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 S_n for n=(G:H), the index of H in G, called the transitive degree. Conversely, all transitive subgroups of S_n arise in this way. The transitive group database in GAP and Magma contains all transitive subgroups of S_n up to conjugacy for n≤31, numbered nTi (or T_n,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).

On 1 point

Groups of order 1

		Label	ID	Tr ID
C₁	Trivial group	C1	1,1	1T1

On 2 points

Groups of order 2

		Label	ID	Tr ID
C₂	Cyclic group	C2	2,1	2T1

On 3 points

Groups of order 3

		Label	ID	Tr ID
C₃	Cyclic group; = A₃ = triangle rotations	C3	3,1	3T1

Groups of order 6

		Label	ID	Tr ID
S₃	Symmetric group on 3 letters; = D₃ = GL₂(𝔽₂) = triangle symmetries = 1^st non-abelian group	S3	6,1	3T2

On 4 points

Groups of order 4

		Label	ID	Tr ID
C₄	Cyclic group; = square rotations	C4	4,1	4T1
C₂²	Klein 4-group V₄ = elementary abelian group of type [2,2]; = rectangle symmetries	C2^2	4,2	4T2

Groups of order 8

		Label	ID	Tr ID
D₄	Dihedral group; = He₂ = AΣL₁(𝔽₄) = 2₊¹⁺² = square symmetries	D4	8,3	4T3

Groups of order 12

		Label	ID	Tr ID
A₄	Alternating group on 4 letters; = PSL₂(𝔽₃) = L₂(3) = tetrahedron rotations	A4	12,3	4T4

Groups of order 24

		Label	ID	Tr ID
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	S4	24,12	4T5

On 5 points

Groups of order 5

		Label	ID	Tr ID
C₅	Cyclic group; = pentagon rotations	C5	5,1	5T1

Groups of order 10

		Label	ID	Tr ID
D₅	Dihedral group; = pentagon symmetries	D5	10,1	5T2

Groups of order 20

		Label	ID	Tr ID
F₅	Frobenius group; = C₅ ⋊C₄ = AGL₁(𝔽₅) = Aut(D₅) = Hol(C₅) = Sz(2)	F5	20,3	5T3

Groups of order 60

		Label	ID	Tr ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	5T4

Groups of order 120

		Label	ID	Tr ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	5T5

On 6 points

Groups of order 6

		Label	ID	Tr ID
C₆	Cyclic group; = hexagon rotations	C6	6,2	6T1
S₃	Symmetric group on 3 letters; = D₃ = GL₂(𝔽₂) = triangle symmetries = 1^st non-abelian group	S3	6,1	6T2

Groups of order 12

		Label	ID	Tr ID
D₆	Dihedral group; = C₂×S₃ = hexagon symmetries	D6	12,4	6T3
A₄	Alternating group on 4 letters; = PSL₂(𝔽₃) = L₂(3) = tetrahedron rotations	A4	12,3	6T4

Groups of order 18

		Label	ID	Tr ID
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	C3xS3	18,3	6T5

Groups of order 24

		Label	ID	Tr ID
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	C2xA4	24,13	6T6
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	S4	24,12	6T7
				6T8

Groups of order 36

		Label	ID	Tr ID
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	S3^2	36,10	6T9
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	C3^2:C4	36,9	6T10

Groups of order 48

		Label	ID	Tr ID
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	C2xS4	48,48	6T11

Groups of order 60

		Label	ID	Tr ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	6T12

Groups of order 72

		Label	ID	Tr ID
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	S3wrC2	72,40	6T13

Groups of order 120

		Label	ID	Tr ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	6T14

Groups of order 360

		Label	ID	Tr ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	A6	360,118	6T15

On 7 points

Groups of order 7

		Label	ID	Tr ID
C₇	Cyclic group	C7	7,1	7T1

Groups of order 14

		Label	ID	Tr ID
D₇	Dihedral group	D7	14,1	7T2

Groups of order 21

		Label	ID	Tr ID
C₇⋊C₃	The semidirect product of C₇ and C₃ acting faithfully	C7:C3	21,1	7T3

Groups of order 42

		Label	ID	Tr ID
F₇	Frobenius group; = C₇ ⋊C₆ = AGL₁(𝔽₇) = Aut(D₇) = Hol(C₇)	F7	42,1	7T4

Groups of order 168

		Label	ID	Tr ID
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	GL(3,2)	168,42	7T5

On 8 points

Groups of order 8

		Label	ID	Tr ID
C₈	Cyclic group	C8	8,1	8T1
C₂×C₄	Abelian group of type [2,4]	C2xC4	8,2	8T2
C₂³	Elementary abelian group of type [2,2,2]	C2^3	8,5	8T3
D₄	Dihedral group; = He₂ = AΣL₁(𝔽₄) = 2₊¹⁺² = square symmetries	D4	8,3	8T4
Q₈	Quaternion group; = C₄ .C₂ = Dic₂ = 2_-¹⁺²	Q8	8,4	8T5

Groups of order 16

		Label	ID	Tr ID
D₈	Dihedral group	D8	16,7	8T6
M₄(2)	Modular maximal-cyclic group; = C₈ ⋊₃ C₂	M4(2)	16,6	8T7
SD₁₆	Semidihedral group; = Q₈ ⋊C₂ = QD₁₆	SD16	16,8	8T8
C₂×D₄	Direct product of C₂ and D₄	C2xD4	16,11	8T9
C₂²⋊C₄	The semidirect product of C₂² and C₄ acting via C₄/C₂=C₂	C2^2:C4	16,3	8T10
C₄○D₄	Pauli group = central product of C₄ and D₄	C4oD4	16,13	8T11

Groups of order 24

		Label	ID	Tr ID
SL₂(𝔽₃)	Special linear group on 𝔽₃²; = Q₈ ⋊C₃ = 2T = <2,3,3> = 1^st non-monomial group	SL(2,3)	24,3	8T12
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	C2xA4	24,13	8T13
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	S4	24,12	8T14

Groups of order 32

		Label	ID	Tr ID
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	C8:C2^2	32,43	8T15
C₄.D₄	1^st non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	C4.D4	32,7	8T16
C₄≀C₂	Wreath product of C₄ by C₂	C4wrC2	32,11	8T17
C₂²≀C₂	Wreath product of C₂² by C₂	C2^2wrC2	32,27	8T18
C₂³⋊C₄	The semidirect product of C₂³ and C₄ acting faithfully	C2^3:C4	32,6	8T19
				8T20
				8T21
2₊¹⁺⁴	Extraspecial group; = D₄ ○D₄	ES+(2,2)	32,49	8T22

Groups of order 48

		Label	ID	Tr ID
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	GL(2,3)	48,29	8T23
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	C2xS4	48,48	8T24

Groups of order 56

		Label	ID	Tr ID
F₈	Frobenius group; = C₂³ ⋊C₇ = AGL₁(𝔽₈)	F8	56,11	8T25

Groups of order 64

		Label	ID	Tr ID
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	D4:4D4	64,134	8T26
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	C2wrC4	64,32	8T27
				8T28
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	C2wrC2^2	64,138	8T29
C₄²⋊C₄	2^nd semidirect product of C₄² and C₄ acting faithfully	C4^2:C4	64,34	8T30
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	C2wrC2^2	64,138	8T31

Groups of order 96

		Label	ID	Tr ID
C₂³⋊A₄	2^nd semidirect product of C₂³ and A₄ acting faithfully	C2^3:A4	96,204	8T32
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	C2^4:C6	96,70	8T33
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	C2^2:S4	96,227	8T34

Groups of order 128

		Label	ID	Tr ID
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	8T35

Groups of order 168

		Label	ID	Tr ID
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	AGammaL(1,8)	168,43	8T36
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	GL(3,2)	168,42	8T37

Groups of order 192

		Label	ID	Tr ID
C₂≀A₄	Wreath product of C₂ by A₄	C2wrA4	192,201	8T38
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	C2^3:S4	192,1493	8T39
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	Q8:2S4	192,1494	8T40
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	C2^4:D6	192,955	8T41

Groups of order 288

		Label	ID	Tr ID
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	8T42

Groups of order 336

		Label	ID	Tr ID
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	8T43

On 9 points

Groups of order 9

		Label	ID	Tr ID
C₉	Cyclic group	C9	9,1	9T1
C₃²	Elementary abelian group of type [3,3]	C3^2	9,2	9T2

Groups of order 18

		Label	ID	Tr ID
D₉	Dihedral group	D9	18,1	9T3
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	C3xS3	18,3	9T4
C₃⋊S₃	The semidirect product of C₃ and S₃ acting via S₃/C₃=C₂	C3:S3	18,4	9T5

Groups of order 27

		Label	ID	Tr ID
3_-¹⁺²	Extraspecial group	ES-(3,1)	27,4	9T6
He₃	Heisenberg group; = C₃² ⋊C₃ = 3₊¹⁺²	He3	27,3	9T7

Groups of order 36

		Label	ID	Tr ID
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	S3^2	36,10	9T8
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	C3^2:C4	36,9	9T9

Groups of order 54

		Label	ID	Tr ID
C₉⋊C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	C9:C6	54,6	9T10
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	C3^2:C6	54,5	9T11
He₃⋊C₂	2^nd semidirect product of He₃ and C₂ acting faithfully; = Aut(3_-¹⁺²)	He3:C2	54,8	9T12
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	C3^2:C6	54,5	9T13

Groups of order 72

		Label	ID	Tr ID
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	PSU(3,2)	72,41	9T14
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	F9	72,39	9T15
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	S3wrC2	72,40	9T16

Groups of order 81

		Label	ID	Tr ID
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	C3wrC3	81,7	9T17

Groups of order 108

		Label	ID	Tr ID
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	C3^2:D6	108,17	9T18

Groups of order 144

		Label	ID	Tr ID
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	AGammaL(1,9)	144,182	9T19

Groups of order 162

		Label	ID	Tr ID
C₃≀S₃	Wreath product of C₃ by S₃	C3wrS3	162,10	9T20
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	C3^3:S3	162,19	9T21
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	C3^3:C6	162,11	9T22

Groups of order 216

		Label	ID	Tr ID
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	ASL(2,3)	216,153	9T23

Groups of order 324

		Label	ID	Tr ID
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	He3:D6	324,39	9T24
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	C3^3:A4	324,160	9T25

Groups of order 432

		Label	ID	Tr ID
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	AGL(2,3)	432,734	9T26

On 10 points

Groups of order 10

		Label	ID	Tr ID
C₁₀	Cyclic group	C10	10,2	10T1
D₅	Dihedral group; = pentagon symmetries	D5	10,1	10T2

Groups of order 20

		Label	ID	Tr ID
D₁₀	Dihedral group; = C₂×D₅	D10	20,4	10T3
F₅	Frobenius group; = C₅ ⋊C₄ = AGL₁(𝔽₅) = Aut(D₅) = Hol(C₅) = Sz(2)	F5	20,3	10T4

Groups of order 40

		Label	ID	Tr ID
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	C2xF5	40,12	10T5

Groups of order 50

		Label	ID	Tr ID
C₅×D₅	Direct product of C₅ and D₅; = AΣL₁(𝔽₂₅)	C5xD5	50,3	10T6

Groups of order 60

		Label	ID	Tr ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	10T7

Groups of order 80

		Label	ID	Tr ID
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	C2^4:C5	80,49	10T8

Groups of order 100

		Label	ID	Tr ID
D₅²	Direct product of D₅ and D₅	D5^2	100,13	10T9
C₅²⋊C₄	4^th semidirect product of C₅² and C₄ acting faithfully	C5^2:C4	100,12	10T10

Groups of order 120

		Label	ID	Tr ID
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	C2xA5	120,35	10T11
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	10T12
				10T13

Groups of order 160

		Label	ID	Tr ID
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	C2xC2^4:C5	160,235	10T14
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	C2^4:D5	160,234	10T15
				10T16

Groups of order 200

		Label	ID	Tr ID
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	D5:F5	200,42	10T17
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	C5^2:C8	200,40	10T18
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	10T19
C₅²⋊Q₈	The semidirect product of C₅² and Q₈ acting faithfully	C5^2:Q8	200,44	10T20
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	10T21

Groups of order 240

		Label	ID	Tr ID
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	10T22

Groups of order 320

		Label	ID	Tr ID
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	10T23
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	C2^4:F5	320,1635	10T24
				10T25

Groups of order 360

		Label	ID	Tr ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	A6	360,118	10T26

Groups of order 400

		Label	ID	Tr ID
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	D5wrC2:C2	400,207	10T27
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	C5^2:M4(2)	400,206	10T28

On 11 points

Groups of order 11

		Label	ID	Tr ID
C₁₁	Cyclic group	C11	11,1	11T1

Groups of order 22

		Label	ID	Tr ID
D₁₁	Dihedral group	D11	22,1	11T2

Groups of order 55

		Label	ID	Tr ID
C₁₁⋊C₅	The semidirect product of C₁₁ and C₅ acting faithfully	C11:C5	55,1	11T3

Groups of order 110

		Label	ID	Tr ID
F₁₁	Frobenius group; = C₁₁ ⋊C₁₀ = AGL₁(𝔽₁₁) = Aut(D₁₁) = Hol(C₁₁)	F11	110,1	11T4

On 12 points

Groups of order 12

		Label	ID	Tr ID
C₁₂	Cyclic group	C12	12,2	12T1
C₂×C₆	Abelian group of type [2,6]	C2xC6	12,5	12T2
D₆	Dihedral group; = C₂×S₃ = hexagon symmetries	D6	12,4	12T3
A₄	Alternating group on 4 letters; = PSL₂(𝔽₃) = L₂(3) = tetrahedron rotations	A4	12,3	12T4
Dic₃	Dicyclic group; = C₃ ⋊C₄	Dic3	12,1	12T5

Groups of order 24

		Label	ID	Tr ID
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	C2xA4	24,13	12T6
				12T7
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	S4	24,12	12T8
				12T9
C₂²×S₃	Direct product of C₂² and S₃	C2^2xS3	24,14	12T10
C₄×S₃	Direct product of C₄ and S₃	C4xS3	24,5	12T11
D₁₂	Dihedral group	D12	24,6	12T12
C₃⋊D₄	The semidirect product of C₃ and D₄ acting via D₄/C₂²=C₂	C3:D4	24,8	12T13
C₃×D₄	Direct product of C₃ and D₄	C3xD4	24,10	12T14
C₃⋊D₄	The semidirect product of C₃ and D₄ acting via D₄/C₂²=C₂	C3:D4	24,8	12T15

Groups of order 36

		Label	ID	Tr ID
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	S3^2	36,10	12T16
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	C3^2:C4	36,9	12T17
S₃×C₆	Direct product of C₆ and S₃	S3xC6	36,12	12T18
C₃×Dic₃	Direct product of C₃ and Dic₃	C3xDic3	36,6	12T19
C₃×A₄	Direct product of C₃ and A₄	C3xA4	36,11	12T20

Groups of order 48

		Label	ID	Tr ID
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	C2xS4	48,48	12T21
				12T22
				12T23
				12T24
C₂²×A₄	Direct product of C₂² and A₄	C2^2xA4	48,49	12T25
				12T26
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	A4:C4	48,30	12T27
S₃×D₄	Direct product of S₃ and D₄; = Aut(D₁₂) = Hol(C₁₂)	S3xD4	48,38	12T28
C₄×A₄	Direct product of C₄ and A₄	C4xA4	48,31	12T29
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	A4:C4	48,30	12T30
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	C4^2:C3	48,3	12T31
C₂²⋊A₄	The semidirect product of C₂² and A₄ acting via A₄/C₂²=C₃	C2^2:A4	48,50	12T32

Groups of order 60

		Label	ID	Tr ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	12T33

Groups of order 72

		Label	ID	Tr ID
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	S3wrC2	72,40	12T34
				12T35
				12T36
C₂×S₃²	Direct product of C₂, S₃ and S₃	C2xS3^2	72,46	12T37
C₃⋊D₁₂	The semidirect product of C₃ and D₁₂ acting via D₁₂/D₆=C₂	C3:D12	72,23	12T38
C₆.D₆	2^nd non-split extension by C₆ of D₆ acting via D₆/S₃=C₂	C6.D6	72,21	12T39
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	C2xC3^2:C4	72,45	12T40
				12T41
C₃×C₃⋊D₄	Direct product of C₃ and C₃⋊D₄	C3xC3:D4	72,30	12T42
S₃×A₄	Direct product of S₃ and A₄	S3xA4	72,44	12T43
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	C3:S4	72,43	12T44
C₃×S₄	Direct product of C₃ and S₄	C3xS4	72,42	12T45
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	F9	72,39	12T46
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	PSU(3,2)	72,41	12T47

Groups of order 96

		Label	ID	Tr ID
C₂²×S₄	Direct product of C₂² and S₄	C2^2xS4	96,226	12T48
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	A4:D4	96,195	12T49
				12T50
D₄×A₄	Direct product of D₄ and A₄	D4xA4	96,197	12T51
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	A4:D4	96,195	12T52
C₄×S₄	Direct product of C₄ and S₄	C4xS4	96,186	12T53
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	C4:S4	96,187	12T54
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	C2xC4^2:C3	96,68	12T55
C₂×C₂²⋊A₄	Direct product of C₂ and C₂²⋊A₄	C2xC2^2:A4	96,229	12T56
C₂³.₃A₄	1^st non-split extension by C₂³ of A₄ acting via A₄/C₂²=C₃	C2^3.3A4	96,3	12T57
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	C2^4:C6	96,70	12T58
				12T59
C₂³.A₄	2^nd non-split extension by C₂³ of A₄ acting faithfully	C2^3.A4	96,72	12T60
				12T61
C₄²⋊S₃	The semidirect product of C₄² and S₃ acting faithfully	C4^2:S3	96,64	12T62
				12T63
				12T64
				12T65
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	C2^2:S4	96,227	12T66
				12T67
				12T68
				12T69

Groups of order 108

		Label	ID	Tr ID
C₃×S₃²	Direct product of C₃, S₃ and S₃	C3xS3^2	108,38	12T70
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	C3^2:4D6	108,40	12T71
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	C3^3:C4	108,37	12T72
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	C3xC3^2:C4	108,36	12T73

Groups of order 120

		Label	ID	Tr ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	12T74
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	C2xA5	120,35	12T75
				12T76

Groups of order 144

		Label	ID	Tr ID
C₂×S₃≀C₂	Direct product of C₂ and S₃≀C₂	C2xS3wrC2	144,186	12T77
				12T78
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	S3^2:C4	144,115	12T79
				12T80
Dic₃⋊D₆	2^nd semidirect product of Dic₃ and D₆ acting via D₆/S₃=C₂; = Hol(Dic₃)	Dic3:D6	144,154	12T81
C₆²⋊C₄	1^st semidirect product of C₆² and C₄ acting faithfully	C6^2:C4	144,136	12T82
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	S3xS4	144,183	12T83
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	AGammaL(1,9)	144,182	12T84
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	A4^2	144,184	12T85

Groups of order 192

		Label	ID	Tr ID
D₄×S₄	Direct product of D₄ and S₄	D4xS4	192,1472	12T86
C₂×C₂⁴⋊C₆	Direct product of C₂ and C₂⁴⋊C₆	C2xC2^4:C6	192,1000	12T87
				12T88
C₂×C₂³.A₄	Direct product of C₂ and C₂³.A₄	C2xC2^3.A4	192,1002	12T89
C₂²×C₂²⋊A₄	Direct product of C₂² and C₂²⋊A₄	C2^2xC2^2:A4	192,1540	12T90
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.2A4	192,197	12T91
C₂×C₂³.A₄	Direct product of C₂ and C₂³.A₄	C2xC2^3.A4	192,1002	12T92
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.2A4	192,197	12T93
C₄×C₄²⋊C₃	Direct product of C₄ and C₄²⋊C₃	C4xC4^2:C3	192,188	12T94
C₂×C₄²⋊S₃	Direct product of C₂ and C₄²⋊S₃	C2xC4^2:S3	192,944	12T95
				12T96
				12T97
C₂³.₉S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.9S4	192,182	12T98
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	C2^4:C12	192,191	12T99
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	12T100
				12T101
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	12T102
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	12T103
C₂³⋊₂D₄⋊C₃	The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully	C2^3:2D4:C3	192,194	12T104
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	C2^4:C12	192,191	12T105
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	12T106
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	12T107
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	C2^4:D6	192,955	12T108
				12T109
				12T110
				12T111
C₄²⋊D₆	The semidirect product of C₄² and D₆ acting faithfully	C4^2:D6	192,956	12T112
				12T113
				12T114
				12T115

Groups of order 216

		Label	ID	Tr ID
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	12T116
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	S3^3	216,162	12T117
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	C3^2:2D12	216,159	12T118
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	S3xC3^2:C4	216,156	12T119
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	12T120
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	C3xS3wrC2	216,157	12T121
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	ASL(2,3)	216,153	12T122

Groups of order 240

		Label	ID	Tr ID
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	12T123
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	A5:C4	240,91	12T124

Groups of order 288

		Label	ID	Tr ID
D₆≀C₂	Wreath product of D₆ by C₂	D6wrC2	288,889	12T125
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	12T126
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	PSO+(4,3)	288,1026	12T127
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	12T128
				12T129

Groups of order 324

		Label	ID	Tr ID
C₃×C₃²⋊₄D₆	Direct product of C₃ and C₃²⋊₄D₆	C3xC3^2:4D6	324,167	12T130
C₃×C₃³⋊C₄	Direct product of C₃ and C₃³⋊C₄; = AΣL₁(𝔽₈₁)	C3xC3^3:C4	324,162	12T131
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	C3^3:A4	324,160	12T132
				12T133

Groups of order 432

		Label	ID	Tr ID
S₃×S₃≀C₂	Direct product of S₃ and S₃≀C₂	S3xS3wrC2	432,741	12T156
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	AGL(2,3)	432,734	12T157

On 13 points

Groups of order 13

		Label	ID	Tr ID
C₁₃	Cyclic group	C13	13,1	13T1

Groups of order 26

		Label	ID	Tr ID
D₁₃	Dihedral group	D13	26,1	13T2

Groups of order 39

		Label	ID	Tr ID
C₁₃⋊C₃	The semidirect product of C₁₃ and C₃ acting faithfully	C13:C3	39,1	13T3

Groups of order 52

		Label	ID	Tr ID
C₁₃⋊C₄	The semidirect product of C₁₃ and C₄ acting faithfully	C13:C4	52,3	13T4

Groups of order 78

		Label	ID	Tr ID
C₁₃⋊C₆	The semidirect product of C₁₃ and C₆ acting faithfully	C13:C6	78,1	13T5

Groups of order 156

		Label	ID	Tr ID
F₁₃	Frobenius group; = C₁₃ ⋊C₁₂ = AGL₁(𝔽₁₃) = Aut(D₁₃) = Hol(C₁₃)	F13	156,7	13T6

On 14 points

Groups of order 14

		Label	ID	Tr ID
C₁₄	Cyclic group	C14	14,2	14T1
D₇	Dihedral group	D7	14,1	14T2

Groups of order 28

		Label	ID	Tr ID
D₁₄	Dihedral group; = C₂×D₇	D14	28,3	14T3

Groups of order 42

		Label	ID	Tr ID
F₇	Frobenius group; = C₇ ⋊C₆ = AGL₁(𝔽₇) = Aut(D₇) = Hol(C₇)	F7	42,1	14T4
C₂×C₇⋊C₃	Direct product of C₂ and C₇⋊C₃	C2xC7:C3	42,2	14T5

Groups of order 56

		Label	ID	Tr ID
F₈	Frobenius group; = C₂³ ⋊C₇ = AGL₁(𝔽₈)	F8	56,11	14T6

Groups of order 84

		Label	ID	Tr ID
C₂×F₇	Direct product of C₂ and F₇; = Aut(D₁₄) = Hol(C₁₄)	C2xF7	84,7	14T7

Groups of order 98

		Label	ID	Tr ID
C₇×D₇	Direct product of C₇ and D₇; = AΣL₁(𝔽₄₉)	C7xD7	98,3	14T8

Groups of order 112

		Label	ID	Tr ID
C₂×F₈	Direct product of C₂ and F₈	C2xF8	112,41	14T9

Groups of order 168

		Label	ID	Tr ID
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	GL(3,2)	168,42	14T10
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	AGammaL(1,8)	168,43	14T11

Groups of order 196

		Label	ID	Tr ID
C₇²⋊C₄	The semidirect product of C₇² and C₄ acting faithfully	C7^2:C4	196,8	14T12
D₇²	Direct product of D₇ and D₇	D7^2	196,9	14T13

Groups of order 294

		Label	ID	Tr ID
C₇⋊₄F₇	2^nd semidirect product of C₇ and F₇ acting via F₇/D₇=C₃	C7:4F7	294,12	14T14
C₇²⋊S₃	The semidirect product of C₇² and S₃ acting faithfully	C7^2:S3	294,7	14T15

Groups of order 336

		Label	ID	Tr ID
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	14T16
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	C2xGL(3,2)	336,209	14T17
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	C2xAGammaL(1,8)	336,210	14T18
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	C2xGL(3,2)	336,209	14T19

Groups of order 392

		Label	ID	Tr ID
D₇≀C₂	Wreath product of D₇ by C₂	D7wrC2	392,37	14T20

Groups of order 448

		Label	ID	Tr ID
C₂³⋊F₈	2^nd semidirect product of C₂³ and F₈ acting via F₈/C₂³=C₇	C2^3:F8	448,1394	14T21

On 15 points

Groups of order 15

		Label	ID	Tr ID
C₁₅	Cyclic group	C15	15,1	15T1

Groups of order 30

		Label	ID	Tr ID
D₁₅	Dihedral group	D15	30,3	15T2
C₃×D₅	Direct product of C₃ and D₅	C3xD5	30,2	15T3
C₅×S₃	Direct product of C₅ and S₃	C5xS3	30,1	15T4

Groups of order 60

		Label	ID	Tr ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	15T5
C₃⋊F₅	The semidirect product of C₃ and F₅ acting via F₅/D₅=C₂	C3:F5	60,7	15T6
S₃×D₅	Direct product of S₃ and D₅	S3xD5	60,8	15T7
C₃×F₅	Direct product of C₃ and F₅	C3xF5	60,6	15T8

Groups of order 75

		Label	ID	Tr ID
C₅²⋊C₃	The semidirect product of C₅² and C₃ acting faithfully	C5^2:C3	75,2	15T9

Groups of order 120

		Label	ID	Tr ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	15T10
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	S3xF5	120,36	15T11

Groups of order 150

		Label	ID	Tr ID
C₅²⋊C₆	The semidirect product of C₅² and C₆ acting faithfully	C5^2:C6	150,6	15T12
C₅²⋊S₃	The semidirect product of C₅² and S₃ acting faithfully	C5^2:S3	150,5	15T13
				15T14

Groups of order 180

		Label	ID	Tr ID
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	C3xA5	180,19	15T15
				15T16

Groups of order 300

		Label	ID	Tr ID
C₅²⋊Dic₃	The semidirect product of C₅² and Dic₃ acting faithfully	C5^2:Dic3	300,23	15T17
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	C5^2:D6	300,25	15T18
C₅²⋊C₁₂	The semidirect product of C₅² and C₁₂ acting faithfully	C5^2:C12	300,24	15T19

Groups of order 360

		Label	ID	Tr ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	A6	360,118	15T20
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	GammaL(2,4)	360,120	15T21
				15T22
S₃×A₅	Direct product of S₃ and A₅	S3xA5	360,121	15T23
C₃×S₅	Direct product of C₃ and S₅	C3xS5	360,119	15T24

Groups of order 375

		Label	ID	Tr ID
C₅×C₅²⋊C₃	Direct product of C₅ and C₅²⋊C₃; = AΣL₁(𝔽₁₂₅)	C5xC5^2:C3	375,6	15T25

Groups of order 405

		Label	ID	Tr ID
C₃⁴⋊C₅	The semidirect product of C₃⁴ and C₅ acting faithfully	C3^4:C5	405,15	15T26

On 16 points

Groups of order 16

		Label	ID	Tr ID
C₁₆	Cyclic group	C16	16,1	16T1
C₂²×C₄	Abelian group of type [2,2,4]	C2^2xC4	16,10	16T2
C₂⁴	Elementary abelian group of type [2,2,2,2]	C2^4	16,14	16T3
C₄²	Abelian group of type [4,4]	C4^2	16,2	16T4
C₂×C₈	Abelian group of type [2,8]	C2xC8	16,5	16T5
M₄(2)	Modular maximal-cyclic group; = C₈ ⋊₃ C₂	M4(2)	16,6	16T6
C₂×Q₈	Direct product of C₂ and Q₈	C2xQ8	16,12	16T7
C₄⋊C₄	The semidirect product of C₄ and C₄ acting via C₄/C₂=C₂	C4:C4	16,4	16T8
C₂×D₄	Direct product of C₂ and D₄	C2xD4	16,11	16T9
C₂²⋊C₄	The semidirect product of C₂² and C₄ acting via C₄/C₂=C₂	C2^2:C4	16,3	16T10
C₄○D₄	Pauli group = central product of C₄ and D₄	C4oD4	16,13	16T11
SD₁₆	Semidihedral group; = Q₈ ⋊C₂ = QD₁₆	SD16	16,8	16T12
D₈	Dihedral group	D8	16,7	16T13
Q₁₆	Generalised quaternion group; = C₈ .C₂ = Dic₄	Q16	16,9	16T14

