# Transitive groups of degree up to 31

When G acts on a (finite) set, the set is a disjoint union of orbits, the transitive G-sets. There is a natural bijection

 {transitive G-sets up to ≅} ↔ {subgroups of G up to conjugacy} X ↦ stabiliser of a point G/H ↤ H

Transitive G-sets on which G acts faithfully correspond to subgroups H with trivial core (or core-free), that is those where the intersection of H with all of its conjugates is trivial; equivalently, H contains no non-trivial normal subgroup of G. In this case G can be viewed as a transitive subgroup of Sn for n=(G:H), the index of H in G, called the transitive degree. Conversely, all transitive subgroups of Sn arise in this way. The transitive group database in GAP and Magma contains all transitive subgroups of Sn up to conjugacy for n≤31, numbered nTi (or Tn,i).

The table below lists all transitive groups with n≤31. See also a smaller table with n≤15 and the smallest transitive degree table (n≤120).

### Groups of order 1

LabelIDTr ID
C1Trivial groupC11,11T1

### Groups of order 2

LabelIDTr ID
C2Cyclic groupC22,12T1

### Groups of order 3

LabelIDTr ID
C3Cyclic group; = A3 = triangle rotationsC33,13T1

### Groups of order 6

LabelIDTr ID
S3Symmetric group on 3 letters; = D3 = GL2(𝔽2) = triangle symmetries = 1st non-abelian groupS36,13T2

### Groups of order 4

LabelIDTr ID
C4Cyclic group; = square rotationsC44,14T1
C22Klein 4-group V4 = elementary abelian group of type [2,2]; = rectangle symmetriesC2^24,24T2

### Groups of order 8

LabelIDTr ID
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetriesD48,34T3

### Groups of order 12

LabelIDTr ID
A4Alternating group on 4 letters; = PSL2(𝔽3) = L2(3) = tetrahedron rotationsA412,34T4

### Groups of order 24

LabelIDTr ID
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotationsS424,124T5

### Groups of order 5

LabelIDTr ID
C5Cyclic group; = pentagon rotationsC55,15T1

### Groups of order 10

LabelIDTr ID
D5Dihedral group; = pentagon symmetriesD510,15T2

### Groups of order 20

LabelIDTr ID
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)F520,35T3

### Groups of order 60

LabelIDTr ID
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,55T4

### Groups of order 120

LabelIDTr ID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,345T5

### Groups of order 6

LabelIDTr ID
C6Cyclic group; = hexagon rotationsC66,26T1
S3Symmetric group on 3 letters; = D3 = GL2(𝔽2) = triangle symmetries = 1st non-abelian groupS36,16T2

### Groups of order 12

LabelIDTr ID
D6Dihedral group; = C2×S3 = hexagon symmetriesD612,46T3
A4Alternating group on 4 letters; = PSL2(𝔽3) = L2(3) = tetrahedron rotationsA412,36T4

### Groups of order 18

LabelIDTr ID
C3×S3Direct product of C3 and S3; = U2(𝔽2)C3xS318,36T5

### Groups of order 24

LabelIDTr ID
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)C2xA424,136T6
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotationsS424,126T7
6T8

### Groups of order 36

LabelIDTr ID
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)S3^236,106T9
C32⋊C4The semidirect product of C32 and C4 acting faithfullyC3^2:C436,96T10

### Groups of order 48

LabelIDTr ID
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetriesC2xS448,486T11

### Groups of order 60

LabelIDTr ID
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,56T12

### Groups of order 72

LabelIDTr ID
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)S3wrC272,406T13

### Groups of order 120

LabelIDTr ID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,346T14

### Groups of order 360

LabelIDTr ID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simpleA6360,1186T15

### Groups of order 7

LabelIDTr ID
C7Cyclic groupC77,17T1

### Groups of order 14

LabelIDTr ID
D7Dihedral groupD714,17T2

### Groups of order 21

LabelIDTr ID
C7⋊C3The semidirect product of C7 and C3 acting faithfullyC7:C321,17T3

### Groups of order 42

LabelIDTr ID
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)F742,17T4

### Groups of order 168

LabelIDTr ID
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simpleGL(3,2)168,427T5

### Groups of order 8

LabelIDTr ID
C8Cyclic groupC88,18T1
C2×C4Abelian group of type [2,4]C2xC48,28T2
C23Elementary abelian group of type [2,2,2]C2^38,58T3
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetriesD48,38T4
Q8Quaternion group; = C4.C2 = Dic2 = 2- 1+2Q88,48T5

### Groups of order 16

LabelIDTr ID
D8Dihedral groupD816,78T6
M4(2)Modular maximal-cyclic group; = C83C2M4(2)16,68T7
SD16Semidihedral group; = Q8C2 = QD16SD1616,88T8
C2×D4Direct product of C2 and D4C2xD416,118T9
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C2C2^2:C416,38T10
C4○D4Pauli group = central product of C4 and D4C4oD416,138T11

### Groups of order 24

LabelIDTr ID
SL2(𝔽3)Special linear group on 𝔽32; = Q8C3 = 2T = <2,3,3> = 1st non-monomial groupSL(2,3)24,38T12
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)C2xA424,138T13
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotationsS424,128T14

### Groups of order 32

LabelIDTr ID
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)C8:C2^232,438T15
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C2C4.D432,78T16
C4≀C2Wreath product of C4 by C2C4wrC232,118T17
C22≀C2Wreath product of C22 by C2C2^2wrC232,278T18
C23⋊C4The semidirect product of C23 and C4 acting faithfullyC2^3:C432,68T19
8T20
8T21
2+ 1+4Extraspecial group; = D4D4ES+(2,2)32,498T22

### Groups of order 48

LabelIDTr ID
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32) = 2O = <2,3,4>GL(2,3)48,298T23
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetriesC2xS448,488T24

### Groups of order 56

LabelIDTr ID
F8Frobenius group; = C23C7 = AGL1(𝔽8)F856,118T25

### Groups of order 64

LabelIDTr ID
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)D4:4D464,1348T26
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)C2wrC464,328T27
8T28
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)C2wrC2^264,1388T29
C42⋊C42nd semidirect product of C42 and C4 acting faithfullyC4^2:C464,348T30
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)C2wrC2^264,1388T31

### Groups of order 96

LabelIDTr ID
C23⋊A42nd semidirect product of C23 and A4 acting faithfullyC2^3:A496,2048T32
C24⋊C61st semidirect product of C24 and C6 acting faithfullyC2^4:C696,708T33
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S3C2^2:S496,2278T34

### Groups of order 128

LabelIDTr ID
C2≀D4Wreath product of C2 by D4C2wrD4128,9288T35

### Groups of order 168

LabelIDTr ID
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)AGammaL(1,8)168,438T36
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simpleGL(3,2)168,428T37

### Groups of order 192

LabelIDTr ID
C2≀A4Wreath product of C2 by A4C2wrA4192,2018T38
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)C2^3:S4192,14938T39
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)Q8:2S4192,14948T40
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)C2^4:D6192,9558T41

### Groups of order 288

LabelIDTr ID
A4≀C2Wreath product of A4 by C2A4wrC2288,10258T42

### Groups of order 336

LabelIDTr ID
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,2088T43

### Groups of order 9

LabelIDTr ID
C9Cyclic groupC99,19T1
C32Elementary abelian group of type [3,3]C3^29,29T2

### Groups of order 18

LabelIDTr ID
D9Dihedral groupD918,19T3
C3×S3Direct product of C3 and S3; = U2(𝔽2)C3xS318,39T4
C3⋊S3The semidirect product of C3 and S3 acting via S3/C3=C2C3:S318,49T5

### Groups of order 27

LabelIDTr ID
3- 1+2Extraspecial groupES-(3,1)27,49T6
He3Heisenberg group; = C32C3 = 3+ 1+2He327,39T7

### Groups of order 36

LabelIDTr ID
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)S3^236,109T8
C32⋊C4The semidirect product of C32 and C4 acting faithfullyC3^2:C436,99T9

### Groups of order 54

LabelIDTr ID
C9⋊C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)C9:C654,69T10
C32⋊C6The semidirect product of C32 and C6 acting faithfullyC3^2:C654,59T11
He3⋊C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)He3:C254,89T12
C32⋊C6The semidirect product of C32 and C6 acting faithfullyC3^2:C654,59T13

### Groups of order 72

LabelIDTr ID
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M9PSU(3,2)72,419T14
F9Frobenius group; = C32C8 = AGL1(𝔽9)F972,399T15
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)S3wrC272,409T16

### Groups of order 81

LabelIDTr ID
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)C3wrC381,79T17

### Groups of order 108

LabelIDTr ID
C32⋊D6The semidirect product of C32 and D6 acting faithfullyC3^2:D6108,179T18

### Groups of order 144

LabelIDTr ID
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)AGammaL(1,9)144,1829T19

### Groups of order 162

LabelIDTr ID
C3≀S3Wreath product of C3 by S3C3wrS3162,109T20
C33⋊S32nd semidirect product of C33 and S3 acting faithfullyC3^3:S3162,199T21
C33⋊C61st semidirect product of C33 and C6 acting faithfullyC3^3:C6162,119T22

### Groups of order 216

LabelIDTr ID
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C3ASL(2,3)216,1539T23

### Groups of order 324

LabelIDTr ID
He3⋊D6The semidirect product of He3 and D6 acting faithfullyHe3:D6324,399T24
C33⋊A4The semidirect product of C33 and A4 acting faithfullyC3^3:A4324,1609T25

### Groups of order 432

LabelIDTr ID
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)AGL(2,3)432,7349T26

### Groups of order 10

LabelIDTr ID
C10Cyclic groupC1010,210T1
D5Dihedral group; = pentagon symmetriesD510,110T2

### Groups of order 20

LabelIDTr ID
D10Dihedral group; = C2×D5D1020,410T3
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)F520,310T4

### Groups of order 40

LabelIDTr ID
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)C2xF540,1210T5

### Groups of order 50

LabelIDTr ID
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)C5xD550,310T6

### Groups of order 60

LabelIDTr ID
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,510T7

### Groups of order 80

LabelIDTr ID
C24⋊C5The semidirect product of C24 and C5 acting faithfullyC2^4:C580,4910T8

### Groups of order 100

LabelIDTr ID
D52Direct product of D5 and D5D5^2100,1310T9
C52⋊C44th semidirect product of C52 and C4 acting faithfullyC5^2:C4100,1210T10

### Groups of order 120

LabelIDTr ID
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetriesC2xA5120,3510T11
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3410T12
10T13

### Groups of order 160

LabelIDTr ID
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)C2xC2^4:C5160,23510T14
C24⋊D5The semidirect product of C24 and D5 acting faithfullyC2^4:D5160,23410T15
10T16

### Groups of order 200

LabelIDTr ID
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)D5:F5200,4210T17
C52⋊C8The semidirect product of C52 and C8 acting faithfullyC5^2:C8200,4010T18
D5≀C2Wreath product of D5 by C2D5wrC2200,4310T19
C52⋊Q8The semidirect product of C52 and Q8 acting faithfullyC5^2:Q8200,4410T20
D5≀C2Wreath product of D5 by C2D5wrC2200,4310T21

### Groups of order 240

LabelIDTr ID
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18910T22

### Groups of order 320

LabelIDTr ID
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163610T23
C24⋊F5The semidirect product of C24 and F5 acting faithfullyC2^4:F5320,163510T24
10T25

### Groups of order 360

LabelIDTr ID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simpleA6360,11810T26

### Groups of order 400

LabelIDTr ID
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfullyD5wrC2:C2400,20710T27
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfullyC5^2:M4(2)400,20610T28

### Groups of order 11

LabelIDTr ID
C11Cyclic groupC1111,111T1

### Groups of order 22

LabelIDTr ID
D11Dihedral groupD1122,111T2

### Groups of order 55

LabelIDTr ID
C11⋊C5The semidirect product of C11 and C5 acting faithfullyC11:C555,111T3

### Groups of order 110

LabelIDTr ID
F11Frobenius group; = C11C10 = AGL1(𝔽11) = Aut(D11) = Hol(C11)F11110,111T4

### Groups of order 12

LabelIDTr ID
C12Cyclic groupC1212,212T1
C2×C6Abelian group of type [2,6]C2xC612,512T2
D6Dihedral group; = C2×S3 = hexagon symmetriesD612,412T3
A4Alternating group on 4 letters; = PSL2(𝔽3) = L2(3) = tetrahedron rotationsA412,312T4
Dic3Dicyclic group; = C3C4Dic312,112T5

### Groups of order 24

LabelIDTr ID
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)C2xA424,1312T6
12T7
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotationsS424,1212T8
12T9
C22×S3Direct product of C22 and S3C2^2xS324,1412T10
C4×S3Direct product of C4 and S3C4xS324,512T11
D12Dihedral groupD1224,612T12
C3⋊D4The semidirect product of C3 and D4 acting via D4/C22=C2C3:D424,812T13
C3×D4Direct product of C3 and D4C3xD424,1012T14
C3⋊D4The semidirect product of C3 and D4 acting via D4/C22=C2C3:D424,812T15

### Groups of order 36

LabelIDTr ID
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)S3^236,1012T16
C32⋊C4The semidirect product of C32 and C4 acting faithfullyC3^2:C436,912T17
S3×C6Direct product of C6 and S3S3xC636,1212T18
C3×Dic3Direct product of C3 and Dic3C3xDic336,612T19
C3×A4Direct product of C3 and A4C3xA436,1112T20

### Groups of order 48

LabelIDTr ID
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetriesC2xS448,4812T21
12T22
12T23
12T24
C22×A4Direct product of C22 and A4C2^2xA448,4912T25
12T26
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)A4:C448,3012T27
S3×D4Direct product of S3 and D4; = Aut(D12) = Hol(C12)S3xD448,3812T28
C4×A4Direct product of C4 and A4C4xA448,3112T29
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)A4:C448,3012T30
C42⋊C3The semidirect product of C42 and C3 acting faithfullyC4^2:C348,312T31
C22⋊A4The semidirect product of C22 and A4 acting via A4/C22=C3C2^2:A448,5012T32

### Groups of order 60

LabelIDTr ID
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,512T33

### Groups of order 72

LabelIDTr ID
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)S3wrC272,4012T34
12T35
12T36
C2×S32Direct product of C2, S3 and S3C2xS3^272,4612T37
C3⋊D12The semidirect product of C3 and D12 acting via D12/D6=C2C3:D1272,2312T38
C6.D62nd non-split extension by C6 of D6 acting via D6/S3=C2C6.D672,2112T39
C2×C32⋊C4Direct product of C2 and C32⋊C4C2xC3^2:C472,4512T40
12T41
C3×C3⋊D4Direct product of C3 and C3⋊D4C3xC3:D472,3012T42
S3×A4Direct product of S3 and A4S3xA472,4412T43
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2C3:S472,4312T44
C3×S4Direct product of C3 and S4C3xS472,4212T45
F9Frobenius group; = C32C8 = AGL1(𝔽9)F972,3912T46
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M9PSU(3,2)72,4112T47

### Groups of order 96

LabelIDTr ID
C22×S4Direct product of C22 and S4C2^2xS496,22612T48
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)A4:D496,19512T49
12T50
D4×A4Direct product of D4 and A4D4xA496,19712T51
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)A4:D496,19512T52
C4×S4Direct product of C4 and S4C4xS496,18612T53
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2C4:S496,18712T54
C2×C42⋊C3Direct product of C2 and C42⋊C3C2xC4^2:C396,6812T55
C2×C22⋊A4Direct product of C2 and C22⋊A4C2xC2^2:A496,22912T56
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3C2^3.3A496,312T57
C24⋊C61st semidirect product of C24 and C6 acting faithfullyC2^4:C696,7012T58
12T59
C23.A42nd non-split extension by C23 of A4 acting faithfullyC2^3.A496,7212T60
12T61
C42⋊S3The semidirect product of C42 and S3 acting faithfullyC4^2:S396,6412T62
12T63
12T64
12T65
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S3C2^2:S496,22712T66
12T67
12T68
12T69

### Groups of order 108

LabelIDTr ID
C3×S32Direct product of C3, S3 and S3C3xS3^2108,3812T70
C324D6The semidirect product of C32 and D6 acting via D6/C3=C22C3^2:4D6108,4012T71
C33⋊C42nd semidirect product of C33 and C4 acting faithfullyC3^3:C4108,3712T72
C3×C32⋊C4Direct product of C3 and C32⋊C4C3xC3^2:C4108,3612T73

### Groups of order 120

LabelIDTr ID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3412T74
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetriesC2xA5120,3512T75
12T76

### Groups of order 144

LabelIDTr ID
C2×S3≀C2Direct product of C2 and S3≀C2C2xS3wrC2144,18612T77
12T78
(S32)⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2(S3^2):C4144,11512T79
12T80
Dic3⋊D62nd semidirect product of Dic3 and D6 acting via D6/S3=C2; = Hol(Dic3)Dic3:D6144,15412T81
C62⋊C41st semidirect product of C62 and C4 acting faithfullyC6^2:C4144,13612T82
S3×S4Direct product of S3 and S4; = Hol(C2×C6)S3xS4144,18312T83
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)AGammaL(1,9)144,18212T84
A42Direct product of A4 and A4; = PΩ+4(𝔽3)A4^2144,18412T85

### Groups of order 192

LabelIDTr ID
D4×S4Direct product of D4 and S4D4xS4192,147212T86
C2×C24⋊C6Direct product of C2 and C24⋊C6C2xC2^4:C6192,100012T87
12T88
C2×C23.A4Direct product of C2 and C23.A4C2xC2^3.A4192,100212T89
C22×C22⋊A4Direct product of C22 and C22⋊A4C2^2xC2^2:A4192,154012T90
C24.2A42nd non-split extension by C24 of A4 acting faithfullyC2^4.2A4192,19712T91
C2×C23.A4Direct product of C2 and C23.A4C2xC2^3.A4192,100212T92
C24.2A42nd non-split extension by C24 of A4 acting faithfullyC2^4.2A4192,19712T93
C4×C42⋊C3Direct product of C4 and C42⋊C3C4xC4^2:C3192,18812T94
C2×C42⋊S3Direct product of C2 and C42⋊S3C2xC4^2:S3192,94412T95
12T96
12T97
C23.9S43rd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.9S4192,18212T98
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6C2^4:C12192,19112T99
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153812T100
12T101
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149512T102
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153812T103
C232D4⋊C3The semidirect product of C232D4 and C3 acting faithfullyC2^3:2D4:C3192,19412T104
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6C2^4:C12192,19112T105
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153812T106
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149512T107
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)C2^4:D6192,95512T108
12T109
12T110
12T111
C42⋊D6The semidirect product of C42 and D6 acting faithfullyC4^2:D6192,95612T112
12T113
12T114
12T115

### Groups of order 216

LabelIDTr ID
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15812T116
S33Direct product of S3, S3 and S3; = Hol(C3×S3)S3^3216,16212T117
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4C3^2:2D12216,15912T118
S3×C32⋊C4Direct product of S3 and C32⋊C4S3xC3^2:C4216,15612T119
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15812T120
C3×S3≀C2Direct product of C3 and S3≀C2C3xS3wrC2216,15712T121
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C3ASL(2,3)216,15312T122

### Groups of order 240

LabelIDTr ID
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18912T123
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2A5:C4240,9112T124

### Groups of order 288

LabelIDTr ID
D6≀C2Wreath product of D6 by C2D6wrC2288,88912T125
A4≀C2Wreath product of A4 by C2A4wrC2288,102512T126
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)PSO+(4,3)288,102612T127
A4≀C2Wreath product of A4 by C2A4wrC2288,102512T128
12T129

### Groups of order 324

LabelIDTr ID
C3×C324D6Direct product of C3 and C324D6C3xC3^2:4D6324,16712T130
C3×C33⋊C4Direct product of C3 and C33⋊C4; = AΣL1(𝔽81)C3xC3^3:C4324,16212T131
C33⋊A4The semidirect product of C33 and A4 acting faithfullyC3^3:A4324,16012T132
12T133

### Groups of order 432

LabelIDTr ID
S3×S3≀C2Direct product of S3 and S3≀C2S3xS3wrC2432,74112T156
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)AGL(2,3)432,73412T157

### Groups of order 13

LabelIDTr ID
C13Cyclic groupC1313,113T1

### Groups of order 26

LabelIDTr ID
D13Dihedral groupD1326,113T2

### Groups of order 39

LabelIDTr ID
C13⋊C3The semidirect product of C13 and C3 acting faithfullyC13:C339,113T3

### Groups of order 52

LabelIDTr ID
C13⋊C4The semidirect product of C13 and C4 acting faithfullyC13:C452,313T4

### Groups of order 78

LabelIDTr ID
C13⋊C6The semidirect product of C13 and C6 acting faithfullyC13:C678,113T5

### Groups of order 156

LabelIDTr ID
F13Frobenius group; = C13C12 = AGL1(𝔽13) = Aut(D13) = Hol(C13)F13156,713T6

### Groups of order 14

LabelIDTr ID
C14Cyclic groupC1414,214T1
D7Dihedral groupD714,114T2

### Groups of order 28

LabelIDTr ID
D14Dihedral group; = C2×D7D1428,314T3

### Groups of order 42

LabelIDTr ID
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)F742,114T4
C2×C7⋊C3Direct product of C2 and C7⋊C3C2xC7:C342,214T5

### Groups of order 56

LabelIDTr ID
F8Frobenius group; = C23C7 = AGL1(𝔽8)F856,1114T6

### Groups of order 84

LabelIDTr ID
C2×F7Direct product of C2 and F7; = Aut(D14) = Hol(C14)C2xF784,714T7

### Groups of order 98

LabelIDTr ID
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)C7xD798,314T8

### Groups of order 112

LabelIDTr ID
C2×F8Direct product of C2 and F8C2xF8112,4114T9

### Groups of order 168

LabelIDTr ID
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simpleGL(3,2)168,4214T10
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)AGammaL(1,8)168,4314T11

### Groups of order 196

LabelIDTr ID
C72⋊C4The semidirect product of C72 and C4 acting faithfullyC7^2:C4196,814T12
D72Direct product of D7 and D7D7^2196,914T13

### Groups of order 294

LabelIDTr ID
C74F72nd semidirect product of C7 and F7 acting via F7/D7=C3C7:4F7294,1214T14
C72⋊S3The semidirect product of C72 and S3 acting faithfullyC7^2:S3294,714T15

### Groups of order 336

LabelIDTr ID
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,20814T16
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)C2xGL(3,2)336,20914T17
C2×AΓL1(𝔽8)Direct product of C2 and AΓL1(𝔽8)C2xAGammaL(1,8)336,21014T18
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)C2xGL(3,2)336,20914T19

### Groups of order 392

LabelIDTr ID
D7≀C2Wreath product of D7 by C2D7wrC2392,3714T20

### Groups of order 448

LabelIDTr ID
C23⋊F82nd semidirect product of C23 and F8 acting via F8/C23=C7C2^3:F8448,139414T21

### Groups of order 15

LabelIDTr ID
C15Cyclic groupC1515,115T1

### Groups of order 30

LabelIDTr ID
D15Dihedral groupD1530,315T2
C3×D5Direct product of C3 and D5C3xD530,215T3
C5×S3Direct product of C5 and S3C5xS330,115T4

### Groups of order 60

LabelIDTr ID
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,515T5
C3⋊F5The semidirect product of C3 and F5 acting via F5/D5=C2C3:F560,715T6
S3×D5Direct product of S3 and D5S3xD560,815T7
C3×F5Direct product of C3 and F5C3xF560,615T8

### Groups of order 75

LabelIDTr ID
C52⋊C3The semidirect product of C52 and C3 acting faithfullyC5^2:C375,215T9

### Groups of order 120

LabelIDTr ID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3415T10
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)S3xF5120,3615T11

### Groups of order 150

LabelIDTr ID
C52⋊C6The semidirect product of C52 and C6 acting faithfullyC5^2:C6150,615T12
C52⋊S3The semidirect product of C52 and S3 acting faithfullyC5^2:S3150,515T13
15T14

