Subgroups — #65470

Order 320.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#4090	C₂	1	2	yes	maximal
3	C₂×#689	C₂	1	2	yes	maximal
4	C₂×Dic₂₀	C₂	1	1	yes	maximal, characteristic
5	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×Q₈	C₂²	1	2	yes	—
7	C₂×Dic₁₀	C₂²	1	2	yes	—
8	C₅×Q₁₆	—	2	2	no	—
9	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
10	#689	—	2	4	no	—
11	#683	—	2	4	no	—
12	C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₂×#168	C₂²	1	1	yes	characteristic
14	Dic₂₀	—	2	2	no	—
15	#494	—	5	1	no	maximal, Sylow
16	C₅×Q₈	—	2	2	no	—
17	C₅×Q₈	—	2	2	no	—
18	C₂×C₄×C₅	—	2	2	no	—
19	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂×Dic₅	—	2	2	no	—
21	C₂×Dic₅	D₄	1	2	yes	—
22	Dic₁₀	—	2	2	no	—
23	Dic₁₀	—	2	2	no	—
24	C₅×C₈	D₄	1	2	yes	—
25	#168	D₄	1	2	yes	—
26	C₂×Q₁₆	—	5	2	no	—
27	C₂×Q₁₆	—	5	1	no	—
28	C₂×Q₁₆	D₅	1	1	yes	characteristic
29	C₄⋊Q₈	—	5	2	no	—
30	C₄×C₈	—	5	1	no	—
31	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
32	C₄×C₅	—	4	2	no	—
33	C₄×C₅	C₂×D₄	1	1	yes	characteristic
34	C₄×C₅	C₂×D₄	1	1	yes	characteristic
35	Dic₅	—	4	2	no	—
36	Dic₅	Q₁₆	1	4	yes	complemented
37	C₂×Q₈	—	5	2	no	—
38	C₂×Q₈	C₂×D₅	1	2	yes	—
39	Q₁₆	—	2	2	no	—
40	Q₁₆	—	10	4	no	—
41	Q₁₆	—	10	2	no	—
42	C₂×C₈	—	5	1	no	—
43	C₂×C₈	C₂×D₅	1	1	yes	characteristic
44	C₄⋊C₄	—	10	4	no	—
45	C₄²	—	5	1	no	—
46	C₂×C₅	#127	1	1	yes	characteristic
47	C₂×C₅	C₂×Q₁₆	1	2	yes	—
48	Q₈	—	2	2	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	10	2	no	—
51	Q₈	—	10	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	5	2	no	—
54	C₂×C₄	—	10	2	no	—
55	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
56	C₈	—	5	2	no	—
57	C₈	C₂²⋊D₅	1	2	yes	—
58	C₅	#494	1	1	yes	characteristic, complemented, Sylow
59	C₂²	D₄×D₅	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	5	4	no	—
62	C₄	—	20	2	no	—
63	C₄	D₄×D₅	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
65	C₂	D₅×Q₁₆	1	2	yes	—
66	C₂	#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂×C₅×Q₁₆	C₂
socle, prime radical	C₂²×C₅	C₂×D₄
hypercenter	C₂×Q₁₆	D₅
hypocenter	C₅	#494
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
36. Dic₅	Q₁₆	semidirect
58. C₅	#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₁₆	2
#4090	2
C₂×#689	2
C₂×Dic₂₀	2
C₈×Dic₅	2
#494	5