Subgroups — C₅×C₈×D₅ #87782

Order 400.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	C₄	1	1	yes	characteristic
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	C₄	1	1	yes	characteristic
7	C₂×C₅×C₈	—	5	1	no	maximal
8	C₈×D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₅×D₅	C₈	1	2	yes	direct product factor
11	C₂×C₄×C₅	—	5	1	no	—
12	C₄×D₅	C₂×C₅	1	1	yes	characteristic
13	C₅×C₈	—	2	2	no	—
14	C₅×C₈	—	5	1	no	—
15	C₅×C₈	D₅	1	1	yes	characteristic, direct product factor
16	C₅×C₈	C₂×C₅	1	1	yes	characteristic, complemented
17	#168	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	5	1	no	—
20	C₂×D₅	C₄×C₅	1	1	yes	characteristic
21	C₄×C₅	—	2	2	no	—
22	C₄×C₅	—	5	1	no	—
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
25	Dic₅	C₄×C₅	1	1	yes	characteristic
26	C₂×C₈	—	5	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	—	5	2	no	—
29	C₂×C₅	C₄×D₅	1	1	yes	characteristic
30	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
31	D₅	C₅×C₈	1	2	yes	direct product factor
32	C₂×C₄	—	5	1	no	—
33	C₈	—	5	1	no	—
34	C₈	C₅×D₅	1	1	yes	characteristic, direct product factor
35	C₅	—	2	2	no	—
36	C₅	C₈×D₅	1	1	yes	characteristic, direct product factor
37	C₅	C₂×C₅×C₈	1	1	yes	characteristic, complemented
38	C₂²	—	5	1	no	—
39	C₄	—	5	1	no	—
40	C₄	C₂×C₅×D₅	1	1	yes	characteristic
41	C₂	—	5	2	no	—
42	C₂	C₄×C₅×D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅²×C₈	C₂	semidirect
3. C₅×#168	C₂	semidirect
8. C₈×D₅	C₅	direct (N × H)
10. C₅×D₅	C₈	direct (N × H)
15. C₅×C₈	D₅	direct (N × H)
16. C₅×C₈	C₂×C₅	semidirect
17. #168	C₂×C₅	semidirect
18. C₅²	C₂×C₈	semidirect
31. D₅	C₅×C₈	direct (N × H)
34. C₈	C₅×D₅	direct (N × H)
36. C₅	C₈×D₅	direct (N × H)
37. C₅	C₂×C₅×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₅	2
C₅²×C₈	2
C₅×#168	2
C₂×C₅×C₈	5
C₈×D₅	5

Subgroups — C5×C8×D5 #87782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈×D₅ #87782