### Groups of order 180

LabelIDTr ID
C3×A5Direct product of C3 and A5; = GL2(𝔽4)C3xA5180,1915T15
15T16

### Groups of order 300

LabelIDTr ID
C52⋊Dic3The semidirect product of C52 and Dic3 acting faithfullyC5^2:Dic3300,2315T17
C52⋊D6The semidirect product of C52 and D6 acting faithfullyC5^2:D6300,2515T18
C52⋊C12The semidirect product of C52 and C12 acting faithfullyC5^2:C12300,2415T19

### Groups of order 360

LabelIDTr ID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simpleA6360,11815T20
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5GammaL(2,4)360,12015T21
15T22
S3×A5Direct product of S3 and A5S3xA5360,12115T23
C3×S5Direct product of C3 and S5C3xS5360,11915T24

### Groups of order 375

LabelIDTr ID
C5×C52⋊C3Direct product of C5 and C52⋊C3; = AΣL1(𝔽125)C5xC5^2:C3375,615T25

### Groups of order 405

LabelIDTr ID
C34⋊C5The semidirect product of C34 and C5 acting faithfullyC3^4:C5405,1515T26

### Groups of order 16

LabelIDTr ID
C16Cyclic groupC1616,116T1
C22×C4Abelian group of type [2,2,4]C2^2xC416,1016T2
C24Elementary abelian group of type [2,2,2,2]C2^416,1416T3
C42Abelian group of type [4,4]C4^216,216T4
C2×C8Abelian group of type [2,8]C2xC816,516T5
M4(2)Modular maximal-cyclic group; = C83C2M4(2)16,616T6
C2×Q8Direct product of C2 and Q8C2xQ816,1216T7
C4⋊C4The semidirect product of C4 and C4 acting via C4/C2=C2C4:C416,416T8
C2×D4Direct product of C2 and D4C2xD416,1116T9
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C2C2^2:C416,316T10
C4○D4Pauli group = central product of C4 and D4C4oD416,1316T11
SD16Semidihedral group; = Q8C2 = QD16SD1616,816T12
D8Dihedral groupD816,716T13
Q16Generalised quaternion group; = C8.C2 = Dic4Q1616,916T14

### Groups of order 32

LabelIDTr ID
C2×M4(2)Direct product of C2 and M4(2)C2xM4(2)32,3716T15
C8○D4Central product of C8 and D4C8oD432,3816T16
C42⋊C21st semidirect product of C42 and C2 acting faithfullyC4^2:C232,2416T17
C2×C4○D4Direct product of C2 and C4○D4C2xC4oD432,4816T18
C4×D4Direct product of C4 and D4C4xD432,2516T19
2- 1+4Extraspecial group; = D4Q8ES-(2,2)32,5016T20
C2×C22⋊C4Direct product of C2 and C22⋊C4C2xC2^2:C432,2216T21
M5(2)Modular maximal-cyclic group; = C163C2M5(2)32,1716T22
2+ 1+4Extraspecial group; = D4D4ES+(2,2)32,4916T23
C22⋊C8The semidirect product of C22 and C8 acting via C8/C4=C2C2^2:C832,516T24
C22×D4Direct product of C22 and D4C2^2xD432,4616T25
D4⋊C41st semidirect product of D4 and C4 acting via C4/C2=C2D4:C432,916T26
C422C22nd semidirect product of C42 and C2 acting faithfullyC4^2:2C232,3316T27
C4≀C2Wreath product of C4 by C2C4wrC232,1116T28
C2×D8Direct product of C2 and D8C2xD832,3916T29
C4.4D44th non-split extension by C4 of D4 acting via D4/C4=C2C4.4D432,3116T30
C22⋊Q8The semidirect product of C22 and Q8 acting via Q8/C4=C2C2^2:Q832,2916T31
C8.C22The non-split extension by C8 of C22 acting faithfullyC8.C2^232,4416T32
C23⋊C4The semidirect product of C23 and C4 acting faithfullyC2^3:C432,616T33
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C2C4:D432,2816T34
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)C8:C2^232,4316T35
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C2C4.D432,716T36
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C2C2^2.D432,3016T37
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)C8:C2^232,4316T38
C22≀C2Wreath product of C22 by C2C2^2wrC232,2716T39
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2C4.10D432,816T40
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C2C4.D432,716T41
C4≀C2Wreath product of C4 by C2C4wrC232,1116T42
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C2C4:D432,2816T43
C4○D8Central product of C4 and D8C4oD832,4216T44
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)C8:C2^232,4316T45
C22≀C2Wreath product of C22 by C2C2^2wrC232,2716T46
C4○D8Central product of C4 and D8C4oD832,4216T47
C2×SD16Direct product of C2 and SD16C2xSD1632,4016T48
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2C8.C432,1516T49
C8.C22The non-split extension by C8 of C22 acting faithfullyC8.C2^232,4416T50
C41D4The semidirect product of C4 and D4 acting via D4/C4=C2C4:1D432,3416T51
C23⋊C4The semidirect product of C23 and C4 acting faithfullyC2^3:C432,616T52
16T53
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C2C2^2.D432,3016T54
SD32Semidihedral group; = C162C2 = QD32SD3232,1916T55
D16Dihedral groupD1632,1816T56

### Groups of order 48

LabelIDTr ID
C4×A4Direct product of C4 and A4C4xA448,3116T57
C22×A4Direct product of C22 and A4C2^2xA448,4916T58
C2×SL2(𝔽3)Direct product of C2 and SL2(𝔽3)C2xSL(2,3)48,3216T59
C4.A4The central extension by C4 of A4C4.A448,3316T60
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetriesC2xS448,4816T61
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)A4:C448,3016T62
C42⋊C3The semidirect product of C42 and C3 acting faithfullyC4^2:C348,316T63
C22⋊A4The semidirect product of C22 and A4 acting via A4/C22=C3C2^2:A448,5016T64
CSU2(𝔽3)Conformal special unitary group on 𝔽32; = Q8.S3CSU(2,3)48,2816T65
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32) = 2O = <2,3,4>GL(2,3)48,2916T66

### Groups of order 64

LabelIDTr ID
C2.C256th central stem extension by C2 of C25C2.C2^564,26616T67
C22.11C247th central extension by C22 of C24C2^2.11C2^464,19916T68
C2×2+ 1+4Direct product of C2 and 2+ 1+4C2xES+(2,2)64,26416T69
Q8○M4(2)Central product of Q8 and M4(2)Q8oM4(2)64,24916T70
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2M4(2).8C2^264,9416T71
C2×C4.D4Direct product of C2 and C4.D4C2xC4.D464,9216T72
C22.29C2415th central stem extension by C22 of C24C2^2.29C2^464,21616T73
C4.9C421st central stem extension by C4 of C42C4.9C4^264,1816T74
C23.37D48th non-split extension by C23 of D4 acting via D4/C22=C2C2^3.37D464,9916T75
C2×C23⋊C4Direct product of C2 and C23⋊C4C2xC2^3:C464,9016T76
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C22C2^3.9D464,2316T77
C2×C23⋊C4Direct product of C2 and C23⋊C4C2xC2^3:C464,9016T78
C243C41st semidirect product of C24 and C4 acting via C4/C2=C2C2^4:3C464,6016T79
D4○D8Central product of D4 and D8D4oD864,25716T80
C22.45C2431st central stem extension by C22 of C24C2^2.45C2^464,23216T81
C22.32C2418th central stem extension by C22 of C24C2^2.32C2^464,21916T82
C22.54C2440th central stem extension by C22 of C24C2^2.54C2^464,24116T83
C23⋊C8The semidirect product of C23 and C8 acting via C8/C2=C4C2^3:C864,416T84
16T85
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2M4(2).8C2^264,9416T86
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C22C2^3:3D464,21516T87
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C22C2^3.9D464,2316T88
C2×C8⋊C22Direct product of C2 and C8⋊C22C2xC8:C2^264,25416T89
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2M4(2):4C464,2516T90
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C22C2^3.9D464,2316T91
C2×C23⋊C4Direct product of C2 and C23⋊C4C2xC2^3:C464,9016T92
16T93
16T94
C24.4C42nd non-split extension by C24 of C4 acting via C4/C2=C2C2^4.4C464,8816T95
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C22C2^3.9D464,2316T96
C232Q82nd semidirect product of C23 and Q8 acting via Q8/C2=C22C2^3:2Q864,22416T97
C24⋊C224th semidirect product of C24 and C22 acting faithfullyC2^4:C2^264,24216T98
C2×C4.D4Direct product of C2 and C4.D4C2xC4.D464,9216T99
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2D8:C2^264,25616T100
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22C2^3.C2^364,9116T101
C2×C23⋊C4Direct product of C2 and C23⋊C4C2xC2^3:C464,9016T102
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2M4(2).C464,11116T103
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4C2^3.C864,3016T104
C2×C22≀C2Direct product of C2 and C22≀C2C2xC2^2wrC264,20216T105
C42⋊C221st semidirect product of C42 and C22 acting faithfullyC4^2:C2^264,10216T106
16T107
C4.10C422nd central stem extension by C4 of C42C4.10C4^264,1916T108
D42Direct product of D4 and D4D4^264,22616T109
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2M4(2):4C464,2516T110
C2×C4≀C2Direct product of C2 and C4≀C2C2xC4wrC264,10116T111
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22C2^3.C2^364,9116T112
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2C8.26D464,12516T113
C8○D8Central product of C8 and D8C8oD864,12416T114
D45D41st semidirect product of D4 and D4 acting through Inn(D4)D4:5D464,22716T115
D4○SD16Central product of D4 and SD16D4oSD1664,25816T116
C22.19C245th central stem extension by C22 of C24C2^2.19C2^464,20616T117
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2D8:C2^264,25616T118
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C22C2^3:3D464,21516T119
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22C2^3.C2^364,9116T120
C426C43rd semidirect product of C42 and C4 acting via C4/C2=C2C4^2:6C464,2016T121
C42⋊C221st semidirect product of C42 and C22 acting faithfullyC4^2:C2^264,10216T122
C4.9C421st central stem extension by C4 of C42C4.9C4^264,1816T123
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2C8.C864,4516T124
C16⋊C42nd semidirect product of C16 and C4 acting faithfullyC16:C464,2816T125
C22⋊D8The semidirect product of C22 and D8 acting via D8/D4=C2C2^2:D864,12816T126
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)C2wrC2^264,13816T127
16T128
16T129
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)C2wrC464,3216T130
C42.C42nd non-split extension by C42 of C4 acting faithfullyC4^2.C464,3616T131
D4.3D43rd non-split extension by D4 of D4 acting via D4/C4=C2D4.3D464,15216T132
D4.4D44th non-split extension by D4 of D4 acting via D4/C4=C2D4.4D464,15316T133
C16⋊C22The semidirect product of C16 and C22 acting faithfullyC16:C2^264,19016T134
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)D4:4D464,13416T135
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22C8.Q864,4616T136
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2D4.10D464,13716T137
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2D4.9D464,13616T138
C42.3C43rd non-split extension by C42 of C4 acting faithfullyC4^2.3C464,3716T139
C23.D42nd non-split extension by C23 of D4 acting faithfullyC2^3.D464,3316T140
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)D4:4D464,13416T141
16T142
C42⋊C42nd semidirect product of C42 and C4 acting faithfullyC4^2:C464,3416T143
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfullyM5(2):C264,4216T144
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2D4.9D464,13616T145
C23.7D47th non-split extension by C23 of D4 acting faithfullyC2^3.7D464,13916T146
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)C2wrC2^264,13816T147
C23.D42nd non-split extension by C23 of D4 acting faithfullyC2^3.D464,3316T148
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)C2wrC2^264,13816T149
16T150
C42.C42nd non-split extension by C42 of C4 acting faithfullyC4^2.C464,3616T151
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)D4:4D464,13416T152
C23.D42nd non-split extension by C23 of D4 acting faithfullyC2^3.D464,3316T153
C423C43rd semidirect product of C42 and C4 acting faithfullyC4^2:3C464,3516T154
C22⋊SD16The semidirect product of C22 and SD16 acting via SD16/D4=C2C2^2:SD1664,13116T155
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2D8:2C464,4116T156
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)C2wrC464,3216T157
16T158
16T159
C23.D42nd non-split extension by C23 of D4 acting faithfullyC2^3.D464,3316T160
C23.31D42nd non-split extension by C23 of D4 acting via D4/C22=C2C2^3.31D464,916T161
D4.8D43rd non-split extension by D4 of D4 acting via D4/C22=C2D4.8D464,13516T162
C22.SD161st non-split extension by C22 of SD16 acting via SD16/Q8=C2C2^2.SD1664,816T163
D4.8D43rd non-split extension by D4 of D4 acting via D4/C22=C2D4.8D464,13516T164
C23.7D47th non-split extension by C23 of D4 acting faithfullyC2^3.7D464,13916T165
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)C2wrC464,3216T166
C42⋊C42nd semidirect product of C42 and C4 acting faithfullyC4^2:C464,3416T167
16T168
16T169
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)C2wrC464,3216T170
16T171
16T172
C23.7D47th non-split extension by C23 of D4 acting faithfullyC2^3.7D464,13916T173
C423C43rd semidirect product of C42 and C4 acting faithfullyC4^2:3C464,3516T174
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2D4.9D464,13616T175
C423C43rd semidirect product of C42 and C4 acting faithfullyC4^2:3C464,3516T176
C23.7D47th non-split extension by C23 of D4 acting faithfullyC2^3.7D464,13916T177

### Groups of order 80

LabelIDTr ID
C24⋊C5The semidirect product of C24 and C5 acting faithfullyC2^4:C580,4916T178

### Groups of order 96

LabelIDTr ID
D4×A4Direct product of D4 and A4D4xA496,19716T179
D4.A4The non-split extension by D4 of A4 acting through Inn(D4)D4.A496,20216T180
C4×S4Direct product of C4 and S4C4xS496,18616T181
C22×S4Direct product of C22 and S4C2^2xS496,22616T182
C24⋊C61st semidirect product of C24 and C6 acting faithfullyC2^4:C696,7016T183
C42⋊C61st semidirect product of C42 and C6 acting faithfullyC4^2:C696,7116T184
C23.A42nd non-split extension by C23 of A4 acting faithfullyC2^3.A496,7216T185
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)A4:D496,19516T186
Q8.D62nd non-split extension by Q8 of D6 acting via D6/C2=S3Q8.D696,19016T187
C2×GL2(𝔽3)Direct product of C2 and GL2(𝔽3)C2xGL(2,3)96,18916T188
C4.6S43rd central extension by C4 of S4C4.6S496,19216T189
C4.3S43rd non-split extension by C4 of S4 acting via S4/A4=C2C4.3S496,19316T190
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2C4:S496,18716T191
Q8.D62nd non-split extension by Q8 of D6 acting via D6/C2=S3Q8.D696,19016T192
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)A4:D496,19516T193
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S3C2^2:S496,22716T194
C42⋊S3The semidirect product of C42 and S3 acting faithfullyC4^2:S396,6416T195

