Subgroups — C₅×C₃⋊D₃₅₇ #24924231

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	C₅×D₃₅₇	—	3	4	no	maximal
3	C₃⋊D₃₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	D₃	1	4	yes	complemented
5	C₅×C₃⋊D₅₁	—	7	1	no	maximal, Hall
6	C₅×D₁₁₉	—	9	1	no	Hall
7	C₃²×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
9	D₃₅₇	—	3	4	no	—
10	C₅×C₃⋊D₂₁	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	C₅×D₅₁	—	21	4	no	—
13	C₃×C₇×C₁₇	C₅×D₃	1	4	yes	complemented
14	C₃²×C₅×C₇	D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃⋊D₅₁	—	7	1	no	Hall
16	C₃×C₅×C₁₇	D₂₁	1	4	yes	complemented
17	D₁₁₉	—	9	1	no	Hall
18	C₅×D₂₁	—	51	4	no	—
19	C₅×D₁₇	—	63	1	no	Hall
20	C₃²×C₁₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
21	C₃⋊D₂₁	—	17	1	no	Hall
22	C₇×C₁₇	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	D₅₁	1	4	yes	complemented
24	D₅₁	—	21	4	no	—
25	C₅×C₃⋊D₃	—	119	1	no	Hall
26	C₅×C₁₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
27	C₅×D₇	—	153	1	no	Hall
28	C₃²×C₇	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₅×D₂₁	1	4	yes	complemented
30	C₃²×C₅	D₁₁₉	1	1	yes	characteristic, complemented, Hall
31	D₂₁	—	51	4	no	—
32	C₅×C₇	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Hall
33	D₁₇	—	63	1	no	Hall
34	C₅×D₃	—	357	4	no	—
35	C₃×C₇	C₅×D₅₁	1	4	yes	complemented
36	C₃⋊D₃	—	119	1	no	Hall
37	C₁₇	C₅×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	D₃₅₇	1	4	yes	complemented
39	D₇	—	153	1	no	Hall
40	C₂×C₅	—	1071	1	no	Hall
41	C₃²	C₅×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	357	4	no	—
44	C₅	C₃⋊D₃₅₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₃₅₇	1	4	yes	complemented
46	C₂	—	1071	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₃₅₇
commutator, cosocle, hypocenter	C₃²×C₇×C₁₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃²×C₇×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₇	C₂	semidirect
3. C₃⋊D₃₅₇	C₅	direct (N × H)
4. C₃×C₅×C₇×C₁₇	D₃	semidirect
7. C₃²×C₇×C₁₇	C₂×C₅	semidirect
8. C₃²×C₅×C₁₇	D₇	semidirect
11. C₅×C₇×C₁₇	C₃⋊D₃	semidirect
13. C₃×C₇×C₁₇	C₅×D₃	semidirect
14. C₃²×C₅×C₇	D₁₇	semidirect
16. C₃×C₅×C₁₇	D₂₁	semidirect
20. C₃²×C₁₇	C₅×D₇	semidirect
22. C₇×C₁₇	C₅×C₃⋊D₃	semidirect
23. C₃×C₅×C₇	D₅₁	semidirect
26. C₅×C₁₇	C₃⋊D₂₁	semidirect
28. C₃²×C₇	C₅×D₁₇	semidirect
29. C₃×C₁₇	C₅×D₂₁	semidirect
30. C₃²×C₅	D₁₁₉	semidirect
32. C₅×C₇	C₃⋊D₅₁	semidirect
35. C₃×C₇	C₅×D₅₁	semidirect
37. C₁₇	C₅×C₃⋊D₂₁	semidirect
38. C₃×C₅	D₃₅₇	semidirect
41. C₃²	C₅×D₁₁₉	semidirect
42. C₇	C₅×C₃⋊D₅₁	semidirect
44. C₅	C₃⋊D₃₅₇	direct (N × H)
45. C₃	C₅×D₃₅₇	semidirect

Subgroups — C5×C3⋊D357 #24924231

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊D₃₅₇ #24924231