Subgroups — C₂₅×#689 #14522206

Order 2000.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₅×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#168	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₂₅	—	2	1	no	—
5	C₄×C₅×C₂₅	C₂²	1	1	yes	characteristic
6	Dic₅×C₂₅	—	2	1	no	—
7	C₅×#689	C₅	1	1	yes	maximal, characteristic
8	Q₁₆×C₂₅	—	5	1	no	maximal
9	C₂×C₅×C₂₅	D₄	1	1	yes	characteristic
10	C₅²×Q₈	C₂×C₅	1	1	yes	characteristic
11	C₅×Dic₁₀	C₂×C₅	1	1	yes	characteristic
12	C₅×#168	C₂×C₅	1	1	yes	characteristic
13	Q₈×C₂₅	—	2	2	no	—
14	Q₈×C₂₅	—	5	1	no	—
15	Q₈×C₂₅	D₅	1	1	yes	characteristic
16	C₈×C₂₅	—	5	1	no	—
17	C₅×C₂₅	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅²	—	2	1	no	—
19	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
20	C₅×Dic₅	—	2	1	no	—
21	C₄×C₂₅	—	2	4	no	—
22	C₄×C₂₅	—	2	1	no	—
23	C₄×C₂₅	—	2	2	no	—
24	C₄×C₂₅	—	10	1	no	—
25	C₄×C₂₅	C₂×D₅	1	1	yes	characteristic
26	C₅×Q₁₆	—	5	1	no	—
27	#689	C₂₅	1	1	yes	characteristic, direct product factor
28	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
29	C₂×C₂₅	—	2	2	no	—
30	C₂×C₂₅	C₂²⋊D₅	1	1	yes	characteristic
31	C₅×Q₈	—	2	2	no	—
32	C₅×Q₈	—	5	1	no	—
33	C₅×Q₈	C₂×C₂₅	1	1	yes	characteristic
34	C₅×Q₈	C₅×D₅	1	1	yes	characteristic
35	Dic₁₀	C₂×C₂₅	1	1	yes	characteristic
36	C₅×C₈	—	5	1	no	—
37	#168	C₂×C₂₅	1	1	yes	characteristic
38	C₅²	C₅×Q₁₆	1	1	yes	characteristic
39	C₂₅	—	2	2	no	—
40	C₂₅	#689	1	1	yes	characteristic, direct product factor
41	C₄×C₅	—	2	4	no	—
42	C₄×C₅	—	2	1	no	—
43	C₄×C₅	—	2	1	no	—
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	—	10	1	no	—
46	C₄×C₅	C₂²×C₂₅	1	1	yes	characteristic
47	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
48	Dic₅	—	2	1	no	—
49	Q₁₆	—	5	1	no	Sylow
50	C₂×C₅	—	2	2	no	—
51	C₂×C₅	D₄×C₂₅	1	1	yes	characteristic
52	C₂×C₅	C₅×C₂²⋊D₅	1	1	yes	characteristic
53	Q₈	—	5	1	no	—
54	Q₈	D₅×C₂₅	1	1	yes	characteristic
55	C₈	—	5	1	no	—
56	C₅	—	2	2	no	—
57	C₅	Q₁₆×C₂₅	1	1	yes	characteristic, complemented
58	C₅	C₅×#689	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	10	1	no	—
61	C₄	C₂×D₅×C₂₅	1	1	yes	characteristic
62	C₂	C₂₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	C₂²⋊D₅
commutator	C₄×C₅	C₂²×C₂₅
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₅×Q₈×C₂₅	C₂
socle, prime radical	C₂×C₅²	C₅×D₄
cosocle	C₄×C₅²	C₂²×C₅
hypercenter	Q₈×C₂₅	D₅
hypocenter	C₅	Q₁₆×C₂₅
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₂₅ ◁ C₄×C₂₅ ◁ Q₈×C₂₅

Complements

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

N	H ≅ G/N	type
17. C₅×C₂₅	Q₁₆	semidirect
27. #689	C₂₅	direct (N × H)
40. C₂₅	#689	direct (N × H)
57. C₅	Q₁₆×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×Q₈×C₂₅	2
C₂₅×Dic₁₀	2
C₂₅×#168	2
C₅×#689	5
Q₁₆×C₂₅	5

Subgroups — C25×#689 #14522206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#689 #14522206