### Groups of order 112

LabelIDTr ID
C2×F8Direct product of C2 and F8C2xF8112,4116T196

### Groups of order 128

LabelIDTr ID
2+ 1+6Extraspecial group; = Q82- 1+4ES+(2,3)128,232616T197
C22.73C2554th central stem extension by C22 of C25C2^2.73C2^5128,221616T198
C23.C243rd non-split extension by C23 of C24 acting via C24/C22=C22C2^3.C2^4128,161516T199
M4(2).24C236th non-split extension by M4(2) of C23 acting via C23/C22=C2M4(2).24C2^3128,162016T200
C22.79C2560th central stem extension by C22 of C25C2^2.79C2^5128,222216T201
C23.C243rd non-split extension by C23 of C24 acting via C24/C22=C22C2^3.C2^4128,161516T202
16T203
D8⋊C236th semidirect product of D8 and C23 acting via C23/C22=C2D8:C2^3128,231716T204
M4(2).51D41st non-split extension by M4(2) of D4 acting through Inn(M4(2))M4(2).51D4128,168816T205
C42⋊C234th semidirect product of C42 and C23 acting faithfullyC4^2:C2^3128,226416T206
2+ 1+46C45th semidirect product of 2+ 1+4 and C4 acting via C4/C2=C2ES+(2,2):6C4128,163316T207
C25.C229th non-split extension by C25 of C22 acting faithfullyC2^5.C2^2128,62116T208
(C2×C8)⋊D43rd semidirect product of C2×C8 and D4 acting faithfully(C2xC8):D4128,62316T209
C25.C229th non-split extension by C25 of C22 acting faithfullyC2^5.C2^2128,62116T210
(C2×C4)≀C2Wreath product of C2×C4 by C2(C2xC4)wrC2128,62816T211
C24.C231st non-split extension by C24 of C23 acting faithfullyC2^4.C2^3128,56016T212
C2≀C4⋊C26th semidirect product of C2≀C4 and C2 acting faithfullyC2wrC4:C2128,85416T213
M4(2)⋊C233rd semidirect product of M4(2) and C23 acting via C23/C2=C22M4(2):C2^3128,175116T214
M4(2).41D45th non-split extension by M4(2) of D4 acting via D4/C22=C2M4(2).41D4128,59316T215
M4(2)⋊21D48th semidirect product of M4(2) and D4 acting via D4/C22=C2M4(2):21D4128,64616T216
C25.C229th non-split extension by C25 of C22 acting faithfullyC2^5.C2^2128,62116T217
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T218
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T219
C8.5M4(2)5th non-split extension by C8 of M4(2) acting via M4(2)/C4=C22C8.5M4(2)128,89716T220
C42.5D45th non-split extension by C42 of D4 acting faithfullyC4^2.5D4128,63616T221
C42⋊D41st semidirect product of C42 and D4 acting faithfullyC4^2:D4128,64316T222
C23.7C247th non-split extension by C23 of C24 acting via C24/C22=C22C2^3.7C2^4128,175716T223
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T224
C42.426D459th non-split extension by C42 of D4 acting via D4/C22=C2C4^2.426D4128,63816T225
C41D4.C45th non-split extension by C41D4 of C4 acting faithfullyC4:1D4.C4128,86616T226
C2×C2≀C4Direct product of C2 and C2≀C4C2xC2wrC4128,85016T227
C24⋊C81st semidirect product of C24 and C8 acting via C8/C2=C4C2^4:C8128,4816T228
C24.C231st non-split extension by C24 of C23 acting faithfullyC2^4.C2^3128,56016T229
C24.78D433rd non-split extension by C24 of D4 acting via D4/C2=C22C2^4.78D4128,63016T230
C24.C231st non-split extension by C24 of C23 acting faithfullyC2^4.C2^3128,56016T231
C4○D4.D43rd non-split extension by C4○D4 of D4 acting via D4/C2=C22C4oD4.D4128,52716T232
C24.6(C2×C4)6th non-split extension by C24 of C2×C4 acting faithfullyC2^4.6(C2xC4)128,56116T233
C24.39D439th non-split extension by C24 of D4 acting faithfullyC2^4.39D4128,85916T234
C2×C42⋊C4Direct product of C2 and C42⋊C4C2xC4^2:C4128,85616T235
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T236
C24.78D433rd non-split extension by C24 of D4 acting via D4/C2=C22C2^4.78D4128,63016T237
(C2×C8)⋊4D44th semidirect product of C2×C8 and D4 acting faithfully(C2xC8):4D4128,64216T238
C23.9C249th non-split extension by C23 of C24 acting via C24/C22=C22C2^3.9C2^4128,175916T239
C25⋊C41st semidirect product of C25 and C4 acting faithfullyC2^5:C4128,51316T240
C24⋊C232nd semidirect product of C24 and C23 acting faithfullyC2^4:C2^3128,175816T241
C42.C81st non-split extension by C42 of C8 acting via C8/C2=C4C4^2.C8128,5916T242
C4○C2≀C4Central product of C4 and C2≀C4C4oC2wrC4128,85216T243
C4.4D4⋊C46th semidirect product of C4.4D4 and C4 acting faithfullyC4.4D4:C4128,86016T244
C2×C2≀C22Direct product of C2 and C2≀C22C2xC2wrC2^2128,175516T245
16T246
C25.C229th non-split extension by C25 of C22 acting faithfullyC2^5.C2^2128,62116T247
C2×C42⋊C4Direct product of C2 and C42⋊C4C2xC4^2:C4128,85616T248
C24.78D433rd non-split extension by C24 of D4 acting via D4/C2=C22C2^4.78D4128,63016T249
C24.39D439th non-split extension by C24 of D4 acting faithfullyC2^4.39D4128,85916T250
M4(2)⋊19D46th semidirect product of M4(2) and D4 acting via D4/C22=C2M4(2):19D4128,61616T251
C25.3C43rd non-split extension by C25 of C4 acting faithfullyC2^5.3C4128,19416T252
C25.C44th non-split extension by C25 of C4 acting faithfullyC2^5.C4128,51516T253
C24.150D45th non-split extension by C24 of D4 acting via D4/C22=C2C2^4.150D4128,23616T254
C24.177D432nd non-split extension by C24 of D4 acting via D4/C22=C2C2^4.177D4128,173516T255
D16⋊C4The semidirect product of D16 and C4 acting faithfully; = Aut(D16) = Hol(C16)D16:C4128,91316T256
C24⋊C81st semidirect product of C24 and C8 acting via C8/C2=C4C2^4:C8128,4816T257
16T258
C2×C2≀C4Direct product of C2 and C2≀C4C2xC2wrC4128,85016T259
C8.32D89th non-split extension by C8 of D8 acting via D8/D4=C2C8.32D8128,6816T260
C2×C2≀C4Direct product of C2 and C2≀C4C2xC2wrC4128,85016T261
M4(2)⋊C233rd semidirect product of M4(2) and C23 acting via C23/C2=C22M4(2):C2^3128,175116T262
C4.4D4⋊C46th semidirect product of C4.4D4 and C4 acting faithfullyC4.4D4:C4128,86016T263
C42.313C23174th non-split extension by C42 of C23 acting via C23/C2=C22C4^2.313C2^3128,175016T264
C2×D44D4Direct product of C2 and D44D4C2xD4:4D4128,174616T265
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T266
M4(2).47D411st non-split extension by M4(2) of D4 acting via D4/C22=C2M4(2).47D4128,63516T267
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T268
C42.12C2312nd non-split extension by C42 of C23 acting faithfullyC4^2.12C2^3128,175316T269
C23.7C247th non-split extension by C23 of C24 acting via C24/C22=C22C2^3.7C2^4128,175716T270
C2×C2≀C22Direct product of C2 and C2≀C22C2xC2wrC2^2128,175516T271
C24.6(C2×C4)6th non-split extension by C24 of C2×C4 acting faithfullyC2^4.6(C2xC4)128,56116T272
C2×C2≀C4Direct product of C2 and C2≀C4C2xC2wrC4128,85016T273
C24.68D423rd non-split extension by C24 of D4 acting via D4/C2=C22C2^4.68D4128,55116T274
C25⋊C41st semidirect product of C25 and C4 acting faithfullyC2^5:C4128,51316T275
C42⋊D41st semidirect product of C42 and D4 acting faithfullyC4^2:D4128,64316T276
C24⋊C232nd semidirect product of C24 and C23 acting faithfullyC2^4:C2^3128,175816T277
M4(2)⋊21D48th semidirect product of M4(2) and D4 acting via D4/C22=C2M4(2):21D4128,64616T278
(C2×C8)⋊D43rd semidirect product of C2×C8 and D4 acting faithfully(C2xC8):D4128,62316T279
C4○C2≀C4Central product of C4 and C2≀C4C4oC2wrC4128,85216T280
C2≀C4⋊C26th semidirect product of C2≀C4 and C2 acting faithfullyC2wrC4:C2128,85416T281
C42.12C2312nd non-split extension by C42 of C23 acting faithfullyC4^2.12C2^3128,175316T282
C2×C2≀C4Direct product of C2 and C2≀C4C2xC2wrC4128,85016T283
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T284
C41D4.C45th non-split extension by C41D4 of C4 acting faithfullyC4:1D4.C4128,86616T285
C24.C231st non-split extension by C24 of C23 acting faithfullyC2^4.C2^3128,56016T286
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T287
M4(2)⋊C233rd semidirect product of M4(2) and C23 acting via C23/C2=C22M4(2):C2^3128,175116T288
C8≀C2Wreath product of C8 by C2C8wrC2128,6716T289
C4○D4.D43rd non-split extension by C4○D4 of D4 acting via D4/C2=C22C4oD4.D4128,52716T290
(C2×C42)⋊C48th semidirect product of C2×C42 and C4 acting faithfully(C2xC4^2):C4128,55916T291
C4○C2≀C4Central product of C4 and C2≀C4C4oC2wrC4128,85216T292
C4⋊Q829C424th semidirect product of C4⋊Q8 and C4 acting via C4/C2=C2C4:Q8:29C4128,85816T293
C8⋊C417C412nd semidirect product of C8⋊C4 and C4 acting via C4/C2=C2C8:C4:17C4128,57316T294
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T295
D8○D8Central product of D8 and D8D8oD8128,202416T296
C24.39D439th non-split extension by C24 of D4 acting faithfullyC2^4.39D4128,85916T297
(C2×C8)⋊4D44th semidirect product of C2×C8 and D4 acting faithfully(C2xC8):4D4128,64216T298
M4(2)⋊19D46th semidirect product of M4(2) and D4 acting via D4/C22=C2M4(2):19D4128,61616T299
(C2×D4).135D497th non-split extension by C2×D4 of D4 acting via D4/C2=C22(C2xD4).135D4128,86416T300
C24⋊C232nd semidirect product of C24 and C23 acting faithfullyC2^4:C2^3128,175816T301
C24.24D424th non-split extension by C24 of D4 acting faithfullyC2^4.24D4128,61916T302
C42.313C23174th non-split extension by C42 of C23 acting via C23/C2=C22C4^2.313C2^3128,175016T303
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T304
C42⋊D41st semidirect product of C42 and D4 acting faithfullyC4^2:D4128,64316T305
C24.C82nd non-split extension by C24 of C8 acting via C8/C2=C4C2^4.C8128,5216T306
C42.5D45th non-split extension by C42 of D4 acting faithfullyC4^2.5D4128,63616T307
D811D45th semidirect product of D8 and D4 acting via D4/C22=C2D8:11D4128,202016T308
C24⋊C232nd semidirect product of C24 and C23 acting faithfullyC2^4:C2^3128,175816T309
C24.39D439th non-split extension by C24 of D4 acting faithfullyC2^4.39D4128,85916T310
C42.426D459th non-split extension by C42 of D4 acting via D4/C22=C2C4^2.426D4128,63816T311
M4(2).37D41st non-split extension by M4(2) of D4 acting via D4/C22=C2M4(2).37D4128,180016T312
C23.9C249th non-split extension by C23 of C24 acting via C24/C22=C22C2^3.9C2^4128,175916T313
(C2×C42)⋊C48th semidirect product of C2×C42 and C4 acting faithfully(C2xC4^2):C4128,55916T314
C2≀C4⋊C26th semidirect product of C2≀C4 and C2 acting faithfullyC2wrC4:C2128,85416T315
C24.C231st non-split extension by C24 of C23 acting faithfullyC2^4.C2^3128,56016T316
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T317
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T318
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T319
C24⋊C232nd semidirect product of C24 and C23 acting faithfullyC2^4:C2^3128,175816T320
C42.427D460th non-split extension by C42 of D4 acting via D4/C22=C2C4^2.427D4128,66416T321
C4⋊Q829C424th semidirect product of C4⋊Q8 and C4 acting via C4/C2=C2C4:Q8:29C4128,85816T322
C24.4Q83rd non-split extension by C24 of Q8 acting via Q8/C2=C22C2^4.4Q8128,3616T323
C24.36D436th non-split extension by C24 of D4 acting faithfullyC2^4.36D4128,85316T324
C23≀C2Wreath product of C23 by C2C2^3wrC2128,157816T325
C24.28D428th non-split extension by C24 of D4 acting faithfullyC2^4.28D4128,64516T326
(C2×D4).135D497th non-split extension by C2×D4 of D4 acting via D4/C2=C22(C2xD4).135D4128,86416T327
D86D45th semidirect product of D8 and D4 acting via D4/C4=C2D8:6D4128,202316T328
C24⋊C232nd semidirect product of C24 and C23 acting faithfullyC2^4:C2^3128,175816T329
C24.D41st non-split extension by C24 of D4 acting faithfullyC2^4.D4128,7516T330
M4(2)⋊5D45th semidirect product of M4(2) and D4 acting via D4/C2=C22M4(2):5D4128,74016T331
C24⋊Q8The semidirect product of C24 and Q8 acting faithfullyC2^4:Q8128,76416T332
C242Q81st semidirect product of C24 and Q8 acting via Q8/C2=C22C2^4:2Q8128,76116T333
C42.32Q832nd non-split extension by C42 of Q8 acting via Q8/C2=C22C4^2.32Q8128,83416T334
C42.D41st non-split extension by C42 of D4 acting faithfullyC4^2.D4128,13416T335
C426D46th semidirect product of C42 and D4 acting faithfullyC4^2:6D4128,93216T336
C42.17D417th non-split extension by C42 of D4 acting faithfullyC4^2.17D4128,93616T337
C42.8D48th non-split extension by C42 of D4 acting faithfullyC4^2.8D4128,76316T338
C24.D41st non-split extension by C24 of D4 acting faithfullyC2^4.D4128,7516T339
C426D46th semidirect product of C42 and D4 acting faithfullyC4^2:6D4128,93216T340
16T341
C243D43rd semidirect product of C24 and D4 acting faithfullyC2^4:3D4128,93116T342
C42.D41st non-split extension by C42 of D4 acting faithfullyC4^2.D4128,13416T343
C42.13D413rd non-split extension by C42 of D4 acting faithfullyC4^2.13D4128,93016T344
C424D44th semidirect product of C42 and D4 acting faithfullyC4^2:4D4128,92916T345
C8.29D86th non-split extension by C8 of D8 acting via D8/D4=C2C8.29D8128,9116T346
C242Q81st semidirect product of C24 and Q8 acting via Q8/C2=C22C2^4:2Q8128,76116T347
C23.SD161st non-split extension by C23 of SD16 acting via SD16/C2=D4C2^3.SD16128,7316T348
C42.15D415th non-split extension by C42 of D4 acting faithfullyC4^2.15D4128,93416T349
C24⋊D41st semidirect product of C24 and D4 acting faithfullyC2^4:D4128,75316T350
D83Q83rd semidirect product of D8 and Q8 acting via Q8/C4=C2D8:3Q8128,96216T351
C426D46th semidirect product of C42 and D4 acting faithfullyC4^2:6D4128,93216T352
C42.8D48th non-split extension by C42 of D4 acting faithfullyC4^2.8D4128,76316T353
C24⋊Q8The semidirect product of C24 and Q8 acting faithfullyC2^4:Q8128,76416T354
C4.C4≀C29th non-split extension by C4 of C4≀C2 acting via C4≀C2/C42=C2C4.C4wrC2128,8716T355
C8.24D81st non-split extension by C8 of D8 acting via D8/D4=C2C8.24D8128,8916T356
C42.15D415th non-split extension by C42 of D4 acting faithfullyC4^2.15D4128,93416T357
C24⋊Q8The semidirect product of C24 and Q8 acting faithfullyC2^4:Q8128,76416T358
C426D46th semidirect product of C42 and D4 acting faithfullyC4^2:6D4128,93216T359
C42.131D4113rd non-split extension by C42 of D4 acting via D4/C2=C22C4^2.131D4128,78216T360
C42.4D44th non-split extension by C42 of D4 acting faithfullyC4^2.4D4128,13716T361
C8⋊C4⋊C41st semidirect product of C8⋊C4 and C4 acting faithfullyC8:C4:C4128,13816T362
(C4×C8)⋊6C46th semidirect product of C4×C8 and C4 acting faithfully(C4xC8):6C4128,14116T363
C24⋊D41st semidirect product of C24 and D4 acting faithfullyC2^4:D4128,75316T364
C243D43rd semidirect product of C24 and D4 acting faithfullyC2^4:3D4128,93116T365
C426D46th semidirect product of C42 and D4 acting faithfullyC4^2:6D4128,93216T366
M4(2)⋊5D45th semidirect product of M4(2) and D4 acting via D4/C2=C22M4(2):5D4128,74016T367
C24⋊Q8The semidirect product of C24 and Q8 acting faithfullyC2^4:Q8128,76416T368
C24.Q8The non-split extension by C24 of Q8 acting faithfullyC2^4.Q8128,80116T369
Q8≀C2Wreath product of Q8 by C2Q8wrC2128,93716T370
C23.D81st non-split extension by C23 of D8 acting via D8/C2=D4C2^3.D8128,7116T371
C24.4C234th non-split extension by C24 of C23 acting faithfullyC2^4.4C2^3128,83616T372
C24⋊D41st semidirect product of C24 and D4 acting faithfullyC2^4:D4128,75316T373
M5(2).C228th non-split extension by M5(2) of C22 acting faithfullyM5(2).C2^2128,97016T374
C8⋊C45C45th semidirect product of C8⋊C4 and C4 acting faithfullyC8:C4:5C4128,14416T375
C2≀D4Wreath product of C2 by D4C2wrD4128,92816T376
C41D4⋊C42nd semidirect product of C41D4 and C4 acting faithfullyC4:1D4:C4128,14016T377
(C4×C8).C46th non-split extension by C4×C8 of C4 acting faithfully(C4xC8).C4128,14216T378
D83D42nd semidirect product of D8 and D4 acting via D4/C4=C2D8:3D4128,94516T379
C42.13D413rd non-split extension by C42 of D4 acting faithfullyC4^2.13D4128,93016T380
C243D43rd semidirect product of C24 and D4 acting faithfullyC2^4:3D4128,93116T381
C422D42nd semidirect product of C42 and D4 acting faithfullyC4^2:2D4128,74216T382
C24.4C234th non-split extension by C24 of C23 acting faithfullyC2^4.4C2^3128,83616T383
C24⋊Q8The semidirect product of C24 and Q8 acting faithfullyC2^4:Q8128,76416T384
D8⋊D4The semidirect product of D8 and D4 acting via D4/C2=C22D8:D4128,92216T385
C243D43rd semidirect product of C24 and D4 acting faithfullyC2^4:3D4128,93116T386
C42.D41st non-split extension by C42 of D4 acting faithfullyC4^2.D4128,13416T387
C2≀D4Wreath product of C2 by D4C2wrD4128,92816T388
C24.9D49th non-split extension by C24 of D4 acting faithfullyC2^4.9D4128,33216T389
C2≀D4Wreath product of C2 by D4C2wrD4128,92816T390
16T391
C24⋊D41st semidirect product of C24 and D4 acting faithfullyC2^4:D4128,75316T392
C2≀D4Wreath product of C2 by D4C2wrD4128,92816T393
C243D43rd semidirect product of C24 and D4 acting faithfullyC2^4:3D4128,93116T394
C2≀D4Wreath product of C2 by D4C2wrD4128,92816T395
16T396
C42.3D43rd non-split extension by C42 of D4 acting faithfullyC4^2.3D4128,13616T397
C42.2D42nd non-split extension by C42 of D4 acting faithfullyC4^2.2D4128,13516T398
C424D44th semidirect product of C42 and D4 acting faithfullyC4^2:4D4128,92916T399
16T400
C2≀D4Wreath product of C2 by D4C2wrD4128,92816T401
C426D46th semidirect product of C42 and D4 acting faithfullyC4^2:6D4128,93216T402
C24.11Q810th non-split extension by C24 of Q8 acting via Q8/C2=C22C2^4.11Q8128,82316T403
C42.15D415th non-split extension by C42 of D4 acting faithfullyC4^2.15D4128,93416T404
C23⋊SD161st semidirect product of C23 and SD16 acting via SD16/C2=D4C2^3:SD16128,32816T405
C422D42nd semidirect product of C42 and D4 acting faithfullyC4^2:2D4128,74216T406
C42.17D417th non-split extension by C42 of D4 acting faithfullyC4^2.17D4128,93616T407
C429D43rd semidirect product of C42 and D4 acting via D4/C2=C22C4^2:9D4128,73416T408
C23⋊D8The semidirect product of C23 and D8 acting via D8/C2=D4C2^3:D8128,32716T409
C424D44th semidirect product of C42 and D4 acting faithfullyC4^2:4D4128,92916T410
M4(2).8D48th non-split extension by M4(2) of D4 acting via D4/C2=C22M4(2).8D4128,78016T411
(C2×C8).D45th non-split extension by C2×C8 of D4 acting faithfully(C2xC8).D4128,81316T412
C41D4⋊C42nd semidirect product of C41D4 and C4 acting faithfullyC4:1D4:C4128,14016T413

### Groups of order 144

LabelIDTr ID
A42Direct product of A4 and A4; = PΩ+4(𝔽3)A4^2144,18416T414

### Groups of order 160

LabelIDTr ID
C24⋊D5The semidirect product of C24 and D5 acting faithfullyC2^4:D5160,23416T415

### Groups of order 192

LabelIDTr ID
C2×C24⋊C6Direct product of C2 and C24⋊C6C2xC2^4:C6192,100016T416
C24⋊A43rd semidirect product of C24 and A4 acting faithfullyC2^4:A4192,100916T417
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6C2^4:C12192,19116T418
C24⋊A43rd semidirect product of C24 and A4 acting faithfullyC2^4:A4192,100916T419
C24.6A46th non-split extension by C24 of A4 acting faithfullyC2^4.6A4192,100816T420
D4×S4Direct product of D4 and S4D4xS4192,147216T421
D4.4S41st non-split extension by D4 of S4 acting through Inn(D4)D4.4S4192,148516T422
2+ 1+4.3C6The non-split extension by 2+ 1+4 of C6 acting via C6/C2=C3ES+(2,2).3C6192,150916T423
C2×C23⋊A4Direct product of C2 and C23⋊A4C2xC2^3:A4192,150816T424
C2≀A4Wreath product of C2 by A4C2wrA4192,20116T425
2+ 1+4.C61st non-split extension by 2+ 1+4 of C6 acting faithfullyES+(2,2).C6192,20216T426
C2≀A4Wreath product of C2 by A4C2wrA4192,20116T427
2+ 1+4.C61st non-split extension by 2+ 1+4 of C6 acting faithfullyES+(2,2).C6192,20216T428
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153816T429
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfullyC4^2:Dic3192,18516T430
C42⋊D6The semidirect product of C42 and D6 acting faithfullyC4^2:D6192,95616T431
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfullyC2^4:Dic3192,18416T432
16T433
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149516T434
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)C2^4:D6192,95516T435
16T436
C245A45th semidirect product of C24 and A4 acting faithfullyC2^4:5A4192,102416T437
C24.7A47th non-split extension by C24 of A4 acting faithfullyC2^4.7A4192,102116T438
C23.SL2(𝔽3)1st non-split extension by C23 of SL2(𝔽3) acting via SL2(𝔽3)/C2=A4C2^3.SL(2,3)192,416T439
C42⋊A4The semidirect product of C42 and A4 acting faithfullyC4^2:A4192,102316T440
C23.S44th non-split extension by C23 of S4 acting faithfullyC2^3.S4192,149116T441
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)C2^3:S4192,149316T442
Q8.S42nd non-split extension by Q8 of S4 acting via S4/C22=S3Q8.S4192,149216T443
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)Q8:2S4192,149416T444
16T445
Q8.S42nd non-split extension by Q8 of S4 acting via S4/C22=S3Q8.S4192,149216T446

### Groups of order 240

LabelIDTr ID
F16Frobenius group; = C24C15 = AGL1(𝔽16)F16240,19116T447

### Groups of order 288

LabelIDTr ID
A4≀C2Wreath product of A4 by C2A4wrC2288,102516T708
A4×S4Direct product of A4 and S4A4xS4288,102416T709
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)PSO+(4,3)288,102616T710

### Groups of order 320

LabelIDTr ID
C24⋊F5The semidirect product of C24 and F5 acting faithfullyC2^4:F5320,163516T711

### Groups of order 336

LabelIDTr ID
C2×AΓL1(𝔽8)Direct product of C2 and AΓL1(𝔽8)C2xAGammaL(1,8)336,21016T712
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,20816T713
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)C2xGL(3,2)336,20916T714
SL2(𝔽7)Special linear group on 𝔽72; = C2.GL3(𝔽2)SL(2,7)336,11416T715

### Groups of order 480

LabelIDTr ID
F16⋊C2The semidirect product of F16 and C2 acting faithfullyF16:C2480,118816T777

### Groups of order 17

LabelIDTr ID
C17Cyclic groupC1717,117T1

### Groups of order 34

LabelIDTr ID
D17Dihedral groupD1734,117T2

### Groups of order 68

LabelIDTr ID
C17⋊C4The semidirect product of C17 and C4 acting faithfullyC17:C468,317T3

### Groups of order 136

LabelIDTr ID
C17⋊C8The semidirect product of C17 and C8 acting faithfullyC17:C8136,1217T4

### Groups of order 272

LabelIDTr ID
F17Frobenius group; = C17C16 = AGL1(𝔽17) = Aut(D17) = Hol(C17)F17272,5017T5

### Groups of order 18

LabelIDTr ID
C18Cyclic groupC1818,218T1
C3×C6Abelian group of type [3,6]C3xC618,518T2
C3×S3Direct product of C3 and S3; = U2(𝔽2)C3xS318,318T3
C3⋊S3The semidirect product of C3 and S3 acting via S3/C3=C2C3:S318,418T4
D9Dihedral groupD918,118T5

### Groups of order 36

LabelIDTr ID
S3×C6Direct product of C6 and S3S3xC636,1218T6
C3.A4The central extension by C3 of A4C3.A436,318T7
C3×A4Direct product of C3 and A4C3xA436,1118T8
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)S3^236,1018T9
C32⋊C4The semidirect product of C32 and C4 acting faithfullyC3^2:C436,918T10
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)S3^236,1018T11
C2×C3⋊S3Direct product of C2 and C3⋊S3C2xC3:S336,1318T12
D18Dihedral group; = C2×D9D1836,418T13

### Groups of order 54

LabelIDTr ID
C2×3- 1+2Direct product of C2 and 3- 1+2C2xES-(3,1)54,1118T14
C2×He3Direct product of C2 and He3C2xHe354,1018T15
S3×C9Direct product of C9 and S3S3xC954,418T16
S3×C32Direct product of C32 and S3S3xC3^254,1218T17
C9⋊C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)C9:C654,618T18
C3×D9Direct product of C3 and D9C3xD954,318T19
C32⋊C6The semidirect product of C32 and C6 acting faithfullyC3^2:C654,518T20
18T21
18T22
C3×C3⋊S3Direct product of C3 and C3⋊S3C3xC3:S354,1318T23
He3⋊C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)He3:C254,818T24

### Groups of order 72

LabelIDTr ID
C6×A4Direct product of C6 and A4C6xA472,4718T25
C2×C3.A4Direct product of C2 and C3.A4C2xC3.A472,1618T26
C2×C32⋊C4Direct product of C2 and C32⋊C4C2xC3^2:C472,4518T27
F9Frobenius group; = C32C8 = AGL1(𝔽9)F972,3918T28
C2×S32Direct product of C2, S3 and S3C2xS3^272,4618T29
C3×S4Direct product of C3 and S4C3xS472,4218T30
S3×A4Direct product of S3 and A4S3xA472,4418T31
18T32
C3×S4Direct product of C3 and S4C3xS472,4218T33
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)S3wrC272,4018T34
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M9PSU(3,2)72,4118T35
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)S3wrC272,4018T36
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2C3:S472,4318T37
C3.S4The non-split extension by C3 of S4 acting via S4/A4=C2C3.S472,1518T38
18T39
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2C3:S472,4318T40

### Groups of order 108

LabelIDTr ID
C2×C32⋊C6Direct product of C2 and C32⋊C6C2xC3^2:C6108,2518T41
18T42
C3×S32Direct product of C3, S3 and S3C3xS3^2108,3818T43
C3×C32⋊C4Direct product of C3 and C32⋊C4C3xC3^2:C4108,3618T44
C2×C9⋊C6Direct product of C2 and C9⋊C6; = Aut(D18) = Hol(C18)C2xC9:C6108,2618T45
C3×S32Direct product of C3, S3 and S3C3xS3^2108,3818T46
C32.A4The non-split extension by C32 of A4 acting via A4/C22=C3C3^2.A4108,2118T47
C32⋊A4The semidirect product of C32 and A4 acting via A4/C22=C3C3^2:A4108,2218T48
He3⋊C4The semidirect product of He3 and C4 acting faithfullyHe3:C4108,1518T49
S3×D9Direct product of S3 and D9S3xD9108,1618T50
C32⋊D6The semidirect product of C32 and D6 acting faithfullyC3^2:D6108,1718T51
C2×He3⋊C2Direct product of C2 and He3⋊C2C2xHe3:C2108,2818T52
C324D6The semidirect product of C32 and D6 acting via D6/C3=C22C3^2:4D6108,4018T53
C33⋊C42nd semidirect product of C33 and C4 acting faithfullyC3^3:C4108,3718T54
C32⋊D6The semidirect product of C32 and D6 acting faithfullyC3^2:D6108,1718T55
18T56
18T57
S3×C3⋊S3Direct product of S3 and C3⋊S3S3xC3:S3108,3918T58

### Groups of order 144

LabelIDTr ID
C2×F9Direct product of C2 and F9C2xF9144,18518T59
C2×S3×A4Direct product of C2, S3 and A4C2xS3xA4144,19018T60
C6×S4Direct product of C6 and S4C6xS4144,18818T61
A42Direct product of A4 and A4; = PΩ+4(𝔽3)A4^2144,18418T62
C2×S3≀C2Direct product of C2 and S3≀C2C2xS3wrC2144,18618T63
C2×PSU3(𝔽2)Direct product of C2 and PSU3(𝔽2)C2xPSU(3,2)144,18718T64
S3×S4Direct product of S3 and S4; = Hol(C2×C6)S3xS4144,18318T65
C2×C3⋊S4Direct product of C2 and C3⋊S4C2xC3:S4144,18918T66
C2×C3.S4Direct product of C2 and C3.S4C2xC3.S4144,10918T67
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)AGammaL(1,9)144,18218T68
S3×S4Direct product of S3 and S4; = Hol(C2×C6)S3xS4144,18318T69
18T70
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)AGammaL(1,9)144,18218T71
S3×S4Direct product of S3 and S4; = Hol(C2×C6)S3xS4144,18318T72
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)AGammaL(1,9)144,18218T73

### Groups of order 162

LabelIDTr ID
C9×D9Direct product of C9 and D9C9xD9162,318T74
C2×C3≀C3Direct product of C2 and C3≀C3C2xC3wrC3162,2818T75
C3×C32⋊C6Direct product of C3 and C32⋊C6C3xC3^2:C6162,3418T76
S3×He3Direct product of S3 and He3S3xHe3162,3518T77
C3×C32⋊C6Direct product of C3 and C32⋊C6C3xC3^2:C6162,3418T78
C32×C3⋊S3Direct product of C32 and C3⋊S3C3^2xC3:S3162,5218T79
C9⋊C18The semidirect product of C9 and C18 acting via C18/C3=C6C9:C18162,618T80
C3×C32⋊C6Direct product of C3 and C32⋊C6C3xC3^2:C6162,3418T81
C32⋊C18The semidirect product of C32 and C18 acting via C18/C3=C6C3^2:C18162,418T82
C3×C9⋊C6Direct product of C3 and C9⋊C6C3xC9:C6162,3618T83
S3×3- 1+2Direct product of S3 and 3- 1+2S3xES-(3,1)162,3718T84
C33⋊C61st semidirect product of C33 and C6 acting faithfullyC3^3:C6162,1118T85
C3≀S3Wreath product of C3 by S3C3wrS3162,1018T86
C322D92nd semidirect product of C32 and D9 acting via D9/C3=S3C3^2:2D9162,1718T87
C33⋊S32nd semidirect product of C33 and S3 acting faithfullyC3^3:S3162,1918T88
He35S32nd semidirect product of He3 and S3 acting via S3/C3=C2He3:5S3162,4618T89

