Subgroups — C₁₇×C₃⋊D₁₀₅ #24924228

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	C₁₇×D₁₀₅	—	3	4	no	maximal
3	C₁₇×C₃⋊D₂₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₁₇	D₃	1	4	yes	complemented
5	C₁₇×C₃⋊D₁₅	—	7	1	no	maximal, Hall
6	C₁₇×D₃₅	—	9	1	no	Hall
7	C₃²×C₇×C₁₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×D₂₁	—	15	4	no	—
10	C₃⋊D₁₀₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₁₅	—	21	4	no	—
13	C₃×C₇×C₁₇	D₁₅	1	4	yes	complemented
14	C₃²×C₅×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₇×C₃⋊D₃	—	35	1	no	Hall
16	C₃×C₅×C₁₇	D₂₁	1	4	yes	complemented
17	D₇×C₁₇	—	45	1	no	Hall
18	D₁₀₅	—	3	4	no	—
19	D₅×C₁₇	—	63	1	no	Hall
20	C₃²×C₁₇	D₃₅	1	1	yes	characteristic, complemented, Hall
21	C₃⋊D₂₁	—	5	1	no	Hall
22	C₇×C₁₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	D₃×C₁₇	1	4	yes	complemented
24	D₃×C₁₇	—	105	4	no	—
25	C₃⋊D₁₅	—	7	1	no	Hall
26	C₅×C₁₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
27	D₃₅	—	9	1	no	Hall
28	C₃²×C₇	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	D₁₀₅	1	4	yes	complemented
30	C₃²×C₅	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
31	D₂₁	—	15	4	no	—
32	C₅×C₇	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₇	—	315	1	no	Hall
34	D₁₅	—	21	4	no	—
35	C₃×C₇	C₁₇×D₁₅	1	4	yes	complemented
36	C₃⋊D₃	—	35	1	no	Hall
37	C₁₇	C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₁₇×D₂₁	1	4	yes	complemented
39	D₇	—	45	1	no	Hall
40	D₅	—	63	1	no	Hall
41	C₃²	C₁₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₁₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	105	4	no	—
44	C₅	C₁₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₁₇×D₁₀₅	1	4	yes	complemented
46	C₂	—	315	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊D₁₀₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₇	C₂	semidirect
4. C₃×C₅×C₇×C₁₇	D₃	semidirect
7. C₃²×C₇×C₁₇	D₅	semidirect
8. C₃²×C₅×C₁₇	D₇	semidirect
10. C₃⋊D₁₀₅	C₁₇	direct (N × H)
11. C₅×C₇×C₁₇	C₃⋊D₃	semidirect
13. C₃×C₇×C₁₇	D₁₅	semidirect
14. C₃²×C₅×C₇	C₂×C₁₇	semidirect
16. C₃×C₅×C₁₇	D₂₁	semidirect
20. C₃²×C₁₇	D₃₅	semidirect
22. C₇×C₁₇	C₃⋊D₁₅	semidirect
23. C₃×C₅×C₇	D₃×C₁₇	semidirect
26. C₅×C₁₇	C₃⋊D₂₁	semidirect
28. C₃²×C₇	D₅×C₁₇	semidirect
29. C₃×C₁₇	D₁₀₅	semidirect
30. C₃²×C₅	D₇×C₁₇	semidirect
32. C₅×C₇	C₁₇×C₃⋊D₃	semidirect
35. C₃×C₇	C₁₇×D₁₅	semidirect
37. C₁₇	C₃⋊D₁₀₅	direct (N × H)
38. C₃×C₅	C₁₇×D₂₁	semidirect
41. C₃²	C₁₇×D₃₅	semidirect
42. C₇	C₁₇×C₃⋊D₁₅	semidirect
44. C₅	C₁₇×C₃⋊D₂₁	semidirect
45. C₃	C₁₇×D₁₀₅	semidirect

Subgroups — C17×C3⋊D105 #24924228

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×C₃⋊D₁₀₅ #24924228