Subgroups — #65118

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4016	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	#3950	C₂	1	1	yes	maximal, characteristic
5	#3949	C₂	1	1	yes	maximal, characteristic
6	#3948	C₂	1	1	yes	maximal, characteristic
7	#3948	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
9	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₅	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₅	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₅	C₂²	1	1	yes	characteristic
15	#683	—	2	1	no	—
16	#683	—	2	1	no	—
17	#683	—	2	1	no	—
18	C₄×Dic₅	—	2	1	no	—
19	#479	—	5	1	no	maximal, Sylow
20	C₂×C₄×C₅	D₄	1	1	yes	characteristic
21	C₂×C₄×C₅	D₄	1	1	yes	characteristic
22	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂×Dic₅	—	2	1	no	—
24	C₂×Dic₅	—	2	1	no	—
25	C₂×Dic₅	—	2	1	no	—
26	C₂×Dic₅	—	2	1	no	—
27	Dic₁₀	—	2	1	no	—
28	Dic₁₀	Q₈	1	2	yes	—
29	C₅×C₈	—	2	1	no	—
30	C₅×C₈	—	2	1	no	—
31	#125	—	5	1	no	—
32	C₄×Q₈	—	5	1	no	—
33	#107	—	5	1	no	—
34	#106	—	5	1	no	—
35	C₄⋊C₈	D₅	1	1	yes	characteristic
36	#103	—	5	1	no	—
37	#103	—	5	1	no	—
38	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
39	C₄×C₅	—	2	1	no	—
40	C₄×C₅	—	2	1	no	—
41	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
42	C₄×C₅	#41	1	1	yes	characteristic
43	Dic₅	—	2	2	no	—
44	Dic₅	—	4	1	no	—
45	Dic₅	—	4	1	no	—
46	Dic₅	—	4	1	no	—
47	C₂×Q₈	—	5	1	no	—
48	C₂×C₈	C₂×D₅	1	1	yes	characteristic
49	C₂×C₈	C₂×D₅	1	1	yes	characteristic
50	C₄⋊C₄	—	5	1	no	—
51	C₄⋊C₄	—	5	1	no	—
52	C₄⋊C₄	—	5	1	no	—
53	C₄⋊C₄	—	10	1	no	—
54	C₄⋊C₄	—	10	1	no	—
55	C₄⋊C₄	—	10	1	no	—
56	C₄²	—	10	1	no	—
57	C₄²	C₂×D₅	1	1	yes	characteristic
58	C₂×C₅	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂×C₅	#135	1	1	yes	characteristic
60	C₂×C₅	#137	1	1	yes	characteristic
61	Q₈	—	5	2	no	—
62	Q₈	—	10	1	no	—
63	C₂×C₄	—	10	1	no	—
64	C₂×C₄	—	10	1	no	—
65	C₂×C₄	—	10	1	no	—
66	C₂×C₄	—	10	1	no	—
67	C₂×C₄	D₂₀	1	1	yes	characteristic
68	C₂×C₄	D₂₀	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₅	#479	1	1	yes	characteristic, complemented, Sylow
73	C₂²	C₂×D₂₀	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	10	2	no	—
77	C₄	—	20	1	no	—
78	C₄	—	20	1	no	—
79	C₄	—	20	1	no	—
80	C₄	#711	1	1	yes	characteristic
81	C₄	Q₈×D₅	1	1	yes	characteristic
82	C₂	#4043	1	1	yes	characteristic
83	C₂	#4050	1	1	yes	characteristic
84	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	#479
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
72. C₅	#479	semidirect

Maximal subgroups

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

subgroup	index
#4016	2
C₄×Dic₁₀	2
C₅×C₄⋊C₈	2
#3950	2
#3949	2
#3948	2
#479	5