Subgroups — C₁₁×C₃⋊(C₅⋊D₈₅) #43242549

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	—	3	1	no	maximal, Hall
3	C₁₁×D₂₅₅	—	5	6	no	maximal
4	C₅²×C₁₁×C₁₇	D₃	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	—	15	6	no	—
8	C₁₁×C₃⋊(C₅⋊D₅)	—	17	1	no	maximal, Hall
9	C₃×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₅₁	—	25	1	no	Hall
11	C₅×C₁₁×C₁₇	D₁₅	1	6	yes	complemented
12	C₅⋊D₈₅	—	3	1	no	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	—	51	1	no	Hall
16	D₂₅₅	—	5	6	no	—
17	C₅²×C₁₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₁×D₁₇	—	75	1	no	Hall
19	C₁₁×D₁₅	—	85	6	no	—
20	C₅²×C₁₁	D₅₁	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	—	15	6	no	—
24	C₃×C₅×C₁₁	D₈₅	1	6	yes	complemented
25	C₃⋊(C₅⋊D₅)	—	17	1	no	Hall
26	D₅×C₁₁	—	255	6	no	—
27	D₅₁	—	25	1	no	Hall
28	C₅×C₁₇	C₁₁×D₁₅	1	6	yes	complemented
29	C₃×C₅²	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₁	—	425	1	no	Hall
31	C₅×C₁₁	D₂₅₅	1	6	yes	complemented
32	C₃×C₁₇	C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₅⋊D₅	—	51	1	no	Hall
34	D₁₇	—	75	1	no	Hall
35	C₃×C₁₁	C₅⋊D₈₅	1	1	yes	characteristic, complemented, Hall
36	D₁₅	—	85	6	no	—
37	C₅²	C₁₁×D₅₁	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₁	—	1275	1	no	Hall
39	C₁₇	C₁₁×C₃⋊(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	—	255	6	no	—
43	D₃	—	425	1	no	Hall
44	C₅	C₁₁×D₂₅₅	1	6	yes	complemented
45	C₃	C₁₁×C₅⋊D₈₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	1275	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₇	C₂	semidirect
4. C₅²×C₁₁×C₁₇	D₃	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	D₁₅	semidirect
13. C₃×C₅²×C₁₁	D₁₇	semidirect
14. C₃×C₁₁×C₁₇	C₅⋊D₅	semidirect
17. C₅²×C₁₇	D₃×C₁₁	semidirect
20. C₅²×C₁₁	D₅₁	semidirect
21. C₃×C₅×C₁₇	D₅×C₁₁	semidirect
22. C₁₁×C₁₇	C₃⋊(C₅⋊D₅)	semidirect
24. C₃×C₅×C₁₁	D₈₅	semidirect
28. C₅×C₁₇	C₁₁×D₁₅	semidirect
29. C₃×C₅²	C₁₁×D₁₇	semidirect
31. C₅×C₁₁	D₂₅₅	semidirect
32. C₃×C₁₇	C₁₁×C₅⋊D₅	semidirect
35. C₃×C₁₁	C₅⋊D₈₅	semidirect
37. C₅²	C₁₁×D₅₁	semidirect
39. C₁₇	C₁₁×C₃⋊(C₅⋊D₅)	semidirect
40. C₃×C₅	C₁₁×D₈₅	semidirect
41. C₁₁	C₃⋊(C₅⋊D₈₅)	direct (N × H)
44. C₅	C₁₁×D₂₅₅	semidirect
45. C₃	C₁₁×C₅⋊D₈₅	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
C₁₁×C₅⋊D₈₅	3
C₁₁×D₂₅₅	5
C₃⋊(C₅⋊D₈₅)	11
C₁₁×C₃⋊(C₅⋊D₅)	17

Subgroups — C11×C3⋊(C5⋊D85) #43242549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃⋊(C₅⋊D₈₅) #43242549