Subgroups — C₃²×C₅⋊D₅×C₇₁ #44544082

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	C₃×C₅⋊D₅×C₇₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₅×C₇₁	—	5	6	no	maximal
4	C₃×C₅²×C₇₁	C₂×C₃	1	4	yes	complemented
5	C₅⋊D₅×C₇₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅×C₇₁	D₅	1	6	yes	complemented
7	C₃×D₅×C₇₁	—	5	24	no	—
8	C₅²×C₇₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃²×C₇₁	—	25	1	no	Hall
10	C₃×C₅×C₇₁	C₃×D₅	1	24	yes	complemented
11	D₅×C₇₁	—	5	6	no	—
12	C₃²×C₇₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃²×C₅⋊D₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₇₁	—	25	4	no	—
15	C₅×C₇₁	C₃²×D₅	1	6	yes	complemented
16	C₃²×C₅²	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₃×C₅⋊D₅	1	4	yes	direct product factor
18	C₃×C₅⋊D₅	C₃×C₇₁	1	4	yes	direct product factor
19	C₂×C₇₁	—	25	1	no	Hall
20	C₃²×D₅	—	5	6	no	—
21	C₃×C₅²	C₂×C₃×C₇₁	1	4	yes	complemented
22	C₇₁	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₅⋊D₅	C₃²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₅	D₅×C₇₁	1	6	yes	complemented
25	C₃×D₅	—	5	24	no	—
26	C₅²	C₂×C₃²×C₇₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	—	25	1	no	Hall
28	C₃×C₅	C₃×D₅×C₇₁	1	24	yes	complemented
29	D₅	—	5	6	no	—
30	C₃²	C₅⋊D₅×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	25	4	no	—
32	C₅	C₃²×D₅×C₇₁	1	6	yes	complemented
33	C₃	C₃×C₅⋊D₅×C₇₁	1	4	yes	direct product factor
34	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃²×C₇₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃²×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇₁	C₂	semidirect
2. C₃×C₅⋊D₅×C₇₁	C₃	direct (N × H)
4. C₃×C₅²×C₇₁	C₂×C₃	semidirect
5. C₅⋊D₅×C₇₁	C₃²	direct (N × H)
6. C₃²×C₅×C₇₁	D₅	semidirect
8. C₅²×C₇₁	C₂×C₃²	semidirect
10. C₃×C₅×C₇₁	C₃×D₅	semidirect
12. C₃²×C₇₁	C₅⋊D₅	direct (N × H)
13. C₃²×C₅⋊D₅	C₇₁	direct (N × H)
15. C₅×C₇₁	C₃²×D₅	semidirect
16. C₃²×C₅²	C₂×C₇₁	semidirect
17. C₃×C₇₁	C₃×C₅⋊D₅	direct (N × H)
18. C₃×C₅⋊D₅	C₃×C₇₁	direct (N × H)
21. C₃×C₅²	C₂×C₃×C₇₁	semidirect
22. C₇₁	C₃²×C₅⋊D₅	direct (N × H)
23. C₅⋊D₅	C₃²×C₇₁	direct (N × H)
24. C₃²×C₅	D₅×C₇₁	semidirect
26. C₅²	C₂×C₃²×C₇₁	semidirect
28. C₃×C₅	C₃×D₅×C₇₁	semidirect
30. C₃²	C₅⋊D₅×C₇₁	direct (N × H)
32. C₅	C₃²×D₅×C₇₁	semidirect
33. C₃	C₃×C₅⋊D₅×C₇₁	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×C₅²×C₇₁	2
C₃×C₅⋊D₅×C₇₁	3
C₃²×D₅×C₇₁	5
C₃²×C₅⋊D₅	71

Subgroups — C32×C5⋊D5×C71 #44544082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅⋊D₅×C₇₁ #44544082