Subgroups — C₅²×D₉×C₇₁ #44544048

Order 31950.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₃×C₇₁	—	3	1	no	maximal
3	C₅×D₉×C₇₁	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₇₁	D₃	1	1	yes	characteristic
5	C₂×C₅²×C₇₁	—	9	1	no	Hall
6	C₅×C₉×C₇₁	C₂×C₅	1	6	yes	complemented
7	C₅×D₃×C₇₁	—	3	6	no	—
8	C₅²×C₇₁	D₉	1	1	yes	characteristic, direct product factor, Hall
9	D₉×C₇₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₇₁	C₅×D₃	1	6	yes	—
11	C₂×C₅×C₇₁	—	9	6	no	—
12	C₉×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅²×D₉	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	D₃×C₇₁	—	3	1	no	—
15	C₅×C₇₁	C₅×D₉	1	6	yes	direct product factor
16	C₅²×C₉	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₅²×D₃	1	1	yes	characteristic
18	C₅²×D₃	—	3	1	no	—
19	C₂×C₇₁	—	9	1	no	Hall
20	C₅×D₉	C₅×C₇₁	1	6	yes	direct product factor
21	C₃×C₅²	D₃×C₇₁	1	1	yes	characteristic
22	C₇₁	C₅²×D₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₅²	—	9	1	no	Hall
24	C₅×C₉	C₂×C₅×C₇₁	1	6	yes	complemented
25	C₅×D₃	—	3	6	no	—
26	C₅²	D₉×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
27	D₉	C₅²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₅×D₃×C₇₁	1	6	yes	—
29	C₂×C₅	—	9	6	no	—
30	C₉	C₂×C₅²×C₇₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	1	no	—
32	C₅	C₅×D₉×C₇₁	1	6	yes	direct product factor
33	C₃	C₅²×D₃×C₇₁	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₇₁	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅²×C₇₁
Frattini	C₃	C₅²×D₃×C₇₁
Fitting	C₅²×C₉×C₇₁	C₂
socle	C₃×C₅²×C₇₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅²×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₉×C₇₁	C₂	semidirect
3. C₅×D₉×C₇₁	C₅	direct (N × H)
6. C₅×C₉×C₇₁	C₂×C₅	semidirect
8. C₅²×C₇₁	D₉	direct (N × H)
9. D₉×C₇₁	C₅²	direct (N × H)
12. C₉×C₇₁	C₂×C₅²	semidirect
13. C₅²×D₉	C₇₁	direct (N × H)
15. C₅×C₇₁	C₅×D₉	direct (N × H)
16. C₅²×C₉	C₂×C₇₁	semidirect
20. C₅×D₉	C₅×C₇₁	direct (N × H)
22. C₇₁	C₅²×D₉	direct (N × H)
24. C₅×C₉	C₂×C₅×C₇₁	semidirect
26. C₅²	D₉×C₇₁	direct (N × H)
27. D₉	C₅²×C₇₁	direct (N × H)
30. C₉	C₂×C₅²×C₇₁	semidirect
32. C₅	C₅×D₉×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
C₅²×C₉×C₇₁	2
C₅²×D₃×C₇₁	3
C₅×D₉×C₇₁	5
C₅²×D₉	71

Subgroups — C52×D9×C71 #44544048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₉×C₇₁ #44544048