# Faithful irreducible representation

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

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

### Dimension 1  (ρ=1,1+)

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

### Orthogonal of dimension 2  (ρ=2+)

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

### Symplectic of dimension 2  (ρ=2-)

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

### Groups of order 24

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

### Groups of order 48

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

### Groups of order 120

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

### Groups of order 16

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

### Groups of order 18

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

### Groups of order 24

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

### Groups of order 30

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

### Groups of order 32

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

### Groups of order 36

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

### Groups of order 40

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

### Groups of order 42

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

### Groups of order 48

dρLabelID
C3⋊C16The semidirect product of C3 and C16 acting via C16/C8=C2482C3:C1648,1
S3×C8Direct product of C8 and S3242S3xC848,4
C8⋊S33rd semidirect product of C8 and S3 acting via S3/C3=C2242C8:S348,5
C24⋊C22nd semidirect product of C24 and C2 acting faithfully242C24:C248,6
C4.Dic3The non-split extension by C4 of Dic3 acting via Dic3/C6=C2242C4.Dic348,10
C3×M4(2)Direct product of C3 and M4(2)242C3xM4(2)48,24
C3×D8Direct product of C3 and D8242C3xD848,25
C3×SD16Direct product of C3 and SD16242C3xSD1648,26
C3×Q16Direct product of C3 and Q16482C3xQ1648,27
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32)82GL(2,3)48,29
C4.A4The central extension by C4 of A4162C4.A448,33
C4○D12Central product of C4 and D12242C4oD1248,37
C3×C4○D4Direct product of C3 and C4○D4242C3xC4oD448,47

### Groups of order 50

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

### Groups of order 54

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

### Groups of order 56

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

### Groups of order 60

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

### Groups of order 64

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

### Groups of order 66

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

### Groups of order 70

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

### Groups of order 72

dρLabelID
C9⋊C8The semidirect product of C9 and C8 acting via C8/C4=C2722C9:C872,1
Q8⋊C9The semidirect product of Q8 and C9 acting via C9/C3=C3722Q8:C972,3
C4×D9Direct product of C4 and D9362C4xD972,5
C9⋊D4The semidirect product of C9 and D4 acting via D4/C22=C2362C9:D472,8
D4×C9Direct product of C9 and D4362D4xC972,10
Q8×C9Direct product of C9 and Q8722Q8xC972,11
C3×C3⋊C8Direct product of C3 and C3⋊C8242C3xC3:C872,12
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)242C3xSL(2,3)72,25
C3×Dic6Direct product of C3 and Dic6242C3xDic672,26
S3×C12Direct product of C12 and S3242S3xC1272,27
C3×D12Direct product of C3 and D12242C3xD1272,28
C3×C3⋊D4Direct product of C3 and C3⋊D4122C3xC3:D472,30

### Groups of order 78

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

### Groups of order 80

dρLabelID
C52C16The semidirect product of C5 and C16 acting via C16/C8=C2802C5:2C1680,1
C8×D5Direct product of C8 and D5402C8xD580,4
C8⋊D53rd semidirect product of C8 and D5 acting via D5/C5=C2402C8:D580,5
C40⋊C22nd semidirect product of C40 and C2 acting faithfully402C40:C280,6
C4.Dic5The non-split extension by C4 of Dic5 acting via Dic5/C10=C2402C4.Dic580,10
C5×M4(2)Direct product of C5 and M4(2)402C5xM4(2)80,24
C5×D8Direct product of C5 and D8402C5xD880,25
C5×SD16Direct product of C5 and SD16402C5xSD1680,26
C5×Q16Direct product of C5 and Q16802C5xQ1680,27
C4○D20Central product of C4 and D20402C4oD2080,38
C5×C4○D4Direct product of C5 and C4○D4402C5xC4oD480,48

### Groups of order 84

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

### Groups of order 88

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

### Groups of order 90

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

### Groups of order 96

dρLabelID
C3⋊C32The semidirect product of C3 and C32 acting via C32/C16=C2962C3:C3296,1
S3×C16Direct product of C16 and S3482S3xC1696,4
D6.C8The non-split extension by D6 of C8 acting via C8/C4=C2482D6.C896,5
C48⋊C22nd semidirect product of C48 and C2 acting faithfully482C48:C296,7
C424S33rd semidirect product of C42 and S3 acting via S3/C3=C2242C4^2:4S396,12
C12.C81st non-split extension by C12 of C8 acting via C8/C4=C2482C12.C896,19
C24.C41st non-split extension by C24 of C4 acting via C4/C2=C2482C24.C496,26
C3×C4≀C2Direct product of C3 and C4≀C2242C3xC4wrC296,54
C3×C8.C4Direct product of C3 and C8.C4482C3xC8.C496,58
C3×M5(2)Direct product of C3 and M5(2)482C3xM5(2)96,60
C3×D16Direct product of C3 and D16482C3xD1696,61
C3×SD32Direct product of C3 and SD32482C3xSD3296,62
C3×Q32Direct product of C3 and Q32962C3xQ3296,63
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4242U(2,3)96,67
C8.A4The central extension by C8 of A4322C8.A496,74
C8○D12Central product of C8 and D12482C8oD1296,108
C4○D24Central product of C4 and D24482C4oD2496,111
C3×C8○D4Direct product of C3 and C8○D4482C3xC8oD496,178
C3×C4○D8Direct product of C3 and C4○D8482C3xC4oD896,182
C4.6S43rd central extension by C4 of S4162C4.6S496,192

### Groups of order 98

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

### Groups of order 100

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

### Groups of order 102

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

### Groups of order 104

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

### Groups of order 108

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

### Groups of order 110

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

### Groups of order 112

dρLabelID
C7⋊C16The semidirect product of C7 and C16 acting via C16/C8=C21122C7:C16112,1
C8×D7Direct product of C8 and D7562C8xD7112,3
C8⋊D73rd semidirect product of C8 and D7 acting via D7/C7=C2562C8:D7112,4
C56⋊C22nd semidirect product of C56 and C2 acting faithfully562C56:C2112,5
C4.Dic7The non-split extension by C4 of Dic7 acting via Dic7/C14=C2562C4.Dic7112,9
C7×M4(2)Direct product of C7 and M4(2)562C7xM4(2)112,23
C7×D8Direct product of C7 and D8562C7xD8112,24
C7×SD16Direct product of C7 and SD16562C7xSD16112,25
C7×Q16Direct product of C7 and Q161122C7xQ16112,26
C4○D28Central product of C4 and D28562C4oD28112,30
C7×C4○D4Direct product of C7 and C4○D4562C7xC4oD4112,40

