Subgroups — #64966

Order 320.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#685	C₂	1	3	yes	maximal
2	C₂×C₄⋊Dic₅	C₂	1	3	yes	maximal, complemented
3	C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₅	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₅	C₂²	1	3	yes	—
6	C₂²×Dic₅	C₂²	1	3	yes	—
7	#685	—	2	6	no	—
8	C₄⋊Dic₅	—	2	6	no	—
9	#399	—	5	1	no	maximal, Sylow
10	C₂³×C₅	C₂³	1	1	yes	characteristic
11	C₂²×D₅	—	2	3	no	—
12	C₂²×D₅	—	2	3	no	—
13	C₂²×D₅	Q₈	1	2	yes	—
14	C₂×C₄×C₅	—	2	6	no	—
15	C₂×C₄×C₅	D₄	1	6	yes	—
16	C₂×Dic₅	—	2	6	no	—
17	C₂×Dic₅	—	2	3	no	—
18	C₂×C₄⋊C₄	—	5	3	no	—
19	C₂×C₂²⋊C₄	—	5	3	no	—
20	#95	D₅	1	1	yes	characteristic, complemented
21	C₂²×C₅	C₂×D₄	1	3	yes	—
22	C₂²×C₅	C₂×Q₈	1	1	yes	characteristic
23	C₂²×C₅	#41	1	3	yes	—
24	C₂×D₅	—	2	6	no	—
25	C₂×D₅	—	4	3	no	—
26	C₂×D₅	—	4	1	no	—
27	C₄×C₅	—	2	6	no	—
28	Dic₅	—	4	3	no	—
29	C₂⁴	—	5	1	no	—
30	C₂²×C₄	—	5	3	no	—
31	C₂²×C₄	C₂×D₅	1	3	yes	—
32	C₄⋊C₄	—	10	6	no	—
33	C₂²⋊C₄	—	10	6	no	—
34	C₂×C₅	C₂²⋊Q₈	1	3	yes	—
35	C₂×C₅	#123	1	3	yes	—
36	C₂×C₅	#127	1	1	yes	characteristic
37	D₅	—	4	2	no	—
38	C₂³	—	5	2	no	—
39	C₂³	—	10	3	no	—
40	C₂³	—	10	3	no	—
41	C₂³	C₂²×D₅	1	1	yes	characteristic
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	—	10	3	no	—
44	C₂×C₄	—	10	6	no	—
45	C₂×C₄	D₂₀	1	6	yes	—
46	C₅	#399	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	10	6	no	—
48	C₂²	—	20	1	no	—
49	C₂²	—	20	3	no	—
50	C₂²	C₂×D₂₀	1	3	yes	—
51	C₂²	#711	1	3	yes	—
52	C₂²	Q₈×D₅	1	1	yes	characteristic
53	C₄	—	2	6	no	—
54	C₄	—	20	3	no	—
55	C₂	—	20	2	no	—
56	C₂	#4020	1	1	yes	characteristic
57	C₂	#4032	1	3	yes	—
58	C₂	#4043	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₅
commutator, socle, cosocle	C₂³×C₅	C₂³
Fitting	C₅×#95	C₂
prime radical	C₂³×D₅	C₂²
hypercenter	#95	D₅
hypocenter	C₅	#399
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₅	C₂	semidirect
3. C₅×#95	C₂	semidirect
20. #95	D₅	semidirect
46. C₅	#399	semidirect

Maximal subgroups

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

subgroup	index
C₂×#685	2
C₂×C₄⋊Dic₅	2
C₅×#95	2
#399	5