Subgroups — C₂₅×#677 #14522158

Order 2000.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂₅×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₂₅	—	2	1	no	—
5	C₄×C₅×C₂₅	C₂²	1	1	yes	characteristic
6	Dic₅×C₂₅	—	2	1	no	—
7	C₅×#677	C₅	1	1	yes	maximal, characteristic
8	SD₁₆×C₂₅	—	5	1	no	maximal
9	C₂×C₅×C₂₅	D₄	1	1	yes	characteristic
10	D₅×C₂₅	—	4	1	no	—
11	C₅×D₂₀	C₂×C₅	1	1	yes	characteristic
12	C₅×Dic₁₀	C₂×C₅	1	1	yes	characteristic
13	C₅²×C₈	C₂×C₅	1	1	yes	characteristic
14	Q₈×C₂₅	—	5	1	no	—
15	D₄×C₂₅	—	5	1	no	—
16	C₈×C₂₅	—	2	2	no	—
17	C₈×C₂₅	D₅	1	1	yes	characteristic, complemented
18	C₅×C₂₅	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×D₅	—	2	1	no	—
20	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
21	C₅×Dic₅	—	2	1	no	—
22	C₂²×C₂₅	—	10	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×SD₁₆	—	5	1	no	—
27	#677	C₂₅	1	1	yes	characteristic, direct product factor
28	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
29	C₅×D₅	—	4	1	no	—
30	C₂×C₂₅	—	2	2	no	—
31	C₂×C₂₅	—	20	1	no	—
32	C₂×C₂₅	D₂₀	1	1	yes	characteristic
33	C₅×Q₈	—	5	1	no	—
34	C₅×D₄	—	5	1	no	—
35	D₂₀	C₂×C₂₅	1	1	yes	characteristic
36	Dic₁₀	C₂×C₂₅	1	1	yes	characteristic, complemented
37	C₅×C₈	—	2	2	no	—
38	C₅×C₈	C₂×C₂₅	1	1	yes	characteristic, complemented
39	C₅×C₈	C₅×D₅	1	1	yes	characteristic
40	C₅²	C₅×SD₁₆	1	1	yes	characteristic
41	C₂₅	—	2	2	no	—
42	C₂₅	#677	1	1	yes	characteristic, direct product factor
43	C₂²×C₅	—	10	1	no	—
44	C₂×D₅	—	2	1	no	—
45	C₄×C₅	—	2	2	no	—
46	C₄×C₅	—	10	1	no	—
47	C₄×C₅	C₂²×C₂₅	1	1	yes	characteristic
48	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
49	Dic₅	—	2	1	no	—
50	SD₁₆	—	5	1	no	Sylow
51	C₂×C₅	—	2	2	no	—
52	C₂×C₅	—	20	1	no	—
53	C₂×C₅	D₄×C₂₅	1	1	yes	characteristic
54	C₂×C₅	C₅×D₂₀	1	1	yes	characteristic
55	D₅	—	4	1	no	—
56	Q₈	—	5	1	no	—
57	D₄	—	5	1	no	—
58	C₈	D₅×C₂₅	1	1	yes	characteristic, complemented
59	C₅	—	2	2	no	—
60	C₅	SD₁₆×C₂₅	1	1	yes	characteristic, complemented
61	C₅	C₅×#677	1	1	yes	characteristic
62	C₂²	—	10	1	no	—
63	C₄	—	10	1	no	—
64	C₄	C₂×D₅×C₂₅	1	1	yes	characteristic
65	C₂	—	20	1	no	—
66	C₂	C₂₅×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	D₂₀
commutator	C₄×C₅	C₂²×C₂₅
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₅×C₈×C₂₅	C₂
socle	C₂×C₅²	C₅×D₄
prime radical	C₅×D₂₀	C₂×C₅
cosocle	C₄×C₅²	C₂²×C₅
hypercenter	C₈×C₂₅	D₅
hypocenter	C₅	SD₁₆×C₂₅
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₂₅ ◁ C₄×C₂₅ ◁ C₈×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₂₅×Dic₁₀	C₂	semidirect
3. C₅×C₈×C₂₅	C₂	semidirect
17. C₈×C₂₅	D₅	semidirect
18. C₅×C₂₅	SD₁₆	semidirect
27. #677	C₂₅	direct (N × H)
36. Dic₁₀	C₂×C₂₅	semidirect
38. C₅×C₈	C₂×C₂₅	semidirect
42. C₂₅	#677	direct (N × H)
58. C₈	D₅×C₂₅	semidirect
60. C₅	SD₁₆×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×D₂₀	2
C₂₅×Dic₁₀	2
C₅×C₈×C₂₅	2
C₅×#677	5
SD₁₆×C₂₅	5

Subgroups — C25×#677 #14522158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#677 #14522158