### Groups of order 180

LabelIDTr ID
C3×A5Direct product of C3 and A5; = GL2(𝔽4)C3xA5180,1918T90

### Groups of order 216

LabelIDTr ID
C2×C32⋊A4Direct product of C2 and C32⋊A4C2xC3^2:A4216,10718T91
C2×C32.A4Direct product of C2 and C32.A4C2xC3^2.A4216,10618T92
C3×S3≀C2Direct product of C3 and S3≀C2C3xS3wrC2216,15718T93
C2×C32⋊D6Direct product of C2 and C32⋊D6C2xC3^2:D6216,10218T94
S3×C32⋊C4Direct product of S3 and C32⋊C4S3xC3^2:C4216,15618T95
S33Direct product of S3, S3 and S3; = Hol(C3×S3)S3^3216,16218T96
C32⋊S41st semidirect product of C32 and S4 acting via S4/C22=S3C3^2:S4216,9218T97
C32.S4The non-split extension by C32 of S4 acting via S4/C22=S3C3^2.S4216,9018T98
C32⋊S41st semidirect product of C32 and S4 acting via S4/C22=S3C3^2:S4216,9218T99
C62⋊C63rd semidirect product of C62 and C6 acting faithfullyC6^2:C6216,9918T100
C32.S4The non-split extension by C32 of S4 acting via S4/C22=S3C3^2.S4216,9018T101
C62⋊C63rd semidirect product of C62 and C6 acting faithfullyC6^2:C6216,9918T102
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15818T103
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4C3^2:2D12216,15918T104
He3⋊D4The semidirect product of He3 and D4 acting faithfullyHe3:D4216,8718T105
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15818T106
C62⋊S35th semidirect product of C62 and S3 acting faithfullyC6^2:S3216,9518T107
18T108

### Groups of order 288

LabelIDTr ID
C2×A42Direct product of C2, A4 and A4C2xA4^2288,102918T109
C2×AΓL1(𝔽9)Direct product of C2 and AΓL1(𝔽9)C2xAGammaL(1,9)288,102718T110
C2×S3×S4Direct product of C2, S3 and S4; = Aut(S3×SL2(𝔽3))C2xS3xS4288,102818T111
A4≀C2Wreath product of A4 by C2A4wrC2288,102518T112
18T113
A4×S4Direct product of A4 and S4A4xS4288,102418T114
18T115
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)PSO+(4,3)288,102618T116
18T117

### Groups of order 324

LabelIDTr ID
C3×C32⋊D6Direct product of C3 and C32⋊D6C3xC3^2:D6324,11718T118
C2×C3≀S3Direct product of C2 and C3≀S3C2xC3wrS3324,6818T119
C3×C324D6Direct product of C3 and C324D6C3xC3^2:4D6324,16718T120
S3×C32⋊C6Direct product of S3 and C32⋊C6S3xC3^2:C6324,11618T121
S3×C9⋊C6Direct product of S3 and C9⋊C6S3xC9:C6324,11818T122
C3×C33⋊C4Direct product of C3 and C33⋊C4; = AΣL1(𝔽81)C3xC3^3:C4324,16218T123
S3×C32⋊C6Direct product of S3 and C32⋊C6S3xC3^2:C6324,11618T124
C2×C33⋊C6Direct product of C2 and C33⋊C6C2xC3^3:C6324,6918T125
C3×C32⋊D6Direct product of C3 and C32⋊D6C3xC3^2:D6324,11718T126
C332A41st semidirect product of C33 and A4 acting via A4/C22=C3C3^3:2A4324,6018T127
C344C44th semidirect product of C34 and C4 acting faithfullyC3^4:4C4324,16418T128
He3⋊D6The semidirect product of He3 and D6 acting faithfullyHe3:D6324,3918T129
C92⋊C4The semidirect product of C92 and C4 acting faithfullyC9^2:C4324,3518T130
He34Dic3The semidirect product of He3 and Dic3 acting via Dic3/C3=C4He3:4Dic3324,11318T131
C32⋊D18The semidirect product of C32 and D18 acting via D18/C3=D6C3^2:D18324,3718T132
He35D61st semidirect product of He3 and D6 acting via D6/C3=C22He3:5D6324,12118T133
C2×C33⋊S3Direct product of C2 and C33⋊S3C2xC3^3:S3324,7718T134
S3×He3⋊C2Direct product of S3 and He3⋊C2S3xHe3:C2324,12218T135
He3⋊D6The semidirect product of He3 and D6 acting faithfullyHe3:D6324,3918T136
18T137
C3⋊S32Direct product of C3⋊S3 and C3⋊S3C3:S3^2324,16918T138
He35D61st semidirect product of He3 and D6 acting via D6/C3=C22He3:5D6324,12118T139
D92Direct product of D9 and D9D9^2324,3618T140
C33⋊A4The semidirect product of C33 and A4 acting faithfullyC3^3:A4324,16018T141
18T142
18T143

### Groups of order 360

LabelIDTr ID
C3×S5Direct product of C3 and S5C3xS5360,11918T144
S3×A5Direct product of S3 and A5S3xA5360,12118T145
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5GammaL(2,4)360,12018T146

### Groups of order 432

LabelIDTr ID
C2×C32.S4Direct product of C2 and C32.S4C2xC3^2.S4432,53318T147
C2×C62⋊C6Direct product of C2 and C62⋊C6C2xC6^2:C6432,54218T148
C2×C32⋊S4Direct product of C2 and C32⋊S4C2xC3^2:S4432,53518T149
S3×S3≀C2Direct product of S3 and S3≀C2S3xS3wrC2432,74118T150
C2×ASL2(𝔽3)Direct product of C2 and ASL2(𝔽3)C2xASL(2,3)432,73518T151
C625D65th semidirect product of C62 and D6 acting faithfullyC6^2:5D6432,52318T152
18T153
18T154
18T155
C2×C62⋊S3Direct product of C2 and C62⋊S3C2xC6^2:S3432,53818T156
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)AGL(2,3)432,73418T157

### Groups of order 486

LabelIDTr ID
C928C68th semidirect product of C92 and C6 acting faithfullyC9^2:8C6486,11018T158
C331C181st semidirect product of C33 and C18 acting via C18/C3=C6C3^3:1C18486,1818T159
C34.C64th non-split extension by C34 of C6 acting faithfullyC3^4.C6486,10418T160
C34⋊C61st semidirect product of C34 and C6 acting faithfullyC3^4:C6486,10218T161
C3×C33⋊C6Direct product of C3 and C33⋊C6C3xC3^3:C6486,11618T162
S3×C3≀C3Direct product of S3 and C3≀C3S3xC3wrC3486,11718T163
C34⋊C61st semidirect product of C34 and C6 acting faithfullyC3^4:C6486,10218T164
C343S33rd semidirect product of C34 and S3 acting faithfullyC3^4:3S3486,14518T165
C926S36th semidirect product of C92 and S3 acting faithfullyC9^2:6S3486,15318T166
C345S35th semidirect product of C34 and S3 acting faithfullyC3^4:5S3486,16618T167
C343S33rd semidirect product of C34 and S3 acting faithfullyC3^4:3S3486,14518T168
C3×C33⋊S3Direct product of C3 and C33⋊S3C3xC3^3:S3486,16518T169
C32⋊C9.C61st non-split extension by C32⋊C9 of C6 acting faithfullyC3^2:C9.C6486,518T170
C34.7S37th non-split extension by C34 of S3 acting faithfullyC3^4.7S3486,14718T171
C331D91st semidirect product of C33 and D9 acting via D9/C3=S3C3^3:1D9486,1918T172
C32⋊C9⋊S31st semidirect product of C32⋊C9 and S3 acting faithfullyC3^2:C9:S3486,718T173
C32⋊C9⋊C61st semidirect product of C32⋊C9 and C6 acting faithfullyC3^2:C9:C6486,618T174

### Groups of order 19

LabelIDTr ID
C19Cyclic groupC1919,119T1

### Groups of order 38

LabelIDTr ID
D19Dihedral groupD1938,119T2

### Groups of order 57

LabelIDTr ID
C19⋊C3The semidirect product of C19 and C3 acting faithfullyC19:C357,119T3

### Groups of order 114

LabelIDTr ID
C19⋊C6The semidirect product of C19 and C6 acting faithfullyC19:C6114,119T4

### Groups of order 171

LabelIDTr ID
C19⋊C9The semidirect product of C19 and C9 acting faithfullyC19:C9171,319T5

### Groups of order 342

LabelIDTr ID
F19Frobenius group; = C19C18 = AGL1(𝔽19) = Aut(D19) = Hol(C19)F19342,719T6

### Groups of order 20

LabelIDTr ID
C20Cyclic groupC2020,220T1
Dic5Dicyclic group; = C52C4Dic520,120T2
C2×C10Abelian group of type [2,10]C2xC1020,520T3
D10Dihedral group; = C2×D5D1020,420T4
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)F520,320T5

### Groups of order 40

LabelIDTr ID
C4×D5Direct product of C4 and D5C4xD540,520T6
C5⋊D4The semidirect product of C5 and D4 acting via D4/C22=C2C5:D440,820T7
C22×D5Direct product of C22 and D5C2^2xD540,1320T8
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)C2xF540,1220T9
D20Dihedral groupD2040,620T10
C5⋊D4The semidirect product of C5 and D4 acting via D4/C22=C2C5:D440,820T11
C5×D4Direct product of C5 and D4C5xD440,1020T12
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)C2xF540,1220T13

### Groups of order 60

LabelIDTr ID
C5×A4Direct product of C5 and A4C5xA460,920T14
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,520T15

### Groups of order 80

LabelIDTr ID
C22×F5Direct product of C22 and F5C2^2xF580,5020T16
C24⋊C5The semidirect product of C24 and C5 acting faithfullyC2^4:C580,4920T17
C4⋊F5The semidirect product of C4 and F5 acting via F5/D5=C2C4:F580,3120T18
C22⋊F5The semidirect product of C22 and F5 acting via F5/D5=C2C2^2:F580,3420T19
C4×F5Direct product of C4 and F5C4xF580,3020T20
D4×D5Direct product of D4 and D5D4xD580,3920T21
C22⋊F5The semidirect product of C22 and F5 acting via F5/D5=C2C2^2:F580,3420T22
C24⋊C5The semidirect product of C24 and C5 acting faithfullyC2^4:C580,4920T23

### Groups of order 100

LabelIDTr ID
D5×C10Direct product of C10 and D5D5xC10100,1420T24
C5×Dic5Direct product of C5 and Dic5C5xDic5100,620T25
D5.D5The non-split extension by D5 of D5 acting via D5/C5=C2D5.D5100,1020T26
C52⋊C44th semidirect product of C52 and C4 acting faithfullyC5^2:C4100,1220T27
D52Direct product of D5 and D5D5^2100,1320T28
C5×F5Direct product of C5 and F5C5xF5100,920T29

### Groups of order 120

LabelIDTr ID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3420T30
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetriesC2xA5120,3520T31
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3420T32
C5⋊S4The semidirect product of C5 and S4 acting via S4/A4=C2C5:S4120,3820T33
C5×S4Direct product of C5 and S4C5xS4120,3720T34
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3420T35
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetriesC2xA5120,3520T36
D5×A4Direct product of D5 and A4D5xA4120,3920T37

### Groups of order 160

LabelIDTr ID
C24⋊D5The semidirect product of C24 and D5 acting faithfullyC2^4:D5160,23420T38
20T39
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)C2xC2^4:C5160,23520T40
20T41
D4×F5Direct product of D4 and F5; = Aut(D20) = Hol(C20)D4xF5160,20720T42
C24⋊D5The semidirect product of C24 and D5 acting faithfullyC2^4:D5160,23420T43
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)C2xC2^4:C5160,23520T44
C24⋊D5The semidirect product of C24 and D5 acting faithfullyC2^4:D5160,23420T45
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)C2xC2^4:C5160,23520T46

### Groups of order 200

LabelIDTr ID
C52⋊Q8The semidirect product of C52 and Q8 acting faithfullyC5^2:Q8200,4420T47
D5≀C2Wreath product of D5 by C2D5wrC2200,4320T48
C2×C52⋊C4Direct product of C2 and C52⋊C4C2xC5^2:C4200,4820T49
D5≀C2Wreath product of D5 by C2D5wrC2200,4320T50
D5×F5Direct product of D5 and F5D5xF5200,4120T51
C2×C52⋊C4Direct product of C2 and C52⋊C4C2xC5^2:C4200,4820T52
C5×C5⋊D4Direct product of C5 and C5⋊D4C5xC5:D4200,3120T53
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)D5:F5200,4220T54
D5≀C2Wreath product of D5 by C2D5wrC2200,4320T55
C52⋊C8The semidirect product of C52 and C8 acting faithfullyC5^2:C8200,4020T56
D5≀C2Wreath product of D5 by C2D5wrC2200,4320T57
Dic52D5The semidirect product of Dic5 and D5 acting through Inn(Dic5)Dic5:2D5200,2320T58
C2×D52Direct product of C2, D5 and D5C2xD5^2200,4920T59
C5⋊D20The semidirect product of C5 and D20 acting via D20/D10=C2C5:D20200,2520T60

### Groups of order 240

LabelIDTr ID
A4⋊F5The semidirect product of A4 and F5 acting via F5/D5=C2A4:F5240,19220T61
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18920T62
C4×A5Direct product of C4 and A5C4xA5240,9220T63
C22×A5Direct product of C22 and A5C2^2xA5240,19020T64
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18920T65
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2A5:C4240,9120T66
F16Frobenius group; = C24C15 = AGL1(𝔽16)F16240,19120T67
A4×F5Direct product of A4 and F5A4xF5240,19320T68
D5×S4Direct product of D5 and S4D5xS4240,19420T69
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18920T70

### Groups of order 320

LabelIDTr ID
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163620T71
C22×C24⋊C5Direct product of C22 and C24⋊C5C2^2xC2^4:C5320,163720T72
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163620T73
C22×C24⋊C5Direct product of C22 and C24⋊C5C2^2xC2^4:C5320,163720T74
C4×C24⋊C5Direct product of C4 and C24⋊C5C4xC2^4:C5320,158420T75
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163620T76
C24⋊F5The semidirect product of C24 and F5 acting faithfullyC2^4:F5320,163520T77
20T78
20T79
20T80
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163620T81
C25.D5The non-split extension by C25 of D5 acting faithfullyC2^5.D5320,158320T82
C24⋊F5The semidirect product of C24 and F5 acting faithfullyC2^4:F5320,163520T83
C25.D5The non-split extension by C25 of D5 acting faithfullyC2^5.D5320,158320T84
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163620T85
C22×C24⋊C5Direct product of C22 and C24⋊C5C2^2xC2^4:C5320,163720T86
C2×C24⋊D5Direct product of C2 and C24⋊D5C2xC2^4:D5320,163620T87
C24⋊F5The semidirect product of C24 and F5 acting faithfullyC2^4:F5320,163520T88

### Groups of order 360

LabelIDTr ID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simpleA6360,11820T89

### Groups of order 400

LabelIDTr ID
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfullyD5wrC2:C2400,20720T90
C523C422nd semidirect product of C52 and C42 acting via C42/C2=C2×C4C5^2:3C4^2400,12420T91
C2×D5≀C2Direct product of C2 and D5≀C2C2xD5wrC2400,21120T92
(D52)⋊C41st semidirect product of D52 and C4 acting via C4/C2=C2(D5^2):C4400,12920T93
20T94
20T95
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfullyD5wrC2:C2400,20720T96
20T97
C2×D5≀C2Direct product of C2 and D5≀C2C2xD5wrC2400,21120T98
C2×C52⋊Q8Direct product of C2 and C52⋊Q8C2xC5^2:Q8400,21220T99
C2×D5≀C2Direct product of C2 and D5≀C2C2xD5wrC2400,21120T100
D10⋊F52nd semidirect product of D10 and F5 acting via F5/D5=C2D10:F5400,12520T101
F52Direct product of F5 and F5; = Hol(F5)F5^2400,20520T102
C1024C44th semidirect product of C102 and C4 acting faithfullyC10^2:4C4400,16220T103
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfullyC5^2:M4(2)400,20620T104
C2.D5≀C22nd central extension by C2 of D5≀C2C2.D5wrC2400,13020T105
D10⋊D103rd semidirect product of D10 and D10 acting via D10/D5=C2D10:D10400,18020T106
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfullyC5^2:M4(2)400,20620T107
Dic5⋊F53rd semidirect product of Dic5 and F5 acting via F5/D5=C2Dic5:F5400,12620T108
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfullyC5^2:M4(2)400,20620T109
C2×C52⋊C8Direct product of C2 and C52⋊C8C2xC5^2:C8400,20820T110
(C5×C10).Q8The non-split extension by C5×C10 of Q8 acting faithfully(C5xC10).Q8400,13420T111
20T112
C2×C52⋊C8Direct product of C2 and C52⋊C8C2xC5^2:C8400,20820T113
C2×D5⋊F5Direct product of C2 and D5⋊F5C2xD5:F5400,21020T114
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfullyC5^2:M4(2)400,20620T115

### Groups of order 480

LabelIDTr ID
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2C2^2:S5480,95120T116
C22×S5Direct product of C22 and S5C2^2xS5480,118620T117
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2C2^2:S5480,95120T118
D4×A5Direct product of D4 and A5D4xA5480,95620T119
C4⋊S5The semidirect product of C4 and S5 acting via S5/A5=C2C4:S5480,94420T120
F5×S4Direct product of F5 and S4; = Hol(C2×C10)F5xS4480,118920T121
F16⋊C2The semidirect product of F16 and C2 acting faithfullyF16:C2480,118820T122
C4×S5Direct product of C4 and S5; = CO3(𝔽5)C4xS5480,94320T123

### Groups of order 500

LabelIDTr ID
C5×D52Direct product of C5, D5 and D5C5xD5^2500,5020T124
C536C46th semidirect product of C53 and C4 acting faithfullyC5^3:6C4500,4620T125
C5×C52⋊C4Direct product of C5 and C52⋊C4C5xC5^2:C4500,4420T126
C5×D5.D5Direct product of C5 and D5.D5C5xD5.D5500,4220T127
C525D102nd semidirect product of C52 and D10 acting via D10/C5=C22C5^2:5D10500,5220T128

### Groups of order 21

LabelIDTr ID
C21Cyclic groupC2121,221T1
C7⋊C3The semidirect product of C7 and C3 acting faithfullyC7:C321,121T2

### Groups of order 42

LabelIDTr ID
C3×D7Direct product of C3 and D7C3xD742,421T3
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)F742,121T4
D21Dihedral groupD2142,521T5
S3×C7Direct product of C7 and S3S3xC742,321T6

### Groups of order 63

LabelIDTr ID
C3×C7⋊C3Direct product of C3 and C7⋊C3C3xC7:C363,321T7

### Groups of order 84

LabelIDTr ID
S3×D7Direct product of S3 and D7S3xD784,821T8

### Groups of order 126

LabelIDTr ID
C3×F7Direct product of C3 and F7C3xF7126,721T9
C3⋊F7The semidirect product of C3 and F7 acting via F7/C7⋊C3=C2C3:F7126,921T10
S3×C7⋊C3Direct product of S3 and C7⋊C3S3xC7:C3126,821T11

### Groups of order 147

LabelIDTr ID
C723C33rd semidirect product of C72 and C3 acting faithfullyC7^2:3C3147,521T12
C7×C7⋊C3Direct product of C7 and C7⋊C3C7xC7:C3147,321T13

### Groups of order 168

LabelIDTr ID
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simpleGL(3,2)168,4221T14

### Groups of order 252

LabelIDTr ID
S3×F7Direct product of S3 and F7; = Aut(D21) = Hol(C21)S3xF7252,2621T15

### Groups of order 294

LabelIDTr ID
C75F7The semidirect product of C7 and F7 acting via F7/C7⋊C3=C2C7:5F7294,1021T16
C72⋊S3The semidirect product of C72 and S3 acting faithfullyC7^2:S3294,721T17
21T18
C72⋊C67th semidirect product of C72 and C6 acting faithfullyC7^2:C6294,1421T19

### Groups of order 336

LabelIDTr ID
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,20821T20

### Groups of order 441

LabelIDTr ID
C7⋊C32Direct product of C7⋊C3 and C7⋊C3C7:C3^2441,921T21

### Groups of order 22

LabelIDTr ID
C22Cyclic groupC2222,222T1
D11Dihedral groupD1122,122T2

### Groups of order 44

LabelIDTr ID
D22Dihedral group; = C2×D11D2244,322T3

### Groups of order 110

LabelIDTr ID
F11Frobenius group; = C11C10 = AGL1(𝔽11) = Aut(D11) = Hol(C11)F11110,122T4
C2×C11⋊C5Direct product of C2 and C11⋊C5C2xC11:C5110,222T5

### Groups of order 220

LabelIDTr ID
C2×F11Direct product of C2 and F11; = Aut(D22) = Hol(C22)C2xF11220,722T6

### Groups of order 242

LabelIDTr ID
C11×D11Direct product of C11 and D11; = AΣL1(𝔽121)C11xD11242,322T7

### Groups of order 484

LabelIDTr ID
C112⋊C4The semidirect product of C112 and C4 acting faithfullyC11^2:C4484,822T8
D112Direct product of D11 and D11D11^2484,922T9

### Groups of order 23

LabelIDTr ID
C23Cyclic groupC2323,123T1

### Groups of order 46

LabelIDTr ID
D23Dihedral groupD2346,123T2

### Groups of order 253

LabelIDTr ID
C23⋊C11The semidirect product of C23 and C11 acting faithfullyC23:C11253,123T3

### Groups of order 24

LabelIDTr ID
C24Cyclic groupC2424,224T1
C2×C12Abelian group of type [2,12]C2xC1224,924T2
C22×C6Abelian group of type [2,2,6]C2^2xC624,1524T3
C3×Q8Direct product of C3 and Q8C3xQ824,1124T4
Dic6Dicyclic group; = C3Q8Dic624,424T5
C2×Dic3Direct product of C2 and Dic3C2xDic324,724T6
SL2(𝔽3)Special linear group on 𝔽32; = Q8C3 = 2T = <2,3,3> = 1st non-monomial groupSL(2,3)24,324T7
C3⋊C8The semidirect product of C3 and C8 acting via C8/C4=C2C3:C824,124T8
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)C2xA424,1324T9
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotationsS424,1224T10
C22×S3Direct product of C22 and S3C2^2xS324,1424T11
C4×S3Direct product of C4 and S3C4xS324,524T12
D12Dihedral groupD1224,624T13
C3⋊D4The semidirect product of C3 and D4 acting via D4/C22=C2C3:D424,824T14
C3×D4Direct product of C3 and D4C3xD424,1024T15

### Groups of order 48

LabelIDTr ID
C3×M4(2)Direct product of C3 and M4(2)C3xM4(2)48,2424T16
C3×C4○D4Direct product of C3 and C4○D4C3xC4oD448,4724T17
D42S3The semidirect product of D4 and S3 acting through Inn(D4)D4:2S348,3924T18
C4○D12Central product of C4 and D12C4oD1248,3724T19
C4.Dic3The non-split extension by C4 of Dic3 acting via Dic3/C6=C2C4.Dic348,1024T20
C4.A4The central extension by C4 of A4C4.A448,3324T21
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32) = 2O = <2,3,4>GL(2,3)48,2924T22
D42S3The semidirect product of D4 and S3 acting through Inn(D4)D4:2S348,3924T23
C4○D12Central product of C4 and D12C4oD1248,3724T24
C2×C3⋊D4Direct product of C2 and C3⋊D4C2xC3:D448,4324T25
S3×Q8Direct product of S3 and Q8S3xQ848,4024T26
S3×C2×C4Direct product of C2×C4 and S3S3xC2xC448,3524T27
Q83S3The semidirect product of Q8 and S3 acting through Inn(Q8)Q8:3S348,4124T28
C2×D12Direct product of C2 and D12C2xD1248,3624T29
S3×C23Direct product of C23 and S3S3xC2^348,5124T30
C8⋊S33rd semidirect product of C8 and S3 acting via S3/C3=C2C8:S348,524T31
S3×C8Direct product of C8 and S3S3xC848,424T32
D6⋊C4The semidirect product of D6 and C4 acting via C4/C2=C2D6:C448,1424T33
D24Dihedral groupD2448,724T34
C24⋊C22nd semidirect product of C24 and C2 acting faithfullyC24:C248,624T35
Q82S3The semidirect product of Q8 and S3 acting via S3/C3=C2Q8:2S348,1724T36
D4⋊S3The semidirect product of D4 and S3 acting via S3/C3=C2D4:S348,1524T37
C6×D4Direct product of C6 and D4C6xD448,4524T38
C3×C22⋊C4Direct product of C3 and C22⋊C4C3xC2^2:C448,2124T39
C3×D8Direct product of C3 and D8C3xD848,2524T40
C3×SD16Direct product of C3 and SD16C3xSD1648,2624T41
D4.S3The non-split extension by D4 of S3 acting via S3/C3=C2D4.S348,1624T42
D4⋊S3The semidirect product of D4 and S3 acting via S3/C3=C2D4:S348,1524T43
C6.D47th non-split extension by C6 of D4 acting via D4/C22=C2C6.D448,1924T44
C2×C3⋊D4Direct product of C2 and C3⋊D4C2xC3:D448,4324T45
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetriesC2xS448,4824T46
24T47
24T48
C22×A4Direct product of C22 and A4C2^2xA448,4924T49
24T50
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)A4:C448,3024T51
S3×D4Direct product of S3 and D4; = Aut(D12) = Hol(C12)S3xD448,3824T52
24T53
24T54
C4×A4Direct product of C4 and A4C4xA448,3124T55
24T56
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)A4:C448,3024T57
C42⋊C3The semidirect product of C42 and C3 acting faithfullyC4^2:C348,324T58
C22⋊A4The semidirect product of C22 and A4 acting via A4/C22=C3C2^2:A448,5024T59

