Subgroups — C₈×D₂₅⋊C₅ #14522167

Order 2000.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₂₅⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₈×5₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	#6014⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₅⋊C₅	C₄	1	1	yes	characteristic
5	C₄×5₋¹⁺²	C₂²	1	1	yes	characteristic
6	Dic₂₅⋊C₅	C₄	1	1	yes	characteristic
7	C₅×C₈×D₅	—	5	1	no	maximal
8	C₈×D₂₅	C₅	1	1	yes	maximal, characteristic, complemented
9	C₂×5₋¹⁺²	C₂×C₄	1	1	yes	characteristic
10	D₂₅⋊C₅	C₈	1	2	yes	direct product factor
11	C₄×C₅×D₅	—	5	1	no	—
12	C₅²×C₈	D₅	1	1	yes	characteristic
13	C₅×#168	—	5	1	no	—
14	C₄×D₂₅	C₂×C₅	1	1	yes	characteristic
15	C₈×C₂₅	—	2	2	no	—
16	C₈×C₂₅	C₂×C₅	1	1	yes	characteristic, complemented
17	#6014	C₂×C₅	1	1	yes	characteristic, complemented
18	5₋¹⁺²	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×D₅	—	5	1	no	—
20	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
21	C₅×Dic₅	—	5	1	no	—
22	C₂×D₂₅	C₄×C₅	1	1	yes	characteristic
23	C₄×C₂₅	—	2	2	no	—
24	C₄×C₂₅	C₂²×C₅	1	1	yes	characteristic
25	Dic₂₅	C₄×C₅	1	1	yes	characteristic
26	C₂×C₅×C₈	—	25	1	no	—
27	C₈×D₅	—	5	1	no	—
28	C₂×C₅²	C₄×D₅	1	1	yes	characteristic
29	C₅×D₅	—	5	2	no	—
30	C₂×C₂₅	—	2	2	no	—
31	C₂×C₂₅	C₂×C₄×C₅	1	1	yes	characteristic
32	D₂₅	C₅×C₈	1	2	yes	complemented
33	C₂×C₄×C₅	—	25	1	no	—
34	C₄×D₅	—	5	1	no	—
35	C₅×C₈	—	5	1	no	—
36	C₅×C₈	—	25	1	no	—
37	C₅×C₈	C₅×D₅	1	1	yes	characteristic
38	#168	—	5	1	no	—
39	C₅²	C₈×D₅	1	1	yes	characteristic
40	C₂₅	—	2	2	no	—
41	C₂₅	C₂×C₅×C₈	1	1	yes	characteristic, complemented
42	C₂²×C₅	—	25	1	no	—
43	C₂×D₅	—	5	1	no	—
44	C₄×C₅	—	5	1	no	—
45	C₄×C₅	—	25	1	no	—
46	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
47	Dic₅	—	5	1	no	—
48	C₂×C₈	—	25	1	no	Sylow
49	C₂×C₅	—	5	1	no	—
50	C₂×C₅	—	25	2	no	—
51	C₂×C₅	C₄×C₅×D₅	1	1	yes	characteristic
52	D₅	—	5	2	no	—
53	C₂×C₄	—	25	1	no	—
54	C₈	—	25	1	no	—
55	C₈	D₂₅⋊C₅	1	1	yes	characteristic, direct product factor
56	C₅	—	5	1	no	—
57	C₅	C₅×C₈×D₅	1	1	yes	characteristic
58	C₂²	—	25	1	no	—
59	C₄	—	25	1	no	—
60	C₄	C₂×D₂₅⋊C₅	1	1	yes	characteristic
61	C₂	—	25	2	no	—
62	C₂	C₄×D₂₅⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	D₂₅⋊C₅
commutator, hypocenter	C₂₅	C₂×C₅×C₈
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₈×5₋¹⁺²	C₂
socle	C₂×C₅	C₄×C₅×D₅
prime radical	C₂×D₂₅⋊C₅	C₄
cosocle	C₄×C₂₅	C₂²×C₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₈×5₋¹⁺²	C₂	semidirect
3. #6014⋊C₅	C₂	semidirect
8. C₈×D₂₅	C₅	semidirect
10. D₂₅⋊C₅	C₈	direct (N × H)
16. C₈×C₂₅	C₂×C₅	semidirect
17. #6014	C₂×C₅	semidirect
18. 5₋¹⁺²	C₂×C₈	semidirect
32. D₂₅	C₅×C₈	semidirect
41. C₂₅	C₂×C₅×C₈	semidirect
55. C₈	D₂₅⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×D₂₅⋊C₅	2
C₈×5₋¹⁺²	2
#6014⋊C₅	2
C₅×C₈×D₅	5
C₈×D₂₅	5

Subgroups — C8×D25⋊C5 #14522167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₂₅⋊C₅ #14522167