### Groups of order 114

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

### Groups of order 120

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

### Groups of order 126

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

### Groups of order 128

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

### Groups of order 130

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

### Groups of order 132

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

### Groups of order 136

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

### Groups of order 138

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

### Groups of order 140

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

### Groups of order 144

dρLabelID
C9⋊C16The semidirect product of C9 and C16 acting via C16/C8=C21442C9:C16144,1
C8×D9Direct product of C8 and D9722C8xD9144,5
C8⋊D93rd semidirect product of C8 and D9 acting via D9/C9=C2722C8:D9144,6
C72⋊C22nd semidirect product of C72 and C2 acting faithfully722C72:C2144,7
C4.Dic9The non-split extension by C4 of Dic9 acting via Dic9/C18=C2722C4.Dic9144,10
C9×M4(2)Direct product of C9 and M4(2)722C9xM4(2)144,24
C9×D8Direct product of C9 and D8722C9xD8144,25
C9×SD16Direct product of C9 and SD16722C9xSD16144,26
C9×Q16Direct product of C9 and Q161442C9xQ16144,27
C3×C3⋊C16Direct product of C3 and C3⋊C16482C3xC3:C16144,28
Q8.C18The non-split extension by Q8 of C18 acting via C18/C6=C3722Q8.C18144,36
D365C2The semidirect product of D36 and C2 acting through Inn(D36)722D36:5C2144,40
C9×C4○D4Direct product of C9 and C4○D4722C9xC4oD4144,50
S3×C24Direct product of C24 and S3482S3xC24144,69
C3×C8⋊S3Direct product of C3 and C8⋊S3482C3xC8:S3144,70
C3×C24⋊C2Direct product of C3 and C24⋊C2482C3xC24:C2144,71
C3×D24Direct product of C3 and D24482C3xD24144,72
C3×Dic12Direct product of C3 and Dic12482C3xDic12144,73
C3×C4.Dic3Direct product of C3 and C4.Dic3242C3xC4.Dic3144,75
C3×CSU2(𝔽3)Direct product of C3 and CSU2(𝔽3)482C3xCSU(2,3)144,121
C3×GL2(𝔽3)Direct product of C3 and GL2(𝔽3)242C3xGL(2,3)144,122
C3×C4.A4Direct product of C3 and C4.A4482C3xC4.A4144,157
C3×C4○D12Direct product of C3 and C4○D12242C3xC4oD12144,161

### Groups of order 150

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

### Groups of order 152

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

### Groups of order 154

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

### Groups of order 156

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

### Groups of order 160

dρLabelID
C52C32The semidirect product of C5 and C32 acting via C32/C16=C21602C5:2C32160,1
D5×C16Direct product of C16 and D5802D5xC16160,4
C80⋊C25th semidirect product of C80 and C2 acting faithfully802C80:C2160,5
C16⋊D52nd semidirect product of C16 and D5 acting via D5/C5=C2802C16:D5160,7
D204C41st semidirect product of D20 and C4 acting via C4/C2=C2402D20:4C4160,12
C20.4C81st non-split extension by C20 of C8 acting via C8/C4=C2802C20.4C8160,19
C40.6C41st non-split extension by C40 of C4 acting via C4/C2=C2802C40.6C4160,26
C5×C4≀C2Direct product of C5 and C4≀C2402C5xC4wrC2160,54
C5×C8.C4Direct product of C5 and C8.C4802C5xC8.C4160,58
C5×M5(2)Direct product of C5 and M5(2)802C5xM5(2)160,60
C5×D16Direct product of C5 and D16802C5xD16160,61
C5×SD32Direct product of C5 and SD32802C5xSD32160,62
C5×Q32Direct product of C5 and Q321602C5xQ32160,63
D20.3C4The non-split extension by D20 of C4 acting through Inn(D20)802D20.3C4160,122
D407C2The semidirect product of D40 and C2 acting through Inn(D40)802D40:7C2160,125
C5×C8○D4Direct product of C5 and C8○D4802C5xC8oD4160,192
C5×C4○D8Direct product of C5 and C4○D8802C5xC4oD8160,196

### Groups of order 162

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

### Groups of order 168

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

### Groups of order 170

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

### Groups of order 174

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

### Groups of order 176

dρLabelID
C11⋊C16The semidirect product of C11 and C16 acting via C16/C8=C21762C11:C16176,1
C8×D11Direct product of C8 and D11882C8xD11176,3
C88⋊C24th semidirect product of C88 and C2 acting faithfully882C88:C2176,4
C8⋊D112nd semidirect product of C8 and D11 acting via D11/C11=C2882C8:D11176,5
C44.C41st non-split extension by C44 of C4 acting via C4/C2=C2882C44.C4176,9
C11×M4(2)Direct product of C11 and M4(2)882C11xM4(2)176,23
C11×D8Direct product of C11 and D8882C11xD8176,24
C11×SD16Direct product of C11 and SD16882C11xSD16176,25
C11×Q16Direct product of C11 and Q161762C11xQ16176,26
D445C2The semidirect product of D44 and C2 acting through Inn(D44)882D44:5C2176,30
C11×C4○D4Direct product of C11 and C4○D4882C11xC4oD4176,40

### Groups of order 180

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

### Groups of order 182

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

### Groups of order 184

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

### Groups of order 186

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

### Groups of order 190

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

### Groups of order 192

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

### Groups of order 196

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

### Groups of order 198

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

### Groups of order 200

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

### Groups of order 204

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

### Groups of order 208

dρLabelID
C132C16The semidirect product of C13 and C16 acting via C16/C8=C22082C13:2C16208,1
C8×D13Direct product of C8 and D131042C8xD13208,4
C8⋊D133rd semidirect product of C8 and D13 acting via D13/C13=C21042C8:D13208,5
C104⋊C22nd semidirect product of C104 and C2 acting faithfully1042C104:C2208,6
C52.4C41st non-split extension by C52 of C4 acting via C4/C2=C21042C52.4C4208,10
C13×M4(2)Direct product of C13 and M4(2)1042C13xM4(2)208,24
C13×D8Direct product of C13 and D81042C13xD8208,25
C13×SD16Direct product of C13 and SD161042C13xSD16208,26
C13×Q16Direct product of C13 and Q162082C13xQ16208,27
D525C2The semidirect product of D52 and C2 acting through Inn(D52)1042D52:5C2208,38
C13×C4○D4Direct product of C13 and C4○D41042C13xC4oD4208,48

### Groups of order 210

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

### Groups of order 216

dρLabelID
C27⋊C8The semidirect product of C27 and C8 acting via C8/C4=C22162C27:C8216,1
Q8⋊C27The semidirect product of Q8 and C27 acting via C27/C9=C32162Q8:C27216,3
C4×D27Direct product of C4 and D271082C4xD27216,5
C27⋊D4The semidirect product of C27 and D4 acting via D4/C22=C21082C27:D4216,8
D4×C27Direct product of C27 and D41082D4xC27216,10
Q8×C27Direct product of C27 and Q82162Q8xC27216,11
C3×C9⋊C8Direct product of C3 and C9⋊C8722C3xC9:C8216,12
C9×C3⋊C8Direct product of C9 and C3⋊C8722C9xC3:C8216,13
C9×SL2(𝔽3)Direct product of C9 and SL2(𝔽3)722C9xSL(2,3)216,38
C3×Dic18Direct product of C3 and Dic18722C3xDic18216,43
C9×Dic6Direct product of C9 and Dic6722C9xDic6216,44
C12×D9Direct product of C12 and D9722C12xD9216,45
C3×D36Direct product of C3 and D36722C3xD36216,46
S3×C36Direct product of C36 and S3722S3xC36216,47
C9×D12Direct product of C9 and D12722C9xD12216,48
C3×C9⋊D4Direct product of C3 and C9⋊D4362C3xC9:D4216,57
C9×C3⋊D4Direct product of C9 and C3⋊D4362C9xC3:D4216,58

### Groups of order 220

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

### Groups of order 222

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

### Groups of order 224

dρLabelID
C7⋊C32The semidirect product of C7 and C32 acting via C32/C16=C22242C7:C32224,1
D7×C16Direct product of C16 and D71122D7xC16224,3
C16⋊D73rd semidirect product of C16 and D7 acting via D7/C7=C21122C16:D7224,4
C112⋊C22nd semidirect product of C112 and C2 acting faithfully1122C112:C2224,6
Dic14⋊C41st semidirect product of Dic14 and C4 acting via C4/C2=C2562Dic14:C4224,11
C28.C81st non-split extension by C28 of C8 acting via C8/C4=C21122C28.C8224,18
C56.C41st non-split extension by C56 of C4 acting via C4/C2=C21122C56.C4224,25
C7×C4≀C2Direct product of C7 and C4≀C2562C7xC4wrC2224,53
C7×C8.C4Direct product of C7 and C8.C41122C7xC8.C4224,57
C7×M5(2)Direct product of C7 and M5(2)1122C7xM5(2)224,59
C7×D16Direct product of C7 and D161122C7xD16224,60
C7×SD32Direct product of C7 and SD321122C7xSD32224,61
C7×Q32Direct product of C7 and Q322242C7xQ32224,62
D28.2C4The non-split extension by D28 of C4 acting through Inn(D28)1122D28.2C4224,96
D567C2The semidirect product of D56 and C2 acting through Inn(D56)1122D56:7C2224,99
C7×C8○D4Direct product of C7 and C8○D41122C7xC8oD4224,166
C7×C4○D8Direct product of C7 and C4○D81122C7xC4oD8224,170

