Subgroups — C₂×C₁₇×C₅⋊D₅₅ #34035270

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	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×C₁₇×D₅₅	—	5	6	no	maximal
5	C₂×C₅×C₁₁×C₁₇	D₅	1	6	yes	complemented
6	C₁₇×D₅₅	—	5	12	no	—
7	C₂×C₁₇×C₅⋊D₅	—	11	1	no	maximal, Hall
8	C₂×C₅⋊D₅₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₁₇	C₂×D₅	1	6	yes	complemented
10	C₂×C₅²×C₁₇	D₁₁	1	1	yes	characteristic, complemented
11	C₁₇×C₅⋊D₅	—	11	2	no	—
12	C₂×C₁₇×D₁₁	—	25	1	no	Hall
13	C₂×C₅²×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
14	C₅⋊D₅₅	C₂×C₁₇	1	2	yes	direct product factor
15	C₅²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented
17	C₁₇×D₁₁	—	25	2	no	—
18	C₂×D₅×C₁₇	—	55	6	no	—
19	C₅²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅₅	—	5	6	no	—
21	C₁₁×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₁₇	D₅₅	1	6	yes	complemented
23	D₅×C₁₇	—	55	12	no	—
24	C₂×C₅×C₁₁	D₅×C₁₇	1	6	yes	complemented
25	D₅₅	—	5	12	no	—
26	C₂×C₅⋊D₅	—	11	1	no	Hall
27	C₅×C₁₇	C₂×D₅₅	1	6	yes	complemented
28	C₂²×C₁₇	—	275	1	no	Hall
29	C₅×C₁₁	C₂×D₅×C₁₇	1	6	yes	complemented
30	C₂×C₅²	C₁₇×D₁₁	1	1	yes	characteristic, complemented
31	C₅⋊D₅	—	11	2	no	—
32	C₂×D₁₁	—	25	1	no	Hall
33	C₂×C₁₇	—	275	2	no	—
34	C₂×C₁₇	C₅⋊D₅₅	1	1	yes	characteristic, direct product factor
35	C₅²	C₂×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₁	C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented
37	D₁₁	—	25	2	no	—
38	C₂×D₅	—	55	6	no	—
39	C₁₇	C₂×C₅⋊D₅₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₁₁	C₂×C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	C₁₇×D₅₅	1	6	yes	complemented
42	D₅	—	55	12	no	—
43	C₅	C₂×C₁₇×D₅₅	1	6	yes	complemented
44	C₂²	—	275	1	no	Sylow
45	C₂	—	275	2	no	—
46	C₂	C₁₇×C₅⋊D₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₅⋊D₅₅
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅⋊D₅₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₁×C₁₇	C₂	semidirect
3. C₅²×C₁₁×C₁₇	C₂²	semidirect
5. C₂×C₅×C₁₁×C₁₇	D₅	semidirect
8. C₂×C₅⋊D₅₅	C₁₇	direct (N × H)
9. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
10. C₂×C₅²×C₁₇	D₁₁	semidirect
13. C₂×C₅²×C₁₁	C₂×C₁₇	semidirect
14. C₅⋊D₅₅	C₂×C₁₇	direct (N × H)
15. C₅²×C₁₇	C₂×D₁₁	semidirect
16. C₂×C₁₁×C₁₇	C₅⋊D₅	semidirect
19. C₅²×C₁₁	C₂²×C₁₇	semidirect
21. C₁₁×C₁₇	C₂×C₅⋊D₅	semidirect
22. C₂×C₅×C₁₇	D₅₅	semidirect
24. C₂×C₅×C₁₁	D₅×C₁₇	semidirect
27. C₅×C₁₇	C₂×D₅₅	semidirect
29. C₅×C₁₁	C₂×D₅×C₁₇	semidirect
30. C₂×C₅²	C₁₇×D₁₁	semidirect
34. C₂×C₁₇	C₅⋊D₅₅	direct (N × H)
35. C₅²	C₂×C₁₇×D₁₁	semidirect
36. C₂×C₁₁	C₁₇×C₅⋊D₅	semidirect
39. C₁₇	C₂×C₅⋊D₅₅	direct (N × H)
40. C₁₁	C₂×C₁₇×C₅⋊D₅	semidirect
41. C₂×C₅	C₁₇×D₅₅	semidirect
43. C₅	C₂×C₁₇×D₅₅	semidirect
46. C₂	C₁₇×C₅⋊D₅₅	direct (N × H)

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

Subgroups — C2×C17×C5⋊D55 #34035270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₅⋊D₅₅ #34035270