16Frobenius group; = C24C15 = AGL1(𝔽16)1615+F16240,191

Groups of order 480

dρLabelID
F16⋊C2The semidirect product of F16 and C2 acting faithfully1615+F16:C2480,1188
C2×F16Direct product of C2 and F163015+C2xF16480,1190

Complex of dimension 15  (ρ=15)

Groups of order 465

dρLabelID
C31⋊C15The semidirect product of C31 and C15 acting faithfully3115C31:C15465,1

Orthogonal of dimension 16  (ρ=16+)

Groups of order 272

dρLabelID
F17Frobenius group; = C17C16 = AGL1(𝔽17) = Aut(D17) = Hol(C17)1716+F17272,50

Groups of order 400

dρLabelID
F52Direct product of F5 and F5; = Hol(F5)2016+F5^2400,205

Groups of order 432

dρLabelID
S3×F9Direct product of S3 and F92416+S3xF9432,736
C333SD163rd semidirect product of C33 and SD16 acting faithfully2416+C3^3:3SD16432,739
F9⋊S3The semidirect product of F9 and S3 acting via S3/C3=C22416+F9:S3432,740
S3×PSU3(𝔽2)Direct product of S3 and PSU3(𝔽2)2416+S3xPSU(3,2)432,742

Orthogonal of dimension 18  (ρ=18+)

Groups of order 342

dρLabelID
F19Frobenius group; = C19C18 = AGL1(𝔽19) = Aut(D19) = Hol(C19)1918+F19342,7

Groups of order 486

dρLabelID
C27⋊C18The semidirect product of C27 and C18 acting faithfully; = Aut(D27) = Hol(C27)2718+C27:C18486,31
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
C9⋊C9⋊S31st semidirect product of C9⋊C9 and S3 acting faithfully2718+C9:C9:S3486,41
(C3×He3)⋊C68th semidirect product of C3×He3 and C6 acting faithfully2718+(C3xHe3):C6486,127
C9⋊S3⋊C322nd semidirect product of C9⋊S3 and C32 acting faithfully2718+C9:S3:C3^2486,129
He3.(C3×S3)5th non-split extension by He3 of C3×S3 acting via C3×S3/C3=S32718+He3.(C3xS3)486,131
C33⋊(C3×S3)4th semidirect product of C33 and C3×S3 acting faithfully2718+C3^3:(C3xS3)486,176
He3.C32C62nd semidirect product of He3.C3 and C6 acting faithfully2718+He3.C3:2C6486,177
He3⋊(C3×S3)4th semidirect product of He3 and C3×S3 acting via C3×S3/C3=S32718+He3:(C3xS3)486,178
C3.He3⋊C6The semidirect product of C3.He3 and C6 acting faithfully2718+C3.He3:C6486,179
3+ 1+4⋊C21st semidirect product of 3+ 1+4 and C2 acting faithfully2718+ES+(3,2):C2486,236
3- 1+4⋊C21st semidirect product of 3- 1+4 and C2 acting faithfully2718+ES-(3,2):C2486,238

Orthogonal of dimension 20  (ρ=20+)

Groups of order 500

dρLabelID
C52⋊C20The semidirect product of C52 and C20 acting faithfully2520+C5^2:C20500,17
C25⋊C20The semidirect product of C25 and C20 acting faithfully; = Aut(D25) = Hol(C25)2520+C25:C20500,18
He5⋊C42nd semidirect product of He5 and C4 acting faithfully2520+He5:C4500,21
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