### Groups of order 228

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

### Groups of order 230

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

### Groups of order 232

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

### Groups of order 234

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

### Groups of order 238

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

### Groups of order 240

dρLabelID
C5×C3⋊C16Direct product of C5 and C3⋊C162402C5xC3:C16240,1
C3×C52C16Direct product of C3 and C52C162402C3xC5:2C16240,2
C153C161st semidirect product of C15 and C16 acting via C16/C8=C22402C15:3C16240,3
D5×C24Direct product of C24 and D51202D5xC24240,33
C3×C8⋊D5Direct product of C3 and C8⋊D51202C3xC8:D5240,34
C3×C40⋊C2Direct product of C3 and C40⋊C21202C3xC40:C2240,35
C3×D40Direct product of C3 and D401202C3xD40240,36
C3×Dic20Direct product of C3 and Dic202402C3xDic20240,37
C3×C4.Dic5Direct product of C3 and C4.Dic51202C3xC4.Dic5240,39
S3×C40Direct product of C40 and S31202S3xC40240,49
C5×C8⋊S3Direct product of C5 and C8⋊S31202C5xC8:S3240,50
C5×C24⋊C2Direct product of C5 and C24⋊C21202C5xC24:C2240,51
C5×D24Direct product of C5 and D241202C5xD24240,52
C5×Dic12Direct product of C5 and Dic122402C5xDic12240,53
C5×C4.Dic3Direct product of C5 and C4.Dic31202C5xC4.Dic3240,55
C8×D15Direct product of C8 and D151202C8xD15240,65
C40⋊S34th semidirect product of C40 and S3 acting via S3/C3=C21202C40:S3240,66
C24⋊D52nd semidirect product of C24 and D5 acting via D5/C5=C21202C24:D5240,67
C60.7C41st non-split extension by C60 of C4 acting via C4/C2=C21202C60.7C4240,71
C15×M4(2)Direct product of C15 and M4(2)1202C15xM4(2)240,85
C15×D8Direct product of C15 and D81202C15xD8240,86
C15×SD16Direct product of C15 and SD161202C15xSD16240,87
C15×Q16Direct product of C15 and Q162402C15xQ16240,88
C4.A5The central extension by C4 of A5242C4.A5240,93
C5×CSU2(𝔽3)Direct product of C5 and CSU2(𝔽3)802C5xCSU(2,3)240,102
C5×GL2(𝔽3)Direct product of C5 and GL2(𝔽3)402C5xGL(2,3)240,103
C5×C4.A4Direct product of C5 and C4.A4802C5xC4.A4240,154
C3×C4○D20Direct product of C3 and C4○D201202C3xC4oD20240,158
C5×C4○D12Direct product of C5 and C4○D121202C5xC4oD12240,168
D6011C2The semidirect product of D60 and C2 acting through Inn(D60)1202D60:11C2240,178
C15×C4○D4Direct product of C15 and C4○D41202C15xC4oD4240,188

### Groups of order 242

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

### Groups of order 246

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

### Groups of order 248

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

### Groups of order 250

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

### Groups of order 252

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

### Groups of order 258

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

### Groups of order 260

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

### Groups of order 264

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

### Groups of order 266

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

### Groups of order 270

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

### Groups of order 272

dρLabelID
C174C16The semidirect product of C17 and C16 acting via C16/C8=C22722C17:4C16272,1
C8×D17Direct product of C8 and D171362C8xD17272,4
C8⋊D173rd semidirect product of C8 and D17 acting via D17/C17=C21362C8:D17272,5
C136⋊C22nd semidirect product of C136 and C2 acting faithfully1362C136:C2272,6
C68.4C41st non-split extension by C68 of C4 acting via C4/C2=C21362C68.4C4272,10
M4(2)×C17Direct product of C17 and M4(2)1362M4(2)xC17272,24
D8×C17Direct product of C17 and D81362D8xC17272,25
SD16×C17Direct product of C17 and SD161362SD16xC17272,26
Q16×C17Direct product of C17 and Q162722Q16xC17272,27
D685C2The semidirect product of D68 and C2 acting through Inn(D68)1362D68:5C2272,39
C4○D4×C17Direct product of C17 and C4○D41362C4oD4xC17272,49

### Groups of order 276

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

### Groups of order 280

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

### Groups of order 282

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

### Groups of order 286

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

### Groups of order 288

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

### Groups of order 290

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

### Groups of order 294

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

### Groups of order 296

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

### Groups of order 300

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

### Groups of order 304

dρLabelID
C19⋊C16The semidirect product of C19 and C16 acting via C16/C8=C23042C19:C16304,1
C8×D19Direct product of C8 and D191522C8xD19304,3
C8⋊D193rd semidirect product of C8 and D19 acting via D19/C19=C21522C8:D19304,4
C152⋊C22nd semidirect product of C152 and C2 acting faithfully1522C152:C2304,5
C76.C41st non-split extension by C76 of C4 acting via C4/C2=C21522C76.C4304,9
M4(2)×C19Direct product of C19 and M4(2)1522M4(2)xC19304,23
D8×C19Direct product of C19 and D81522D8xC19304,24
SD16×C19Direct product of C19 and SD161522SD16xC19304,25
Q16×C19Direct product of C19 and Q163042Q16xC19304,26
D765C2The semidirect product of D76 and C2 acting through Inn(D76)1522D76:5C2304,30
C4○D4×C19Direct product of C19 and C4○D41522C4oD4xC19304,40

