Subgroups — C₅²×D₄₀ #14522609

Order 2000.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₅²	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₅²
Frattini	C₄	C₂×C₅²×D₅
Fitting	C₅³×C₈	C₂
socle	C₂×C₅³	D₄
hypercenter	C₅²×C₈	D₅
hypocenter	C₅	C₅²×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅² ◁ C₄×C₅² ◁ C₅²×C₈

Complements

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

N	H ≅ G/N	type
1. C₅²×D₂₀	C₂	semidirect
2. C₅³×C₈	C₂	semidirect
6. C₅×D₄₀	C₅	direct (N × H)
10. C₅×D₂₀	C₂×C₅	semidirect
12. C₅²×C₈	D₅	semidirect
13. C₅²×C₈	C₂×C₅	semidirect
14. C₅³	D₈	semidirect
21. D₄₀	C₅²	direct (N × H)
28. D₂₀	C₂×C₅²	semidirect
30. C₅×C₈	C₅×D₅	semidirect
31. C₅×C₈	C₂×C₅²	semidirect
33. C₅²	D₄₀	direct (N × H)
34. C₅²	C₅×D₈	semidirect
47. C₈	C₅²×D₅	semidirect
49. C₅	C₅×D₄₀	direct (N × H)
50. C₅	C₅²×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₂₀	2
C₅³×C₈	2
C₅²×D₈	5
C₅×D₄₀	5

Subgroups — C52×D40 #14522609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₄₀ #14522609