Subgroups — #65167

Order 320.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4036	C₂	1	2	yes	maximal
2	C₅×#107	C₂	1	1	yes	maximal, characteristic
3	#3950	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
5	#3940	C₂	1	2	yes	maximal
6	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₅×C₄⋊C₄	C₂²	1	2	yes	—
8	C₄⋊Dic₅	—	2	2	no	—
9	C₄⋊Dic₅	C₂²	1	2	yes	—
10	#683	—	2	2	no	—
11	C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×#168	C₂²	1	1	yes	characteristic
13	#499	—	5	1	no	maximal, Sylow
14	C₂×C₄×C₅	—	2	2	no	—
15	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
16	C₂×Dic₅	—	2	2	no	—
17	C₂×Dic₅	D₄	1	1	yes	characteristic
18	C₂×Dic₅	D₄	1	1	yes	characteristic
19	C₅×C₈	Q₈	1	2	yes	—
20	#168	Q₈	1	2	yes	—
21	#125	—	5	2	no	—
22	#107	—	5	1	no	—
23	#107	D₅	1	1	yes	characteristic
24	#106	—	5	2	no	—
25	C₄×C₈	—	5	1	no	—
26	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
27	C₄×C₅	—	4	2	no	—
28	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
30	Dic₅	—	2	1	no	—
31	Dic₅	—	2	1	no	—
32	Dic₅	—	4	2	no	—
33	C₂×C₈	—	5	1	no	—
34	C₂×C₈	C₂×D₅	1	1	yes	characteristic
35	C₄⋊C₄	—	5	2	no	—
36	C₄⋊C₄	—	10	2	no	—
37	C₄⋊C₄	—	10	2	no	—
38	C₄⋊C₄	C₂×D₅	1	2	yes	—
39	C₄²	—	5	1	no	—
40	C₂×C₅	C₄⋊Q₈	1	1	yes	characteristic
41	C₂×C₅	#135	1	1	yes	characteristic
42	C₂×C₅	#135	1	1	yes	characteristic
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	5	1	no	—
45	C₂×C₄	—	5	1	no	—
46	C₂×C₄	—	10	2	no	—
47	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
48	C₈	—	5	2	no	—
49	C₈	Dic₁₀	1	2	yes	—
50	C₅	#499	1	1	yes	characteristic, complemented, Sylow
51	C₂²	D₄×D₅	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	—	10	1	no	—
54	C₄	—	10	1	no	—
55	C₄	—	20	2	no	—
56	C₄	C₂×Dic₁₀	1	1	yes	characteristic
57	C₄	Q₈×D₅	1	1	yes	characteristic
58	C₂	#4034	1	1	yes	characteristic
59	C₂	#4058	1	1	yes	characteristic
60	C₂	#4065	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#107	C₂
socle, prime radical	C₂²×C₅	C₂×D₄
hypercenter	#107	D₅
hypocenter	C₅	#499
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
50. C₅	#499	semidirect

Maximal subgroups

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

subgroup	index
#4036	2
C₅×#107	2
#3950	2
C₈×Dic₅	2
#3940	2
#499	5