Subgroups — C₂₅×#500 #13098649

Order 1600.

147 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₂₅×#107	C₂	1	4	yes	maximal
3	C₄×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₂₅	—	2	2	no	—
5	C₂×C₈×C₂₅	C₂²	1	2	yes	—
6	C₄⋊C₄×C₂₅	—	2	2	no	—
7	C₄⋊C₄×C₂₅	C₂²	1	4	yes	—
8	C₄²×C₂₅	C₂²	1	1	yes	characteristic
9	C₅×#500	C₅	1	1	yes	maximal, characteristic
10	Q₈×C₂₅	—	4	4	no	—
11	C₂×C₄×C₂₅	—	2	4	no	—
12	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
13	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
15	C₈×C₂₅	Q₈	1	4	yes	complemented
16	C₅×C₄⋊Q₈	C₂×C₅	1	2	yes	—
17	C₅×#107	C₂×C₅	1	4	yes	—
18	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
20	C₄×C₂₅	—	4	4	no	—
21	C₄×C₂₅	D₈	1	2	yes	—
22	C₄×C₂₅	Q₁₆	1	2	yes	—
23	C₄×C₂₅	C₂×Q₈	1	2	yes	—
24	C₂×C₅×Q₈	—	2	2	no	—
25	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
26	C₅×C₄⋊C₄	—	2	2	no	—
27	C₅×C₄⋊C₄	C₂²×C₅	1	4	yes	—
28	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
29	#500	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₂₅	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₂₅	C₂×D₈	1	1	yes	characteristic
32	C₂×C₂₅	C₂×Q₁₆	1	1	yes	characteristic
33	C₅×Q₈	—	4	4	no	—
34	C₂×C₄×C₅	—	2	4	no	—
35	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
36	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
38	C₅×C₈	C₅×Q₈	1	4	yes	—
39	C₄⋊Q₈	C₂×C₂₅	1	2	yes	—
40	#107	C₂×C₂₅	1	4	yes	—
41	C₄×C₈	C₂×C₂₅	1	1	yes	characteristic
42	C₂₅	#500	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
44	C₄×C₅	—	4	4	no	—
45	C₄×C₅	C₅×D₈	1	2	yes	—
46	C₄×C₅	C₅×Q₁₆	1	2	yes	—
47	C₄×C₅	C₂×C₅×Q₈	1	2	yes	—
48	C₂×Q₈	—	2	2	no	—
49	C₂×C₈	C₂²×C₂₅	1	2	yes	—
50	C₄⋊C₄	—	2	2	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	C₂×C₅×D₈	1	1	yes	characteristic
55	C₂×C₅	C₂×C₅×Q₁₆	1	1	yes	characteristic
56	Q₈	—	4	4	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
59	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
60	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
61	C₈	Q₈×C₂₅	1	4	yes	complemented
62	C₅	C₅×#500	1	1	yes	characteristic
63	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
64	C₄	—	4	4	no	—
65	C₄	D₈×C₂₅	1	2	yes	—
66	C₄	Q₁₆×C₂₅	1	2	yes	—
67	C₄	C₂×Q₈×C₂₅	1	2	yes	—
68	C₂	C₂₅×C₄⋊Q₈	1	1	yes	characteristic
69	C₂	C₂×D₈×C₂₅	1	1	yes	characteristic
70	C₂	C₂×Q₁₆×C₂₅	1	1	yes	characteristic

	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
15. C₈×C₂₅	Q₈	semidirect
29. #500	C₂₅	direct (N × H)
42. C₂₅	#500	direct (N × H)
61. C₈	Q₈×C₂₅	semidirect

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×#107	2
C₄×C₈×C₂₅	2
C₅×#500	5

Subgroups — C25×#500 #13098649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#500 #13098649