Subgroups — #64698

Order 320.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4090	C₂	1	1	yes	maximal, characteristic
2	C₅×#101	C₂	1	1	yes	maximal, characteristic
3	#3968	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₀	C₄	1	1	yes	characteristic
6	C₅×M₁₆	—	2	1	no	—
7	#683	—	2	1	no	—
8	#683	—	2	1	no	—
9	C₄×Dic₅	C₄	1	1	yes	characteristic
10	#681	—	2	1	no	—
11	#356	—	5	1	no	maximal, Sylow
12	C₅×Q₈	—	4	1	no	—
13	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₅	D₄	1	1	yes	characteristic
15	C₂×C₄×C₅	D₄	1	1	yes	characteristic
16	C₂×Dic₅	—	2	1	no	—
17	C₂×Dic₅	—	2	1	no	—
18	Dic₁₀	—	4	1	no	—
19	C₅×C₈	—	4	1	no	—
20	#168	—	4	1	no	—
21	C₄⋊Q₈	—	5	1	no	—
22	#101	—	5	1	no	—
23	#101	D₅	1	1	yes	characteristic
24	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₅	—	2	1	no	—
26	C₄×C₅	—	2	1	no	—
27	C₄×C₅	—	2	1	no	—
28	Dic₅	—	2	2	no	—
29	Dic₅	—	4	1	no	—
30	C₂×Q₈	—	5	1	no	—
31	C₂×Q₈	C₂×D₅	1	1	yes	characteristic
32	M₁₆	—	2	1	no	—
33	M₁₆	—	10	1	no	—
34	C₄⋊C₄	—	10	1	no	—
35	C₄⋊C₄	—	10	1	no	—
36	C₄²	—	5	1	no	—
37	C₂×C₅	—	2	1	no	—
38	C₂×C₅	#99	1	1	yes	characteristic
39	Q₈	—	4	1	no	—
40	Q₈	—	20	1	no	—
41	C₂×C₄	—	10	1	no	—
42	C₂×C₄	—	10	1	no	—
43	C₂×C₄	C₄×D₅	1	1	yes	characteristic
44	C₂×C₄	D₂₀	1	1	yes	characteristic
45	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
46	C₈	—	4	1	no	—
47	C₈	—	20	1	no	—
48	C₅	#356	1	1	yes	characteristic, complemented, Sylow
49	C₂²	#685	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	10	2	no	—
54	C₄	—	20	1	no	—
55	C₂	—	2	1	no	—
56	C₂	#3938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#3938
commutator	C₂×C₄×C₅	C₂×C₄
Frattini	C₂×Q₈	C₂×D₅
Fitting	C₅×#101	C₂
socle	C₂×C₅	#99
prime radical	C₂²×C₅	C₂²⋊C₄
cosocle	C₂×C₅×Q₈	C₂²
hypercenter	#101	D₅
hypocenter	C₅	#356
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
48. C₅	#356	semidirect

Maximal subgroups

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

subgroup	index
#4090	2
C₅×#101	2
#3968	2
#356	5