Subgroups — C₂×C₅×C₇×C₉×C₁₇ #24924186

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, direct product factor, Hall
2	C₂×C₃×C₅×C₇×C₁₇	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₉×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	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₁₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₉×C₁₇	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₁₇	C₃×C₅	1	1	yes	characteristic
10	C₂×C₅×C₇×C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×C₁₇	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×C₁₇	C₃×C₇	1	1	yes	characteristic
13	C₃×C₇×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
14	C₅×C₇×C₉	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₉×C₁₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic
17	C₂×C₇×C₁₇	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₅×C₇	C₃×C₁₇	1	1	yes	characteristic
19	C₂×C₅×C₁₇	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₉×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₇	C₂×C₃×C₁₇	1	1	yes	characteristic
24	C₂×C₃×C₁₇	C₃×C₅×C₇	1	1	yes	characteristic
25	C₂×C₅×C₉	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₅×C₁₇	C₂×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₇	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₉	C₂×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₁₇	C₂×C₃×C₅×C₇	1	1	yes	characteristic
30	C₅×C₉	C₂×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₇	C₃×C₅×C₁₇	1	1	yes	characteristic
32	C₅×C₇	C₂×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₇	C₅×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅	C₃×C₇×C₁₇	1	1	yes	characteristic
35	C₃×C₇	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
36	C₂×C₉	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
37	C₁₇	C₂×C₅×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₂×C₃×C₇×C₁₇	1	1	yes	characteristic
39	C₂×C₇	C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	C₇×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
41	C₉	C₂×C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃×C₅×C₇×C₁₇	1	1	yes	characteristic
44	C₅	C₂×C₇×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂×C₃×C₅×C₇×C₁₇	1	1	yes	characteristic
46	C₂	C₅×C₇×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₇	C₂	direct (N × H)
3. C₂×C₇×C₉×C₁₇	C₅	direct (N × H)
5. C₂×C₅×C₉×C₁₇	C₇	direct (N × H)
6. C₂×C₅×C₇×C₁₇	C₉	direct (N × H)
7. C₇×C₉×C₁₇	C₂×C₅	direct (N × H)
8. C₅×C₉×C₁₇	C₂×C₇	direct (N × H)
10. C₂×C₅×C₇×C₉	C₁₇	direct (N × H)
11. C₅×C₇×C₁₇	C₂×C₉	direct (N × H)
14. C₅×C₇×C₉	C₂×C₁₇	direct (N × H)
15. C₂×C₉×C₁₇	C₅×C₇	direct (N × H)
17. C₂×C₇×C₁₇	C₅×C₉	direct (N × H)
19. C₂×C₅×C₁₇	C₇×C₉	direct (N × H)
20. C₉×C₁₇	C₂×C₅×C₇	direct (N × H)
21. C₂×C₇×C₉	C₅×C₁₇	direct (N × H)
22. C₇×C₁₇	C₂×C₅×C₉	direct (N × H)
25. C₂×C₅×C₉	C₇×C₁₇	direct (N × H)
26. C₅×C₁₇	C₂×C₇×C₉	direct (N × H)
27. C₂×C₅×C₇	C₉×C₁₇	direct (N × H)
28. C₇×C₉	C₂×C₅×C₁₇	direct (N × H)
30. C₅×C₉	C₂×C₇×C₁₇	direct (N × H)
32. C₅×C₇	C₂×C₉×C₁₇	direct (N × H)
33. C₂×C₁₇	C₅×C₇×C₉	direct (N × H)
36. C₂×C₉	C₅×C₇×C₁₇	direct (N × H)
37. C₁₇	C₂×C₅×C₇×C₉	direct (N × H)
39. C₂×C₇	C₅×C₉×C₁₇	direct (N × H)
40. C₂×C₅	C₇×C₉×C₁₇	direct (N × H)
41. C₉	C₂×C₅×C₇×C₁₇	direct (N × H)
42. C₇	C₂×C₅×C₉×C₁₇	direct (N × H)
44. C₅	C₂×C₇×C₉×C₁₇	direct (N × H)
46. C₂	C₅×C₇×C₉×C₁₇	direct (N × H)

Subgroups — C2×C5×C7×C9×C17 #24924186

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×C₉×C₁₇ #24924186