Subgroups — C₅×C₇×C₃⋊D₃×C₃₁ #34086296

Order 19530.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₇×C₃₁	—	3	4	no	maximal
3	C₇×C₃⋊D₃×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₃₁	D₃	1	4	yes	complemented
5	C₅×C₃⋊D₃×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₃₁	—	9	1	no	Hall
7	C₃²×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	D₃×C₇×C₃₁	—	3	4	no	—
10	C₅×C₇×C₃₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₃×C₃₁	—	3	4	no	—
12	C₃×C₇×C₃₁	C₅×D₃	1	4	yes	complemented
13	C₅×C₇×C₃⋊D₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃⋊D₃×C₃₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₃₁	D₃×C₇	1	4	yes	complemented
16	C₂×C₇×C₃₁	—	9	1	no	Hall
17	C₃²×C₅×C₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₃₁	—	9	1	no	Hall
19	C₃²×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₃₁	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
21	C₅×D₃×C₇	—	3	4	no	—
22	D₃×C₃₁	—	3	4	no	—
23	C₅×C₃₁	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₃⋊D₃	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅×C₇	D₃×C₃₁	1	4	yes	complemented
26	C₃×C₃₁	C₅×D₃×C₇	1	4	yes	complemented
27	C₅×C₃⋊D₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₅×C₇	—	9	1	no	Hall
29	C₃²×C₇	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₁	—	9	1	no	Hall
31	C₃²×C₅	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
32	D₃×C₇	—	3	4	no	—
33	C₅×C₇	C₃⋊D₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₃₁	C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₅×D₃	—	3	4	no	—
36	C₃×C₇	C₅×D₃×C₃₁	1	4	yes	complemented
37	C₃⋊D₃	C₅×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	D₃×C₇×C₃₁	1	4	yes	complemented
39	C₂×C₇	—	9	1	no	Hall
40	C₂×C₅	—	9	1	no	Hall
41	C₃²	C₂×C₅×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×C₃⋊D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	3	4	no	—
44	C₅	C₇×C₃⋊D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₃×C₇×C₃₁	1	4	yes	complemented
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇×C₃₁	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₃₁	C₂	semidirect
3. C₇×C₃⋊D₃×C₃₁	C₅	direct (N × H)
4. C₃×C₅×C₇×C₃₁	D₃	semidirect
5. C₅×C₃⋊D₃×C₃₁	C₇	direct (N × H)
7. C₃²×C₇×C₃₁	C₂×C₅	semidirect
8. C₃²×C₅×C₃₁	C₂×C₇	semidirect
10. C₅×C₇×C₃₁	C₃⋊D₃	direct (N × H)
12. C₃×C₇×C₃₁	C₅×D₃	semidirect
13. C₅×C₇×C₃⋊D₃	C₃₁	direct (N × H)
14. C₃⋊D₃×C₃₁	C₅×C₇	direct (N × H)
15. C₃×C₅×C₃₁	D₃×C₇	semidirect
17. C₃²×C₅×C₇	C₂×C₃₁	semidirect
19. C₃²×C₃₁	C₂×C₅×C₇	semidirect
20. C₇×C₃₁	C₅×C₃⋊D₃	direct (N × H)
23. C₅×C₃₁	C₇×C₃⋊D₃	direct (N × H)
24. C₇×C₃⋊D₃	C₅×C₃₁	direct (N × H)
25. C₃×C₅×C₇	D₃×C₃₁	semidirect
26. C₃×C₃₁	C₅×D₃×C₇	semidirect
27. C₅×C₃⋊D₃	C₇×C₃₁	direct (N × H)
29. C₃²×C₇	C₂×C₅×C₃₁	semidirect
31. C₃²×C₅	C₂×C₇×C₃₁	semidirect
33. C₅×C₇	C₃⋊D₃×C₃₁	direct (N × H)
34. C₃₁	C₅×C₇×C₃⋊D₃	direct (N × H)
36. C₃×C₇	C₅×D₃×C₃₁	semidirect
37. C₃⋊D₃	C₅×C₇×C₃₁	direct (N × H)
38. C₃×C₅	D₃×C₇×C₃₁	semidirect
41. C₃²	C₂×C₅×C₇×C₃₁	semidirect
42. C₇	C₅×C₃⋊D₃×C₃₁	direct (N × H)
44. C₅	C₇×C₃⋊D₃×C₃₁	direct (N × H)
45. C₃	C₅×D₃×C₇×C₃₁	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×C₃₁	2
C₅×D₃×C₇×C₃₁	3
C₇×C₃⋊D₃×C₃₁	5
C₅×C₃⋊D₃×C₃₁	7
C₅×C₇×C₃⋊D₃	31

Subgroups — C5×C7×C3⋊D3×C31 #34086296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₃⋊D₃×C₃₁ #34086296