Groups of order 32

		Label	ID	Tr ID
C₂×M₄(2)	Direct product of C₂ and M₄(2)	C2xM4(2)	32,37	16T15
C₈○D₄	Central product of C₈ and D₄	C8oD4	32,38	16T16
C₄²⋊C₂	1^st semidirect product of C₄² and C₂ acting faithfully	C4^2:C2	32,24	16T17
C₂×C₄○D₄	Direct product of C₂ and C₄○D₄	C2xC4oD4	32,48	16T18
C₄×D₄	Direct product of C₄ and D₄	C4xD4	32,25	16T19
2_-¹⁺⁴	Gamma matrices = Extraspecial group; = D₄ ○Q₈	ES-(2,2)	32,50	16T20
C₂×C₂²⋊C₄	Direct product of C₂ and C₂²⋊C₄	C2xC2^2:C4	32,22	16T21
M₅(2)	Modular maximal-cyclic group; = C₁₆ ⋊₃ C₂	M5(2)	32,17	16T22
2₊¹⁺⁴	Extraspecial group; = D₄ ○D₄	ES+(2,2)	32,49	16T23
C₂²⋊C₈	The semidirect product of C₂² and C₈ acting via C₈/C₄=C₂	C2^2:C8	32,5	16T24
C₂²×D₄	Direct product of C₂² and D₄	C2^2xD4	32,46	16T25
D₄⋊C₄	1^st semidirect product of D₄ and C₄ acting via C₄/C₂=C₂	D4:C4	32,9	16T26
C₄²⋊₂C₂	2^nd semidirect product of C₄² and C₂ acting faithfully	C4^2:2C2	32,33	16T27
C₄≀C₂	Wreath product of C₄ by C₂	C4wrC2	32,11	16T28
C₂×D₈	Direct product of C₂ and D₈	C2xD8	32,39	16T29
C₄.₄D₄	4^th non-split extension by C₄ of D₄ acting via D₄/C₄=C₂	C4.4D4	32,31	16T30
C₂²⋊Q₈	The semidirect product of C₂² and Q₈ acting via Q₈/C₄=C₂	C2^2:Q8	32,29	16T31
C₈.C₂²	The non-split extension by C₈ of C₂² acting faithfully	C8.C2^2	32,44	16T32
C₂³⋊C₄	The semidirect product of C₂³ and C₄ acting faithfully	C2^3:C4	32,6	16T33
C₄⋊D₄	The semidirect product of C₄ and D₄ acting via D₄/C₂²=C₂	C4:D4	32,28	16T34
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	C8:C2^2	32,43	16T35
C₄.D₄	1^st non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	C4.D4	32,7	16T36
C₂².D₄	3^rd non-split extension by C₂² of D₄ acting via D₄/C₂²=C₂	C2^2.D4	32,30	16T37
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	C8:C2^2	32,43	16T38
C₂²≀C₂	Wreath product of C₂² by C₂	C2^2wrC2	32,27	16T39
C₄.₁₀D₄	2^nd non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	C4.10D4	32,8	16T40
C₄.D₄	1^st non-split extension by C₄ of D₄ acting via D₄/C₂²=C₂	C4.D4	32,7	16T41
C₄≀C₂	Wreath product of C₄ by C₂	C4wrC2	32,11	16T42
C₄⋊D₄	The semidirect product of C₄ and D₄ acting via D₄/C₂²=C₂	C4:D4	32,28	16T43
C₄○D₈	Central product of C₄ and D₈	C4oD8	32,42	16T44
C₈⋊C₂²	The semidirect product of C₈ and C₂² acting faithfully; = Aut(D₈) = Hol(C₈)	C8:C2^2	32,43	16T45
C₂²≀C₂	Wreath product of C₂² by C₂	C2^2wrC2	32,27	16T46
C₄○D₈	Central product of C₄ and D₈	C4oD8	32,42	16T47
C₂×SD₁₆	Direct product of C₂ and SD₁₆	C2xSD16	32,40	16T48
C₈.C₄	1^st non-split extension by C₈ of C₄ acting via C₄/C₂=C₂	C8.C4	32,15	16T49
C₈.C₂²	The non-split extension by C₈ of C₂² acting faithfully	C8.C2^2	32,44	16T50
C₄⋊₁D₄	The semidirect product of C₄ and D₄ acting via D₄/C₄=C₂	C4:1D4	32,34	16T51
C₂³⋊C₄	The semidirect product of C₂³ and C₄ acting faithfully	C2^3:C4	32,6	16T52
				16T53
C₂².D₄	3^rd non-split extension by C₂² of D₄ acting via D₄/C₂²=C₂	C2^2.D4	32,30	16T54
SD₃₂	Semidihedral group; = C₁₆ ⋊₂ C₂ = QD₃₂	SD32	32,19	16T55
D₁₆	Dihedral group	D16	32,18	16T56

Groups of order 48

		Label	ID	Tr ID
C₄×A₄	Direct product of C₄ and A₄	C4xA4	48,31	16T57
C₂²×A₄	Direct product of C₂² and A₄	C2^2xA4	48,49	16T58
C₂×SL₂(𝔽₃)	Direct product of C₂ and SL₂(𝔽₃)	C2xSL(2,3)	48,32	16T59
C₄.A₄	The central extension by C₄ of A₄	C4.A4	48,33	16T60
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	C2xS4	48,48	16T61
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	A4:C4	48,30	16T62
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	C4^2:C3	48,3	16T63
C₂²⋊A₄	The semidirect product of C₂² and A₄ acting via A₄/C₂²=C₃	C2^2:A4	48,50	16T64
CSU₂(𝔽₃)	Conformal special unitary group on 𝔽₃²; = Q₈ .S₃ = 2O = <2,3,4>	CSU(2,3)	48,28	16T65
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	GL(2,3)	48,29	16T66

Groups of order 64

		Label	ID	Tr ID
C₂.C₂⁵	6^th central stem extension by C₂ of C₂⁵	C2.C2^5	64,266	16T67
C₂².₁₁C₂⁴	7^th central extension by C₂² of C₂⁴	C2^2.11C2^4	64,199	16T68
C₂×2₊¹⁺⁴	Direct product of C₂ and 2₊¹⁺⁴	C2xES+(2,2)	64,264	16T69
Q₈○M₄(2)	Central product of Q₈ and M₄(2)	Q8oM4(2)	64,249	16T70
M₄(2).₈C₂²	3^rd non-split extension by M₄(2) of C₂² acting via C₂²/C₂=C₂	M4(2).8C2^2	64,94	16T71
C₂×C₄.D₄	Direct product of C₂ and C₄.D₄	C2xC4.D4	64,92	16T72
C₂².₂₉C₂⁴	15^th central stem extension by C₂² of C₂⁴	C2^2.29C2^4	64,216	16T73
C₄.₉C₄²	1^st central stem extension by C₄ of C₄²	C4.9C4^2	64,18	16T74
C₂³.₃₇D₄	8^th non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	C2^3.37D4	64,99	16T75
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	C2xC2^3:C4	64,90	16T76
C₂³.₉D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	C2^3.9D4	64,23	16T77
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	C2xC2^3:C4	64,90	16T78
C₂⁴⋊₃C₄	1^st semidirect product of C₂⁴ and C₄ acting via C₄/C₂=C₂	C2^4:3C4	64,60	16T79
D₄○D₈	Central product of D₄ and D₈	D4oD8	64,257	16T80
C₂².₄₅C₂⁴	31^st central stem extension by C₂² of C₂⁴	C2^2.45C2^4	64,232	16T81
C₂².₃₂C₂⁴	18^th central stem extension by C₂² of C₂⁴	C2^2.32C2^4	64,219	16T82
C₂².₅₄C₂⁴	40^th central stem extension by C₂² of C₂⁴	C2^2.54C2^4	64,241	16T83
C₂³⋊C₈	The semidirect product of C₂³ and C₈ acting via C₈/C₂=C₄	C2^3:C8	64,4	16T84
				16T85
M₄(2).₈C₂²	3^rd non-split extension by M₄(2) of C₂² acting via C₂²/C₂=C₂	M4(2).8C2^2	64,94	16T86
C₂³⋊₃D₄	2^nd semidirect product of C₂³ and D₄ acting via D₄/C₂=C₂²	C2^3:3D4	64,215	16T87
C₂³.₉D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	C2^3.9D4	64,23	16T88
C₂×C₈⋊C₂²	Direct product of C₂ and C₈⋊C₂²	C2xC8:C2^2	64,254	16T89
M₄(2)⋊₄C₄	4^th semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	M4(2):4C4	64,25	16T90
C₂³.₉D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	C2^3.9D4	64,23	16T91
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	C2xC2^3:C4	64,90	16T92
				16T93
				16T94
C₂⁴.₄C₄	2^nd non-split extension by C₂⁴ of C₄ acting via C₄/C₂=C₂	C2^4.4C4	64,88	16T95
C₂³.₉D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂=C₂²	C2^3.9D4	64,23	16T96
C₂³⋊₂Q₈	2^nd semidirect product of C₂³ and Q₈ acting via Q₈/C₂=C₂²	C2^3:2Q8	64,224	16T97
C₂⁴⋊C₂²	4^th semidirect product of C₂⁴ and C₂² acting faithfully	C2^4:C2^2	64,242	16T98
C₂×C₄.D₄	Direct product of C₂ and C₄.D₄	C2xC4.D4	64,92	16T99
D₈⋊C₂²	4^th semidirect product of D₈ and C₂² acting via C₂²/C₂=C₂	D8:C2^2	64,256	16T100
C₂³.C₂³	2^nd non-split extension by C₂³ of C₂³ acting via C₂³/C₂=C₂²	C2^3.C2^3	64,91	16T101
C₂×C₂³⋊C₄	Direct product of C₂ and C₂³⋊C₄	C2xC2^3:C4	64,90	16T102
M₄(2).C₄	1^st non-split extension by M₄(2) of C₄ acting via C₄/C₂=C₂	M4(2).C4	64,111	16T103
C₂³.C₈	The non-split extension by C₂³ of C₈ acting via C₈/C₂=C₄	C2^3.C8	64,30	16T104
C₂×C₂²≀C₂	Direct product of C₂ and C₂²≀C₂	C2xC2^2wrC2	64,202	16T105
C₄²⋊C₂²	1^st semidirect product of C₄² and C₂² acting faithfully	C4^2:C2^2	64,102	16T106
				16T107
C₄.₁₀C₄²	2^nd central stem extension by C₄ of C₄²	C4.10C4^2	64,19	16T108
D₄²	Direct product of D₄ and D₄	D4^2	64,226	16T109
M₄(2)⋊₄C₄	4^th semidirect product of M₄(2) and C₄ acting via C₄/C₂=C₂	M4(2):4C4	64,25	16T110
C₂×C₄≀C₂	Direct product of C₂ and C₄≀C₂	C2xC4wrC2	64,101	16T111
C₂³.C₂³	2^nd non-split extension by C₂³ of C₂³ acting via C₂³/C₂=C₂²	C2^3.C2^3	64,91	16T112
C₈.₂₆D₄	13^rd non-split extension by C₈ of D₄ acting via D₄/C₂²=C₂	C8.26D4	64,125	16T113
C₈○D₈	Central product of C₈ and D₈	C8oD8	64,124	16T114
D₄⋊₅D₄	1^st semidirect product of D₄ and D₄ acting through Inn(D₄)	D4:5D4	64,227	16T115
D₄○SD₁₆	Central product of D₄ and SD₁₆	D4oSD16	64,258	16T116
C₂².₁₉C₂⁴	5^th central stem extension by C₂² of C₂⁴	C2^2.19C2^4	64,206	16T117
D₈⋊C₂²	4^th semidirect product of D₈ and C₂² acting via C₂²/C₂=C₂	D8:C2^2	64,256	16T118
C₂³⋊₃D₄	2^nd semidirect product of C₂³ and D₄ acting via D₄/C₂=C₂²	C2^3:3D4	64,215	16T119
C₂³.C₂³	2^nd non-split extension by C₂³ of C₂³ acting via C₂³/C₂=C₂²	C2^3.C2^3	64,91	16T120
C₄²⋊₆C₄	3^rd semidirect product of C₄² and C₄ acting via C₄/C₂=C₂	C4^2:6C4	64,20	16T121
C₄²⋊C₂²	1^st semidirect product of C₄² and C₂² acting faithfully	C4^2:C2^2	64,102	16T122
C₄.₉C₄²	1^st central stem extension by C₄ of C₄²	C4.9C4^2	64,18	16T123
C₈.C₈	1^st non-split extension by C₈ of C₈ acting via C₈/C₄=C₂	C8.C8	64,45	16T124
C₁₆⋊C₄	2^nd semidirect product of C₁₆ and C₄ acting faithfully	C16:C4	64,28	16T125
C₂²⋊D₈	The semidirect product of C₂² and D₈ acting via D₈/D₄=C₂	C2^2:D8	64,128	16T126
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	C2wrC2^2	64,138	16T127
				16T128
				16T129
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	C2wrC4	64,32	16T130
C₄².C₄	2^nd non-split extension by C₄² of C₄ acting faithfully	C4^2.C4	64,36	16T131
D₄.₃D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	D4.3D4	64,152	16T132
D₄.₄D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₄=C₂	D4.4D4	64,153	16T133
C₁₆⋊C₂²	The semidirect product of C₁₆ and C₂² acting faithfully	C16:C2^2	64,190	16T134
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	D4:4D4	64,134	16T135
C₈.Q₈	The non-split extension by C₈ of Q₈ acting via Q₈/C₂=C₂²	C8.Q8	64,46	16T136
D₄.₁₀D₄	5^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	D4.10D4	64,137	16T137
D₄.₉D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	D4.9D4	64,136	16T138
C₄².₃C₄	3^rd non-split extension by C₄² of C₄ acting faithfully	C4^2.3C4	64,37	16T139
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	C2^3.D4	64,33	16T140
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	D4:4D4	64,134	16T141
				16T142
C₄²⋊C₄	2^nd semidirect product of C₄² and C₄ acting faithfully	C4^2:C4	64,34	16T143
M₅(2)⋊C₂	6^th semidirect product of M₅(2) and C₂ acting faithfully	M5(2):C2	64,42	16T144
D₄.₉D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	D4.9D4	64,136	16T145
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	C2^3.7D4	64,139	16T146
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	C2wrC2^2	64,138	16T147
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	C2^3.D4	64,33	16T148
C₂≀C₂²	Wreath product of C₂ by C₂²; = Hol(C₂×C₄)	C2wrC2^2	64,138	16T149
				16T150
C₄².C₄	2^nd non-split extension by C₄² of C₄ acting faithfully	C4^2.C4	64,36	16T151
D₄⋊₄D₄	3^rd semidirect product of D₄ and D₄ acting via D₄/C₂²=C₂; = Hol(D₄)	D4:4D4	64,134	16T152
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	C2^3.D4	64,33	16T153
C₄²⋊₃C₄	3^rd semidirect product of C₄² and C₄ acting faithfully	C4^2:3C4	64,35	16T154
C₂²⋊SD₁₆	The semidirect product of C₂² and SD₁₆ acting via SD₁₆/D₄=C₂	C2^2:SD16	64,131	16T155
D₈⋊₂C₄	2^nd semidirect product of D₈ and C₄ acting via C₄/C₂=C₂	D8:2C4	64,41	16T156
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	C2wrC4	64,32	16T157
				16T158
				16T159
C₂³.D₄	2^nd non-split extension by C₂³ of D₄ acting faithfully	C2^3.D4	64,33	16T160
C₂³.₃₁D₄	2^nd non-split extension by C₂³ of D₄ acting via D₄/C₂²=C₂	C2^3.31D4	64,9	16T161
D₄.₈D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	D4.8D4	64,135	16T162
C₂².SD₁₆	1^st non-split extension by C₂² of SD₁₆ acting via SD₁₆/Q₈=C₂	C2^2.SD16	64,8	16T163
D₄.₈D₄	3^rd non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	D4.8D4	64,135	16T164
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	C2^3.7D4	64,139	16T165
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	C2wrC4	64,32	16T166
C₄²⋊C₄	2^nd semidirect product of C₄² and C₄ acting faithfully	C4^2:C4	64,34	16T167
				16T168
				16T169
C₂≀C₄	Wreath product of C₂ by C₄; = AΣL₁(𝔽₁₆)	C2wrC4	64,32	16T170
				16T171
				16T172
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	C2^3.7D4	64,139	16T173
C₄²⋊₃C₄	3^rd semidirect product of C₄² and C₄ acting faithfully	C4^2:3C4	64,35	16T174
D₄.₉D₄	4^th non-split extension by D₄ of D₄ acting via D₄/C₂²=C₂	D4.9D4	64,136	16T175
C₄²⋊₃C₄	3^rd semidirect product of C₄² and C₄ acting faithfully	C4^2:3C4	64,35	16T176
C₂³.₇D₄	7^th non-split extension by C₂³ of D₄ acting faithfully	C2^3.7D4	64,139	16T177

Groups of order 80

		Label	ID	Tr ID
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	C2^4:C5	80,49	16T178

Groups of order 96

		Label	ID	Tr ID
D₄×A₄	Direct product of D₄ and A₄	D4xA4	96,197	16T179
D₄.A₄	The non-split extension by D₄ of A₄ acting through Inn(D₄)	D4.A4	96,202	16T180
C₄×S₄	Direct product of C₄ and S₄	C4xS4	96,186	16T181
C₂²×S₄	Direct product of C₂² and S₄	C2^2xS4	96,226	16T182
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	C2^4:C6	96,70	16T183
C₄²⋊C₆	1^st semidirect product of C₄² and C₆ acting faithfully	C4^2:C6	96,71	16T184
C₂³.A₄	2^nd non-split extension by C₂³ of A₄ acting faithfully	C2^3.A4	96,72	16T185
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	A4:D4	96,195	16T186
Q₈.D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/C₂=S₃	Q8.D6	96,190	16T187
C₂×GL₂(𝔽₃)	Direct product of C₂ and GL₂(𝔽₃)	C2xGL(2,3)	96,189	16T188
C₄.₆S₄	3^rd central extension by C₄ of S₄	C4.6S4	96,192	16T189
C₄.₃S₄	3^rd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	C4.3S4	96,193	16T190
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	C4:S4	96,187	16T191
Q₈.D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/C₂=S₃	Q8.D6	96,190	16T192
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	A4:D4	96,195	16T193
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	C2^2:S4	96,227	16T194
C₄²⋊S₃	The semidirect product of C₄² and S₃ acting faithfully	C4^2:S3	96,64	16T195