### Groups of order 72

LabelIDTr ID
S3×Dic3Direct product of S3 and Dic3S3xDic372,2024T60
D6⋊S31st semidirect product of D6 and S3 acting via S3/C3=C2D6:S372,2224T61
C322Q8The semidirect product of C32 and Q8 acting via Q8/C2=C22C3^2:2Q872,2424T62
C322C8The semidirect product of C32 and C8 acting via C8/C2=C4C3^2:2C872,1924T63
C3×Dic6Direct product of C3 and Dic6C3xDic672,2624T64
S3×C12Direct product of C12 and S3S3xC1272,2724T65
C6×Dic3Direct product of C6 and Dic3C6xDic372,2924T66
C3×D12Direct product of C3 and D12C3xD1272,2824T67
S3×C2×C6Direct product of C2×C6 and S3S3xC2xC672,4824T68
C3×C3⋊C8Direct product of C3 and C3⋊C8C3xC3:C872,1224T69
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)C3xSL(2,3)72,2524T70
C6×A4Direct product of C6 and A4C6xA472,4724T71
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)S3wrC272,4024T72
C2×S32Direct product of C2, S3 and S3C2xS3^272,4624T73
C3⋊D12The semidirect product of C3 and D12 acting via D12/D6=C2C3:D1272,2324T74
C6.D62nd non-split extension by C6 of D6 acting via D6/S3=C2C6.D672,2124T75
C2×C32⋊C4Direct product of C2 and C32⋊C4C2xC3^2:C472,4524T76
C3×C3⋊D4Direct product of C3 and C3⋊D4C3xC3:D472,3024T77
S3×A4Direct product of S3 and A4S3xA472,4424T78
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2C3:S472,4324T79
C3×S4Direct product of C3 and S4C3xS472,4224T80
F9Frobenius group; = C32C8 = AGL1(𝔽9)F972,3924T81
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M9PSU(3,2)72,4124T82
S3×A4Direct product of S3 and A4S3xA472,4424T83
C3×S4Direct product of C3 and S4C3xS472,4224T84

### Groups of order 96

LabelIDTr ID
C8×A4Direct product of C8 and A4C8xA496,7324T85
Q8×A4Direct product of Q8 and A4Q8xA496,19924T86
A4⋊Q8The semidirect product of A4 and Q8 acting via Q8/C4=C2A4:Q896,18524T87
Q8⋊A41st semidirect product of Q8 and A4 acting via A4/C22=C3Q8:A496,20324T88
A4⋊C8The semidirect product of A4 and C8 acting via C8/C4=C2A4:C896,6524T89
C3×C4.D4Direct product of C3 and C4.D4C3xC4.D496,5024T90
C3×C23⋊C4Direct product of C3 and C23⋊C4C3xC2^3:C496,4924T91
C3×2+ 1+4Direct product of C3 and 2+ 1+4C3xES+(2,2)96,22424T92
C3×C23⋊C4Direct product of C3 and C23⋊C4C3xC2^3:C496,4924T93
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22C2^3.6D696,1324T94
D46D62nd semidirect product of D4 and D6 acting through Inn(D4)D4:6D696,21124T95
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22C2^3.7D696,4124T96
C23⋊A42nd semidirect product of C23 and A4 acting faithfullyC2^3:A496,20424T97
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22C2^3.7D696,4124T98
C12.D48th non-split extension by C12 of D4 acting via D4/C2=C22C12.D496,4024T99
D46D62nd semidirect product of D4 and D6 acting through Inn(D4)D4:6D696,21124T100
S3×C4○D4Direct product of S3 and C4○D4S3xC4oD496,21524T101
D4○D12Central product of D4 and D12D4oD1296,21624T102
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22C2^3.6D696,1324T103
S3×M4(2)Direct product of S3 and M4(2)S3xM4(2)96,11324T104
M4(2)⋊S33rd semidirect product of M4(2) and S3 acting via S3/C3=C2M4(2):S396,3024T105
D12⋊C44th semidirect product of D12 and C4 acting via C4/C2=C2D12:C496,3224T106
C8⋊D61st semidirect product of C8 and D6 acting via D6/C3=C22C8:D696,11524T107
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22C2^3.6D696,1324T108
Q83Dic32nd semidirect product of Q8 and Dic3 acting via Dic3/C6=C2Q8:3Dic396,4424T109
D4⋊D62nd semidirect product of D4 and D6 acting via D6/C6=C2D4:D696,15624T110
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22C2^3.7D696,4124T111
C3×C22≀C2Direct product of C3 and C22≀C2C3xC2^2wrC296,16724T112
C3×C4≀C2Direct product of C3 and C4≀C2C3xC4wrC296,5424T113
C3×C8⋊C22Direct product of C3 and C8⋊C22C3xC8:C2^296,18324T114
C3×C23⋊C4Direct product of C3 and C23⋊C4C3xC2^3:C496,4924T115
C244S31st semidirect product of C24 and S3 acting via S3/C3=C2C2^4:4S396,16024T116
C424S33rd semidirect product of C42 and S3 acting via S3/C3=C2C4^2:4S396,1224T117
D126C224th semidirect product of D12 and C22 acting via C22/C2=C2D12:6C2^296,13924T118
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22C2^3.6D696,1324T119
C42⋊C61st semidirect product of C42 and C6 acting faithfullyC4^2:C696,7124T120
24T121
24T122
C2×A4⋊C4Direct product of C2 and A4⋊C4C2xA4:C496,19424T123
24T124
C22×S4Direct product of C22 and S4C2^2xS496,22624T125
24T126
C4.3S43rd non-split extension by C4 of S4 acting via S4/A4=C2C4.3S496,19324T127
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2C4:S496,18724T128
C4×S4Direct product of C4 and S4C4xS496,18624T129
24T130
A4⋊Q8The semidirect product of A4 and Q8 acting via Q8/C4=C2A4:Q896,18524T131
C2×A4⋊C4Direct product of C2 and A4⋊C4C2xA4:C496,19424T132
C2×C4×A4Direct product of C2×C4 and A4C2xC4xA496,19624T133
24T134
C23×A4Direct product of C23 and A4C2^3xA496,22824T135
24T136
Q8.A4The non-split extension by Q8 of A4 acting through Inn(Q8)Q8.A496,20124T137
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4U(2,3)96,6724T138
S3×D8Direct product of S3 and D8S3xD896,11724T139
Q83D62nd semidirect product of Q8 and D6 acting via D6/S3=C2Q8:3D696,12124T140
D8⋊S32nd semidirect product of D8 and S3 acting via S3/C3=C2D8:S396,11824T141
S3×SD16Direct product of S3 and SD16S3xSD1696,12024T142
C2×S3×D4Direct product of C2, S3 and D4C2xS3xD496,20924T143
D6⋊D41st semidirect product of D6 and D4 acting via D4/C22=C2D6:D496,8924T144
C232D61st semidirect product of C23 and D6 acting via D6/C3=C22C2^3:2D696,14424T145
S3×C22⋊C4Direct product of S3 and C22⋊C4S3xC2^2:C496,8724T146
C2×C4×A4Direct product of C2×C4 and A4C2xC4xA496,19624T147
C2×A4⋊C4Direct product of C2 and A4⋊C4C2xA4:C496,19424T148
C23⋊A42nd semidirect product of C23 and A4 acting faithfullyC2^3:A496,20424T149
C22×S4Direct product of C22 and S4C2^2xS496,22624T150
24T151
24T152
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)A4:D496,19524T153
24T154
24T155
24T156
24T157
24T158
24T159
D4×A4Direct product of D4 and A4D4xA496,19724T160
24T161
24T162
24T163
24T164
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)A4:D496,19524T165
24T166
C4×S4Direct product of C4 and S4C4xS496,18624T167
24T168
24T169
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2C4:S496,18724T170
24T171
24T172
C2×C42⋊C3Direct product of C2 and C42⋊C3C2xC4^2:C396,6824T173
24T174
24T175
C2×C22⋊A4Direct product of C2 and C22⋊A4C2xC2^2:A496,22924T176
24T177
24T178
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3C2^3.3A496,324T179
24T180
C24⋊C61st semidirect product of C24 and C6 acting faithfullyC2^4:C696,7024T181
24T182
24T183
24T184
24T185
24T186
C23.A42nd non-split extension by C23 of A4 acting faithfullyC2^3.A496,7224T187
24T188
24T189
24T190
C42⋊S3The semidirect product of C42 and S3 acting faithfullyC4^2:S396,6424T191
24T192
24T193
24T194
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S3C2^2:S496,22724T195
24T196
24T197
24T198
24T199
24T200

### Groups of order 120

LabelIDTr ID
SL2(𝔽5)Special linear group on 𝔽52; = C2.A5 = 2I = <2,3,5>SL(2,5)120,524T201
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3424T202
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetriesC2xA5120,3524T203

### Groups of order 144

LabelIDTr ID
S3×C3⋊D4Direct product of S3 and C3⋊D4S3xC3:D4144,15324T204
D6.3D63rd non-split extension by D6 of D6 acting via D6/S3=C2D6.3D6144,14724T205
D6.4D64th non-split extension by D6 of D6 acting via D6/S3=C2D6.4D6144,14824T206
C62.C42nd non-split extension by C62 of C4 acting faithfullyC6^2.C4144,13524T207
C3×S3×D4Direct product of C3, S3 and D4C3xS3xD4144,16224T208
C3×D42S3Direct product of C3 and D42S3C3xD4:2S3144,16324T209
C3×C4○D12Direct product of C3 and C4○D12C3xC4oD12144,16124T210
C3×C4.Dic3Direct product of C3 and C4.Dic3C3xC4.Dic3144,7524T211
A42Direct product of A4 and A4; = PΩ+4(𝔽3)A4^2144,18424T212
(S32)⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2(S3^2):C4144,11524T213
C3⋊S3.Q8The non-split extension by C3⋊S3 of Q8 acting via Q8/C2=C22C3:S3.Q8144,11624T214
(S32)⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2(S3^2):C4144,11524T215
C3⋊S3.Q8The non-split extension by C3⋊S3 of Q8 acting via Q8/C2=C22C3:S3.Q8144,11624T216
C322SD16The semidirect product of C32 and SD16 acting via SD16/C2=D4C3^2:2SD16144,11824T217
C32⋊D8The semidirect product of C32 and D8 acting via D8/C2=D4C3^2:D8144,11724T218
24T219
C322SD16The semidirect product of C32 and SD16 acting via SD16/C2=D4C3^2:2SD16144,11824T220
D6.3D63rd non-split extension by D6 of D6 acting via D6/S3=C2D6.3D6144,14724T221
D6.6D62nd non-split extension by D6 of D6 acting via D6/C6=C2D6.6D6144,14224T222
Dic3.D62nd non-split extension by Dic3 of D6 acting via D6/S3=C2Dic3.D6144,14024T223
C4×S32Direct product of C4, S3 and S3C4xS3^2144,14324T224
C2×C6.D6Direct product of C2 and C6.D6C2xC6.D6144,14924T225
S3×C3⋊D4Direct product of S3 and C3⋊D4S3xC3:D4144,15324T226
D12⋊S33rd semidirect product of D12 and S3 acting via S3/C3=C2D12:S3144,13924T227
D6.D61st non-split extension by D6 of D6 acting via D6/C6=C2D6.D6144,14124T228
S3×D12Direct product of S3 and D12S3xD12144,14424T229
C2×C3⋊D12Direct product of C2 and C3⋊D12C2xC3:D12144,15124T230
D6⋊D62nd semidirect product of D6 and D6 acting via D6/S3=C2D6:D6144,14524T231
C22×S32Direct product of C22, S3 and S3C2^2xS3^2144,19224T232
C325SD163rd semidirect product of C32 and SD16 acting via SD16/C4=C22C3^2:5SD16144,6024T233
C3⋊D24The semidirect product of C3 and D24 acting via D24/D12=C2C3:D24144,5724T234
C6.D126th non-split extension by C6 of D12 acting via D12/D6=C2C6.D12144,6524T235
C12.31D65th non-split extension by C12 of D6 acting via D6/S3=C2C12.31D6144,5524T236
C12.29D63rd non-split extension by C12 of D6 acting via D6/S3=C2C12.29D6144,5324T237
C4⋊(C32⋊C4)The semidirect product of C4 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2C4:(C3^2:C4)144,13324T238
24T239
C4×C32⋊C4Direct product of C4 and C32⋊C4C4xC3^2:C4144,13224T240
C22×C32⋊C4Direct product of C22 and C32⋊C4C2^2xC3^2:C4144,19124T241
24T242
C32⋊M4(2)The semidirect product of C32 and M4(2) acting via M4(2)/C4=C4C3^2:M4(2)144,13124T243
C3⋊S33C82nd semidirect product of C3⋊S3 and C8 acting via C8/C4=C2C3:S3:3C8144,13024T244
C3×D4.S3Direct product of C3 and D4.S3C3xD4.S3144,8124T245
C3×D4⋊S3Direct product of C3 and D4⋊S3C3xD4:S3144,8024T246
C3×C6.D4Direct product of C3 and C6.D4C3xC6.D4144,8424T247
C6×C3⋊D4Direct product of C6 and C3⋊D4C6xC3:D4144,16724T248
S3×SL2(𝔽3)Direct product of S3 and SL2(𝔽3); = SL2(ℤ/6ℤ)S3xSL(2,3)144,12824T249
C2×S3×A4Direct product of C2, S3 and A4C2xS3xA4144,19024T250
C2×C3⋊S4Direct product of C2 and C3⋊S4C2xC3:S4144,18924T251
C6.6S46th non-split extension by C6 of S4 acting via S4/A4=C2C6.6S4144,12524T252
C3×GL2(𝔽3)Direct product of C3 and GL2(𝔽3)C3xGL(2,3)144,12224T253
C6×S4Direct product of C6 and S4C6xS4144,18824T254
C2×F9Direct product of C2 and F9C2xF9144,18524T255
24T256
C2×PSU3(𝔽2)Direct product of C2 and PSU3(𝔽2)C2xPSU(3,2)144,18724T257
C2.PSU3(𝔽2)The central extension by C2 of PSU3(𝔽2)C2.PSU(3,2)144,12024T258
24T259
C2×PSU3(𝔽2)Direct product of C2 and PSU3(𝔽2)C2xPSU(3,2)144,18724T260
C2×S3≀C2Direct product of C2 and S3≀C2C2xS3wrC2144,18624T261
24T262
24T263
24T264
(S32)⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2(S3^2):C4144,11524T265
24T266
24T267
24T268
Dic3⋊D62nd semidirect product of Dic3 and D6 acting via D6/S3=C2; = Hol(Dic3)Dic3:D6144,15424T269
24T270
24T271
C62⋊C41st semidirect product of C62 and C4 acting faithfullyC6^2:C4144,13624T272
24T273
24T274
S3×S4Direct product of S3 and S4; = Hol(C2×C6)S3xS4144,18324T275
24T276
24T277
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)AGammaL(1,9)144,18224T278
24T279
24T280
S3×S4Direct product of S3 and S4; = Hol(C2×C6)S3xS4144,18324T281

### Groups of order 168

LabelIDTr ID
C3×F8Direct product of C3 and F8C3xF8168,4424T282
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)AGammaL(1,8)168,4324T283
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simpleGL(3,2)168,4224T284

