Subgroups — C₅²×D₃×C₁₁×C₁₇ #43242540

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	C₂×C₅²×C₁₁×C₁₇	—	3	1	no	maximal, Hall
3	C₅×D₃×C₁₁×C₁₇	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₁₁×C₁₇	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₁₁×C₁₇	C₂×C₅	1	6	yes	complemented
6	C₅²×D₃×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₁×C₁₇	—	3	6	no	—
8	C₅²×D₃×C₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₁×C₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₇	C₅×D₃	1	6	yes	direct product factor
12	C₂×C₅²×C₁₇	—	3	1	no	Hall
13	C₃×C₅²×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅²×C₁₁	—	3	1	no	Hall
16	C₅×D₃×C₁₇	C₅×C₁₁	1	6	yes	direct product factor
17	C₅²×C₁₇	D₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₁₁×C₁₇	—	3	1	no	Hall
19	C₅×D₃×C₁₁	C₅×C₁₇	1	6	yes	direct product factor
20	C₅²×C₁₁	D₃×C₁₇	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, direct product factor, Hall
23	C₂×C₅×C₁₇	—	3	6	no	—
24	C₃×C₅×C₁₁	C₂×C₅×C₁₇	1	6	yes	complemented
25	C₅²×D₃	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₁₁	—	3	6	no	—
27	D₃×C₁₇	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₇	C₅×D₃×C₁₁	1	6	yes	direct product factor
29	C₃×C₅²	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₁	C₅²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₁₁	C₅×D₃×C₁₇	1	6	yes	direct product factor
32	C₃×C₁₇	C₂×C₅²×C₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅²	—	3	1	no	Hall
34	C₂×C₁₇	—	3	1	no	Hall
35	C₃×C₁₁	C₂×C₅²×C₁₇	1	1	yes	characteristic, complemented, Hall
36	C₅×D₃	C₅×C₁₁×C₁₇	1	6	yes	direct product factor
37	C₅²	D₃×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	—	3	1	no	Hall
39	C₁₇	C₅²×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₅	C₂×C₅×C₁₁×C₁₇	1	6	yes	complemented
41	C₁₁	C₅²×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	—	3	6	no	—
43	D₃	C₅²×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
44	C₅	C₅×D₃×C₁₁×C₁₇	1	6	yes	direct product factor
45	C₃	C₂×C₅²×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₁₁×C₁₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅²×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅²×C₁₁×C₁₇

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×D₃×C₁₁×C₁₇	C₅	direct (N × H)
4. C₅²×C₁₁×C₁₇	D₃	direct (N × H)
5. C₃×C₅×C₁₁×C₁₇	C₂×C₅	semidirect
6. C₅²×D₃×C₁₇	C₁₁	direct (N × H)
8. C₅²×D₃×C₁₁	C₁₇	direct (N × H)
9. C₃×C₅²×C₁₇	C₂×C₁₁	semidirect
10. D₃×C₁₁×C₁₇	C₅²	direct (N × H)
11. C₅×C₁₁×C₁₇	C₅×D₃	direct (N × H)
13. C₃×C₅²×C₁₁	C₂×C₁₇	semidirect
14. C₃×C₁₁×C₁₇	C₂×C₅²	semidirect
16. C₅×D₃×C₁₇	C₅×C₁₁	direct (N × H)
17. C₅²×C₁₇	D₃×C₁₁	direct (N × H)
19. C₅×D₃×C₁₁	C₅×C₁₇	direct (N × H)
20. C₅²×C₁₁	D₃×C₁₇	direct (N × H)
21. C₃×C₅×C₁₇	C₂×C₅×C₁₁	semidirect
22. C₁₁×C₁₇	C₅²×D₃	direct (N × H)
24. C₃×C₅×C₁₁	C₂×C₅×C₁₇	semidirect
25. C₅²×D₃	C₁₁×C₁₇	direct (N × H)
27. D₃×C₁₇	C₅²×C₁₁	direct (N × H)
28. C₅×C₁₇	C₅×D₃×C₁₁	direct (N × H)
29. C₃×C₅²	C₂×C₁₁×C₁₇	semidirect
30. D₃×C₁₁	C₅²×C₁₇	direct (N × H)
31. C₅×C₁₁	C₅×D₃×C₁₇	direct (N × H)
32. C₃×C₁₇	C₂×C₅²×C₁₁	semidirect
35. C₃×C₁₁	C₂×C₅²×C₁₇	semidirect
36. C₅×D₃	C₅×C₁₁×C₁₇	direct (N × H)
37. C₅²	D₃×C₁₁×C₁₇	direct (N × H)
39. C₁₇	C₅²×D₃×C₁₁	direct (N × H)
40. C₃×C₅	C₂×C₅×C₁₁×C₁₇	semidirect
41. C₁₁	C₅²×D₃×C₁₇	direct (N × H)
43. D₃	C₅²×C₁₁×C₁₇	direct (N × H)
44. C₅	C₅×D₃×C₁₁×C₁₇	direct (N × H)
45. C₃	C₂×C₅²×C₁₁×C₁₇	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
C₂×C₅²×C₁₁×C₁₇	3
C₅×D₃×C₁₁×C₁₇	5
C₅²×D₃×C₁₇	11
C₅²×D₃×C₁₁	17

Subgroups — C52×D3×C11×C17 #43242540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×C₁₁×C₁₇ #43242540