Groups of order 112

		Label	ID	Tr ID
C₂×F₈	Direct product of C₂ and F₈	C2xF8	112,41	16T196

Groups of order 128

		Label	ID	Tr ID
2₊¹⁺⁶	Extraspecial group; = D₄ ○2₊¹⁺⁴	ES+(2,3)	128,2326	16T197
C₂².₇₃C₂⁵	54^th central stem extension by C₂² of C₂⁵	C2^2.73C2^5	128,2216	16T198
C₂³.C₂⁴	3^rd non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	C2^3.C2^4	128,1615	16T199
M₄(2).₂₄C₂³	6^th non-split extension by M₄(2) of C₂³ acting via C₂³/C₂²=C₂	M4(2).24C2^3	128,1620	16T200
C₂².₇₉C₂⁵	60^th central stem extension by C₂² of C₂⁵	C2^2.79C2^5	128,2222	16T201
C₂³.C₂⁴	3^rd non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	C2^3.C2^4	128,1615	16T202
				16T203
D₈⋊C₂³	6^th semidirect product of D₈ and C₂³ acting via C₂³/C₂²=C₂	D8:C2^3	128,2317	16T204
M₄(2).₅₁D₄	1^st non-split extension by M₄(2) of D₄ acting through Inn(M₄(2))	M4(2).51D4	128,1688	16T205
C₄²⋊C₂³	4^th semidirect product of C₄² and C₂³ acting faithfully	C4^2:C2^3	128,2264	16T206
2_-¹⁺⁴⋊₅C₄	4^th semidirect product of 2_-¹⁺⁴ and C₄ acting via C₄/C₂=C₂	ES-(2,2):5C4	128,1633	16T207
C₂⁵.C₂²	9^th non-split extension by C₂⁵ of C₂² acting faithfully	C2^5.C2^2	128,621	16T208
(C₂×C₈)⋊D₄	3^rd semidirect product of C₂×C₈ and D₄ acting faithfully	(C2xC8):D4	128,623	16T209
C₂⁵.C₂²	9^th non-split extension by C₂⁵ of C₂² acting faithfully	C2^5.C2^2	128,621	16T210
(C₂×C₄)≀C₂	Wreath product of C₂×C₄ by C₂	(C2xC4)wrC2	128,628	16T211
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.C2^3	128,560	16T212
C₂≀C₄⋊C₂	6^th semidirect product of C₂≀C₄ and C₂ acting faithfully	C2wrC4:C2	128,854	16T213
M₄(2)⋊C₂³	3^rd semidirect product of M₄(2) and C₂³ acting via C₂³/C₂=C₂²	M4(2):C2^3	128,1751	16T214
M₄(2).₄₁D₄	5^th non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	M4(2).41D4	128,593	16T215
M₄(2)⋊₂₁D₄	8^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	M4(2):21D4	128,646	16T216
C₂⁵.C₂²	9^th non-split extension by C₂⁵ of C₂² acting faithfully	C2^5.C2^2	128,621	16T217
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T218
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T219
C₈.₅M₄(2)	5^th non-split extension by C₈ of M₄(2) acting via M₄(2)/C₄=C₂²	C8.5M4(2)	128,897	16T220
C₄².₅D₄	5^th non-split extension by C₄² of D₄ acting faithfully	C4^2.5D4	128,636	16T221
C₄²⋊D₄	1^st semidirect product of C₄² and D₄ acting faithfully	C4^2:D4	128,643	16T222
C₂³.₇C₂⁴	7^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	C2^3.7C2^4	128,1757	16T223
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T224
C₄².₄₂₆D₄	59^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	C4^2.426D4	128,638	16T225
C₄⋊₁D₄.C₄	5^th non-split extension by C₄⋊₁D₄ of C₄ acting faithfully	C4:1D4.C4	128,866	16T226
C₂×C₂≀C₄	Direct product of C₂ and C₂≀C₄	C2xC2wrC4	128,850	16T227
C₂⁴⋊C₈	1^st semidirect product of C₂⁴ and C₈ acting via C₈/C₂=C₄	C2^4:C8	128,48	16T228
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.C2^3	128,560	16T229
C₂⁴.₇₈D₄	33^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	C2^4.78D4	128,630	16T230
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.C2^3	128,560	16T231
C₄○D₄.D₄	3^rd non-split extension by C₄○D₄ of D₄ acting via D₄/C₂=C₂²	C4oD4.D4	128,527	16T232
C₂⁴.₆(C₂×C₄)	6^th non-split extension by C₂⁴ of C₂×C₄ acting faithfully	C2^4.6(C2xC4)	128,561	16T233
C₂⁴.₃₉D₄	39^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.39D4	128,859	16T234
C₂×C₄²⋊C₄	Direct product of C₂ and C₄²⋊C₄	C2xC4^2:C4	128,856	16T235
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T236
C₂⁴.₇₈D₄	33^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	C2^4.78D4	128,630	16T237
(C₂×C₈)⋊₄D₄	4^th semidirect product of C₂×C₈ and D₄ acting faithfully	(C2xC8):4D4	128,642	16T238
C₂³.₉C₂⁴	9^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	C2^3.9C2^4	128,1759	16T239
C₂⁵⋊C₄	1^st semidirect product of C₂⁵ and C₄ acting faithfully	C2^5:C4	128,513	16T240
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	C2^4:C2^3	128,1758	16T241
C₄².C₈	1^st non-split extension by C₄² of C₈ acting via C₈/C₂=C₄	C4^2.C8	128,59	16T242
C₄○C₂≀C₄	Central product of C₄ and C₂≀C₄	C4oC2wrC4	128,852	16T243
C₄.₄D₄⋊C₄	6^th semidirect product of C₄.₄D₄ and C₄ acting faithfully	C4.4D4:C4	128,860	16T244
C₂×C₂≀C₂²	Direct product of C₂ and C₂≀C₂²	C2xC2wrC2^2	128,1755	16T245
				16T246
C₂⁵.C₂²	9^th non-split extension by C₂⁵ of C₂² acting faithfully	C2^5.C2^2	128,621	16T247
C₂×C₄²⋊C₄	Direct product of C₂ and C₄²⋊C₄	C2xC4^2:C4	128,856	16T248
C₂⁴.₇₈D₄	33^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	C2^4.78D4	128,630	16T249
C₂⁴.₃₉D₄	39^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.39D4	128,859	16T250
M₄(2)⋊₁₉D₄	6^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	M4(2):19D4	128,616	16T251
C₂⁵.₃C₄	3^rd non-split extension by C₂⁵ of C₄ acting faithfully	C2^5.3C4	128,194	16T252
C₂⁵.C₄	4^th non-split extension by C₂⁵ of C₄ acting faithfully	C2^5.C4	128,515	16T253
C₂⁴.₁₅₀D₄	5^th non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	C2^4.150D4	128,236	16T254
C₂⁴.₁₇₇D₄	32^nd non-split extension by C₂⁴ of D₄ acting via D₄/C₂²=C₂	C2^4.177D4	128,1735	16T255
D₁₆⋊C₄	The semidirect product of D₁₆ and C₄ acting faithfully; = Aut(D₁₆) = Hol(C₁₆)	D16:C4	128,913	16T256
C₂⁴⋊C₈	1^st semidirect product of C₂⁴ and C₈ acting via C₈/C₂=C₄	C2^4:C8	128,48	16T257
				16T258
C₂×C₂≀C₄	Direct product of C₂ and C₂≀C₄	C2xC2wrC4	128,850	16T259
C₈.₃₂D₈	9^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	C8.32D8	128,68	16T260
C₂×C₂≀C₄	Direct product of C₂ and C₂≀C₄	C2xC2wrC4	128,850	16T261
M₄(2)⋊C₂³	3^rd semidirect product of M₄(2) and C₂³ acting via C₂³/C₂=C₂²	M4(2):C2^3	128,1751	16T262
C₄.₄D₄⋊C₄	6^th semidirect product of C₄.₄D₄ and C₄ acting faithfully	C4.4D4:C4	128,860	16T263
C₄².₃₁₃C₂³	174^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	C4^2.313C2^3	128,1750	16T264
C₂×D₄⋊₄D₄	Direct product of C₂ and D₄⋊₄D₄	C2xD4:4D4	128,1746	16T265
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T266
M₄(2).₄₇D₄	11^st non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	M4(2).47D4	128,635	16T267
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T268
C₄².₁₂C₂³	12^nd non-split extension by C₄² of C₂³ acting faithfully	C4^2.12C2^3	128,1753	16T269
C₂³.₇C₂⁴	7^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	C2^3.7C2^4	128,1757	16T270
C₂×C₂≀C₂²	Direct product of C₂ and C₂≀C₂²	C2xC2wrC2^2	128,1755	16T271
C₂⁴.₆(C₂×C₄)	6^th non-split extension by C₂⁴ of C₂×C₄ acting faithfully	C2^4.6(C2xC4)	128,561	16T272
C₂×C₂≀C₄	Direct product of C₂ and C₂≀C₄	C2xC2wrC4	128,850	16T273
C₂⁴.₆₈D₄	23^rd non-split extension by C₂⁴ of D₄ acting via D₄/C₂=C₂²	C2^4.68D4	128,551	16T274
C₂⁵⋊C₄	1^st semidirect product of C₂⁵ and C₄ acting faithfully	C2^5:C4	128,513	16T275
C₄²⋊D₄	1^st semidirect product of C₄² and D₄ acting faithfully	C4^2:D4	128,643	16T276
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	C2^4:C2^3	128,1758	16T277
M₄(2)⋊₂₁D₄	8^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	M4(2):21D4	128,646	16T278
(C₂×C₈)⋊D₄	3^rd semidirect product of C₂×C₈ and D₄ acting faithfully	(C2xC8):D4	128,623	16T279
C₄○C₂≀C₄	Central product of C₄ and C₂≀C₄	C4oC2wrC4	128,852	16T280
C₂≀C₄⋊C₂	6^th semidirect product of C₂≀C₄ and C₂ acting faithfully	C2wrC4:C2	128,854	16T281
C₄².₁₂C₂³	12^nd non-split extension by C₄² of C₂³ acting faithfully	C4^2.12C2^3	128,1753	16T282
C₂×C₂≀C₄	Direct product of C₂ and C₂≀C₄	C2xC2wrC4	128,850	16T283
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T284
C₄⋊₁D₄.C₄	5^th non-split extension by C₄⋊₁D₄ of C₄ acting faithfully	C4:1D4.C4	128,866	16T285
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.C2^3	128,560	16T286
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T287
M₄(2)⋊C₂³	3^rd semidirect product of M₄(2) and C₂³ acting via C₂³/C₂=C₂²	M4(2):C2^3	128,1751	16T288
C₈≀C₂	Wreath product of C₈ by C₂	C8wrC2	128,67	16T289
C₄○D₄.D₄	3^rd non-split extension by C₄○D₄ of D₄ acting via D₄/C₂=C₂²	C4oD4.D4	128,527	16T290
(C₂×C₄²)⋊C₄	8^th semidirect product of C₂×C₄² and C₄ acting faithfully	(C2xC4^2):C4	128,559	16T291
C₄○C₂≀C₄	Central product of C₄ and C₂≀C₄	C4oC2wrC4	128,852	16T292
C₄⋊Q₈⋊₂₉C₄	24^th semidirect product of C₄⋊Q₈ and C₄ acting via C₄/C₂=C₂	C4:Q8:29C4	128,858	16T293
C₈⋊C₄⋊₁₇C₄	12^nd semidirect product of C₈⋊C₄ and C₄ acting via C₄/C₂=C₂	C8:C4:17C4	128,573	16T294
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T295
D₈○D₈	Central product of D₈ and D₈	D8oD8	128,2024	16T296
C₂⁴.₃₉D₄	39^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.39D4	128,859	16T297
(C₂×C₈)⋊₄D₄	4^th semidirect product of C₂×C₈ and D₄ acting faithfully	(C2xC8):4D4	128,642	16T298
M₄(2)⋊₁₉D₄	6^th semidirect product of M₄(2) and D₄ acting via D₄/C₂²=C₂	M4(2):19D4	128,616	16T299
(C₂×D₄).₁₃₅D₄	97^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂=C₂²	(C2xD4).135D4	128,864	16T300
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	C2^4:C2^3	128,1758	16T301
C₂⁴.₂₄D₄	24^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.24D4	128,619	16T302
C₄².₃₁₃C₂³	174^th non-split extension by C₄² of C₂³ acting via C₂³/C₂=C₂²	C4^2.313C2^3	128,1750	16T303
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T304
C₄²⋊D₄	1^st semidirect product of C₄² and D₄ acting faithfully	C4^2:D4	128,643	16T305
C₂⁴.C₈	2^nd non-split extension by C₂⁴ of C₈ acting via C₈/C₂=C₄	C2^4.C8	128,52	16T306
C₄².₅D₄	5^th non-split extension by C₄² of D₄ acting faithfully	C4^2.5D4	128,636	16T307
D₈⋊₁₁D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₂²=C₂	D8:11D4	128,2020	16T308
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	C2^4:C2^3	128,1758	16T309
C₂⁴.₃₉D₄	39^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.39D4	128,859	16T310
C₄².₄₂₆D₄	59^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	C4^2.426D4	128,638	16T311
M₄(2).₃₇D₄	1^st non-split extension by M₄(2) of D₄ acting via D₄/C₂²=C₂	M4(2).37D4	128,1800	16T312
C₂³.₉C₂⁴	9^th non-split extension by C₂³ of C₂⁴ acting via C₂⁴/C₂²=C₂²	C2^3.9C2^4	128,1759	16T313
(C₂×C₄²)⋊C₄	8^th semidirect product of C₂×C₄² and C₄ acting faithfully	(C2xC4^2):C4	128,559	16T314
C₂≀C₄⋊C₂	6^th semidirect product of C₂≀C₄ and C₂ acting faithfully	C2wrC4:C2	128,854	16T315
C₂⁴.C₂³	1^st non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.C2^3	128,560	16T316
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T317
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T318
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T319
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	C2^4:C2^3	128,1758	16T320
C₄².₄₂₇D₄	60^th non-split extension by C₄² of D₄ acting via D₄/C₂²=C₂	C4^2.427D4	128,664	16T321
C₄⋊Q₈⋊₂₉C₄	24^th semidirect product of C₄⋊Q₈ and C₄ acting via C₄/C₂=C₂	C4:Q8:29C4	128,858	16T322
C₂⁴.₄Q₈	3^rd non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	C2^4.4Q8	128,36	16T323
C₂⁴.₃₆D₄	36^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.36D4	128,853	16T324
C₂³≀C₂	Wreath product of C₂³ by C₂	C2^3wrC2	128,1578	16T325
C₂⁴.₂₈D₄	28^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.28D4	128,645	16T326
(C₂×D₄).₁₃₅D₄	97^th non-split extension by C₂×D₄ of D₄ acting via D₄/C₂=C₂²	(C2xD4).135D4	128,864	16T327
D₈⋊₆D₄	5^th semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	D8:6D4	128,2023	16T328
C₂⁴⋊C₂³	2^nd semidirect product of C₂⁴ and C₂³ acting faithfully	C2^4:C2^3	128,1758	16T329
C₂⁴.D₄	1^st non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.D4	128,75	16T330
M₄(2)⋊₅D₄	5^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	M4(2):5D4	128,740	16T331
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	C2^4:Q8	128,764	16T332
C₂⁴⋊₂Q₈	1^st semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	C2^4:2Q8	128,761	16T333
C₄².₃₂Q₈	32^nd non-split extension by C₄² of Q₈ acting via Q₈/C₂=C₂²	C4^2.32Q8	128,834	16T334
C₄².D₄	1^st non-split extension by C₄² of D₄ acting faithfully	C4^2.D4	128,134	16T335
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	C4^2:6D4	128,932	16T336
C₄².₁₇D₄	17^th non-split extension by C₄² of D₄ acting faithfully	C4^2.17D4	128,936	16T337
C₄².₈D₄	8^th non-split extension by C₄² of D₄ acting faithfully	C4^2.8D4	128,763	16T338
C₂⁴.D₄	1^st non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.D4	128,75	16T339
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	C4^2:6D4	128,932	16T340
				16T341
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	C4^2:5D4	128,931	16T342
C₄².D₄	1^st non-split extension by C₄² of D₄ acting faithfully	C4^2.D4	128,134	16T343
C₄².₁₃D₄	13^rd non-split extension by C₄² of D₄ acting faithfully	C4^2.13D4	128,930	16T344
C₄²⋊₄D₄	4^th semidirect product of C₄² and D₄ acting faithfully	C4^2:4D4	128,929	16T345
C₈.₂₉D₈	6^th non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	C8.29D8	128,91	16T346
C₂⁴⋊₂Q₈	1^st semidirect product of C₂⁴ and Q₈ acting via Q₈/C₂=C₂²	C2^4:2Q8	128,761	16T347
C₂³.SD₁₆	1^st non-split extension by C₂³ of SD₁₆ acting via SD₁₆/C₂=D₄	C2^3.SD16	128,73	16T348
C₄².₁₅D₄	15^th non-split extension by C₄² of D₄ acting faithfully	C4^2.15D4	128,934	16T349
C₂⁴⋊D₄	1^st semidirect product of C₂⁴ and D₄ acting faithfully	C2^4:D4	128,753	16T350
D₈⋊₃Q₈	3^rd semidirect product of D₈ and Q₈ acting via Q₈/C₄=C₂	D8:3Q8	128,962	16T351
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	C4^2:6D4	128,932	16T352
C₄².₈D₄	8^th non-split extension by C₄² of D₄ acting faithfully	C4^2.8D4	128,763	16T353
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	C2^4:Q8	128,764	16T354
C₄.C₄≀C₂	9^th non-split extension by C₄ of C₄≀C₂ acting via C₄≀C₂/C₄²=C₂	C4.C4wrC2	128,87	16T355
C₈.₂₄D₈	1^st non-split extension by C₈ of D₈ acting via D₈/D₄=C₂	C8.24D8	128,89	16T356
C₄².₁₅D₄	15^th non-split extension by C₄² of D₄ acting faithfully	C4^2.15D4	128,934	16T357
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	C2^4:Q8	128,764	16T358
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	C4^2:6D4	128,932	16T359
C₄².₁₃₁D₄	113^rd non-split extension by C₄² of D₄ acting via D₄/C₂=C₂²	C4^2.131D4	128,782	16T360
C₄².₄D₄	4^th non-split extension by C₄² of D₄ acting faithfully	C4^2.4D4	128,137	16T361
C₈⋊C₄⋊C₄	1^st semidirect product of C₈⋊C₄ and C₄ acting faithfully	C8:C4:C4	128,138	16T362
(C₄×C₈)⋊₆C₄	6^th semidirect product of C₄×C₈ and C₄ acting faithfully	(C4xC8):6C4	128,141	16T363
C₂⁴⋊D₄	1^st semidirect product of C₂⁴ and D₄ acting faithfully	C2^4:D4	128,753	16T364
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	C4^2:5D4	128,931	16T365
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	C4^2:6D4	128,932	16T366
M₄(2)⋊₅D₄	5^th semidirect product of M₄(2) and D₄ acting via D₄/C₂=C₂²	M4(2):5D4	128,740	16T367
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	C2^4:Q8	128,764	16T368
C₂⁴.Q₈	The non-split extension by C₂⁴ of Q₈ acting faithfully	C2^4.Q8	128,801	16T369
Q₈≀C₂	Wreath product of Q₈ by C₂	Q8wrC2	128,937	16T370
C₂³.D₈	1^st non-split extension by C₂³ of D₈ acting via D₈/C₂=D₄	C2^3.D8	128,71	16T371
C₂⁴.₄C₂³	4^th non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.4C2^3	128,836	16T372
C₂⁴⋊D₄	1^st semidirect product of C₂⁴ and D₄ acting faithfully	C2^4:D4	128,753	16T373
M₅(2).C₂²	8^th non-split extension by M₅(2) of C₂² acting faithfully	M5(2).C2^2	128,970	16T374
C₈⋊C₄⋊₅C₄	5^th semidirect product of C₈⋊C₄ and C₄ acting faithfully	C8:C4:5C4	128,144	16T375
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	16T376
C₄⋊₁D₄⋊C₄	2^nd semidirect product of C₄⋊₁D₄ and C₄ acting faithfully	C4:1D4:C4	128,140	16T377
(C₄×C₈).C₄	6^th non-split extension by C₄×C₈ of C₄ acting faithfully	(C4xC8).C4	128,142	16T378
D₈⋊₃D₄	2^nd semidirect product of D₈ and D₄ acting via D₄/C₄=C₂	D8:3D4	128,945	16T379
C₄².₁₃D₄	13^rd non-split extension by C₄² of D₄ acting faithfully	C4^2.13D4	128,930	16T380
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	C4^2:5D4	128,931	16T381
C₄²⋊₂D₄	2^nd semidirect product of C₄² and D₄ acting faithfully	C4^2:2D4	128,742	16T382
C₂⁴.₄C₂³	4^th non-split extension by C₂⁴ of C₂³ acting faithfully	C2^4.4C2^3	128,836	16T383
C₂⁴⋊Q₈	The semidirect product of C₂⁴ and Q₈ acting faithfully	C2^4:Q8	128,764	16T384
D₈⋊D₄	The semidirect product of D₈ and D₄ acting via D₄/C₂=C₂²	D8:D4	128,922	16T385
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	C4^2:5D4	128,931	16T386
C₄².D₄	1^st non-split extension by C₄² of D₄ acting faithfully	C4^2.D4	128,134	16T387
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	16T388
C₂⁴.₉D₄	9^th non-split extension by C₂⁴ of D₄ acting faithfully	C2^4.9D4	128,332	16T389
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	16T390
				16T391
C₂⁴⋊D₄	1^st semidirect product of C₂⁴ and D₄ acting faithfully	C2^4:D4	128,753	16T392
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	16T393
C₄²⋊₅D₄	5^th semidirect product of C₄² and D₄ acting faithfully	C4^2:5D4	128,931	16T394
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	16T395
				16T396
C₄².₃D₄	3^rd non-split extension by C₄² of D₄ acting faithfully	C4^2.3D4	128,136	16T397
C₄².₂D₄	2^nd non-split extension by C₄² of D₄ acting faithfully	C4^2.2D4	128,135	16T398
C₄²⋊₄D₄	4^th semidirect product of C₄² and D₄ acting faithfully	C4^2:4D4	128,929	16T399
				16T400
D₄≀C₂	Wreath product of D₄ by C₂	D4wrC2	128,928	16T401
C₄²⋊₆D₄	6^th semidirect product of C₄² and D₄ acting faithfully	C4^2:6D4	128,932	16T402
C₂⁴.₁₁Q₈	10^th non-split extension by C₂⁴ of Q₈ acting via Q₈/C₂=C₂²	C2^4.11Q8	128,823	16T403
C₄².₁₅D₄	15^th non-split extension by C₄² of D₄ acting faithfully	C4^2.15D4	128,934	16T404
C₂³⋊SD₁₆	1^st semidirect product of C₂³ and SD₁₆ acting via SD₁₆/C₂=D₄	C2^3:SD16	128,328	16T405
C₄²⋊₂D₄	2^nd semidirect product of C₄² and D₄ acting faithfully	C4^2:2D4	128,742	16T406
C₄².₁₇D₄	17^th non-split extension by C₄² of D₄ acting faithfully	C4^2.17D4	128,936	16T407
C₄²⋊₉D₄	3^rd semidirect product of C₄² and D₄ acting via D₄/C₂=C₂²	C4^2:9D4	128,734	16T408
C₂³⋊D₈	The semidirect product of C₂³ and D₈ acting via D₈/C₂=D₄	C2^3:D8	128,327	16T409
C₄²⋊₄D₄	4^th semidirect product of C₄² and D₄ acting faithfully	C4^2:4D4	128,929	16T410
M₄(2).₈D₄	8^th non-split extension by M₄(2) of D₄ acting via D₄/C₂=C₂²	M4(2).8D4	128,780	16T411
(C₂×C₈).D₄	5^th non-split extension by C₂×C₈ of D₄ acting faithfully	(C2xC8).D4	128,813	16T412
C₄⋊₁D₄⋊C₄	2^nd semidirect product of C₄⋊₁D₄ and C₄ acting faithfully	C4:1D4:C4	128,140	16T413

Groups of order 144

		Label	ID	Tr ID
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	A4^2	144,184	16T414

Groups of order 160

		Label	ID	Tr ID
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	C2^4:D5	160,234	16T415

Groups of order 192

		Label	ID	Tr ID
C₂×C₂⁴⋊C₆	Direct product of C₂ and C₂⁴⋊C₆	C2xC2^4:C6	192,1000	16T416
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:A4	192,1009	16T417
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	C2^4:C12	192,191	16T418
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:A4	192,1009	16T419
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.6A4	192,1008	16T420
D₄×S₄	Direct product of D₄ and S₄	D4xS4	192,1472	16T421
D₄.₄S₄	1^st non-split extension by D₄ of S₄ acting through Inn(D₄)	D4.4S4	192,1485	16T422
2₊¹⁺⁴.₃C₆	The non-split extension by 2₊¹⁺⁴ of C₆ acting via C₆/C₂=C₃	ES+(2,2).3C6	192,1509	16T423
C₂×C₂³⋊A₄	Direct product of C₂ and C₂³⋊A₄	C2xC2^3:A4	192,1508	16T424
C₂≀A₄	Wreath product of C₂ by A₄	C2wrA4	192,201	16T425
2₊¹⁺⁴.C₆	1^st non-split extension by 2₊¹⁺⁴ of C₆ acting faithfully	ES+(2,2).C6	192,202	16T426
C₂≀A₄	Wreath product of C₂ by A₄	C2wrA4	192,201	16T427
2₊¹⁺⁴.C₆	1^st non-split extension by 2₊¹⁺⁴ of C₆ acting faithfully	ES+(2,2).C6	192,202	16T428
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	16T429
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	C4^2:Dic3	192,185	16T430
C₄²⋊D₆	The semidirect product of C₄² and D₆ acting faithfully	C4^2:D6	192,956	16T431
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	C2^4:Dic3	192,184	16T432
				16T433
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	16T434
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	C2^4:D6	192,955	16T435
				16T436
C₂⁴⋊₅A₄	5^th semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:5A4	192,1024	16T437
C₂⁴.₇A₄	7^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.7A4	192,1021	16T438
C₂³.SL₂(𝔽₃)	1^st non-split extension by C₂³ of SL₂(𝔽₃) acting via SL₂(𝔽₃)/C₂=A₄	C2^3.SL(2,3)	192,4	16T439
C₄²⋊A₄	The semidirect product of C₄² and A₄ acting faithfully	C4^2:A4	192,1023	16T440
C₂³.S₄	4^th non-split extension by C₂³ of S₄ acting faithfully	C2^3.S4	192,1491	16T441
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	C2^3:S4	192,1493	16T442
Q₈.S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	Q8.S4	192,1492	16T443
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	Q8:2S4	192,1494	16T444
				16T445
Q₈.S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	Q8.S4	192,1492	16T446

Groups of order 240

		Label	ID	Tr ID
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	F16	240,191	16T447

Groups of order 288

		Label	ID	Tr ID
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	16T708
A₄×S₄	Direct product of A₄ and S₄	A4xS4	288,1024	16T709
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	PSO+(4,3)	288,1026	16T710

Groups of order 320

		Label	ID	Tr ID
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	C2^4:F5	320,1635	16T711

Groups of order 336

		Label	ID	Tr ID
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	C2xAGammaL(1,8)	336,210	16T712
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	16T713
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	C2xGL(3,2)	336,209	16T714
SL₂(𝔽₇)	Special linear group on 𝔽₇²; = C₂ .GL₃(𝔽₂)	SL(2,7)	336,114	16T715

Groups of order 480

		Label	ID	Tr ID
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	F16:C2	480,1188	16T777

On 17 points

Groups of order 17

		Label	ID	Tr ID
C₁₇	Cyclic group	C17	17,1	17T1

Groups of order 34

		Label	ID	Tr ID
D₁₇	Dihedral group	D17	34,1	17T2

Groups of order 68

		Label	ID	Tr ID
C₁₇⋊C₄	The semidirect product of C₁₇ and C₄ acting faithfully	C17:C4	68,3	17T3

Groups of order 136

		Label	ID	Tr ID
C₁₇⋊C₈	The semidirect product of C₁₇ and C₈ acting faithfully	C17:C8	136,12	17T4

Groups of order 272

		Label	ID	Tr ID
F₁₇	Frobenius group; = C₁₇ ⋊C₁₆ = AGL₁(𝔽₁₇) = Aut(D₁₇) = Hol(C₁₇)	F17	272,50	17T5

On 18 points

Groups of order 18

		Label	ID	Tr ID
C₁₈	Cyclic group	C18	18,2	18T1
C₃×C₆	Abelian group of type [3,6]	C3xC6	18,5	18T2
C₃×S₃	Direct product of C₃ and S₃; = U₂(𝔽₂)	C3xS3	18,3	18T3
C₃⋊S₃	The semidirect product of C₃ and S₃ acting via S₃/C₃=C₂	C3:S3	18,4	18T4
D₉	Dihedral group	D9	18,1	18T5

Groups of order 36

		Label	ID	Tr ID
S₃×C₆	Direct product of C₆ and S₃	S3xC6	36,12	18T6
C₃.A₄	The central extension by C₃ of A₄	C3.A4	36,3	18T7
C₃×A₄	Direct product of C₃ and A₄	C3xA4	36,11	18T8
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	S3^2	36,10	18T9
C₃²⋊C₄	The semidirect product of C₃² and C₄ acting faithfully	C3^2:C4	36,9	18T10
S₃²	Direct product of S₃ and S₃; = Spin+₄(𝔽₂) = Hol(S₃)	S3^2	36,10	18T11
C₂×C₃⋊S₃	Direct product of C₂ and C₃⋊S₃	C2xC3:S3	36,13	18T12
D₁₈	Dihedral group; = C₂×D₉	D18	36,4	18T13

Groups of order 54

		Label	ID	Tr ID
C₂×3_-¹⁺²	Direct product of C₂ and 3_-¹⁺²	C2xES-(3,1)	54,11	18T14
C₂×He₃	Direct product of C₂ and He₃	C2xHe3	54,10	18T15
S₃×C₉	Direct product of C₉ and S₃	S3xC9	54,4	18T16
S₃×C₃²	Direct product of C₃² and S₃	S3xC3^2	54,12	18T17
C₉⋊C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	C9:C6	54,6	18T18
C₃×D₉	Direct product of C₃ and D₉	C3xD9	54,3	18T19
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	C3^2:C6	54,5	18T20
				18T21
				18T22
C₃×C₃⋊S₃	Direct product of C₃ and C₃⋊S₃	C3xC3:S3	54,13	18T23
He₃⋊C₂	2^nd semidirect product of He₃ and C₂ acting faithfully; = Aut(3_-¹⁺²)	He3:C2	54,8	18T24

Groups of order 72

		Label	ID	Tr ID
C₆×A₄	Direct product of C₆ and A₄	C6xA4	72,47	18T25
C₂×C₃.A₄	Direct product of C₂ and C₃.A₄	C2xC3.A4	72,16	18T26
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	C2xC3^2:C4	72,45	18T27
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	F9	72,39	18T28
C₂×S₃²	Direct product of C₂, S₃ and S₃	C2xS3^2	72,46	18T29
C₃×S₄	Direct product of C₃ and S₄	C3xS4	72,42	18T30
S₃×A₄	Direct product of S₃ and A₄	S3xA4	72,44	18T31
				18T32
C₃×S₄	Direct product of C₃ and S₄	C3xS4	72,42	18T33
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	S3wrC2	72,40	18T34
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	PSU(3,2)	72,41	18T35
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	S3wrC2	72,40	18T36
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	C3:S4	72,43	18T37
C₃.S₄	The non-split extension by C₃ of S₄ acting via S₄/A₄=C₂	C3.S4	72,15	18T38
				18T39
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	C3:S4	72,43	18T40

Groups of order 108

		Label	ID	Tr ID
C₂×C₃²⋊C₆	Direct product of C₂ and C₃²⋊C₆	C2xC3^2:C6	108,25	18T41
				18T42
C₃×S₃²	Direct product of C₃, S₃ and S₃	C3xS3^2	108,38	18T43
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	C3xC3^2:C4	108,36	18T44
C₂×C₉⋊C₆	Direct product of C₂ and C₉⋊C₆; = Aut(D₁₈) = Hol(C₁₈)	C2xC9:C6	108,26	18T45
C₃×S₃²	Direct product of C₃, S₃ and S₃	C3xS3^2	108,38	18T46
C₃².A₄	The non-split extension by C₃² of A₄ acting via A₄/C₂²=C₃	C3^2.A4	108,21	18T47
C₃²⋊A₄	The semidirect product of C₃² and A₄ acting via A₄/C₂²=C₃	C3^2:A4	108,22	18T48
He₃⋊C₄	The semidirect product of He₃ and C₄ acting faithfully	He3:C4	108,15	18T49
S₃×D₉	Direct product of S₃ and D₉	S3xD9	108,16	18T50
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	C3^2:D6	108,17	18T51
C₂×He₃⋊C₂	Direct product of C₂ and He₃⋊C₂	C2xHe3:C2	108,28	18T52
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	C3^2:4D6	108,40	18T53
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	C3^3:C4	108,37	18T54
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	C3^2:D6	108,17	18T55
				18T56
				18T57
S₃×C₃⋊S₃	Direct product of S₃ and C₃⋊S₃	S3xC3:S3	108,39	18T58

Groups of order 144

		Label	ID	Tr ID
C₂×F₉	Direct product of C₂ and F₉	C2xF9	144,185	18T59
C₂×S₃×A₄	Direct product of C₂, S₃ and A₄	C2xS3xA4	144,190	18T60
C₆×S₄	Direct product of C₆ and S₄	C6xS4	144,188	18T61
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	A4^2	144,184	18T62
C₂×S₃≀C₂	Direct product of C₂ and S₃≀C₂	C2xS3wrC2	144,186	18T63
C₂×PSU₃(𝔽₂)	Direct product of C₂ and PSU₃(𝔽₂)	C2xPSU(3,2)	144,187	18T64
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	S3xS4	144,183	18T65
C₂×C₃⋊S₄	Direct product of C₂ and C₃⋊S₄	C2xC3:S4	144,189	18T66
C₂×C₃.S₄	Direct product of C₂ and C₃.S₄	C2xC3.S4	144,109	18T67
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	AGammaL(1,9)	144,182	18T68
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	S3xS4	144,183	18T69
				18T70
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	AGammaL(1,9)	144,182	18T71
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	S3xS4	144,183	18T72
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	AGammaL(1,9)	144,182	18T73

Groups of order 162

		Label	ID	Tr ID
C₉×D₉	Direct product of C₉ and D₉	C9xD9	162,3	18T74
C₂×C₃≀C₃	Direct product of C₂ and C₃≀C₃	C2xC3wrC3	162,28	18T75
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	C3xC3^2:C6	162,34	18T76
S₃×He₃	Direct product of S₃ and He₃	S3xHe3	162,35	18T77
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	C3xC3^2:C6	162,34	18T78
C₃²×C₃⋊S₃	Direct product of C₃² and C₃⋊S₃	C3^2xC3:S3	162,52	18T79
C₉⋊C₁₈	The semidirect product of C₉ and C₁₈ acting via C₁₈/C₃=C₆	C9:C18	162,6	18T80
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	C3xC3^2:C6	162,34	18T81
C₃²⋊C₁₈	The semidirect product of C₃² and C₁₈ acting via C₁₈/C₃=C₆	C3^2:C18	162,4	18T82
C₃×C₉⋊C₆	Direct product of C₃ and C₉⋊C₆	C3xC9:C6	162,36	18T83
S₃×3_-¹⁺²	Direct product of S₃ and 3_-¹⁺²	S3xES-(3,1)	162,37	18T84
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	C3^3:C6	162,11	18T85
C₃≀S₃	Wreath product of C₃ by S₃	C3wrS3	162,10	18T86
C₃²⋊₂D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	C3^2:2D9	162,17	18T87
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	C3^3:S3	162,19	18T88
He₃⋊₅S₃	2^nd semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	He3:5S3	162,46	18T89

Groups of order 180

		Label	ID	Tr ID
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	C3xA5	180,19	18T90

Groups of order 216

		Label	ID	Tr ID
C₂×C₃²⋊A₄	Direct product of C₂ and C₃²⋊A₄	C2xC3^2:A4	216,107	18T91
C₂×C₃².A₄	Direct product of C₂ and C₃².A₄	C2xC3^2.A4	216,106	18T92
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	C3xS3wrC2	216,157	18T93
C₂×C₃²⋊D₆	Direct product of C₂ and C₃²⋊D₆	C2xC3^2:D6	216,102	18T94
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	S3xC3^2:C4	216,156	18T95
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	S3^3	216,162	18T96
C₆²⋊S₃	4^th semidirect product of C₆² and S₃ acting faithfully	C6^2:S3	216,92	18T97
C₃².S₄	The non-split extension by C₃² of S₄ acting via S₄/C₂²=S₃	C3^2.S4	216,90	18T98
C₆²⋊S₃	4^th semidirect product of C₆² and S₃ acting faithfully	C6^2:S3	216,92	18T99
C₆²⋊C₆	3^rd semidirect product of C₆² and C₆ acting faithfully	C6^2:C6	216,99	18T100
C₃².S₄	The non-split extension by C₃² of S₄ acting via S₄/C₂²=S₃	C3^2.S4	216,90	18T101
C₆²⋊C₆	3^rd semidirect product of C₆² and C₆ acting faithfully	C6^2:C6	216,99	18T102
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	18T103
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	C3^2:2D12	216,159	18T104
He₃⋊D₄	The semidirect product of He₃ and D₄ acting faithfully	He3:D4	216,87	18T105
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	18T106
C₃²⋊S₄	2^nd semidirect product of C₃² and S₄ acting via S₄/C₂²=S₃	C3^2:S4	216,95	18T107
				18T108

Groups of order 288

		Label	ID	Tr ID
C₂×A₄²	Direct product of C₂, A₄ and A₄	C2xA4^2	288,1029	18T109
C₂×AΓL₁(𝔽₉)	Direct product of C₂ and AΓL₁(𝔽₉)	C2xAGammaL(1,9)	288,1027	18T110
C₂×S₃×S₄	Direct product of C₂, S₃ and S₄; = Aut(S₃×SL₂(𝔽₃))	C2xS3xS4	288,1028	18T111
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	18T112
				18T113
A₄×S₄	Direct product of A₄ and S₄	A4xS4	288,1024	18T114
				18T115
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	PSO+(4,3)	288,1026	18T116
				18T117

Groups of order 324

		Label	ID	Tr ID
C₃×C₃²⋊D₆	Direct product of C₃ and C₃²⋊D₆	C3xC3^2:D6	324,117	18T118
C₂×C₃≀S₃	Direct product of C₂ and C₃≀S₃	C2xC3wrS3	324,68	18T119
C₃×C₃²⋊₄D₆	Direct product of C₃ and C₃²⋊₄D₆	C3xC3^2:4D6	324,167	18T120
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	S3xC3^2:C6	324,116	18T121
S₃×C₉⋊C₆	Direct product of S₃ and C₉⋊C₆	S3xC9:C6	324,118	18T122
C₃×C₃³⋊C₄	Direct product of C₃ and C₃³⋊C₄; = AΣL₁(𝔽₈₁)	C3xC3^3:C4	324,162	18T123
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	S3xC3^2:C6	324,116	18T124
C₂×C₃³⋊C₆	Direct product of C₂ and C₃³⋊C₆	C2xC3^3:C6	324,69	18T125
C₃×C₃²⋊D₆	Direct product of C₃ and C₃²⋊D₆	C3xC3^2:D6	324,117	18T126
C₃³⋊₂A₄	1^st semidirect product of C₃³ and A₄ acting via A₄/C₂²=C₃	C3^3:2A4	324,60	18T127
C₃⁴⋊₄C₄	4^th semidirect product of C₃⁴ and C₄ acting faithfully	C3^4:4C4	324,164	18T128
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	He3:D6	324,39	18T129
C₉²⋊C₄	The semidirect product of C₉² and C₄ acting faithfully	C9^2:C4	324,35	18T130
He₃⋊₄Dic₃	The semidirect product of He₃ and Dic₃ acting via Dic₃/C₃=C₄	He3:4Dic3	324,113	18T131
C₃²⋊D₁₈	The semidirect product of C₃² and D₁₈ acting via D₁₈/C₃=D₆	C3^2:D18	324,37	18T132
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	He3:5D6	324,121	18T133
C₂×C₃³⋊S₃	Direct product of C₂ and C₃³⋊S₃	C2xC3^3:S3	324,77	18T134
S₃×He₃⋊C₂	Direct product of S₃ and He₃⋊C₂	S3xHe3:C2	324,122	18T135
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	He3:D6	324,39	18T136
				18T137
C₃⋊S₃²	Direct product of C₃⋊S₃ and C₃⋊S₃	C3:S3^2	324,169	18T138
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	He3:5D6	324,121	18T139
D₉²	Direct product of D₉ and D₉	D9^2	324,36	18T140
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	C3^3:A4	324,160	18T141
				18T142
				18T143

