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 has a faithful 2-dimensional symplectic irreducible representation if and only if it is either dicyclic (e.g. generalized quaternion) or is one of the following groups.

Groups of order 24

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

Groups of order 48

dρLabelID
CSU2(𝔽3)Conformal special unitary group on 𝔽32; = Q8.S3162-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) = 2O = <2,3,4>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
C24.C44th non-split extension by C24 of C4 acting via C4/C2=C2482C24.C496,19
C8.Dic31st non-split extension by C8 of Dic3 acting via Dic3/C6=C2482C8.Dic396,26
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
C40.9C44th non-split extension by C40 of C4 acting via C4/C2=C2802C40.9C4160,19
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
C56.C44th non-split extension by C56 of C4 acting via C4/C2=C21122C56.C4224,18
C8.Dic71st non-split extension by C8 of Dic7 acting via Dic7/C14=C21122C8.Dic7224,25
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
C8⋊D152nd semidirect product of C8 and D15 acting via D15/C15=C21202C8:D15240,67
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
C72.C44th non-split extension by C72 of C4 acting via C4/C2=C21442C72.C4288,19
C8.Dic91st non-split extension by C8 of Dic9 acting via Dic9/C18=C21442C8.Dic9288,20
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×C24.C4Direct product of C3 and C24.C4482C3xC24.C4288,246
C3×C8.Dic3Direct product of C3 and C8.Dic3482C3xC8.Dic3288,253
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
C24⋊D72nd semidirect product of C24 and D7 acting via D7/C7=C21682C24:D7336,92
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
Dic22⋊C41st semidirect product of Dic22 and C4 acting via C4/C2=C2882Dic22:C4352,11
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×C40.9C4Direct product of C3 and C40.9C42402C3xC40.9C4480,90
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×C24.C4Direct product of C5 and C24.C42402C5xC24.C4480,131
C5×C8.Dic3Direct product of C5 and C8.Dic32402C5xC8.Dic3480,138
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
C4.20D605th central extension by C4 of D602402C4.20D60480,869
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
C62⋊S35th semidirect product of C62 and S3 acting faithfully183C6^2:S3216,95
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×C62⋊S3Direct product of C2 and C62⋊S3183C2xC6^2:S3432,538

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
M4(2)⋊S33rd semidirect product of M4(2) and S3 acting via S3/C3=C2244+M4(2):S396,30
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
Q85D62nd semidirect product of Q8 and D6 acting via D6/C6=C2244+Q8:5D696,156
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
C2≀D4Wreath product of C2 by D484+C2wrD4128,928
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
M4(2)⋊D53rd semidirect product of M4(2) and D5 acting via D5/C5=C2404+M4(2):D5160,30
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
M4(2)⋊D73rd semidirect product of M4(2) and D7 acting via D7/C7=C2564+M4(2):D7224,29
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
D15⋊D4The semidirect product of D15 and D4 acting via D4/C22=C2604+D15:D4240,151
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
M4(2)⋊D93rd semidirect product of M4(2) and D9 acting via D9/C9=C2724+M4(2):D9288,31
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
C40.19D419th non-split extension by C40 of D4 acting via D4/C2=C22804+C40.19D4320,524
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
C12.28D147th non-split extension by C12 of D14 acting via D14/D7=C21684+C12.28D14336,146
D7×D12Direct product of D7 and D12844+D7xD12336,148
S3×D28Direct product of S3 and D28844+S3xD28336,149
D21⋊D4The semidirect product of D21 and D4 acting via D4/C22=C2844+D21:D4336,163
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
M4(2)⋊D113rd semidirect product of M4(2) and D11 acting via D11/C11=C2884+M4(2):D11352,29
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
D4⋊D222nd semidirect product of D4 and D22 acting via D22/C22=C2884+D4: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
C45⋊D41st semidirect product of C45 and D4 acting via D4/C2=C221804+C45:D4360,10
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
M4(2)⋊D133rd semidirect product of M4(2) and D13 acting via D13/C13=C21044+M4(2):D13416,30
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
D44D262nd semidirect product of D4 and D26 acting via D26/C26=C21044+D4:4D26416,170
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
C36.31D62nd non-split extension by C36 of D6 acting via D6/S3=C2724+C36.31D6432,63
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
D6⋊D184th semidirect product of D6 and D18 acting via D18/D9=C2364+D6:D18432,315

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
C56.19D419th non-split extension by C56 of D4 acting via D4/C2=C221124+C56.19D4448,431
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
Q85D302nd semidirect product of Q8 and D30 acting via D30/C30=C21204+Q8:5D30480,914
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
D4.11D86th non-split extension by D4 of D8 acting via D8/D4=C2644-D4.11D8128,927
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
D4○Q32Central product of D4 and Q32644-D4oQ32128,2149

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
C20.47D44th non-split extension by C20 of D4 acting via D4/C22=C2804-C20.47D4160,31
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
D8.10D10The non-split extension by D8 of D10 acting through Inn(D8)1604-D8.10D10320,1443
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
D6.D143rd non-split extension by D6 of D14 acting via D14/D7=C21684-D6.D14336,153
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
C4.12D444th non-split extension by C4 of D44 acting via D44/D22=C21764-C4.12D44352,30
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
D10⋊D91st semidirect product of D10 and D9 acting via D9/C9=C21804-D10:D9360,12
(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-C56.31C2^3