Subgroups — C₅⋊(#120⋊C₃) #91192

Order 480.

70 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	#4099	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₅×A₄	—	4	1	no	maximal
4	#120⋊C₃	—	5	1	no	maximal, Hall
5	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₂²⋊D₅	—	3	1	no	—
7	C₂²⋊Dic₅	—	3	1	no	—
8	C₅×A₄	—	4	1	no	—
9	C₅×A₄	—	8	2	no	—
10	C₂²⋊A₄	D₅	1	1	yes	characteristic, complemented
11	C₂³×C₅	—	3	1	no	—
12	C₂³×C₅	—	6	2	no	—
13	C₂²×D₅	A₄	1	1	yes	characteristic, complemented
14	C₂²⋊D₅	—	6	2	no	—
15	C₂×Dic₅	—	3	1	no	—
16	#120	—	5	1	no	Sylow
17	C₃×D₅	—	16	1	no	—
18	C₂×A₄	—	20	1	no	—
19	C₂²×C₅	—	2	2	no	—
20	C₂²×C₅	—	3	2	no	—
21	C₂²×C₅	—	6	2	no	—
22	C₂²×C₅	—	6	2	no	—
23	C₂²×C₅	C₂×A₄	1	1	yes	characteristic
24	C₂×D₅	—	6	1	no	—
25	Dic₅	—	6	1	no	—
26	C₂⁴	C₃×D₅	1	1	yes	characteristic, complemented
27	C₂×D₄	—	15	1	no	—
28	C₂²⋊C₄	—	15	1	no	—
29	C₃×C₅	—	16	1	no	Hall
30	A₄	—	4	1	no	—
31	A₄	—	8	2	no	—
32	C₂×C₅	—	3	1	no	—
33	C₂×C₅	—	6	2	no	—
34	D₅	—	4	1	no	—
35	C₂³	—	3	1	no	—
36	C₂³	—	5	1	no	—
37	C₂³	—	6	2	no	—
38	D₄	—	30	2	no	—
39	C₂×C₄	—	15	1	no	—
40	C₂×C₃	—	80	1	no	—
41	C₅	#120⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	2	2	no	—
43	C₂²	—	3	2	no	—
44	C₂²	—	6	2	no	—
45	C₂²	—	6	2	no	—
46	C₂²	—	30	1	no	—
47	C₂²	D₅×A₄	1	1	yes	characteristic
48	C₄	—	30	1	no	—
49	C₃	—	16	1	no	Sylow
50	C₂	—	3	1	no	—
51	C₂	—	6	2	no	—
52	C₂	—	20	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂⁴×C₅	C₂×C₃
Frattini	C₂²	D₅×A₄
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₂⁴×C₅
UCS	C₁

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.