Subgroups — C₃₇×C₃⋊D₁₀₅ #37552148

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	C₃₇×D₁₀₅	—	3	4	no	maximal
3	C₃₇×C₃⋊D₂₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₃₇	D₃	1	4	yes	complemented
5	C₃₇×C₃⋊D₁₅	—	7	1	no	maximal, Hall
6	C₃₇×D₃₅	—	9	1	no	Hall
7	C₃²×C₇×C₃₇	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
9	C₃₇×D₂₁	—	15	4	no	—
10	C₅×C₇×C₃₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₅×C₃₇	—	21	4	no	—
12	C₃×C₇×C₃₇	D₁₅	1	4	yes	complemented
13	C₃⋊D₃×C₃₇	—	35	1	no	Hall
14	C₃⋊D₁₀₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₃₇	D₂₁	1	4	yes	complemented
16	D₇×C₃₇	—	45	1	no	Hall
17	D₅×C₃₇	—	63	1	no	Hall
18	C₃²×C₃₇	D₃₅	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅×C₇	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
21	D₃×C₃₇	—	105	4	no	—
22	D₁₀₅	—	3	4	no	—
23	C₅×C₃₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
24	C₃⋊D₂₁	—	5	1	no	Hall
25	C₃×C₃₇	D₁₀₅	1	4	yes	complemented
26	C₃×C₅×C₇	D₃×C₃₇	1	4	yes	complemented
27	C₃⋊D₁₅	—	7	1	no	Hall
28	C₂×C₃₇	—	315	1	no	Hall
29	D₃₅	—	9	1	no	Hall
30	C₃²×C₇	D₅×C₃₇	1	1	yes	characteristic, complemented, Hall
31	C₃²×C₅	D₇×C₃₇	1	1	yes	characteristic, complemented, Hall
32	D₂₁	—	15	4	no	—
33	C₃₇	C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₅×C₇	C₃⋊D₃×C₃₇	1	1	yes	characteristic, complemented, Hall
35	D₁₅	—	21	4	no	—
36	C₃×C₇	D₁₅×C₃₇	1	4	yes	complemented
37	C₃⋊D₃	—	35	1	no	Hall
38	C₃×C₅	C₃₇×D₂₁	1	4	yes	complemented
39	D₇	—	45	1	no	Hall
40	D₅	—	63	1	no	Hall
41	C₃²	C₃₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₃₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	105	4	no	—
44	C₅	C₃₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃₇×D₁₀₅	1	4	yes	complemented
46	C₂	—	315	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	C₃⋊D₁₀₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂×C₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₇	C₂
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₃₇	C₂	semidirect
4. C₃×C₅×C₇×C₃₇	D₃	semidirect
7. C₃²×C₇×C₃₇	D₅	semidirect
8. C₃²×C₅×C₃₇	D₇	semidirect
10. C₅×C₇×C₃₇	C₃⋊D₃	semidirect
12. C₃×C₇×C₃₇	D₁₅	semidirect
14. C₃⋊D₁₀₅	C₃₇	direct (N × H)
15. C₃×C₅×C₃₇	D₂₁	semidirect
18. C₃²×C₃₇	D₃₅	semidirect
19. C₃²×C₅×C₇	C₂×C₃₇	semidirect
20. C₇×C₃₇	C₃⋊D₁₅	semidirect
23. C₅×C₃₇	C₃⋊D₂₁	semidirect
25. C₃×C₃₇	D₁₀₅	semidirect
26. C₃×C₅×C₇	D₃×C₃₇	semidirect
30. C₃²×C₇	D₅×C₃₇	semidirect
31. C₃²×C₅	D₇×C₃₇	semidirect
33. C₃₇	C₃⋊D₁₀₅	direct (N × H)
34. C₅×C₇	C₃⋊D₃×C₃₇	semidirect
36. C₃×C₇	D₁₅×C₃₇	semidirect
38. C₃×C₅	C₃₇×D₂₁	semidirect
41. C₃²	C₃₇×D₃₅	semidirect
42. C₇	C₃₇×C₃⋊D₁₅	semidirect
44. C₅	C₃₇×C₃⋊D₂₁	semidirect
45. C₃	C₃₇×D₁₀₅	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×C₃₇	2
C₃₇×D₁₀₅	3
C₃₇×C₃⋊D₂₁	5
C₃₇×C₃⋊D₁₅	7
C₃⋊D₁₀₅	37

Subgroups — C37×C3⋊D105 #37552148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×C₃⋊D₁₀₅ #37552148