Subgroups — C₁₇×D₁₁×C₅⋊D₅ #34035255

Order 18700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅⋊D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₇×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×C₁₇×D₁₁	—	5	6	no	maximal
6	C₁₇×D₅₅	—	5	6	no	—
7	D₅×C₁₁×C₁₇	—	5	6	no	—
8	C₅×C₁₇×D₁₁	D₅	1	6	yes	complemented
9	C₂×C₁₇×C₅⋊D₅	—	11	1	no	maximal, Hall
10	D₁₁×C₅⋊D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₇	C₂×D₅	1	6	yes	complemented
12	C₂×C₅²×C₁₇	—	11	1	no	—
13	C₁₇×C₅⋊D₅	—	11	1	no	—
14	C₁₇×C₅⋊D₅	D₁₁	1	1	yes	characteristic, direct product factor
15	C₂×C₁₇×D₁₁	—	25	1	no	Hall
16	C₅⋊D₅₅	C₂×C₁₇	1	1	yes	characteristic, complemented
17	C₁₁×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₅²×D₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
19	C₅²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁×C₁₇	—	25	1	no	—
21	C₁₇×D₁₁	—	25	1	no	—
22	C₁₇×D₁₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	C₂×D₅×C₁₇	—	55	6	no	—
24	C₅²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
25	D₅×D₁₁	—	5	6	no	—
26	C₁₁×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₇	—	11	6	no	—
28	D₅×C₁₇	—	5	6	no	—
29	D₅×C₁₇	—	55	6	no	—
30	D₅₅	—	5	6	no	—
31	C₅×D₁₁	D₅×C₁₇	1	6	yes	complemented
32	D₅×C₁₁	—	5	6	no	—
33	C₂×C₅⋊D₅	—	11	1	no	Hall
34	C₅×C₁₇	D₅×D₁₁	1	6	yes	complemented
35	C₂²×C₁₇	—	275	1	no	Hall
36	C₅×C₁₁	C₂×D₅×C₁₇	1	6	yes	complemented
37	C₂×C₅²	—	11	1	no	—
38	C₅⋊D₅	—	11	1	no	—
39	C₅⋊D₅	C₁₇×D₁₁	1	1	yes	characteristic, direct product factor
40	C₂×D₁₁	—	25	1	no	Hall
41	C₂×C₁₇	—	11	1	no	—
42	C₂×C₁₇	—	275	1	no	—
43	C₂×C₁₇	—	25	1	no	—
44	C₅²	C₂×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	25	1	no	—
46	D₁₁	—	25	1	no	—
47	D₁₁	C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor
48	C₂×D₅	—	55	6	no	—
49	C₁₇	D₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
50	C₁₁	C₂×C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	11	6	no	—
52	D₅	—	5	6	no	—
53	D₅	—	55	6	no	—
54	C₅	D₅×C₁₇×D₁₁	1	6	yes	complemented
55	C₂²	—	275	1	no	Sylow
56	C₂	—	11	1	no	—
57	C₂	—	275	1	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₁₁×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅⋊D₅₅	C₂	semidirect
2. C₁₁×C₁₇×C₅⋊D₅	C₂	semidirect
3. C₅²×C₁₇×D₁₁	C₂	semidirect
4. C₅²×C₁₁×C₁₇	C₂²	semidirect
8. C₅×C₁₇×D₁₁	D₅	semidirect
10. D₁₁×C₅⋊D₅	C₁₇	direct (N × H)
11. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
14. C₁₇×C₅⋊D₅	D₁₁	direct (N × H)
16. C₅⋊D₅₅	C₂×C₁₇	semidirect
17. C₁₁×C₅⋊D₅	C₂×C₁₇	semidirect
18. C₅²×D₁₁	C₂×C₁₇	semidirect
19. C₅²×C₁₇	C₂×D₁₁	semidirect
22. C₁₇×D₁₁	C₅⋊D₅	direct (N × H)
24. C₅²×C₁₁	C₂²×C₁₇	semidirect
26. C₁₁×C₁₇	C₂×C₅⋊D₅	semidirect
31. C₅×D₁₁	D₅×C₁₇	semidirect
34. C₅×C₁₇	D₅×D₁₁	semidirect
36. C₅×C₁₁	C₂×D₅×C₁₇	semidirect
39. C₅⋊D₅	C₁₇×D₁₁	direct (N × H)
44. C₅²	C₂×C₁₇×D₁₁	semidirect
47. D₁₁	C₁₇×C₅⋊D₅	direct (N × H)
49. C₁₇	D₁₁×C₅⋊D₅	direct (N × H)
50. C₁₁	C₂×C₁₇×C₅⋊D₅	semidirect
54. C₅	D₅×C₁₇×D₁₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₇×C₅⋊D₅₅	2
C₁₁×C₁₇×C₅⋊D₅	2
C₅²×C₁₇×D₁₁	2
D₅×C₁₇×D₁₁	5
C₂×C₁₇×C₅⋊D₅	11
D₁₁×C₅⋊D₅	17

Subgroups — C17×D11×C5⋊D5 #34035255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₁₁×C₅⋊D₅ #34035255