Subgroups — C₉×C₅⋊D₅×C₇₁ #44544050

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	C₃×C₅⋊D₅×C₇₁	C₃	1	1	yes	maximal, characteristic
3	C₉×D₅×C₇₁	—	5	6	no	maximal
4	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic
5	C₅⋊D₅×C₇₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉×C₇₁	D₅	1	6	yes	complemented
7	C₃×D₅×C₇₁	—	5	6	no	—
8	C₅²×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₉×C₇₁	—	25	1	no	Hall
10	C₃×C₅×C₇₁	C₃×D₅	1	6	yes	—
11	D₅×C₇₁	—	5	6	no	—
12	C₉×C₇₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
13	C₉×C₅⋊D₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₇₁	—	25	1	no	—
15	C₅×C₇₁	C₉×D₅	1	6	yes	complemented
16	C₅²×C₉	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₃×C₅⋊D₅	1	1	yes	characteristic
18	C₃×C₅⋊D₅	C₃×C₇₁	1	1	yes	characteristic
19	C₂×C₇₁	—	25	1	no	Hall
20	C₉×D₅	—	5	6	no	—
21	C₃×C₅²	C₂×C₃×C₇₁	1	1	yes	characteristic
22	C₇₁	C₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₅⋊D₅	C₉×C₇₁	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₉	D₅×C₇₁	1	6	yes	complemented
25	C₃×D₅	—	5	6	no	—
26	C₅²	C₂×C₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	25	1	no	Hall
28	C₃×C₅	C₃×D₅×C₇₁	1	6	yes	—
29	D₅	—	5	6	no	—
30	C₉	C₅⋊D₅×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	25	1	no	—
32	C₅	C₉×D₅×C₇₁	1	6	yes	complemented
33	C₃	C₃×C₅⋊D₅×C₇₁	1	1	yes	characteristic
34	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₇₁	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₉×C₇₁
Frattini	C₃	C₃×C₅⋊D₅×C₇₁
Fitting	C₅²×C₉×C₇₁	C₂
socle	C₃×C₅²×C₇₁	C₂×C₃
prime radical	C₃×C₅⋊D₅×C₇₁	C₃
cosocle	C₃×C₅²	C₂×C₃×C₇₁
LCS	G ▷ C₅²
UCS	C₁ ◁ C₉×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₉×C₇₁	C₂	semidirect
5. C₅⋊D₅×C₇₁	C₉	direct (N × H)
6. C₅×C₉×C₇₁	D₅	semidirect
8. C₅²×C₇₁	C₂×C₉	semidirect
12. C₉×C₇₁	C₅⋊D₅	direct (N × H)
13. C₉×C₅⋊D₅	C₇₁	direct (N × H)
15. C₅×C₇₁	C₉×D₅	semidirect
16. C₅²×C₉	C₂×C₇₁	semidirect
22. C₇₁	C₉×C₅⋊D₅	direct (N × H)
23. C₅⋊D₅	C₉×C₇₁	direct (N × H)
24. C₅×C₉	D₅×C₇₁	semidirect
26. C₅²	C₂×C₉×C₇₁	semidirect
30. C₉	C₅⋊D₅×C₇₁	direct (N × H)
32. C₅	C₉×D₅×C₇₁	semidirect

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
C₃×C₅⋊D₅×C₇₁	3
C₉×D₅×C₇₁	5
C₉×C₅⋊D₅	71

Subgroups — C9×C5⋊D5×C71 #44544050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₅⋊D₅×C₇₁ #44544050