Subgroups — C₂×#6729 #91874

Order 480.

78 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, complemented
2	#6729	C₂	1	2	yes	maximal, direct product factor
3	SL(2,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
4	C₂×GL(2,𝔽₃)	—	5	1	no	maximal, Hall
5	C₂×#170	—	6	1	no	maximal
6	C₂×#67	—	10	1	no	maximal
7	C₂×SL(2,𝔽₃)	—	5	1	no	—
8	GL(2,𝔽₃)	—	5	2	no	—
9	C₂×Dic₅	—	6	1	no	—
10	#170	—	6	2	no	—
11	C₂×SD₁₆	—	15	1	no	Sylow
12	C₂³×C₃	—	10	1	no	—
13	C₂²×D₃	—	10	1	no	—
14	#67	—	10	2	no	—
15	#67	—	10	2	no	—
16	C₂×Dic₃	—	10	1	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×D₄	—	15	1	no	—
23	SD₁₆	—	15	2	no	—
24	SD₁₆	—	15	2	no	—
25	C₂×C₈	—	15	1	no	—
26	C₂²×C₃	—	10	2	no	—
27	C₂²×C₃	—	10	1	no	—
28	C₂²×C₃	—	20	2	no	—
29	C₂×D₃	—	10	2	no	—
30	C₂×D₃	—	20	2	no	—
31	Dic₃	—	10	1	no	—
32	Dic₃	—	10	1	no	—
33	C₂×C₅	—	6	2	no	—
34	C₂×C₅	—	6	1	no	—
35	C₂³	—	10	1	no	—
36	Q₈	—	5	1	no	—
37	Q₈	—	15	1	no	—
38	D₄	—	15	2	no	—
39	D₄	—	30	1	no	—
40	C₂×C₄	—	15	1	no	—
41	C₈	—	15	2	no	—
42	C₂×C₃	—	10	2	no	—
43	C₂×C₃	—	10	1	no	—
44	C₂×C₃	—	20	2	no	—
45	D₃	—	20	2	no	—
46	C₅	—	6	1	no	Sylow
47	C₂²	—	10	2	no	—
48	C₂²	—	20	2	no	—
49	C₂²	S₅	1	1	yes	characteristic
50	C₄	—	15	1	no	—
51	C₄	—	15	1	no	—
52	C₃	—	10	1	no	Sylow
53	C₂	—	20	2	no	—
54	C₂	#6729	1	2	yes	direct product factor
55	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
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂²

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

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