Subgroups — C₅×C₈×Dic₅ #11716639

Order 800.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₅×Dic₅	C₄	1	2	yes	—
6	C₅²×C₈	C₄	1	2	yes	complemented
7	C₅×#168	C₄	1	2	yes	complemented
8	C₄×C₅×C₈	—	5	1	no	maximal
9	C₈×Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₅²	C₂×C₄	1	1	yes	characteristic
11	C₄×C₅²	C₂×C₄	1	1	yes	characteristic
12	C₄×C₅²	C₂×C₄	1	1	yes	characteristic
13	C₅×Dic₅	C₈	1	4	yes	direct product factor
14	C₂×C₅×C₈	—	2	2	no	—
15	C₂×C₅×C₈	—	5	1	no	—
16	C₂×C₅×C₈	D₅	1	1	yes	characteristic
17	C₂×C₅×C₈	C₂×C₅	1	1	yes	characteristic
18	C₄²×C₅	—	5	1	no	—
19	C₄×Dic₅	C₂×C₅	1	1	yes	characteristic
20	C₂×#168	C₂×C₅	1	1	yes	characteristic
21	C₂×C₅²	C₄²	1	1	yes	characteristic
22	C₂×C₅²	C₂×C₈	1	2	yes	—
23	C₂×C₄×C₅	—	2	2	no	—
24	C₂×C₄×C₅	—	5	2	no	—
25	C₂×C₄×C₅	C₂×D₅	1	1	yes	characteristic
26	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
27	C₂×Dic₅	C₄×C₅	1	2	yes	—
28	C₅×C₈	—	2	4	no	—
29	C₅×C₈	—	5	2	no	—
30	C₅×C₈	Dic₅	1	2	yes	direct product factor
31	C₅×C₈	C₄×C₅	1	2	yes	complemented
32	#168	C₄×C₅	1	2	yes	complemented
33	C₄×C₈	—	5	1	no	Sylow
34	C₅²	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₅	—	2	2	no	—
36	C₂²×C₅	C₄×D₅	1	1	yes	characteristic
37	C₂²×C₅	C₂×C₄×C₅	1	1	yes	characteristic
38	C₄×C₅	—	2	2	no	—
39	C₄×C₅	—	2	2	no	—
40	C₄×C₅	—	5	4	no	—
41	C₄×C₅	C₄×D₅	1	1	yes	characteristic
42	C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
43	C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
44	C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
45	Dic₅	C₅×C₈	1	4	yes	direct product factor
46	C₂×C₈	—	5	1	no	—
47	C₂×C₈	C₅×D₅	1	1	yes	characteristic
48	C₄²	—	5	1	no	—
49	C₂×C₅	—	2	4	no	—
50	C₂×C₅	—	2	2	no	—
51	C₂×C₅	C₈×D₅	1	2	yes	—
52	C₂×C₅	C₄×Dic₅	1	1	yes	characteristic
53	C₂×C₅	C₄²×C₅	1	1	yes	characteristic
54	C₂×C₅	C₂×C₅×C₈	1	2	yes	—
55	C₂×C₄	—	5	2	no	—
56	C₂×C₄	C₂×C₅×D₅	1	1	yes	characteristic
57	C₈	—	5	2	no	—
58	C₈	C₅×Dic₅	1	2	yes	direct product factor
59	C₅	—	2	2	no	—
60	C₅	C₈×Dic₅	1	1	yes	characteristic, direct product factor
61	C₅	C₄×C₅×C₈	1	1	yes	characteristic, complemented
62	C₂²	C₄×C₅×D₅	1	1	yes	characteristic
63	C₄	—	5	4	no	—
64	C₄	C₄×C₅×D₅	1	1	yes	characteristic
65	C₄	C₂×C₅×Dic₅	1	1	yes	characteristic
66	C₂	C₅×C₈×D₅	1	2	yes	—
67	C₂	C₄×C₅×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₈	D₅
commutator, hypocenter	C₅	C₄×C₅×C₈
Frattini	C₂×C₄	C₂×C₅×D₅
Fitting	C₂×C₅²×C₈	C₂
socle, prime radical	C₂²×C₅²	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
6. C₅²×C₈	C₄	semidirect
7. C₅×#168	C₄	semidirect
9. C₈×Dic₅	C₅	direct (N × H)
13. C₅×Dic₅	C₈	direct (N × H)
30. C₅×C₈	Dic₅	direct (N × H)
31. C₅×C₈	C₄×C₅	semidirect
32. #168	C₄×C₅	semidirect
34. C₅²	C₄×C₈	semidirect
45. Dic₅	C₅×C₈	direct (N × H)
58. C₈	C₅×Dic₅	direct (N × H)
60. C₅	C₈×Dic₅	direct (N × H)
61. C₅	C₄×C₅×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₈	2
C₄×C₅×Dic₅	2
C₂×C₅×#168	2
C₄×C₅×C₈	5
C₈×Dic₅	5

Subgroups — C5×C8×Dic5 #11716639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈×Dic₅ #11716639