Subgroups — #64708

Order 320.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4050	C₂	1	1	yes	maximal, characteristic
2	C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	#3944	C₂	1	1	yes	maximal, characteristic, complemented
4	#709	—	2	1	no	—
5	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₅×C₄⋊C₄	—	2	1	no	—
7	Dic₂₀	C₄	1	1	yes	characteristic, complemented
8	D₄₀	C₄	1	1	yes	characteristic, complemented
9	#677	—	2	1	no	—
10	#672	—	2	1	no	—
11	#360	—	5	1	no	maximal, Sylow
12	C₂×C₄×C₅	—	4	1	no	—
13	C₂×C₄×C₅	D₄	1	1	yes	characteristic
14	C₂²⋊D₅	—	4	1	no	—
15	D₂₀	—	2	1	no	—
16	C₄×D₅	—	4	1	no	—
17	Dic₁₀	—	2	1	no	—
18	C₅×C₈	C₂×C₄	1	1	yes	characteristic
19	C₅×C₈	D₄	1	1	yes	characteristic
20	#135	—	5	1	no	—
21	M₃₂	—	5	1	no	—
22	#106	D₅	1	1	yes	characteristic, complemented
23	C₂²×C₅	D₈	1	1	yes	characteristic
24	C₂×D₅	—	4	1	no	—
25	C₄×C₅	—	8	1	no	—
26	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
27	C₄×C₅	SD₁₆	1	1	yes	characteristic
28	Dic₅	—	4	1	no	—
29	#41	—	10	1	no	—
30	Q₁₆	—	5	1	no	—
31	SD₁₆	—	10	1	no	—
32	D₈	—	5	1	no	—
33	C₂×C₈	C₂×D₅	1	1	yes	characteristic
34	C₄⋊C₄	—	2	1	no	—
35	C₁₆	—	10	1	no	—
36	C₂×C₅	—	2	1	no	—
37	C₂×C₅	#102	1	1	yes	characteristic
38	D₅	—	8	1	no	—
39	Q₈	—	10	1	no	—
40	D₄	—	10	1	no	—
41	D₄	—	20	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	—	20	1	no	—
44	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
45	C₈	C₄×D₅	1	1	yes	characteristic
46	C₈	D₂₀	1	1	yes	characteristic
47	C₅	#360	1	1	yes	characteristic, complemented, Sylow
48	C₂²	—	20	1	no	—
49	C₂²	#686	1	1	yes	characteristic
50	C₄	—	8	1	no	—
51	C₄	—	20	1	no	—
52	C₄	#685	1	1	yes	characteristic
53	C₄	#688	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	40	1	no	—
56	C₂	#3941	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#3941
commutator	C₅×C₈	C₂×C₄
Frattini	C₂×C₈	C₂×D₅
Fitting	C₅×#106	C₂
socle	C₂×C₅	#102
prime radical	#4050	C₂
cosocle	C₂×C₅×C₈	C₂²
hypercenter	#106	D₅
hypocenter	C₅	#360
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
2. C₅×#106	C₂	semidirect
3. #3944	C₂	semidirect
7. Dic₂₀	C₄	semidirect
8. D₄₀	C₄	semidirect
22. #106	D₅	semidirect
47. C₅	#360	semidirect

Maximal subgroups

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

subgroup	index
#4050	2
C₅×#106	2
#3944	2
#360	5