Groups of order 360

		Label	ID	Tr ID
C₃×S₅	Direct product of C₃ and S₅	C3xS5	360,119	18T144
S₃×A₅	Direct product of S₃ and A₅	S3xA5	360,121	18T145
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	GammaL(2,4)	360,120	18T146

Groups of order 432

		Label	ID	Tr ID
C₂×C₃².S₄	Direct product of C₂ and C₃².S₄	C2xC3^2.S4	432,533	18T147
C₂×C₆²⋊C₆	Direct product of C₂ and C₆²⋊C₆	C2xC6^2:C6	432,542	18T148
C₂×C₆²⋊S₃	Direct product of C₂ and C₆²⋊S₃	C2xC6^2:S3	432,535	18T149
S₃×S₃≀C₂	Direct product of S₃ and S₃≀C₂	S3xS3wrC2	432,741	18T150
C₂×ASL₂(𝔽₃)	Direct product of C₂ and ASL₂(𝔽₃)	C2xASL(2,3)	432,735	18T151
C₆²⋊₅D₆	5^th semidirect product of C₆² and D₆ acting faithfully	C6^2:5D6	432,523	18T152
				18T153
				18T154
				18T155
C₂×C₃²⋊S₄	Direct product of C₂ and C₃²⋊S₄	C2xC3^2:S4	432,538	18T156
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	AGL(2,3)	432,734	18T157

Groups of order 486

		Label	ID	Tr ID
C₉²⋊₈C₆	8^th semidirect product of C₉² and C₆ acting faithfully	C9^2:8C6	486,110	18T158
C₃³⋊₁C₁₈	1^st semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	C3^3:1C18	486,18	18T159
C₃⁴.C₆	4^th non-split extension by C₃⁴ of C₆ acting faithfully	C3^4.C6	486,104	18T160
C₃⁴⋊C₆	1^st semidirect product of C₃⁴ and C₆ acting faithfully	C3^4:C6	486,102	18T161
C₃×C₃³⋊C₆	Direct product of C₃ and C₃³⋊C₆	C3xC3^3:C6	486,116	18T162
S₃×C₃≀C₃	Direct product of S₃ and C₃≀C₃	S3xC3wrC3	486,117	18T163
C₃⁴⋊C₆	1^st semidirect product of C₃⁴ and C₆ acting faithfully	C3^4:C6	486,102	18T164
C₃⁴⋊₃S₃	3^rd semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:3S3	486,145	18T165
C₉²⋊₆S₃	6^th semidirect product of C₉² and S₃ acting faithfully	C9^2:6S3	486,153	18T166
C₃⁴⋊₅S₃	5^th semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:5S3	486,166	18T167
C₃⁴⋊₃S₃	3^rd semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:3S3	486,145	18T168
C₃×C₃³⋊S₃	Direct product of C₃ and C₃³⋊S₃	C3xC3^3:S3	486,165	18T169
C₃²⋊C₉.S₃	1^st non-split extension by C₃²⋊C₉ of S₃ acting faithfully	C3^2:C9.S3	486,5	18T170
C₃⁴.₇S₃	7^th non-split extension by C₃⁴ of S₃ acting faithfully	C3^4.7S3	486,147	18T171
C₃³⋊₁D₉	1^st semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	C3^3:1D9	486,19	18T172
C₃²⋊C₉⋊S₃	1^st semidirect product of C₃²⋊C₉ and S₃ acting faithfully	C3^2:C9:S3	486,7	18T173
C₃²⋊C₉⋊C₆	1^st semidirect product of C₃²⋊C₉ and C₆ acting faithfully	C3^2:C9:C6	486,6	18T174

On 19 points

Groups of order 19

		Label	ID	Tr ID
C₁₉	Cyclic group	C19	19,1	19T1

Groups of order 38

		Label	ID	Tr ID
D₁₉	Dihedral group	D19	38,1	19T2

Groups of order 57

		Label	ID	Tr ID
C₁₉⋊C₃	The semidirect product of C₁₉ and C₃ acting faithfully	C19:C3	57,1	19T3

Groups of order 114

		Label	ID	Tr ID
C₁₉⋊C₆	The semidirect product of C₁₉ and C₆ acting faithfully	C19:C6	114,1	19T4

Groups of order 171

		Label	ID	Tr ID
C₁₉⋊C₉	The semidirect product of C₁₉ and C₉ acting faithfully	C19:C9	171,3	19T5

Groups of order 342

		Label	ID	Tr ID
F₁₉	Frobenius group; = C₁₉ ⋊C₁₈ = AGL₁(𝔽₁₉) = Aut(D₁₉) = Hol(C₁₉)	F19	342,7	19T6

On 20 points

Groups of order 20

		Label	ID	Tr ID
C₂₀	Cyclic group	C20	20,2	20T1
Dic₅	Dicyclic group; = C₅ ⋊₂ C₄	Dic5	20,1	20T2
C₂×C₁₀	Abelian group of type [2,10]	C2xC10	20,5	20T3
D₁₀	Dihedral group; = C₂×D₅	D10	20,4	20T4
F₅	Frobenius group; = C₅ ⋊C₄ = AGL₁(𝔽₅) = Aut(D₅) = Hol(C₅) = Sz(2)	F5	20,3	20T5

Groups of order 40

		Label	ID	Tr ID
C₄×D₅	Direct product of C₄ and D₅	C4xD5	40,5	20T6
C₅⋊D₄	The semidirect product of C₅ and D₄ acting via D₄/C₂²=C₂	C5:D4	40,8	20T7
C₂²×D₅	Direct product of C₂² and D₅	C2^2xD5	40,13	20T8
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	C2xF5	40,12	20T9
D₂₀	Dihedral group	D20	40,6	20T10
C₅⋊D₄	The semidirect product of C₅ and D₄ acting via D₄/C₂²=C₂	C5:D4	40,8	20T11
C₅×D₄	Direct product of C₅ and D₄	C5xD4	40,10	20T12
C₂×F₅	Direct product of C₂ and F₅; = Aut(D₁₀) = Hol(C₁₀)	C2xF5	40,12	20T13

Groups of order 60

		Label	ID	Tr ID
C₅×A₄	Direct product of C₅ and A₄	C5xA4	60,9	20T14
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	20T15

Groups of order 80

		Label	ID	Tr ID
C₂²×F₅	Direct product of C₂² and F₅	C2^2xF5	80,50	20T16
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	C2^4:C5	80,49	20T17
C₄⋊F₅	The semidirect product of C₄ and F₅ acting via F₅/D₅=C₂	C4:F5	80,31	20T18
C₂²⋊F₅	The semidirect product of C₂² and F₅ acting via F₅/D₅=C₂	C2^2:F5	80,34	20T19
C₄×F₅	Direct product of C₄ and F₅	C4xF5	80,30	20T20
D₄×D₅	Direct product of D₄ and D₅	D4xD5	80,39	20T21
C₂²⋊F₅	The semidirect product of C₂² and F₅ acting via F₅/D₅=C₂	C2^2:F5	80,34	20T22
C₂⁴⋊C₅	The semidirect product of C₂⁴ and C₅ acting faithfully	C2^4:C5	80,49	20T23

Groups of order 100

		Label	ID	Tr ID
D₅×C₁₀	Direct product of C₁₀ and D₅	D5xC10	100,14	20T24
C₅×Dic₅	Direct product of C₅ and Dic₅	C5xDic5	100,6	20T25
D₅.D₅	The non-split extension by D₅ of D₅ acting via D₅/C₅=C₂	D5.D5	100,10	20T26
C₅²⋊C₄	4^th semidirect product of C₅² and C₄ acting faithfully	C5^2:C4	100,12	20T27
D₅²	Direct product of D₅ and D₅	D5^2	100,13	20T28
C₅×F₅	Direct product of C₅ and F₅	C5xF5	100,9	20T29

Groups of order 120

		Label	ID	Tr ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	20T30
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	C2xA5	120,35	20T31
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	20T32
C₅⋊S₄	The semidirect product of C₅ and S₄ acting via S₄/A₄=C₂	C5:S4	120,38	20T33
C₅×S₄	Direct product of C₅ and S₄	C5xS4	120,37	20T34
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	20T35
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	C2xA5	120,35	20T36
D₅×A₄	Direct product of D₅ and A₄	D5xA4	120,39	20T37

Groups of order 160

		Label	ID	Tr ID
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	C2^4:D5	160,234	20T38
				20T39
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	C2xC2^4:C5	160,235	20T40
				20T41
D₄×F₅	Direct product of D₄ and F₅; = Aut(D₂₀) = Hol(C₂₀)	D4xF5	160,207	20T42
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	C2^4:D5	160,234	20T43
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	C2xC2^4:C5	160,235	20T44
C₂⁴⋊D₅	The semidirect product of C₂⁴ and D₅ acting faithfully	C2^4:D5	160,234	20T45
C₂×C₂⁴⋊C₅	Direct product of C₂ and C₂⁴⋊C₅; = AΣL₁(𝔽₃₂)	C2xC2^4:C5	160,235	20T46

Groups of order 200

		Label	ID	Tr ID
C₅²⋊Q₈	The semidirect product of C₅² and Q₈ acting faithfully	C5^2:Q8	200,44	20T47
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	20T48
C₂×C₅²⋊C₄	Direct product of C₂ and C₅²⋊C₄	C2xC5^2:C4	200,48	20T49
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	20T50
D₅×F₅	Direct product of D₅ and F₅	D5xF5	200,41	20T51
C₂×C₅²⋊C₄	Direct product of C₂ and C₅²⋊C₄	C2xC5^2:C4	200,48	20T52
C₅×C₅⋊D₄	Direct product of C₅ and C₅⋊D₄	C5xC5:D4	200,31	20T53
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	D5:F5	200,42	20T54
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	20T55
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	C5^2:C8	200,40	20T56
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	20T57
Dic₅⋊₂D₅	The semidirect product of Dic₅ and D₅ acting through Inn(Dic₅)	Dic5:2D5	200,23	20T58
C₂×D₅²	Direct product of C₂, D₅ and D₅	C2xD5^2	200,49	20T59
C₅⋊D₂₀	The semidirect product of C₅ and D₂₀ acting via D₂₀/D₁₀=C₂	C5:D20	200,25	20T60

Groups of order 240

		Label	ID	Tr ID
A₄⋊F₅	The semidirect product of A₄ and F₅ acting via F₅/D₅=C₂	A4:F5	240,192	20T61
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	20T62
C₄×A₅	Direct product of C₄ and A₅	C4xA5	240,92	20T63
C₂²×A₅	Direct product of C₂² and A₅	C2^2xA5	240,190	20T64
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	20T65
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	A5:C4	240,91	20T66
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	F16	240,191	20T67
A₄×F₅	Direct product of A₄ and F₅	A4xF5	240,193	20T68
D₅×S₄	Direct product of D₅ and S₄	D5xS4	240,194	20T69
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	20T70

Groups of order 320

		Label	ID	Tr ID
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	20T71
C₂²×C₂⁴⋊C₅	Direct product of C₂² and C₂⁴⋊C₅	C2^2xC2^4:C5	320,1637	20T72
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	20T73
C₂²×C₂⁴⋊C₅	Direct product of C₂² and C₂⁴⋊C₅	C2^2xC2^4:C5	320,1637	20T74
C₄×C₂⁴⋊C₅	Direct product of C₄ and C₂⁴⋊C₅	C4xC2^4:C5	320,1584	20T75
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	20T76
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	C2^4:F5	320,1635	20T77
				20T78
				20T79
				20T80
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	20T81
C₂⁵.D₅	The non-split extension by C₂⁵ of D₅ acting faithfully	C2^5.D5	320,1583	20T82
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	C2^4:F5	320,1635	20T83
C₂⁵.D₅	The non-split extension by C₂⁵ of D₅ acting faithfully	C2^5.D5	320,1583	20T84
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	20T85
C₂²×C₂⁴⋊C₅	Direct product of C₂² and C₂⁴⋊C₅	C2^2xC2^4:C5	320,1637	20T86
C₂×C₂⁴⋊D₅	Direct product of C₂ and C₂⁴⋊D₅	C2xC2^4:D5	320,1636	20T87
C₂⁴⋊F₅	The semidirect product of C₂⁴ and F₅ acting faithfully	C2^4:F5	320,1635	20T88

Groups of order 360

		Label	ID	Tr ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	A6	360,118	20T89

Groups of order 400

		Label	ID	Tr ID
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	D5wrC2:C2	400,207	20T90
C₅²⋊₃C₄²	2^nd semidirect product of C₅² and C₄² acting via C₄²/C₂=C₂×C₄	C5^2:3C4^2	400,124	20T91
C₂×D₅≀C₂	Direct product of C₂ and D₅≀C₂	C2xD5wrC2	400,211	20T92
D₅²⋊C₄	1^st semidirect product of D₅² and C₄ acting via C₄/C₂=C₂	D5^2:C4	400,129	20T93
				20T94
				20T95
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	D5wrC2:C2	400,207	20T96
				20T97
C₂×D₅≀C₂	Direct product of C₂ and D₅≀C₂	C2xD5wrC2	400,211	20T98
C₂×C₅²⋊Q₈	Direct product of C₂ and C₅²⋊Q₈	C2xC5^2:Q8	400,212	20T99
C₂×D₅≀C₂	Direct product of C₂ and D₅≀C₂	C2xD5wrC2	400,211	20T100
D₁₀⋊F₅	2^nd semidirect product of D₁₀ and F₅ acting via F₅/D₅=C₂	D10:F5	400,125	20T101
F₅²	Direct product of F₅ and F₅; = Hol(F₅)	F5^2	400,205	20T102
C₁₀²⋊₄C₄	4^th semidirect product of C₁₀² and C₄ acting faithfully	C10^2:4C4	400,162	20T103
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	C5^2:M4(2)	400,206	20T104
C₂.D₅≀C₂	2^nd central extension by C₂ of D₅≀C₂	C2.D5wrC2	400,130	20T105
D₁₀⋊D₁₀	3^rd semidirect product of D₁₀ and D₁₀ acting via D₁₀/D₅=C₂	D10:D10	400,180	20T106
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	C5^2:M4(2)	400,206	20T107
Dic₅⋊F₅	3^rd semidirect product of Dic₅ and F₅ acting via F₅/D₅=C₂	Dic5:F5	400,126	20T108
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	C5^2:M4(2)	400,206	20T109
C₂×C₅²⋊C₈	Direct product of C₂ and C₅²⋊C₈	C2xC5^2:C8	400,208	20T110
(C₅×C₁₀).Q₈	The non-split extension by C₅×C₁₀ of Q₈ acting faithfully	(C5xC10).Q8	400,134	20T111
				20T112
C₂×C₅²⋊C₈	Direct product of C₂ and C₅²⋊C₈	C2xC5^2:C8	400,208	20T113
C₂×D₅⋊F₅	Direct product of C₂ and D₅⋊F₅	C2xD5:F5	400,210	20T114
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	C5^2:M4(2)	400,206	20T115

Groups of order 480

		Label	ID	Tr ID
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	C2^2:S5	480,951	20T116
C₂²×S₅	Direct product of C₂² and S₅	C2^2xS5	480,1186	20T117
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	C2^2:S5	480,951	20T118
D₄×A₅	Direct product of D₄ and A₅	D4xA5	480,956	20T119
C₄⋊S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	C4:S5	480,944	20T120
F₅×S₄	Direct product of F₅ and S₄; = Hol(C₂×C₁₀)	F5xS4	480,1189	20T121
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	F16:C2	480,1188	20T122
C₄×S₅	Direct product of C₄ and S₅; = CO₃(𝔽₅)	C4xS5	480,943	20T123

Groups of order 500

		Label	ID	Tr ID
C₅×D₅²	Direct product of C₅, D₅ and D₅	C5xD5^2	500,50	20T124
C₅³⋊₆C₄	6^th semidirect product of C₅³ and C₄ acting faithfully	C5^3:6C4	500,46	20T125
C₅×C₅²⋊C₄	Direct product of C₅ and C₅²⋊C₄	C5xC5^2:C4	500,44	20T126
C₅×D₅.D₅	Direct product of C₅ and D₅.D₅	C5xD5.D5	500,42	20T127
C₅²⋊₅D₁₀	2^nd semidirect product of C₅² and D₁₀ acting via D₁₀/C₅=C₂²	C5^2:5D10	500,52	20T128

On 21 points

Groups of order 21

		Label	ID	Tr ID
C₂₁	Cyclic group	C21	21,2	21T1
C₇⋊C₃	The semidirect product of C₇ and C₃ acting faithfully	C7:C3	21,1	21T2

Groups of order 42

		Label	ID	Tr ID
C₃×D₇	Direct product of C₃ and D₇	C3xD7	42,4	21T3
F₇	Frobenius group; = C₇ ⋊C₆ = AGL₁(𝔽₇) = Aut(D₇) = Hol(C₇)	F7	42,1	21T4
D₂₁	Dihedral group	D21	42,5	21T5
S₃×C₇	Direct product of C₇ and S₃	S3xC7	42,3	21T6

Groups of order 63

		Label	ID	Tr ID
C₃×C₇⋊C₃	Direct product of C₃ and C₇⋊C₃	C3xC7:C3	63,3	21T7

Groups of order 84

		Label	ID	Tr ID
S₃×D₇	Direct product of S₃ and D₇	S3xD7	84,8	21T8

Groups of order 126

		Label	ID	Tr ID
C₃×F₇	Direct product of C₃ and F₇	C3xF7	126,7	21T9
C₃⋊F₇	The semidirect product of C₃ and F₇ acting via F₇/C₇⋊C₃=C₂	C3:F7	126,9	21T10
S₃×C₇⋊C₃	Direct product of S₃ and C₇⋊C₃	S3xC7:C3	126,8	21T11

Groups of order 147

		Label	ID	Tr ID
C₇²⋊₃C₃	3^rd semidirect product of C₇² and C₃ acting faithfully	C7^2:3C3	147,5	21T12
C₇×C₇⋊C₃	Direct product of C₇ and C₇⋊C₃	C7xC7:C3	147,3	21T13

Groups of order 168

		Label	ID	Tr ID
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	GL(3,2)	168,42	21T14

Groups of order 252

		Label	ID	Tr ID
S₃×F₇	Direct product of S₃ and F₇; = Aut(D₂₁) = Hol(C₂₁)	S3xF7	252,26	21T15

Groups of order 294

		Label	ID	Tr ID
C₇⋊₅F₇	The semidirect product of C₇ and F₇ acting via F₇/C₇⋊C₃=C₂	C7:5F7	294,10	21T16
C₇²⋊S₃	The semidirect product of C₇² and S₃ acting faithfully	C7^2:S3	294,7	21T17
				21T18
C₇²⋊C₆	7^th semidirect product of C₇² and C₆ acting faithfully	C7^2:C6	294,14	21T19

Groups of order 336

		Label	ID	Tr ID
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	21T20

Groups of order 441

		Label	ID	Tr ID
C₇⋊C₃²	Direct product of C₇⋊C₃ and C₇⋊C₃	C7:C3^2	441,9	21T21

On 22 points

Groups of order 22

		Label	ID	Tr ID
C₂₂	Cyclic group	C22	22,2	22T1
D₁₁	Dihedral group	D11	22,1	22T2

Groups of order 44

		Label	ID	Tr ID
D₂₂	Dihedral group; = C₂×D₁₁	D22	44,3	22T3

Groups of order 110

		Label	ID	Tr ID
F₁₁	Frobenius group; = C₁₁ ⋊C₁₀ = AGL₁(𝔽₁₁) = Aut(D₁₁) = Hol(C₁₁)	F11	110,1	22T4
C₂×C₁₁⋊C₅	Direct product of C₂ and C₁₁⋊C₅	C2xC11:C5	110,2	22T5

Groups of order 220

		Label	ID	Tr ID
C₂×F₁₁	Direct product of C₂ and F₁₁; = Aut(D₂₂) = Hol(C₂₂)	C2xF11	220,7	22T6

Groups of order 242

		Label	ID	Tr ID
C₁₁×D₁₁	Direct product of C₁₁ and D₁₁; = AΣL₁(𝔽₁₂₁)	C11xD11	242,3	22T7

Groups of order 484

		Label	ID	Tr ID
C₁₁²⋊C₄	The semidirect product of C₁₁² and C₄ acting faithfully	C11^2:C4	484,8	22T8
D₁₁²	Direct product of D₁₁ and D₁₁	D11^2	484,9	22T9

On 23 points

Groups of order 23

		Label	ID	Tr ID
C₂₃	Cyclic group	C23	23,1	23T1

Groups of order 46

		Label	ID	Tr ID
D₂₃	Dihedral group	D23	46,1	23T2

Groups of order 253

		Label	ID	Tr ID
C₂₃⋊C₁₁	The semidirect product of C₂₃ and C₁₁ acting faithfully	C23:C11	253,1	23T3

On 24 points

Groups of order 24

		Label	ID	Tr ID
C₂₄	Cyclic group	C24	24,2	24T1
C₂×C₁₂	Abelian group of type [2,12]	C2xC12	24,9	24T2
C₂²×C₆	Abelian group of type [2,2,6]	C2^2xC6	24,15	24T3
C₃×Q₈	Direct product of C₃ and Q₈	C3xQ8	24,11	24T4
Dic₆	Dicyclic group; = C₃ ⋊Q₈	Dic6	24,4	24T5
C₂×Dic₃	Direct product of C₂ and Dic₃	C2xDic3	24,7	24T6
SL₂(𝔽₃)	Special linear group on 𝔽₃²; = Q₈ ⋊C₃ = 2T = <2,3,3> = 1^st non-monomial group	SL(2,3)	24,3	24T7
C₃⋊C₈	The semidirect product of C₃ and C₈ acting via C₈/C₄=C₂	C3:C8	24,1	24T8
C₂×A₄	Direct product of C₂ and A₄; = AΣL₁(𝔽₈)	C2xA4	24,13	24T9
S₄	Symmetric group on 4 letters; = PGL₂(𝔽₃) = Aut(Q₈) = Hol(C₂²) = tetrahedron symmetries = cube/octahedron rotations	S4	24,12	24T10
C₂²×S₃	Direct product of C₂² and S₃	C2^2xS3	24,14	24T11
C₄×S₃	Direct product of C₄ and S₃	C4xS3	24,5	24T12
D₁₂	Dihedral group	D12	24,6	24T13
C₃⋊D₄	The semidirect product of C₃ and D₄ acting via D₄/C₂²=C₂	C3:D4	24,8	24T14
C₃×D₄	Direct product of C₃ and D₄	C3xD4	24,10	24T15

Groups of order 48

		Label	ID	Tr ID
C₃×M₄(2)	Direct product of C₃ and M₄(2)	C3xM4(2)	48,24	24T16
C₃×C₄○D₄	Direct product of C₃ and C₄○D₄	C3xC4oD4	48,47	24T17
D₄⋊₂S₃	The semidirect product of D₄ and S₃ acting through Inn(D₄)	D4:2S3	48,39	24T18
C₄○D₁₂	Central product of C₄ and D₁₂	C4oD12	48,37	24T19
C₄.Dic₃	The non-split extension by C₄ of Dic₃ acting via Dic₃/C₆=C₂	C4.Dic3	48,10	24T20
C₄.A₄	The central extension by C₄ of A₄	C4.A4	48,33	24T21
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	GL(2,3)	48,29	24T22
D₄⋊₂S₃	The semidirect product of D₄ and S₃ acting through Inn(D₄)	D4:2S3	48,39	24T23
C₄○D₁₂	Central product of C₄ and D₁₂	C4oD12	48,37	24T24
C₂×C₃⋊D₄	Direct product of C₂ and C₃⋊D₄	C2xC3:D4	48,43	24T25
S₃×Q₈	Direct product of S₃ and Q₈	S3xQ8	48,40	24T26
S₃×C₂×C₄	Direct product of C₂×C₄ and S₃	S3xC2xC4	48,35	24T27
Q₈⋊₃S₃	The semidirect product of Q₈ and S₃ acting through Inn(Q₈)	Q8:3S3	48,41	24T28
C₂×D₁₂	Direct product of C₂ and D₁₂	C2xD12	48,36	24T29
S₃×C₂³	Direct product of C₂³ and S₃	S3xC2^3	48,51	24T30
C₈⋊S₃	3^rd semidirect product of C₈ and S₃ acting via S₃/C₃=C₂	C8:S3	48,5	24T31
S₃×C₈	Direct product of C₈ and S₃	S3xC8	48,4	24T32
D₆⋊C₄	The semidirect product of D₆ and C₄ acting via C₄/C₂=C₂	D6:C4	48,14	24T33
D₂₄	Dihedral group	D24	48,7	24T34
C₂₄⋊C₂	2^nd semidirect product of C₂₄ and C₂ acting faithfully	C24:C2	48,6	24T35
Q₈⋊₂S₃	The semidirect product of Q₈ and S₃ acting via S₃/C₃=C₂	Q8:2S3	48,17	24T36
D₄⋊S₃	The semidirect product of D₄ and S₃ acting via S₃/C₃=C₂	D4:S3	48,15	24T37
C₆×D₄	Direct product of C₆ and D₄	C6xD4	48,45	24T38
C₃×C₂²⋊C₄	Direct product of C₃ and C₂²⋊C₄	C3xC2^2:C4	48,21	24T39
C₃×D₈	Direct product of C₃ and D₈	C3xD8	48,25	24T40
C₃×SD₁₆	Direct product of C₃ and SD₁₆	C3xSD16	48,26	24T41
D₄.S₃	The non-split extension by D₄ of S₃ acting via S₃/C₃=C₂	D4.S3	48,16	24T42
D₄⋊S₃	The semidirect product of D₄ and S₃ acting via S₃/C₃=C₂	D4:S3	48,15	24T43
C₆.D₄	7^th non-split extension by C₆ of D₄ acting via D₄/C₂²=C₂	C6.D4	48,19	24T44
C₂×C₃⋊D₄	Direct product of C₂ and C₃⋊D₄	C2xC3:D4	48,43	24T45
C₂×S₄	Direct product of C₂ and S₄; = O₃(𝔽₃) = cube/octahedron symmetries	C2xS4	48,48	24T46
				24T47
				24T48
C₂²×A₄	Direct product of C₂² and A₄	C2^2xA4	48,49	24T49
				24T50
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	A4:C4	48,30	24T51
S₃×D₄	Direct product of S₃ and D₄; = Aut(D₁₂) = Hol(C₁₂)	S3xD4	48,38	24T52
				24T53
				24T54
C₄×A₄	Direct product of C₄ and A₄	C4xA4	48,31	24T55
				24T56
A₄⋊C₄	The semidirect product of A₄ and C₄ acting via C₄/C₂=C₂; = SL₂(ℤ/4ℤ)	A4:C4	48,30	24T57
C₄²⋊C₃	The semidirect product of C₄² and C₃ acting faithfully	C4^2:C3	48,3	24T58
C₂²⋊A₄	The semidirect product of C₂² and A₄ acting via A₄/C₂²=C₃	C2^2:A4	48,50	24T59

Groups of order 72

		Label	ID	Tr ID
S₃×Dic₃	Direct product of S₃ and Dic₃	S3xDic3	72,20	24T60
D₆⋊S₃	1^st semidirect product of D₆ and S₃ acting via S₃/C₃=C₂	D6:S3	72,22	24T61
C₃²⋊₂Q₈	The semidirect product of C₃² and Q₈ acting via Q₈/C₂=C₂²	C3^2:2Q8	72,24	24T62
C₃²⋊₂C₈	The semidirect product of C₃² and C₈ acting via C₈/C₂=C₄	C3^2:2C8	72,19	24T63
C₃×Dic₆	Direct product of C₃ and Dic₆	C3xDic6	72,26	24T64
S₃×C₁₂	Direct product of C₁₂ and S₃	S3xC12	72,27	24T65
C₆×Dic₃	Direct product of C₆ and Dic₃	C6xDic3	72,29	24T66
C₃×D₁₂	Direct product of C₃ and D₁₂	C3xD12	72,28	24T67
S₃×C₂×C₆	Direct product of C₂×C₆ and S₃	S3xC2xC6	72,48	24T68
C₃×C₃⋊C₈	Direct product of C₃ and C₃⋊C₈	C3xC3:C8	72,12	24T69
C₃×SL₂(𝔽₃)	Direct product of C₃ and SL₂(𝔽₃)	C3xSL(2,3)	72,25	24T70
C₆×A₄	Direct product of C₆ and A₄	C6xA4	72,47	24T71
S₃≀C₂	Wreath product of S₃ by C₂; = SO+₄(𝔽₂)	S3wrC2	72,40	24T72
C₂×S₃²	Direct product of C₂, S₃ and S₃	C2xS3^2	72,46	24T73
C₃⋊D₁₂	The semidirect product of C₃ and D₁₂ acting via D₁₂/D₆=C₂	C3:D12	72,23	24T74
C₆.D₆	2^nd non-split extension by C₆ of D₆ acting via D₆/S₃=C₂	C6.D6	72,21	24T75
C₂×C₃²⋊C₄	Direct product of C₂ and C₃²⋊C₄	C2xC3^2:C4	72,45	24T76
C₃×C₃⋊D₄	Direct product of C₃ and C₃⋊D₄	C3xC3:D4	72,30	24T77
S₃×A₄	Direct product of S₃ and A₄	S3xA4	72,44	24T78
C₃⋊S₄	The semidirect product of C₃ and S₄ acting via S₄/A₄=C₂	C3:S4	72,43	24T79
C₃×S₄	Direct product of C₃ and S₄	C3xS4	72,42	24T80
F₉	Frobenius group; = C₃² ⋊C₈ = AGL₁(𝔽₉)	F9	72,39	24T81
PSU₃(𝔽₂)	Projective special unitary group on 𝔽₂³; = C₃² ⋊Q₈ = M₉	PSU(3,2)	72,41	24T82
S₃×A₄	Direct product of S₃ and A₄	S3xA4	72,44	24T83
C₃×S₄	Direct product of C₃ and S₄	C3xS4	72,42	24T84

