Subgroups — C₅×#686 #87793

Order 400.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅²	—	2	1	no	—
5	C₂×C₅×D₅	—	2	1	no	—
6	C₄×C₅²	C₂²	1	1	yes	characteristic
7	C₅×D₈	—	5	1	no	maximal
8	#686	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	—	4	1	no	—
10	C₂×C₅²	D₄	1	1	yes	characteristic
11	C₅×D₅	—	4	1	no	—
12	C₅×D₄	—	2	2	no	—
13	C₅×D₄	—	5	1	no	—
14	C₅×D₄	D₅	1	1	yes	characteristic, complemented
15	C₅×D₄	C₂×C₅	1	1	yes	characteristic, complemented
16	D₂₀	C₂×C₅	1	1	yes	characteristic, complemented
17	C₅×C₈	—	5	1	no	—
18	#168	C₂×C₅	1	1	yes	characteristic, complemented
19	C₅²	D₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₅	—	2	4	no	—
21	C₂²×C₅	—	2	1	no	—
22	C₂²×C₅	—	2	1	no	—
23	C₂²×C₅	—	10	1	no	—
24	C₂×D₅	—	2	1	no	—
25	C₄×C₅	—	2	2	no	—
26	C₄×C₅	C₂×D₅	1	1	yes	characteristic
27	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
28	D₈	—	5	1	no	Sylow
29	C₂×C₅	—	2	2	no	—
30	C₂×C₅	—	4	4	no	—
31	C₂×C₅	—	4	1	no	—
32	C₂×C₅	—	4	1	no	—
33	C₂×C₅	—	20	1	no	—
34	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
35	C₂×C₅	C₅×D₄	1	1	yes	characteristic
36	D₅	—	4	1	no	—
37	D₄	—	5	1	no	—
38	D₄	C₅×D₅	1	1	yes	characteristic, complemented
39	C₈	—	5	1	no	—
40	C₅	—	2	2	no	—
41	C₅	#686	1	1	yes	characteristic, direct product factor
42	C₅	C₅×D₈	1	1	yes	characteristic, complemented
43	C₂²	—	2	1	no	—
44	C₂²	—	10	1	no	—
45	C₄	C₂×C₅×D₅	1	1	yes	characteristic
46	C₂	—	4	1	no	—
47	C₂	—	20	1	no	—
48	C₂	C₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂²×C₅
Frattini	C₄	C₂×C₅×D₅
Fitting	C₅²×D₄	C₂
socle	C₂×C₅²	D₄
hypercenter	C₅×D₄	D₅
hypocenter	C₅	C₅×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₅²×D₄	C₂	semidirect
2. C₅×D₂₀	C₂	semidirect
3. C₅×#168	C₂	semidirect
8. #686	C₅	direct (N × H)
14. C₅×D₄	D₅	semidirect
15. C₅×D₄	C₂×C₅	semidirect
16. D₂₀	C₂×C₅	semidirect
18. #168	C₂×C₅	semidirect
19. C₅²	D₈	semidirect
38. D₄	C₅×D₅	semidirect
41. C₅	#686	direct (N × H)
42. C₅	C₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₄	2
C₅×D₂₀	2
C₅×#168	2
C₅×D₈	5
#686	5

Subgroups — C5×#686 #87793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#686 #87793