### Groups of order 306

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

### Groups of order 308

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

### Groups of order 310

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

### Groups of order 312

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

### Groups of order 318

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

### Groups of order 320

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

### Groups of order 322

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

### Groups of order 324

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

### Groups of order 328

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

### Groups of order 330

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

### Groups of order 336

dρLabelID
C7×C3⋊C16Direct product of C7 and C3⋊C163362C7xC3:C16336,3
C3×C7⋊C16Direct product of C3 and C7⋊C163362C3xC7:C16336,4
C21⋊C161st semidirect product of C21 and C16 acting via C16/C8=C23362C21:C16336,5
D7×C24Direct product of C24 and D71682D7xC24336,58
C3×C8⋊D7Direct product of C3 and C8⋊D71682C3xC8:D7336,59
C3×C56⋊C2Direct product of C3 and C56⋊C21682C3xC56:C2336,60
C3×D56Direct product of C3 and D561682C3xD56336,61
C3×Dic28Direct product of C3 and Dic283362C3xDic28336,62
C3×C4.Dic7Direct product of C3 and C4.Dic71682C3xC4.Dic7336,64
S3×C56Direct product of C56 and S31682S3xC56336,74
C7×C8⋊S3Direct product of C7 and C8⋊S31682C7xC8:S3336,75
C7×C24⋊C2Direct product of C7 and C24⋊C21682C7xC24:C2336,76
C7×D24Direct product of C7 and D241682C7xD24336,77
C7×Dic12Direct product of C7 and Dic123362C7xDic12336,78
C7×C4.Dic3Direct product of C7 and C4.Dic31682C7xC4.Dic3336,80
C8×D21Direct product of C8 and D211682C8xD21336,90
C56⋊S34th semidirect product of C56 and S3 acting via S3/C3=C21682C56:S3336,91
C8⋊D212nd semidirect product of C8 and D21 acting via D21/C21=C21682C8:D21336,92
C84.C41st non-split extension by C84 of C4 acting via C4/C2=C21682C84.C4336,96
M4(2)×C21Direct product of C21 and M4(2)1682M4(2)xC21336,110
D8×C21Direct product of C21 and D81682D8xC21336,111
SD16×C21Direct product of C21 and SD161682SD16xC21336,112
Q16×C21Direct product of C21 and Q163362Q16xC21336,113
C7×CSU2(𝔽3)Direct product of C7 and CSU2(𝔽3)1122C7xCSU(2,3)336,115
C7×GL2(𝔽3)Direct product of C7 and GL2(𝔽3)562C7xGL(2,3)336,116
C7×C4.A4Direct product of C7 and C4.A41122C7xC4.A4336,170
C3×C4○D28Direct product of C3 and C4○D281682C3xC4oD28336,177
C7×C4○D12Direct product of C7 and C4○D121682C7xC4oD12336,187
D8411C2The semidirect product of D84 and C2 acting through Inn(D84)1682D84:11C2336,197
C4○D4×C21Direct product of C21 and C4○D41682C4oD4xC21336,207

### Groups of order 338

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

### Groups of order 340

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

### Groups of order 342

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

### Groups of order 344

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

### Groups of order 348

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

### Groups of order 350

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

### Groups of order 352

dρLabelID
C11⋊C32The semidirect product of C11 and C32 acting via C32/C16=C23522C11:C32352,1
C16×D11Direct product of C16 and D111762C16xD11352,3
D22.C8The non-split extension by D22 of C8 acting via C8/C4=C21762D22.C8352,4
C176⋊C22nd semidirect product of C176 and C2 acting faithfully1762C176:C2352,6
D441C41st semidirect product of D44 and C4 acting via C4/C2=C2882D44:1C4352,11
C44.C81st non-split extension by C44 of C8 acting via C8/C4=C21762C44.C8352,18
C88.C41st non-split extension by C88 of C4 acting via C4/C2=C21762C88.C4352,25
C11×C4≀C2Direct product of C11 and C4≀C2882C11xC4wrC2352,53
C11×C8.C4Direct product of C11 and C8.C41762C11xC8.C4352,57
C11×M5(2)Direct product of C11 and M5(2)1762C11xM5(2)352,59
C11×D16Direct product of C11 and D161762C11xD16352,60
C11×SD32Direct product of C11 and SD321762C11xSD32352,61
C11×Q32Direct product of C11 and Q323522C11xQ32352,62
D44.2C4The non-split extension by D44 of C4 acting through Inn(D44)1762D44.2C4352,96
D887C2The semidirect product of D88 and C2 acting through Inn(D88)1762D88:7C2352,99
C11×C8○D4Direct product of C11 and C8○D41762C11xC8oD4352,166
C11×C4○D8Direct product of C11 and C4○D81762C11xC4oD8352,170

### Groups of order 354

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

### Groups of order 360

dρLabelID
C5×C9⋊C8Direct product of C5 and C9⋊C83602C5xC9:C8360,1
C9×C52C8Direct product of C9 and C52C83602C9xC5:2C8360,2
C453C81st semidirect product of C45 and C8 acting via C8/C4=C23602C45:3C8360,3
C5×Q8⋊C9Direct product of C5 and Q8⋊C93602C5xQ8:C9360,14
C9×Dic10Direct product of C9 and Dic103602C9xDic10360,15
D5×C36Direct product of C36 and D51802D5xC36360,16
C9×D20Direct product of C9 and D201802C9xD20360,17
C9×C5⋊D4Direct product of C9 and C5⋊D41802C9xC5:D4360,19
C5×Dic18Direct product of C5 and Dic183602C5xDic18360,20
D9×C20Direct product of C20 and D91802D9xC20360,21
C5×D36Direct product of C5 and D361802C5xD36360,22
C5×C9⋊D4Direct product of C5 and C9⋊D41802C5xC9:D4360,24
C4×D45Direct product of C4 and D451802C4xD45360,26
C457D41st semidirect product of C45 and D4 acting via D4/C22=C21802C45:7D4360,29
D4×C45Direct product of C45 and D41802D4xC45360,31
Q8×C45Direct product of C45 and Q83602Q8xC45360,32
C15×C3⋊C8Direct product of C15 and C3⋊C81202C15xC3:C8360,34
C3×C153C8Direct product of C3 and C153C81202C3xC15:3C8360,35
C3×SL2(𝔽5)Direct product of C3 and SL2(𝔽5)722C3xSL(2,5)360,51
C15×SL2(𝔽3)Direct product of C15 and SL2(𝔽3)1202C15xSL(2,3)360,89
C15×Dic6Direct product of C15 and Dic61202C15xDic6360,95
S3×C60Direct product of C60 and S31202S3xC60360,96
C15×D12Direct product of C15 and D121202C15xD12360,97
C15×C3⋊D4Direct product of C15 and C3⋊D4602C15xC3:D4360,99
C3×Dic30Direct product of C3 and Dic301202C3xDic30360,100
C12×D15Direct product of C12 and D151202C12xD15360,101
C3×D60Direct product of C3 and D601202C3xD60360,102
C3×C157D4Direct product of C3 and C157D4602C3xC15:7D4360,104

### Groups of order 364

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

### Groups of order 366

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

### Groups of order 368

dρLabelID
C23⋊C16The semidirect product of C23 and C16 acting via C16/C8=C23682C23:C16368,1
C8×D23Direct product of C8 and D231842C8xD23368,3
C8⋊D233rd semidirect product of C8 and D23 acting via D23/C23=C21842C8:D23368,4
C184⋊C22nd semidirect product of C184 and C2 acting faithfully1842C184:C2368,5
C92.C41st non-split extension by C92 of C4 acting via C4/C2=C21842C92.C4368,9
M4(2)×C23Direct product of C23 and M4(2)1842M4(2)xC23368,23
D8×C23Direct product of C23 and D81842D8xC23368,24
SD16×C23Direct product of C23 and SD161842SD16xC23368,25
Q16×C23Direct product of C23 and Q163682Q16xC23368,26
D925C2The semidirect product of D92 and C2 acting through Inn(D92)1842D92:5C2368,30
C4○D4×C23Direct product of C23 and C4○D41842C4oD4xC23368,40

### Groups of order 370

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

### Groups of order 372

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

### Groups of order 374

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

### Groups of order 376

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

### Groups of order 378

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

### Groups of order 380

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

### Groups of order 390

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

### Groups of order 392

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

### Groups of order 396

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

### Groups of order 400

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

### Groups of order 402

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

### Groups of order 406

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

### Groups of order 408

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

### Groups of order 410

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

### Groups of order 414

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

### Groups of order 416

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

### Groups of order 418

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

### Groups of order 420

dρLabelID
C15×Dic7Direct product of C15 and Dic74202C15xDic7420,5
Dic5×C21Direct product of C21 and Dic54202Dic5xC21420,6
C3×Dic35Direct product of C3 and Dic354202C3xDic35420,7
Dic3×C35Direct product of C35 and Dic34202Dic3xC35420,8
C5×Dic21Direct product of C5 and Dic214202C5xDic21420,9
C7×Dic15Direct product of C7 and Dic154202C7xDic15420,10
D7×C30Direct product of C30 and D72102D7xC30420,34
D5×C42Direct product of C42 and D52102D5xC42420,35
C6×D35Direct product of C6 and D352102C6xD35420,36
S3×C70Direct product of C70 and S32102S3xC70420,37
C10×D21Direct product of C10 and D212102C10xD21420,38
C14×D15Direct product of C14 and D152102C14xD15420,39