### Groups of order 192

LabelIDTr ID
C3×C2≀C4Direct product of C3 and C2≀C4C3xC2wrC4192,15724T285
C3×C2≀C22Direct product of C3 and C2≀C22C3xC2wrC2^2192,89024T286
C246D61st semidirect product of C24 and D6 acting via D6/C3=C22C2^4:6D6192,59124T287
C2≀A4Wreath product of C2 by A4C2wrA4192,20124T288
C245Dic31st semidirect product of C24 and Dic3 acting via Dic3/C3=C4C2^4:5Dic3192,9524T289
C2×C42⋊C6Direct product of C2 and C42⋊C6C2xC4^2:C6192,100124T290
C24.A41st non-split extension by C24 of A4 acting faithfullyC2^4.A4192,19524T291
C24.10D69th non-split extension by C24 of D6 acting via D6/C2=S3C2^4.10D6192,147124T292
C24.3A43rd non-split extension by C24 of A4 acting faithfullyC2^4.3A4192,19824T293
A4⋊M4(2)The semidirect product of A4 and M4(2) acting via M4(2)/C2×C4=C2A4:M4(2)192,96824T294
D42S4The semidirect product of D4 and S4 acting through Inn(D4)D4:2S4192,147324T295
A4×C4○D4Direct product of A4 and C4○D4A4xC4oD4192,150124T296
A4×M4(2)Direct product of A4 and M4(2)A4xM4(2)192,101124T297
C23.19(C2×A4)12nd non-split extension by C23 of C2×A4 acting via C2×A4/C23=C3C2^3.19(C2xA4)192,19924T298
C42⋊C121st semidirect product of C42 and C12 acting via C12/C2=C6C4^2:C12192,19224T299
C2×C42⋊C6Direct product of C2 and C42⋊C6C2xC4^2:C6192,100124T300
C424C4⋊C3The semidirect product of C424C4 and C3 acting faithfullyC4^2:4C4:C3192,19024T301
C4○D4⋊A41st semidirect product of C4○D4 and A4 acting via A4/C22=C3C4oD4:A4192,150724T302
C24.A41st non-split extension by C24 of A4 acting faithfullyC2^4.A4192,19524T303
(C22×C4).A44th non-split extension by C22×C4 of A4 acting faithfully(C2^2xC4).A4192,19624T304
C42⋊C121st semidirect product of C42 and C12 acting via C12/C2=C6C4^2:C12192,19224T305
C2×C42⋊C6Direct product of C2 and C42⋊C6C2xC4^2:C6192,100124T306
C24.3A43rd non-split extension by C24 of A4 acting faithfullyC2^4.3A4192,19824T307
C42⋊C121st semidirect product of C42 and C12 acting via C12/C2=C6C4^2:C12192,19224T308
C424C4⋊C3The semidirect product of C424C4 and C3 acting faithfullyC4^2:4C4:C3192,19024T309
C23.19(C2×A4)12nd non-split extension by C23 of C2×A4 acting via C2×A4/C23=C3C2^3.19(C2xA4)192,19924T310
C422C122nd semidirect product of C42 and C12 acting via C12/C2=C6C4^2:2C12192,19324T311
C23.19(C2×A4)12nd non-split extension by C23 of C2×A4 acting via C2×A4/C23=C3C2^3.19(C2xA4)192,19924T312
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.8S4192,18124T313
Q8⋊S41st semidirect product of Q8 and S4 acting via S4/C22=S3Q8:S4192,149024T314
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.8S4192,18124T315
C23.7S41st non-split extension by C23 of S4 acting via S4/C22=S3C2^3.7S4192,18024T316
C23.9S43rd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.9S4192,18224T317
D42S4The semidirect product of D4 and S4 acting through Inn(D4)D4:2S4192,147324T318
C24.10D69th non-split extension by C24 of D6 acting via D6/C2=S3C2^4.10D6192,147124T319
Q84S4The semidirect product of Q8 and S4 acting through Inn(Q8)Q8:4S4192,147824T320
Q8×S4Direct product of Q8 and S4Q8xS4192,147724T321
C8×S4Direct product of C8 and S4C8xS4192,95824T322
C8⋊S43rd semidirect product of C8 and S4 acting via S4/A4=C2C8:S4192,95924T323
A4⋊D8The semidirect product of A4 and D8 acting via D8/C8=C2A4:D8192,96124T324
C82S42nd semidirect product of C8 and S4 acting via S4/A4=C2C8:2S4192,96024T325
Q83S4The semidirect product of Q8 and S4 acting via S4/A4=C2Q8:3S4192,97624T326
D4⋊S4The semidirect product of D4 and S4 acting via S4/A4=C2D4:S4192,97424T327
A4×D8Direct product of A4 and D8A4xD8192,101424T328
A4×SD16Direct product of A4 and SD16A4xSD16192,101524T329
D4⋊S4The semidirect product of D4 and S4 acting via S4/A4=C2D4:S4192,97424T330
A4⋊SD16The semidirect product of A4 and SD16 acting via SD16/D4=C2A4:SD16192,97324T331
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)Q8:2S4192,149424T332
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)C2^3:S4192,149324T333
2+ 1+47S32nd semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2ES+(2,2):7S3192,80324T334
S3×2+ 1+4Direct product of S3 and 2+ 1+4S3xES+(2,2)192,152424T335
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4C2^3:D12192,30024T336
S3×C23⋊C4Direct product of S3 and C23⋊C4S3xC2^3:C4192,30224T337
C23.3D123rd non-split extension by C23 of D12 acting via D12/C3=D4C2^3.3D12192,3424T338
S3×C4.D4Direct product of S3 and C4.D4S3xC4.D4192,30324T339
C3⋊C2≀C4The semidirect product of C3 and C2≀C4 acting via C2≀C4/C23⋊C4=C2C3:C2wrC4192,3024T340
S3×C23⋊C4Direct product of S3 and C23⋊C4S3xC2^3:C4192,30224T341
C23.3D123rd non-split extension by C23 of D12 acting via D12/C3=D4C2^3.3D12192,3424T342
D121D41st semidirect product of D12 and D4 acting via D4/C2=C22D12:1D4192,30624T343
C23.2D122nd non-split extension by C23 of D12 acting via D12/C3=D4C2^3.2D12192,3324T344
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4C2^3:D12192,30024T345
C23.2D122nd non-split extension by C23 of D12 acting via D12/C3=D4C2^3.2D12192,3324T346
2+ 1+46S31st semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2ES+(2,2):6S3192,80024T347
C3⋊C2≀C4The semidirect product of C3 and C2≀C4 acting via C2≀C4/C23⋊C4=C2C3:C2wrC4192,3024T348
2+ 1+47S32nd semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2ES+(2,2):7S3192,80324T349
C3×D44D4Direct product of C3 and D44D4C3xD4:4D4192,88624T350
C3×C2≀C4Direct product of C3 and C2≀C4C3xC2wrC4192,15724T351
C3×C2≀C22Direct product of C3 and C2≀C22C3xC2wrC2^2192,89024T352
C3×C42⋊C4Direct product of C3 and C42⋊C4C3xC4^2:C4192,15924T353
C425Dic33rd semidirect product of C42 and Dic3 acting via Dic3/C3=C4C4^2:5Dic3192,10424T354
C428D66th semidirect product of C42 and D6 acting via D6/C3=C22C4^2:8D6192,63624T355
C245Dic31st semidirect product of C24 and Dic3 acting via Dic3/C3=C4C2^4:5Dic3192,9524T356
C246D61st semidirect product of C24 and D6 acting via D6/C3=C22C2^4:6D6192,59124T357
D4×S4Direct product of D4 and S4D4xS4192,147224T358
D42S4The semidirect product of D4 and S4 acting through Inn(D4)D4:2S4192,147324T359
S3×C22≀C2Direct product of S3 and C22≀C2S3xC2^2wrC2192,114724T360
S3×C4≀C2Direct product of S3 and C4≀C2S3xC4wrC2192,37924T361
S3×C8⋊C22Direct product of S3 and C8⋊C22; = Aut(D24) = Hol(C24)S3xC8:C2^2192,133124T362
S3×C23⋊C4Direct product of S3 and C23⋊C4S3xC2^3:C4192,30224T363
C246D61st semidirect product of C24 and D6 acting via D6/C3=C22C2^4:6D6192,59124T364
Q85D123rd semidirect product of Q8 and D12 acting via D12/D6=C2Q8:5D12192,38124T365
D1218D46th semidirect product of D12 and D4 acting via D4/C22=C2D12:18D4192,75724T366
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4C2^3:D12192,30024T367
C24.6A46th non-split extension by C24 of A4 acting faithfullyC2^4.6A4192,100824T368
C24⋊A43rd semidirect product of C24 and A4 acting faithfullyC2^4:A4192,100924T369
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfullyC2^4:Dic3192,18424T370
C24⋊A43rd semidirect product of C24 and A4 acting faithfullyC2^4:A4192,100924T371
C42⋊A4The semidirect product of C42 and A4 acting faithfullyC4^2:A4192,102324T372
C24.6A46th non-split extension by C24 of A4 acting faithfullyC2^4.6A4192,100824T373
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfullyC4^2:Dic3192,18524T374
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfullyC2^4:Dic3192,18424T375
C24⋊A43rd semidirect product of C24 and A4 acting faithfullyC2^4:A4192,100924T376
C24.6A46th non-split extension by C24 of A4 acting faithfullyC2^4.6A4192,100824T377
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfullyC4^2:Dic3192,18524T378
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfullyC2^4:Dic3192,18424T379
C24.6A46th non-split extension by C24 of A4 acting faithfullyC2^4.6A4192,100824T380
C24⋊A43rd semidirect product of C24 and A4 acting faithfullyC2^4:A4192,100924T381
C24.6A46th non-split extension by C24 of A4 acting faithfullyC2^4.6A4192,100824T382
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfullyC2^4:Dic3192,18424T383
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfullyC4^2:Dic3192,18524T384
C4×C22⋊A4Direct product of C4 and C22⋊A4C4xC2^2:A4192,150524T385
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149524T386
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfullyC4^2:Dic3192,18524T387
C422A4The semidirect product of C42 and A4 acting via A4/C22=C3C4^2:2A4192,102024T388
C82⋊C3The semidirect product of C82 and C3 acting faithfullyC8^2:C3192,324T389
C26⋊C33rd semidirect product of C26 and C3 acting faithfullyC2^6:C3192,154124T390
C42⋊A4The semidirect product of C42 and A4 acting faithfullyC4^2:A4192,102324T391
24T392
D4×S4Direct product of D4 and S4D4xS4192,147224T393
C2×C4⋊S4Direct product of C2 and C4⋊S4C2xC4:S4192,147024T394
C24.10D69th non-split extension by C24 of D6 acting via D6/C2=S3C2^4.10D6192,147124T395
D42S4The semidirect product of D4 and S4 acting through Inn(D4)D4:2S4192,147324T396
C2×C4×S4Direct product of C2×C4 and S4C2xC4xS4192,146924T397
C2×A4⋊D4Direct product of C2 and A4⋊D4C2xA4:D4192,148824T398
24T399
C23×S4Direct product of C23 and S4C2^3xS4192,153724T400
Q8.5S43rd non-split extension by Q8 of S4 acting via S4/A4=C2Q8.5S4192,98824T401
C25.S31st non-split extension by C25 of S3 acting faithfullyC2^5.S3192,99124T402
24T403
24T404
C2×A4⋊D4Direct product of C2 and A4⋊D4C2xA4:D4192,148824T405
24T406
24T407
A4×C22⋊C4Direct product of A4 and C22⋊C4A4xC2^2:C4192,99424T408
24T409
24T410
C2×D4×A4Direct product of C2, D4 and A4C2xD4xA4192,149724T411
24T412
24T413
C24.5D64th non-split extension by C24 of D6 acting via D6/C2=S3C2^4.5D6192,97224T414
24T415
C2×A4⋊D4Direct product of C2 and A4⋊D4C2xA4:D4192,148824T416
C24.5D64th non-split extension by C24 of D6 acting via D6/C2=S3C2^4.5D6192,97224T417
C2×C4×S4Direct product of C2×C4 and S4C2xC4xS4192,146924T418
C2×C4⋊S4Direct product of C2 and C4⋊S4C2xC4:S4192,147024T419
C22×C42⋊C3Direct product of C22 and C42⋊C3C2^2xC4^2:C3192,99224T420
24T421
C2×C23.3A4Direct product of C2 and C23.3A4C2xC2^3.3A4192,18924T422
24T423
24T424
C2≀A4Wreath product of C2 by A4C2wrA4192,20124T425
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.8S4192,18124T426
C23.7S41st non-split extension by C23 of S4 acting via S4/C22=S3C2^3.7S4192,18024T427
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.8S4192,18124T428
C23.7S41st non-split extension by C23 of S4 acting via S4/C22=S3C2^3.7S4192,18024T429
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)Q8:2S4192,149424T430
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)C2^3:S4192,149324T431
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153824T432
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149524T433
D4×S4Direct product of D4 and S4D4xS4192,147224T434
24T435
24T436
24T437
24T438
24T439
24T440
C2×C24⋊C6Direct product of C2 and C24⋊C6C2xC2^4:C6192,100024T441
24T442
24T443
24T444
24T445
24T446
24T447
24T448
24T449
24T450
24T451
24T452
C2×C23.A4Direct product of C2 and C23.A4C2xC2^3.A4192,100224T453
24T454
24T455
24T456
C22×C22⋊A4Direct product of C22 and C22⋊A4C2^2xC2^2:A4192,154024T457
24T458
24T459
C24.2A42nd non-split extension by C24 of A4 acting faithfullyC2^4.2A4192,19724T460
24T461
24T462
C2×C23.A4Direct product of C2 and C23.A4C2xC2^3.A4192,100224T463
24T464
24T465
24T466
C24.2A42nd non-split extension by C24 of A4 acting faithfullyC2^4.2A4192,19724T467
24T468
C4×C42⋊C3Direct product of C4 and C42⋊C3C4xC4^2:C3192,18824T469
24T470
C2×C42⋊S3Direct product of C2 and C42⋊S3C2xC4^2:S3192,94424T471
24T472
24T473
24T474
24T475
24T476
24T477
24T478
24T479
24T480
C23.9S43rd non-split extension by C23 of S4 acting via S4/C22=S3C2^3.9S4192,18224T481
24T482
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6C2^4:C12192,19124T483
24T484
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153824T485
24T486
24T487
24T488
24T489
24T490
24T491
24T492
24T493
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149524T494
24T495
C232D4⋊C3The semidirect product of C232D4 and C3 acting faithfullyC2^3:2D4:C3192,19424T496
24T497
24T498
24T499
24T500
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6C2^4:C12192,19124T501
24T502
24T503
24T504
24T505
24T506
24T507
C2×C22⋊S4Direct product of C2 and C22⋊S4C2xC2^2:S4192,153824T508
24T509
24T510
24T511
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3C2^4:4Dic3192,149524T512
24T513
24T514
24T515
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)C2^4:D6192,95524T516
24T517
24T518
24T519
24T520
24T521
24T522
24T523
24T524
24T525
24T526
24T527
24T528
24T529
C42⋊D6The semidirect product of C42 and D6 acting faithfullyC4^2:D6192,95624T530
24T531
24T532
24T533
24T534
24T535
24T536
24T537
24T538
24T539
24T540
24T541

### Groups of order 216

LabelIDTr ID
C3×C322Q8Direct product of C3 and C322Q8C3xC3^2:2Q8216,12324T542
C3×C3⋊D12Direct product of C3 and C3⋊D12C3xC3:D12216,12224T543
C3×C6.D6Direct product of C3 and C6.D6C3xC6.D6216,12024T544
C3×S3×Dic3Direct product of C3, S3 and Dic3C3xS3xDic3216,11924T545
C3×D6⋊S3Direct product of C3 and D6⋊S3C3xD6:S3216,12124T546
S32×C6Direct product of C6, S3 and S3S3^2xC6216,17024T547
C2×C324D6Direct product of C2 and C324D6C2xC3^2:4D6216,17224T548
C339(C2×C4)6th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22C3^3:9(C2xC4)216,13124T549
C339D46th semidirect product of C33 and D4 acting via D4/C2=C22C3^3:9D4216,13224T550
C335Q83rd semidirect product of C33 and Q8 acting via Q8/C2=C22C3^3:5Q8216,13324T551
C334C82nd semidirect product of C33 and C8 acting via C8/C2=C4C3^3:4C8216,11824T552
C2×C33⋊C4Direct product of C2 and C33⋊C4C2xC3^3:C4216,16924T553
C3×C322C8Direct product of C3 and C322C8C3xC3^2:2C8216,11724T554
C6×C32⋊C4Direct product of C6 and C32⋊C4C6xC3^2:C4216,16824T555
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15824T556
S33Direct product of S3, S3 and S3; = Hol(C3×S3)S3^3216,16224T557
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4C3^2:2D12216,15924T558
S3×C32⋊C4Direct product of S3 and C32⋊C4S3xC3^2:C4216,15624T559
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15824T560
C3×S3≀C2Direct product of C3 and S3≀C2C3xS3wrC2216,15724T561
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C3ASL(2,3)216,15324T562
C3×S3×A4Direct product of C3, S3 and A4C3xS3xA4216,16624T563
C3×C3⋊S4Direct product of C3 and C3⋊S4C3xC3:S4216,16424T564
C3×PSU3(𝔽2)Direct product of C3 and PSU3(𝔽2)C3xPSU(3,2)216,16024T565
C33⋊Q82nd semidirect product of C33 and Q8 acting faithfullyC3^3:Q8216,16124T566
C3×F9Direct product of C3 and F9C3xF9216,15424T567
C3⋊F9The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2C3:F9216,15524T568
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C3ASL(2,3)216,15324T569

### Groups of order 240

LabelIDTr ID
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18924T570
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2A5:C4240,9124T571
C22×A5Direct product of C22 and A5C2^2xA5240,19024T572
24T573
C4×A5Direct product of C4 and A5C4xA5240,9224T574
24T575
C4.A5The central extension by C4 of A5C4.A5240,9324T576
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18924T577
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2A5:C4240,9124T578

### Groups of order 288

LabelIDTr ID
C2×A42Direct product of C2, A4 and A4C2xA4^2288,102924T579
A4×SL2(𝔽3)Direct product of A4 and SL2(𝔽3)A4xSL(2,3)288,85924T580
C62.31D415th non-split extension by C62 of D4 acting via D4/C2=C22C6^2.31D4288,22824T581
C32⋊2+ 1+4The semidirect product of C32 and 2+ 1+4 acting via 2+ 1+4/C23=C22C3^2:ES+(2,2)288,97824T582
C62.32D416th non-split extension by C62 of D4 acting via D4/C2=C22C6^2.32D4288,22924T583
(C2×C62)⋊C44th semidirect product of C2×C62 and C4 acting faithfully(C2xC6^2):C4288,43424T584
(C2×C62).C45th non-split extension by C2×C62 of C4 acting faithfully(C2xC6^2).C4288,43624T585
C3×C23.7D6Direct product of C3 and C23.7D6C3xC2^3.7D6288,26824T586
C3×C23.6D6Direct product of C3 and C23.6D6C3xC2^3.6D6288,24024T587
C3×D46D6Direct product of C3 and D46D6C3xD4:6D6288,99424T588
C3×C23.7D6Direct product of C3 and C23.7D6C3xC2^3.7D6288,26824T589
C3×C12.D4Direct product of C3 and C12.D4C3xC12.D4288,26724T590
C3×C23⋊A4Direct product of C3 and C23⋊A4C3xC2^3:A4288,98724T591
C62⋊D42nd semidirect product of C62 and D4 acting faithfullyC6^2:D4288,89024T592
24T593
D6≀C2Wreath product of D6 by C2D6wrC2288,88924T594
C62.9D49th non-split extension by C62 of D4 acting faithfullyC6^2.9D4288,88124T595
C62.2D42nd non-split extension by C62 of D4 acting faithfullyC6^2.2D4288,38624T596
24T597
24T598
C62.9D49th non-split extension by C62 of D4 acting faithfullyC6^2.9D4288,88124T599
Dic3≀C2Wreath product of Dic3 by C2Dic3wrC2288,38924T600
C62.12D412nd non-split extension by C62 of D4 acting faithfullyC6^2.12D4288,88424T601
C62.2D42nd non-split extension by C62 of D4 acting faithfullyC6^2.2D4288,38624T602
C62.12D412nd non-split extension by C62 of D4 acting faithfullyC6^2.12D4288,88424T603
Dic3≀C2Wreath product of Dic3 by C2Dic3wrC2288,38924T604
C62.2D42nd non-split extension by C62 of D4 acting faithfullyC6^2.2D4288,38624T605
S32×D4Direct product of S3, S3 and D4S3^2xD4288,95824T606
D1213D67th semidirect product of D12 and D6 acting via D6/S3=C2D12:13D6288,96224T607
Dic612D66th semidirect product of Dic6 and D6 acting via D6/S3=C2Dic6:12D6288,96024T608
C32⋊2+ 1+4The semidirect product of C32 and 2+ 1+4 acting via 2+ 1+4/C23=C22C3^2:ES+(2,2)288,97824T609
D1223D67th semidirect product of D12 and D6 acting via D6/C6=C2D12:23D6288,95424T610
D1227D63rd semidirect product of D12 and D6 acting through Inn(D12)D12:27D6288,95624T611
D124Dic34th semidirect product of D12 and Dic3 acting via Dic3/C6=C2D12:4Dic3288,21624T612
D1218D62nd semidirect product of D12 and D6 acting via D6/C6=C2D12:18D6288,47324T613
C62.31D415th non-split extension by C62 of D4 acting via D4/C2=C22C6^2.31D4288,22824T614
C62.32D416th non-split extension by C62 of D4 acting via D4/C2=C22C6^2.32D4288,22924T615
C3⋊C820D69th semidirect product of C3⋊C8 and D6 acting via D6/S3=C2C3:C8:20D6288,46624T616
C12.70D121st non-split extension by C12 of D12 acting via D12/D6=C2C12.70D12288,20724T617
D4×C32⋊C4Direct product of D4 and C32⋊C4D4xC3^2:C4288,93624T618
24T619
(C2×C62)⋊C44th semidirect product of C2×C62 and C4 acting faithfully(C2xC6^2):C4288,43424T620
(C6×C12)⋊5C45th semidirect product of C6×C12 and C4 acting faithfully(C6xC12):5C4288,93424T621
(C6×C12)⋊C41st semidirect product of C6×C12 and C4 acting faithfully(C6xC12):C4288,42224T622
24T623
C3⋊S3⋊M4(2)2nd semidirect product of C3⋊S3 and M4(2) acting via M4(2)/C2×C4=C2C3:S3:M4(2)288,93124T624
(C2×C62).C45th non-split extension by C2×C62 of C4 acting faithfully(C2xC6^2).C4288,43624T625
C3×C244S3Direct product of C3 and C244S3C3xC2^4:4S3288,72424T626
C3×C424S3Direct product of C3 and C424S3C3xC4^2:4S3288,23924T627
C3×D126C22Direct product of C3 and D126C22C3xD12:6C2^2288,70324T628
C3×C23.6D6Direct product of C3 and C23.6D6C3xC2^3.6D6288,24024T629
C22⋊F9The semidirect product of C22 and F9 acting via F9/C32⋊C4=C2C2^2:F9288,86724T630
24T631
C62⋊Q81st semidirect product of C62 and Q8 acting faithfullyC6^2:Q8288,89524T632
24T633
A4×S4Direct product of A4 and S4A4xS4288,102424T634
24T635
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)PSO+(4,3)288,102624T636
24T637
A4×S4Direct product of A4 and S4A4xS4288,102424T638
24T639
C62⋊D42nd semidirect product of C62 and D4 acting faithfullyC6^2:D4288,89024T640
(S32)⋊Q8The semidirect product of S32 and Q8 acting via Q8/C4=C2(S3^2):Q8288,86824T641
C4.4S3≀C24th non-split extension by C4 of S3≀C2 acting via S3≀C2/C32⋊C4=C2C4.4S3wrC2288,86924T642
C4×S3≀C2Direct product of C4 and S3≀C2C4xS3wrC2288,87724T643
C4⋊S3≀C2The semidirect product of C4 and S3≀C2 acting via S3≀C2/S32=C2C4:S3wrC2288,87824T644
C2×(S32)⋊C4Direct product of C2 and (S32)⋊C4C2x(S3^2):C4288,88024T645
C62.9D49th non-split extension by C62 of D4 acting faithfullyC6^2.9D4288,88124T646
C62⋊D42nd semidirect product of C62 and D4 acting faithfullyC6^2:D4288,89024T647
(S32)⋊Q8The semidirect product of S32 and Q8 acting via Q8/C4=C2(S3^2):Q8288,86824T648
C4⋊S3≀C2The semidirect product of C4 and S3≀C2 acting via S3≀C2/S32=C2C4:S3wrC2288,87824T649
C4×S3≀C2Direct product of C4 and S3≀C2C4xS3wrC2288,87724T650
C2×(S32)⋊C4Direct product of C2 and (S32)⋊C4C2x(S3^2):C4288,88024T651
C4⋊S3≀C2The semidirect product of C4 and S3≀C2 acting via S3≀C2/S32=C2C4:S3wrC2288,87824T652
(C3×C12)⋊D42nd semidirect product of C3×C12 and D4 acting faithfully(C3xC12):D4288,87924T653
C22×S3≀C2Direct product of C22 and S3≀C2C2^2xS3wrC2288,103124T654
D6≀C2Wreath product of D6 by C2D6wrC2288,88924T655
C4⋊S3≀C2The semidirect product of C4 and S3≀C2 acting via S3≀C2/S32=C2C4:S3wrC2288,87824T656
C22×S3≀C2Direct product of C22 and S3≀C2C2^2xS3wrC2288,103124T657
C32⋊D8⋊C23rd semidirect product of C32⋊D8 and C2 acting faithfullyC3^2:D8:C2288,87224T658
C3⋊S3⋊D8The semidirect product of C3⋊S3 and D8 acting via D8/C4=C22C3:S3:D8288,87324T659
C3⋊S32SD16The semidirect product of C3⋊S3 and SD16 acting via SD16/C4=C22C3:S3:2SD16288,87524T660
C2×(S32)⋊C4Direct product of C2 and (S32)⋊C4C2x(S3^2):C4288,88024T661
C4.S3≀C21st non-split extension by C4 of S3≀C2 acting via S3≀C2/S32=C2C4.S3wrC2288,37524T662
(S32)⋊C8The semidirect product of S32 and C8 acting via C8/C4=C2(S3^2):C8288,37424T663
24T664
C62.2D42nd non-split extension by C62 of D4 acting faithfullyC6^2.2D4288,38624T665
C3⋊S3.2D81st non-split extension by C3⋊S3 of D8 acting via D8/C4=C22C3:S3.2D8288,37724T666
24T667
D12⋊D64th semidirect product of D12 and D6 acting via D6/C3=C22D12:D6288,57424T668
D125D65th semidirect product of D12 and D6 acting via D6/C3=C22D12:5D6288,58524T669
Dic6⋊D64th semidirect product of Dic6 and D6 acting via D6/C3=C22Dic6:D6288,57824T670
C2×Dic3⋊D6Direct product of C2 and Dic3⋊D6C2xDic3:D6288,97724T671
C628D45th semidirect product of C62 and D4 acting via D4/C2=C22C6^2:8D4288,62924T672
C62.116C23111st non-split extension by C62 of C23 acting via C23/C2=C22C6^2.116C2^3288,62224T673
C2×C62⋊C4Direct product of C2 and C62⋊C4C2xC6^2:C4288,94124T674
24T675
C3⋊S3.5D8The non-split extension by C3⋊S3 of D8 acting via D8/D4=C2C3:S3.5D8288,43024T676
24T677
S3×GL2(𝔽3)Direct product of S3 and GL2(𝔽3); = GL2(ℤ/6ℤ)S3xGL(2,3)288,85124T678
C2×S3×S4Direct product of C2, S3 and S4; = Aut(S3×SL2(𝔽3))C2xS3xS4288,102824T679
C2.AΓL1(𝔽9)1st central extension by C2 of AΓL1(𝔽9)C2.AGammaL(1,9)288,84124T680
C2×AΓL1(𝔽9)Direct product of C2 and AΓL1(𝔽9)C2xAGammaL(1,9)288,102724T681
24T682
C2.AΓL1(𝔽9)1st central extension by C2 of AΓL1(𝔽9)C2.AGammaL(1,9)288,84124T683
C2×A42Direct product of C2, A4 and A4C2xA4^2288,102924T684
Ω4+ (𝔽3)Omega group of + type on 𝔽34; = SL2(𝔽3)A4Omega+(4,3)288,86024T685
D6≀C2Wreath product of D6 by C2D6wrC2288,88924T686
24T687
24T688
24T689
24T690
24T691
A4≀C2Wreath product of A4 by C2A4wrC2288,102524T692
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)PSO+(4,3)288,102624T693
A4≀C2Wreath product of A4 by C2A4wrC2288,102524T694
24T695
(C22×S3)⋊A4The semidirect product of C22×S3 and A4 acting faithfully(C2^2xS3):A4288,41124T696
24T697
C3×C24⋊C6Direct product of C3 and C24⋊C6C3xC2^4:C6288,63424T698
(C2×C6)⋊S42nd semidirect product of C2×C6 and S4 acting via S4/C22=S3(C2xC6):S4288,103624T699
C3×C22⋊S4Direct product of C3 and C22⋊S4C3xC2^2:S4288,103524T700
24T701
A4≀C2Wreath product of A4 by C2A4wrC2288,102524T702
24T703
24T704
A4×S4Direct product of A4 and S4A4xS4288,102424T705

### Groups of order 336

LabelIDTr ID
S3×F8Direct product of S3 and F8S3xF8336,21124T706
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,20824T707

