Subgroups — C₂×C₂₅×D₂₅₃ #38760708

Order 25300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×D₂₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₂₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₂₃×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₂₅₃	C₅	1	1	yes	maximal, characteristic
5	C₅×D₂₅₃	C₂×C₅	1	2	yes	—
6	C₂×C₅×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic
7	C₂×C₂₅×D₂₃	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₂₃	C₂²×C₅	1	1	yes	characteristic
9	C₂×C₂₃×C₂₅	D₁₁	1	1	yes	characteristic, complemented
10	C₂₅×D₂₃	—	11	2	no	—
11	C₂×D₁₁×C₂₅	—	23	1	no	maximal, Hall
12	C₂×D₂₅₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂₃×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×C₂₅	D₂₃	1	1	yes	characteristic, complemented
15	D₁₁×C₂₅	—	23	2	no	—
16	C₂×C₁₁×C₂₃	C₂×C₂₅	1	1	yes	characteristic, complemented
17	D₂₅₃	C₂×C₂₅	1	2	yes	direct product factor
18	C₂×C₅×D₂₃	—	11	1	no	—
19	C₁₁×C₂₅	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
20	C₁₁×C₂₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₂₃	C₅×D₁₁	1	1	yes	characteristic
22	C₅×D₂₃	—	11	2	no	—
23	C₂×C₅×D₁₁	—	23	1	no	—
24	C₅×C₂₃	C₂×C₅×D₁₁	1	1	yes	characteristic
25	C₂×C₅×C₁₁	C₅×D₂₃	1	1	yes	characteristic
26	C₅×D₁₁	—	23	2	no	—
27	C₂²×C₂₅	—	253	1	no	Hall
28	C₂×D₂₃	—	11	1	no	Hall
29	C₅×C₁₁	C₂×C₅×D₂₃	1	1	yes	characteristic
30	C₂×C₂₅	—	253	2	no	—
31	C₂×C₂₅	D₂₅₃	1	1	yes	characteristic, direct product factor
32	C₂×C₂₃	D₁₁×C₂₅	1	1	yes	characteristic, complemented
33	D₂₃	—	11	2	no	—
34	C₂×D₁₁	—	23	1	no	Hall
35	C₂₅	C₂×D₂₅₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂₃	C₂×D₁₁×C₂₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₁	C₂₅×D₂₃	1	1	yes	characteristic, complemented
38	D₁₁	—	23	2	no	—
39	C₂²×C₅	—	253	1	no	—
40	C₁₁	C₂×C₂₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	253	2	no	—
42	C₂×C₅	C₅×D₂₅₃	1	1	yes	characteristic
43	C₅	C₂×C₅×D₂₅₃	1	1	yes	characteristic
44	C₂²	—	253	1	no	Sylow
45	C₂	—	253	2	no	—
46	C₂	C₂₅×D₂₅₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂₅×D₂₅₃	C₂	direct (N × H)
2. C₂×C₁₁×C₂₃×C₂₅	C₂	semidirect
3. C₁₁×C₂₃×C₂₅	C₂²	semidirect
9. C₂×C₂₃×C₂₅	D₁₁	semidirect
12. C₂×D₂₅₃	C₂₅	direct (N × H)
13. C₂₃×C₂₅	C₂×D₁₁	semidirect
14. C₂×C₁₁×C₂₅	D₂₃	semidirect
16. C₂×C₁₁×C₂₃	C₂×C₂₅	semidirect
17. D₂₅₃	C₂×C₂₅	direct (N × H)
19. C₁₁×C₂₅	C₂×D₂₃	semidirect
20. C₁₁×C₂₃	C₂²×C₂₅	semidirect
31. C₂×C₂₅	D₂₅₃	direct (N × H)
32. C₂×C₂₃	D₁₁×C₂₅	semidirect
35. C₂₅	C₂×D₂₅₃	direct (N × H)
36. C₂₃	C₂×D₁₁×C₂₅	semidirect
37. C₂×C₁₁	C₂₅×D₂₃	semidirect
40. C₁₁	C₂×C₂₅×D₂₃	semidirect
46. C₂	C₂₅×D₂₅₃	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×D₂₅₃	2
C₂×C₁₁×C₂₃×C₂₅	2
C₂×C₅×D₂₅₃	5
C₂×C₂₅×D₂₃	11
C₂×D₁₁×C₂₅	23

Subgroups — C2×C25×D253 #38760708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×D₂₅₃ #38760708