Subgroups — C₃×C₁₇×C₅⋊D₆₅ #45684185

Order 33150.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₅⋊D₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×D₆₅	—	5	6	no	maximal
4	C₅²×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃×C₁₇	D₅	1	6	yes	complemented
6	C₃×C₁₇×C₅⋊D₅	—	13	1	no	maximal, Hall
7	C₁₇×D₆₅	—	5	6	no	—
8	C₃×C₅⋊D₆₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₇×D₁₃	—	25	1	no	Hall
10	C₃×C₅²×C₁₇	D₁₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₃×C₁₇	C₃×D₅	1	6	yes	complemented
12	C₃×C₅²×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₁₇×C₅⋊D₅	—	13	1	no	Hall
14	C₃×C₁₃×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₅⋊D₆₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×D₅×C₁₇	—	65	6	no	—
17	C₁₇×D₁₃	—	25	1	no	Hall
18	C₅²×C₁₇	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₆₅	—	5	6	no	—
20	C₅²×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₇	D₆₅	1	6	yes	complemented
22	C₁₃×C₁₇	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	D₅×C₁₇	1	6	yes	complemented
24	D₅×C₁₇	—	65	6	no	—
25	C₃×C₅⋊D₅	—	13	1	no	Hall
26	D₆₅	—	5	6	no	—
27	C₂×C₃×C₁₇	—	325	1	no	Hall
28	C₅×C₁₇	C₃×D₆₅	1	6	yes	complemented
29	C₃×D₁₃	—	25	1	no	Hall
30	C₃×C₅²	C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₃	C₃×D₅×C₁₇	1	6	yes	complemented
32	C₃×C₁₇	C₅⋊D₆₅	1	1	yes	characteristic, direct product factor, Hall
33	C₅⋊D₅	—	13	1	no	Hall
34	C₃×C₁₃	C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₇	—	325	1	no	Hall
36	C₃×D₅	—	65	6	no	—
37	D₁₃	—	25	1	no	Hall
38	C₅²	C₃×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₁₇	C₃×C₅⋊D₆₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₅	C₁₇×D₆₅	1	6	yes	complemented
41	C₁₃	C₃×C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
42	D₅	—	65	6	no	—
43	C₂×C₃	—	325	1	no	Hall
44	C₅	C₃×C₁₇×D₆₅	1	6	yes	complemented
45	C₃	C₁₇×C₅⋊D₆₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	325	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₅⋊D₆₅
commutator, cosocle, hypocenter	C₅²×C₁₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₇	C₂
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×C₁₇	C₂	semidirect
2. C₁₇×C₅⋊D₆₅	C₃	direct (N × H)
4. C₅²×C₁₃×C₁₇	C₂×C₃	semidirect
5. C₃×C₅×C₁₃×C₁₇	D₅	semidirect
8. C₃×C₅⋊D₆₅	C₁₇	direct (N × H)
10. C₃×C₅²×C₁₇	D₁₃	semidirect
11. C₅×C₁₃×C₁₇	C₃×D₅	semidirect
12. C₃×C₅²×C₁₃	C₂×C₁₇	semidirect
14. C₃×C₁₃×C₁₇	C₅⋊D₅	semidirect
15. C₅⋊D₆₅	C₃×C₁₇	direct (N × H)
18. C₅²×C₁₇	C₃×D₁₃	semidirect
20. C₅²×C₁₃	C₂×C₃×C₁₇	semidirect
21. C₃×C₅×C₁₇	D₆₅	semidirect
22. C₁₃×C₁₇	C₃×C₅⋊D₅	semidirect
23. C₃×C₅×C₁₃	D₅×C₁₇	semidirect
28. C₅×C₁₇	C₃×D₆₅	semidirect
30. C₃×C₅²	C₁₇×D₁₃	semidirect
31. C₅×C₁₃	C₃×D₅×C₁₇	semidirect
32. C₃×C₁₇	C₅⋊D₆₅	direct (N × H)
34. C₃×C₁₃	C₁₇×C₅⋊D₅	semidirect
38. C₅²	C₃×C₁₇×D₁₃	semidirect
39. C₁₇	C₃×C₅⋊D₆₅	direct (N × H)
40. C₃×C₅	C₁₇×D₆₅	semidirect
41. C₁₃	C₃×C₁₇×C₅⋊D₅	semidirect
44. C₅	C₃×C₁₇×D₆₅	semidirect
45. C₃	C₁₇×C₅⋊D₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₃×C₁₇	2
C₁₇×C₅⋊D₆₅	3
C₃×C₁₇×D₆₅	5
C₃×C₁₇×C₅⋊D₅	13
C₃×C₅⋊D₆₅	17

Subgroups — C3×C17×C5⋊D65 #45684185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×C₅⋊D₆₅ #45684185