Subgroups — #65345

Order 320.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#124	C₂	1	1	yes	maximal, characteristic
2	#4016	C₂	1	1	yes	maximal, characteristic, complemented
3	#3967	C₂	1	2	yes	maximal, complemented
4	#3964	C₂	1	2	yes	maximal
5	C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₅×C₂²⋊C₄	—	2	2	no	—
9	C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₅	C₂²	1	2	yes	—
11	#683	—	2	2	no	—
12	C₂×#168	C₂²	1	2	yes	—
13	#488	—	5	1	no	maximal, Sylow
14	C₂³×C₅	—	2	1	no	—
15	C₅×Q₈	—	2	2	no	—
16	C₅×D₄	—	2	2	no	—
17	C₂×C₄×C₅	—	2	1	no	—
18	C₂×C₄×C₅	D₄	1	2	yes	—
19	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂×Dic₅	—	2	2	no	—
21	#168	—	2	2	no	—
22	#125	—	5	1	no	—
23	#124	D₅	1	1	yes	characteristic
24	#103	—	5	2	no	—
25	#102	—	5	2	no	—
26	C₄×C₈	—	5	1	no	—
27	C₂²×C₅	—	4	1	no	—
28	C₂²×C₅	—	4	2	no	—
29	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
30	C₄×C₅	—	2	2	no	—
31	C₄×C₅	—	4	1	no	—
32	C₄×C₅	#41	1	2	yes	—
33	Dic₅	—	4	2	no	—
34	C₂×Q₈	C₂×D₅	1	1	yes	characteristic
35	C₂×D₄	C₂×D₅	1	1	yes	characteristic
36	C₂×C₈	—	5	2	no	—
37	C₄⋊C₄	—	5	2	no	—
38	C₄⋊C₄	—	10	2	no	—
39	C₂²⋊C₄	—	2	2	no	—
40	C₄²	C₂×D₅	1	1	yes	characteristic
41	C₂×C₅	—	8	1	no	—
42	C₂×C₅	#124	1	1	yes	characteristic
43	C₂×C₅	#135	1	2	yes	—
44	C₂³	—	2	1	no	—
45	Q₈	—	2	2	no	—
46	D₄	—	2	2	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	—	10	2	no	—
49	C₂×C₄	C₂²⋊D₅	1	2	yes	—
50	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
51	C₈	—	10	2	no	—
52	C₅	#488	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	4	2	no	—
54	C₂²	—	4	1	no	—
55	C₂²	C₂×C₂²⋊D₅	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	1	no	—
58	C₄	—	20	2	no	—
59	C₄	#711	1	2	yes	—
60	C₂	—	8	1	no	—
61	C₂	#4082	1	1	yes	characteristic
62	C₂	#4096	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#124	C₂
socle	C₂²×C₅	C₂×D₄
prime radical	C₂×C₅×D₄	C₂²
hypercenter	#124	D₅
hypocenter	C₅	#488
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
2. #4016	C₂	semidirect
3. #3967	C₂	semidirect
5. C₄×#168	C₂	semidirect
52. C₅	#488	semidirect

Maximal subgroups

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

subgroup	index
C₅×#124	2
#4016	2
#3967	2
#3964	2
C₄×#168	2
#488	5