Subgroups — #65147

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×#106	C₂	1	1	yes	maximal, characteristic
3	#3949	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
5	#3939	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	2	yes	—
18	C₅×C₈	Q₈	1	2	yes	—
19	#168	Q₈	1	2	yes	—
20	#125	—	5	2	no	—
21	#107	—	5	2	no	—
22	#106	—	5	1	no	—
23	#106	D₅	1	1	yes	characteristic
24	C₄×C₈	—	5	1	no	—
25	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
26	C₄×C₅	—	4	2	no	—
27	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
28	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
29	Dic₅	—	2	2	no	—
30	Dic₅	—	4	2	no	—
31	C₂×C₈	—	5	1	no	—
32	C₂×C₈	C₂×D₅	1	1	yes	characteristic
33	C₄⋊C₄	—	5	2	no	—
34	C₄⋊C₄	—	10	2	no	—
35	C₄⋊C₄	—	10	2	no	—
36	C₄⋊C₄	C₂×D₅	1	2	yes	—
37	C₄²	—	5	1	no	—
38	C₂×C₅	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₅	#135	1	2	yes	—
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	—	5	2	no	—
42	C₂×C₄	—	10	2	no	—
43	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
44	C₈	—	5	2	no	—
45	C₈	Dic₁₀	1	2	yes	—
46	C₅	#499	1	1	yes	characteristic, complemented, Sylow
47	C₂²	D₄×D₅	1	1	yes	characteristic
48	C₄	—	4	2	no	—
49	C₄	—	10	2	no	—
50	C₄	—	20	2	no	—
51	C₄	C₂×Dic₁₀	1	1	yes	characteristic
52	C₄	Q₈×D₅	1	1	yes	characteristic
53	C₂	#4034	1	1	yes	characteristic
54	C₂	#4062	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#106	C₂
socle, prime radical	C₂²×C₅	C₂×D₄
hypercenter	#106	D₅
hypocenter	C₅	#499
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
46. 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×#106	2
#3949	2
C₈×Dic₅	2
#3939	2
#499	5