Subgroups — C₇×C₉×D₈₅ #24924192

Order 10710.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₈₅	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×D₁₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₉×D₈₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₈₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₁₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×D₁₇	—	5	1	no	—
10	C₇×C₉×D₅	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×D₈₅	C₃×C₇	1	1	yes	characteristic
13	C₃×C₇×C₁₇	C₃×D₅	1	1	yes	characteristic
14	C₅×C₇×C₉	D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₉×D₁₇	—	5	1	no	Hall
16	C₃×C₅×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic
17	C₇×D₁₇	—	5	1	no	Hall
18	C₃×C₇×D₅	—	17	1	no	—
19	D₈₅	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₉×C₁₇	C₇×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₉	—	85	1	no	Hall
22	C₇×C₁₇	C₉×D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	C₃×D₁₇	1	1	yes	characteristic
24	C₃×D₁₇	—	5	1	no	—
25	C₉×D₅	—	17	1	no	Hall
26	C₅×C₁₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Hall
27	C₇×D₅	—	17	1	no	Hall
28	C₇×C₉	D₈₅	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₁₇	C₃×C₇×D₅	1	1	yes	characteristic
30	C₅×C₉	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₇	—	85	1	no	—
32	C₅×C₇	C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
33	D₁₇	—	5	1	no	Hall
34	C₃×D₅	—	17	1	no	—
35	C₃×C₇	C₃×D₈₅	1	1	yes	characteristic
36	C₂×C₉	—	85	1	no	Hall
37	C₁₇	C₇×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	C₃×C₇×D₁₇	1	1	yes	characteristic
39	C₂×C₇	—	85	1	no	Hall
40	D₅	—	17	1	no	Hall
41	C₉	C₇×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₉×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	85	1	no	—
44	C₅	C₇×C₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×C₇×D₈₅	1	1	yes	characteristic
46	C₂	—	85	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₉	D₈₅
commutator, hypocenter	C₅×C₁₇	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₈₅
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₇×D₈₅	C₃
cosocle	C₃×C₅×C₁₇	C₂×C₃×C₇
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₇×C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₇	C₂	semidirect
5. C₉×D₈₅	C₇	direct (N × H)
6. C₇×D₈₅	C₉	direct (N × H)
7. C₇×C₉×C₁₇	D₅	semidirect
8. C₅×C₉×C₁₇	C₂×C₇	semidirect
11. C₅×C₇×C₁₇	C₂×C₉	semidirect
14. C₅×C₇×C₉	D₁₇	semidirect
19. D₈₅	C₇×C₉	direct (N × H)
20. C₉×C₁₇	C₇×D₅	semidirect
22. C₇×C₁₇	C₉×D₅	semidirect
26. C₅×C₁₇	C₂×C₇×C₉	semidirect
28. C₇×C₉	D₈₅	direct (N × H)
30. C₅×C₉	C₇×D₁₇	semidirect
32. C₅×C₇	C₉×D₁₇	semidirect
37. C₁₇	C₇×C₉×D₅	semidirect
41. C₉	C₇×D₈₅	direct (N × H)
42. C₇	C₉×D₈₅	direct (N × H)
44. C₅	C₇×C₉×D₁₇	semidirect

Subgroups — C7×C9×D85 #24924192

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₉×D₈₅ #24924192