Subgroups — C₂₅×#493 #13098642

Order 1600.

243 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₂₅	C₂	1	4	yes	maximal, complemented
2	C₂₅×#127	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₂₅	—	2	4	no	—
5	C₂×D₄×C₂₅	C₂²	1	4	yes	—
6	D₈×C₂₅	—	2	8	no	—
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	C₄²×C₂₅	C₂²	1	1	yes	characteristic
9	C₅×#493	C₅	1	1	yes	maximal, characteristic
10	C₂³×C₂₅	—	2	4	no	—
11	D₄×C₂₅	—	2	8	no	—
12	D₄×C₂₅	—	4	8	no	—
13	C₂×C₄×C₂₅	D₄	1	2	yes	—
14	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
15	C₈×C₂₅	D₄	1	4	yes	complemented
16	C₂×C₅×D₈	C₂×C₅	1	4	yes	—
17	C₅×#127	C₂×C₅	1	2	yes	—
18	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₂₅	—	4	4	no	—
20	C₂²×C₂₅	—	4	8	no	—
21	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
22	C₄×C₂₅	D₈	1	4	yes	complemented
23	C₄×C₂₅	C₂×D₄	1	2	yes	—
24	C₂×C₅×D₄	—	2	4	no	—
25	C₂×C₅×D₄	C₂²×C₅	1	4	yes	—
26	C₅×D₈	—	2	8	no	—
27	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
28	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
29	#493	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₂₅	—	8	4	no	—
31	C₂×C₂₅	#127	1	1	yes	characteristic
32	C₂×C₂₅	C₂×D₈	1	2	yes	—
33	C₂³×C₅	—	2	4	no	—
34	C₅×D₄	—	2	8	no	—
35	C₅×D₄	—	4	8	no	—
36	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
37	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
38	C₅×C₈	C₅×D₄	1	4	yes	—
39	C₂×D₈	C₂×C₂₅	1	4	yes	complemented
40	#127	C₂×C₂₅	1	2	yes	complemented
41	C₄×C₈	C₂×C₂₅	1	1	yes	characteristic, complemented
42	C₂₅	#493	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	—	4	4	no	—
44	C₂²×C₅	—	4	8	no	—
45	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
46	C₄×C₅	C₅×D₈	1	4	yes	—
47	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
48	C₂×D₄	—	2	4	no	—
49	C₂×D₄	C₂²×C₂₅	1	4	yes	—
50	D₈	—	2	8	no	—
51	C₂×C₈	C₂²×C₂₅	1	2	yes	—
52	C₄²	C₂²×C₂₅	1	1	yes	characteristic
53	C₂×C₅	—	8	4	no	—
54	C₂×C₅	C₅×#127	1	1	yes	characteristic
55	C₂×C₅	C₂×C₅×D₈	1	2	yes	—
56	C₂³	—	2	4	no	—
57	D₄	—	2	8	no	—
58	D₄	—	4	8	no	—
59	C₂×C₄	D₄×C₂₅	1	2	yes	—
60	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
61	C₈	D₄×C₂₅	1	4	yes	complemented
62	C₅	C₅×#493	1	1	yes	characteristic
63	C₂²	—	4	4	no	—
64	C₂²	—	4	8	no	—
65	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
66	C₄	D₈×C₂₅	1	4	yes	complemented
67	C₄	C₂×D₄×C₂₅	1	2	yes	—
68	C₂	—	8	4	no	—
69	C₂	C₂₅×#127	1	1	yes	characteristic
70	C₂	C₂×D₈×C₂₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle	C₂²×C₅	C₂×C₅×D₄
prime radical	C₅×#493	C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ C₄²×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×C₂₅	C₂	semidirect
2. C₂₅×#127	C₂	semidirect
3. C₄×C₈×C₂₅	C₂	semidirect
15. C₈×C₂₅	D₄	semidirect
22. C₄×C₂₅	D₈	semidirect
29. #493	C₂₅	direct (N × H)
39. C₂×D₈	C₂×C₂₅	semidirect
40. #127	C₂×C₂₅	semidirect
41. C₄×C₈	C₂×C₂₅	semidirect
42. C₂₅	#493	direct (N × H)
61. C₈	D₄×C₂₅	semidirect
66. C₄	D₈×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₂₅	2
C₂₅×#127	2
C₄×C₈×C₂₅	2
C₅×#493	5

Subgroups — C25×#493 #13098642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#493 #13098642