Subgroups — C₂×C₅×D₂₀ #87889

Order 400.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₂₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₅×D₅	—	2	4	no	—
6	C₂×C₅×D₅	C₂²	1	4	yes	complemented
7	C₄×C₅²	C₂²	1	2	yes	complemented
8	C₂×C₅×D₄	—	5	1	no	maximal
9	C₂×D₂₀	C₅	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₅²	D₄	1	2	yes	complemented
11	C₂×C₅²	C₂³	1	1	yes	characteristic
12	C₅×D₅	—	2	4	no	—
13	C₂³×C₅	—	5	2	no	—
14	C₂²×D₅	C₂×C₅	1	2	yes	complemented
15	C₅×D₄	—	5	4	no	—
16	C₂×C₄×C₅	—	2	2	no	—
17	C₂×C₄×C₅	D₅	1	1	yes	characteristic, complemented
18	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic, complemented
19	D₂₀	C₂×C₅	1	4	yes	direct product factor
20	C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅	—	2	2	no	—
22	C₂²×C₅	—	5	4	no	—
23	C₂²×C₅	—	10	4	no	—
24	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
25	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
26	C₂×D₅	—	2	4	no	—
27	C₂×D₅	C₂²×C₅	1	4	yes	complemented
28	C₄×C₅	—	2	4	no	—
29	C₄×C₅	C₂×D₅	1	2	yes	complemented
30	C₄×C₅	C₂²×C₅	1	2	yes	complemented
31	C₂×D₄	—	5	1	no	Sylow
32	C₂×C₅	—	2	4	no	—
33	C₂×C₅	—	2	2	no	—
34	C₂×C₅	—	10	4	no	—
35	C₂×C₅	D₂₀	1	2	yes	direct product factor
36	C₂×C₅	C₅×D₄	1	2	yes	complemented
37	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
38	C₂×C₅	C₂³×C₅	1	1	yes	characteristic
39	D₅	—	2	4	no	—
40	C₂³	—	5	2	no	—
41	D₄	—	5	4	no	—
42	C₂×C₄	C₅×D₅	1	1	yes	characteristic, complemented
43	C₅	—	2	2	no	—
44	C₅	C₂×D₂₀	1	1	yes	characteristic, direct product factor
45	C₅	C₂×C₅×D₄	1	1	yes	characteristic, complemented
46	C₂²	—	5	4	no	—
47	C₂²	—	10	4	no	—
48	C₂²	C₂×C₅×D₅	1	1	yes	characteristic
49	C₄	C₂×C₅×D₅	1	2	yes	complemented
50	C₂	—	10	4	no	—
51	C₂	C₅×D₂₀	1	2	yes	direct product factor
52	C₂	C₂²×C₅×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₅
commutator, cosocle	C₂×C₅	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₅
Fitting	C₂×C₄×C₅²	C₂
socle	C₂²×C₅²	C₂²
hypercenter	C₂×C₄×C₅	D₅
hypocenter	C₅	C₂×C₅×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₅	C₂	semidirect
2. C₂×C₄×C₅²	C₂	semidirect
3. C₅×D₂₀	C₂	direct (N × H)
6. C₂×C₅×D₅	C₂²	semidirect
7. C₄×C₅²	C₂²	semidirect
9. C₂×D₂₀	C₅	direct (N × H)
10. C₂×C₅²	D₄	semidirect
14. C₂²×D₅	C₂×C₅	semidirect
17. C₂×C₄×C₅	D₅	semidirect
18. C₂×C₄×C₅	C₂×C₅	semidirect
19. D₂₀	C₂×C₅	direct (N × H)
20. C₅²	C₂×D₄	semidirect
27. C₂×D₅	C₂²×C₅	semidirect
29. C₄×C₅	C₂×D₅	semidirect
30. C₄×C₅	C₂²×C₅	semidirect
35. C₂×C₅	D₂₀	direct (N × H)
36. C₂×C₅	C₅×D₄	semidirect
42. C₂×C₄	C₅×D₅	semidirect
44. C₅	C₂×D₂₀	direct (N × H)
45. C₅	C₂×C₅×D₄	semidirect
49. C₄	C₂×C₅×D₅	semidirect
51. C₂	C₅×D₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₅	2
C₂×C₄×C₅²	2
C₅×D₂₀	2
C₂×C₅×D₄	5
C₂×D₂₀	5

Subgroups — C2×C5×D20 #87889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₂₀ #87889