Subgroups — C₂₅×#491 #13098640

Order 1600.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#125	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#103	C₂	1	4	yes	maximal
4	C₂₅×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₅	C₂²	1	2	yes	—
6	C₂×C₈×C₂₅	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₅	—	2	2	no	—
8	C₄⋊C₄×C₂₅	—	2	2	no	—
9	C₄⋊C₄×C₂₅	C₂²	1	2	yes	—
10	C₄²×C₂₅	C₂²	1	1	yes	characteristic
11	C₅×#491	C₅	1	1	yes	maximal, characteristic
12	Q₈×C₂₅	—	2	4	no	—
13	C₂×C₄×C₂₅	—	2	2	no	—
14	C₂×C₄×C₂₅	—	2	2	no	—
15	C₂×C₄×C₂₅	D₄	1	2	yes	—
16	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
17	C₈×C₂₅	—	2	2	no	—
18	C₅×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
19	C₅×#125	C₂×C₅	1	1	yes	characteristic
20	C₅×#103	C₂×C₅	1	4	yes	—
21	C₅×#97	C₂×C₅	1	1	yes	characteristic
22	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
23	C₄×C₂₅	—	2	2	no	—
24	C₄×C₂₅	—	4	2	no	—
25	C₄×C₂₅	—	4	2	no	—
26	C₄×C₂₅	#41	1	2	yes	—
27	C₂×C₅×Q₈	C₂²×C₅	1	2	yes	—
28	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
29	C₅×C₄⋊C₄	—	2	2	no	—
30	C₅×C₄⋊C₄	—	2	2	no	—
31	C₅×C₄⋊C₄	C₂²×C₅	1	2	yes	—
32	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
33	#491	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₂₅	#124	1	1	yes	characteristic
35	C₂×C₂₅	#137	1	2	yes	—
36	C₅×Q₈	—	2	4	no	—
37	C₂×C₄×C₅	—	2	2	no	—
38	C₂×C₄×C₅	—	2	2	no	—
39	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
40	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
41	C₅×C₈	—	2	2	no	—
42	C₄⋊Q₈	C₂×C₂₅	1	1	yes	characteristic
43	#125	C₂×C₂₅	1	1	yes	characteristic
44	#103	C₂×C₂₅	1	4	yes	—
45	#97	C₂×C₂₅	1	1	yes	characteristic
46	C₂₅	#491	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
48	C₄×C₅	—	2	2	no	—
49	C₄×C₅	—	4	2	no	—
50	C₄×C₅	—	4	2	no	—
51	C₄×C₅	C₅×#41	1	2	yes	—
52	C₂×Q₈	C₂²×C₂₅	1	2	yes	—
53	C₂×C₈	C₂²×C₂₅	1	2	yes	—
54	C₄⋊C₄	—	2	2	no	—
55	C₄⋊C₄	—	2	2	no	—
56	C₄⋊C₄	C₂²×C₂₅	1	2	yes	—
57	C₄²	C₂²×C₂₅	1	1	yes	characteristic
58	C₂×C₅	C₅×#124	1	1	yes	characteristic
59	C₂×C₅	C₅×#137	1	2	yes	—
60	Q₈	—	2	4	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	D₄×C₂₅	1	2	yes	—
64	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₅	C₅×#491	1	1	yes	characteristic
67	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	—	4	2	no	—
70	C₄	—	4	2	no	—
71	C₄	#41×C₂₅	1	2	yes	—
72	C₂	C₂₅×#124	1	1	yes	characteristic
73	C₂	C₂₅×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle, prime radical	C₂²×C₅	C₂×C₅×D₄
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
33. #491	C₂₅	direct (N × H)
46. C₂₅	#491	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×C₄⋊Q₈	2
C₂₅×#125	2
C₂₅×#103	2
C₂₅×#97	2
C₅×#491	5

Subgroups — C25×#491 #13098640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#491 #13098640