### Groups of order 424

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

### Groups of order 426

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

### Groups of order 430

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

### Groups of order 432

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

### Groups of order 434

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

### Groups of order 438

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

### Groups of order 440

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

### Groups of order 442

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

### Groups of order 444

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

### Groups of order 448

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

### Groups of order 450

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

### Groups of order 456

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

### Groups of order 460

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

### Groups of order 462

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

### Groups of order 464

dρLabelID
C292C16The semidirect product of C29 and C16 acting via C16/C8=C24642C29:2C16464,1
C8×D29Direct product of C8 and D292322C8xD29464,4
C8⋊D293rd semidirect product of C8 and D29 acting via D29/C29=C22322C8:D29464,5
C232⋊C22nd semidirect product of C232 and C2 acting faithfully2322C232:C2464,6
C4.Dic29The non-split extension by C4 of Dic29 acting via Dic29/C58=C22322C4.Dic29464,10
M4(2)×C29Direct product of C29 and M4(2)2322M4(2)xC29464,24
D8×C29Direct product of C29 and D82322D8xC29464,25
SD16×C29Direct product of C29 and SD162322SD16xC29464,26
Q16×C29Direct product of C29 and Q164642Q16xC29464,27
D1165C2The semidirect product of D116 and C2 acting through Inn(D116)2322D116:5C2464,38
C4○D4×C29Direct product of C29 and C4○D42322C4oD4xC29464,48

### Groups of order 468

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

### Groups of order 470

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

### Groups of order 472

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

### Groups of order 474

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

### Groups of order 476

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

### Groups of order 480

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

### Groups of order 484

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

### Groups of order 486

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

### Groups of order 488

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

### Groups of order 490

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

### Groups of order 492

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

### Groups of order 494

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

### Groups of order 496

dρLabelID
C31⋊C16The semidirect product of C31 and C16 acting via C16/C8=C24962C31:C16496,1
C8×D31Direct product of C8 and D312482C8xD31496,3
C8⋊D313rd semidirect product of C8 and D31 acting via D31/C31=C22482C8:D31496,4
C248⋊C22nd semidirect product of C248 and C2 acting faithfully2482C248:C2496,5
C4.Dic31The non-split extension by C4 of Dic31 acting via Dic31/C62=C22482C4.Dic31496,9
M4(2)×C31Direct product of C31 and M4(2)2482M4(2)xC31496,23
D8×C31Direct product of C31 and D82482D8xC31496,24
SD16×C31Direct product of C31 and SD162482SD16xC31496,25
Q16×C31Direct product of C31 and Q164962Q16xC31496,26
D1245C2The semidirect product of D124 and C2 acting through Inn(D124)2482D124:5C2496,30
C4○D4×C31Direct product of C31 and C4○D42482C4oD4xC31496,40

### Groups of order 498

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

### Groups of order 500

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

### 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

### Groups of order 21

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

### Groups of order 27

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

### Groups of order 36

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

### Groups of order 39

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

### Groups of order 42

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

### Groups of order 48

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

### Groups of order 54

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

### Groups of order 57

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

### Groups of order 60

dρLabelID
C5×A4Direct product of C5 and A4203C5xA460,9

### Groups of order 63

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

### Groups of order 72

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

### Groups of order 75

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

### Groups of order 78

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

### Groups of order 81

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

### Groups of order 84

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

### Groups of order 93

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

### Groups of order 96

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

### Groups of order 105

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

### Groups of order 108

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

### Groups of order 111

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

### Groups of order 114

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

### Groups of order 117

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

### Groups of order 120

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

### Groups of order 126

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

### Groups of order 129

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

### Groups of order 132

dρLabelID
C11×A4Direct product of C11 and A4443C11xA4132,6

### Groups of order 135

dρLabelID
C5×He3Direct product of C5 and He3453C5xHe3135,3
C5×3- 1+2Direct product of C5 and 3- 1+2453C5xES-(3,1)135,4

### Groups of order 144

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

### Groups of order 147

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

### Groups of order 150

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

### Groups of order 156

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

### Groups of order 162

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

### Groups of order 168

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

### Groups of order 171

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

### Groups of order 180

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

### Groups of order 183

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

### Groups of order 186

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

### Groups of order 189

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

### Groups of order 192

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

### Groups of order 195

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

### Groups of order 201

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

### Groups of order 204

dρLabelID
A4×C17Direct product of C17 and A4683A4xC17204,8

### Groups of order 210

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

### Groups of order 216

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

### Groups of order 219

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

### Groups of order 222

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

### Groups of order 225

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

### Groups of order 228

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

### Groups of order 231

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

### Groups of order 234

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

### Groups of order 237

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

### Groups of order 240

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

### Groups of order 243

dρLabelID
C9.4He32nd central extension by C9 of He3273C9.4He3243,16
C9.5He33rd central extension by C9 of He3813C9.5He3243,19
C9.6He34th central extension by C9 of He3813C9.6He3243,20
C81⋊C3The semidirect product of C81 and C3 acting faithfully813C81:C3243,24
C92⋊C31st semidirect product of C92 and C3 acting faithfully273C9^2:C3243,25
C922C32nd semidirect product of C92 and C3 acting faithfully273C9^2:2C3243,26
C92.C32nd non-split extension by C92 of C3 acting faithfully273C9^2.C3243,27
C27○He3Central product of C27 and He3813C27oHe3243,50
C9.He31st non-split extension by C9 of He3 acting via He3/C32=C3273C9.He3243,55

### Groups of order 252

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

### Groups of order 258

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

### Groups of order 264

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

### Groups of order 270

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

### Groups of order 273

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

### Groups of order 276

dρLabelID
A4×C23Direct product of C23 and A4923A4xC23276,6

### Groups of order 279

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

### Groups of order 285

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

### Groups of order 288

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

### Groups of order 291

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

### Groups of order 294

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

### Groups of order 297

dρLabelID
C11×He3Direct product of C11 and He3993C11xHe3297,3
C11×3- 1+2Direct product of C11 and 3- 1+2993C11xES-(3,1)297,4

### Groups of order 300

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

### Groups of order 309

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

### Groups of order 312

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

### Groups of order 315

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

### Groups of order 324

dρLabelID
C27.A4The central extension by C27 of A41623C27.A4324,3
He3⋊C12The semidirect product of He3 and C12 acting via C12/C2=C6363He3:C12324,13
He3.C121st non-split extension by He3 of C12 acting via C12/C2=C61083He3.C12324,15
He3.2C122nd non-split extension by He3 of C12 acting via C12/C2=C61083He3.2C12324,17
C4×C27⋊C3Direct product of C4 and C27⋊C31083C4xC27:C3324,30
C4×C3≀C3Direct product of C4 and C3≀C3363C4xC3wrC3324,31
C4×He3.C3Direct product of C4 and He3.C31083C4xHe3.C3324,32
C4×He3⋊C3Direct product of C4 and He3⋊C31083C4xHe3:C3324,33
C4×C3.He3Direct product of C4 and C3.He31083C4xC3.He3324,34
A4×C27Direct product of C27 and A41083A4xC27324,42
C27⋊A4The semidirect product of C27 and A4 acting via A4/C22=C31083C27:A4324,43
C62.C92nd non-split extension by C62 of C9 acting via C9/C3=C3543C6^2.C9324,45
C62.13C324th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.13C3^2324,49
C62.14C325th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.14C3^2324,50
C62.15C326th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.15C3^2324,51
C332A41st semidirect product of C33 and A4 acting via A4/C22=C3183C3^3:2A4324,60
C2×C3≀S3Direct product of C2 and C3≀S3183C2xC3wrS3324,68
C2×He3.C6Direct product of C2 and He3.C6543C2xHe3.C6324,70
C2×He3.2C6Direct product of C2 and He3.2C6543C2xHe3.2C6324,72
He3.5C12The non-split extension by He3 of C12 acting via C12/C6=C21083He3.5C12324,102
C4×C9○He3Direct product of C4 and C9○He31083C4xC9oHe3324,108
He3.3C12The non-split extension by He3 of C12 acting via C12/C3=C4543He3.3C12324,111
C62.25C3216th non-split extension by C62 of C32 acting via C32/C3=C3543C6^2.25C3^2324,128
C2×He3.4C6Direct product of C2 and He3.4C6543C2xHe3.4C6324,148

