Subgroups — C₉×C₁₇×D₆₅ #34091023

Order 19890.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₇×D₆₅	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₇×D₁₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₁₇×D₆₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₃×C₁₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₉×D₅×C₁₇	—	13	1	no	maximal, Hall
8	C₃×C₁₇×D₁₃	—	5	1	no	—
9	C₉×D₆₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₇	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₇	C₃×D₅	1	1	yes	characteristic
13	C₅×C₉×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅×C₁₇	—	13	1	no	—
15	C₁₇×D₁₃	—	5	1	no	Hall
16	C₃×D₆₅	C₃×C₁₇	1	1	yes	characteristic
17	C₂×C₉×C₁₇	—	65	1	no	Hall
18	C₃×C₅×C₁₇	C₃×D₁₃	1	1	yes	characteristic
19	C₉×D₁₃	—	5	1	no	Hall
20	C₁₃×C₁₇	C₉×D₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
22	D₅×C₁₇	—	13	1	no	Hall
23	C₉×C₁₇	D₆₅	1	1	yes	characteristic, direct product factor, Hall
24	D₆₅	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₉×C₁₃	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₇	—	65	1	no	—
27	C₉×D₅	—	13	1	no	Hall
28	C₅×C₁₇	C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₁₃	—	5	1	no	—
30	C₅×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₇	C₃×D₆₅	1	1	yes	characteristic
32	C₅×C₉	C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃	C₃×D₅×C₁₇	1	1	yes	characteristic
34	C₂×C₁₇	—	65	1	no	Hall
35	C₃×D₅	—	13	1	no	—
36	D₁₃	—	5	1	no	Hall
37	C₂×C₉	—	65	1	no	Hall
38	C₁₇	C₉×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₃×C₁₇×D₁₃	1	1	yes	characteristic
40	C₁₃	C₉×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	13	1	no	Hall
42	C₉	C₁₇×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	65	1	no	—
44	C₅	C₉×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×C₁₇×D₆₅	1	1	yes	characteristic
46	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₁₇	D₆₅
commutator, hypocenter	C₅×C₁₃	C₂×C₉×C₁₇
Frattini	C₃	C₃×C₁₇×D₆₅
Fitting	C₅×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₁₇×D₆₅	C₃
cosocle	C₃×C₅×C₁₃	C₂×C₃×C₁₇
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₉×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₃×C₁₇	C₂	semidirect
5. C₁₇×D₆₅	C₉	direct (N × H)
6. C₉×C₁₃×C₁₇	D₅	semidirect
9. C₉×D₆₅	C₁₇	direct (N × H)
10. C₅×C₁₃×C₁₇	C₂×C₉	semidirect
11. C₅×C₉×C₁₇	D₁₃	semidirect
13. C₅×C₉×C₁₃	C₂×C₁₇	semidirect
20. C₁₃×C₁₇	C₉×D₅	semidirect
23. C₉×C₁₇	D₆₅	direct (N × H)
24. D₆₅	C₉×C₁₇	direct (N × H)
25. C₉×C₁₃	D₅×C₁₇	semidirect
28. C₅×C₁₇	C₉×D₁₃	semidirect
30. C₅×C₁₃	C₂×C₉×C₁₇	semidirect
32. C₅×C₉	C₁₇×D₁₃	semidirect
38. C₁₇	C₉×D₆₅	direct (N × H)
40. C₁₃	C₉×D₅×C₁₇	semidirect
42. C₉	C₁₇×D₆₅	direct (N × H)
44. C₅	C₉×C₁₇×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₃×C₁₇	2
C₃×C₁₇×D₆₅	3
C₉×C₁₇×D₁₃	5
C₉×D₅×C₁₇	13
C₉×D₆₅	17

Subgroups — C9×C17×D65 #34091023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₇×D₆₅ #34091023