Subgroups — C₅²×C₃⋊D₃×C₇₁ #44544090

Order 31950.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₃×C₇₁	—	3	4	no	maximal
3	C₅×C₃⋊D₃×C₇₁	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₇₁	D₃	1	4	yes	complemented
5	C₂×C₅²×C₇₁	—	9	1	no	Hall
6	C₃²×C₅×C₇₁	C₂×C₅	1	6	yes	complemented
7	C₅×D₃×C₇₁	—	3	24	no	—
8	C₅²×C₇₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃⋊D₃×C₇₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₇₁	C₅×D₃	1	24	yes	complemented
11	C₂×C₅×C₇₁	—	9	6	no	—
12	C₃²×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅²×C₃⋊D₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	D₃×C₇₁	—	3	4	no	—
15	C₅×C₇₁	C₅×C₃⋊D₃	1	6	yes	direct product factor
16	C₃²×C₅²	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₅²×D₃	1	4	yes	complemented
18	C₅²×D₃	—	3	4	no	—
19	C₂×C₇₁	—	9	1	no	Hall
20	C₅×C₃⋊D₃	C₅×C₇₁	1	6	yes	direct product factor
21	C₃×C₅²	D₃×C₇₁	1	4	yes	complemented
22	C₇₁	C₅²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₅²	—	9	1	no	Hall
24	C₃²×C₅	C₂×C₅×C₇₁	1	6	yes	complemented
25	C₅×D₃	—	3	24	no	—
26	C₅²	C₃⋊D₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₃⋊D₃	C₅²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₅×D₃×C₇₁	1	24	yes	complemented
29	C₂×C₅	—	9	6	no	—
30	C₃²	C₂×C₅²×C₇₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	4	no	—
32	C₅	C₅×C₃⋊D₃×C₇₁	1	6	yes	direct product factor
33	C₃	C₅²×D₃×C₇₁	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₇₁	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅²×C₇₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅²×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇₁	C₂	semidirect
3. C₅×C₃⋊D₃×C₇₁	C₅	direct (N × H)
4. C₃×C₅²×C₇₁	D₃	semidirect
6. C₃²×C₅×C₇₁	C₂×C₅	semidirect
8. C₅²×C₇₁	C₃⋊D₃	direct (N × H)
9. C₃⋊D₃×C₇₁	C₅²	direct (N × H)
10. C₃×C₅×C₇₁	C₅×D₃	semidirect
12. C₃²×C₇₁	C₂×C₅²	semidirect
13. C₅²×C₃⋊D₃	C₇₁	direct (N × H)
15. C₅×C₇₁	C₅×C₃⋊D₃	direct (N × H)
16. C₃²×C₅²	C₂×C₇₁	semidirect
17. C₃×C₇₁	C₅²×D₃	semidirect
20. C₅×C₃⋊D₃	C₅×C₇₁	direct (N × H)
21. C₃×C₅²	D₃×C₇₁	semidirect
22. C₇₁	C₅²×C₃⋊D₃	direct (N × H)
24. C₃²×C₅	C₂×C₅×C₇₁	semidirect
26. C₅²	C₃⋊D₃×C₇₁	direct (N × H)
27. C₃⋊D₃	C₅²×C₇₁	direct (N × H)
28. C₃×C₅	C₅×D₃×C₇₁	semidirect
30. C₃²	C₂×C₅²×C₇₁	semidirect
32. C₅	C₅×C₃⋊D₃×C₇₁	direct (N × H)
33. C₃	C₅²×D₃×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×C₇₁	2
C₅²×D₃×C₇₁	3
C₅×C₃⋊D₃×C₇₁	5
C₅²×C₃⋊D₃	71

Subgroups — C52×C3⋊D3×C71 #44544090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊D₃×C₇₁ #44544090