Subgroups — C₈×C₅⋊D₂₅ #14522216

Order 2000.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅⋊D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758634	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₂₅	C₄	1	1	yes	characteristic
5	C₄×C₅×C₂₅	C₂²	1	1	yes	characteristic
6	#92524	C₄	1	1	yes	characteristic
7	C₈×C₅⋊D₅	—	5	1	no	maximal
8	C₈×D₂₅	—	5	5	no	maximal
9	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
10	C₅⋊D₂₅	C₈	1	2	yes	direct product factor
11	C₄×C₅⋊D₅	—	5	1	no	—
12	C₅²×C₈	D₅	1	1	yes	characteristic
13	#6029	—	5	1	no	—
14	C₄×D₂₅	—	5	5	no	—
15	C₈×C₂₅	D₅	1	5	yes	complemented
16	#6014	—	5	5	no	—
17	C₅×C₂₅	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅⋊D₅	—	5	1	no	—
19	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
20	#1039	—	5	1	no	—
21	C₂×D₂₅	—	5	5	no	—
22	C₄×C₂₅	C₂×D₅	1	5	yes	—
23	Dic₂₅	—	5	5	no	—
24	C₈×D₅	—	25	1	no	—
25	C₈×D₅	—	25	5	no	—
26	C₂×C₅²	C₄×D₅	1	1	yes	characteristic
27	C₅⋊D₅	—	5	2	no	—
28	C₂×C₂₅	C₄×D₅	1	5	yes	—
29	D₂₅	—	5	10	no	—
30	C₄×D₅	—	25	5	no	—
31	C₄×D₅	—	25	1	no	—
32	C₅×C₈	D₂₅	1	5	yes	complemented
33	C₅×C₈	C₅⋊D₅	1	1	yes	characteristic
34	#168	—	25	5	no	—
35	#168	—	25	1	no	—
36	C₅²	C₈×D₅	1	1	yes	characteristic
37	C₂₅	C₈×D₅	1	5	yes	complemented
38	C₂×D₅	—	25	5	no	—
39	C₂×D₅	—	25	1	no	—
40	C₄×C₅	C₂×D₂₅	1	5	yes	—
41	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
42	Dic₅	—	25	5	no	—
43	Dic₅	—	25	1	no	—
44	C₂×C₈	—	125	1	no	Sylow
45	C₂×C₅	C₄×D₂₅	1	5	yes	—
46	C₂×C₅	C₄×C₅⋊D₅	1	1	yes	characteristic
47	D₅	—	25	10	no	—
48	D₅	—	25	2	no	—
49	C₂×C₄	—	125	1	no	—
50	C₈	—	125	1	no	—
51	C₈	C₅⋊D₂₅	1	1	yes	characteristic, direct product factor
52	C₅	C₈×D₂₅	1	5	yes	complemented
53	C₅	C₈×C₅⋊D₅	1	1	yes	characteristic
54	C₂²	—	125	1	no	—
55	C₄	—	125	1	no	—
56	C₄	C₂×C₅⋊D₂₅	1	1	yes	characteristic
57	C₂	—	125	2	no	—
58	C₂	C₄×C₅⋊D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	C₅⋊D₂₅
commutator, hypocenter	C₅×C₂₅	C₂×C₈
Frattini	C₄×C₅	C₂×C₅⋊D₅
Fitting	C₅×C₈×C₂₅	C₂
socle	C₂×C₅²	C₄×D₅
prime radical	C₂×C₅⋊D₂₅	C₄
cosocle	C₄×C₅×C₂₅	C₂²
LCS	G ▷ C₅×C₂₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₅×C₈×C₂₅	C₂	semidirect
3. #11758634	C₂	semidirect
10. C₅⋊D₂₅	C₈	direct (N × H)
15. C₈×C₂₅	D₅	semidirect
17. C₅×C₂₅	C₂×C₈	semidirect
32. C₅×C₈	D₂₅	semidirect
37. C₂₅	C₈×D₅	semidirect
51. C₈	C₅⋊D₂₅	direct (N × H)
52. C₅	C₈×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅⋊D₂₅	2
C₅×C₈×C₂₅	2
#11758634	2
C₈×C₅⋊D₅	5
C₈×D₂₅	5

Subgroups — C8×C5⋊D25 #14522216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₅⋊D₂₅ #14522216