Subgroups — C₂×#6038 #87883

Order 400.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#6038	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅²	C₂²	1	1	yes	characteristic
6	C₂×C₅⋊D₅	—	2	2	no	—
7	C₂×C₅⋊D₅	C₂²	1	2	yes	complemented
8	C₂×C₅×D₅	—	2	2	no	—
9	C₂×C₅×D₅	C₂²	1	2	yes	complemented
10	C₅×Dic₅	C₂²	1	2	yes	complemented
11	C₂×C₂²⋊D₅	—	5	1	no	maximal
12	C₂×D₂₀	—	5	1	no	maximal
13	C₂×C₅²	D₄	1	2	yes	complemented
14	C₂×C₅²	C₂³	1	1	yes	characteristic
15	C₅⋊D₅	—	2	2	no	—
16	C₅×D₅	—	2	2	no	—
17	C₂³×C₅	—	5	1	no	—
18	C₂²×D₅	—	5	1	no	—
19	C₂²×D₅	—	5	1	no	—
20	C₂²×D₅	—	10	2	no	—
21	C₂²×D₅	D₅	1	1	yes	characteristic, complemented
22	C₂×C₄×C₅	—	5	1	no	—
23	C₂²⋊D₅	—	5	4	no	—
24	C₂×Dic₅	D₅	1	1	yes	characteristic, complemented
25	D₂₀	—	5	4	no	—
26	C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₅	—	2	2	no	—
28	C₂²×C₅	—	5	2	no	—
29	C₂²×C₅	—	10	2	no	—
30	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
31	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
32	C₂×D₅	—	2	2	no	—
33	C₂×D₅	—	5	2	no	—
34	C₂×D₅	—	5	2	no	—
35	C₂×D₅	—	10	4	no	—
36	C₂×D₅	—	10	8	no	—
37	C₂×D₅	—	10	2	no	—
38	C₂×D₅	—	10	2	no	—
39	C₂×D₅	C₂×D₅	1	2	yes	complemented
40	C₄×C₅	—	5	2	no	—
41	Dic₅	C₂×D₅	1	2	yes	complemented
42	C₂×D₄	—	25	1	no	Sylow
43	C₂×C₅	—	2	4	no	—
44	C₂×C₅	—	2	2	no	—
45	C₂×C₅	—	10	2	no	—
46	C₂×C₅	D₂₀	1	2	yes	complemented
47	C₂×C₅	C₂²⋊D₅	1	2	yes	complemented
48	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
49	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
50	D₅	—	2	2	no	—
51	D₅	—	10	8	no	—
52	D₅	—	10	2	no	—
53	D₅	—	10	2	no	—
54	C₂³	—	5	1	no	—
55	C₂³	—	25	1	no	—
56	D₄	—	25	4	no	—
57	C₂×C₄	—	5	1	no	—
58	C₅	—	2	2	no	—
59	C₅	C₂×D₂₀	1	1	yes	characteristic, complemented
60	C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic, complemented
61	C₂²	—	5	2	no	—
62	C₂²	—	10	2	no	—
63	C₂²	—	25	2	no	—
64	C₂²	—	50	2	no	—
65	C₂²	D₅²	1	1	yes	characteristic
66	C₄	—	5	2	no	—
67	C₂	—	10	2	no	—
68	C₂	—	50	2	no	—
69	C₂	#6038	1	2	yes	direct product factor
70	C₂	C₂×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₅²
commutator, cosocle	C₂×C₅²	C₂³
Frattini	C₂	C₂×D₅²
Fitting, socle	C₂²×C₅²	C₂²
hypocenter	C₅²	C₂×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅⋊D₅	C₂	semidirect
2. C₂²×C₅×D₅	C₂	semidirect
3. C₂×C₅×Dic₅	C₂	semidirect
4. #6038	C₂	direct (N × H)
7. C₂×C₅⋊D₅	C₂²	semidirect
9. C₂×C₅×D₅	C₂²	semidirect
10. C₅×Dic₅	C₂²	semidirect
13. C₂×C₅²	D₄	semidirect
21. C₂²×D₅	D₅	semidirect
24. C₂×Dic₅	D₅	semidirect
26. C₅²	C₂×D₄	semidirect
39. C₂×D₅	C₂×D₅	semidirect
41. Dic₅	C₂×D₅	semidirect
46. C₂×C₅	D₂₀	semidirect
47. C₂×C₅	C₂²⋊D₅	semidirect
59. C₅	C₂×D₂₀	semidirect
60. C₅	C₂×C₂²⋊D₅	semidirect
69. C₂	#6038	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
C₂²×C₅×D₅	2
C₂×C₅×Dic₅	2
#6038	2
C₂×C₂²⋊D₅	5
C₂×D₂₀	5

Subgroups — C2×#6038 #87883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6038 #87883