Subgroups — C₅×#87801 #14522625

Order 2000.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊(C₅⋊D₅)	C₂	1	2	yes	maximal, complemented
2	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₅⋊D₅	—	2	2	no	—
4	C₄×C₅³	C₂²	1	1	yes	characteristic
5	#87801	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×D₄₀	—	5	6	no	maximal
7	C₂×C₅³	D₄	1	1	yes	characteristic
8	C₅×C₅⋊D₅	—	4	2	no	—
9	C₄⋊(C₅⋊D₅)	C₂×C₅	1	2	yes	complemented
10	C₅×D₂₀	—	5	12	no	—
11	C₅²×C₈	—	2	12	no	—
12	C₅²×C₈	D₅	1	6	yes	complemented
13	C₅²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅³	D₈	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅⋊D₅	—	2	2	no	—
16	C₂×C₅×D₅	—	10	12	no	—
17	C₄×C₅²	—	2	12	no	—
18	C₄×C₅²	C₂×D₅	1	6	yes	—
19	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
20	C₅×D₈	—	25	1	no	—
21	D₄₀	—	5	6	no	—
22	C₂×C₅²	—	2	12	no	—
23	C₂×C₅²	D₂₀	1	6	yes	—
24	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
25	C₅⋊D₅	—	4	2	no	—
26	C₅×D₅	—	20	12	no	—
27	C₅×D₄	—	25	2	no	—
28	D₂₀	—	5	12	no	—
29	C₅×C₈	—	2	12	no	—
30	C₅×C₈	C₅×D₅	1	6	yes	complemented
31	C₅×C₈	C₅⋊D₅	1	1	yes	characteristic, complemented
32	C₅²	—	2	12	no	—
33	C₅²	D₄₀	1	6	yes	complemented
34	C₅²	C₅×D₈	1	1	yes	characteristic, complemented
35	C₂²×C₅	—	50	2	no	—
36	C₂×D₅	—	10	12	no	—
37	C₄×C₅	—	2	12	no	—
38	C₄×C₅	C₂×C₅×D₅	1	6	yes	—
39	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
40	D₈	—	25	1	no	Sylow
41	C₂×C₅	—	2	12	no	—
42	C₂×C₅	—	100	2	no	—
43	C₂×C₅	C₅×D₂₀	1	6	yes	—
44	C₂×C₅	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
45	D₅	—	20	12	no	—
46	D₄	—	25	2	no	—
47	C₈	C₅×C₅⋊D₅	1	1	yes	characteristic, complemented
48	C₅	—	2	12	no	—
49	C₅	C₅×D₄₀	1	6	yes	complemented
50	C₅	#87801	1	1	yes	characteristic, direct product factor
51	C₂²	—	50	2	no	—
52	C₄	C₂×C₅×C₅⋊D₅	1	1	yes	characteristic
53	C₂	—	100	2	no	—
54	C₂	C₅×C₄⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₄⋊(C₅⋊D₅)
commutator, cosocle	C₄×C₅²	C₂²×C₅
Frattini	C₄	C₂×C₅×C₅⋊D₅
Fitting	C₅³×C₈	C₂
socle	C₂×C₅³	D₄
hypercenter	C₅×C₈	C₅⋊D₅
hypocenter	C₅²	C₅×D₈
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
1. C₅×C₄⋊(C₅⋊D₅)	C₂	semidirect
2. C₅³×C₈	C₂	semidirect
5. #87801	C₅	direct (N × H)
9. C₄⋊(C₅⋊D₅)	C₂×C₅	semidirect
12. C₅²×C₈	D₅	semidirect
13. C₅²×C₈	C₂×C₅	semidirect
14. C₅³	D₈	semidirect
30. C₅×C₈	C₅×D₅	semidirect
31. C₅×C₈	C₅⋊D₅	semidirect
33. C₅²	D₄₀	semidirect
34. C₅²	C₅×D₈	semidirect
47. C₈	C₅×C₅⋊D₅	semidirect
49. C₅	C₅×D₄₀	semidirect
50. C₅	#87801	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₄⋊(C₅⋊D₅)	2
C₅³×C₈	2
#87801	5
C₅×D₄₀	5

Subgroups — C5×#87801 #14522625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87801 #14522625