Subgroups — C₇×C₃⋊D₈₈₅ #49151237

Order 37170.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₈₈₅	—	3	4	no	maximal
3	C₇×C₃⋊D₁₇₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₅₉	D₃	1	4	yes	complemented
5	C₃⋊D₈₈₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₂₉₅	—	9	1	no	Hall
7	C₃²×C₇×C₅₉	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₁₇₇	—	15	4	no	—
10	C₅×C₇×C₅₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	D₈₈₅	—	3	4	no	—
12	C₃×C₇×C₅₉	D₁₅	1	4	yes	complemented
13	C₃⋊D₁₇₇	—	5	1	no	Hall
14	C₃×C₅×C₅₉	D₃×C₇	1	4	yes	complemented
15	C₇×D₅₉	—	45	1	no	Hall
16	C₇×C₃⋊D₁₅	—	59	1	no	maximal, Hall
17	D₂₉₅	—	9	1	no	Hall
18	C₃²×C₅₉	C₇×D₅	1	1	yes	characteristic, complemented, Hall
19	C₇×C₅₉	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
20	D₁₇₇	—	15	4	no	—
21	C₃²×C₅×C₇	D₅₉	1	1	yes	characteristic, complemented, Hall
22	C₅×C₅₉	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₅	—	177	4	no	—
24	C₃×C₅₉	C₇×D₁₅	1	4	yes	complemented
25	C₇×C₃⋊D₃	—	295	1	no	Hall
26	D₅₉	—	45	1	no	Hall
27	C₃×C₅×C₇	D₁₇₇	1	4	yes	complemented
28	C₃⋊D₁₅	—	59	1	no	Hall
29	C₇×D₅	—	531	1	no	Hall
30	C₃²×C₇	D₂₉₅	1	1	yes	characteristic, complemented, Hall
31	C₅₉	C₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
32	C₃²×C₅	C₇×D₅₉	1	1	yes	characteristic, complemented, Hall
33	D₃×C₇	—	885	4	no	—
34	C₅×C₇	C₃⋊D₁₇₇	1	1	yes	characteristic, complemented, Hall
35	D₁₅	—	177	4	no	—
36	C₃×C₇	D₈₈₅	1	4	yes	complemented
37	C₃⋊D₃	—	295	1	no	Hall
38	C₃×C₅	C₇×D₁₇₇	1	4	yes	complemented
39	C₂×C₇	—	2655	1	no	Hall
40	D₅	—	531	1	no	Hall
41	C₃²	C₇×D₂₉₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₃⋊D₈₈₅	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	885	4	no	—
44	C₅	C₇×C₃⋊D₁₇₇	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇×D₈₈₅	1	4	yes	complemented
46	C₂	—	2655	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₈₈₅
commutator, cosocle, hypocenter	C₃²×C₅×C₅₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₅₉	C₂
LCS	G ▷ C₃²×C₅×C₅₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₅₉	C₂	semidirect
4. C₃×C₅×C₇×C₅₉	D₃	semidirect
5. C₃⋊D₈₈₅	C₇	direct (N × H)
7. C₃²×C₇×C₅₉	D₅	semidirect
8. C₃²×C₅×C₅₉	C₂×C₇	semidirect
10. C₅×C₇×C₅₉	C₃⋊D₃	semidirect
12. C₃×C₇×C₅₉	D₁₅	semidirect
14. C₃×C₅×C₅₉	D₃×C₇	semidirect
18. C₃²×C₅₉	C₇×D₅	semidirect
19. C₇×C₅₉	C₃⋊D₁₅	semidirect
21. C₃²×C₅×C₇	D₅₉	semidirect
22. C₅×C₅₉	C₇×C₃⋊D₃	semidirect
24. C₃×C₅₉	C₇×D₁₅	semidirect
27. C₃×C₅×C₇	D₁₇₇	semidirect
30. C₃²×C₇	D₂₉₅	semidirect
31. C₅₉	C₇×C₃⋊D₁₅	semidirect
32. C₃²×C₅	C₇×D₅₉	semidirect
34. C₅×C₇	C₃⋊D₁₇₇	semidirect
36. C₃×C₇	D₈₈₅	semidirect
38. C₃×C₅	C₇×D₁₇₇	semidirect
41. C₃²	C₇×D₂₉₅	semidirect
42. C₇	C₃⋊D₈₈₅	direct (N × H)
44. C₅	C₇×C₃⋊D₁₇₇	semidirect
45. C₃	C₇×D₈₈₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅×C₇×C₅₉	2
C₇×D₈₈₅	3
C₇×C₃⋊D₁₇₇	5
C₃⋊D₈₈₅	7
C₇×C₃⋊D₁₅	59

Subgroups — C7×C3⋊D885 #49151237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₈₈₅ #49151237