### Groups of order 432

LabelIDTr ID
C3×S3×C3⋊D4Direct product of C3, S3 and C3⋊D4C3xS3xC3:D4432,65824T1280
C3×D6.3D6Direct product of C3 and D6.3D6C3xD6.3D6432,65224T1281
C3×Dic3⋊D6Direct product of C3 and Dic3⋊D6C3xDic3:D6432,65924T1282
C3×D6.4D6Direct product of C3 and D6.4D6C3xD6.4D6432,65324T1283
C6224D65th semidirect product of C62 and D6 acting via D6/C3=C22C6^2:24D6432,69624T1284
C62.96D644th non-split extension by C62 of D6 acting via D6/C3=C22C6^2.96D6432,69324T1285
C6211Dic31st semidirect product of C62 and Dic3 acting via Dic3/C3=C4C6^2:11Dic3432,64124T1286
C3312M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C22=C4C3^3:12M4(2)432,64024T1287
C3×C62⋊C4Direct product of C3 and C62⋊C4C3xC6^2:C4432,63424T1288
C3×C62.C4Direct product of C3 and C62.C4C3xC6^2.C4432,63324T1289
C33⋊D82nd semidirect product of C33 and D8 acting via D8/C2=D4C3^3:D8432,58224T1290
C337SD163rd semidirect product of C33 and SD16 acting via SD16/C2=D4C3^3:7SD16432,58424T1291
C2×C33⋊D4Direct product of C2 and C33⋊D4C2xC3^3:D4432,75524T1292
(S32)⋊Dic3The semidirect product of S32 and Dic3 acting via Dic3/C6=C2(S3^2):Dic3432,58024T1293
(S3×C6)⋊D61st semidirect product of S3×C6 and D6 acting via D6/C3=C22(S3xC6):D6432,60124T1294
S3×C3⋊D12Direct product of S3 and C3⋊D12S3xC3:D12432,59824T1295
C2×S33Direct product of C2, S3, S3 and S3C2xS3^3432,75924T1296
C3⋊S34D12The semidirect product of C3⋊S3 and D12 acting via D12/D6=C2C3:S3:4D12432,60224T1297
S3×C6.D6Direct product of S3 and C6.D6S3xC6.D6432,59524T1298
D6⋊(S32)1st semidirect product of D6 and S32 acting via S32/C3⋊S3=C2D6:(S3^2)432,59924T1299
C6.D6⋊S33rd semidirect product of C6.D6 and S3 acting via S3/C3=C2C6.D6:S3432,61224T1300
(S3×Dic3)⋊S33rd semidirect product of S3×Dic3 and S3 acting via S3/C3=C2(S3xDic3):S3432,60924T1301
C336(C2×Q8)3rd semidirect product of C33 and C2×Q8 acting via C2×Q8/C2=C23C3^3:6(C2xQ8)432,60524T1302
D6.(S32)1st non-split extension by D6 of S32 acting via S32/C3×S3=C2D6.(S3^2)432,60624T1303
C2×C322D12Direct product of C2 and C322D12C2xC3^2:2D12432,75624T1304
(C3×C6).8D121st non-split extension by C3×C6 of D12 acting via D12/C3=D4(C3xC6).8D12432,58624T1305
C322D24The semidirect product of C32 and D24 acting via D24/C6=D4C3^2:2D24432,58824T1306
C338SD164th semidirect product of C33 and SD16 acting via SD16/C2=D4C3^3:8SD16432,58924T1307
C335(C2×C8)2nd semidirect product of C33 and C2×C8 acting via C2×C8/C2=C2×C4C3^3:5(C2xC8)432,57124T1308
C332M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C2=C2×C4C3^3:2M4(2)432,57324T1309
C2×S3×C32⋊C4Direct product of C2, S3 and C32⋊C4C2xS3xC3^2:C4432,75324T1310
D6⋊(C32⋊C4)The semidirect product of D6 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2D6:(C3^2:C4)432,56824T1311
C2×C33⋊D4Direct product of C2 and C33⋊D4C2xC3^3:D4432,75524T1312
C3⋊S3.2D121st non-split extension by C3⋊S3 of D12 acting via D12/C6=C22C3:S3.2D12432,57924T1313
C33⋊D82nd semidirect product of C33 and D8 acting via D8/C2=D4C3^3:D8432,58224T1314
C336SD162nd semidirect product of C33 and SD16 acting via SD16/C2=D4C3^3:6SD16432,58324T1315
C6×S3≀C2Direct product of C6 and S3≀C2C6xS3wrC2432,75424T1316
C3×(S32)⋊C4Direct product of C3 and (S32)⋊C4C3x(S3^2):C4432,57424T1317
C3×C32⋊D8Direct product of C3 and C32⋊D8C3xC3^2:D8432,57624T1318
C3×C322SD16Direct product of C3 and C322SD16C3xC3^2:2SD16432,57724T1319
C2×ASL2(𝔽3)Direct product of C2 and ASL2(𝔽3)C2xASL(2,3)432,73524T1320
24T1321
S3×S3≀C2Direct product of S3 and S3≀C2S3xS3wrC2432,74124T1322
24T1323
24T1324
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)AGL(2,3)432,73424T1325
24T1326
24T1327
C3×S3×S4Direct product of C3, S3 and S4C3xS3xS4432,74524T1328
S3×C3⋊S4Direct product of S3 and C3⋊S4S3xC3:S4432,74724T1329
C3×AΓL1(𝔽9)Direct product of C3 and AΓL1(𝔽9)C3xAGammaL(1,9)432,73724T1330
C33⋊SD162nd semidirect product of C33 and SD16 acting faithfullyC3^3:SD16432,73824T1331
C333SD163rd semidirect product of C33 and SD16 acting faithfullyC3^3:3SD16432,73924T1332
F9⋊S3The semidirect product of F9 and S3 acting via S3/C3=C2F9:S3432,74024T1333
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)AGL(2,3)432,73424T1334
S3×PSU3(𝔽2)Direct product of S3 and PSU3(𝔽2)S3xPSU(3,2)432,74224T1335
S3×F9Direct product of S3 and F9S3xF9432,73624T1336
A4×C32⋊C4Direct product of A4 and C32⋊C4A4xC3^2:C4432,74424T1337
S32×A4Direct product of S3, S3 and A4S3^2xA4432,74924T1338
C62⋊Dic3The semidirect product of C62 and Dic3 acting faithfullyC6^2:Dic3432,74324T1339
C6210D610th semidirect product of C62 and D6 acting faithfullyC6^2:10D6432,74824T1340

### Groups of order 480

LabelIDTr ID
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2C2^2:S5480,95124T1341
24T1342
D4×A5Direct product of D4 and A5D4xA5480,95624T1343
24T1344
C22×S5Direct product of C22 and S5C2^2xS5480,118624T1345
C2×A5⋊C4Direct product of C2 and A5⋊C4C2xA5:C4480,95224T1346
C4×S5Direct product of C4 and S5; = CO3(𝔽5)C4xS5480,94324T1347
24T1348
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2C2^2:S5480,95124T1349
24T1350
A5⋊Q8The semidirect product of A5 and Q8 acting via Q8/C4=C2A5:Q8480,94524T1351
C4⋊S5The semidirect product of C4 and S5 acting via S5/A5=C2C4:S5480,94424T1352
GL2(𝔽5)General linear group on 𝔽52; = SL2(𝔽5)1C4 = Aut(C52)GL(2,5)480,21824T1353

### Groups of order 25

LabelIDTr ID
C25Cyclic groupC2525,125T1
C52Elementary abelian group of type [5,5]C5^225,225T2

### Groups of order 50

LabelIDTr ID
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)C5xD550,325T3
D25Dihedral groupD2550,125T4
C5⋊D5The semidirect product of C5 and D5 acting via D5/C5=C2C5:D550,425T5

### Groups of order 75

LabelIDTr ID
C52⋊C3The semidirect product of C52 and C3 acting faithfullyC5^2:C375,225T6

### Groups of order 100

LabelIDTr ID
C5×F5Direct product of C5 and F5C5xF5100,925T7
C25⋊C4The semidirect product of C25 and C4 acting faithfullyC25:C4100,325T8
C5⋊F51st semidirect product of C5 and F5 acting via F5/C5=C4C5:F5100,1125T9
C52⋊C44th semidirect product of C52 and C4 acting faithfullyC5^2:C4100,1225T10
D5.D5The non-split extension by D5 of D5 acting via D5/C5=C2D5.D5100,1025T11
D52Direct product of D5 and D5D5^2100,1325T12

### Groups of order 125

LabelIDTr ID
5- 1+2Extraspecial groupES-(5,1)125,425T13
He5Heisenberg group; = C52C5 = 5+ 1+2He5125,325T14

### Groups of order 150

LabelIDTr ID
C52⋊C6The semidirect product of C52 and C6 acting faithfullyC5^2:C6150,625T15
C52⋊S3The semidirect product of C52 and S3 acting faithfullyC5^2:S3150,525T16

### Groups of order 200

LabelIDTr ID
C52⋊Q8The semidirect product of C52 and Q8 acting faithfullyC5^2:Q8200,4425T17
D5×F5Direct product of D5 and F5D5xF5200,4125T18
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)D5:F5200,4225T19
C52⋊C8The semidirect product of C52 and C8 acting faithfullyC5^2:C8200,4025T20
D5≀C2Wreath product of D5 by C2D5wrC2200,4325T21

### Groups of order 250

LabelIDTr ID
He5⋊C22nd semidirect product of He5 and C2 acting faithfullyHe5:C2250,825T22
C52⋊C10The semidirect product of C52 and C10 acting faithfullyC5^2:C10250,525T23
25T24
C25⋊C10The semidirect product of C25 and C10 acting faithfullyC25:C10250,625T25

### Groups of order 300

LabelIDTr ID
C52⋊C12The semidirect product of C52 and C12 acting faithfullyC5^2:C12300,2425T26
C52⋊D6The semidirect product of C52 and D6 acting faithfullyC5^2:D6300,2525T27
C52⋊Dic3The semidirect product of C52 and Dic3 acting faithfullyC5^2:Dic3300,2325T28
C5×A5Direct product of C5 and A5; = U2(𝔽4)C5xA5300,2225T29

### Groups of order 400

LabelIDTr ID
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfullyD5wrC2:C2400,20725T30
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfullyC5^2:M4(2)400,20625T31
F52Direct product of F5 and F5; = Hol(F5)F5^2400,20525T32

### Groups of order 500

LabelIDTr ID
C52⋊F53rd semidirect product of C52 and F5 acting faithfullyC5^2:F5500,2325T33
C52⋊C20The semidirect product of C52 and C20 acting faithfullyC5^2:C20500,1725T34
He54C44th semidirect product of He5 and C4 acting faithfully; = Aut(5- 1+2)He5:4C4500,2525T35
He5⋊C42nd semidirect product of He5 and C4 acting faithfullyHe5:C4500,2125T36
C52⋊C20The semidirect product of C52 and C20 acting faithfullyC5^2:C20500,1725T37
C52⋊D10The semidirect product of C52 and D10 acting faithfullyC5^2:D10500,2725T38
He5⋊C42nd semidirect product of He5 and C4 acting faithfullyHe5:C4500,2125T39
C25⋊C20The semidirect product of C25 and C20 acting faithfully; = Aut(D25) = Hol(C25)C25:C20500,1825T40

### Groups of order 26

LabelIDTr ID
C26Cyclic groupC2626,226T1
D13Dihedral groupD1326,126T2

### Groups of order 52

LabelIDTr ID
D26Dihedral group; = C2×D13D2652,426T3
C13⋊C4The semidirect product of C13 and C4 acting faithfullyC13:C452,326T4

### Groups of order 78

LabelIDTr ID
C2×C13⋊C3Direct product of C2 and C13⋊C3C2xC13:C378,226T5
C13⋊C6The semidirect product of C13 and C6 acting faithfullyC13:C678,126T6

### Groups of order 104

LabelIDTr ID
C2×C13⋊C4Direct product of C2 and C13⋊C4C2xC13:C4104,1226T7

### Groups of order 156

LabelIDTr ID
F13Frobenius group; = C13C12 = AGL1(𝔽13) = Aut(D13) = Hol(C13)F13156,726T8
C2×C13⋊C6Direct product of C2 and C13⋊C6C2xC13:C6156,826T9

### Groups of order 312

LabelIDTr ID
C2×F13Direct product of C2 and F13; = Aut(D26) = Hol(C26)C2xF13312,4526T10

### Groups of order 338

LabelIDTr ID
C13×D13Direct product of C13 and D13; = AΣL1(𝔽169)C13xD13338,326T11

### Groups of order 27

LabelIDTr ID
C27Cyclic groupC2727,127T1
C3×C9Abelian group of type [3,9]C3xC927,227T2
He3Heisenberg group; = C32C3 = 3+ 1+2He327,327T3
C33Elementary abelian group of type [3,3,3]C3^327,527T4
3- 1+2Extraspecial groupES-(3,1)27,427T5

### Groups of order 54

LabelIDTr ID
He3⋊C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)He3:C254,827T6
C33⋊C23rd semidirect product of C33 and C2 acting faithfullyC3^3:C254,1427T7
D27Dihedral groupD2754,127T8
C3×D9Direct product of C3 and D9C3xD954,327T9
C9⋊S3The semidirect product of C9 and S3 acting via S3/C3=C2C9:S354,727T10
C32⋊C6The semidirect product of C32 and C6 acting faithfullyC3^2:C654,527T11
S3×C9Direct product of C9 and S3S3xC954,427T12
C3×C3⋊S3Direct product of C3 and C3⋊S3C3xC3:S354,1327T13
C9⋊C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)C9:C654,627T14
S3×C32Direct product of C32 and S3S3xC3^254,1227T15

### Groups of order 81

LabelIDTr ID
C3×3- 1+2Direct product of C3 and 3- 1+2C3xES-(3,1)81,1327T16
C32⋊C9The semidirect product of C32 and C9 acting via C9/C3=C3C3^2:C981,327T17
C3×He3Direct product of C3 and He3C3xHe381,1227T18
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)C3wrC381,727T19
He3.C3The non-split extension by He3 of C3 acting faithfullyHe3.C381,827T20
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)C3wrC381,727T21
C27⋊C3The semidirect product of C27 and C3 acting faithfullyC27:C381,627T22
He3⋊C32nd semidirect product of He3 and C3 acting faithfullyHe3:C381,927T23
27T24
C3.He34th central stem extension by C3 of He3C3.He381,1027T25
He3.C3The non-split extension by He3 of C3 acting faithfullyHe3.C381,827T26
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)C3wrC381,727T27
C9○He3Central product of C9 and He3C9oHe381,1427T28

### Groups of order 108

LabelIDTr ID
C32⋊D6The semidirect product of C32 and D6 acting faithfullyC3^2:D6108,1727T29
S3×D9Direct product of S3 and D9S3xD9108,1627T30
C33⋊C42nd semidirect product of C33 and C4 acting faithfullyC3^3:C4108,3727T31
He3⋊C4The semidirect product of He3 and C4 acting faithfullyHe3:C4108,1527T32
C3×C32⋊C4Direct product of C3 and C32⋊C4C3xC3^2:C4108,3627T33
S3×C3⋊S3Direct product of S3 and C3⋊S3S3xC3:S3108,3927T34
C324D6The semidirect product of C32 and D6 acting via D6/C3=C22C3^2:4D6108,4027T35
C3×S32Direct product of C3, S3 and S3C3xS3^2108,3827T36

### Groups of order 162

LabelIDTr ID
C3≀S3Wreath product of C3 by S3C3wrS3162,1027T37
He3.2S32nd non-split extension by He3 of S3 acting faithfullyHe3.2S3162,1527T38
He3.4C6The non-split extension by He3 of C6 acting via C6/C3=C2He3.4C6162,4427T39
He3.2C62nd non-split extension by He3 of C6 acting faithfullyHe3.2C6162,1427T40
He3.S31st non-split extension by He3 of S3 acting faithfullyHe3.S3162,1327T41
He3.3S33rd non-split extension by He3 of S3 acting faithfullyHe3.3S3162,2027T42
3- 1+2.S3The non-split extension by 3- 1+2 of S3 acting faithfullyES-(3,1).S3162,2227T43
He3⋊S33rd semidirect product of He3 and S3 acting faithfullyHe3:S3162,2127T44
He3.C61st non-split extension by He3 of C6 acting faithfullyHe3.C6162,1227T45
C3×He3⋊C2Direct product of C3 and He3⋊C2C3xHe3:C2162,4127T46
C32⋊C18The semidirect product of C32 and C18 acting via C18/C3=C6C3^2:C18162,427T47
C3×C32⋊C6Direct product of C3 and C32⋊C6C3xC3^2:C6162,3427T48
He3.2C62nd non-split extension by He3 of C6 acting faithfullyHe3.2C6162,1427T49
C3≀S3Wreath product of C3 by S3C3wrS3162,1027T50
C33⋊S32nd semidirect product of C33 and S3 acting faithfullyC3^3:S3162,1927T51
27T52
C33⋊C61st semidirect product of C33 and C6 acting faithfullyC3^3:C6162,1127T53
He3.4S3The non-split extension by He3 of S3 acting via S3/C3=C2He3.4S3162,4327T54
C27⋊C6The semidirect product of C27 and C6 acting faithfullyC27:C6162,927T55
He3.4S3The non-split extension by He3 of S3 acting via S3/C3=C2He3.4S3162,4327T56
C3×C9⋊C6Direct product of C3 and C9⋊C6C3xC9:C6162,3627T57
C33.S34th non-split extension by C33 of S3 acting faithfullyC3^3.S3162,4227T58
C32⋊D91st semidirect product of C32 and D9 acting via D9/C3=S3C3^2:D9162,527T59
C3×C32⋊C6Direct product of C3 and C32⋊C6C3xC3^2:C6162,3427T60
He34S31st semidirect product of He3 and S3 acting via S3/C3=C2He3:4S3162,4027T61
C33⋊C61st semidirect product of C33 and C6 acting faithfullyC3^3:C6162,1127T62
27T63
He3.2S32nd non-split extension by He3 of S3 acting faithfullyHe3.2S3162,1527T64
C322D92nd semidirect product of C32 and D9 acting via D9/C3=S3C3^2:2D9162,1727T65
He3⋊S33rd semidirect product of He3 and S3 acting faithfullyHe3:S3162,2127T66
C33⋊S32nd semidirect product of C33 and S3 acting faithfullyC3^3:S3162,1927T67
He3.3S33rd non-split extension by He3 of S3 acting faithfullyHe3.3S3162,2027T68
He3.C61st non-split extension by He3 of C6 acting faithfullyHe3.C6162,1227T69
C3≀S3Wreath product of C3 by S3C3wrS3162,1027T70
He34S31st semidirect product of He3 and S3 acting via S3/C3=C2He3:4S3162,4027T71
He3.S31st non-split extension by He3 of S3 acting faithfullyHe3.S3162,1327T72
S3×He3Direct product of S3 and He3S3xHe3162,3527T73
He35S32nd semidirect product of He3 and S3 acting via S3/C3=C2He3:5S3162,4627T74
S3×3- 1+2Direct product of S3 and 3- 1+2S3xES-(3,1)162,3727T75

### Groups of order 216

LabelIDTr ID
He3⋊D4The semidirect product of He3 and D4 acting faithfullyHe3:D4216,8727T76
He3⋊C8The semidirect product of He3 and C8 acting faithfullyHe3:C8216,8627T77
C3×F9Direct product of C3 and F9C3xF9216,15427T78
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4C3^2:2D12216,15927T79
C3⋊F9The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2C3:F9216,15527T80
C33⋊D42nd semidirect product of C33 and D4 acting faithfullyC3^3:D4216,15827T81
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C3ASL(2,3)216,15327T82
SU3(𝔽2)Special unitary group on 𝔽23; = He3Q8SU(3,2)216,8827T83
C3×S3≀C2Direct product of C3 and S3≀C2C3xS3wrC2216,15727T84
S3×C32⋊C4Direct product of S3 and C32⋊C4S3xC3^2:C4216,15627T85
S33Direct product of S3, S3 and S3; = Hol(C3×S3)S3^3216,16227T86
C33⋊Q82nd semidirect product of C33 and Q8 acting faithfullyC3^3:Q8216,16127T87
C3×PSU3(𝔽2)Direct product of C3 and PSU3(𝔽2)C3xPSU(3,2)216,16027T88

### Groups of order 243

LabelIDTr ID
C33⋊C91st semidirect product of C33 and C9 acting via C9/C3=C3C3^3:C9243,1327T89
C32.5He35th non-split extension by C32 of He3 acting via He3/C32=C3C3^2.5He3243,2927T90
C32.6He36th non-split extension by C32 of He3 acting via He3/C32=C3C3^2.6He3243,3027T91
C9.4He32nd central extension by C9 of He3C9.4He3243,1627T92
C9.He31st non-split extension by C9 of He3 acting via He3/C32=C3C9.He3243,5527T93
C32.He34th non-split extension by C32 of He3 acting via He3/C32=C3C3^2.He3243,2827T94
C32⋊He3The semidirect product of C32 and He3 acting via He3/C32=C3C3^2:He3243,3727T95
He3⋊C323rd semidirect product of He3 and C32 acting via C32/C3=C3He3:C3^2243,5827T96
27T97
C33⋊C91st semidirect product of C33 and C9 acting via C9/C3=C3C3^3:C9243,1327T98
He3.C324th non-split extension by He3 of C32 acting via C32/C3=C3He3.C3^2243,5727T99
C33⋊C322nd semidirect product of C33 and C32 acting faithfullyC3^3:C3^2243,5627T100
3+ 1+4Extraspecial group; = He3He3ES+(3,2)243,6527T101
C33⋊C322nd semidirect product of C33 and C32 acting faithfullyC3^3:C3^2243,5627T102
C9.2He32nd non-split extension by C9 of He3 acting via He3/C32=C3C9.2He3243,6027T103
C922C32nd semidirect product of C92 and C3 acting faithfullyC9^2:2C3243,2627T104
C3×C3≀C3Direct product of C3 and C3≀C3C3xC3wrC3243,5127T105
27T106
C27⋊C9The semidirect product of C27 and C9 acting faithfullyC27:C9243,2227T107
C92⋊C31st semidirect product of C92 and C3 acting faithfullyC9^2:C3243,2527T108
He3.C324th non-split extension by He3 of C32 acting via C32/C3=C3He3.C3^2243,5727T109
C34.C33rd non-split extension by C34 of C3 acting faithfullyC3^4.C3243,3827T110
C32.C339th non-split extension by C32 of C33 acting via C33/C32=C3C3^2.C3^3243,5927T111
C92.C32nd non-split extension by C92 of C3 acting faithfullyC9^2.C3243,2727T112
3- 1+4Extraspecial group; = He33- 1+2ES-(3,2)243,6627T113
C33⋊C322nd semidirect product of C33 and C32 acting faithfullyC3^3:C3^2243,5627T114

### Groups of order 324

LabelIDTr ID
S3×C32⋊C6Direct product of S3 and C32⋊C6S3xC3^2:C6324,11627T115
S3×C9⋊C6Direct product of S3 and C9⋊C6S3xC9:C6324,11827T116
He35D61st semidirect product of He3 and D6 acting via D6/C3=C22He3:5D6324,12127T117
S3×He3⋊C2Direct product of S3 and He3⋊C2S3xHe3:C2324,12227T118
S3×C32⋊C6Direct product of S3 and C32⋊C6S3xC3^2:C6324,11627T119
He36D62nd semidirect product of He3 and D6 acting via D6/C3=C22He3:6D6324,12427T120
He3⋊D6The semidirect product of He3 and D6 acting faithfullyHe3:D6324,3927T121
He3.6D6The non-split extension by He3 of D6 acting via D6/C3=C22He3.6D6324,12527T122
He3.2D62nd non-split extension by He3 of D6 acting faithfullyHe3.2D6324,4127T123
He3.D61st non-split extension by He3 of D6 acting faithfullyHe3.D6324,4027T124
C3×C32⋊D6Direct product of C3 and C32⋊D6C3xC3^2:D6324,11727T125
C32⋊D18The semidirect product of C32 and D18 acting via D18/C3=D6C3^2:D18324,3727T126
He35D61st semidirect product of He3 and D6 acting via D6/C3=C22He3:5D6324,12127T127
He3⋊D6The semidirect product of He3 and D6 acting faithfullyHe3:D6324,3927T128
27T129
C33⋊A4The semidirect product of C33 and A4 acting faithfullyC3^3:A4324,16027T130
27T131
He3.D61st non-split extension by He3 of D6 acting faithfullyHe3.D6324,4027T132
He3.2D62nd non-split extension by He3 of D6 acting faithfullyHe3.2D6324,4127T133

### Groups of order 351

LabelIDTr ID
C33⋊C13The semidirect product of C33 and C13 acting faithfullyC3^3:C13351,1227T134

### Groups of order 432

LabelIDTr ID
S3×PSU3(𝔽2)Direct product of S3 and PSU3(𝔽2)S3xPSU(3,2)432,74227T135
C33⋊SD162nd semidirect product of C33 and SD16 acting faithfullyC3^3:SD16432,73827T136
S3×S3≀C2Direct product of S3 and S3≀C2S3xS3wrC2432,74127T137
S3×F9Direct product of S3 and F9S3xF9432,73627T138
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)AGL(2,3)432,73427T139
C333SD163rd semidirect product of C33 and SD16 acting faithfullyC3^3:3SD16432,73927T140
He3⋊SD16The semidirect product of He3 and SD16 acting faithfullyHe3:SD16432,52027T141
C3×AΓL1(𝔽9)Direct product of C3 and AΓL1(𝔽9)C3xAGammaL(1,9)432,73727T142
F9⋊S3The semidirect product of F9 and S3 acting via S3/C3=C2F9:S3432,74027T143

