Subgroups — A₅×ΓL(1,𝔽₃₂) #22604947

Order 9300.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×ΓL(1,𝔽₃₂)	—	5	1	no	maximal
2	C₃₁×A₅	C₅	1	1	yes	maximal, characteristic, complemented
3	D₅×ΓL(1,𝔽₃₂)	—	6	1	no	maximal
4	D₃×ΓL(1,𝔽₃₂)	—	10	1	no	maximal
5	C₅×ΓL(1,𝔽₃₂)	—	6	1	no	Hall
6	C₂²×ΓL(1,𝔽₃₂)	—	5	1	no	—
7	C₃×ΓL(1,𝔽₃₂)	—	10	1	no	—
8	A₄×C₃₁	—	5	1	no	Hall
9	D₅×C₃₁	—	6	1	no	—
10	C₂×ΓL(1,𝔽₃₂)	—	15	1	no	—
11	C₅×A₅	—	31	1	no	maximal, Hall
12	D₃×C₃₁	—	10	1	no	—
13	C₅×C₃₁	—	6	1	no	—
14	ΓL(1,𝔽₃₂)	—	12	2	no	—
15	ΓL(1,𝔽₃₂)	A₅	1	1	yes	maximal normal, characteristic, direct product factor
16	C₂²×C₃₁	—	5	1	no	Hall
17	C₃×C₃₁	—	10	1	no	Hall
18	C₂×C₃₁	—	15	1	no	—
19	C₅×A₄	—	155	1	no	—
20	A₅	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
21	C₅×D₅	—	186	1	no	—
22	C₃₁	C₅×A₅	1	1	yes	characteristic, complemented, Sylow
23	C₅×D₃	—	310	1	no	—
24	C₅²	—	186	1	no	Sylow
25	C₂²×C₅	—	155	1	no	—
26	C₃×C₅	—	310	1	no	—
27	A₄	—	5	1	no	Hall
28	C₂×C₅	—	465	1	no	—
29	D₅	—	6	1	no	—
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	—
32	C₅	—	31	1	no	—
33	C₅	—	372	2	no	—
34	C₂²	—	5	1	no	Sylow
35	C₃	—	10	1	no	Sylow
36	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₃₁×A₅	C₅
Fitting	C₃₁	C₅×A₅
LCS	G ▷ C₃₁×A₅
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.