Subgroups — C₂₅×#499 #13098648

Order 1600.

129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#125	C₂	1	2	yes	maximal
2	C₂₅×#107	C₂	1	2	yes	maximal
3	C₂₅×#106	C₂	1	2	yes	maximal
4	C₄×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₅	—	2	4	no	—
8	C₄⋊C₄×C₂₅	C₂²	1	4	yes	—
9	C₄²×C₂₅	C₂²	1	1	yes	characteristic
10	C₅×#499	C₅	1	1	yes	maximal, characteristic
11	C₂×C₄×C₂₅	—	2	4	no	—
12	C₂×C₄×C₂₅	D₄	1	2	yes	—
13	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
14	C₈×C₂₅	Q₈	1	2	yes	—
15	C₈×C₂₅	Q₈	1	2	yes	—
16	C₅×#125	C₂×C₅	1	2	yes	—
17	C₅×#107	C₂×C₅	1	2	yes	—
18	C₅×#106	C₂×C₅	1	2	yes	—
19	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
20	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
21	C₄×C₂₅	—	2	2	no	—
22	C₄×C₂₅	—	4	4	no	—
23	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
26	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
27	C₅×C₄⋊C₄	—	2	4	no	—
28	C₅×C₄⋊C₄	C₂²×C₅	1	4	yes	—
29	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
30	#499	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₂₅	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₂₅	#135	1	2	yes	—
33	C₂×C₄×C₅	—	2	4	no	—
34	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
35	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
36	C₅×C₈	C₅×Q₈	1	2	yes	—
37	C₅×C₈	C₅×Q₈	1	2	yes	—
38	#125	C₂×C₂₅	1	2	yes	—
39	#107	C₂×C₂₅	1	2	yes	—
40	#106	C₂×C₂₅	1	2	yes	—
41	C₄×C₈	C₂×C₂₅	1	1	yes	characteristic
42	C₂₅	#499	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	—	4	4	no	—
46	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
47	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
48	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
49	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
50	C₄⋊C₄	—	2	4	no	—
51	C₄⋊C₄	C₂²×C₂₅	1	4	yes	—
52	C₄²	C₂²×C₂₅	1	1	yes	characteristic
53	C₂×C₅	C₅×C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₅	C₅×#135	1	2	yes	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	D₄×C₂₅	1	2	yes	—
57	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
58	C₈	Q₈×C₂₅	1	2	yes	—
59	C₈	Q₈×C₂₅	1	2	yes	—
60	C₅	C₅×#499	1	1	yes	characteristic
61	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
62	C₄	—	2	2	no	—
63	C₄	—	4	4	no	—
64	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
65	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
66	C₂	C₂₅×C₄⋊Q₈	1	1	yes	characteristic
67	C₂	C₂₅×#135	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
30. #499	C₂₅	direct (N × H)
42. C₂₅	#499	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×#125	2
C₂₅×#107	2
C₂₅×#106	2
C₄×C₈×C₂₅	2
C₅×#499	5

Subgroups — C25×#499 #13098648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#499 #13098648