Groups of order 96

		Label	ID	Tr ID
C₈×A₄	Direct product of C₈ and A₄	C8xA4	96,73	24T85
Q₈×A₄	Direct product of Q₈ and A₄	Q8xA4	96,199	24T86
A₄⋊Q₈	The semidirect product of A₄ and Q₈ acting via Q₈/C₄=C₂	A4:Q8	96,185	24T87
Q₈⋊A₄	1^st semidirect product of Q₈ and A₄ acting via A₄/C₂²=C₃	Q8:A4	96,203	24T88
A₄⋊C₈	The semidirect product of A₄ and C₈ acting via C₈/C₄=C₂	A4:C8	96,65	24T89
C₃×C₄.D₄	Direct product of C₃ and C₄.D₄	C3xC4.D4	96,50	24T90
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	C3xC2^3:C4	96,49	24T91
C₃×2₊¹⁺⁴	Direct product of C₃ and 2₊¹⁺⁴	C3xES+(2,2)	96,224	24T92
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	C3xC2^3:C4	96,49	24T93
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.6D6	96,13	24T94
D₄⋊₆D₆	2^nd semidirect product of D₄ and D₆ acting through Inn(D₄)	D4:6D6	96,211	24T95
C₂³.₇D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.7D6	96,41	24T96
C₂³⋊A₄	2^nd semidirect product of C₂³ and A₄ acting faithfully	C2^3:A4	96,204	24T97
C₂³.₇D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.7D6	96,41	24T98
C₁₂.D₄	8^th non-split extension by C₁₂ of D₄ acting via D₄/C₂=C₂²	C12.D4	96,40	24T99
D₄⋊₆D₆	2^nd semidirect product of D₄ and D₆ acting through Inn(D₄)	D4:6D6	96,211	24T100
S₃×C₄○D₄	Direct product of S₃ and C₄○D₄	S3xC4oD4	96,215	24T101
D₄○D₁₂	Central product of D₄ and D₁₂	D4oD12	96,216	24T102
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.6D6	96,13	24T103
S₃×M₄(2)	Direct product of S₃ and M₄(2)	S3xM4(2)	96,113	24T104
C₁₂.₄₆D₄	3^rd non-split extension by C₁₂ of D₄ acting via D₄/C₂²=C₂	C12.46D4	96,30	24T105
D₁₂⋊C₄	4^th semidirect product of D₁₂ and C₄ acting via C₄/C₂=C₂	D12:C4	96,32	24T106
C₈⋊D₆	1^st semidirect product of C₈ and D₆ acting via D₆/C₃=C₂²	C8:D6	96,115	24T107
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.6D6	96,13	24T108
Q₈⋊₃Dic₃	2^nd semidirect product of Q₈ and Dic₃ acting via Dic₃/C₆=C₂	Q8:3Dic3	96,44	24T109
D₄⋊D₆	2^nd semidirect product of D₄ and D₆ acting via D₆/C₆=C₂	D4:D6	96,156	24T110
C₂³.₇D₆	2^nd non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.7D6	96,41	24T111
C₃×C₂²≀C₂	Direct product of C₃ and C₂²≀C₂	C3xC2^2wrC2	96,167	24T112
C₃×C₄≀C₂	Direct product of C₃ and C₄≀C₂	C3xC4wrC2	96,54	24T113
C₃×C₈⋊C₂²	Direct product of C₃ and C₈⋊C₂²	C3xC8:C2^2	96,183	24T114
C₃×C₂³⋊C₄	Direct product of C₃ and C₂³⋊C₄	C3xC2^3:C4	96,49	24T115
C₂⁴⋊₄S₃	1^st semidirect product of C₂⁴ and S₃ acting via S₃/C₃=C₂	C2^4:4S3	96,160	24T116
C₄²⋊₄S₃	3^rd semidirect product of C₄² and S₃ acting via S₃/C₃=C₂	C4^2:4S3	96,12	24T117
D₁₂⋊₆C₂²	4^th semidirect product of D₁₂ and C₂² acting via C₂²/C₂=C₂	D12:6C2^2	96,139	24T118
C₂³.₆D₆	1^st non-split extension by C₂³ of D₆ acting via D₆/C₃=C₂²	C2^3.6D6	96,13	24T119
C₄²⋊C₆	1^st semidirect product of C₄² and C₆ acting faithfully	C4^2:C6	96,71	24T120
				24T121
				24T122
C₂×A₄⋊C₄	Direct product of C₂ and A₄⋊C₄	C2xA4:C4	96,194	24T123
				24T124
C₂²×S₄	Direct product of C₂² and S₄	C2^2xS4	96,226	24T125
				24T126
C₄.₃S₄	3^rd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	C4.3S4	96,193	24T127
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	C4:S4	96,187	24T128
C₄×S₄	Direct product of C₄ and S₄	C4xS4	96,186	24T129
				24T130
A₄⋊Q₈	The semidirect product of A₄ and Q₈ acting via Q₈/C₄=C₂	A4:Q8	96,185	24T131
C₂×A₄⋊C₄	Direct product of C₂ and A₄⋊C₄	C2xA4:C4	96,194	24T132
C₂×C₄×A₄	Direct product of C₂×C₄ and A₄	C2xC4xA4	96,196	24T133
				24T134
C₂³×A₄	Direct product of C₂³ and A₄	C2^3xA4	96,228	24T135
				24T136
Q₈.A₄	The non-split extension by Q₈ of A₄ acting through Inn(Q₈)	Q8.A4	96,201	24T137
U₂(𝔽₃)	Unitary group on 𝔽₃²; = SL₂(𝔽₃)⋊₂ C₄	U(2,3)	96,67	24T138
S₃×D₈	Direct product of S₃ and D₈	S3xD8	96,117	24T139
Q₈⋊₃D₆	2^nd semidirect product of Q₈ and D₆ acting via D₆/S₃=C₂	Q8:3D6	96,121	24T140
D₈⋊S₃	2^nd semidirect product of D₈ and S₃ acting via S₃/C₃=C₂	D8:S3	96,118	24T141
S₃×SD₁₆	Direct product of S₃ and SD₁₆	S3xSD16	96,120	24T142
C₂×S₃×D₄	Direct product of C₂, S₃ and D₄	C2xS3xD4	96,209	24T143
D₆⋊D₄	1^st semidirect product of D₆ and D₄ acting via D₄/C₂²=C₂	D6:D4	96,89	24T144
C₂³⋊₂D₆	1^st semidirect product of C₂³ and D₆ acting via D₆/C₃=C₂²	C2^3:2D6	96,144	24T145
S₃×C₂²⋊C₄	Direct product of S₃ and C₂²⋊C₄	S3xC2^2:C4	96,87	24T146
C₂×C₄×A₄	Direct product of C₂×C₄ and A₄	C2xC4xA4	96,196	24T147
C₂×A₄⋊C₄	Direct product of C₂ and A₄⋊C₄	C2xA4:C4	96,194	24T148
C₂³⋊A₄	2^nd semidirect product of C₂³ and A₄ acting faithfully	C2^3:A4	96,204	24T149
C₂²×S₄	Direct product of C₂² and S₄	C2^2xS4	96,226	24T150
				24T151
				24T152
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	A4:D4	96,195	24T153
				24T154
				24T155
				24T156
				24T157
				24T158
				24T159
D₄×A₄	Direct product of D₄ and A₄	D4xA4	96,197	24T160
				24T161
				24T162
				24T163
				24T164
A₄⋊D₄	The semidirect product of A₄ and D₄ acting via D₄/C₂²=C₂; = Aut(C₄²) = GL₂(ℤ/4ℤ)	A4:D4	96,195	24T165
				24T166
C₄×S₄	Direct product of C₄ and S₄	C4xS4	96,186	24T167
				24T168
				24T169
C₄⋊S₄	The semidirect product of C₄ and S₄ acting via S₄/A₄=C₂	C4:S4	96,187	24T170
				24T171
				24T172
C₂×C₄²⋊C₃	Direct product of C₂ and C₄²⋊C₃	C2xC4^2:C3	96,68	24T173
				24T174
				24T175
C₂×C₂²⋊A₄	Direct product of C₂ and C₂²⋊A₄	C2xC2^2:A4	96,229	24T176
				24T177
				24T178
C₂³.₃A₄	1^st non-split extension by C₂³ of A₄ acting via A₄/C₂²=C₃	C2^3.3A4	96,3	24T179
				24T180
C₂⁴⋊C₆	1^st semidirect product of C₂⁴ and C₆ acting faithfully	C2^4:C6	96,70	24T181
				24T182
				24T183
				24T184
				24T185
				24T186
C₂³.A₄	2^nd non-split extension by C₂³ of A₄ acting faithfully	C2^3.A4	96,72	24T187
				24T188
				24T189
				24T190
C₄²⋊S₃	The semidirect product of C₄² and S₃ acting faithfully	C4^2:S3	96,64	24T191
				24T192
				24T193
				24T194
C₂²⋊S₄	The semidirect product of C₂² and S₄ acting via S₄/C₂²=S₃	C2^2:S4	96,227	24T195
				24T196
				24T197
				24T198
				24T199
				24T200

Groups of order 120

		Label	ID	Tr ID
SL₂(𝔽₅)	Special linear group on 𝔽₅²; = C₂ .A₅ = 2I = <2,3,5>	SL(2,5)	120,5	24T201
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	24T202
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	C2xA5	120,35	24T203

Groups of order 144

		Label	ID	Tr ID
S₃×C₃⋊D₄	Direct product of S₃ and C₃⋊D₄	S3xC3:D4	144,153	24T204
D₆.₃D₆	3^rd non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	D6.3D6	144,147	24T205
D₆.₄D₆	4^th non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	D6.4D6	144,148	24T206
C₆².C₄	2^nd non-split extension by C₆² of C₄ acting faithfully	C6^2.C4	144,135	24T207
C₃×S₃×D₄	Direct product of C₃, S₃ and D₄	C3xS3xD4	144,162	24T208
C₃×D₄⋊₂S₃	Direct product of C₃ and D₄⋊₂S₃	C3xD4:2S3	144,163	24T209
C₃×C₄○D₁₂	Direct product of C₃ and C₄○D₁₂	C3xC4oD12	144,161	24T210
C₃×C₄.Dic₃	Direct product of C₃ and C₄.Dic₃	C3xC4.Dic3	144,75	24T211
A₄²	Direct product of A₄ and A₄; = PΩ+₄(𝔽₃)	A4^2	144,184	24T212
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	S3^2:C4	144,115	24T213
C₃⋊S₃.Q₈	The non-split extension by C₃⋊S₃ of Q₈ acting via Q₈/C₂=C₂²	C3:S3.Q8	144,116	24T214
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	S3^2:C4	144,115	24T215
C₃⋊S₃.Q₈	The non-split extension by C₃⋊S₃ of Q₈ acting via Q₈/C₂=C₂²	C3:S3.Q8	144,116	24T216
C₃²⋊₂SD₁₆	The semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₂=D₄	C3^2:2SD16	144,118	24T217
C₃²⋊D₈	The semidirect product of C₃² and D₈ acting via D₈/C₂=D₄	C3^2:D8	144,117	24T218
				24T219
C₃²⋊₂SD₁₆	The semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₂=D₄	C3^2:2SD16	144,118	24T220
D₆.₃D₆	3^rd non-split extension by D₆ of D₆ acting via D₆/S₃=C₂	D6.3D6	144,147	24T221
D₆.₆D₆	2^nd non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	D6.6D6	144,142	24T222
Dic₃.D₆	2^nd non-split extension by Dic₃ of D₆ acting via D₆/S₃=C₂	Dic3.D6	144,140	24T223
C₄×S₃²	Direct product of C₄, S₃ and S₃	C4xS3^2	144,143	24T224
C₂×C₆.D₆	Direct product of C₂ and C₆.D₆	C2xC6.D6	144,149	24T225
S₃×C₃⋊D₄	Direct product of S₃ and C₃⋊D₄	S3xC3:D4	144,153	24T226
D₁₂⋊S₃	3^rd semidirect product of D₁₂ and S₃ acting via S₃/C₃=C₂	D12:S3	144,139	24T227
D₆.D₆	1^st non-split extension by D₆ of D₆ acting via D₆/C₆=C₂	D6.D6	144,141	24T228
S₃×D₁₂	Direct product of S₃ and D₁₂	S3xD12	144,144	24T229
C₂×C₃⋊D₁₂	Direct product of C₂ and C₃⋊D₁₂	C2xC3:D12	144,151	24T230
D₆⋊D₆	2^nd semidirect product of D₆ and D₆ acting via D₆/S₃=C₂	D6:D6	144,145	24T231
C₂²×S₃²	Direct product of C₂², S₃ and S₃	C2^2xS3^2	144,192	24T232
C₃²⋊₅SD₁₆	3^rd semidirect product of C₃² and SD₁₆ acting via SD₁₆/C₄=C₂²	C3^2:5SD16	144,60	24T233
C₃⋊D₂₄	The semidirect product of C₃ and D₂₄ acting via D₂₄/D₁₂=C₂	C3:D24	144,57	24T234
C₆.D₁₂	6^th non-split extension by C₆ of D₁₂ acting via D₁₂/D₆=C₂	C6.D12	144,65	24T235
C₁₂.₃₁D₆	5^th non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	C12.31D6	144,55	24T236
C₁₂.₂₉D₆	3^rd non-split extension by C₁₂ of D₆ acting via D₆/S₃=C₂	C12.29D6	144,53	24T237
C₄⋊(C₃²⋊C₄)	The semidirect product of C₄ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	C4:(C3^2:C4)	144,133	24T238
				24T239
C₄×C₃²⋊C₄	Direct product of C₄ and C₃²⋊C₄	C4xC3^2:C4	144,132	24T240
C₂²×C₃²⋊C₄	Direct product of C₂² and C₃²⋊C₄	C2^2xC3^2:C4	144,191	24T241
				24T242
C₃²⋊M₄(2)	The semidirect product of C₃² and M₄(2) acting via M₄(2)/C₄=C₄	C3^2:M4(2)	144,131	24T243
C₃⋊S₃⋊₃C₈	2^nd semidirect product of C₃⋊S₃ and C₈ acting via C₈/C₄=C₂	C3:S3:3C8	144,130	24T244
C₃×D₄.S₃	Direct product of C₃ and D₄.S₃	C3xD4.S3	144,81	24T245
C₃×D₄⋊S₃	Direct product of C₃ and D₄⋊S₃	C3xD4:S3	144,80	24T246
C₃×C₆.D₄	Direct product of C₃ and C₆.D₄	C3xC6.D4	144,84	24T247
C₆×C₃⋊D₄	Direct product of C₆ and C₃⋊D₄	C6xC3:D4	144,167	24T248
S₃×SL₂(𝔽₃)	Direct product of S₃ and SL₂(𝔽₃); = SL₂(ℤ/6ℤ)	S3xSL(2,3)	144,128	24T249
C₂×S₃×A₄	Direct product of C₂, S₃ and A₄	C2xS3xA4	144,190	24T250
C₂×C₃⋊S₄	Direct product of C₂ and C₃⋊S₄	C2xC3:S4	144,189	24T251
C₆.₆S₄	6^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	C6.6S4	144,125	24T252
C₃×GL₂(𝔽₃)	Direct product of C₃ and GL₂(𝔽₃)	C3xGL(2,3)	144,122	24T253
C₆×S₄	Direct product of C₆ and S₄	C6xS4	144,188	24T254
C₂×F₉	Direct product of C₂ and F₉	C2xF9	144,185	24T255
				24T256
C₂×PSU₃(𝔽₂)	Direct product of C₂ and PSU₃(𝔽₂)	C2xPSU(3,2)	144,187	24T257
C₂.PSU₃(𝔽₂)	The central extension by C₂ of PSU₃(𝔽₂)	C2.PSU(3,2)	144,120	24T258
				24T259
C₂×PSU₃(𝔽₂)	Direct product of C₂ and PSU₃(𝔽₂)	C2xPSU(3,2)	144,187	24T260
C₂×S₃≀C₂	Direct product of C₂ and S₃≀C₂	C2xS3wrC2	144,186	24T261
				24T262
				24T263
				24T264
S₃²⋊C₄	The semidirect product of S₃² and C₄ acting via C₄/C₂=C₂	S3^2:C4	144,115	24T265
				24T266
				24T267
				24T268
Dic₃⋊D₆	2^nd semidirect product of Dic₃ and D₆ acting via D₆/S₃=C₂; = Hol(Dic₃)	Dic3:D6	144,154	24T269
				24T270
				24T271
C₆²⋊C₄	1^st semidirect product of C₆² and C₄ acting faithfully	C6^2:C4	144,136	24T272
				24T273
				24T274
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	S3xS4	144,183	24T275
				24T276
				24T277
AΓL₁(𝔽₉)	Affine semilinear group on 𝔽₉¹; = F₉ ⋊C₂ = Aut(C₃²⋊C₄)	AGammaL(1,9)	144,182	24T278
				24T279
				24T280
S₃×S₄	Direct product of S₃ and S₄; = Hol(C₂×C₆)	S3xS4	144,183	24T281

Groups of order 168

		Label	ID	Tr ID
C₃×F₈	Direct product of C₃ and F₈	C3xF8	168,44	24T282
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	AGammaL(1,8)	168,43	24T283
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	GL(3,2)	168,42	24T284

Groups of order 192

		Label	ID	Tr ID
C₃×C₂≀C₄	Direct product of C₃ and C₂≀C₄	C3xC2wrC4	192,157	24T285
C₃×C₂≀C₂²	Direct product of C₃ and C₂≀C₂²	C3xC2wrC2^2	192,890	24T286
C₂⁴⋊₆D₆	1^st semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	C2^4:6D6	192,591	24T287
C₂≀A₄	Wreath product of C₂ by A₄	C2wrA4	192,201	24T288
C₂⁴⋊₅Dic₃	1^st semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₃=C₄	C2^4:5Dic3	192,95	24T289
C₂×C₄²⋊C₆	Direct product of C₂ and C₄²⋊C₆	C2xC4^2:C6	192,1001	24T290
C₂⁴.A₄	1^st non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.A4	192,195	24T291
C₂⁴.₁₀D₆	9^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	C2^4.10D6	192,1471	24T292
C₂⁴.₃A₄	3^rd non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.3A4	192,198	24T293
A₄⋊M₄(2)	The semidirect product of A₄ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	A4:M4(2)	192,968	24T294
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	D4:2S4	192,1473	24T295
A₄×C₄○D₄	Direct product of A₄ and C₄○D₄	A4xC4oD4	192,1501	24T296
A₄×M₄(2)	Direct product of A₄ and M₄(2)	A4xM4(2)	192,1011	24T297
C₂³.₁₉(C₂×A₄)	12^nd non-split extension by C₂³ of C₂×A₄ acting via C₂×A₄/C₂³=C₃	C2^3.19(C2xA4)	192,199	24T298
C₄²⋊C₁₂	1^st semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	C4^2:C12	192,192	24T299
C₂×C₄²⋊C₆	Direct product of C₂ and C₄²⋊C₆	C2xC4^2:C6	192,1001	24T300
C₄²⋊₄C₄⋊C₃	The semidirect product of C₄²⋊₄C₄ and C₃ acting faithfully	C4^2:4C4:C3	192,190	24T301
C₄○D₄⋊A₄	1^st semidirect product of C₄○D₄ and A₄ acting via A₄/C₂²=C₃	C4oD4:A4	192,1507	24T302
C₂⁴.A₄	1^st non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.A4	192,195	24T303
(C₂²×C₄).A₄	4^th non-split extension by C₂²×C₄ of A₄ acting faithfully	(C2^2xC4).A4	192,196	24T304
C₄²⋊C₁₂	1^st semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	C4^2:C12	192,192	24T305
C₂×C₄²⋊C₆	Direct product of C₂ and C₄²⋊C₆	C2xC4^2:C6	192,1001	24T306
C₂⁴.₃A₄	3^rd non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.3A4	192,198	24T307
C₄²⋊C₁₂	1^st semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	C4^2:C12	192,192	24T308
C₄²⋊₄C₄⋊C₃	The semidirect product of C₄²⋊₄C₄ and C₃ acting faithfully	C4^2:4C4:C3	192,190	24T309
C₂³.₁₉(C₂×A₄)	12^nd non-split extension by C₂³ of C₂×A₄ acting via C₂×A₄/C₂³=C₃	C2^3.19(C2xA4)	192,199	24T310
C₄²⋊₂C₁₂	2^nd semidirect product of C₄² and C₁₂ acting via C₁₂/C₂=C₆	C4^2:2C12	192,193	24T311
C₂³.₁₉(C₂×A₄)	12^nd non-split extension by C₂³ of C₂×A₄ acting via C₂×A₄/C₂³=C₃	C2^3.19(C2xA4)	192,199	24T312
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.8S4	192,181	24T313
Q₈⋊S₄	1^st semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃	Q8:S4	192,1490	24T314
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.8S4	192,181	24T315
C₂³.₇S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.7S4	192,180	24T316
C₂³.₉S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.9S4	192,182	24T317
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	D4:2S4	192,1473	24T318
C₂⁴.₁₀D₆	9^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	C2^4.10D6	192,1471	24T319
Q₈⋊₄S₄	The semidirect product of Q₈ and S₄ acting through Inn(Q₈)	Q8:4S4	192,1478	24T320
Q₈×S₄	Direct product of Q₈ and S₄	Q8xS4	192,1477	24T321
C₈×S₄	Direct product of C₈ and S₄	C8xS4	192,958	24T322
C₈⋊S₄	3^rd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	C8:S4	192,959	24T323
A₄⋊D₈	The semidirect product of A₄ and D₈ acting via D₈/C₈=C₂	A4:D8	192,961	24T324
C₈⋊₂S₄	2^nd semidirect product of C₈ and S₄ acting via S₄/A₄=C₂	C8:2S4	192,960	24T325
Q₈⋊₃S₄	The semidirect product of Q₈ and S₄ acting via S₄/A₄=C₂	Q8:3S4	192,976	24T326
D₄⋊S₄	The semidirect product of D₄ and S₄ acting via S₄/A₄=C₂	D4:S4	192,974	24T327
A₄×D₈	Direct product of A₄ and D₈	A4xD8	192,1014	24T328
A₄×SD₁₆	Direct product of A₄ and SD₁₆	A4xSD16	192,1015	24T329
D₄⋊S₄	The semidirect product of D₄ and S₄ acting via S₄/A₄=C₂	D4:S4	192,974	24T330
A₄⋊SD₁₆	The semidirect product of A₄ and SD₁₆ acting via SD₁₆/D₄=C₂	A4:SD16	192,973	24T331
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	Q8:2S4	192,1494	24T332
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	C2^3:S4	192,1493	24T333
2₊¹⁺⁴⋊₇S₃	2^nd semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	ES+(2,2):7S3	192,803	24T334
S₃×2₊¹⁺⁴	Direct product of S₃ and 2₊¹⁺⁴	S3xES+(2,2)	192,1524	24T335
C₂³⋊D₁₂	The semidirect product of C₂³ and D₁₂ acting via D₁₂/C₃=D₄	C2^3:D12	192,300	24T336
S₃×C₂³⋊C₄	Direct product of S₃ and C₂³⋊C₄	S3xC2^3:C4	192,302	24T337
C₂³.₃D₁₂	3^rd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	C2^3.3D12	192,34	24T338
S₃×C₄.D₄	Direct product of S₃ and C₄.D₄	S3xC4.D4	192,303	24T339
C₃⋊C₂≀C₄	The semidirect product of C₃ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	C3:C2wrC4	192,30	24T340
S₃×C₂³⋊C₄	Direct product of S₃ and C₂³⋊C₄	S3xC2^3:C4	192,302	24T341
C₂³.₃D₁₂	3^rd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	C2^3.3D12	192,34	24T342
D₁₂⋊₁D₄	1^st semidirect product of D₁₂ and D₄ acting via D₄/C₂=C₂²	D12:1D4	192,306	24T343
C₂³.₂D₁₂	2^nd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	C2^3.2D12	192,33	24T344
C₂³⋊D₁₂	The semidirect product of C₂³ and D₁₂ acting via D₁₂/C₃=D₄	C2^3:D12	192,300	24T345
C₂³.₂D₁₂	2^nd non-split extension by C₂³ of D₁₂ acting via D₁₂/C₃=D₄	C2^3.2D12	192,33	24T346
2₊¹⁺⁴⋊₆S₃	1^st semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	ES+(2,2):6S3	192,800	24T347
C₃⋊C₂≀C₄	The semidirect product of C₃ and C₂≀C₄ acting via C₂≀C₄/C₂³⋊C₄=C₂	C3:C2wrC4	192,30	24T348
2₊¹⁺⁴⋊₇S₃	2^nd semidirect product of 2₊¹⁺⁴ and S₃ acting via S₃/C₃=C₂	ES+(2,2):7S3	192,803	24T349
C₃×D₄⋊₄D₄	Direct product of C₃ and D₄⋊₄D₄	C3xD4:4D4	192,886	24T350
C₃×C₂≀C₄	Direct product of C₃ and C₂≀C₄	C3xC2wrC4	192,157	24T351
C₃×C₂≀C₂²	Direct product of C₃ and C₂≀C₂²	C3xC2wrC2^2	192,890	24T352
C₃×C₄²⋊C₄	Direct product of C₃ and C₄²⋊C₄	C3xC4^2:C4	192,159	24T353
C₄²⋊₅Dic₃	3^rd semidirect product of C₄² and Dic₃ acting via Dic₃/C₃=C₄	C4^2:5Dic3	192,104	24T354
C₄²⋊₈D₆	6^th semidirect product of C₄² and D₆ acting via D₆/C₃=C₂²	C4^2:8D6	192,636	24T355
C₂⁴⋊₅Dic₃	1^st semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₃=C₄	C2^4:5Dic3	192,95	24T356
C₂⁴⋊₆D₆	1^st semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	C2^4:6D6	192,591	24T357
D₄×S₄	Direct product of D₄ and S₄	D4xS4	192,1472	24T358
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	D4:2S4	192,1473	24T359
S₃×C₂²≀C₂	Direct product of S₃ and C₂²≀C₂	S3xC2^2wrC2	192,1147	24T360
S₃×C₄≀C₂	Direct product of S₃ and C₄≀C₂	S3xC4wrC2	192,379	24T361
S₃×C₈⋊C₂²	Direct product of S₃ and C₈⋊C₂²; = Aut(D₂₄) = Hol(C₂₄)	S3xC8:C2^2	192,1331	24T362
S₃×C₂³⋊C₄	Direct product of S₃ and C₂³⋊C₄	S3xC2^3:C4	192,302	24T363
C₂⁴⋊₆D₆	1^st semidirect product of C₂⁴ and D₆ acting via D₆/C₃=C₂²	C2^4:6D6	192,591	24T364
Q₈⋊₅D₁₂	3^rd semidirect product of Q₈ and D₁₂ acting via D₁₂/D₆=C₂	Q8:5D12	192,381	24T365
D₁₂⋊₁₈D₄	6^th semidirect product of D₁₂ and D₄ acting via D₄/C₂²=C₂	D12:18D4	192,757	24T366
C₂³⋊D₁₂	The semidirect product of C₂³ and D₁₂ acting via D₁₂/C₃=D₄	C2^3:D12	192,300	24T367
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.6A4	192,1008	24T368
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:A4	192,1009	24T369
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	C2^4:Dic3	192,184	24T370
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:A4	192,1009	24T371
C₄²⋊A₄	The semidirect product of C₄² and A₄ acting faithfully	C4^2:A4	192,1023	24T372
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.6A4	192,1008	24T373
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	C4^2:Dic3	192,185	24T374
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	C2^4:Dic3	192,184	24T375
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:A4	192,1009	24T376
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.6A4	192,1008	24T377
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	C4^2:Dic3	192,185	24T378
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	C2^4:Dic3	192,184	24T379
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.6A4	192,1008	24T380
C₂⁴⋊A₄	3^rd semidirect product of C₂⁴ and A₄ acting faithfully	C2^4:A4	192,1009	24T381
C₂⁴.₆A₄	6^th non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.6A4	192,1008	24T382
C₂⁴⋊Dic₃	The semidirect product of C₂⁴ and Dic₃ acting faithfully	C2^4:Dic3	192,184	24T383
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	C4^2:Dic3	192,185	24T384
C₄×C₂²⋊A₄	Direct product of C₄ and C₂²⋊A₄	C4xC2^2:A4	192,1505	24T385
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	24T386
C₄²⋊Dic₃	The semidirect product of C₄² and Dic₃ acting faithfully	C4^2:Dic3	192,185	24T387
C₄²⋊₂A₄	The semidirect product of C₄² and A₄ acting via A₄/C₂²=C₃	C4^2:2A4	192,1020	24T388
C₈²⋊C₃	The semidirect product of C₈² and C₃ acting faithfully	C8^2:C3	192,3	24T389
C₂⁶⋊C₃	3^rd semidirect product of C₂⁶ and C₃ acting faithfully	C2^6:C3	192,1541	24T390
C₄²⋊A₄	The semidirect product of C₄² and A₄ acting faithfully	C4^2:A4	192,1023	24T391
				24T392
D₄×S₄	Direct product of D₄ and S₄	D4xS4	192,1472	24T393
C₂×C₄⋊S₄	Direct product of C₂ and C₄⋊S₄	C2xC4:S4	192,1470	24T394
C₂⁴.₁₀D₆	9^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	C2^4.10D6	192,1471	24T395
D₄⋊₂S₄	The semidirect product of D₄ and S₄ acting through Inn(D₄)	D4:2S4	192,1473	24T396
C₂×C₄×S₄	Direct product of C₂×C₄ and S₄	C2xC4xS4	192,1469	24T397
C₂×A₄⋊D₄	Direct product of C₂ and A₄⋊D₄	C2xA4:D4	192,1488	24T398
				24T399
C₂³×S₄	Direct product of C₂³ and S₄	C2^3xS4	192,1537	24T400
Q₈.₅S₄	3^rd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	Q8.5S4	192,988	24T401
C₂⁵.S₃	1^st non-split extension by C₂⁵ of S₃ acting faithfully	C2^5.S3	192,991	24T402
				24T403
				24T404
C₂×A₄⋊D₄	Direct product of C₂ and A₄⋊D₄	C2xA4:D4	192,1488	24T405
				24T406
				24T407
A₄×C₂²⋊C₄	Direct product of A₄ and C₂²⋊C₄	A4xC2^2:C4	192,994	24T408
				24T409
				24T410
C₂×D₄×A₄	Direct product of C₂, D₄ and A₄	C2xD4xA4	192,1497	24T411
				24T412
				24T413
C₂⁴.₅D₆	4^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	C2^4.5D6	192,972	24T414
				24T415
C₂×A₄⋊D₄	Direct product of C₂ and A₄⋊D₄	C2xA4:D4	192,1488	24T416
C₂⁴.₅D₆	4^th non-split extension by C₂⁴ of D₆ acting via D₆/C₂=S₃	C2^4.5D6	192,972	24T417
C₂×C₄×S₄	Direct product of C₂×C₄ and S₄	C2xC4xS4	192,1469	24T418
C₂×C₄⋊S₄	Direct product of C₂ and C₄⋊S₄	C2xC4:S4	192,1470	24T419
C₂²×C₄²⋊C₃	Direct product of C₂² and C₄²⋊C₃	C2^2xC4^2:C3	192,992	24T420
				24T421
C₂×C₂³.₃A₄	Direct product of C₂ and C₂³.₃A₄	C2xC2^3.3A4	192,189	24T422
				24T423
				24T424
C₂≀A₄	Wreath product of C₂ by A₄	C2wrA4	192,201	24T425
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.8S4	192,181	24T426
C₂³.₇S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.7S4	192,180	24T427
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.8S4	192,181	24T428
C₂³.₇S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.7S4	192,180	24T429
Q₈⋊₂S₄	2^nd semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃; = Hol(Q₈)	Q8:2S4	192,1494	24T430
C₂³⋊S₄	2^nd semidirect product of C₂³ and S₄ acting faithfully; = Aut(C₂²×C₄)	C2^3:S4	192,1493	24T431
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	24T432
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	24T433
D₄×S₄	Direct product of D₄ and S₄	D4xS4	192,1472	24T434
				24T435
				24T436
				24T437
				24T438
				24T439
				24T440
C₂×C₂⁴⋊C₆	Direct product of C₂ and C₂⁴⋊C₆	C2xC2^4:C6	192,1000	24T441
				24T442
				24T443
				24T444
				24T445
				24T446
				24T447
				24T448
				24T449
				24T450
				24T451
				24T452
C₂×C₂³.A₄	Direct product of C₂ and C₂³.A₄	C2xC2^3.A4	192,1002	24T453
				24T454
				24T455
				24T456
C₂²×C₂²⋊A₄	Direct product of C₂² and C₂²⋊A₄	C2^2xC2^2:A4	192,1540	24T457
				24T458
				24T459
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.2A4	192,197	24T460
				24T461
				24T462
C₂×C₂³.A₄	Direct product of C₂ and C₂³.A₄	C2xC2^3.A4	192,1002	24T463
				24T464
				24T465
				24T466
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	C2^4.2A4	192,197	24T467
				24T468
C₄×C₄²⋊C₃	Direct product of C₄ and C₄²⋊C₃	C4xC4^2:C3	192,188	24T469
				24T470
C₂×C₄²⋊S₃	Direct product of C₂ and C₄²⋊S₃	C2xC4^2:S3	192,944	24T471
				24T472
				24T473
				24T474
				24T475
				24T476
				24T477
				24T478
				24T479
				24T480
C₂³.₉S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	C2^3.9S4	192,182	24T481
				24T482
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	C2^4:C12	192,191	24T483
				24T484
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	24T485
				24T486
				24T487
				24T488
				24T489
				24T490
				24T491
				24T492
				24T493
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	24T494
				24T495
C₂³⋊₂D₄⋊C₃	The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully	C2^3:2D4:C3	192,194	24T496
				24T497
				24T498
				24T499
				24T500
C₂⁴⋊C₁₂	1^st semidirect product of C₂⁴ and C₁₂ acting via C₁₂/C₂=C₆	C2^4:C12	192,191	24T501
				24T502
				24T503
				24T504
				24T505
				24T506
				24T507
C₂×C₂²⋊S₄	Direct product of C₂ and C₂²⋊S₄	C2xC2^2:S4	192,1538	24T508
				24T509
				24T510
				24T511
C₂⁴⋊₄Dic₃	3^rd semidirect product of C₂⁴ and Dic₃ acting via Dic₃/C₂=S₃	C2^4:4Dic3	192,1495	24T512
				24T513
				24T514
				24T515
C₂⁴⋊D₆	1^st semidirect product of C₂⁴ and D₆ acting faithfully; = Aut(C₂×Q₈)	C2^4:D6	192,955	24T516
				24T517
				24T518
				24T519
				24T520
				24T521
				24T522
				24T523
				24T524
				24T525
				24T526
				24T527
				24T528
				24T529
C₄²⋊D₆	The semidirect product of C₄² and D₆ acting faithfully	C4^2:D6	192,956	24T530
				24T531
				24T532
				24T533
				24T534
				24T535
				24T536
				24T537
				24T538
				24T539
				24T540
				24T541