### Groups of order 486

LabelIDTr ID
3- 1+4⋊C21st semidirect product of 3- 1+4 and C2 acting faithfullyES-(3,2):C2486,23827T144
27T145
C34.7S37th non-split extension by C34 of S3 acting faithfullyC3^4.7S3486,14727T146
He3⋊(C3×S3)4th semidirect product of He3 and C3×S3 acting via C3×S3/C3=S3He3:(C3xS3)486,17827T147
C9⋊S3⋊C322nd semidirect product of C9⋊S3 and C32 acting faithfullyC9:S3:C3^2486,12927T148
C3≀S33C3The semidirect product of C3≀S3 and C3 acting through Inn(C3≀S3)C3wrS3:3C3486,12527T149
C3≀C3⋊C62nd semidirect product of C3≀C3 and C6 acting faithfullyC3wrC3:C6486,12627T150
C34⋊S31st semidirect product of C34 and S3 acting faithfullyC3^4:S3486,10327T151
C9⋊C9.S32nd non-split extension by C9⋊C9 of S3 acting faithfullyC9:C9.S3486,3927T152
He3.C32C62nd semidirect product of He3.C3 and C6 acting faithfullyHe3.C3:2C6486,17727T153
C346S36th semidirect product of C34 and S3 acting faithfullyC3^4:6S3486,18327T154
(C3×He3)⋊C68th semidirect product of C3×He3 and C6 acting faithfully(C3xHe3):C6486,12727T155
C33.D93rd non-split extension by C33 of D9 acting via D9/C3=S3C3^3.D9486,5527T156
C9⋊C9⋊S31st semidirect product of C9⋊C9 and S3 acting faithfullyC9:C9:S3486,4127T157
C922C62nd semidirect product of C92 and C6 acting faithfullyC9^2:2C6486,3727T158
C3≀C3⋊S32nd semidirect product of C3≀C3 and S3 acting via S3/C3=C2C3wrC3:S3486,18927T159
C33⋊(C3×S3)4th semidirect product of C33 and C3×S3 acting faithfullyC3^3:(C3xS3)486,17627T160
He3⋊(C3×S3)4th semidirect product of He3 and C3×S3 acting via C3×S3/C3=S3He3:(C3xS3)486,17827T161
3+ 1+4⋊C21st semidirect product of 3+ 1+4 and C2 acting faithfullyES+(3,2):C2486,23627T162
C3.He3⋊C6The semidirect product of C3.He3 and C6 acting faithfullyC3.He3:C6486,17927T163
C3×C33⋊S3Direct product of C3 and C33⋊S3C3xC3^3:S3486,16527T164
C347S37th semidirect product of C34 and S3 acting faithfullyC3^4:7S3486,18527T165
C33⋊(C3×S3)4th semidirect product of C33 and C3×S3 acting faithfullyC3^3:(C3xS3)486,17627T166
3- 1+42C22nd semidirect product of 3- 1+4 and C2 acting faithfullyES-(3,2):2C2486,23927T167
C3≀C3⋊C62nd semidirect product of C3≀C3 and C6 acting faithfullyC3wrC3:C6486,12627T168
3+ 1+42C22nd semidirect product of 3+ 1+4 and C2 acting faithfullyES+(3,2):2C2486,23727T169
C3≀C3.S3The non-split extension by C3≀C3 of S3 acting via S3/C3=C2C3wrC3.S3486,17527T170
(C3×He3)⋊C68th semidirect product of C3×He3 and C6 acting faithfully(C3xHe3):C6486,12727T171
C92⋊C61st semidirect product of C92 and C6 acting faithfullyC9^2:C6486,3527T172
He3.C32C62nd semidirect product of He3.C3 and C6 acting faithfullyHe3.C3:2C6486,17727T173
3+ 1+43C23rd semidirect product of 3+ 1+4 and C2 acting faithfullyES+(3,2):3C2486,24927T174
He3.(C3×S3)5th non-split extension by He3 of C3×S3 acting via C3×S3/C3=S3He3.(C3xS3)486,13127T175
C27⋊C18The semidirect product of C27 and C18 acting faithfully; = Aut(D27) = Hol(C27)C27:C18486,3127T176
C3×C3≀S3Direct product of C3 and C3≀S3C3xC3wrS3486,11527T177
C3×C33⋊S3Direct product of C3 and C33⋊S3C3xC3^3:S3486,16527T178
C922S32nd semidirect product of C92 and S3 acting faithfullyC9^2:2S3486,6127T179
C34⋊C61st semidirect product of C34 and C6 acting faithfullyC3^4:C6486,10227T180
3+ 1+4⋊C21st semidirect product of 3+ 1+4 and C2 acting faithfullyES+(3,2):C2486,23627T181
(C3×He3)⋊C68th semidirect product of C3×He3 and C6 acting faithfully(C3xHe3):C6486,12727T182
He3.(C3×C6)6th non-split extension by He3 of C3×C6 acting via C3×C6/C3=C6He3.(C3xC6)486,13027T183
C92.S32nd non-split extension by C92 of S3 acting faithfullyC9^2.S3486,3827T184
C92⋊S31st semidirect product of C92 and S3 acting faithfullyC9^2:S3486,3627T185
C343S33rd semidirect product of C34 and S3 acting faithfullyC3^4:3S3486,14527T186
C33⋊(C3×S3)4th semidirect product of C33 and C3×S3 acting faithfullyC3^3:(C3xS3)486,17627T187
C331D91st semidirect product of C33 and D9 acting via D9/C3=S3C3^3:1D9486,1927T188
27T189
He3.C3⋊C63rd semidirect product of He3.C3 and C6 acting faithfullyHe3.C3:C6486,12827T190
C3≀C3⋊C62nd semidirect product of C3≀C3 and C6 acting faithfullyC3wrC3:C6486,12627T191
C9⋊S3⋊C322nd semidirect product of C9⋊S3 and C32 acting faithfullyC9:S3:C3^2486,12927T192
C332D92nd semidirect product of C33 and D9 acting via D9/C3=S3C3^3:2D9486,5227T193
C345S35th semidirect product of C34 and S3 acting faithfullyC3^4:5S3486,16627T194
27T195
3+ 1+4⋊C21st semidirect product of 3+ 1+4 and C2 acting faithfullyES+(3,2):C2486,23627T196
C344C64th semidirect product of C34 and C6 acting faithfullyC3^4:4C6486,14627T197
C34.S34th non-split extension by C34 of S3 acting faithfullyC3^4.S3486,10527T198
C3×C33⋊C6Direct product of C3 and C33⋊C6C3xC3^3:C6486,11627T199
C331C181st semidirect product of C33 and C18 acting via C18/C3=C6C3^3:1C18486,1827T200
C3≀C3.C6The non-split extension by C3≀C3 of C6 acting faithfullyC3wrC3.C6486,13227T201
C345C65th semidirect product of C34 and C6 acting faithfullyC3^4:5C6486,16727T202
He3.(C3×C6)6th non-split extension by He3 of C3×C6 acting via C3×C6/C3=C6He3.(C3xC6)486,13027T203
He3.C3⋊C63rd semidirect product of He3.C3 and C6 acting faithfullyHe3.C3:C6486,12827T204
C345C65th semidirect product of C34 and C6 acting faithfullyC3^4:5C6486,16727T205
He3.(C3×S3)5th non-split extension by He3 of C3×S3 acting via C3×S3/C3=S3He3.(C3xS3)486,13127T206
S3×C3≀C3Direct product of S3 and C3≀C3S3xC3wrC3486,11727T207
C34.C64th non-split extension by C34 of C6 acting faithfullyC3^4.C6486,10427T208
C9⋊C9.3S33rd non-split extension by C9⋊C9 of S3 acting faithfullyC9:C9.3S3486,4027T209

### Groups of order 28

LabelIDTr ID
C28Cyclic groupC2828,228T1
C2×C14Abelian group of type [2,14]C2xC1428,428T2
Dic7Dicyclic group; = C7C4Dic728,128T3
D14Dihedral group; = C2×D7D1428,328T4

### Groups of order 56

LabelIDTr ID
C7×D4Direct product of C7 and D4C7xD456,928T5
C7⋊D4The semidirect product of C7 and D4 acting via D4/C22=C2C7:D456,728T6
28T7
C4×D7Direct product of C4 and D7C4xD756,428T8
C22×D7Direct product of C22 and D7C2^2xD756,1228T9
D28Dihedral groupD2856,528T10
F8Frobenius group; = C23C7 = AGL1(𝔽8)F856,1128T11

### Groups of order 84

LabelIDTr ID
C7⋊C12The semidirect product of C7 and C12 acting via C12/C2=C6C7:C1284,128T12
C4×C7⋊C3Direct product of C4 and C7⋊C3C4xC7:C384,228T13
C22×C7⋊C3Direct product of C22 and C7⋊C3C2^2xC7:C384,928T14
C2×F7Direct product of C2 and F7; = Aut(D14) = Hol(C14)C2xF784,728T15
C7⋊A4The semidirect product of C7 and A4 acting via A4/C22=C3C7:A484,1128T16
C7×A4Direct product of C7 and A4C7xA484,1028T17

### Groups of order 112

LabelIDTr ID
D4×D7Direct product of D4 and D7D4xD7112,3128T18
C2×F8Direct product of C2 and F8C2xF8112,4128T19
28T20

### Groups of order 168

LabelIDTr ID
Dic7⋊C6The semidirect product of Dic7 and C6 acting faithfullyDic7:C6168,1128T21
D4×C7⋊C3Direct product of D4 and C7⋊C3D4xC7:C3168,2028T22
C4⋊F7The semidirect product of C4 and F7 acting via F7/C7⋊C3=C2C4:F7168,928T23
C22×F7Direct product of C22 and F7C2^2xF7168,4728T24
Dic7⋊C6The semidirect product of Dic7 and C6 acting faithfullyDic7:C6168,1128T25
C4×F7Direct product of C4 and F7C4xF7168,828T26
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)AGammaL(1,8)168,4328T27
D7⋊A4The semidirect product of D7 and A4 acting via A4/C22=C3D7:A4168,4928T28
A4×D7Direct product of A4 and D7A4xD7168,4828T29
C7⋊S4The semidirect product of C7 and S4 acting via S4/A4=C2C7:S4168,4628T30
C7×S4Direct product of C7 and S4C7xS4168,4528T31
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simpleGL(3,2)168,4228T32

### Groups of order 196

LabelIDTr ID
C7×Dic7Direct product of C7 and Dic7C7xDic7196,528T33
D7×C14Direct product of C14 and D7D7xC14196,1028T34
C72⋊C4The semidirect product of C72 and C4 acting faithfullyC7^2:C4196,828T35
D72Direct product of D7 and D7D7^2196,928T36

### Groups of order 224

LabelIDTr ID
C4×F8Direct product of C4 and F8C4xF8224,17328T37
C22×F8Direct product of C22 and F8C2^2xF8224,19528T38
28T39

### Groups of order 252

LabelIDTr ID
A4×C7⋊C3Direct product of A4 and C7⋊C3A4xC7:C3252,2728T40

### Groups of order 336

LabelIDTr ID
D4×F7Direct product of D4 and F7; = Aut(D28) = Hol(C28)D4xF7336,12528T41
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,20828T42
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)C2xGL(3,2)336,20928T43
C2×AΓL1(𝔽8)Direct product of C2 and AΓL1(𝔽8)C2xAGammaL(1,8)336,21028T44
D7×S4Direct product of D7 and S4D7xS4336,21228T45
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simplePGL(2,7)336,20828T46

### Groups of order 392

LabelIDTr ID
C7×C7⋊D4Direct product of C7 and C7⋊D4C7xC7:D4392,2728T47
C2×C72⋊C4Direct product of C2 and C72⋊C4C2xC7^2:C4392,4028T48
28T49
C7⋊D28The semidirect product of C7 and D28 acting via D28/D14=C2C7:D28392,2128T50
Dic72D7The semidirect product of Dic7 and D7 acting through Inn(Dic7)Dic7:2D7392,1928T51
C2×D72Direct product of C2, D7 and D7C2xD7^2392,4128T52
D7≀C2Wreath product of D7 by C2D7wrC2392,3728T53
28T54
28T55
C72⋊C8The semidirect product of C72 and C8 acting faithfullyC7^2:C8392,3628T56
D7≀C2Wreath product of D7 by C2D7wrC2392,3728T57
C72⋊Q8The semidirect product of C72 and Q8 acting faithfullyC7^2:Q8392,3828T58

### Groups of order 448

LabelIDTr ID
D4×F8Direct product of D4 and F8D4xF8448,136328T59
C26⋊C72nd semidirect product of C26 and C7 acting faithfullyC2^6:C7448,139328T60
C43⋊C7The semidirect product of C43 and C7 acting faithfullyC4^3:C7448,17828T61
C23⋊F82nd semidirect product of C23 and F8 acting via F8/C23=C7C2^3:F8448,139428T62
28T63
28T64
28T65
28T66

### Groups of order 29

LabelIDTr ID
C29Cyclic groupC2929,129T1

### Groups of order 58

LabelIDTr ID
D29Dihedral groupD2958,129T2

### Groups of order 116

LabelIDTr ID
C29⋊C4The semidirect product of C29 and C4 acting faithfullyC29:C4116,329T3

### Groups of order 203

LabelIDTr ID
C29⋊C7The semidirect product of C29 and C7 acting faithfullyC29:C7203,129T4

### Groups of order 406

LabelIDTr ID
C29⋊C14The semidirect product of C29 and C14 acting faithfullyC29:C14406,129T5

### Groups of order 30

LabelIDTr ID
C30Cyclic groupC3030,430T1
C5×S3Direct product of C5 and S3C5xS330,130T2
D15Dihedral groupD1530,330T3
C3×D5Direct product of C3 and D5C3xD530,230T4

### Groups of order 60

LabelIDTr ID
C6×D5Direct product of C6 and D5C6xD560,1030T5
C3⋊F5The semidirect product of C3 and F5 acting via F5/D5=C2C3:F560,730T6
C3×F5Direct product of C3 and F5C3xF560,630T7
S3×D5Direct product of S3 and D5S3xD560,830T8
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simpleA560,530T9
S3×D5Direct product of S3 and D5S3xD560,830T10
C5×A4Direct product of C5 and A4C5xA460,930T11
S3×C10Direct product of C10 and S3S3xC1060,1130T12
S3×D5Direct product of S3 and D5S3xD560,830T13
D30Dihedral group; = C2×D15D3060,1230T14

### Groups of order 90

LabelIDTr ID
S3×C15Direct product of C15 and S3S3xC1590,630T15
C3×D15Direct product of C3 and D15C3xD1590,730T16

### Groups of order 120

LabelIDTr ID
C2×C3⋊F5Direct product of C2 and C3⋊F5C2xC3:F5120,4130T17
C10×A4Direct product of C10 and A4C10xA4120,4330T18
C5⋊S4The semidirect product of C5 and S4 acting via S4/A4=C2C5:S4120,3830T19
D5×A4Direct product of D5 and A4D5xA4120,3930T20
C2×S3×D5Direct product of C2, S3 and D5C2xS3xD5120,4230T21
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3430T22
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)S3xF5120,3630T23
30T24
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3430T25
C6×F5Direct product of C6 and F5C6xF5120,4030T26
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simpleS5120,3430T27
D5×A4Direct product of D5 and A4D5xA4120,3930T28
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetriesC2xA5120,3530T29
30T30
C5⋊S4The semidirect product of C5 and S4 acting via S4/A4=C2C5:S4120,3830T31
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)S3xF5120,3630T32
C5×S4Direct product of C5 and S4C5xS4120,3730T33
30T34

### Groups of order 150

LabelIDTr ID
C52⋊C6The semidirect product of C52 and C6 acting faithfullyC5^2:C6150,630T35
C5×D15Direct product of C5 and D15C5xD15150,1130T36
C52⋊S3The semidirect product of C52 and S3 acting faithfullyC5^2:S3150,530T37
30T38
D5×C15Direct product of C15 and D5D5xC15150,830T39
C2×C52⋊C3Direct product of C2 and C52⋊C3C2xC5^2:C3150,730T40

### Groups of order 180

LabelIDTr ID
C5×S32Direct product of C5, S3 and S3C5xS3^2180,2830T41
S3×D15Direct product of S3 and D15S3xD15180,2930T42
D15⋊S3The semidirect product of D15 and S3 acting via S3/C3=C2D15:S3180,3030T43
C3×S3×D5Direct product of C3, S3 and D5C3xS3xD5180,2630T44
C3×A5Direct product of C3 and A5; = GL2(𝔽4)C3xA5180,1930T45
C32⋊F5The semidirect product of C32 and F5 acting via F5/C5=C4C3^2:F5180,2530T46
C3×C3⋊F5Direct product of C3 and C3⋊F5C3xC3:F5180,2130T47
C32⋊Dic5The semidirect product of C32 and Dic5 acting via Dic5/C5=C4C3^2:Dic5180,2430T48
C5×C32⋊C4Direct product of C5 and C32⋊C4C5xC3^2:C4180,2330T49

### Groups of order 240

LabelIDTr ID
F16Frobenius group; = C24C15 = AGL1(𝔽16)F16240,19130T50
C2×S3×F5Direct product of C2, S3 and F5; = Aut(D30) = Hol(C30)C2xS3xF5240,19530T51
C3×C24⋊C5Direct product of C3 and C24⋊C5C3xC2^4:C5240,19930T52
A4⋊F5The semidirect product of A4 and F5 acting via F5/D5=C2A4:F5240,19230T53
D5×S4Direct product of D5 and S4D5xS4240,19430T54
C2×D5×A4Direct product of C2, D5 and A4C2xD5xA4240,19830T55
A4×F5Direct product of A4 and F5A4xF5240,19330T56
30T57
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18930T58
D5×S4Direct product of D5 and S4D5xS4240,19430T59
C2×S5Direct product of C2 and S5; = O3(𝔽5)C2xS5240,18930T60
C2×C5⋊S4Direct product of C2 and C5⋊S4C2xC5:S4240,19730T61
D5×S4Direct product of D5 and S4D5xS4240,19430T62
30T63
A4⋊F5The semidirect product of A4 and F5 acting via F5/D5=C2A4:F5240,19230T64
C10×S4Direct product of C10 and S4C10xS4240,19630T65

### Groups of order 300

LabelIDTr ID
C52⋊D6The semidirect product of C52 and D6 acting faithfullyC5^2:D6300,2530T66
D5×D15Direct product of D5 and D15D5xD15300,3930T67
C2×C52⋊C6Direct product of C2 and C52⋊C6C2xC5^2:C6300,2730T68
C5×A5Direct product of C5 and A5; = U2(𝔽4)C5xA5300,2230T69
C52⋊A4The semidirect product of C52 and A4 acting via A4/C22=C3C5^2:A4300,4330T70
C52⋊Dic3The semidirect product of C52 and Dic3 acting faithfullyC5^2:Dic3300,2330T71
C52⋊D6The semidirect product of C52 and D6 acting faithfullyC5^2:D6300,2530T72
C3×C52⋊C4Direct product of C3 and C52⋊C4C3xC5^2:C4300,3130T73
C3×D52Direct product of C3, D5 and D5C3xD5^2300,3630T74
C5×S3×D5Direct product of C5, S3 and D5C5xS3xD5300,3730T75
C152F52nd semidirect product of C15 and F5 acting via F5/C5=C4C15:2F5300,3530T76
C2×C52⋊S3Direct product of C2 and C52⋊S3C2xC5^2:S3300,2630T77
C52⋊C12The semidirect product of C52 and C12 acting faithfullyC5^2:C12300,2430T78
D15⋊D5The semidirect product of D15 and D5 acting via D5/C5=C2D15:D5300,4030T79
C52⋊D6The semidirect product of C52 and D6 acting faithfullyC5^2:D6300,2530T80
C2×C52⋊S3Direct product of C2 and C52⋊S3C2xC5^2:S3300,2630T81

### Groups of order 360

LabelIDTr ID
C5×S3≀C2Direct product of C5 and S3≀C2C5xS3wrC2360,13230T82
S3×C3⋊F5Direct product of S3 and C3⋊F5S3xC3:F5360,12830T83
S32×D5Direct product of S3, S3 and D5S3^2xD5360,13730T84
S3×A5Direct product of S3 and A5S3xA5360,12130T85
C3⋊F5⋊S3The semidirect product of C3⋊F5 and S3 acting via S3/C3=C2C3:F5:S3360,12930T86
C6×A5Direct product of C6 and A5C6xA5360,12230T87
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simpleA6360,11830T88
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5GammaL(2,4)360,12030T89
C3×S5Direct product of C3 and S5C3xS5360,11930T90
C3×S3×F5Direct product of C3, S3 and F5C3xS3xF5360,12630T91
C6×A5Direct product of C6 and A5C6xA5360,12230T92
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5GammaL(2,4)360,12030T93
S3×A5Direct product of S3 and A5S3xA5360,12130T94
C32⋊D20The semidirect product of C32 and D20 acting via D20/C5=D4C3^2:D20360,13430T95
C5⋊S3≀C2The semidirect product of C5 and S3≀C2 acting via S3≀C2/S32=C2C5:S3wrC2360,13330T96
C32⋊F5⋊C2The semidirect product of C32⋊F5 and C2 acting faithfullyC3^2:F5:C2360,13130T97
C3×S5Direct product of C3 and S5C3xS5360,11930T98
D5×C32⋊C4Direct product of D5 and C32⋊C4D5xC3^2:C4360,13030T99
C5⋊S3≀C2The semidirect product of C5 and S3≀C2 acting via S3≀C2/S32=C2C5:S3wrC2360,13330T100
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5GammaL(2,4)360,12030T101
S3×A5Direct product of S3 and A5S3xA5360,12130T102
C3×S5Direct product of C3 and S5C3xS5360,11930T103

### Groups of order 450

LabelIDTr ID
C15×D15Direct product of C15 and D15C15xD15450,2930T104

### Groups of order 480

LabelIDTr ID
C6×C24⋊C5Direct product of C6 and C24⋊C5C6xC2^4:C5480,120430T105
C24⋊D15The semidirect product of C24 and D15 acting via D15/C3=D5C2^4:D15480,119530T106
C2×A4×F5Direct product of C2, A4 and F5C2xA4xF5480,119230T107
C2×F16Direct product of C2 and F16C2xF16480,119030T108
C2×D5×S4Direct product of C2, D5 and S4C2xD5xS4480,119330T109
F5×S4Direct product of F5 and S4; = Hol(C2×C10)F5xS4480,118930T110
S3×C24⋊C5Direct product of S3 and C24⋊C5S3xC2^4:C5480,119630T111
F16⋊C2The semidirect product of F16 and C2 acting faithfullyF16:C2480,118830T112
C3×C24⋊D5Direct product of C3 and C24⋊D5C3xC2^4:D5480,119430T113
F5×S4Direct product of F5 and S4; = Hol(C2×C10)F5xS4480,118930T114
30T115
F16⋊C2The semidirect product of F16 and C2 acting faithfullyF16:C2480,118830T116
F5×S4Direct product of F5 and S4; = Hol(C2×C10)F5xS4480,118930T117
C3×C24⋊D5Direct product of C3 and C24⋊D5C3xC2^4:D5480,119430T118
C24⋊D15The semidirect product of C24 and D15 acting via D15/C3=D5C2^4:D15480,119530T119
S3×C24⋊C5Direct product of S3 and C24⋊C5S3xC2^4:C5480,119630T120
C2×A4⋊F5Direct product of C2 and A4⋊F5C2xA4:F5480,119130T121

### Groups of order 31

LabelIDTr ID
C31Cyclic groupC3131,131T1

### Groups of order 62

LabelIDTr ID
D31Dihedral groupD3162,131T2

### Groups of order 93

LabelIDTr ID
C31⋊C3The semidirect product of C31 and C3 acting faithfullyC31:C393,131T3

### Groups of order 155

LabelIDTr ID
C31⋊C5The semidirect product of C31 and C5 acting faithfullyC31:C5155,131T4

### Groups of order 186

LabelIDTr ID
C31⋊C6The semidirect product of C31 and C6 acting faithfullyC31:C6186,131T5

### Groups of order 310

LabelIDTr ID
C31⋊C10The semidirect product of C31 and C10 acting faithfullyC31:C10310,131T6

### Groups of order 465

LabelIDTr ID
C31⋊C15The semidirect product of C31 and C15 acting faithfullyC31:C15465,131T7
׿
×
𝔽