Subgroups — C₅×C₇×C₁₇×D₉ #24924195

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	C₅×D₃×C₇×C₁₇	—	3	1	no	maximal
3	C₇×C₁₇×D₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	D₃	1	1	yes	characteristic
5	C₅×C₁₇×D₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₇	—	9	1	no	Hall
7	C₇×C₉×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	D₃×C₇×C₁₇	—	3	1	no	—
10	C₅×C₇×D₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×C₁₇	D₉	1	1	yes	characteristic, direct product factor, Hall
12	C₅×D₃×C₁₇	—	3	1	no	—
13	C₃×C₇×C₁₇	C₅×D₃	1	1	yes	characteristic
14	C₅×C₇×C₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₇×D₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅×C₁₇	D₃×C₇	1	1	yes	characteristic
17	C₂×C₇×C₁₇	—	9	1	no	Hall
18	C₅×D₃×C₇	—	3	1	no	—
19	C₂×C₅×C₁₇	—	9	1	no	Hall
20	C₉×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
21	C₇×D₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₁₇	C₅×D₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₇	D₃×C₁₇	1	1	yes	characteristic
24	D₃×C₁₇	—	3	1	no	—
25	C₅×D₉	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₅×C₁₇	C₇×D₉	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₇	—	9	1	no	Hall
28	C₇×C₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₅×D₃×C₇	1	1	yes	characteristic
30	C₅×C₉	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
31	D₃×C₇	—	3	1	no	—
32	C₅×C₇	C₁₇×D₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₇	—	9	1	no	Hall
34	C₅×D₃	—	3	1	no	—
35	C₃×C₇	C₅×D₃×C₁₇	1	1	yes	characteristic
36	D₉	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
37	C₁₇	C₅×C₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	D₃×C₇×C₁₇	1	1	yes	characteristic
39	C₂×C₇	—	9	1	no	Hall
40	C₂×C₅	—	9	1	no	Hall
41	C₉	C₂×C₅×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×C₁₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	3	1	no	—
44	C₅	C₇×C₁₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₃×C₇×C₁₇	1	1	yes	characteristic
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₇×C₁₇
Frattini	C₃	C₅×D₃×C₇×C₁₇
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₇	C₂	semidirect
3. C₇×C₁₇×D₉	C₅	direct (N × H)
5. C₅×C₁₇×D₉	C₇	direct (N × H)
7. C₇×C₉×C₁₇	C₂×C₅	semidirect
8. C₅×C₉×C₁₇	C₂×C₇	semidirect
10. C₅×C₇×D₉	C₁₇	direct (N × H)
11. C₅×C₇×C₁₇	D₉	direct (N × H)
14. C₅×C₇×C₉	C₂×C₁₇	semidirect
15. C₁₇×D₉	C₅×C₇	direct (N × H)
20. C₉×C₁₇	C₂×C₅×C₇	semidirect
21. C₇×D₉	C₅×C₁₇	direct (N × H)
22. C₇×C₁₇	C₅×D₉	direct (N × H)
25. C₅×D₉	C₇×C₁₇	direct (N × H)
26. C₅×C₁₇	C₇×D₉	direct (N × H)
28. C₇×C₉	C₂×C₅×C₁₇	semidirect
30. C₅×C₉	C₂×C₇×C₁₇	semidirect
32. C₅×C₇	C₁₇×D₉	direct (N × H)
36. D₉	C₅×C₇×C₁₇	direct (N × H)
37. C₁₇	C₅×C₇×D₉	direct (N × H)
41. C₉	C₂×C₅×C₇×C₁₇	semidirect
42. C₇	C₅×C₁₇×D₉	direct (N × H)
44. C₅	C₇×C₁₇×D₉	direct (N × H)

Subgroups — C5×C7×C17×D9 #24924195

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₇×C₁₇×D₉ #24924195