### Groups of order 327

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

### Groups of order 333

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

### Groups of order 336

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

### Groups of order 342

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

### Groups of order 348

dρLabelID
A4×C29Direct product of C29 and A41163A4xC29348,8

### Groups of order 351

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

### Groups of order 357

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

### Groups of order 360

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

### Groups of order 363

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

### Groups of order 366

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

### Groups of order 372

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

### Groups of order 375

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

### Groups of order 378

dρLabelID
C2×C7⋊C27Direct product of C2 and C7⋊C273783C2xC7:C27378,2
C18×C7⋊C3Direct product of C18 and C7⋊C31263C18xC7:C3378,23
C2×C63⋊C3Direct product of C2 and C63⋊C31263C2xC63:C3378,24
C2×C633C3Direct product of C2 and C633C31263C2xC63:3C3378,25
C2×C21.C32Direct product of C2 and C21.C321263C2xC21.C3^2378,27
C2×C7⋊He3Direct product of C2 and C7⋊He31263C2xC7:He3378,28
C7×He3⋊C2Direct product of C7 and He3⋊C2633C7xHe3:C2378,41
C14×He3Direct product of C14 and He31263C14xHe3378,45
C14×3- 1+2Direct product of C14 and 3- 1+21263C14xES-(3,1)378,46

### Groups of order 381

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

### Groups of order 387

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

### Groups of order 390

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

### Groups of order 396

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

### Groups of order 399

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

### Groups of order 402

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

### Groups of order 405

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

### Groups of order 408

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

### Groups of order 417

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

### Groups of order 420

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

### Groups of order 429

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

### Groups of order 432

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

### Groups of order 438

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

### Groups of order 441

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

### Groups of order 444

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

### Groups of order 450

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

### Groups of order 453

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

### Groups of order 456

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

### Groups of order 459

dρLabelID
C17×He3Direct product of C17 and He31533C17xHe3459,3
C17×3- 1+2Direct product of C17 and 3- 1+21533C17xES-(3,1)459,4

### Groups of order 462

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

### Groups of order 465

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

### Groups of order 468

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

### Groups of order 471

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

### Groups of order 474

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

### Groups of order 480

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

### Groups of order 483

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

### Groups of order 486

dρLabelID
He3.C181st non-split extension by He3 of C18 acting via C18/C3=C6813He3.C18486,26
He3.2C182nd non-split extension by He3 of C18 acting via C18/C3=C6813He3.2C18486,28
C922S32nd semidirect product of C92 and S3 acting faithfully273C9^2:2S3486,61
C2×C9.4He3Direct product of C2 and C9.4He3543C2xC9.4He3486,76
C2×C9.5He3Direct product of C2 and C9.5He31623C2xC9.5He3486,79
C2×C9.6He3Direct product of C2 and C9.6He31623C2xC9.6He3486,80
C2×C81⋊C3Direct product of C2 and C81⋊C31623C2xC81:C3486,84
C2×C92⋊C3Direct product of C2 and C92⋊C3543C2xC9^2:C3486,85
C2×C922C3Direct product of C2 and C922C3543C2xC9^2:2C3486,86
C2×C92.C3Direct product of C2 and C92.C3543C2xC9^2.C3486,87
C3≀S33C3The semidirect product of C3≀S3 and C3 acting through Inn(C3≀S3)273C3wrS3:3C3486,125
He3.5C18The non-split extension by He3 of C18 acting via C18/C9=C2813He3.5C18486,164
C2×C27○He3Direct product of C2 and C27○He31623C2xC27oHe3486,209
C2×C9.He3Direct product of C2 and C9.He3543C2xC9.He3486,214

### Groups of order 489

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

### Groups of order 492

dρLabelID
A4×C41Direct product of C41 and A41643A4xC41492,8

### Groups of order 20

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

### Groups of order 32

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

### Groups of order 36

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

### Groups of order 40

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

### Groups of order 48

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

### Groups of order 52

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

### Groups of order 60

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

### Groups of order 64

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

### Groups of order 68

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

### Groups of order 72

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

### Groups of order 80

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

### Groups of order 84

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

### Groups of order 96

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

### Groups of order 100

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

### Groups of order 104

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

### Groups of order 108

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

### Groups of order 112

dρLabelID
D4⋊D7The semidirect product of D4 and D7 acting via D7/C7=C2564+D4:D7112,14
Q8⋊D7The semidirect product of Q8 and D7 acting via D7/C7=C2564+Q8:D7112,16
D4×D7Direct product of D4 and D7284+D4xD7112,31
Q82D7The semidirect product of Q8 and D7 acting through Inn(Q8)564+Q8:2D7112,34

### Groups of order 116

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

### Groups of order 120

dρLabelID
D30.C2The non-split extension by D30 of C2 acting faithfully604+D30.C2120,10
C3⋊D20The semidirect product of C3 and D20 acting via D20/D10=C2604+C3:D20120,12
C5⋊D12The semidirect product of C5 and D12 acting via D12/D6=C2604+C5:D12120,13
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simple54+S5120,34
C2×S3×D5Direct product of C2, S3 and D5304+C2xS3xD5120,42

### Groups of order 128

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

### Groups of order 132

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

### Groups of order 136

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

### Groups of order 140

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

### Groups of order 144

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

### Groups of order 148

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

### Groups of order 156

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

### Groups of order 160

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

### Groups of order 164

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

### Groups of order 168

dρLabelID
D21⋊C4The semidirect product of D21 and C4 acting via C4/C2=C2844+D21:C4168,14
C3⋊D28The semidirect product of C3 and D28 acting via D28/D14=C2844+C3:D28168,16
C7⋊D12The semidirect product of C7 and D12 acting via D12/D6=C2844+C7:D12168,17
C2×S3×D7Direct product of C2, S3 and D7424+C2xS3xD7168,50

### Groups of order 176

dρLabelID
D4⋊D11The semidirect product of D4 and D11 acting via D11/C11=C2884+D4:D11176,14
Q8⋊D11The semidirect product of Q8 and D11 acting via D11/C11=C2884+Q8:D11176,16
D4×D11Direct product of D4 and D11444+D4xD11176,31
D44⋊C24th semidirect product of D44 and C2 acting faithfully884+D44:C2176,34

### Groups of order 180

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

### Groups of order 192

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

### Groups of order 196

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

### Groups of order 200

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

### Groups of order 204

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

### Groups of order 208

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

### Groups of order 212

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

### Groups of order 216

dρLabelID
C18.D63rd non-split extension by C18 of D6 acting via D6/S3=C2364+C18.D6216,28
C3⋊D36The semidirect product of C3 and D36 acting via D36/D18=C2364+C3:D36216,29
C9⋊D12The semidirect product of C9 and D12 acting via D12/D6=C2364+C9:D12216,32
C2×S3×D9Direct product of C2, S3 and D9364+C2xS3xD9216,101

