Subgroups — C₂₅×#329 #13097782

Order 1600.

105 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#97	C₂	1	2	yes	maximal, complemented
3	C₂×Q₈×C₂₅	C₄	1	1	yes	characteristic
4	C₂×D₄×C₂₅	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₅	—	2	2	no	—
6	C₂²⋊C₄×C₂₅	—	2	2	no	—
7	C₄²×C₂₅	C₂²	1	1	yes	characteristic
8	C₅×#329	C₅	1	1	yes	maximal, characteristic
9	C₂³×C₂₅	—	2	1	no	—
10	Q₈×C₂₅	—	4	1	no	—
11	D₄×C₂₅	—	4	1	no	—
12	C₂×C₄×C₂₅	—	2	1	no	—
13	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₅	D₄	1	2	yes	—
15	C₈×C₂₅	—	2	4	no	—
16	C₅×#124	C₂×C₅	1	1	yes	characteristic
17	C₅×#97	C₂×C₅	1	2	yes	—
18	C₂²×C₂₅	—	4	1	no	—
19	C₂²×C₂₅	—	4	2	no	—
20	C₂²×C₂₅	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₅	—	2	1	no	—
22	C₄×C₂₅	—	2	2	no	—
23	C₄×C₂₅	—	4	1	no	—
24	C₂×C₅×Q₈	C₄×C₅	1	1	yes	characteristic
25	C₂×C₅×D₄	C₄×C₅	1	1	yes	characteristic
26	C₂×C₅×C₈	—	2	2	no	—
27	C₅×C₂²⋊C₄	—	2	2	no	—
28	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
29	#329	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₂₅	—	8	1	no	—
31	C₂×C₂₅	#100	1	1	yes	characteristic
32	C₂×C₂₅	#104	1	2	yes	—
33	C₂³×C₅	—	2	1	no	—
34	C₅×Q₈	—	4	1	no	—
35	C₅×D₄	—	4	1	no	—
36	C₂×C₄×C₅	—	2	1	no	—
37	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
38	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
39	C₅×C₈	—	2	4	no	—
40	#124	C₂×C₂₅	1	1	yes	characteristic
41	#97	C₂×C₂₅	1	2	yes	complemented
42	C₂₅	#329	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	—	4	1	no	—
44	C₂²×C₅	—	4	2	no	—
45	C₂²×C₅	C₅×C₂²⋊C₄	1	1	yes	characteristic
46	C₄×C₅	—	2	1	no	—
47	C₄×C₅	—	2	2	no	—
48	C₄×C₅	—	4	1	no	—
49	C₂×Q₈	C₄×C₂₅	1	1	yes	characteristic
50	C₂×D₄	C₄×C₂₅	1	1	yes	characteristic
51	C₂×C₈	—	2	2	no	—
52	C₂²⋊C₄	—	2	2	no	—
53	C₄²	C₂²×C₂₅	1	1	yes	characteristic
54	C₂×C₅	—	8	1	no	—
55	C₂×C₅	C₅×#100	1	1	yes	characteristic
56	C₂×C₅	C₅×#104	1	2	yes	—
57	C₂³	—	2	1	no	—
58	Q₈	—	4	1	no	—
59	D₄	—	4	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₂×C₄×C₂₅	1	1	yes	characteristic
62	C₂×C₄	D₄×C₂₅	1	2	yes	—
63	C₈	—	2	4	no	—
64	C₅	C₅×#329	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	—	4	2	no	—
67	C₂²	C₂²⋊C₄×C₂₅	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	2	no	—
70	C₄	—	4	1	no	—
71	C₂	—	8	1	no	—
72	C₂	C₂₅×#100	1	1	yes	characteristic
73	C₂	C₂₅×#104	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂₅×#97	C₂	semidirect
29. #329	C₂₅	direct (N × H)
41. #97	C₂×C₂₅	semidirect
42. C₂₅	#329	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×#124	2
C₂₅×#97	2
C₅×#329	5

Subgroups — C25×#329 #13097782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#329 #13097782