Subgroups — C₁₁×D₁₇×C₅⋊D₅ #34035252

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	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×C₁₁×D₁₇	—	5	6	no	maximal
6	C₁₁×D₈₅	—	5	6	no	—
7	D₅×C₁₁×C₁₇	—	5	6	no	—
8	C₅×C₁₁×D₁₇	D₅	1	6	yes	complemented
9	D₁₇×C₅⋊D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₁×C₅⋊D₅	—	17	1	no	maximal, Hall
11	C₅×C₁₁×C₁₇	C₂×D₅	1	6	yes	complemented
12	C₅⋊D₈₅	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₁₇×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₅²×D₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₂×C₁₁×D₁₇	—	25	1	no	Hall
16	C₂×C₅²×C₁₁	—	17	1	no	—
17	C₁₁×C₅⋊D₅	—	17	1	no	—
18	C₁₁×C₅⋊D₅	D₁₇	1	1	yes	characteristic, direct product factor
19	C₅²×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁×C₁₇	—	25	1	no	—
21	C₁₁×D₁₇	—	25	1	no	—
22	C₁₁×D₁₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	D₅×D₁₇	—	5	6	no	—
24	C₅²×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₅×C₁₁	—	85	6	no	—
26	C₁₁×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	D₈₅	—	5	6	no	—
28	C₅×D₁₇	D₅×C₁₁	1	6	yes	complemented
29	D₅×C₁₇	—	5	6	no	—
30	C₂×C₅×C₁₁	—	17	6	no	—
31	D₅×C₁₁	—	5	6	no	—
32	D₅×C₁₁	—	85	6	no	—
33	C₂×C₅⋊D₅	—	17	1	no	Hall
34	C₅×C₁₇	C₂×D₅×C₁₁	1	6	yes	complemented
35	C₂×D₁₇	—	25	1	no	Hall
36	C₅×C₁₁	D₅×D₁₇	1	6	yes	complemented
37	C₂×C₅²	—	17	1	no	—
38	C₅⋊D₅	—	17	1	no	—
39	C₅⋊D₅	C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
40	C₂²×C₁₁	—	425	1	no	Hall
41	C₂×C₁₇	—	25	1	no	—
42	D₁₇	—	25	1	no	—
43	D₁₇	C₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor
44	C₅²	C₂×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	17	1	no	—
46	C₂×C₁₁	—	25	1	no	—
47	C₂×C₁₁	—	425	1	no	—
48	C₂×D₅	—	85	6	no	—
49	C₁₇	C₂×C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
50	C₁₁	D₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₅	—	17	6	no	—
52	D₅	—	5	6	no	—
53	D₅	—	85	6	no	—
54	C₅	D₅×C₁₁×D₁₇	1	6	yes	complemented
55	C₂²	—	425	1	no	Sylow
56	C₂	—	17	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	425	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₁₇×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₅⋊D₈₅	C₂	semidirect
2. C₁₁×C₁₇×C₅⋊D₅	C₂	semidirect
3. C₅²×C₁₁×D₁₇	C₂	semidirect
4. C₅²×C₁₁×C₁₇	C₂²	semidirect
8. C₅×C₁₁×D₁₇	D₅	semidirect
9. D₁₇×C₅⋊D₅	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
12. C₅⋊D₈₅	C₂×C₁₁	semidirect
13. C₁₇×C₅⋊D₅	C₂×C₁₁	semidirect
14. C₅²×D₁₇	C₂×C₁₁	semidirect
18. C₁₁×C₅⋊D₅	D₁₇	direct (N × H)
19. C₅²×C₁₇	C₂²×C₁₁	semidirect
22. C₁₁×D₁₇	C₅⋊D₅	direct (N × H)
24. C₅²×C₁₁	C₂×D₁₇	semidirect
26. C₁₁×C₁₇	C₂×C₅⋊D₅	semidirect
28. C₅×D₁₇	D₅×C₁₁	semidirect
34. C₅×C₁₇	C₂×D₅×C₁₁	semidirect
36. C₅×C₁₁	D₅×D₁₇	semidirect
39. C₅⋊D₅	C₁₁×D₁₇	direct (N × H)
43. D₁₇	C₁₁×C₅⋊D₅	direct (N × H)
44. C₅²	C₂×C₁₁×D₁₇	semidirect
49. C₁₇	C₂×C₁₁×C₅⋊D₅	semidirect
50. C₁₁	D₁₇×C₅⋊D₅	direct (N × H)
54. C₅	D₅×C₁₁×D₁₇	semidirect

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
C₁₁×C₁₇×C₅⋊D₅	2
C₅²×C₁₁×D₁₇	2
D₅×C₁₁×D₁₇	5
D₁₇×C₅⋊D₅	11
C₂×C₁₁×C₅⋊D₅	17

Subgroups — C11×D17×C5⋊D5 #34035252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₇×C₅⋊D₅ #34035252