Subgroups — #65144

Order 320.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4034	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	#3940	C₂	1	2	yes	maximal
6	C₂×Dic₁₀	—	2	2	no	—
7	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	#498	—	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	Dic₁₀	—	4	4	no	—
19	C₅×C₈	Q₈	1	2	yes	complemented
20	#168	Q₈	1	2	yes	complemented
21	C₄⋊Q₈	—	5	2	no	—
22	#106	—	5	1	no	—
23	#106	—	5	2	no	—
24	#106	D₅	1	1	yes	characteristic
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	—	4	2	no	—
31	Dic₅	SD₁₆	1	4	yes	—
32	C₂×Q₈	—	10	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	C₂×D₅	1	2	yes	—
38	C₄²	—	5	1	no	—
39	C₂×C₅	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×C₅	C₂×SD₁₆	1	2	yes	—
41	Q₈	—	20	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	5	2	no	—
44	C₂×C₄	—	10	2	no	—
45	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
46	C₈	—	5	2	no	—
47	C₈	Dic₁₀	1	2	yes	complemented
48	C₅	#498	1	1	yes	characteristic, complemented, Sylow
49	C₂²	D₄×D₅	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	5	4	no	—
52	C₄	—	20	2	no	—
53	C₄	C₂×Dic₁₀	1	1	yes	characteristic
54	C₄	Q₈×D₅	1	1	yes	characteristic
55	C₂	#4034	1	1	yes	characteristic
56	C₂	D₅×SD₁₆	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	#498
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
19. C₅×C₈	Q₈	semidirect
20. #168	Q₈	semidirect
47. C₈	Dic₁₀	semidirect
48. C₅	#498	semidirect

Maximal subgroups

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

subgroup	index
#4034	2
C₅×#106	2
#3949	2
C₈×Dic₅	2
#3940	2
#498	5