Subgroups — C₅×#1020 #92124

Order 480.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#120	—	3	1	no	maximal, Hall
3	C₅×S₄	—	4	3	no	maximal
4	#1020	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁴×C₅	D₃	1	1	yes	characteristic, complemented
6	C₂×C₅×D₄	—	3	3	no	—
7	C₅×C₂²⋊C₄	—	3	3	no	—
8	C₅×A₄	—	4	3	no	—
9	C₅×A₄	—	8	1	no	—
10	C₂²⋊A₄	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂³×C₅	—	3	3	no	—
12	C₂³×C₅	—	3	1	no	—
13	C₂³×C₅	—	6	1	no	—
14	C₅×D₄	—	6	3	no	—
15	C₅×D₄	—	6	3	no	—
16	C₂×C₄×C₅	—	3	3	no	—
17	#120	—	3	1	no	Sylow
18	C₅×D₃	—	16	1	no	—
19	S₄	—	4	3	no	—
20	C₂²×C₅	—	2	1	no	—
21	C₂²×C₅	—	3	1	no	—
22	C₂²×C₅	—	3	3	no	—
23	C₂²×C₅	—	6	3	no	—
24	C₂²×C₅	—	6	3	no	—
25	C₂²×C₅	S₄	1	3	yes	complemented
26	C₄×C₅	—	6	3	no	—
27	C₂⁴	C₅×D₃	1	1	yes	characteristic, complemented
28	C₂×D₄	—	3	3	no	—
29	C₂²⋊C₄	—	3	3	no	—
30	C₃×C₅	—	16	1	no	Hall
31	A₄	—	4	3	no	—
32	A₄	—	8	1	no	—
33	C₂×C₅	—	3	3	no	—
34	C₂×C₅	—	6	1	no	—
35	C₂×C₅	—	12	1	no	—
36	C₂³	—	3	3	no	—
37	C₂³	—	3	1	no	—
38	C₂³	—	6	1	no	—
39	D₄	—	6	3	no	—
40	D₄	—	6	3	no	—
41	C₂×C₄	—	3	3	no	—
42	D₃	—	16	1	no	—
43	C₅	#1020	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	—	2	1	no	—
45	C₂²	—	3	1	no	—
46	C₂²	—	3	3	no	—
47	C₂²	—	6	3	no	—
48	C₂²	—	6	3	no	—
49	C₂²	C₅×S₄	1	3	yes	complemented
50	C₄	—	6	3	no	—
51	C₃	—	16	1	no	Sylow
52	C₂	—	3	3	no	—
53	C₂	—	6	1	no	—
54	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#1020
commutator, cosocle, hypocenter	C₂²⋊A₄	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂⁴×C₅	D₃
LCS	G ▷ C₂²⋊A₄
UCS	C₁ ◁ C₅

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.