Subgroups — #64697

Order 320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4093	C₂	1	1	yes	maximal, characteristic
2	C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
3	#3968	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
5	C₂×D₂₀	C₄	1	1	yes	characteristic
6	C₅×M₁₆	—	2	1	no	—
7	#685	—	2	1	no	—
8	#685	—	2	1	no	—
9	C₄×Dic₅	C₄	1	1	yes	characteristic
10	#681	—	2	1	no	—
11	#355	—	5	1	no	maximal, Sylow
12	C₂²×D₅	—	2	1	no	—
13	C₅×Q₈	—	4	1	no	—
14	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₅	D₄	1	1	yes	characteristic
16	C₂×C₄×C₅	D₄	1	1	yes	characteristic
17	C₂×Dic₅	—	2	1	no	—
18	D₂₀	—	4	1	no	—
19	C₅×C₈	—	4	1	no	—
20	#168	—	4	1	no	—
21	#124	—	5	1	no	—
22	#101	—	5	1	no	—
23	#101	D₅	1	1	yes	characteristic, complemented
24	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₅	—	4	2	no	—
26	C₂×D₅	—	4	1	no	—
27	C₄×C₅	—	2	1	no	—
28	C₄×C₅	—	2	1	no	—
29	C₄×C₅	—	2	1	no	—
30	Dic₅	—	4	1	no	—
31	C₂×Q₈	C₂×D₅	1	1	yes	characteristic
32	C₂×D₄	—	5	1	no	—
33	M₁₆	—	2	1	no	—
34	M₁₆	—	10	1	no	—
35	C₂²⋊C₄	—	10	1	no	—
36	C₂²⋊C₄	—	10	1	no	—
37	C₄²	—	5	1	no	—
38	C₂×C₅	—	2	1	no	—
39	C₂×C₅	#99	1	1	yes	characteristic
40	D₅	—	8	1	no	—
41	C₂³	—	10	1	no	—
42	Q₈	—	4	1	no	—
43	D₄	—	20	1	no	—
44	C₂×C₄	—	10	1	no	—
45	C₂×C₄	C₄×D₅	1	1	yes	characteristic
46	C₂×C₄	D₂₀	1	1	yes	characteristic
47	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
48	C₈	—	4	1	no	—
49	C₈	—	20	1	no	—
50	C₅	#355	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	20	2	no	—
52	C₂²	—	20	1	no	—
53	C₂²	#685	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	20	1	no	—
58	C₂	—	2	1	no	—
59	C₂	—	40	1	no	—
60	C₂	#3938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#3938
commutator	C₂×C₄×C₅	C₂×C₄
Frattini	C₂×Q₈	C₂×D₅
Fitting	C₅×#101	C₂
socle	C₂×C₅	#99
prime radical	C₂×D₂₀	C₄
cosocle	C₂×C₅×Q₈	C₂²
hypercenter	#101	D₅
hypocenter	C₅	#355
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
2. C₅×#101	C₂	semidirect
3. #3968	C₂	semidirect
23. #101	D₅	semidirect
50. C₅	#355	semidirect

Maximal subgroups

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

subgroup	index
#4093	2
C₅×#101	2
#3968	2
#355	5