Subgroups — C₂₅×#331 #13097784

Order 1600.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×D₄×C₂₅	—	2	2	no	—
4	C₂×D₄×C₂₅	C₄	1	2	yes	—
5	C₂×C₈×C₂₅	—	2	2	no	—
6	C₄²×C₂₅	C₂²	1	1	yes	characteristic
7	C₅×#331	C₅	1	1	yes	maximal, characteristic
8	C₂³×C₂₅	—	2	2	no	—
9	D₄×C₂₅	—	4	2	no	—
10	D₄×C₂₅	—	4	2	no	—
11	D₄×C₂₅	—	4	2	no	—
12	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₅	D₄	1	2	yes	—
14	C₈×C₂₅	—	4	2	no	—
15	C₅×#127	C₂×C₅	1	1	yes	characteristic
16	C₅×C₄⋊C₈	C₂×C₅	1	2	yes	—
17	C₂²×C₂₅	—	4	2	no	—
18	C₂²×C₂₅	—	4	4	no	—
19	C₂²×C₂₅	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₂₅	—	2	1	no	—
21	C₄×C₂₅	D₈	1	2	yes	—
22	C₄×C₂₅	SD₁₆	1	2	yes	—
23	C₂×C₅×D₄	—	2	2	no	—
24	C₂×C₅×D₄	C₄×C₅	1	2	yes	—
25	C₂×C₅×C₈	—	2	2	no	—
26	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
27	#331	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₂₅	—	8	2	no	—
29	C₂×C₂₅	#100	1	1	yes	characteristic
30	C₂×C₂₅	#102	1	2	yes	—
31	C₂³×C₅	—	2	2	no	—
32	C₅×D₄	—	4	2	no	—
33	C₅×D₄	—	4	2	no	—
34	C₅×D₄	—	4	2	no	—
35	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
36	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
37	C₅×C₈	—	4	2	no	—
38	#127	C₂×C₂₅	1	1	yes	characteristic
39	C₄⋊C₈	C₂×C₂₅	1	2	yes	complemented
40	C₂₅	#331	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₅	—	4	2	no	—
42	C₂²×C₅	—	4	4	no	—
43	C₂²×C₅	C₅×C₂²⋊C₄	1	1	yes	characteristic
44	C₄×C₅	—	2	1	no	—
45	C₄×C₅	C₅×D₈	1	2	yes	—
46	C₄×C₅	C₅×SD₁₆	1	2	yes	—
47	C₂×D₄	—	2	2	no	—
48	C₂×D₄	C₄×C₂₅	1	2	yes	—
49	C₂×C₈	—	2	2	no	—
50	C₄²	C₂²×C₂₅	1	1	yes	characteristic
51	C₂×C₅	—	8	2	no	—
52	C₂×C₅	C₅×#100	1	1	yes	characteristic
53	C₂×C₅	C₅×#102	1	2	yes	—
54	C₂³	—	2	2	no	—
55	D₄	—	4	2	no	—
56	D₄	—	4	2	no	—
57	D₄	—	4	2	no	—
58	C₂×C₄	C₂×C₄×C₂₅	1	1	yes	characteristic
59	C₂×C₄	D₄×C₂₅	1	2	yes	—
60	C₈	—	4	2	no	—
61	C₅	C₅×#331	1	1	yes	characteristic
62	C₂²	—	4	2	no	—
63	C₂²	—	4	4	no	—
64	C₂²	C₂²⋊C₄×C₂₅	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	D₈×C₂₅	1	2	yes	—
67	C₄	SD₁₆×C₂₅	1	2	yes	—
68	C₂	—	8	2	no	—
69	C₂	C₂₅×#100	1	1	yes	characteristic
70	C₂	C₂₅×#102	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	C₅×#127	C₂×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×C₄⋊C₈	C₂	semidirect
27. #331	C₂₅	direct (N × H)
39. C₄⋊C₈	C₂×C₂₅	semidirect
40. C₂₅	#331	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×#127	2
C₂₅×C₄⋊C₈	2
C₅×#331	5

Subgroups — C25×#331 #13097784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#331 #13097784