Subgroups — C₃²×C₅×D₇×C₁₇ #24924248

Order 10710.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₇×C₁₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₇×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	C₂×C₃	1	4	yes	complemented
5	C₂×C₃²×C₅×C₁₇	—	7	1	no	maximal, Hall
6	C₅×D₇×C₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₁₇	D₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₇×C₁₇	C₃×C₅	1	4	yes	direct product factor
10	C₃²×C₅×D₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₇	—	7	4	no	—
13	C₃×C₇×C₁₇	C₂×C₃×C₅	1	4	yes	complemented
14	C₃²×C₅×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃²×C₁₇	—	7	1	no	Hall
16	C₃×C₅×C₁₇	C₃×D₇	1	4	yes	direct product factor
17	D₇×C₁₇	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×D₇	C₃×C₁₇	1	4	yes	direct product factor
19	C₂×C₅×C₁₇	—	7	1	no	Hall
20	C₃²×C₁₇	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃²×D₇	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₁₇	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	C₂×C₃×C₁₇	1	4	yes	complemented
24	C₂×C₃×C₁₇	—	7	4	no	—
25	C₂×C₃²×C₅	—	7	1	no	Hall
26	C₅×C₁₇	C₃²×D₇	1	1	yes	characteristic, direct product factor, Hall
27	C₅×D₇	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃²×C₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₃×C₅×D₇	1	4	yes	direct product factor
30	C₃²×C₅	D₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
31	C₃×D₇	C₃×C₅×C₁₇	1	4	yes	direct product factor
32	C₅×C₇	C₂×C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₇	—	7	1	no	Hall
34	C₂×C₃×C₅	—	7	4	no	—
35	C₃×C₇	C₂×C₃×C₅×C₁₇	1	4	yes	complemented
36	C₂×C₃²	—	7	1	no	Hall
37	C₁₇	C₃²×C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₃×D₇×C₁₇	1	4	yes	direct product factor
39	D₇	C₃²×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	—	7	1	no	Hall
41	C₃²	C₅×D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₃²×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	4	no	—
44	C₅	C₃²×D₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×D₇×C₁₇	1	4	yes	direct product factor
46	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅×C₁₇	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₇	C₂	semidirect
2. C₃×C₅×D₇×C₁₇	C₃	direct (N × H)
3. C₃²×D₇×C₁₇	C₅	direct (N × H)
4. C₃×C₅×C₇×C₁₇	C₂×C₃	semidirect
6. C₅×D₇×C₁₇	C₃²	direct (N × H)
7. C₃²×C₇×C₁₇	C₂×C₅	semidirect
8. C₃²×C₅×C₁₇	D₇	direct (N × H)
9. C₃×D₇×C₁₇	C₃×C₅	direct (N × H)
10. C₃²×C₅×D₇	C₁₇	direct (N × H)
11. C₅×C₇×C₁₇	C₂×C₃²	semidirect
13. C₃×C₇×C₁₇	C₂×C₃×C₅	semidirect
14. C₃²×C₅×C₇	C₂×C₁₇	semidirect
16. C₃×C₅×C₁₇	C₃×D₇	direct (N × H)
17. D₇×C₁₇	C₃²×C₅	direct (N × H)
18. C₃×C₅×D₇	C₃×C₁₇	direct (N × H)
20. C₃²×C₁₇	C₅×D₇	direct (N × H)
21. C₃²×D₇	C₅×C₁₇	direct (N × H)
22. C₇×C₁₇	C₂×C₃²×C₅	semidirect
23. C₃×C₅×C₇	C₂×C₃×C₁₇	semidirect
26. C₅×C₁₇	C₃²×D₇	direct (N × H)
27. C₅×D₇	C₃²×C₁₇	direct (N × H)
28. C₃²×C₇	C₂×C₅×C₁₇	semidirect
29. C₃×C₁₇	C₃×C₅×D₇	direct (N × H)
30. C₃²×C₅	D₇×C₁₇	direct (N × H)
31. C₃×D₇	C₃×C₅×C₁₇	direct (N × H)
32. C₅×C₇	C₂×C₃²×C₁₇	semidirect
35. C₃×C₇	C₂×C₃×C₅×C₁₇	semidirect
37. C₁₇	C₃²×C₅×D₇	direct (N × H)
38. C₃×C₅	C₃×D₇×C₁₇	direct (N × H)
39. D₇	C₃²×C₅×C₁₇	direct (N × H)
41. C₃²	C₅×D₇×C₁₇	direct (N × H)
42. C₇	C₂×C₃²×C₅×C₁₇	semidirect
44. C₅	C₃²×D₇×C₁₇	direct (N × H)
45. C₃	C₃×C₅×D₇×C₁₇	direct (N × H)

Subgroups — C32×C5×D7×C17 #24924248

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₅×D₇×C₁₇ #24924248