Subgroups — C₂×C₈×Dic₅ #65387

Order 320.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₅
commutator, hypocenter	C₅	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂²×C₅×C₈	C₂
socle, prime radical	C₂³×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂³
LCS	G ▷ C₅
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. C₈×Dic₅	C₂	direct (N × H)
7. C₂×C₅×C₈	C₄	semidirect
11. C₂×#168	C₄	semidirect
19. C₂×Dic₅	C₈	direct (N × H)
21. C₅×C₈	C₂×C₄	semidirect
22. #168	C₂×C₄	semidirect
33. Dic₅	C₂×C₈	direct (N × H)
38. C₂×C₈	Dic₅	direct (N × H)
42. C₂×C₅	C₄×C₈	semidirect
53. C₈	C₂×Dic₅	direct (N × H)
54. C₅	C₂×C₄×C₈	semidirect
62. C₂	C₈×Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₈	2
C₂×C₄×Dic₅	2
C₂²×#168	2
C₈×Dic₅	2
C₂×C₄×C₈	5

Subgroups — C2×C8×Dic5 #65387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×Dic₅ #65387