Subgroups — #64685

Order 320.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4016	C₂	1	1	yes	maximal, characteristic
2	C₅×#97	C₂	1	1	yes	maximal, characteristic
3	#3935	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈	—	2	1	no	—
5	C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₅	C₄	1	1	yes	characteristic
7	C₄⋊Dic₅	C₄	1	1	yes	characteristic
8	#683	—	2	1	no	—
9	#683	—	2	1	no	—
10	C₂×#168	—	2	1	no	—
11	#330	—	5	1	no	maximal, Sylow
12	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅	D₄	1	1	yes	characteristic
14	C₂×C₄×C₅	D₄	1	1	yes	characteristic
15	C₂×Dic₅	—	2	1	no	—
16	C₂×Dic₅	—	2	1	no	—
17	C₅×C₈	—	2	2	no	—
18	#168	—	2	2	no	—
19	#125	—	5	1	no	—
20	#97	—	5	1	no	—
21	#97	D₅	1	1	yes	characteristic
22	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₅	—	2	1	no	—
24	C₄×C₅	—	2	1	no	—
25	C₄×C₅	—	2	1	no	—
26	Dic₅	—	4	1	no	—
27	Dic₅	—	4	1	no	—
28	C₂×C₈	—	2	1	no	—
29	C₂×C₈	—	10	1	no	—
30	C₄⋊C₄	—	5	1	no	—
31	C₄⋊C₄	—	5	1	no	—
32	C₄⋊C₄	—	10	1	no	—
33	C₄⋊C₄	—	10	1	no	—
34	C₄²	C₂×D₅	1	1	yes	characteristic
35	C₂×C₅	#101	1	1	yes	characteristic
36	C₂×C₅	#104	1	1	yes	characteristic
37	C₂×C₅	#104	1	1	yes	characteristic
38	C₂×C₄	—	10	1	no	—
39	C₂×C₄	—	10	1	no	—
40	C₂×C₄	C₄×D₅	1	1	yes	characteristic
41	C₂×C₄	D₂₀	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
43	C₈	—	2	2	no	—
44	C₈	—	10	2	no	—
45	C₅	#330	1	1	yes	characteristic, complemented, Sylow
46	C₂²	#685	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	2	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	20	1	no	—
51	C₄	—	20	1	no	—
52	C₂	#3937	1	1	yes	characteristic
53	C₂	#3956	1	1	yes	characteristic
54	C₂	#3957	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#685
commutator	C₂×C₄×C₅	C₂×C₄
Frattini	C₄²	C₂×D₅
Fitting	C₅×#97	C₂
socle, prime radical	C₂²×C₅	C₂²⋊C₄
cosocle	C₄²×C₅	C₂²
hypercenter	#97	D₅
hypocenter	C₅	#330
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
45. C₅	#330	semidirect

Maximal subgroups

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

subgroup	index
#4016	2
C₅×#97	2
#3935	2
#330	5