Subgroups — C₅×#120⋊C₃ #91580

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

	subgroup	G/H
center, hypercenter	C₅	#120⋊C₃
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×A₄
Fitting	C₅×#120	C₃
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂²⋊A₄	C₂	semidirect
2. C₅×#120	C₃	semidirect
4. #120⋊C₃	C₅	direct (N × H)
5. C₂⁴×C₅	C₂×C₃	semidirect
10. C₂²⋊A₄	C₂×C₅	semidirect
13. C₂³×C₅	A₄	semidirect
16. #120	C₃×C₅	semidirect
26. C₂⁴	C₂×C₃×C₅	semidirect
37. C₂³	C₅×A₄	semidirect
41. C₅	#120⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂²⋊A₄	2
C₅×#120	3
C₂×C₅×A₄	4
#120⋊C₃	5

Subgroups — C5×#120⋊C3 #91580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#120⋊C₃ #91580