Subgroups — C₇×C₃⋊D₂₅₅ #24924229

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	C₇×D₂₅₅	—	3	4	no	maximal
3	C₇×C₃⋊D₅₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₁₇	D₃	1	4	yes	complemented
5	C₃⋊D₂₅₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₈₅	—	9	1	no	Hall
7	C₃²×C₇×C₁₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅₁	—	15	4	no	—
10	C₇×C₃⋊D₁₅	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	D₂₅₅	—	3	4	no	—
13	C₃×C₇×C₁₇	D₁₅	1	4	yes	complemented
14	C₃²×C₅×C₇	D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃⋊D₅₁	—	5	1	no	Hall
16	C₃×C₅×C₁₇	D₃×C₇	1	4	yes	complemented
17	C₇×D₁₇	—	45	1	no	Hall
18	C₇×D₁₅	—	51	4	no	—
19	D₈₅	—	9	1	no	Hall
20	C₃²×C₁₇	C₇×D₅	1	1	yes	characteristic, complemented, Hall
21	C₇×C₃⋊D₃	—	85	1	no	Hall
22	C₇×C₁₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	D₅₁	1	4	yes	complemented
24	D₅₁	—	15	4	no	—
25	C₃⋊D₁₅	—	17	1	no	Hall
26	C₅×C₁₇	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
27	C₇×D₅	—	153	1	no	Hall
28	C₃²×C₇	D₈₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₇	C₇×D₁₅	1	4	yes	complemented
30	C₃²×C₅	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
31	D₃×C₇	—	255	4	no	—
32	C₅×C₇	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Hall
33	D₁₇	—	45	1	no	Hall
34	D₁₅	—	51	4	no	—
35	C₃×C₇	D₂₅₅	1	4	yes	complemented
36	C₃⋊D₃	—	85	1	no	Hall
37	C₁₇	C₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	C₇×D₅₁	1	4	yes	complemented
39	C₂×C₇	—	765	1	no	Hall
40	D₅	—	153	1	no	Hall
41	C₃²	C₇×D₈₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₃⋊D₂₅₅	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	255	4	no	—
44	C₅	C₇×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇×D₂₅₅	1	4	yes	complemented
46	C₂	—	765	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₂₅₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃²×C₅×C₁₇
UCS	C₁ ◁ C₇

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
5. C₃⋊D₂₅₅	C₇	direct (N × H)
7. C₃²×C₇×C₁₇	D₅	semidirect
8. C₃²×C₅×C₁₇	C₂×C₇	semidirect
11. C₅×C₇×C₁₇	C₃⋊D₃	semidirect
13. C₃×C₇×C₁₇	D₁₅	semidirect
14. C₃²×C₅×C₇	D₁₇	semidirect
16. C₃×C₅×C₁₇	D₃×C₇	semidirect
20. C₃²×C₁₇	C₇×D₅	semidirect
22. C₇×C₁₇	C₃⋊D₁₅	semidirect
23. C₃×C₅×C₇	D₅₁	semidirect
26. C₅×C₁₇	C₇×C₃⋊D₃	semidirect
28. C₃²×C₇	D₈₅	semidirect
29. C₃×C₁₇	C₇×D₁₅	semidirect
30. C₃²×C₅	C₇×D₁₇	semidirect
32. C₅×C₇	C₃⋊D₅₁	semidirect
35. C₃×C₇	D₂₅₅	semidirect
37. C₁₇	C₇×C₃⋊D₁₅	semidirect
38. C₃×C₅	C₇×D₅₁	semidirect
41. C₃²	C₇×D₈₅	semidirect
42. C₇	C₃⋊D₂₅₅	direct (N × H)
44. C₅	C₇×C₃⋊D₅₁	semidirect
45. C₃	C₇×D₂₅₅	semidirect

Subgroups — C7×C3⋊D255 #24924229

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃⋊D₂₅₅ #24924229