Subgroups — C₅×C₉×D₇×C₁₇ #24924189

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×C₅×D₇×C₁₇	C₃	1	1	yes	maximal, characteristic
3	C₉×D₇×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₉×C₁₇	—	7	1	no	maximal, Hall
6	C₅×D₇×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₁₇	D₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₇×C₁₇	C₃×C₅	1	1	yes	characteristic
10	C₅×C₉×D₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₇	—	7	1	no	—
13	C₃×C₇×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
14	C₅×C₇×C₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₉×C₁₇	—	7	1	no	Hall
16	C₃×C₅×C₁₇	C₃×D₇	1	1	yes	characteristic
17	D₇×C₁₇	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×D₇	C₃×C₁₇	1	1	yes	characteristic
19	C₂×C₅×C₁₇	—	7	1	no	Hall
20	C₉×C₁₇	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
21	C₉×D₇	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	C₂×C₃×C₁₇	1	1	yes	characteristic
24	C₂×C₃×C₁₇	—	7	1	no	—
25	C₂×C₅×C₉	—	7	1	no	Hall
26	C₅×C₁₇	C₉×D₇	1	1	yes	characteristic, direct product factor, Hall
27	C₅×D₇	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₃×C₅×D₇	1	1	yes	characteristic
30	C₅×C₉	D₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
31	C₃×D₇	C₃×C₅×C₁₇	1	1	yes	characteristic
32	C₅×C₇	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₇	—	7	1	no	Hall
34	C₂×C₃×C₅	—	7	1	no	—
35	C₃×C₇	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
36	C₂×C₉	—	7	1	no	Hall
37	C₁₇	C₅×C₉×D₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₃×D₇×C₁₇	1	1	yes	characteristic
39	D₇	C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	—	7	1	no	Hall
41	C₉	C₅×D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₅×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	1	no	—
44	C₅	C₉×D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×D₇×C₁₇	1	1	yes	characteristic
46	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉×C₁₇	D₇
commutator, hypocenter	C₇	C₂×C₅×C₉×C₁₇
Frattini	C₃	C₃×C₅×D₇×C₁₇
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₇×C₁₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₅×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₉×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. C₉×D₇×C₁₇	C₅	direct (N × H)
6. C₅×D₇×C₁₇	C₉	direct (N × H)
7. C₇×C₉×C₁₇	C₂×C₅	semidirect
8. C₅×C₉×C₁₇	D₇	direct (N × H)
10. C₅×C₉×D₇	C₁₇	direct (N × H)
11. C₅×C₇×C₁₇	C₂×C₉	semidirect
14. C₅×C₇×C₉	C₂×C₁₇	semidirect
17. D₇×C₁₇	C₅×C₉	direct (N × H)
20. C₉×C₁₇	C₅×D₇	direct (N × H)
21. C₉×D₇	C₅×C₁₇	direct (N × H)
22. C₇×C₁₇	C₂×C₅×C₉	semidirect
26. C₅×C₁₇	C₉×D₇	direct (N × H)
27. C₅×D₇	C₉×C₁₇	direct (N × H)
28. C₇×C₉	C₂×C₅×C₁₇	semidirect
30. C₅×C₉	D₇×C₁₇	direct (N × H)
32. C₅×C₇	C₂×C₉×C₁₇	semidirect
37. C₁₇	C₅×C₉×D₇	direct (N × H)
39. D₇	C₅×C₉×C₁₇	direct (N × H)
41. C₉	C₅×D₇×C₁₇	direct (N × H)
42. C₇	C₂×C₅×C₉×C₁₇	semidirect
44. C₅	C₉×D₇×C₁₇	direct (N × H)

Subgroups — C5×C9×D7×C17 #24924189

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₉×D₇×C₁₇ #24924189