Subgroups — C₅×D₂₀₀ #14522155

Order 2000.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₀₀	C₂	1	2	yes	maximal, complemented
2	C₅×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₂₅	—	2	2	no	—
4	C₄×C₅×C₂₅	C₂²	1	1	yes	characteristic
5	C₅×D₄₀	—	5	1	no	maximal
6	D₂₀₀	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅×C₂₅	D₄	1	1	yes	characteristic
8	C₅×D₂₅	—	4	2	no	—
9	C₅×D₂₀	—	5	2	no	—
10	C₅²×C₈	D₅	1	1	yes	characteristic
11	D₁₀₀	C₂×C₅	1	2	yes	complemented
12	C₈×C₂₅	—	2	2	no	—
13	C₈×C₂₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₂₅	D₈	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅×D₅	—	10	2	no	—
16	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
17	C₂×D₂₅	—	2	2	no	—
18	C₄×C₂₅	—	2	2	no	—
19	C₄×C₂₅	C₂²×C₅	1	1	yes	characteristic
20	C₅×D₈	—	25	1	no	—
21	D₄₀	—	5	1	no	—
22	C₂×C₅²	D₂₀	1	1	yes	characteristic
23	C₅×D₅	—	20	2	no	—
24	C₂×C₂₅	—	2	2	no	—
25	C₂×C₂₅	C₅×D₄	1	1	yes	characteristic
26	D₂₅	—	4	2	no	—
27	C₅×D₄	—	25	2	no	—
28	D₂₀	—	5	2	no	—
29	C₅×C₈	—	2	2	no	—
30	C₅×C₈	D₂₅	1	1	yes	characteristic, complemented
31	C₅×C₈	C₅×D₅	1	1	yes	characteristic
32	C₅²	D₄₀	1	1	yes	characteristic
33	C₂₅	—	2	2	no	—
34	C₂₅	C₅×D₈	1	1	yes	characteristic, complemented
35	C₂²×C₅	—	50	2	no	—
36	C₂×D₅	—	10	2	no	—
37	C₄×C₅	—	2	2	no	—
38	C₄×C₅	C₂×D₂₅	1	1	yes	characteristic
39	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
40	D₈	—	25	1	no	Sylow
41	C₂×C₅	—	2	2	no	—
42	C₂×C₅	—	100	2	no	—
43	C₂×C₅	D₁₀₀	1	1	yes	characteristic
44	C₂×C₅	C₅×D₂₀	1	1	yes	characteristic
45	D₅	—	20	2	no	—
46	D₄	—	25	2	no	—
47	C₈	C₅×D₂₅	1	1	yes	characteristic, complemented
48	C₅	—	2	2	no	—
49	C₅	D₂₀₀	1	1	yes	characteristic, direct product factor
50	C₅	C₅×D₄₀	1	1	yes	characteristic
51	C₂²	—	50	2	no	—
52	C₄	C₂×C₅×D₂₅	1	1	yes	characteristic
53	C₂	—	100	2	no	—
54	C₂	C₅×D₁₀₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₁₀₀
commutator, cosocle	C₄×C₂₅	C₂²×C₅
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₅×C₈×C₂₅	C₂
socle	C₂×C₅²	D₂₀
hypercenter	C₅×C₈	D₂₅
hypocenter	C₂₅	C₅×D₈
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
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×D₁₀₀	C₂	semidirect
2. C₅×C₈×C₂₅	C₂	semidirect
6. D₂₀₀	C₅	direct (N × H)
11. D₁₀₀	C₂×C₅	semidirect
13. C₈×C₂₅	C₂×C₅	semidirect
14. C₅×C₂₅	D₈	semidirect
30. C₅×C₈	D₂₅	semidirect
34. C₂₅	C₅×D₈	semidirect
47. C₈	C₅×D₂₅	semidirect
49. C₅	D₂₀₀	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×D₁₀₀	2
C₅×C₈×C₂₅	2
C₅×D₄₀	5
D₂₀₀	5

Subgroups — C5×D200 #14522155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₂₀₀ #14522155