Subgroups — #65140

Order 320.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4015	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#3949	C₂	1	2	yes	maximal
5	#3948	C₂	1	2	yes	maximal
6	C₂×Dic₁₀	—	2	1	no	—
7	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
8	C₂×C₅×C₈	C₂²	1	2	yes	—
9	C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₅	—	2	1	no	—
11	C₄⋊Dic₅	C₂²	1	2	yes	—
12	C₄⋊Dic₅	C₂²	1	1	yes	characteristic
13	#683	—	2	1	no	—
14	C₄×Dic₅	—	2	1	no	—
15	#475	—	5	1	no	maximal, Sylow
16	C₂×C₄×C₅	D₄	1	1	yes	characteristic
17	C₂×C₄×C₅	D₄	1	1	yes	characteristic
18	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₅	—	2	1	no	—
20	C₂×Dic₅	—	2	1	no	—
21	C₂×Dic₅	—	2	2	no	—
22	Dic₁₀	—	2	1	no	—
23	Dic₁₀	—	4	2	no	—
24	Dic₁₀	Q₈	1	2	yes	complemented
25	C₅×C₈	—	2	2	no	—
26	C₄⋊Q₈	—	5	1	no	—
27	C₄×Q₈	—	5	1	no	—
28	#106	—	5	2	no	—
29	C₄⋊C₈	D₅	1	1	yes	characteristic
30	#103	—	5	2	no	—
31	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
32	C₄×C₅	—	2	1	no	—
33	C₄×C₅	SD₁₆	1	2	yes	—
34	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₅	#41	1	1	yes	characteristic
36	Dic₅	—	2	2	no	—
37	Dic₅	—	4	2	no	—
38	Dic₅	—	4	1	no	—
39	C₂×Q₈	—	5	1	no	—
40	C₂×Q₈	—	10	1	no	—
41	C₂×C₈	C₂×D₅	1	2	yes	—
42	C₄⋊C₄	—	5	2	no	—
43	C₄⋊C₄	—	5	1	no	—
44	C₄⋊C₄	—	10	1	no	—
45	C₄⋊C₄	—	10	1	no	—
46	C₄²	—	10	1	no	—
47	C₄²	C₂×D₅	1	1	yes	characteristic
48	C₂×C₅	C₂²⋊Q₈	1	1	yes	characteristic
49	C₂×C₅	C₂×SD₁₆	1	1	yes	characteristic
50	C₂×C₅	#137	1	1	yes	characteristic
51	Q₈	—	5	2	no	—
52	Q₈	—	10	1	no	—
53	Q₈	—	20	2	no	—
54	C₂×C₄	—	10	1	no	—
55	C₂×C₄	—	10	1	no	—
56	C₂×C₄	—	10	2	no	—
57	C₂×C₄	D₂₀	1	1	yes	characteristic
58	C₂×C₄	D₂₀	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₅	#475	1	1	yes	characteristic, complemented, Sylow
62	C₂²	C₂×D₂₀	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	10	2	no	—
65	C₄	—	20	2	no	—
66	C₄	—	20	1	no	—
67	C₄	#677	1	2	yes	—
68	C₄	#711	1	1	yes	characteristic
69	C₄	Q₈×D₅	1	1	yes	characteristic
70	C₂	#4043	1	1	yes	characteristic
71	C₂	C₂×#677	1	1	yes	characteristic
72	C₂	#4055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₅	C₂×D₄
hypercenter	C₄⋊C₈	D₅
hypocenter	C₅	#475
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
24. Dic₁₀	Q₈	semidirect
61. C₅	#475	semidirect

Maximal subgroups

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

subgroup	index
#4015	2
C₄×Dic₁₀	2
C₅×C₄⋊C₈	2
#3949	2
#3948	2
#475	5