Subgroups — C₂²⋊(Dic₂₅⋊C₅) #14522214

Order 2000.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×5₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₅⋊C₅	C₂	1	2	yes	maximal, complemented
3	C₂²×5₋¹⁺²	—	2	2	no	—
4	C₂²×5₋¹⁺²	C₄	1	2	yes	complemented
5	C₂²×5₋¹⁺²	C₂²	1	1	yes	characteristic
6	Dic₂₅⋊C₅	—	2	2	no	—
7	C₅×C₂²⋊Dic₅	—	5	1	no	maximal
8	C₂²⋊Dic₂₅	C₅	1	1	yes	maximal, characteristic, complemented
9	C₂×5₋¹⁺²	—	2	2	no	—
10	C₂×5₋¹⁺²	C₂×C₄	1	1	yes	characteristic
11	C₂×5₋¹⁺²	D₄	1	2	yes	—
12	C₂³×C₅²	D₅	1	1	yes	characteristic
13	C₂×C₅×Dic₅	—	5	2	no	—
14	C₂³×C₂₅	—	2	2	no	—
15	C₂³×C₂₅	C₂×C₅	1	1	yes	characteristic
16	C₂×Dic₂₅	C₂×C₅	1	2	yes	complemented
17	5₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅²	—	2	2	no	—
19	C₂²×C₅²	Dic₅	1	2	yes	—
20	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
21	C₅×Dic₅	—	10	2	no	—
22	C₂²×C₂₅	—	2	8	no	—
23	C₂²×C₂₅	—	2	2	no	—
24	C₂²×C₂₅	—	2	4	no	—
25	C₂²×C₂₅	—	2	2	no	—
26	C₂²×C₂₅	C₄×C₅	1	2	yes	complemented
27	C₂²×C₂₅	C₂²×C₅	1	1	yes	characteristic
28	Dic₂₅	—	2	2	no	—
29	C₅×C₂²⋊C₄	—	25	1	no	—
30	C₂²⋊Dic₅	—	5	1	no	—
31	C₂×C₅²	—	2	2	no	—
32	C₂×C₅²	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₅²	C₂²⋊D₅	1	2	yes	—
34	C₂×C₂₅	—	2	8	no	—
35	C₂×C₂₅	—	2	2	no	—
36	C₂×C₂₅	—	2	2	no	—
37	C₂×C₂₅	—	2	4	no	—
38	C₂×C₂₅	C₂×C₄×C₅	1	1	yes	characteristic
39	C₂×C₂₅	C₅×D₄	1	2	yes	—
40	C₂³×C₅	—	5	1	no	—
41	C₂³×C₅	C₅×D₅	1	1	yes	characteristic
42	C₂×C₄×C₅	—	25	2	no	—
43	C₂×Dic₅	—	5	2	no	—
44	C₅²	C₂²⋊Dic₅	1	1	yes	characteristic
45	C₂₅	—	2	2	no	—
46	C₂₅	C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
47	C₂²×C₅	—	2	2	no	—
48	C₂²×C₅	—	5	2	no	—
49	C₂²×C₅	—	5	1	no	—
50	C₂²×C₅	—	10	2	no	—
51	C₂²×C₅	C₅×Dic₅	1	2	yes	—
52	C₂²×C₅	C₂×C₅×D₅	1	1	yes	characteristic
53	C₄×C₅	—	50	2	no	—
54	Dic₅	—	10	2	no	—
55	C₂²⋊C₄	—	25	1	no	Sylow
56	C₂×C₅	—	2	2	no	—
57	C₂×C₅	—	5	1	no	—
58	C₂×C₅	—	5	2	no	—
59	C₂×C₅	—	10	2	no	—
60	C₂×C₅	C₂×C₅×Dic₅	1	1	yes	characteristic
61	C₂×C₅	C₅×C₂²⋊D₅	1	2	yes	—
62	C₂³	D₂₅⋊C₅	1	1	yes	characteristic
63	C₂×C₄	—	25	2	no	—
64	C₅	—	5	1	no	—
65	C₅	C₅×C₂²⋊Dic₅	1	1	yes	characteristic
66	C₂²	—	2	2	no	—
67	C₂²	Dic₂₅⋊C₅	1	2	yes	complemented
68	C₂²	C₂×D₂₅⋊C₅	1	1	yes	characteristic
69	C₄	—	50	2	no	—
70	C₂	—	2	2	no	—
71	C₂	C₂×Dic₂₅⋊C₅	1	1	yes	characteristic
72	C₂	C₂²⋊(D₂₅⋊C₅)	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₅⋊C₅
commutator	C₂×C₂₅	C₂×C₄×C₅
Frattini, socle	C₂²×C₅	C₂×C₅×D₅
Fitting	C₂³×5₋¹⁺²	C₂
prime radical	C₂³×C₅²	D₅
cosocle	C₂²×C₂₅	C₂²×C₅
hypercenter	C₂³	D₂₅⋊C₅
hypocenter	C₂₅	C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₅⋊C₅	C₂	semidirect
4. C₂²×5₋¹⁺²	C₄	semidirect
8. C₂²⋊Dic₂₅	C₅	semidirect
16. C₂×Dic₂₅	C₂×C₅	semidirect
17. 5₋¹⁺²	C₂²⋊C₄	semidirect
26. C₂²×C₂₅	C₄×C₅	semidirect
46. C₂₅	C₅×C₂²⋊C₄	semidirect
67. C₂²	Dic₂₅⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂³×5₋¹⁺²	2
C₂×Dic₂₅⋊C₅	2
C₅×C₂²⋊Dic₅	5
C₂²⋊Dic₂₅	5

Subgroups — C22⋊(Dic25⋊C5) #14522214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(Dic₂₅⋊C₅) #14522214