Subgroups — D₂₅×D₂₅₃ #38760702

Order 25300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₃₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₂₃×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×D₂₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₂₃×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₂₅₃	—	5	1	no	maximal
6	D₁₂₆₅	—	5	1	no	—
7	D₅×C₁₁×C₂₃	—	5	1	no	—
8	C₅×D₂₅₃	D₅	1	1	yes	characteristic
9	D₂₃×D₂₅	—	11	1	no	maximal, Hall
10	C₅×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic
11	D₅₇₅	—	11	1	no	—
12	C₂₅×D₂₃	—	11	1	no	—
13	C₂₃×D₂₅	D₁₁	1	1	yes	characteristic, complemented
14	D₁₁×D₂₅	—	23	1	no	maximal, Hall
15	C₂×D₂₅₃	—	25	1	no	Hall
16	C₂₃×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	D₂₇₅	—	23	1	no	—
18	D₁₁×C₂₅	—	23	1	no	—
19	C₁₁×D₂₅	D₂₃	1	1	yes	characteristic, complemented
20	C₂×C₁₁×C₂₃	—	25	1	no	—
21	D₂₅₃	—	25	1	no	—
22	D₂₅₃	D₂₅	1	1	yes	characteristic, direct product factor
23	D₅×D₂₃	—	55	1	no	—
24	C₁₁×C₂₅	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁×C₂₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
26	D₁₁₅	—	55	1	no	—
27	C₅×D₂₃	—	11	1	no	—
28	D₅×C₂₃	—	5	1	no	—
29	D₅×D₁₁	—	115	1	no	—
30	C₅×C₂₃	D₅×D₁₁	1	1	yes	characteristic
31	D₅₅	—	115	1	no	—
32	C₅×D₁₁	—	23	1	no	—
33	D₅×C₁₁	—	5	1	no	—
34	C₂×D₂₅	—	253	1	no	Hall
35	C₂×D₂₃	—	275	1	no	Hall
36	C₅×C₁₁	D₅×D₂₃	1	1	yes	characteristic
37	C₂×C₂₅	—	253	1	no	—
38	D₂₅	—	253	1	no	—
39	D₂₅	D₂₅₃	1	1	yes	characteristic, direct product factor
40	C₂×C₂₃	—	25	1	no	—
41	D₂₃	—	11	1	no	—
42	D₂₃	—	275	1	no	—
43	C₂×D₁₁	—	575	1	no	Hall
44	C₂₅	C₂×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
45	C₂₃	D₁₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	25	1	no	—
47	D₁₁	—	23	1	no	—
48	D₁₁	—	575	1	no	—
49	C₂×D₅	—	1265	1	no	—
50	C₁₁	D₂₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	253	1	no	—
52	D₅	—	5	1	no	—
53	D₅	—	1265	1	no	—
54	C₅	D₅×D₂₅₃	1	1	yes	characteristic
55	C₂²	—	6325	1	no	Sylow
56	C₂	—	25	1	no	—
57	C₂	—	6325	1	no	—
58	C₂	—	253	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₁×C₂₃×C₂₅	C₂²
Frattini	C₅	D₅×D₂₅₃
socle	C₅×C₁₁×C₂₃	C₂×D₅
LCS	G ▷ C₁₁×C₂₃×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₃₂₅	C₂	semidirect
2. C₁₁×C₂₃×D₂₅	C₂	semidirect
3. C₂₅×D₂₅₃	C₂	semidirect
4. C₁₁×C₂₃×C₂₅	C₂²	semidirect
13. C₂₃×D₂₅	D₁₁	semidirect
16. C₂₃×C₂₅	C₂×D₁₁	semidirect
19. C₁₁×D₂₅	D₂₃	semidirect
22. D₂₅₃	D₂₅	direct (N × H)
24. C₁₁×C₂₅	C₂×D₂₃	semidirect
25. C₁₁×C₂₃	C₂×D₂₅	semidirect
39. D₂₅	D₂₅₃	direct (N × H)
44. C₂₅	C₂×D₂₅₃	semidirect
45. C₂₃	D₁₁×D₂₅	semidirect
50. C₁₁	D₂₃×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
D₆₃₂₅	2
C₁₁×C₂₃×D₂₅	2
C₂₅×D₂₅₃	2
D₅×D₂₅₃	5
D₂₃×D₂₅	11
D₁₁×D₂₅	23

Subgroups — D25×D253 #38760702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₅×D₂₅₃ #38760702