Subgroups — C₅×C₃₇×C₃⋊D₂₁ #37552144

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

	subgroup	G/H
center, hypercenter	C₅×C₃₇	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₃₇

Complements

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

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

Subgroups — C5×C37×C3⋊D21 #37552144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃₇×C₃⋊D₂₁ #37552144