Subgroups — C₃²×D₁₂₉₅ #37552133

Order 23310.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₂₉₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₂₅₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₃₇	C₂×C₃	1	4	yes	complemented
5	C₃²×D₁₈₅	—	7	1	no	maximal, Hall
6	D₁₂₉₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₃₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
9	C₃×D₂₅₉	—	5	4	no	—
10	C₅×C₇×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₈₅	—	7	4	no	—
12	C₃×C₇×C₃₇	C₃×D₅	1	4	yes	complemented
13	C₃²×D₃₇	—	35	1	no	Hall
14	C₃²×D₃₅	—	37	1	no	maximal, Hall
15	C₃×C₅×C₃₇	C₃×D₇	1	4	yes	complemented
16	D₂₅₉	—	5	1	no	Hall
17	D₁₈₅	—	7	1	no	Hall
18	C₃²×C₃₇	D₃₅	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅×C₇	D₃₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃₇	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
21	C₃×D₃₇	—	35	4	no	—
22	C₃×D₃₅	—	37	4	no	—
23	C₅×C₃₇	C₃²×D₇	1	1	yes	characteristic, complemented, Hall
24	C₃²×D₇	—	185	1	no	Hall
25	C₃×C₃₇	C₃×D₃₅	1	4	yes	complemented
26	C₃×C₅×C₇	C₃×D₃₇	1	4	yes	complemented
27	C₃²×D₅	—	259	1	no	Hall
28	D₃₇	—	35	1	no	Hall
29	D₃₅	—	37	1	no	Hall
30	C₃²×C₇	D₁₈₅	1	1	yes	characteristic, complemented, Hall
31	C₃²×C₅	D₂₅₉	1	1	yes	characteristic, complemented, Hall
32	C₃×D₇	—	185	4	no	—
33	C₃₇	C₃²×D₃₅	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	C₃²×D₃₇	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	259	4	no	—
36	C₃×C₇	C₃×D₁₈₅	1	4	yes	complemented
37	C₂×C₃²	—	1295	1	no	Hall
38	C₃×C₅	C₃×D₂₅₉	1	4	yes	complemented
39	D₇	—	185	1	no	Hall
40	D₅	—	259	1	no	Hall
41	C₃²	D₁₂₉₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃²×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	1295	4	no	—
44	C₅	C₃²×D₂₅₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×D₁₂₉₅	1	4	yes	direct product factor
46	C₂	—	1295	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₂₉₅
commutator, cosocle, hypocenter	C₅×C₇×C₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₇	C₂
LCS	G ▷ C₅×C₇×C₃₇
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₃₇	C₂	semidirect
2. C₃×D₁₂₉₅	C₃	direct (N × H)
4. C₃×C₅×C₇×C₃₇	C₂×C₃	semidirect
6. D₁₂₉₅	C₃²	direct (N × H)
7. C₃²×C₇×C₃₇	D₅	semidirect
8. C₃²×C₅×C₃₇	D₇	semidirect
10. C₅×C₇×C₃₇	C₂×C₃²	semidirect
12. C₃×C₇×C₃₇	C₃×D₅	semidirect
15. C₃×C₅×C₃₇	C₃×D₇	semidirect
18. C₃²×C₃₇	D₃₅	semidirect
19. C₃²×C₅×C₇	D₃₇	semidirect
20. C₇×C₃₇	C₃²×D₅	semidirect
23. C₅×C₃₇	C₃²×D₇	semidirect
25. C₃×C₃₇	C₃×D₃₅	semidirect
26. C₃×C₅×C₇	C₃×D₃₇	semidirect
30. C₃²×C₇	D₁₈₅	semidirect
31. C₃²×C₅	D₂₅₉	semidirect
33. C₃₇	C₃²×D₃₅	semidirect
34. C₅×C₇	C₃²×D₃₇	semidirect
36. C₃×C₇	C₃×D₁₈₅	semidirect
38. C₃×C₅	C₃×D₂₅₉	semidirect
41. C₃²	D₁₂₉₅	direct (N × H)
42. C₇	C₃²×D₁₈₅	semidirect
44. C₅	C₃²×D₂₅₉	semidirect
45. C₃	C₃×D₁₂₉₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₃₇	2
C₃×D₁₂₉₅	3
C₃²×D₂₅₉	5
C₃²×D₁₈₅	7
C₃²×D₃₅	37

Subgroups — C32×D1295 #37552133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₁₂₉₅ #37552133