Subgroups — C₃×C₁₁×C₅⋊D₈₅ #43242537

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	C₁₁×C₅⋊D₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₈₅	—	5	6	no	maximal
4	C₅²×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₇	D₅	1	6	yes	complemented
6	C₃×C₅⋊D₈₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₈₅	—	5	6	no	—
8	C₃×C₁₁×C₅⋊D₅	—	17	1	no	maximal, Hall
9	C₃×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₁×D₁₇	—	25	1	no	Hall
11	C₅×C₁₁×C₁₇	C₃×D₅	1	6	yes	complemented
12	C₅⋊D₈₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅²×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₅⋊D₅	—	17	1	no	Hall
16	C₃×D₈₅	—	5	6	no	—
17	C₅²×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₁×D₁₇	—	25	1	no	Hall
19	C₃×D₅×C₁₁	—	85	6	no	—
20	C₅²×C₁₁	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₇	D₅×C₁₁	1	6	yes	complemented
22	C₁₁×C₁₇	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	D₈₅	—	5	6	no	—
24	C₃×C₅×C₁₁	D₈₅	1	6	yes	complemented
25	C₃×C₅⋊D₅	—	17	1	no	Hall
26	D₅×C₁₁	—	85	6	no	—
27	C₃×D₁₇	—	25	1	no	Hall
28	C₅×C₁₇	C₃×D₅×C₁₁	1	6	yes	complemented
29	C₃×C₅²	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₁	—	425	1	no	Hall
31	C₅×C₁₁	C₃×D₈₅	1	6	yes	complemented
32	C₃×C₁₇	C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₅⋊D₅	—	17	1	no	Hall
34	D₁₇	—	25	1	no	Hall
35	C₃×C₁₁	C₅⋊D₈₅	1	1	yes	characteristic, direct product factor, Hall
36	C₃×D₅	—	85	6	no	—
37	C₅²	C₃×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₁	—	425	1	no	Hall
39	C₁₇	C₃×C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	C₁₁×D₈₅	1	6	yes	complemented
41	C₁₁	C₃×C₅⋊D₈₅	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	85	6	no	—
43	C₂×C₃	—	425	1	no	Hall
44	C₅	C₃×C₁₁×D₈₅	1	6	yes	complemented
45	C₃	C₁₁×C₅⋊D₈₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	425	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	C₅⋊D₈₅
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₇	C₂	semidirect
2. C₁₁×C₅⋊D₈₅	C₃	direct (N × H)
4. C₅²×C₁₁×C₁₇	C₂×C₃	semidirect
5. C₃×C₅×C₁₁×C₁₇	D₅	semidirect
6. C₃×C₅⋊D₈₅	C₁₁	direct (N × H)
9. C₃×C₅²×C₁₇	C₂×C₁₁	semidirect
11. C₅×C₁₁×C₁₇	C₃×D₅	semidirect
12. C₅⋊D₈₅	C₃×C₁₁	direct (N × H)
13. C₃×C₅²×C₁₁	D₁₇	semidirect
14. C₃×C₁₁×C₁₇	C₅⋊D₅	semidirect
17. C₅²×C₁₇	C₂×C₃×C₁₁	semidirect
20. C₅²×C₁₁	C₃×D₁₇	semidirect
21. C₃×C₅×C₁₇	D₅×C₁₁	semidirect
22. C₁₁×C₁₇	C₃×C₅⋊D₅	semidirect
24. C₃×C₅×C₁₁	D₈₅	semidirect
28. C₅×C₁₇	C₃×D₅×C₁₁	semidirect
29. C₃×C₅²	C₁₁×D₁₇	semidirect
31. C₅×C₁₁	C₃×D₈₅	semidirect
32. C₃×C₁₇	C₁₁×C₅⋊D₅	semidirect
35. C₃×C₁₁	C₅⋊D₈₅	direct (N × H)
37. C₅²	C₃×C₁₁×D₁₇	semidirect
39. C₁₇	C₃×C₁₁×C₅⋊D₅	semidirect
40. C₃×C₅	C₁₁×D₈₅	semidirect
41. C₁₁	C₃×C₅⋊D₈₅	direct (N × H)
44. C₅	C₃×C₁₁×D₈₅	semidirect
45. C₃	C₁₁×C₅⋊D₈₅	direct (N × H)

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
C₁₁×C₅⋊D₈₅	3
C₃×C₁₁×D₈₅	5
C₃×C₅⋊D₈₅	11
C₃×C₁₁×C₅⋊D₅	17

Subgroups — C3×C11×C5⋊D85 #43242537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₅⋊D₈₅ #43242537