Subgroups — #168×D₂₅ #14522110

Order 2000.

82 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	#11758634	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×#168	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	C₅×Dic₂₅	C₄	1	1	yes	characteristic
7	D₅×#168	—	5	1	no	maximal
8	C₈×D₂₅	—	5	1	no	maximal
9	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
10	C₅×D₂₅	C₈	1	2	yes	complemented
11	C₄×C₅×D₅	—	5	1	no	—
12	#6029	—	5	1	no	—
13	C₅×#168	D₅	1	1	yes	characteristic
14	C₄×D₂₅	D₅	1	1	yes	characteristic
15	C₈×C₂₅	—	5	1	no	—
16	#6014	—	5	1	no	—
17	#6014	—	10	2	no	—
18	C₅×C₂₅	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	Dic₅	1	1	yes	characteristic
23	C₄×C₂₅	—	2	2	no	—
24	C₄×C₂₅	C₂×D₅	1	1	yes	characteristic
25	Dic₂₅	Dic₅	1	1	yes	characteristic
26	C₂×#168	—	25	1	no	—
27	C₈×D₅	—	25	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×Dic₅	1	1	yes	characteristic
32	D₂₅	#168	1	2	yes	direct product factor
33	C₂×C₄×C₅	—	25	1	no	—
34	C₄×D₅	—	5	1	no	—
35	C₅×C₈	—	5	1	no	—
36	#168	—	25	1	no	—
37	#168	—	25	1	no	—
38	#168	—	50	2	no	—
39	#168	D₂₅	1	1	yes	characteristic, direct product factor
40	C₅²	C₈×D₅	1	1	yes	characteristic
41	C₂₅	—	2	2	no	—
42	C₂₅	C₂×#168	1	1	yes	characteristic, complemented
43	C₂²×C₅	—	25	1	no	—
44	C₂×D₅	—	5	1	no	—
45	C₄×C₅	—	2	2	no	—
46	C₄×C₅	—	25	1	no	—
47	C₄×C₅	C₂×D₂₅	1	1	yes	characteristic
48	C₄×C₅	D₅²	1	1	yes	characteristic
49	Dic₅	—	5	1	no	—
50	C₂×C₈	—	125	1	no	Sylow
51	C₂×C₅	—	2	2	no	—
52	C₂×C₅	—	25	2	no	—
53	C₂×C₅	C₄×D₂₅	1	1	yes	characteristic
54	C₂×C₅	D₅×Dic₅	1	1	yes	characteristic
55	D₅	—	5	2	no	—
56	C₂×C₄	—	25	1	no	—
57	C₈	—	5	1	no	—
58	C₈	—	125	1	no	—
59	C₅	—	2	2	no	—
60	C₅	C₈×D₂₅	1	1	yes	characteristic, complemented
61	C₅	D₅×#168	1	1	yes	characteristic
62	C₂²	—	25	1	no	—
63	C₄	—	25	1	no	—
64	C₄	D₅×D₂₅	1	1	yes	characteristic
65	C₂	—	25	2	no	—
66	C₂	Dic₅×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₅×D₂₅
commutator, hypocenter	C₅×C₂₅	C₂×C₈
Frattini	C₄×C₅	D₅²
Fitting, cosocle	C₄×C₅×C₂₅	C₂²
socle	C₂×C₅²	C₄×D₅
prime radical	C₂×C₅×D₂₅	C₄
LCS	G ▷ C₅×C₂₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. #11758634	C₂	semidirect
3. C₂₅×#168	C₂	semidirect
10. C₅×D₂₅	C₈	semidirect
18. C₅×C₂₅	C₂×C₈	semidirect
32. D₂₅	#168	direct (N × H)
39. #168	D₂₅	direct (N × H)
42. C₂₅	C₂×#168	semidirect
60. 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
#11758634	2
C₂₅×#168	2
D₅×#168	5
C₈×D₂₅	5

Subgroups — #168×D25 #14522110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #168×D₂₅ #14522110