Subgroups — C₅²×C₁₁×D₅₁ #43242541

Order 28050.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₁₁×D₁₇	—	3	1	no	maximal, Hall
3	C₅×C₁₁×D₅₁	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₇	C₂×C₅	1	6	yes	complemented
6	C₅²×D₅₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×D₁₇	—	3	6	no	—
8	C₅²×D₃×C₁₁	—	17	1	no	maximal, Hall
9	C₃×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₅₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₇	C₅×D₃	1	6	yes	complemented
12	C₅²×D₁₇	—	3	1	no	Hall
13	C₃×C₅²×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅²×C₁₁	—	51	1	no	Hall
16	C₅×D₅₁	C₅×C₁₁	1	6	yes	direct product factor
17	C₅²×C₁₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₁×D₁₇	—	3	1	no	Hall
19	C₅×D₃×C₁₁	—	17	6	no	—
20	C₅²×C₁₁	D₅₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅×C₁₇	C₂×C₅×C₁₁	1	6	yes	complemented
22	C₁₁×C₁₇	C₅²×D₃	1	1	yes	characteristic, complemented, Hall
23	C₅×D₁₇	—	3	6	no	—
24	C₃×C₅×C₁₁	C₅×D₁₇	1	6	yes	complemented
25	C₅²×D₃	—	17	1	no	Hall
26	C₂×C₅×C₁₁	—	51	6	no	—
27	D₅₁	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₇	C₅×D₃×C₁₁	1	6	yes	complemented
29	C₃×C₅²	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₁	—	17	1	no	Hall
31	C₅×C₁₁	C₅×D₅₁	1	6	yes	direct product factor
32	C₃×C₁₇	C₂×C₅²×C₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅²	—	51	1	no	Hall
34	D₁₇	—	3	1	no	Hall
35	C₃×C₁₁	C₅²×D₁₇	1	1	yes	characteristic, complemented, Hall
36	C₅×D₃	—	17	6	no	—
37	C₅²	C₁₁×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	—	51	1	no	Hall
39	C₁₇	C₅²×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	C₅×C₁₁×D₁₇	1	6	yes	complemented
41	C₁₁	C₅²×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	—	51	6	no	—
43	D₃	—	17	1	no	Hall
44	C₅	C₅×C₁₁×D₅₁	1	6	yes	direct product factor
45	C₃	C₅²×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₁₁	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₅²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₅²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₇	C₂	semidirect
3. C₅×C₁₁×D₅₁	C₅	direct (N × H)
4. C₅²×C₁₁×C₁₇	D₃	semidirect
5. C₃×C₅×C₁₁×C₁₇	C₂×C₅	semidirect
6. C₅²×D₅₁	C₁₁	direct (N × H)
9. C₃×C₅²×C₁₇	C₂×C₁₁	semidirect
10. C₁₁×D₅₁	C₅²	direct (N × H)
11. C₅×C₁₁×C₁₇	C₅×D₃	semidirect
13. C₃×C₅²×C₁₁	D₁₇	semidirect
14. C₃×C₁₁×C₁₇	C₂×C₅²	semidirect
16. C₅×D₅₁	C₅×C₁₁	direct (N × H)
17. C₅²×C₁₇	D₃×C₁₁	semidirect
20. C₅²×C₁₁	D₅₁	direct (N × H)
21. C₃×C₅×C₁₇	C₂×C₅×C₁₁	semidirect
22. C₁₁×C₁₇	C₅²×D₃	semidirect
24. C₃×C₅×C₁₁	C₅×D₁₇	semidirect
27. D₅₁	C₅²×C₁₁	direct (N × H)
28. C₅×C₁₇	C₅×D₃×C₁₁	semidirect
29. C₃×C₅²	C₁₁×D₁₇	semidirect
31. C₅×C₁₁	C₅×D₅₁	direct (N × H)
32. C₃×C₁₇	C₂×C₅²×C₁₁	semidirect
35. C₃×C₁₁	C₅²×D₁₇	semidirect
37. C₅²	C₁₁×D₅₁	direct (N × H)
39. C₁₇	C₅²×D₃×C₁₁	semidirect
40. C₃×C₅	C₅×C₁₁×D₁₇	semidirect
41. C₁₁	C₅²×D₅₁	direct (N × H)
44. C₅	C₅×C₁₁×D₅₁	direct (N × H)
45. C₃	C₅²×C₁₁×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁×C₁₇	2
C₅²×C₁₁×D₁₇	3
C₅×C₁₁×D₅₁	5
C₅²×D₅₁	11
C₅²×D₃×C₁₁	17

Subgroups — C52×C11×D51 #43242541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₁₁×D₅₁ #43242541