Subgroups — #91143

Order 480.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SL(2,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	SL(2,𝔽₅)	C₄	1	1	yes	characteristic, complemented
3	#859	—	5	1	no	maximal, Hall
4	C₂×#170	—	6	1	no	maximal
5	C₂×SL(2,𝔽₃)	—	5	1	no	—
6	Dic₃⋊C₄	—	10	1	no	maximal
7	C₂×Dic₅	—	6	1	no	—
8	#170	—	6	2	no	—
9	#103	—	15	1	no	Sylow
10	C₂×C₃×C₄	—	10	1	no	—
11	C₂×Dic₃	—	10	1	no	—
12	C₂×Dic₃	—	10	1	no	—
13	SL(2,𝔽₃)	—	5	1	no	—
14	C₂²×C₅	—	6	1	no	—
15	Dic₅	—	6	1	no	—
16	Dic₅	—	6	1	no	—
17	C₂×Q₈	—	5	1	no	—
18	C₂×C₈	—	15	1	no	—
19	C₄⋊C₄	—	15	1	no	—
20	C₂²×C₃	—	10	1	no	—
21	C₃×C₄	—	20	1	no	—
22	Dic₃	—	10	1	no	—
23	Dic₃	—	10	1	no	—
24	Dic₃	—	20	1	no	—
25	C₂×C₅	—	6	1	no	—
26	C₂×C₅	—	6	1	no	—
27	C₂×C₅	—	6	1	no	—
28	Q₈	—	5	1	no	—
29	Q₈	—	15	1	no	—
30	C₂×C₄	—	10	1	no	—
31	C₂×C₄	—	15	1	no	—
32	C₈	—	30	1	no	—
33	C₂×C₃	—	10	1	no	—
34	C₂×C₃	—	10	1	no	—
35	C₂×C₃	—	10	1	no	—
36	C₅	—	6	1	no	Sylow
37	C₂²	S₅	1	1	yes	characteristic
38	C₄	—	15	1	no	—
39	C₄	—	15	1	no	—
40	C₄	—	20	1	no	—
41	C₃	—	10	1	no	Sylow
42	C₂	#6728	1	1	yes	characteristic
43	C₂	#6729	1	1	yes	characteristic
44	C₂	A₅⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, Fitting, socle, hypercenter	C₂²	S₅
commutator, hypocenter	SL(2,𝔽₅)	C₄
prime radical, cosocle	C₂×SL(2,𝔽₅)	C₂
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂²

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

N	H ≅ G/N	type
2. SL(2,𝔽₅)	C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.