Groups of order 216

		Label	ID	Tr ID
C₃×C₃²⋊₂Q₈	Direct product of C₃ and C₃²⋊₂Q₈	C3xC3^2:2Q8	216,123	24T542
C₃×C₃⋊D₁₂	Direct product of C₃ and C₃⋊D₁₂	C3xC3:D12	216,122	24T543
C₃×C₆.D₆	Direct product of C₃ and C₆.D₆	C3xC6.D6	216,120	24T544
C₃×S₃×Dic₃	Direct product of C₃, S₃ and Dic₃	C3xS3xDic3	216,119	24T545
C₃×D₆⋊S₃	Direct product of C₃ and D₆⋊S₃	C3xD6:S3	216,121	24T546
S₃²×C₆	Direct product of C₆, S₃ and S₃	S3^2xC6	216,170	24T547
C₂×C₃²⋊₄D₆	Direct product of C₂ and C₃²⋊₄D₆	C2xC3^2:4D6	216,172	24T548
C₃³⋊₉(C₂×C₄)	6^th semidirect product of C₃³ and C₂×C₄ acting via C₂×C₄/C₂=C₂²	C3^3:9(C2xC4)	216,131	24T549
C₃³⋊₉D₄	6^th semidirect product of C₃³ and D₄ acting via D₄/C₂=C₂²	C3^3:9D4	216,132	24T550
C₃³⋊₅Q₈	3^rd semidirect product of C₃³ and Q₈ acting via Q₈/C₂=C₂²	C3^3:5Q8	216,133	24T551
C₃³⋊₄C₈	2^nd semidirect product of C₃³ and C₈ acting via C₈/C₂=C₄	C3^3:4C8	216,118	24T552
C₂×C₃³⋊C₄	Direct product of C₂ and C₃³⋊C₄	C2xC3^3:C4	216,169	24T553
C₃×C₃²⋊₂C₈	Direct product of C₃ and C₃²⋊₂C₈	C3xC3^2:2C8	216,117	24T554
C₆×C₃²⋊C₄	Direct product of C₆ and C₃²⋊C₄	C6xC3^2:C4	216,168	24T555
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	24T556
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	S3^3	216,162	24T557
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	C3^2:2D12	216,159	24T558
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	S3xC3^2:C4	216,156	24T559
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	24T560
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	C3xS3wrC2	216,157	24T561
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	ASL(2,3)	216,153	24T562
C₃×S₃×A₄	Direct product of C₃, S₃ and A₄	C3xS3xA4	216,166	24T563
C₃×C₃⋊S₄	Direct product of C₃ and C₃⋊S₄	C3xC3:S4	216,164	24T564
C₃×PSU₃(𝔽₂)	Direct product of C₃ and PSU₃(𝔽₂)	C3xPSU(3,2)	216,160	24T565
C₃³⋊Q₈	2^nd semidirect product of C₃³ and Q₈ acting faithfully	C3^3:Q8	216,161	24T566
C₃×F₉	Direct product of C₃ and F₉	C3xF9	216,154	24T567
C₃⋊F₉	The semidirect product of C₃ and F₉ acting via F₉/C₃²⋊C₄=C₂	C3:F9	216,155	24T568
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	ASL(2,3)	216,153	24T569

Groups of order 240

		Label	ID	Tr ID
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	24T570
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	A5:C4	240,91	24T571
C₂²×A₅	Direct product of C₂² and A₅	C2^2xA5	240,190	24T572
				24T573
C₄×A₅	Direct product of C₄ and A₅	C4xA5	240,92	24T574
				24T575
C₄.A₅	The central extension by C₄ of A₅	C4.A5	240,93	24T576
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	24T577
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	A5:C4	240,91	24T578

Groups of order 288

		Label	ID	Tr ID
C₂×A₄²	Direct product of C₂, A₄ and A₄	C2xA4^2	288,1029	24T579
A₄×SL₂(𝔽₃)	Direct product of A₄ and SL₂(𝔽₃)	A4xSL(2,3)	288,859	24T580
C₆².₃₁D₄	15^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	C6^2.31D4	288,228	24T581
C₃²⋊2₊¹⁺⁴	The semidirect product of C₃² and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂³=C₂²	C3^2:ES+(2,2)	288,978	24T582
C₆².₃₂D₄	16^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	C6^2.32D4	288,229	24T583
(C₂×C₆²)⋊C₄	4^th semidirect product of C₂×C₆² and C₄ acting faithfully	(C2xC6^2):C4	288,434	24T584
(C₂×C₆²).C₄	5^th non-split extension by C₂×C₆² of C₄ acting faithfully	(C2xC6^2).C4	288,436	24T585
C₃×C₂³.₇D₆	Direct product of C₃ and C₂³.₇D₆	C3xC2^3.7D6	288,268	24T586
C₃×C₂³.₆D₆	Direct product of C₃ and C₂³.₆D₆	C3xC2^3.6D6	288,240	24T587
C₃×D₄⋊₆D₆	Direct product of C₃ and D₄⋊₆D₆	C3xD4:6D6	288,994	24T588
C₃×C₂³.₇D₆	Direct product of C₃ and C₂³.₇D₆	C3xC2^3.7D6	288,268	24T589
C₃×C₁₂.D₄	Direct product of C₃ and C₁₂.D₄	C3xC12.D4	288,267	24T590
C₃×C₂³⋊A₄	Direct product of C₃ and C₂³⋊A₄	C3xC2^3:A4	288,987	24T591
C₆²⋊D₄	2^nd semidirect product of C₆² and D₄ acting faithfully	C6^2:D4	288,890	24T592
				24T593
D₆≀C₂	Wreath product of D₆ by C₂	D6wrC2	288,889	24T594
C₆².₉D₄	9^th non-split extension by C₆² of D₄ acting faithfully	C6^2.9D4	288,881	24T595
C₆².₂D₄	2^nd non-split extension by C₆² of D₄ acting faithfully	C6^2.2D4	288,386	24T596
				24T597
				24T598
C₆².₉D₄	9^th non-split extension by C₆² of D₄ acting faithfully	C6^2.9D4	288,881	24T599
Dic₃≀C₂	Wreath product of Dic₃ by C₂	Dic3wrC2	288,389	24T600
C₆².₁₂D₄	12^nd non-split extension by C₆² of D₄ acting faithfully	C6^2.12D4	288,884	24T601
C₆².₂D₄	2^nd non-split extension by C₆² of D₄ acting faithfully	C6^2.2D4	288,386	24T602
C₆².₁₂D₄	12^nd non-split extension by C₆² of D₄ acting faithfully	C6^2.12D4	288,884	24T603
Dic₃≀C₂	Wreath product of Dic₃ by C₂	Dic3wrC2	288,389	24T604
C₆².₂D₄	2^nd non-split extension by C₆² of D₄ acting faithfully	C6^2.2D4	288,386	24T605
S₃²×D₄	Direct product of S₃, S₃ and D₄	S3^2xD4	288,958	24T606
D₁₂⋊₁₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/S₃=C₂	D12:13D6	288,962	24T607
Dic₆⋊₁₂D₆	6^th semidirect product of Dic₆ and D₆ acting via D₆/S₃=C₂	Dic6:12D6	288,960	24T608
C₃²⋊2₊¹⁺⁴	The semidirect product of C₃² and 2₊¹⁺⁴ acting via 2₊¹⁺⁴/C₂³=C₂²	C3^2:ES+(2,2)	288,978	24T609
D₁₂⋊₂₃D₆	7^th semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	D12:23D6	288,954	24T610
D₁₂⋊₂₇D₆	3^rd semidirect product of D₁₂ and D₆ acting through Inn(D₁₂)	D12:27D6	288,956	24T611
D₁₂⋊₄Dic₃	4^th semidirect product of D₁₂ and Dic₃ acting via Dic₃/C₆=C₂	D12:4Dic3	288,216	24T612
D₁₂⋊₁₈D₆	2^nd semidirect product of D₁₂ and D₆ acting via D₆/C₆=C₂	D12:18D6	288,473	24T613
C₆².₃₁D₄	15^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	C6^2.31D4	288,228	24T614
C₆².₃₂D₄	16^th non-split extension by C₆² of D₄ acting via D₄/C₂=C₂²	C6^2.32D4	288,229	24T615
C₃⋊C₈⋊₂₀D₆	9^th semidirect product of C₃⋊C₈ and D₆ acting via D₆/S₃=C₂	C3:C8:20D6	288,466	24T616
C₁₂.₇₀D₁₂	1^st non-split extension by C₁₂ of D₁₂ acting via D₁₂/D₆=C₂	C12.70D12	288,207	24T617
D₄×C₃²⋊C₄	Direct product of D₄ and C₃²⋊C₄	D4xC3^2:C4	288,936	24T618
				24T619
(C₂×C₆²)⋊C₄	4^th semidirect product of C₂×C₆² and C₄ acting faithfully	(C2xC6^2):C4	288,434	24T620
(C₆×C₁₂)⋊₅C₄	5^th semidirect product of C₆×C₁₂ and C₄ acting faithfully	(C6xC12):5C4	288,934	24T621
(C₆×C₁₂)⋊C₄	1^st semidirect product of C₆×C₁₂ and C₄ acting faithfully	(C6xC12):C4	288,422	24T622
				24T623
C₃⋊S₃⋊M₄(2)	2^nd semidirect product of C₃⋊S₃ and M₄(2) acting via M₄(2)/C₂×C₄=C₂	C3:S3:M4(2)	288,931	24T624
(C₂×C₆²).C₄	5^th non-split extension by C₂×C₆² of C₄ acting faithfully	(C2xC6^2).C4	288,436	24T625
C₃×C₂⁴⋊₄S₃	Direct product of C₃ and C₂⁴⋊₄S₃	C3xC2^4:4S3	288,724	24T626
C₃×C₄²⋊₄S₃	Direct product of C₃ and C₄²⋊₄S₃	C3xC4^2:4S3	288,239	24T627
C₃×D₁₂⋊₆C₂²	Direct product of C₃ and D₁₂⋊₆C₂²	C3xD12:6C2^2	288,703	24T628
C₃×C₂³.₆D₆	Direct product of C₃ and C₂³.₆D₆	C3xC2^3.6D6	288,240	24T629
C₂²⋊F₉	The semidirect product of C₂² and F₉ acting via F₉/C₃²⋊C₄=C₂	C2^2:F9	288,867	24T630
				24T631
C₆²⋊Q₈	1^st semidirect product of C₆² and Q₈ acting faithfully	C6^2:Q8	288,895	24T632
				24T633
A₄×S₄	Direct product of A₄ and S₄	A4xS4	288,1024	24T634
				24T635
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	PSO+(4,3)	288,1026	24T636
				24T637
A₄×S₄	Direct product of A₄ and S₄	A4xS4	288,1024	24T638
				24T639
C₆²⋊D₄	2^nd semidirect product of C₆² and D₄ acting faithfully	C6^2:D4	288,890	24T640
S₃²⋊Q₈	The semidirect product of S₃² and Q₈ acting via Q₈/C₄=C₂	S3^2:Q8	288,868	24T641
C₄.₄S₃≀C₂	4^th non-split extension by C₄ of S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	C4.4S3wrC2	288,869	24T642
C₄×S₃≀C₂	Direct product of C₄ and S₃≀C₂	C4xS3wrC2	288,877	24T643
S₃²⋊D₄	The semidirect product of S₃² and D₄ acting via D₄/C₄=C₂	S3^2:D4	288,878	24T644
C₂×S₃²⋊C₄	Direct product of C₂ and S₃²⋊C₄	C2xS3^2:C4	288,880	24T645
C₆².₉D₄	9^th non-split extension by C₆² of D₄ acting faithfully	C6^2.9D4	288,881	24T646
C₆²⋊D₄	2^nd semidirect product of C₆² and D₄ acting faithfully	C6^2:D4	288,890	24T647
S₃²⋊Q₈	The semidirect product of S₃² and Q₈ acting via Q₈/C₄=C₂	S3^2:Q8	288,868	24T648
S₃²⋊D₄	The semidirect product of S₃² and D₄ acting via D₄/C₄=C₂	S3^2:D4	288,878	24T649
C₄×S₃≀C₂	Direct product of C₄ and S₃≀C₂	C4xS3wrC2	288,877	24T650
C₂×S₃²⋊C₄	Direct product of C₂ and S₃²⋊C₄	C2xS3^2:C4	288,880	24T651
S₃²⋊D₄	The semidirect product of S₃² and D₄ acting via D₄/C₄=C₂	S3^2:D4	288,878	24T652
C₄⋊S₃≀C₂	The semidirect product of C₄ and S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	C4:S3wrC2	288,879	24T653
C₂²×S₃≀C₂	Direct product of C₂² and S₃≀C₂	C2^2xS3wrC2	288,1031	24T654
D₆≀C₂	Wreath product of D₆ by C₂	D6wrC2	288,889	24T655
S₃²⋊D₄	The semidirect product of S₃² and D₄ acting via D₄/C₄=C₂	S3^2:D4	288,878	24T656
C₂²×S₃≀C₂	Direct product of C₂² and S₃≀C₂	C2^2xS3wrC2	288,1031	24T657
C₃²⋊D₈⋊C₂	3^rd semidirect product of C₃²⋊D₈ and C₂ acting faithfully	C3^2:D8:C2	288,872	24T658
C₃⋊S₃⋊D₈	The semidirect product of C₃⋊S₃ and D₈ acting via D₈/C₄=C₂²	C3:S3:D8	288,873	24T659
C₃⋊S₃⋊₂SD₁₆	The semidirect product of C₃⋊S₃ and SD₁₆ acting via SD₁₆/C₄=C₂²	C3:S3:2SD16	288,875	24T660
C₂×S₃²⋊C₄	Direct product of C₂ and S₃²⋊C₄	C2xS3^2:C4	288,880	24T661
C₄.S₃≀C₂	1^st non-split extension by C₄ of S₃≀C₂ acting via S₃≀C₂/S₃²=C₂	C4.S3wrC2	288,375	24T662
S₃²⋊C₈	The semidirect product of S₃² and C₈ acting via C₈/C₄=C₂	S3^2:C8	288,374	24T663
				24T664
C₆².₂D₄	2^nd non-split extension by C₆² of D₄ acting faithfully	C6^2.2D4	288,386	24T665
C₃⋊S₃.₂D₈	1^st non-split extension by C₃⋊S₃ of D₈ acting via D₈/C₄=C₂²	C3:S3.2D8	288,377	24T666
				24T667
D₁₂⋊D₆	4^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	D12:D6	288,574	24T668
D₁₂⋊₅D₆	5^th semidirect product of D₁₂ and D₆ acting via D₆/C₃=C₂²	D12:5D6	288,585	24T669
Dic₆⋊D₆	4^th semidirect product of Dic₆ and D₆ acting via D₆/C₃=C₂²	Dic6:D6	288,578	24T670
C₂×Dic₃⋊D₆	Direct product of C₂ and Dic₃⋊D₆	C2xDic3:D6	288,977	24T671
C₆²⋊₈D₄	5^th semidirect product of C₆² and D₄ acting via D₄/C₂=C₂²	C6^2:8D4	288,629	24T672
C₆².₁₁₆C₂³	111^st non-split extension by C₆² of C₂³ acting via C₂³/C₂=C₂²	C6^2.116C2^3	288,622	24T673
C₂×C₆²⋊C₄	Direct product of C₂ and C₆²⋊C₄	C2xC6^2:C4	288,941	24T674
				24T675
C₃⋊S₃.₅D₈	The non-split extension by C₃⋊S₃ of D₈ acting via D₈/D₄=C₂	C3:S3.5D8	288,430	24T676
				24T677
S₃×GL₂(𝔽₃)	Direct product of S₃ and GL₂(𝔽₃); = GL₂(ℤ/6ℤ)	S3xGL(2,3)	288,851	24T678
C₂×S₃×S₄	Direct product of C₂, S₃ and S₄; = Aut(S₃×SL₂(𝔽₃))	C2xS3xS4	288,1028	24T679
C₂.AΓL₁(𝔽₉)	1^st central extension by C₂ of AΓL₁(𝔽₉)	C2.AGammaL(1,9)	288,841	24T680
C₂×AΓL₁(𝔽₉)	Direct product of C₂ and AΓL₁(𝔽₉)	C2xAGammaL(1,9)	288,1027	24T681
				24T682
C₂.AΓL₁(𝔽₉)	1^st central extension by C₂ of AΓL₁(𝔽₉)	C2.AGammaL(1,9)	288,841	24T683
C₂×A₄²	Direct product of C₂, A₄ and A₄	C2xA4^2	288,1029	24T684
Ω₄⁺ (𝔽₃)	Omega group of + type on 𝔽₃⁴; = SL₂(𝔽₃)⋊A₄	Omega+(4,3)	288,860	24T685
D₆≀C₂	Wreath product of D₆ by C₂	D6wrC2	288,889	24T686
				24T687
				24T688
				24T689
				24T690
				24T691
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	24T692
PSO₄⁺ (𝔽₃)	Projective special orthogonal group of + type on 𝔽₃⁴; = A₄ ⋊S₄ = Hol(A₄)	PSO+(4,3)	288,1026	24T693
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	24T694
				24T695
(C₂²×S₃)⋊A₄	The semidirect product of C₂²×S₃ and A₄ acting faithfully	(C2^2xS3):A4	288,411	24T696
				24T697
C₃×C₂⁴⋊C₆	Direct product of C₃ and C₂⁴⋊C₆	C3xC2^4:C6	288,634	24T698
(C₂×C₆)⋊S₄	2^nd semidirect product of C₂×C₆ and S₄ acting via S₄/C₂²=S₃	(C2xC6):S4	288,1036	24T699
C₃×C₂²⋊S₄	Direct product of C₃ and C₂²⋊S₄	C3xC2^2:S4	288,1035	24T700
				24T701
A₄≀C₂	Wreath product of A₄ by C₂	A4wrC2	288,1025	24T702
				24T703
				24T704
A₄×S₄	Direct product of A₄ and S₄	A4xS4	288,1024	24T705

Groups of order 336

		Label	ID	Tr ID
S₃×F₈	Direct product of S₃ and F₈	S3xF8	336,211	24T706
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	24T707

Groups of order 432

		Label	ID	Tr ID
C₃×S₃×C₃⋊D₄	Direct product of C₃, S₃ and C₃⋊D₄	C3xS3xC3:D4	432,658	24T1280
C₃×D₆.₃D₆	Direct product of C₃ and D₆.₃D₆	C3xD6.3D6	432,652	24T1281
C₃×Dic₃⋊D₆	Direct product of C₃ and Dic₃⋊D₆	C3xDic3:D6	432,659	24T1282
C₃×D₆.₄D₆	Direct product of C₃ and D₆.₄D₆	C3xD6.4D6	432,653	24T1283
C₆²⋊₂₄D₆	5^th semidirect product of C₆² and D₆ acting via D₆/C₃=C₂²	C6^2:24D6	432,696	24T1284
C₆².₉₆D₆	44^th non-split extension by C₆² of D₆ acting via D₆/C₃=C₂²	C6^2.96D6	432,693	24T1285
C₆²⋊₁₁Dic₃	1^st semidirect product of C₆² and Dic₃ acting via Dic₃/C₃=C₄	C6^2:11Dic3	432,641	24T1286
C₃³⋊₁₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂²=C₄	C3^3:12M4(2)	432,640	24T1287
C₃×C₆²⋊C₄	Direct product of C₃ and C₆²⋊C₄	C3xC6^2:C4	432,634	24T1288
C₃×C₆².C₄	Direct product of C₃ and C₆².C₄	C3xC6^2.C4	432,633	24T1289
C₃³⋊D₈	2^nd semidirect product of C₃³ and D₈ acting via D₈/C₂=D₄	C3^3:D8	432,582	24T1290
C₃³⋊₇SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	C3^3:7SD16	432,584	24T1291
C₂×C₃³⋊D₄	Direct product of C₂ and C₃³⋊D₄	C2xC3^3:D4	432,755	24T1292
S₃²⋊Dic₃	The semidirect product of S₃² and Dic₃ acting via Dic₃/C₆=C₂	S3^2:Dic3	432,580	24T1293
(S₃×C₆)⋊D₆	1^st semidirect product of S₃×C₆ and D₆ acting via D₆/C₃=C₂²	(S3xC6):D6	432,601	24T1294
S₃×C₃⋊D₁₂	Direct product of S₃ and C₃⋊D₁₂	S3xC3:D12	432,598	24T1295
C₂×S₃³	Direct product of C₂, S₃, S₃ and S₃	C2xS3^3	432,759	24T1296
C₃⋊S₃⋊₄D₁₂	The semidirect product of C₃⋊S₃ and D₁₂ acting via D₁₂/D₆=C₂	C3:S3:4D12	432,602	24T1297
S₃×C₆.D₆	Direct product of S₃ and C₆.D₆	S3xC6.D6	432,595	24T1298
D₆⋊₄S₃²	1^st semidirect product of D₆ and S₃² acting via S₃²/C₃⋊S₃=C₂	D6:4S3^2	432,599	24T1299
Dic₃.S₃²	4^th non-split extension by Dic₃ of S₃² acting via S₃²/C₃×S₃=C₂	Dic3.S3^2	432,612	24T1300
D₆.₃S₃²	3^rd non-split extension by D₆ of S₃² acting via S₃²/C₃×S₃=C₂	D6.3S3^2	432,609	24T1301
C₃³⋊₆(C₂×Q₈)	3^rd semidirect product of C₃³ and C₂×Q₈ acting via C₂×Q₈/C₂=C₂³	C3^3:6(C2xQ8)	432,605	24T1302
(S₃×C₆).D₆	9^th non-split extension by S₃×C₆ of D₆ acting via D₆/C₃=C₂²	(S3xC6).D6	432,606	24T1303
C₂×C₃²⋊₂D₁₂	Direct product of C₂ and C₃²⋊₂D₁₂	C2xC3^2:2D12	432,756	24T1304
(C₃×C₆).₈D₁₂	1^st non-split extension by C₃×C₆ of D₁₂ acting via D₁₂/C₃=D₄	(C3xC6).8D12	432,586	24T1305
C₃²⋊₂D₂₄	The semidirect product of C₃² and D₂₄ acting via D₂₄/C₆=D₄	C3^2:2D24	432,588	24T1306
C₃³⋊₈SD₁₆	4^th semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	C3^3:8SD16	432,589	24T1307
C₃³⋊₅(C₂×C₈)	2^nd semidirect product of C₃³ and C₂×C₈ acting via C₂×C₈/C₂=C₂×C₄	C3^3:5(C2xC8)	432,571	24T1308
C₃³⋊₂M₄(2)	2^nd semidirect product of C₃³ and M₄(2) acting via M₄(2)/C₂=C₂×C₄	C3^3:2M4(2)	432,573	24T1309
C₂×S₃×C₃²⋊C₄	Direct product of C₂, S₃ and C₃²⋊C₄	C2xS3xC3^2:C4	432,753	24T1310
D₆⋊(C₃²⋊C₄)	The semidirect product of D₆ and C₃²⋊C₄ acting via C₃²⋊C₄/C₃⋊S₃=C₂	D6:(C3^2:C4)	432,568	24T1311
C₂×C₃³⋊D₄	Direct product of C₂ and C₃³⋊D₄	C2xC3^3:D4	432,755	24T1312
C₃⋊S₃.₂D₁₂	1^st non-split extension by C₃⋊S₃ of D₁₂ acting via D₁₂/C₆=C₂²	C3:S3.2D12	432,579	24T1313
C₃³⋊D₈	2^nd semidirect product of C₃³ and D₈ acting via D₈/C₂=D₄	C3^3:D8	432,582	24T1314
C₃³⋊₆SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting via SD₁₆/C₂=D₄	C3^3:6SD16	432,583	24T1315
C₆×S₃≀C₂	Direct product of C₆ and S₃≀C₂	C6xS3wrC2	432,754	24T1316
C₃×S₃²⋊C₄	Direct product of C₃ and S₃²⋊C₄	C3xS3^2:C4	432,574	24T1317
C₃×C₃²⋊D₈	Direct product of C₃ and C₃²⋊D₈	C3xC3^2:D8	432,576	24T1318
C₃×C₃²⋊₂SD₁₆	Direct product of C₃ and C₃²⋊₂SD₁₆	C3xC3^2:2SD16	432,577	24T1319
C₂×ASL₂(𝔽₃)	Direct product of C₂ and ASL₂(𝔽₃)	C2xASL(2,3)	432,735	24T1320
				24T1321
S₃×S₃≀C₂	Direct product of S₃ and S₃≀C₂	S3xS3wrC2	432,741	24T1322
				24T1323
				24T1324
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	AGL(2,3)	432,734	24T1325
				24T1326
				24T1327
C₃×S₃×S₄	Direct product of C₃, S₃ and S₄	C3xS3xS4	432,745	24T1328
S₃×C₃⋊S₄	Direct product of S₃ and C₃⋊S₄	S3xC3:S4	432,747	24T1329
C₃×AΓL₁(𝔽₉)	Direct product of C₃ and AΓL₁(𝔽₉)	C3xAGammaL(1,9)	432,737	24T1330
C₃³⋊SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting faithfully	C3^3:SD16	432,738	24T1331
C₃³⋊₃SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting faithfully	C3^3:3SD16	432,739	24T1332
F₉⋊S₃	The semidirect product of F₉ and S₃ acting via S₃/C₃=C₂	F9:S3	432,740	24T1333
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	AGL(2,3)	432,734	24T1334
S₃×PSU₃(𝔽₂)	Direct product of S₃ and PSU₃(𝔽₂)	S3xPSU(3,2)	432,742	24T1335
S₃×F₉	Direct product of S₃ and F₉	S3xF9	432,736	24T1336
A₄×C₃²⋊C₄	Direct product of A₄ and C₃²⋊C₄	A4xC3^2:C4	432,744	24T1337
S₃²×A₄	Direct product of S₃, S₃ and A₄	S3^2xA4	432,749	24T1338
C₆²⋊Dic₃	The semidirect product of C₆² and Dic₃ acting faithfully	C6^2:Dic3	432,743	24T1339
C₆²⋊₁₀D₆	10^th semidirect product of C₆² and D₆ acting faithfully	C6^2:10D6	432,748	24T1340

