Subgroups — #65137

Order 320.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#677	C₂	1	2	yes	maximal, complemented
2	#4020	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#3953	C₂	1	2	yes	maximal, complemented
6	C₂×D₂₀	—	2	1	no	—
7	C₂×D₂₀	—	2	1	no	—
8	C₂×D₂₀	C₂²	1	2	yes	—
9	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₈	C₂²	1	2	yes	—
11	C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₅	C₂²	1	1	yes	characteristic
13	#683	—	2	1	no	—
14	C₄×Dic₅	—	2	1	no	—
15	#677	—	2	4	no	—
16	#460	—	5	1	no	maximal, Sylow
17	C₂²×D₅	—	2	2	no	—
18	C₂×C₄×C₅	D₄	1	1	yes	characteristic
19	C₂×C₄×C₅	D₄	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂×Dic₅	—	2	1	no	—
22	C₂×Dic₅	—	2	1	no	—
23	D₂₀	—	2	2	no	—
24	D₂₀	—	2	2	no	—
25	D₂₀	—	4	2	no	—
26	D₂₀	—	4	2	no	—
27	Dic₁₀	—	2	1	no	—
28	Dic₁₀	D₄	1	2	yes	complemented
29	C₅×C₈	—	2	2	no	—
30	C₂×SD₁₆	—	5	2	no	—
31	#127	—	5	1	no	—
32	C₄×Q₈	—	5	1	no	—
33	C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
34	#102	—	5	2	no	—
35	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×D₅	—	4	2	no	—
37	C₂×D₅	—	4	2	no	—
38	C₂×D₅	—	4	2	no	—
39	C₄×C₅	—	2	1	no	—
40	C₄×C₅	SD₁₆	1	2	yes	complemented
41	C₄×C₅	C₂×D₄	1	1	yes	characteristic
42	C₄×C₅	#41	1	1	yes	characteristic
43	Dic₅	—	2	2	no	—
44	Dic₅	—	4	1	no	—
45	C₂×Q₈	—	5	1	no	—
46	C₂×D₄	—	5	2	no	—
47	C₂×D₄	—	10	1	no	—
48	C₂×D₄	—	10	1	no	—
49	SD₁₆	—	10	4	no	—
50	C₂×C₈	C₂×D₅	1	2	yes	—
51	C₄⋊C₄	—	5	1	no	—
52	C₄⋊C₄	—	10	1	no	—
53	C₄²	—	10	1	no	—
54	C₄²	C₂×D₅	1	1	yes	characteristic
55	C₂×C₅	#121	1	1	yes	characteristic
56	C₂×C₅	C₂×SD₁₆	1	1	yes	characteristic
57	C₂×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
58	D₅	—	8	2	no	—
59	C₂³	—	10	2	no	—
60	Q₈	—	5	2	no	—
61	Q₈	—	10	1	no	—
62	D₄	—	10	2	no	—
63	D₄	—	10	2	no	—
64	D₄	—	20	2	no	—
65	D₄	—	20	2	no	—
66	C₂×C₄	—	10	1	no	—
67	C₂×C₄	—	10	1	no	—
68	C₂×C₄	D₂₀	1	1	yes	characteristic
69	C₂×C₄	D₂₀	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₅	#460	1	1	yes	characteristic, complemented, Sylow
73	C₂²	—	20	2	no	—
74	C₂²	—	20	2	no	—
75	C₂²	—	20	2	no	—
76	C₂²	C₂×D₂₀	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	10	2	no	—
79	C₄	—	20	1	no	—
80	C₄	#677	1	2	yes	complemented
81	C₄	D₄×D₅	1	1	yes	characteristic
82	C₄	#713	1	1	yes	characteristic
83	C₂	—	40	2	no	—
84	C₂	#4041	1	1	yes	characteristic
85	C₂	C₂×#677	1	1	yes	characteristic
86	C₂	#4054	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	C₂²×C₅	C₂×D₄
prime radical	#4020	C₂
hypercenter	C₄⋊C₈	D₅
hypocenter	C₅	#460
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
1. C₂×#677	C₂	semidirect
3. C₄×Dic₁₀	C₂	semidirect
4. C₅×C₄⋊C₈	C₂	semidirect
5. #3953	C₂	semidirect
28. Dic₁₀	D₄	semidirect
33. C₄⋊C₈	D₅	semidirect
40. C₄×C₅	SD₁₆	semidirect
72. C₅	#460	semidirect
80. C₄	#677	semidirect

Maximal subgroups

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

subgroup	index
C₂×#677	2
#4020	2
C₄×Dic₁₀	2
C₅×C₄⋊C₈	2
#3953	2
#460	5