Non-soluble groups

See soluble groups.

Groups of order 60

		d	ρ	Label	ID
A₅	Alternating group on 5 letters; = SL₂(F₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	5	3+	A5	60,5

Groups of order 120

		d	ρ	Label	ID
S₅	Symmetric group on 5 letters; = PGL₂(F₅) = Aut(A₅) = 5-cell symmetries; almost simple	5	4+	S5	120,34
SL₂(F₅)	Special linear group on F₅²; = C₂ .A₅ = 2I = <2,3,5>	24	2-	SL(2,5)	120,5
C₂xA₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35

Groups of order 168

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

Groups of order 180

		d	ρ	Label	ID
C₃xA₅	Direct product of C₃ and A₅; = GL₂(F₄)	15	3	C3xA5	180,19

Groups of order 240

		d	ρ	Label	ID
CSU₂(F₅)	Conformal special unitary group on F₅²; = C₂ .₂ S₅	48	4-	CSU(2,5)	240,89
A₅:C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	12	4	A5:C4	240,91
C₄.A₅	The central extension by C₄ of A₅	24	2	C4.A5	240,93
C₂.S₅	2^nd central stem extension by C₂ of S₅	40	4-	C2.S5	240,90
C₂xS₅	Direct product of C₂ and S₅; = O₃(F₅)	10	4+	C2xS5	240,189
C₄xA₅	Direct product of C₄ and A₅	20	3	C4xA5	240,92
C₂²xA₅	Direct product of C₂² and A₅	20		C2^2xA5	240,190
C₂xSL₂(F₅)	Direct product of C₂ and SL₂(F₅)	48		C2xSL(2,5)	240,94

Groups of order 300

		d	ρ	Label	ID
C₅xA₅	Direct product of C₅ and A₅; = U₂(F₄)	25	3	C5xA5	300,22

Groups of order 336

		d	ρ	Label	ID
SL₂(F₇)	Special linear group on F₇²; = C₂ .GL₃(F₂)	16	4	SL(2,7)	336,114
PGL₂(F₇)	Projective linear group on F₇²; = GL₃(F₂):C₂ = Aut(GL₃(F₂)); almost simple	8	6+	PGL(2,7)	336,208
C₂xGL₃(F₂)	Direct product of C₂ and GL₃(F₂)	14	3	C2xGL(3,2)	336,209

Groups of order 360

		d	ρ	Label	ID
A₆	Alternating group on 6 letters; = PSL₂(F₉) = L₂(9); 3^rd non-abelian simple	6	5+	A6	360,118
ΓL₂(F₄)	Semilinear group on F₄²; = C₃ :S₅	15	6	GammaL(2,4)	360,120
C₃xS₅	Direct product of C₃ and S₅	15	4	C3xS5	360,119
S₃xA₅	Direct product of S₃ and A₅	15	6+	S3xA5	360,121
C₆xA₅	Direct product of C₆ and A₅	30	3	C6xA5	360,122
C₃xSL₂(F₅)	Direct product of C₃ and SL₂(F₅)	72	2	C3xSL(2,5)	360,51

Groups of order 420

		d	ρ	Label	ID
C₇xA₅	Direct product of C₇ and A₅	35	3	C7xA5	420,13

Groups of order 480

		d	ρ	Label	ID
GL₂(F₅)	General linear group on F₅²; = SL₂(F₅):₁ C₄ = Aut(C₅²)	24	4	GL(2,5)	480,218
C₄:S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	20	6	C4:S5	480,944
C₂²:S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	20	6+	C2^2:S5	480,951
A₅:Q₈	The semidirect product of A₅ and Q₈ acting via Q₈/C₄=C₂	24	6	A5:Q8	480,945
A₅:C₈	The semidirect product of A₅ and C₈ acting via C₈/C₄=C₂	40	4	A5:C8	480,217
C₄.₃S₅	3^rd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	40	4	C4.3S5	480,948
C₈.A₅	The central extension by C₈ of A₅	48	2	C8.A5	480,221
D₄.A₅	The non-split extension by D₄ of A₅ acting through Inn(D₄)	48	4-	D4.A5	480,957
Q₈.A₅	The non-split extension by Q₈ of A₅ acting through Inn(Q₈)	48	4+	Q8.A5	480,959
C₄.₆S₅	3^rd central extension by C₄ of S₅	48	4	C4.6S5	480,946
C₄.S₅	2^nd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	48	4	C4.S5	480,947
C₂².S₅	The non-split extension by C₂² of S₅ acting via S₅/A₅=C₂	48	4-	C2^2.S5	480,953
C₂².₂S₅	1^st central extension by C₂² of S₅	96		C2^2.2S5	480,219
C₄xS₅	Direct product of C₄ and S₅; = CO₃(F₅)	20	4	C4xS5	480,943
D₄xA₅	Direct product of D₄ and A₅	20	6+	D4xA5	480,956
C₂²xS₅	Direct product of C₂² and S₅	20		C2^2xS5	480,1186
C₈xA₅	Direct product of C₈ and A₅	40	3	C8xA5	480,220
Q₈xA₅	Direct product of Q₈ and A₅	40	6-	Q8xA5	480,958
C₂³xA₅	Direct product of C₂³ and A₅	40		C2^3xA5	480,1187
C₄xSL₂(F₅)	Direct product of C₄ and SL₂(F₅)	96		C4xSL(2,5)	480,222
C₂xCSU₂(F₅)	Direct product of C₂ and CSU₂(F₅)	96		C2xCSU(2,5)	480,949
C₂²xSL₂(F₅)	Direct product of C₂² and SL₂(F₅)	96		C2^2xSL(2,5)	480,960
C₂xA₅:C₄	Direct product of C₂ and A₅:C₄	24		C2xA5:C4	480,952
C₂xC₄xA₅	Direct product of C₂xC₄ and A₅	40		C2xC4xA5	480,954
C₂xC₄.A₅	Direct product of C₂ and C₄.A₅	48		C2xC4.A5	480,955
C₂xC₂.S₅	Direct product of C₂ and C₂.S₅	80		C2xC2.S5	480,950