Groups of order 480

		Label	ID	Tr ID
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	C2^2:S5	480,951	24T1341
				24T1342
D₄×A₅	Direct product of D₄ and A₅	D4xA5	480,956	24T1343
				24T1344
C₂²×S₅	Direct product of C₂² and S₅	C2^2xS5	480,1186	24T1345
C₂×A₅⋊C₄	Direct product of C₂ and A₅⋊C₄	C2xA5:C4	480,952	24T1346
C₄×S₅	Direct product of C₄ and S₅; = CO₃(𝔽₅)	C4xS5	480,943	24T1347
				24T1348
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	C2^2:S5	480,951	24T1349
				24T1350
A₅⋊Q₈	The semidirect product of A₅ and Q₈ acting via Q₈/C₄=C₂	A5:Q8	480,945	24T1351
C₄⋊S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	C4:S5	480,944	24T1352
GL₂(𝔽₅)	General linear group on 𝔽₅²; = SL₂(𝔽₅)⋊₁ C₄ = Aut(C₅²)	GL(2,5)	480,218	24T1353

On 25 points

Groups of order 25

		Label	ID	Tr ID
C₂₅	Cyclic group	C25	25,1	25T1
C₅²	Elementary abelian group of type [5,5]	C5^2	25,2	25T2

Groups of order 50

		Label	ID	Tr ID
C₅×D₅	Direct product of C₅ and D₅; = AΣL₁(𝔽₂₅)	C5xD5	50,3	25T3
D₂₅	Dihedral group	D25	50,1	25T4
C₅⋊D₅	The semidirect product of C₅ and D₅ acting via D₅/C₅=C₂	C5:D5	50,4	25T5

Groups of order 75

		Label	ID	Tr ID
C₅²⋊C₃	The semidirect product of C₅² and C₃ acting faithfully	C5^2:C3	75,2	25T6

Groups of order 100

		Label	ID	Tr ID
C₅×F₅	Direct product of C₅ and F₅	C5xF5	100,9	25T7
C₂₅⋊C₄	The semidirect product of C₂₅ and C₄ acting faithfully	C25:C4	100,3	25T8
C₅⋊F₅	1^st semidirect product of C₅ and F₅ acting via F₅/C₅=C₄	C5:F5	100,11	25T9
C₅²⋊C₄	4^th semidirect product of C₅² and C₄ acting faithfully	C5^2:C4	100,12	25T10
D₅.D₅	The non-split extension by D₅ of D₅ acting via D₅/C₅=C₂	D5.D5	100,10	25T11
D₅²	Direct product of D₅ and D₅	D5^2	100,13	25T12

Groups of order 125

		Label	ID	Tr ID
5_-¹⁺²	Extraspecial group	ES-(5,1)	125,4	25T13
He₅	Heisenberg group; = C₅² ⋊C₅ = 5₊¹⁺²	He5	125,3	25T14

Groups of order 150

		Label	ID	Tr ID
C₅²⋊C₆	The semidirect product of C₅² and C₆ acting faithfully	C5^2:C6	150,6	25T15
C₅²⋊S₃	The semidirect product of C₅² and S₃ acting faithfully	C5^2:S3	150,5	25T16

Groups of order 200

		Label	ID	Tr ID
C₅²⋊Q₈	The semidirect product of C₅² and Q₈ acting faithfully	C5^2:Q8	200,44	25T17
D₅×F₅	Direct product of D₅ and F₅	D5xF5	200,41	25T18
D₅⋊F₅	The semidirect product of D₅ and F₅ acting via F₅/D₅=C₂; = Hol(D₅)	D5:F5	200,42	25T19
C₅²⋊C₈	The semidirect product of C₅² and C₈ acting faithfully	C5^2:C8	200,40	25T20
D₅≀C₂	Wreath product of D₅ by C₂	D5wrC2	200,43	25T21

Groups of order 250

		Label	ID	Tr ID
He₅⋊C₂	2^nd semidirect product of He₅ and C₂ acting faithfully	He5:C2	250,8	25T22
C₅²⋊C₁₀	The semidirect product of C₅² and C₁₀ acting faithfully	C5^2:C10	250,5	25T23
				25T24
C₂₅⋊C₁₀	The semidirect product of C₂₅ and C₁₀ acting faithfully	C25:C10	250,6	25T25

Groups of order 300

		Label	ID	Tr ID
C₅²⋊C₁₂	The semidirect product of C₅² and C₁₂ acting faithfully	C5^2:C12	300,24	25T26
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	C5^2:D6	300,25	25T27
C₅²⋊Dic₃	The semidirect product of C₅² and Dic₃ acting faithfully	C5^2:Dic3	300,23	25T28
C₅×A₅	Direct product of C₅ and A₅; = U₂(𝔽₄)	C5xA5	300,22	25T29

Groups of order 400

		Label	ID	Tr ID
D₅≀C₂⋊C₂	The semidirect product of D₅≀C₂ and C₂ acting faithfully	D5wrC2:C2	400,207	25T30
C₅²⋊M₄(2)	The semidirect product of C₅² and M₄(2) acting faithfully	C5^2:M4(2)	400,206	25T31
F₅²	Direct product of F₅ and F₅; = Hol(F₅)	F5^2	400,205	25T32

Groups of order 500

		Label	ID	Tr ID
C₅²⋊F₅	3^rd semidirect product of C₅² and F₅ acting faithfully	C5^2:F5	500,23	25T33
C₅²⋊C₂₀	The semidirect product of C₅² and C₂₀ acting faithfully	C5^2:C20	500,17	25T34
He₅⋊₄C₄	4^th semidirect product of He₅ and C₄ acting faithfully; = Aut(5_-¹⁺²)	He5:4C4	500,25	25T35
He₅⋊C₄	2^nd semidirect product of He₅ and C₄ acting faithfully	He5:C4	500,21	25T36
C₅²⋊C₂₀	The semidirect product of C₅² and C₂₀ acting faithfully	C5^2:C20	500,17	25T37
C₅²⋊D₁₀	The semidirect product of C₅² and D₁₀ acting faithfully	C5^2:D10	500,27	25T38
He₅⋊C₄	2^nd semidirect product of He₅ and C₄ acting faithfully	He5:C4	500,21	25T39
C₂₅⋊C₂₀	The semidirect product of C₂₅ and C₂₀ acting faithfully; = Aut(D₂₅) = Hol(C₂₅)	C25:C20	500,18	25T40

On 26 points

Groups of order 26

		Label	ID	Tr ID
C₂₆	Cyclic group	C26	26,2	26T1
D₁₃	Dihedral group	D13	26,1	26T2

Groups of order 52

		Label	ID	Tr ID
D₂₆	Dihedral group; = C₂×D₁₃	D26	52,4	26T3
C₁₃⋊C₄	The semidirect product of C₁₃ and C₄ acting faithfully	C13:C4	52,3	26T4

Groups of order 78

		Label	ID	Tr ID
C₂×C₁₃⋊C₃	Direct product of C₂ and C₁₃⋊C₃	C2xC13:C3	78,2	26T5
C₁₃⋊C₆	The semidirect product of C₁₃ and C₆ acting faithfully	C13:C6	78,1	26T6

Groups of order 104

		Label	ID	Tr ID
C₂×C₁₃⋊C₄	Direct product of C₂ and C₁₃⋊C₄	C2xC13:C4	104,12	26T7

Groups of order 156

		Label	ID	Tr ID
F₁₃	Frobenius group; = C₁₃ ⋊C₁₂ = AGL₁(𝔽₁₃) = Aut(D₁₃) = Hol(C₁₃)	F13	156,7	26T8
C₂×C₁₃⋊C₆	Direct product of C₂ and C₁₃⋊C₆	C2xC13:C6	156,8	26T9

Groups of order 312

		Label	ID	Tr ID
C₂×F₁₃	Direct product of C₂ and F₁₃; = Aut(D₂₆) = Hol(C₂₆)	C2xF13	312,45	26T10

Groups of order 338

		Label	ID	Tr ID
C₁₃×D₁₃	Direct product of C₁₃ and D₁₃; = AΣL₁(𝔽₁₆₉)	C13xD13	338,3	26T11

On 27 points

Groups of order 27

		Label	ID	Tr ID
C₂₇	Cyclic group	C27	27,1	27T1
C₃×C₉	Abelian group of type [3,9]	C3xC9	27,2	27T2
He₃	Heisenberg group; = C₃² ⋊C₃ = 3₊¹⁺²	He3	27,3	27T3
C₃³	Elementary abelian group of type [3,3,3]	C3^3	27,5	27T4
3_-¹⁺²	Extraspecial group	ES-(3,1)	27,4	27T5

Groups of order 54

		Label	ID	Tr ID
He₃⋊C₂	2^nd semidirect product of He₃ and C₂ acting faithfully; = Aut(3_-¹⁺²)	He3:C2	54,8	27T6
C₃³⋊C₂	3^rd semidirect product of C₃³ and C₂ acting faithfully	C3^3:C2	54,14	27T7
D₂₇	Dihedral group	D27	54,1	27T8
C₃×D₉	Direct product of C₃ and D₉	C3xD9	54,3	27T9
C₉⋊S₃	The semidirect product of C₉ and S₃ acting via S₃/C₃=C₂	C9:S3	54,7	27T10
C₃²⋊C₆	The semidirect product of C₃² and C₆ acting faithfully	C3^2:C6	54,5	27T11
S₃×C₉	Direct product of C₉ and S₃	S3xC9	54,4	27T12
C₃×C₃⋊S₃	Direct product of C₃ and C₃⋊S₃	C3xC3:S3	54,13	27T13
C₉⋊C₆	The semidirect product of C₉ and C₆ acting faithfully; = Aut(D₉) = Hol(C₉)	C9:C6	54,6	27T14
S₃×C₃²	Direct product of C₃² and S₃	S3xC3^2	54,12	27T15

Groups of order 81

		Label	ID	Tr ID
C₃×3_-¹⁺²	Direct product of C₃ and 3_-¹⁺²	C3xES-(3,1)	81,13	27T16
C₃²⋊C₉	The semidirect product of C₃² and C₉ acting via C₉/C₃=C₃	C3^2:C9	81,3	27T17
C₃×He₃	Direct product of C₃ and He₃	C3xHe3	81,12	27T18
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	C3wrC3	81,7	27T19
He₃.C₃	The non-split extension by He₃ of C₃ acting faithfully	He3.C3	81,8	27T20
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	C3wrC3	81,7	27T21
C₂₇⋊C₃	The semidirect product of C₂₇ and C₃ acting faithfully	C27:C3	81,6	27T22
He₃⋊C₃	2^nd semidirect product of He₃ and C₃ acting faithfully	He3:C3	81,9	27T23
				27T24
C₃.He₃	4^th central stem extension by C₃ of He₃	C3.He3	81,10	27T25
He₃.C₃	The non-split extension by He₃ of C₃ acting faithfully	He3.C3	81,8	27T26
C₃≀C₃	Wreath product of C₃ by C₃; = AΣL₁(𝔽₂₇)	C3wrC3	81,7	27T27
C₉○He₃	Central product of C₉ and He₃	C9oHe3	81,14	27T28

Groups of order 108

		Label	ID	Tr ID
C₃²⋊D₆	The semidirect product of C₃² and D₆ acting faithfully	C3^2:D6	108,17	27T29
S₃×D₉	Direct product of S₃ and D₉	S3xD9	108,16	27T30
C₃³⋊C₄	2^nd semidirect product of C₃³ and C₄ acting faithfully	C3^3:C4	108,37	27T31
He₃⋊C₄	The semidirect product of He₃ and C₄ acting faithfully	He3:C4	108,15	27T32
C₃×C₃²⋊C₄	Direct product of C₃ and C₃²⋊C₄	C3xC3^2:C4	108,36	27T33
S₃×C₃⋊S₃	Direct product of S₃ and C₃⋊S₃	S3xC3:S3	108,39	27T34
C₃²⋊₄D₆	The semidirect product of C₃² and D₆ acting via D₆/C₃=C₂²	C3^2:4D6	108,40	27T35
C₃×S₃²	Direct product of C₃, S₃ and S₃	C3xS3^2	108,38	27T36

Groups of order 162

		Label	ID	Tr ID
C₃≀S₃	Wreath product of C₃ by S₃	C3wrS3	162,10	27T37
He₃.₂S₃	2^nd non-split extension by He₃ of S₃ acting faithfully	He3.2S3	162,15	27T38
He₃.₄C₆	The non-split extension by He₃ of C₆ acting via C₆/C₃=C₂	He3.4C6	162,44	27T39
He₃.₂C₆	2^nd non-split extension by He₃ of C₆ acting faithfully	He3.2C6	162,14	27T40
He₃.S₃	1^st non-split extension by He₃ of S₃ acting faithfully	He3.S3	162,13	27T41
He₃.₃S₃	3^rd non-split extension by He₃ of S₃ acting faithfully	He3.3S3	162,20	27T42
3_-¹⁺².S₃	The non-split extension by 3_-¹⁺² of S₃ acting faithfully	ES-(3,1).S3	162,22	27T43
He₃⋊S₃	3^rd semidirect product of He₃ and S₃ acting faithfully	He3:S3	162,21	27T44
He₃.C₆	1^st non-split extension by He₃ of C₆ acting faithfully	He3.C6	162,12	27T45
C₃×He₃⋊C₂	Direct product of C₃ and He₃⋊C₂	C3xHe3:C2	162,41	27T46
C₃²⋊C₁₈	The semidirect product of C₃² and C₁₈ acting via C₁₈/C₃=C₆	C3^2:C18	162,4	27T47
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	C3xC3^2:C6	162,34	27T48
He₃.₂C₆	2^nd non-split extension by He₃ of C₆ acting faithfully	He3.2C6	162,14	27T49
C₃≀S₃	Wreath product of C₃ by S₃	C3wrS3	162,10	27T50
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	C3^3:S3	162,19	27T51
				27T52
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	C3^3:C6	162,11	27T53
He₃.₄S₃	The non-split extension by He₃ of S₃ acting via S₃/C₃=C₂	He3.4S3	162,43	27T54
C₂₇⋊C₆	The semidirect product of C₂₇ and C₆ acting faithfully	C27:C6	162,9	27T55
He₃.₄S₃	The non-split extension by He₃ of S₃ acting via S₃/C₃=C₂	He3.4S3	162,43	27T56
C₃×C₉⋊C₆	Direct product of C₃ and C₉⋊C₆	C3xC9:C6	162,36	27T57
C₃³.S₃	4^th non-split extension by C₃³ of S₃ acting faithfully	C3^3.S3	162,42	27T58
C₃²⋊D₉	1^st semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	C3^2:D9	162,5	27T59
C₃×C₃²⋊C₆	Direct product of C₃ and C₃²⋊C₆	C3xC3^2:C6	162,34	27T60
He₃⋊₄S₃	1^st semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	He3:4S3	162,40	27T61
C₃³⋊C₆	1^st semidirect product of C₃³ and C₆ acting faithfully	C3^3:C6	162,11	27T62
				27T63
He₃.₂S₃	2^nd non-split extension by He₃ of S₃ acting faithfully	He3.2S3	162,15	27T64
C₃²⋊₂D₉	2^nd semidirect product of C₃² and D₉ acting via D₉/C₃=S₃	C3^2:2D9	162,17	27T65
He₃⋊S₃	3^rd semidirect product of He₃ and S₃ acting faithfully	He3:S3	162,21	27T66
C₃³⋊S₃	2^nd semidirect product of C₃³ and S₃ acting faithfully	C3^3:S3	162,19	27T67
He₃.₃S₃	3^rd non-split extension by He₃ of S₃ acting faithfully	He3.3S3	162,20	27T68
He₃.C₆	1^st non-split extension by He₃ of C₆ acting faithfully	He3.C6	162,12	27T69
C₃≀S₃	Wreath product of C₃ by S₃	C3wrS3	162,10	27T70
He₃⋊₄S₃	1^st semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	He3:4S3	162,40	27T71
He₃.S₃	1^st non-split extension by He₃ of S₃ acting faithfully	He3.S3	162,13	27T72
S₃×He₃	Direct product of S₃ and He₃	S3xHe3	162,35	27T73
He₃⋊₅S₃	2^nd semidirect product of He₃ and S₃ acting via S₃/C₃=C₂	He3:5S3	162,46	27T74
S₃×3_-¹⁺²	Direct product of S₃ and 3_-¹⁺²	S3xES-(3,1)	162,37	27T75

Groups of order 216

		Label	ID	Tr ID
He₃⋊D₄	The semidirect product of He₃ and D₄ acting faithfully	He3:D4	216,87	27T76
He₃⋊C₈	The semidirect product of He₃ and C₈ acting faithfully	He3:C8	216,86	27T77
C₃×F₉	Direct product of C₃ and F₉	C3xF9	216,154	27T78
C₃²⋊₂D₁₂	The semidirect product of C₃² and D₁₂ acting via D₁₂/C₃=D₄	C3^2:2D12	216,159	27T79
C₃⋊F₉	The semidirect product of C₃ and F₉ acting via F₉/C₃²⋊C₄=C₂	C3:F9	216,155	27T80
C₃³⋊D₄	2^nd semidirect product of C₃³ and D₄ acting faithfully	C3^3:D4	216,158	27T81
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	ASL(2,3)	216,153	27T82
SU₃(𝔽₂)	Special unitary group on 𝔽₂³; = He₃ ⋊Q₈	SU(3,2)	216,88	27T83
C₃×S₃≀C₂	Direct product of C₃ and S₃≀C₂	C3xS3wrC2	216,157	27T84
S₃×C₃²⋊C₄	Direct product of S₃ and C₃²⋊C₄	S3xC3^2:C4	216,156	27T85
S₃³	Direct product of S₃, S₃ and S₃; = Hol(C₃×S₃)	S3^3	216,162	27T86
C₃³⋊Q₈	2^nd semidirect product of C₃³ and Q₈ acting faithfully	C3^3:Q8	216,161	27T87
C₃×PSU₃(𝔽₂)	Direct product of C₃ and PSU₃(𝔽₂)	C3xPSU(3,2)	216,160	27T88

Groups of order 243

		Label	ID	Tr ID
C₃³⋊C₉	1^st semidirect product of C₃³ and C₉ acting via C₉/C₃=C₃	C3^3:C9	243,13	27T89
C₃².₅He₃	5^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	C3^2.5He3	243,29	27T90
C₃².₆He₃	6^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	C3^2.6He3	243,30	27T91
C₉.₄He₃	2^nd central extension by C₉ of He₃	C9.4He3	243,16	27T92
C₉.He₃	1^st non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	C9.He3	243,55	27T93
C₃².He₃	4^th non-split extension by C₃² of He₃ acting via He₃/C₃²=C₃	C3^2.He3	243,28	27T94
C₃²⋊He₃	The semidirect product of C₃² and He₃ acting via He₃/C₃²=C₃	C3^2:He3	243,37	27T95
He₃⋊C₃²	3^rd semidirect product of He₃ and C₃² acting via C₃²/C₃=C₃	He3:C3^2	243,58	27T96
				27T97
C₃³⋊C₉	1^st semidirect product of C₃³ and C₉ acting via C₉/C₃=C₃	C3^3:C9	243,13	27T98
He₃.C₃²	4^th non-split extension by He₃ of C₃² acting via C₃²/C₃=C₃	He3.C3^2	243,57	27T99
C₃³⋊C₃²	2^nd semidirect product of C₃³ and C₃² acting faithfully	C3^3:C3^2	243,56	27T100
3₊¹⁺⁴	Extraspecial group; = He₃ ○He₃	ES+(3,2)	243,65	27T101
C₃³⋊C₃²	2^nd semidirect product of C₃³ and C₃² acting faithfully	C3^3:C3^2	243,56	27T102
C₉.₂He₃	2^nd non-split extension by C₉ of He₃ acting via He₃/C₃²=C₃	C9.2He3	243,60	27T103
C₉²⋊₂C₃	2^nd semidirect product of C₉² and C₃ acting faithfully	C9^2:2C3	243,26	27T104
C₃×C₃≀C₃	Direct product of C₃ and C₃≀C₃	C3xC3wrC3	243,51	27T105
				27T106
C₂₇⋊C₉	The semidirect product of C₂₇ and C₉ acting faithfully	C27:C9	243,22	27T107
C₉²⋊C₃	1^st semidirect product of C₉² and C₃ acting faithfully	C9^2:C3	243,25	27T108
He₃.C₃²	4^th non-split extension by He₃ of C₃² acting via C₃²/C₃=C₃	He3.C3^2	243,57	27T109
C₃⁴.C₃	3^rd non-split extension by C₃⁴ of C₃ acting faithfully	C3^4.C3	243,38	27T110
C₃².C₃³	9^th non-split extension by C₃² of C₃³ acting via C₃³/C₃²=C₃	C3^2.C3^3	243,59	27T111
C₉².C₃	2^nd non-split extension by C₉² of C₃ acting faithfully	C9^2.C3	243,27	27T112
3_-¹⁺⁴	Extraspecial group; = He₃ ○3_-¹⁺²	ES-(3,2)	243,66	27T113
C₃³⋊C₃²	2^nd semidirect product of C₃³ and C₃² acting faithfully	C3^3:C3^2	243,56	27T114

Groups of order 324

		Label	ID	Tr ID
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	S3xC3^2:C6	324,116	27T115
S₃×C₉⋊C₆	Direct product of S₃ and C₉⋊C₆	S3xC9:C6	324,118	27T116
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	He3:5D6	324,121	27T117
S₃×He₃⋊C₂	Direct product of S₃ and He₃⋊C₂	S3xHe3:C2	324,122	27T118
S₃×C₃²⋊C₆	Direct product of S₃ and C₃²⋊C₆	S3xC3^2:C6	324,116	27T119
He₃⋊₆D₆	2^nd semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	He3:6D6	324,124	27T120
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	He3:D6	324,39	27T121
He₃.₆D₆	The non-split extension by He₃ of D₆ acting via D₆/C₃=C₂²	He3.6D6	324,125	27T122
He₃.₂D₆	2^nd non-split extension by He₃ of D₆ acting faithfully	He3.2D6	324,41	27T123
He₃.D₆	1^st non-split extension by He₃ of D₆ acting faithfully	He3.D6	324,40	27T124
C₃×C₃²⋊D₆	Direct product of C₃ and C₃²⋊D₆	C3xC3^2:D6	324,117	27T125
C₃²⋊D₁₈	The semidirect product of C₃² and D₁₈ acting via D₁₈/C₃=D₆	C3^2:D18	324,37	27T126
He₃⋊₅D₆	1^st semidirect product of He₃ and D₆ acting via D₆/C₃=C₂²	He3:5D6	324,121	27T127
He₃⋊D₆	The semidirect product of He₃ and D₆ acting faithfully	He3:D6	324,39	27T128
				27T129
C₃³⋊A₄	The semidirect product of C₃³ and A₄ acting faithfully	C3^3:A4	324,160	27T130
				27T131
He₃.D₆	1^st non-split extension by He₃ of D₆ acting faithfully	He3.D6	324,40	27T132
He₃.₂D₆	2^nd non-split extension by He₃ of D₆ acting faithfully	He3.2D6	324,41	27T133

Groups of order 351

		Label	ID	Tr ID
C₃³⋊C₁₃	The semidirect product of C₃³ and C₁₃ acting faithfully	C3^3:C13	351,12	27T134

Groups of order 432

		Label	ID	Tr ID
S₃×PSU₃(𝔽₂)	Direct product of S₃ and PSU₃(𝔽₂)	S3xPSU(3,2)	432,742	27T135
C₃³⋊SD₁₆	2^nd semidirect product of C₃³ and SD₁₆ acting faithfully	C3^3:SD16	432,738	27T136
S₃×S₃≀C₂	Direct product of S₃ and S₃≀C₂	S3xS3wrC2	432,741	27T137
S₃×F₉	Direct product of S₃ and F₉	S3xF9	432,736	27T138
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	AGL(2,3)	432,734	27T139
C₃³⋊₃SD₁₆	3^rd semidirect product of C₃³ and SD₁₆ acting faithfully	C3^3:3SD16	432,739	27T140
He₃⋊SD₁₆	The semidirect product of He₃ and SD₁₆ acting faithfully	He3:SD16	432,520	27T141
C₃×AΓL₁(𝔽₉)	Direct product of C₃ and AΓL₁(𝔽₉)	C3xAGammaL(1,9)	432,737	27T142
F₉⋊S₃	The semidirect product of F₉ and S₃ acting via S₃/C₃=C₂	F9:S3	432,740	27T143