### Groups of order 220

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

### Groups of order 224

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

### Groups of order 228

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

### Groups of order 232

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

### Groups of order 240

dρLabelID
C3⋊D40The semidirect product of C3 and D40 acting via D40/D20=C21204+C3:D40240,14
C5⋊D24The semidirect product of C5 and D24 acting via D24/D12=C21204+C5:D24240,15
C15⋊SD164th semidirect product of C15 and SD16 acting via SD16/C4=C221204+C15:SD16240,19
Dic6⋊D51st semidirect product of Dic6 and D5 acting via D5/C5=C21204+Dic6:D5240,21
D4⋊D15The semidirect product of D4 and D15 acting via D15/C15=C21204+D4:D15240,76
Q82D15The semidirect product of Q8 and D15 acting via D15/C15=C21204+Q8:2D15240,78
Q8⋊D15The semidirect product of Q8 and D15 acting via D15/C5=S3404+Q8:D15240,106
Dic5.A4The non-split extension by Dic5 of A4 acting through Inn(Dic5)804+Dic5.A4240,108
D60⋊C26th semidirect product of D60 and C2 acting faithfully1204+D60:C2240,130
C12.28D107th non-split extension by C12 of D10 acting via D10/D5=C21204+C12.28D10240,134
D5×D12Direct product of D5 and D12604+D5xD12240,136
S3×D20Direct product of S3 and D20604+S3xD20240,137
D10⋊D64th semidirect product of D10 and D6 acting via D6/S3=C2604+D10:D6240,151
D4×D15Direct product of D4 and D15604+D4xD15240,179
Q83D15The semidirect product of Q8 and D15 acting through Inn(Q8)1204+Q8:3D15240,182
C2×S5Direct product of C2 and S5; = O3(𝔽5)104+C2xS5240,189

### Groups of order 244

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

### Groups of order 252

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

### Groups of order 260

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

### Groups of order 264

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

### Groups of order 272

dρLabelID
D4⋊D17The semidirect product of D4 and D17 acting via D17/C17=C21364+D4:D17272,15
Q8⋊D17The semidirect product of Q8 and D17 acting via D17/C17=C21364+Q8:D17272,17
D17.D4The non-split extension by D17 of D4 acting via D4/C22=C2684+D17.D4272,35
D4×D17Direct product of D4 and D17684+D4xD17272,40
D68⋊C24th semidirect product of D68 and C2 acting faithfully1364+D68:C2272,43

### Groups of order 276

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

### Groups of order 280

dρLabelID
D70.C2The non-split extension by D70 of C2 acting faithfully1404+D70.C2280,9
C5⋊D28The semidirect product of C5 and D28 acting via D28/D14=C21404+C5:D28280,11
C7⋊D20The semidirect product of C7 and D20 acting via D20/D10=C21404+C7:D20280,12
C2×D5×D7Direct product of C2, D5 and D7704+C2xD5xD7280,36

### Groups of order 288

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

### Groups of order 292

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

### Groups of order 296

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

### Groups of order 300

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

### Groups of order 304

dρLabelID
D4⋊D19The semidirect product of D4 and D19 acting via D19/C19=C21524+D4:D19304,14
Q8⋊D19The semidirect product of Q8 and D19 acting via D19/C19=C21524+Q8:D19304,16
D4×D19Direct product of D4 and D19764+D4xD19304,31
D76⋊C24th semidirect product of D76 and C2 acting faithfully1524+D76:C2304,34

### Groups of order 308

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

### Groups of order 312

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

### Groups of order 320

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

### Groups of order 324

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

### Groups of order 328

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

### Groups of order 336

dρLabelID
C3⋊D56The semidirect product of C3 and D56 acting via D56/D28=C21684+C3:D56336,30
C7⋊D24The semidirect product of C7 and D24 acting via D24/D12=C21684+C7:D24336,31
C21⋊SD164th semidirect product of C21 and SD16 acting via SD16/C4=C221684+C21:SD16336,35
Dic6⋊D71st semidirect product of Dic6 and D7 acting via D7/C7=C21684+Dic6:D7336,37
D4⋊D21The semidirect product of D4 and D21 acting via D21/C21=C21684+D4:D21336,101
Q82D21The semidirect product of Q8 and D21 acting via D21/C21=C21684+Q8:2D21336,103
Q8⋊D21The semidirect product of Q8 and D21 acting via D21/C7=S3564+Q8:D21336,119
Dic7.2A4The non-split extension by Dic7 of A4 acting through Inn(Dic7)1124+Dic7.2A4336,131
D84⋊C26th semidirect product of D84 and C2 acting faithfully1684+D84:C2336,142
D14.D63rd non-split extension by D14 of D6 acting via D6/C6=C21684+D14.D6336,146
D7×D12Direct product of D7 and D12844+D7xD12336,148
S3×D28Direct product of S3 and D28844+S3xD28336,149
D6⋊D144th semidirect product of D6 and D14 acting via D14/D7=C2844+D6:D14336,163
D4×D21Direct product of D4 and D21844+D4xD21336,198
Q83D21The semidirect product of Q8 and D21 acting through Inn(Q8)1684+Q8:3D21336,201

### Groups of order 340

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

### Groups of order 348

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

### Groups of order 352

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

### Groups of order 356

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

### Groups of order 360

dρLabelID
D90.C2The non-split extension by D90 of C2 acting faithfully1804+D90.C2360,9
C5⋊D36The semidirect product of C5 and D36 acting via D36/D18=C21804+C5:D36360,10
C9⋊D20The semidirect product of C9 and D20 acting via D20/D10=C21804+C9:D20360,13
C2×D5×D9Direct product of C2, D5 and D9904+C2xD5xD9360,45
C6.D303rd non-split extension by C6 of D30 acting via D30/D15=C2604+C6.D30360,79
C3⋊D60The semidirect product of C3 and D60 acting via D60/D30=C2604+C3:D60360,81
D62D152nd semidirect product of D6 and D15 acting via D15/C15=C2604+D6:2D15360,82
C2×C32⋊F5Direct product of C2 and C32⋊F5604+C2xC3^2:F5360,150
C2×S3×D15Direct product of C2, S3 and D15604+C2xS3xD15360,154

### Groups of order 364

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

### Groups of order 368

dρLabelID
D4⋊D23The semidirect product of D4 and D23 acting via D23/C23=C21844+D4:D23368,14
Q8⋊D23The semidirect product of Q8 and D23 acting via D23/C23=C21844+Q8:D23368,16
D4×D23Direct product of D4 and D23924+D4xD23368,31
D92⋊C24th semidirect product of D92 and C2 acting faithfully1844+D92:C2368,34

### Groups of order 372

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

### Groups of order 380

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

### Groups of order 388

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

### Groups of order 392

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

### Groups of order 396

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

### Groups of order 400

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

### Groups of order 404

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

### Groups of order 408

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

### Groups of order 416

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

### Groups of order 420

dρLabelID
D7×D15Direct product of D7 and D151054+D7xD15420,26
D5×D21Direct product of D5 and D211054+D5xD21420,28
S3×D35Direct product of S3 and D351054+S3xD35420,29

