Subgroups — #91891

Order 480.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(#41⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₅⋊#226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#226	C₂	1	1	yes	maximal, characteristic, complemented
4	#4064	—	3	1	no	maximal, Hall
5	C₅×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	#1204	—	4	1	no	maximal
7	#984	—	5	1	no	maximal, Hall
8	#713	D₃	1	1	yes	characteristic
9	Q₈×D₅	—	3	1	no	—
10	C₅×Q₁₆	—	3	1	no	—
11	#689	—	3	1	no	—
12	#688	—	3	1	no	—
13	#677	—	3	1	no	—
14	#676	—	3	1	no	—
15	Dic₁₅	—	4	1	no	—
16	C₃×Dic₅	—	4	1	no	—
17	C₅×Dic₃	—	4	1	no	—
18	#41⋊C₃	—	5	1	no	—
19	#226	—	5	1	no	—
20	#226	D₅	1	1	yes	characteristic, complemented
21	C₅×Q₈	—	3	1	no	—
22	C₅×Q₈	C₂×D₃	1	1	yes	characteristic
23	D₂₀	—	3	1	no	—
24	C₄×D₅	—	3	1	no	—
25	C₄×D₅	—	6	1	no	—
26	Dic₁₀	—	3	1	no	—
27	Dic₁₀	—	6	1	no	—
28	C₅×C₈	—	3	1	no	—
29	#168	—	3	1	no	—
30	#137	—	15	1	no	Sylow
31	C₂×C₃×C₅	—	4	1	no	—
32	Dic₆	—	20	1	no	—
33	SL(2,𝔽₃)	C₂×D₅	1	1	yes	characteristic
34	C₂×D₅	—	3	1	no	—
35	C₄×C₅	—	3	1	no	—
36	C₄×C₅	—	6	1	no	—
37	Dic₅	—	6	1	no	—
38	Dic₅	S₄	1	1	yes	characteristic
39	#41	—	5	1	no	—
40	C₂×Q₈	—	15	1	no	—
41	Q₁₆	—	3	1	no	—
42	Q₁₆	—	15	1	no	—
43	SD₁₆	—	15	1	no	—
44	SD₁₆	—	15	1	no	—
45	M₁₆	—	15	1	no	—
46	C₃×C₅	—	4	1	no	Hall
47	C₃×C₄	—	20	1	no	—
48	Dic₃	—	4	1	no	—
49	Dic₃	—	20	1	no	—
50	C₂×C₅	C₂×S₄	1	1	yes	characteristic
51	D₅	—	6	1	no	—
52	Q₈	—	3	1	no	—
53	Q₈	—	15	1	no	—
54	Q₈	—	30	1	no	—
55	Q₈	D₃×D₅	1	1	yes	characteristic
56	D₄	—	15	1	no	—
57	C₂×C₄	—	15	1	no	—
58	C₂×C₄	—	30	1	no	—
59	C₈	—	3	1	no	—
60	C₈	—	15	1	no	—
61	C₂×C₃	—	4	1	no	—
62	C₅	#984	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	15	1	no	—
64	C₄	—	3	1	no	—
65	C₄	—	5	1	no	—
66	C₄	—	6	1	no	—
67	C₄	—	30	1	no	—
68	C₃	—	4	1	no	Sylow
69	C₂	—	30	1	no	—
70	C₂	D₅×S₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×S₄
commutator, cosocle, hypocenter	C₅×SL(2,𝔽₃)	C₂²
Fitting	C₅×Q₈	C₂×D₃
socle	C₂×C₅	C₂×S₄
prime radical	C₅⋊(#41⋊C₃)	C₂
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₅⋊#226	C₂	semidirect
3. C₅×#226	C₂	semidirect
20. #226	D₅	semidirect
62. C₅	#984	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊(#41⋊C₃)	2
C₅⋊#226	2
C₅×#226	2
#4064	3
#1204	4
#984	5