Subgroups — C₅⋊D₅×D₂₅₃ #38760805

Order 25300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₂₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₂₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊D₁₂₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₂₅₃	—	5	6	no	maximal
6	D₁₂₆₅	—	5	6	no	—
7	D₅×C₁₁×C₂₃	—	5	6	no	—
8	C₅×D₂₅₃	D₅	1	6	yes	complemented
9	D₂₃×C₅⋊D₅	—	11	1	no	maximal, Hall
10	C₅×C₁₁×C₂₃	C₂×D₅	1	6	yes	complemented
11	C₅⋊D₁₁₅	—	11	1	no	—
12	C₂₃×C₅⋊D₅	D₁₁	1	1	yes	characteristic, complemented
13	C₅²×D₂₃	—	11	1	no	—
14	D₁₁×C₅⋊D₅	—	23	1	no	maximal, Hall
15	C₂×D₂₅₃	—	25	1	no	Hall
16	C₅²×C₂₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₅⋊D₅₅	—	23	1	no	—
18	C₁₁×C₅⋊D₅	D₂₃	1	1	yes	characteristic, complemented
19	C₅²×D₁₁	—	23	1	no	—
20	C₂×C₁₁×C₂₃	—	25	1	no	—
21	D₂₅₃	—	25	1	no	—
22	D₂₅₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	D₅×D₂₃	—	55	6	no	—
24	C₅²×C₁₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁×C₂₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
26	D₁₁₅	—	55	6	no	—
27	C₅×D₂₃	—	11	6	no	—
28	D₅×C₂₃	—	5	6	no	—
29	D₅×D₁₁	—	115	6	no	—
30	C₅×C₂₃	D₅×D₁₁	1	6	yes	complemented
31	D₅₅	—	115	6	no	—
32	C₅×D₁₁	—	23	6	no	—
33	D₅×C₁₁	—	5	6	no	—
34	C₂×C₅⋊D₅	—	253	1	no	Hall
35	C₂×D₂₃	—	275	1	no	Hall
36	C₅×C₁₁	D₅×D₂₃	1	6	yes	complemented
37	C₂×C₅²	—	253	1	no	—
38	C₅⋊D₅	—	253	1	no	—
39	C₅⋊D₅	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	C₅²	C₂×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
45	C₂₃	D₁₁×C₅⋊D₅	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	6	no	—
50	C₁₁	D₂₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	253	6	no	—
52	D₅	—	5	6	no	—
53	D₅	—	1265	6	no	—
54	C₅	D₅×D₂₅₃	1	6	yes	complemented
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, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁×C₂₃	C₂²
LCS	G ▷ C₅²×C₁₁×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²×D₂₅₃	C₂	semidirect
2. C₁₁×C₂₃×C₅⋊D₅	C₂	semidirect
3. C₅⋊D₁₂₆₅	C₂	semidirect
4. C₅²×C₁₁×C₂₃	C₂²	semidirect
8. C₅×D₂₅₃	D₅	semidirect
10. C₅×C₁₁×C₂₃	C₂×D₅	semidirect
12. C₂₃×C₅⋊D₅	D₁₁	semidirect
16. C₅²×C₂₃	C₂×D₁₁	semidirect
18. C₁₁×C₅⋊D₅	D₂₃	semidirect
22. D₂₅₃	C₅⋊D₅	direct (N × H)
24. C₅²×C₁₁	C₂×D₂₃	semidirect
25. C₁₁×C₂₃	C₂×C₅⋊D₅	semidirect
30. C₅×C₂₃	D₅×D₁₁	semidirect
36. C₅×C₁₁	D₅×D₂₃	semidirect
39. C₅⋊D₅	D₂₅₃	direct (N × H)
44. C₅²	C₂×D₂₅₃	semidirect
45. C₂₃	D₁₁×C₅⋊D₅	semidirect
50. C₁₁	D₂₃×C₅⋊D₅	semidirect
54. C₅	D₅×D₂₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₂₅₃	2
C₁₁×C₂₃×C₅⋊D₅	2
C₅⋊D₁₂₆₅	2
D₅×D₂₅₃	5
D₂₃×C₅⋊D₅	11
D₁₁×C₅⋊D₅	23

Subgroups — C5⋊D5×D253 #38760805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊D₅×D₂₅₃ #38760805