Subgroups — C₂×C₁₁×C₅⋊D₈₅ #34035271

Order 18700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₅⋊D₈₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₈₅	—	5	6	no	maximal
5	C₂×C₅×C₁₁×C₁₇	D₅	1	6	yes	complemented
6	C₁₁×D₈₅	—	5	12	no	—
7	C₂×C₅⋊D₈₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₁×C₅⋊D₅	—	17	1	no	maximal, Hall
9	C₅×C₁₁×C₁₇	C₂×D₅	1	6	yes	complemented
10	C₂×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented
11	C₅⋊D₈₅	C₂×C₁₁	1	2	yes	direct product factor
12	C₂×C₁₁×D₁₇	—	25	1	no	Hall
13	C₂×C₅²×C₁₁	D₁₇	1	1	yes	characteristic, complemented
14	C₁₁×C₅⋊D₅	—	17	2	no	—
15	C₅²×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented
17	C₁₁×D₁₇	—	25	2	no	—
18	C₂×D₈₅	—	5	6	no	—
19	C₅²×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₁₁	—	85	6	no	—
21	C₁₁×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₁₇	D₅×C₁₁	1	6	yes	complemented
23	D₈₅	—	5	12	no	—
24	C₂×C₅×C₁₁	D₈₅	1	6	yes	complemented
25	D₅×C₁₁	—	85	12	no	—
26	C₂×C₅⋊D₅	—	17	1	no	Hall
27	C₅×C₁₇	C₂×D₅×C₁₁	1	6	yes	complemented
28	C₂×D₁₇	—	25	1	no	Hall
29	C₅×C₁₁	C₂×D₈₅	1	6	yes	complemented
30	C₂×C₅²	C₁₁×D₁₇	1	1	yes	characteristic, complemented
31	C₅⋊D₅	—	17	2	no	—
32	C₂²×C₁₁	—	425	1	no	Hall
33	C₂×C₁₇	C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented
34	D₁₇	—	25	2	no	—
35	C₅²	C₂×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₁	—	425	2	no	—
37	C₂×C₁₁	C₅⋊D₈₅	1	1	yes	characteristic, direct product factor
38	C₂×D₅	—	85	6	no	—
39	C₁₇	C₂×C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
40	C₁₁	C₂×C₅⋊D₈₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	C₁₁×D₈₅	1	6	yes	complemented
42	D₅	—	85	12	no	—
43	C₅	C₂×C₁₁×D₈₅	1	6	yes	complemented
44	C₂²	—	425	1	no	Sylow
45	C₂	—	425	2	no	—
46	C₂	C₁₁×C₅⋊D₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	C₅⋊D₈₅
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₅⋊D₈₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₁×C₁₇	C₂	semidirect
3. C₅²×C₁₁×C₁₇	C₂²	semidirect
5. C₂×C₅×C₁₁×C₁₇	D₅	semidirect
7. C₂×C₅⋊D₈₅	C₁₁	direct (N × H)
9. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
10. C₂×C₅²×C₁₇	C₂×C₁₁	semidirect
11. C₅⋊D₈₅	C₂×C₁₁	direct (N × H)
13. C₂×C₅²×C₁₁	D₁₇	semidirect
15. C₅²×C₁₇	C₂²×C₁₁	semidirect
16. C₂×C₁₁×C₁₇	C₅⋊D₅	semidirect
19. C₅²×C₁₁	C₂×D₁₇	semidirect
21. C₁₁×C₁₇	C₂×C₅⋊D₅	semidirect
22. C₂×C₅×C₁₇	D₅×C₁₁	semidirect
24. C₂×C₅×C₁₁	D₈₅	semidirect
27. C₅×C₁₇	C₂×D₅×C₁₁	semidirect
29. C₅×C₁₁	C₂×D₈₅	semidirect
30. C₂×C₅²	C₁₁×D₁₇	semidirect
33. C₂×C₁₇	C₁₁×C₅⋊D₅	semidirect
35. C₅²	C₂×C₁₁×D₁₇	semidirect
37. C₂×C₁₁	C₅⋊D₈₅	direct (N × H)
39. C₁₇	C₂×C₁₁×C₅⋊D₅	semidirect
40. C₁₁	C₂×C₅⋊D₈₅	direct (N × H)
41. C₂×C₅	C₁₁×D₈₅	semidirect
43. C₅	C₂×C₁₁×D₈₅	semidirect
46. C₂	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
C₁₁×C₅⋊D₈₅	2
C₂×C₅²×C₁₁×C₁₇	2
C₂×C₁₁×D₈₅	5
C₂×C₅⋊D₈₅	11
C₂×C₁₁×C₅⋊D₅	17

Subgroups — C2×C11×C5⋊D85 #34035271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₅⋊D₈₅ #34035271