Subgroups — C₂₅⋊#401 #13097938

Order 1600.

177 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#95	C₂	1	1	yes	maximal, characteristic
2	#11716379	C₂	1	3	yes	maximal
3	#11716379	C₂	1	3	yes	maximal
4	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
5	C₂²×Dic₂₅	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₅	C₂²	1	3	yes	—
7	C₅⋊#401	—	5	1	no	maximal
8	C₂³×C₂₅	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₂₅	—	2	3	no	—
10	C₂×C₄×C₂₅	—	2	6	no	—
11	C₂×Dic₂₅	—	2	3	no	—
12	C₂×Dic₂₅	—	2	3	no	—
13	C₂×Dic₂₅	—	2	3	no	—
14	C₂×Dic₂₅	—	2	3	no	—
15	C₅×#95	D₅	1	1	yes	characteristic
16	#3963	—	5	3	no	—
17	#3963	—	5	3	no	—
18	C₂²×C₂₅	#41	1	3	yes	—
19	C₂²×C₂₅	#41	1	3	yes	—
20	C₂²×C₂₅	#41	1	1	yes	characteristic
21	C₄×C₂₅	—	4	3	no	—
22	Dic₂₅	—	4	1	no	—
23	Dic₂₅	—	4	3	no	—
24	C₂²×C₄×C₅	C₂×D₅	1	3	yes	—
25	C₂²×Dic₅	—	5	1	no	—
26	C₂²×Dic₅	—	5	3	no	—
27	#401	—	25	1	no	Sylow
28	C₂×C₂₅	#126	1	1	yes	characteristic
29	C₂×C₂₅	#126	1	3	yes	—
30	C₂×C₂₅	#126	1	3	yes	—
31	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
32	C₂×C₄×C₅	—	2	3	no	—
33	C₂×C₄×C₅	—	2	6	no	—
34	C₂×Dic₅	—	10	3	no	—
35	C₂×Dic₅	—	10	3	no	—
36	C₂×Dic₅	—	10	3	no	—
37	C₂×Dic₅	—	10	3	no	—
38	#95	—	25	3	no	—
39	#95	—	25	3	no	—
40	#95	D₂₅	1	1	yes	characteristic
41	C₂₅	#401	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₅	#709	1	3	yes	—
43	C₂²×C₅	#711	1	3	yes	—
44	C₂²×C₅	#713	1	1	yes	characteristic
45	C₄×C₅	—	4	3	no	—
46	Dic₅	—	20	1	no	—
47	Dic₅	—	20	3	no	—
48	C₂²×C₄	—	25	1	no	—
49	C₂²×C₄	—	25	3	no	—
50	C₂²×C₄	C₂×D₂₅	1	3	yes	—
51	C₂×C₅	#4022	1	1	yes	characteristic
52	C₂×C₅	#4025	1	3	yes	—
53	C₂×C₅	#4044	1	3	yes	—
54	C₂³	C₂²×D₂₅	1	1	yes	characteristic
55	C₂×C₄	—	2	3	no	—
56	C₂×C₄	—	2	6	no	—
57	C₂×C₄	—	50	3	no	—
58	C₂×C₄	—	50	3	no	—
59	C₂×C₄	—	50	3	no	—
60	C₂×C₄	—	50	3	no	—
61	C₅	C₅⋊#401	1	1	yes	characteristic
62	C₂²	#87744	1	3	yes	—
63	C₂²	#87746	1	3	yes	—
64	C₂²	#87748	1	1	yes	characteristic
65	C₄	—	4	3	no	—
66	C₄	—	100	1	no	—
67	C₄	—	100	3	no	—
68	C₂	#11716438	1	1	yes	characteristic
69	C₂	#11716441	1	3	yes	—
70	C₂	#11716460	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂³×C₂₅	C₂³
Frattini, socle, prime radical	C₂³×C₅	C₂²×D₅
Fitting	C₂₅×#95	C₂
hypercenter	#95	D₂₅
hypocenter	C₂₅	#401
LCS	G ▷ C₂³×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
41. C₂₅	#401	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×#95	2
#11716379	2
C₅⋊#401	5

Subgroups — C25⋊#401 #13097938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅⋊#401 #13097938