Subgroups — D₉×C₂₃×C₂₅ #23780331

Order 10350.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₂₃×C₂₅	—	3	1	no	maximal
3	C₅×D₉×C₂₃	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₃×C₂₅	D₃	1	1	yes	characteristic
5	C₂×C₂₃×C₂₅	—	9	1	no	Hall
6	C₅×C₉×C₂₃	C₂×C₅	1	1	yes	characteristic
7	C₅×D₃×C₂₃	—	3	1	no	—
8	C₂₃×C₂₅	D₉	1	1	yes	characteristic, direct product factor, Hall
9	D₉×C₂₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₉×C₂₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₂₃	C₅×D₃	1	1	yes	characteristic
12	C₂×C₅×C₂₃	—	9	1	no	—
13	C₉×C₂₅	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
14	C₉×C₂₃	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
15	D₃×C₂₅	—	3	1	no	—
16	D₃×C₂₃	—	3	1	no	—
17	C₅×C₂₃	C₅×D₉	1	1	yes	characteristic
18	C₅×D₉	C₅×C₂₃	1	1	yes	characteristic
19	C₃×C₂₅	D₃×C₂₃	1	1	yes	characteristic
20	C₃×C₂₃	D₃×C₂₅	1	1	yes	characteristic
21	C₂×C₂₅	—	9	1	no	Hall
22	C₂×C₂₃	—	9	1	no	Hall
23	C₅×C₉	C₂×C₅×C₂₃	1	1	yes	characteristic
24	C₅×D₃	—	3	1	no	—
25	C₂₅	D₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂₃	D₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
27	D₉	C₂₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₅×D₃×C₂₃	1	1	yes	characteristic
29	C₂×C₅	—	9	1	no	—
30	C₉	C₂×C₂₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	1	no	—
32	C₅	C₅×D₉×C₂₃	1	1	yes	characteristic
33	C₃	D₃×C₂₃×C₂₅	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃×C₂₅	D₉
commutator, hypocenter	C₉	C₂×C₂₃×C₂₅
Frattini	C₃×C₅	C₅×D₃×C₂₃
Fitting	C₉×C₂₃×C₂₅	C₂
socle	C₃×C₅×C₂₃	C₅×D₃
prime radical	C₅×D₉×C₂₃	C₅
cosocle	C₅×C₉	C₂×C₅×C₂₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂₃×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₉×C₂₃×C₂₅	C₂	semidirect
8. C₂₃×C₂₅	D₉	direct (N × H)
9. D₉×C₂₅	C₂₃	direct (N × H)
10. D₉×C₂₃	C₂₅	direct (N × H)
13. C₉×C₂₅	C₂×C₂₃	semidirect
14. C₉×C₂₃	C₂×C₂₅	semidirect
25. C₂₅	D₉×C₂₃	direct (N × H)
26. C₂₃	D₉×C₂₅	direct (N × H)
27. D₉	C₂₃×C₂₅	direct (N × H)
30. C₉	C₂×C₂₃×C₂₅	semidirect

Subgroups — D9×C23×C25 #23780331

Conjugacy classes of subgroups

Complements

Subgroups — D₉×C₂₃×C₂₅ #23780331