Subgroups — C₂×#6728 #91873

Order 480.

66 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	#6728	C₂	1	2	yes	maximal, direct product factor
3	SL(2,𝔽₅)	C₂²	1	1	yes	characteristic
4	C₂×#226	—	5	1	no	maximal, Hall
5	C₂×#170	—	6	1	no	maximal
6	C₂×Dic₆	—	10	1	no	maximal
7	C₂×SL(2,𝔽₃)	—	5	1	no	—
8	#226	—	5	2	no	—
9	C₂×Dic₅	—	6	1	no	—
10	#170	—	6	2	no	—
11	C₂×Q₁₆	—	15	1	no	Sylow
12	C₂×C₃×C₄	—	10	1	no	—
13	C₂×Dic₃	—	10	1	no	—
14	C₂×Dic₃	—	10	1	no	—
15	Dic₆	—	10	2	no	—
16	Dic₆	—	10	2	no	—
17	SL(2,𝔽₃)	—	5	1	no	—
18	C₂²×C₅	—	6	1	no	—
19	Dic₅	—	6	1	no	—
20	Dic₅	—	6	1	no	—
21	C₂×Q₈	—	5	1	no	—
22	C₂×Q₈	—	15	1	no	—
23	Q₁₆	—	15	2	no	—
24	Q₁₆	—	15	2	no	—
25	C₂×C₈	—	15	1	no	—
26	C₂²×C₃	—	10	1	no	—
27	C₃×C₄	—	10	2	no	—
28	Dic₃	—	10	2	no	—
29	Dic₃	—	10	1	no	—
30	Dic₃	—	10	1	no	—
31	C₂×C₅	—	6	2	no	—
32	C₂×C₅	—	6	1	no	—
33	Q₈	—	5	1	no	—
34	Q₈	—	15	2	no	—
35	Q₈	—	15	1	no	—
36	Q₈	—	30	1	no	—
37	C₂×C₄	—	10	1	no	—
38	C₂×C₄	—	15	1	no	—
39	C₈	—	15	2	no	—
40	C₂×C₃	—	10	2	no	—
41	C₂×C₃	—	10	1	no	—
42	C₅	—	6	1	no	Sylow
43	C₂²	S₅	1	1	yes	characteristic
44	C₄	—	10	2	no	—
45	C₄	—	15	1	no	—
46	C₄	—	15	1	no	—
47	C₃	—	10	1	no	Sylow
48	C₂	#6728	1	2	yes	direct product factor
49	C₂	C₂×S₅	1	1	yes	characteristic

	subgroup	G/H
center, Fitting, socle, hypercenter	C₂²	S₅
commutator, cosocle, hypocenter	SL(2,𝔽₅)	C₂²
Frattini	C₂	C₂×S₅
prime radical	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. #6728	C₂	direct (N × H)
48. C₂	#6728	direct (N × H)

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