Groups of order 486

		Label	ID	Tr ID
3_-¹⁺⁴⋊C₂	1^st semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	ES-(3,2):C2	486,238	27T144
				27T145
C₃⁴.₇S₃	7^th non-split extension by C₃⁴ of S₃ acting faithfully	C3^4.7S3	486,147	27T146
He₃⋊(C₃×S₃)	4^th semidirect product of He₃ and C₃×S₃ acting via C₃×S₃/C₃=S₃	He3:(C3xS3)	486,178	27T147
C₉⋊S₃⋊C₃²	2^nd semidirect product of C₉⋊S₃ and C₃² acting faithfully	C9:S3:C3^2	486,129	27T148
C₃≀S₃⋊₃C₃	The semidirect product of C₃≀S₃ and C₃ acting through Inn(C₃≀S₃)	C3wrS3:3C3	486,125	27T149
C₃≀C₃⋊C₆	2^nd semidirect product of C₃≀C₃ and C₆ acting faithfully	C3wrC3:C6	486,126	27T150
C₃⁴⋊S₃	1^st semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:S3	486,103	27T151
C₉⋊C₉.S₃	2^nd non-split extension by C₉⋊C₉ of S₃ acting faithfully	C9:C9.S3	486,39	27T152
He₃.C₃⋊₂C₆	2^nd semidirect product of He₃.C₃ and C₆ acting faithfully	He3.C3:2C6	486,177	27T153
C₃⁴⋊₆S₃	6^th semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:6S3	486,183	27T154
(C₃×He₃)⋊C₆	8^th semidirect product of C₃×He₃ and C₆ acting faithfully	(C3xHe3):C6	486,127	27T155
C₃³.D₉	3^rd non-split extension by C₃³ of D₉ acting via D₉/C₃=S₃	C3^3.D9	486,55	27T156
C₉⋊C₉⋊S₃	1^st semidirect product of C₉⋊C₉ and S₃ acting faithfully	C9:C9:S3	486,41	27T157
C₉²⋊₂C₆	2^nd semidirect product of C₉² and C₆ acting faithfully	C9^2:2C6	486,37	27T158
C₃≀C₃⋊S₃	2^nd semidirect product of C₃≀C₃ and S₃ acting via S₃/C₃=C₂	C3wrC3:S3	486,189	27T159
C₃³⋊(C₃×S₃)	4^th semidirect product of C₃³ and C₃×S₃ acting faithfully	C3^3:(C3xS3)	486,176	27T160
He₃⋊(C₃×S₃)	4^th semidirect product of He₃ and C₃×S₃ acting via C₃×S₃/C₃=S₃	He3:(C3xS3)	486,178	27T161
3₊¹⁺⁴⋊C₂	1^st semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	ES+(3,2):C2	486,236	27T162
C₃.He₃⋊C₆	The semidirect product of C₃.He₃ and C₆ acting faithfully	C3.He3:C6	486,179	27T163
C₃×C₃³⋊S₃	Direct product of C₃ and C₃³⋊S₃	C3xC3^3:S3	486,165	27T164
C₃⁴⋊₇S₃	7^th semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:7S3	486,185	27T165
C₃³⋊(C₃×S₃)	4^th semidirect product of C₃³ and C₃×S₃ acting faithfully	C3^3:(C3xS3)	486,176	27T166
3_-¹⁺⁴⋊₂C₂	2^nd semidirect product of 3_-¹⁺⁴ and C₂ acting faithfully	ES-(3,2):2C2	486,239	27T167
C₃≀C₃⋊C₆	2^nd semidirect product of C₃≀C₃ and C₆ acting faithfully	C3wrC3:C6	486,126	27T168
3₊¹⁺⁴⋊₂C₂	2^nd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	ES+(3,2):2C2	486,237	27T169
C₃≀C₃.S₃	The non-split extension by C₃≀C₃ of S₃ acting via S₃/C₃=C₂	C3wrC3.S3	486,175	27T170
(C₃×He₃)⋊C₆	8^th semidirect product of C₃×He₃ and C₆ acting faithfully	(C3xHe3):C6	486,127	27T171
C₉²⋊C₆	1^st semidirect product of C₉² and C₆ acting faithfully	C9^2:C6	486,35	27T172
He₃.C₃⋊₂C₆	2^nd semidirect product of He₃.C₃ and C₆ acting faithfully	He3.C3:2C6	486,177	27T173
3₊¹⁺⁴⋊₃C₂	3^rd semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	ES+(3,2):3C2	486,249	27T174
He₃.(C₃×S₃)	5^th non-split extension by He₃ of C₃×S₃ acting via C₃×S₃/C₃=S₃	He3.(C3xS3)	486,131	27T175
C₂₇⋊C₁₈	The semidirect product of C₂₇ and C₁₈ acting faithfully; = Aut(D₂₇) = Hol(C₂₇)	C27:C18	486,31	27T176
C₃×C₃≀S₃	Direct product of C₃ and C₃≀S₃	C3xC3wrS3	486,115	27T177
C₃×C₃³⋊S₃	Direct product of C₃ and C₃³⋊S₃	C3xC3^3:S3	486,165	27T178
C₉²⋊₂S₃	2^nd semidirect product of C₉² and S₃ acting faithfully	C9^2:2S3	486,61	27T179
C₃⁴⋊C₆	1^st semidirect product of C₃⁴ and C₆ acting faithfully	C3^4:C6	486,102	27T180
3₊¹⁺⁴⋊C₂	1^st semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	ES+(3,2):C2	486,236	27T181
(C₃×He₃)⋊C₆	8^th semidirect product of C₃×He₃ and C₆ acting faithfully	(C3xHe3):C6	486,127	27T182
He₃.(C₃×C₆)	6^th non-split extension by He₃ of C₃×C₆ acting via C₃×C₆/C₃=C₆	He3.(C3xC6)	486,130	27T183
C₉².S₃	2^nd non-split extension by C₉² of S₃ acting faithfully	C9^2.S3	486,38	27T184
C₉²⋊S₃	1^st semidirect product of C₉² and S₃ acting faithfully	C9^2:S3	486,36	27T185
C₃⁴⋊₃S₃	3^rd semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:3S3	486,145	27T186
C₃³⋊(C₃×S₃)	4^th semidirect product of C₃³ and C₃×S₃ acting faithfully	C3^3:(C3xS3)	486,176	27T187
C₃³⋊₁D₉	1^st semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	C3^3:1D9	486,19	27T188
				27T189
He₃.C₃⋊C₆	3^rd semidirect product of He₃.C₃ and C₆ acting faithfully	He3.C3:C6	486,128	27T190
C₃≀C₃⋊C₆	2^nd semidirect product of C₃≀C₃ and C₆ acting faithfully	C3wrC3:C6	486,126	27T191
C₉⋊S₃⋊C₃²	2^nd semidirect product of C₉⋊S₃ and C₃² acting faithfully	C9:S3:C3^2	486,129	27T192
C₃³⋊₂D₉	2^nd semidirect product of C₃³ and D₉ acting via D₉/C₃=S₃	C3^3:2D9	486,52	27T193
C₃⁴⋊₅S₃	5^th semidirect product of C₃⁴ and S₃ acting faithfully	C3^4:5S3	486,166	27T194
				27T195
3₊¹⁺⁴⋊C₂	1^st semidirect product of 3₊¹⁺⁴ and C₂ acting faithfully	ES+(3,2):C2	486,236	27T196
C₃⁴⋊₄C₆	4^th semidirect product of C₃⁴ and C₆ acting faithfully	C3^4:4C6	486,146	27T197
C₃⁴.S₃	4^th non-split extension by C₃⁴ of S₃ acting faithfully	C3^4.S3	486,105	27T198
C₃×C₃³⋊C₆	Direct product of C₃ and C₃³⋊C₆	C3xC3^3:C6	486,116	27T199
C₃³⋊₁C₁₈	1^st semidirect product of C₃³ and C₁₈ acting via C₁₈/C₃=C₆	C3^3:1C18	486,18	27T200
C₃≀C₃.C₆	The non-split extension by C₃≀C₃ of C₆ acting faithfully	C3wrC3.C6	486,132	27T201
C₃⁴⋊₅C₆	5^th semidirect product of C₃⁴ and C₆ acting faithfully	C3^4:5C6	486,167	27T202
He₃.(C₃×C₆)	6^th non-split extension by He₃ of C₃×C₆ acting via C₃×C₆/C₃=C₆	He3.(C3xC6)	486,130	27T203
He₃.C₃⋊C₆	3^rd semidirect product of He₃.C₃ and C₆ acting faithfully	He3.C3:C6	486,128	27T204
C₃⁴⋊₅C₆	5^th semidirect product of C₃⁴ and C₆ acting faithfully	C3^4:5C6	486,167	27T205
He₃.(C₃×S₃)	5^th non-split extension by He₃ of C₃×S₃ acting via C₃×S₃/C₃=S₃	He3.(C3xS3)	486,131	27T206
S₃×C₃≀C₃	Direct product of S₃ and C₃≀C₃	S3xC3wrC3	486,117	27T207
C₃⁴.C₆	4^th non-split extension by C₃⁴ of C₆ acting faithfully	C3^4.C6	486,104	27T208
C₉⋊C₉.₃S₃	3^rd non-split extension by C₉⋊C₉ of S₃ acting faithfully	C9:C9.3S3	486,40	27T209

On 28 points

Groups of order 28

		Label	ID	Tr ID
C₂₈	Cyclic group	C28	28,2	28T1
C₂×C₁₄	Abelian group of type [2,14]	C2xC14	28,4	28T2
Dic₇	Dicyclic group; = C₇ ⋊C₄	Dic7	28,1	28T3
D₁₄	Dihedral group; = C₂×D₇	D14	28,3	28T4

Groups of order 56

		Label	ID	Tr ID
C₇×D₄	Direct product of C₇ and D₄	C7xD4	56,9	28T5
C₇⋊D₄	The semidirect product of C₇ and D₄ acting via D₄/C₂²=C₂	C7:D4	56,7	28T6
				28T7
C₄×D₇	Direct product of C₄ and D₇	C4xD7	56,4	28T8
C₂²×D₇	Direct product of C₂² and D₇	C2^2xD7	56,12	28T9
D₂₈	Dihedral group	D28	56,5	28T10
F₈	Frobenius group; = C₂³ ⋊C₇ = AGL₁(𝔽₈)	F8	56,11	28T11

Groups of order 84

		Label	ID	Tr ID
C₇⋊C₁₂	The semidirect product of C₇ and C₁₂ acting via C₁₂/C₂=C₆	C7:C12	84,1	28T12
C₄×C₇⋊C₃	Direct product of C₄ and C₇⋊C₃	C4xC7:C3	84,2	28T13
C₂²×C₇⋊C₃	Direct product of C₂² and C₇⋊C₃	C2^2xC7:C3	84,9	28T14
C₂×F₇	Direct product of C₂ and F₇; = Aut(D₁₄) = Hol(C₁₄)	C2xF7	84,7	28T15
C₇⋊A₄	The semidirect product of C₇ and A₄ acting via A₄/C₂²=C₃	C7:A4	84,11	28T16
C₇×A₄	Direct product of C₇ and A₄	C7xA4	84,10	28T17

Groups of order 112

		Label	ID	Tr ID
D₄×D₇	Direct product of D₄ and D₇	D4xD7	112,31	28T18
C₂×F₈	Direct product of C₂ and F₈	C2xF8	112,41	28T19
				28T20

Groups of order 168

		Label	ID	Tr ID
Dic₇⋊C₆	The semidirect product of Dic₇ and C₆ acting faithfully	Dic7:C6	168,11	28T21
D₄×C₇⋊C₃	Direct product of D₄ and C₇⋊C₃	D4xC7:C3	168,20	28T22
C₄⋊F₇	The semidirect product of C₄ and F₇ acting via F₇/C₇⋊C₃=C₂	C4:F7	168,9	28T23
C₂²×F₇	Direct product of C₂² and F₇	C2^2xF7	168,47	28T24
Dic₇⋊C₆	The semidirect product of Dic₇ and C₆ acting faithfully	Dic7:C6	168,11	28T25
C₄×F₇	Direct product of C₄ and F₇	C4xF7	168,8	28T26
AΓL₁(𝔽₈)	Affine semilinear group on 𝔽₈¹; = F₈ ⋊C₃ = Aut(F₈)	AGammaL(1,8)	168,43	28T27
D₇⋊A₄	The semidirect product of D₇ and A₄ acting via A₄/C₂²=C₃	D7:A4	168,49	28T28
A₄×D₇	Direct product of A₄ and D₇	A4xD7	168,48	28T29
C₇⋊S₄	The semidirect product of C₇ and S₄ acting via S₄/A₄=C₂	C7:S4	168,46	28T30
C₇×S₄	Direct product of C₇ and S₄	C7xS4	168,45	28T31
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	GL(3,2)	168,42	28T32

Groups of order 196

		Label	ID	Tr ID
C₇×Dic₇	Direct product of C₇ and Dic₇	C7xDic7	196,5	28T33
D₇×C₁₄	Direct product of C₁₄ and D₇	D7xC14	196,10	28T34
C₇²⋊C₄	The semidirect product of C₇² and C₄ acting faithfully	C7^2:C4	196,8	28T35
D₇²	Direct product of D₇ and D₇	D7^2	196,9	28T36

Groups of order 224

		Label	ID	Tr ID
C₄×F₈	Direct product of C₄ and F₈	C4xF8	224,173	28T37
C₂²×F₈	Direct product of C₂² and F₈	C2^2xF8	224,195	28T38
				28T39

Groups of order 252

		Label	ID	Tr ID
A₄×C₇⋊C₃	Direct product of A₄ and C₇⋊C₃	A4xC7:C3	252,27	28T40

Groups of order 336

		Label	ID	Tr ID
D₄×F₇	Direct product of D₄ and F₇; = Aut(D₂₈) = Hol(C₂₈)	D4xF7	336,125	28T41
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	28T42
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	C2xGL(3,2)	336,209	28T43
C₂×AΓL₁(𝔽₈)	Direct product of C₂ and AΓL₁(𝔽₈)	C2xAGammaL(1,8)	336,210	28T44
D₇×S₄	Direct product of D₇ and S₄	D7xS4	336,212	28T45
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	PGL(2,7)	336,208	28T46

Groups of order 392

		Label	ID	Tr ID
C₇×C₇⋊D₄	Direct product of C₇ and C₇⋊D₄	C7xC7:D4	392,27	28T47
C₂×C₇²⋊C₄	Direct product of C₂ and C₇²⋊C₄	C2xC7^2:C4	392,40	28T48
				28T49
C₇⋊D₂₈	The semidirect product of C₇ and D₂₈ acting via D₂₈/D₁₄=C₂	C7:D28	392,21	28T50
Dic₇⋊₂D₇	The semidirect product of Dic₇ and D₇ acting through Inn(Dic₇)	Dic7:2D7	392,19	28T51
C₂×D₇²	Direct product of C₂, D₇ and D₇	C2xD7^2	392,41	28T52
D₇≀C₂	Wreath product of D₇ by C₂	D7wrC2	392,37	28T53
				28T54
				28T55
C₇²⋊C₈	The semidirect product of C₇² and C₈ acting faithfully	C7^2:C8	392,36	28T56
D₇≀C₂	Wreath product of D₇ by C₂	D7wrC2	392,37	28T57
C₇²⋊Q₈	The semidirect product of C₇² and Q₈ acting faithfully	C7^2:Q8	392,38	28T58

Groups of order 448

		Label	ID	Tr ID
D₄×F₈	Direct product of D₄ and F₈	D4xF8	448,1363	28T59
C₂⁶⋊C₇	2^nd semidirect product of C₂⁶ and C₇ acting faithfully	C2^6:C7	448,1393	28T60
C₄³⋊C₇	The semidirect product of C₄³ and C₇ acting faithfully	C4^3:C7	448,178	28T61
C₂³⋊F₈	2^nd semidirect product of C₂³ and F₈ acting via F₈/C₂³=C₇	C2^3:F8	448,1394	28T62
				28T63
				28T64
				28T65
				28T66

On 29 points

Groups of order 29

		Label	ID	Tr ID
C₂₉	Cyclic group	C29	29,1	29T1

Groups of order 58

		Label	ID	Tr ID
D₂₉	Dihedral group	D29	58,1	29T2

Groups of order 116

		Label	ID	Tr ID
C₂₉⋊C₄	The semidirect product of C₂₉ and C₄ acting faithfully	C29:C4	116,3	29T3

Groups of order 203

		Label	ID	Tr ID
C₂₉⋊C₇	The semidirect product of C₂₉ and C₇ acting faithfully	C29:C7	203,1	29T4

Groups of order 406

		Label	ID	Tr ID
C₂₉⋊C₁₄	The semidirect product of C₂₉ and C₁₄ acting faithfully	C29:C14	406,1	29T5

On 30 points

Groups of order 30

		Label	ID	Tr ID
C₃₀	Cyclic group	C30	30,4	30T1
C₅×S₃	Direct product of C₅ and S₃	C5xS3	30,1	30T2
D₁₅	Dihedral group	D15	30,3	30T3
C₃×D₅	Direct product of C₃ and D₅	C3xD5	30,2	30T4

Groups of order 60

		Label	ID	Tr ID
C₆×D₅	Direct product of C₆ and D₅	C6xD5	60,10	30T5
C₃⋊F₅	The semidirect product of C₃ and F₅ acting via F₅/D₅=C₂	C3:F5	60,7	30T6
C₃×F₅	Direct product of C₃ and F₅	C3xF5	60,6	30T7
S₃×D₅	Direct product of S₃ and D₅	S3xD5	60,8	30T8
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	A5	60,5	30T9
S₃×D₅	Direct product of S₃ and D₅	S3xD5	60,8	30T10
C₅×A₄	Direct product of C₅ and A₄	C5xA4	60,9	30T11
S₃×C₁₀	Direct product of C₁₀ and S₃	S3xC10	60,11	30T12
S₃×D₅	Direct product of S₃ and D₅	S3xD5	60,8	30T13
D₃₀	Dihedral group; = C₂×D₁₅	D30	60,12	30T14

Groups of order 90

		Label	ID	Tr ID
S₃×C₁₅	Direct product of C₁₅ and S₃	S3xC15	90,6	30T15
C₃×D₁₅	Direct product of C₃ and D₁₅	C3xD15	90,7	30T16

Groups of order 120

		Label	ID	Tr ID
C₂×C₃⋊F₅	Direct product of C₂ and C₃⋊F₅	C2xC3:F5	120,41	30T17
C₁₀×A₄	Direct product of C₁₀ and A₄	C10xA4	120,43	30T18
C₅⋊S₄	The semidirect product of C₅ and S₄ acting via S₄/A₄=C₂	C5:S4	120,38	30T19
D₅×A₄	Direct product of D₅ and A₄	D5xA4	120,39	30T20
C₂×S₃×D₅	Direct product of C₂, S₃ and D₅	C2xS3xD5	120,42	30T21
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	30T22
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	S3xF5	120,36	30T23
				30T24
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	30T25
C₆×F₅	Direct product of C₆ and F₅	C6xF5	120,40	30T26
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	S5	120,34	30T27
D₅×A₄	Direct product of D₅ and A₄	D5xA4	120,39	30T28
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	C2xA5	120,35	30T29
				30T30
C₅⋊S₄	The semidirect product of C₅ and S₄ acting via S₄/A₄=C₂	C5:S4	120,38	30T31
S₃×F₅	Direct product of S₃ and F₅; = Aut(D₁₅) = Hol(C₁₅)	S3xF5	120,36	30T32
C₅×S₄	Direct product of C₅ and S₄	C5xS4	120,37	30T33
				30T34

Groups of order 150

		Label	ID	Tr ID
C₅²⋊C₆	The semidirect product of C₅² and C₆ acting faithfully	C5^2:C6	150,6	30T35
C₅×D₁₅	Direct product of C₅ and D₁₅	C5xD15	150,11	30T36
C₅²⋊S₃	The semidirect product of C₅² and S₃ acting faithfully	C5^2:S3	150,5	30T37
				30T38
D₅×C₁₅	Direct product of C₁₅ and D₅	D5xC15	150,8	30T39
C₂×C₅²⋊C₃	Direct product of C₂ and C₅²⋊C₃	C2xC5^2:C3	150,7	30T40

Groups of order 180

		Label	ID	Tr ID
C₅×S₃²	Direct product of C₅, S₃ and S₃	C5xS3^2	180,28	30T41
S₃×D₁₅	Direct product of S₃ and D₁₅	S3xD15	180,29	30T42
D₁₅⋊S₃	The semidirect product of D₁₅ and S₃ acting via S₃/C₃=C₂	D15:S3	180,30	30T43
C₃×S₃×D₅	Direct product of C₃, S₃ and D₅	C3xS3xD5	180,26	30T44
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	C3xA5	180,19	30T45
C₃²⋊F₅	The semidirect product of C₃² and F₅ acting via F₅/C₅=C₄	C3^2:F5	180,25	30T46
C₃×C₃⋊F₅	Direct product of C₃ and C₃⋊F₅	C3xC3:F5	180,21	30T47
C₃²⋊Dic₅	The semidirect product of C₃² and Dic₅ acting via Dic₅/C₅=C₄	C3^2:Dic5	180,24	30T48
C₅×C₃²⋊C₄	Direct product of C₅ and C₃²⋊C₄	C5xC3^2:C4	180,23	30T49

Groups of order 240

		Label	ID	Tr ID
F₁₆	Frobenius group; = C₂⁴ ⋊C₁₅ = AGL₁(𝔽₁₆)	F16	240,191	30T50
C₂×S₃×F₅	Direct product of C₂, S₃ and F₅; = Aut(D₃₀) = Hol(C₃₀)	C2xS3xF5	240,195	30T51
C₃×C₂⁴⋊C₅	Direct product of C₃ and C₂⁴⋊C₅	C3xC2^4:C5	240,199	30T52
A₄⋊F₅	The semidirect product of A₄ and F₅ acting via F₅/D₅=C₂	A4:F5	240,192	30T53
D₅×S₄	Direct product of D₅ and S₄	D5xS4	240,194	30T54
C₂×D₅×A₄	Direct product of C₂, D₅ and A₄	C2xD5xA4	240,198	30T55
A₄×F₅	Direct product of A₄ and F₅	A4xF5	240,193	30T56
				30T57
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	30T58
D₅×S₄	Direct product of D₅ and S₄	D5xS4	240,194	30T59
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	C2xS5	240,189	30T60
C₂×C₅⋊S₄	Direct product of C₂ and C₅⋊S₄	C2xC5:S4	240,197	30T61
D₅×S₄	Direct product of D₅ and S₄	D5xS4	240,194	30T62
				30T63
A₄⋊F₅	The semidirect product of A₄ and F₅ acting via F₅/D₅=C₂	A4:F5	240,192	30T64
C₁₀×S₄	Direct product of C₁₀ and S₄	C10xS4	240,196	30T65

Groups of order 300

		Label	ID	Tr ID
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	C5^2:D6	300,25	30T66
D₅×D₁₅	Direct product of D₅ and D₁₅	D5xD15	300,39	30T67
C₂×C₅²⋊C₆	Direct product of C₂ and C₅²⋊C₆	C2xC5^2:C6	300,27	30T68
C₅×A₅	Direct product of C₅ and A₅; = U₂(𝔽₄)	C5xA5	300,22	30T69
C₅²⋊A₄	The semidirect product of C₅² and A₄ acting via A₄/C₂²=C₃	C5^2:A4	300,43	30T70
C₅²⋊Dic₃	The semidirect product of C₅² and Dic₃ acting faithfully	C5^2:Dic3	300,23	30T71
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	C5^2:D6	300,25	30T72
C₃×C₅²⋊C₄	Direct product of C₃ and C₅²⋊C₄	C3xC5^2:C4	300,31	30T73
C₃×D₅²	Direct product of C₃, D₅ and D₅	C3xD5^2	300,36	30T74
C₅×S₃×D₅	Direct product of C₅, S₃ and D₅	C5xS3xD5	300,37	30T75
C₁₅⋊₂F₅	2^nd semidirect product of C₁₅ and F₅ acting via F₅/C₅=C₄	C15:2F5	300,35	30T76
C₂×C₅²⋊S₃	Direct product of C₂ and C₅²⋊S₃	C2xC5^2:S3	300,26	30T77
C₅²⋊C₁₂	The semidirect product of C₅² and C₁₂ acting faithfully	C5^2:C12	300,24	30T78
D₁₅⋊D₅	The semidirect product of D₁₅ and D₅ acting via D₅/C₅=C₂	D15:D5	300,40	30T79
C₅²⋊D₆	The semidirect product of C₅² and D₆ acting faithfully	C5^2:D6	300,25	30T80
C₂×C₅²⋊S₃	Direct product of C₂ and C₅²⋊S₃	C2xC5^2:S3	300,26	30T81

Groups of order 360

		Label	ID	Tr ID
C₅×S₃≀C₂	Direct product of C₅ and S₃≀C₂	C5xS3wrC2	360,132	30T82
S₃×C₃⋊F₅	Direct product of S₃ and C₃⋊F₅	S3xC3:F5	360,128	30T83
S₃²×D₅	Direct product of S₃, S₃ and D₅	S3^2xD5	360,137	30T84
S₃×A₅	Direct product of S₃ and A₅	S3xA5	360,121	30T85
C₃⋊F₅⋊S₃	The semidirect product of C₃⋊F₅ and S₃ acting via S₃/C₃=C₂	C3:F5:S3	360,129	30T86
C₆×A₅	Direct product of C₆ and A₅	C6xA5	360,122	30T87
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	A6	360,118	30T88
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	GammaL(2,4)	360,120	30T89
C₃×S₅	Direct product of C₃ and S₅	C3xS5	360,119	30T90
C₃×S₃×F₅	Direct product of C₃, S₃ and F₅	C3xS3xF5	360,126	30T91
C₆×A₅	Direct product of C₆ and A₅	C6xA5	360,122	30T92
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	GammaL(2,4)	360,120	30T93
S₃×A₅	Direct product of S₃ and A₅	S3xA5	360,121	30T94
C₃²⋊D₂₀	The semidirect product of C₃² and D₂₀ acting via D₂₀/C₅=D₄	C3^2:D20	360,134	30T95
S₃²⋊D₅	The semidirect product of S₃² and D₅ acting via D₅/C₅=C₂	S3^2:D5	360,133	30T96
C₃²⋊F₅⋊C₂	The semidirect product of C₃²⋊F₅ and C₂ acting faithfully	C3^2:F5:C2	360,131	30T97
C₃×S₅	Direct product of C₃ and S₅	C3xS5	360,119	30T98
D₅×C₃²⋊C₄	Direct product of D₅ and C₃²⋊C₄	D5xC3^2:C4	360,130	30T99
S₃²⋊D₅	The semidirect product of S₃² and D₅ acting via D₅/C₅=C₂	S3^2:D5	360,133	30T100
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	GammaL(2,4)	360,120	30T101
S₃×A₅	Direct product of S₃ and A₅	S3xA5	360,121	30T102
C₃×S₅	Direct product of C₃ and S₅	C3xS5	360,119	30T103

Groups of order 450

		Label	ID	Tr ID
C₁₅×D₁₅	Direct product of C₁₅ and D₁₅	C15xD15	450,29	30T104

Groups of order 480

		Label	ID	Tr ID
C₆×C₂⁴⋊C₅	Direct product of C₆ and C₂⁴⋊C₅	C6xC2^4:C5	480,1204	30T105
C₂⁴⋊D₁₅	The semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₃=D₅	C2^4:D15	480,1195	30T106
C₂×A₄×F₅	Direct product of C₂, A₄ and F₅	C2xA4xF5	480,1192	30T107
C₂×F₁₆	Direct product of C₂ and F₁₆	C2xF16	480,1190	30T108
C₂×D₅×S₄	Direct product of C₂, D₅ and S₄	C2xD5xS4	480,1193	30T109
F₅×S₄	Direct product of F₅ and S₄; = Hol(C₂×C₁₀)	F5xS4	480,1189	30T110
S₃×C₂⁴⋊C₅	Direct product of S₃ and C₂⁴⋊C₅	S3xC2^4:C5	480,1196	30T111
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	F16:C2	480,1188	30T112
C₃×C₂⁴⋊D₅	Direct product of C₃ and C₂⁴⋊D₅	C3xC2^4:D5	480,1194	30T113
F₅×S₄	Direct product of F₅ and S₄; = Hol(C₂×C₁₀)	F5xS4	480,1189	30T114
				30T115
F₁₆⋊C₂	The semidirect product of F₁₆ and C₂ acting faithfully	F16:C2	480,1188	30T116
F₅×S₄	Direct product of F₅ and S₄; = Hol(C₂×C₁₀)	F5xS4	480,1189	30T117
C₃×C₂⁴⋊D₅	Direct product of C₃ and C₂⁴⋊D₅	C3xC2^4:D5	480,1194	30T118
C₂⁴⋊D₁₅	The semidirect product of C₂⁴ and D₁₅ acting via D₁₅/C₃=D₅	C2^4:D15	480,1195	30T119
S₃×C₂⁴⋊C₅	Direct product of S₃ and C₂⁴⋊C₅	S3xC2^4:C5	480,1196	30T120
C₂×A₄⋊F₅	Direct product of C₂ and A₄⋊F₅	C2xA4:F5	480,1191	30T121

On 31 points

Groups of order 31

		Label	ID	Tr ID
C₃₁	Cyclic group	C31	31,1	31T1

Groups of order 62

		Label	ID	Tr ID
D₃₁	Dihedral group	D31	62,1	31T2

Groups of order 93

		Label	ID	Tr ID
C₃₁⋊C₃	The semidirect product of C₃₁ and C₃ acting faithfully	C31:C3	93,1	31T3

Groups of order 155

		Label	ID	Tr ID
C₃₁⋊C₅	The semidirect product of C₃₁ and C₅ acting faithfully	C31:C5	155,1	31T4

Groups of order 186

		Label	ID	Tr ID
C₃₁⋊C₆	The semidirect product of C₃₁ and C₆ acting faithfully	C31:C6	186,1	31T5

Groups of order 310

		Label	ID	Tr ID
C₃₁⋊C₁₀	The semidirect product of C₃₁ and C₁₀ acting faithfully	C31:C10	310,1	31T6

Groups of order 465

		Label	ID	Tr ID
C₃₁⋊C₁₅	The semidirect product of C₃₁ and C₁₅ acting faithfully	C31:C15	465,1	31T7

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