### Groups of order 424

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

### Groups of order 432

dρLabelID
D4⋊D27The semidirect product of D4 and D27 acting via D27/C27=C22164+D4:D27432,16
Q82D27The semidirect product of Q8 and D27 acting via D27/C27=C22164+Q8:2D27432,18
Q8⋊D27The semidirect product of Q8 and D27 acting via D27/C9=S32164+Q8:D27432,38
D4×D27Direct product of D4 and D271084+D4xD27432,47
Q83D27The semidirect product of Q8 and D27 acting through Inn(Q8)2164+Q8:3D27432,50
C6.D362nd non-split extension by C6 of D36 acting via D36/D18=C2724+C6.D36432,63
C3⋊D72The semidirect product of C3 and D72 acting via D72/D36=C2724+C3:D72432,64
C9⋊D24The semidirect product of C9 and D24 acting via D24/D12=C2724+C9:D24432,69
C18.D123rd non-split extension by C18 of D12 acting via D12/D6=C2724+C18.D12432,73
C18.6S46th non-split extension by C18 of S4 acting via S4/A4=C2724+C18.6S4432,253
Dic9.2A4The non-split extension by Dic9 of A4 acting through Inn(Dic9)1444+Dic9.2A4432,262
Dic65D9The semidirect product of Dic6 and D9 acting through Inn(Dic6)724+Dic6:5D9432,282
Dic9.D64th non-split extension by Dic9 of D6 acting via D6/S3=C2724+Dic9.D6432,289
S3×D36Direct product of S3 and D36724+S3xD36432,291
D9×D12Direct product of D9 and D12724+D9xD12432,292
D18⋊D64th semidirect product of D18 and D6 acting via D6/S3=C2364+D18:D6432,315

### Groups of order 436

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

### Groups of order 440

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

### Groups of order 444

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

### Groups of order 448

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

### Groups of order 452

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

### Groups of order 456

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

### Groups of order 460

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

### Groups of order 464

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

### Groups of order 468

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

### Groups of order 476

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

### Groups of order 480

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

### Groups of order 484

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

### Groups of order 488

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

### Groups of order 492

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

### Groups of order 496

dρLabelID
D4⋊D31The semidirect product of D4 and D31 acting via D31/C31=C22484+D4:D31496,14
Q8⋊D31The semidirect product of Q8 and D31 acting via D31/C31=C22484+Q8:D31496,16
D4×D31Direct product of D4 and D311244+D4xD31496,31
Q82D31The semidirect product of Q8 and D31 acting through Inn(Q8)2484+Q8:2D31496,34

### Groups of order 500

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

### Groups of order 32

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

### Groups of order 40

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

### Groups of order 48

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

### Groups of order 64

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

### Groups of order 72

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

### Groups of order 80

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

### Groups of order 96

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

### Groups of order 104

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

### Groups of order 112

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

### Groups of order 120

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

### Groups of order 128

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

### Groups of order 136

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

### Groups of order 144

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

### Groups of order 160

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

### Groups of order 168

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

### Groups of order 176

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

### Groups of order 192

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

### Groups of order 200

dρLabelID
C25⋊C8The semidirect product of C25 and C8 acting via C8/C2=C42004-C25:C8200,3
C525C84th semidirect product of C52 and C8 acting via C8/C2=C4404-C5^2:5C8200,21
D5×Dic5Direct product of D5 and Dic5404-D5xDic5200,22
C522D41st semidirect product of C52 and D4 acting via D4/C2=C22404-C5^2:2D4200,24
C522Q8The semidirect product of C52 and Q8 acting via Q8/C2=C22404-C5^2:2Q8200,26

### Groups of order 208

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

### Groups of order 216

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

### Groups of order 224

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

### Groups of order 232

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

### Groups of order 240

dρLabelID
C6.D202nd non-split extension by C6 of D20 acting via D20/D10=C21204-C6.D20240,18
D12.D51st non-split extension by D12 of D5 acting via D5/C5=C21204-D12.D5240,20
C3⋊Dic20The semidirect product of C3 and Dic20 acting via Dic20/Dic10=C22404-C3:Dic20240,23
C5⋊Dic12The semidirect product of C5 and Dic12 acting via Dic12/Dic6=C22404-C5:Dic12240,24
D4.D15The non-split extension by D4 of D15 acting via D15/C15=C21204-D4.D15240,77
C157Q161st semidirect product of C15 and Q16 acting via Q16/Q8=C22404-C15:7Q16240,79
CSU2(𝔽5)Conformal special unitary group on 𝔽52; = C2.2S5484-CSU(2,5)240,89
C2.S52nd central stem extension by C2 of S5404-C2.S5240,90
Q8.D15The non-split extension by Q8 of D15 acting via D15/C5=S3804-Q8.D15240,105
D5×SL2(𝔽3)Direct product of D5 and SL2(𝔽3)404-D5xSL(2,3)240,109
D5×Dic6Direct product of D5 and Dic61204-D5xDic6240,125
D205S3The semidirect product of D20 and S3 acting through Inn(D20)1204-D20:5S3240,126
S3×Dic10Direct product of S3 and Dic101204-S3xDic10240,128
D125D5The semidirect product of D12 and D5 acting through Inn(D12)1204-D12:5D5240,133
C30.C2317th non-split extension by C30 of C23 acting via C23/C2=C221204-C30.C2^3240,141
D42D15The semidirect product of D4 and D15 acting through Inn(D4)1204-D4:2D15240,180
Q8×D15Direct product of Q8 and D151204-Q8xD15240,181

### Groups of order 264

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

### Groups of order 272

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

### Groups of order 280

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

### Groups of order 288

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

### Groups of order 296

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

### Groups of order 304

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

### Groups of order 312

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

### Groups of order 320

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

### Groups of order 328

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

### Groups of order 336

dρLabelID
C6.D282nd non-split extension by C6 of D28 acting via D28/D14=C21684-C6.D28336,34
D12.D71st non-split extension by D12 of D7 acting via D7/C7=C21684-D12.D7336,36
C3⋊Dic28The semidirect product of C3 and Dic28 acting via Dic28/Dic14=C23364-C3:Dic28336,39
C7⋊Dic12The semidirect product of C7 and Dic12 acting via Dic12/Dic6=C23364-C7:Dic12336,40
D4.D21The non-split extension by D4 of D21 acting via D21/C21=C21684-D4.D21336,102
C217Q161st semidirect product of C21 and Q16 acting via Q16/Q8=C23364-C21:7Q16336,104
Q8.D21The non-split extension by Q8 of D21 acting via D21/C7=S31124-Q8.D21336,118
D7×SL2(𝔽3)Direct product of D7 and SL2(𝔽3)564-D7xSL(2,3)336,132
D7×Dic6Direct product of D7 and Dic61684-D7xDic6336,137
D285S3The semidirect product of D28 and S3 acting through Inn(D28)1684-D28:5S3336,138
S3×Dic14Direct product of S3 and Dic141684-S3xDic14336,140
D125D7The semidirect product of D12 and D7 acting through Inn(D12)1684-D12:5D7336,145
C42.C2317th non-split extension by C42 of C23 acting via C23/C2=C221684-C42.C2^3336,153
D42D21The semidirect product of D4 and D21 acting through Inn(D4)1684-D4:2D21336,199
Q8×D21Direct product of Q8 and D211684-Q8xD21336,200

### Groups of order 352

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

### Groups of order 360

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

### Groups of order 368

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

### Groups of order 392

dρLabelID
C722C8The semidirect product of C72 and C8 acting via C8/C2=C4564-C7^2:2C8392,17
D7×Dic7Direct product of D7 and Dic7564-D7xDic7392,18
C722D41st semidirect product of C72 and D4 acting via D4/C2=C22564-C7^2:2D4392,20
C722Q8The semidirect product of C72 and Q8 acting via Q8/C2=C22564-C7^2:2Q8392,22

### Groups of order 400

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

### Groups of order 408

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

### Groups of order 416

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

### Groups of order 424

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

### Groups of order 432

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

### Groups of order 440

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

### Groups of order 448

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

### Groups of order 456

dρLabelID
Dic3×D19Direct product of Dic3 and D192284-Dic3xD19456,12
S3×Dic19Direct product of S3 and Dic192284-S3xDic19456,13
C57⋊D4<