Subgroups — D₉×C₂₅×C₃₁ #28358372

Order 13950.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₂₅×C₃₁	—	3	1	no	maximal
3	C₅×D₉×C₃₁	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₅×C₃₁	D₃	1	1	yes	characteristic
5	C₂×C₂₅×C₃₁	—	9	1	no	Hall
6	C₅×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₅×D₃×C₃₁	—	3	1	no	—
8	C₂₅×C₃₁	D₉	1	1	yes	characteristic, direct product factor, Hall
9	D₉×C₃₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₃₁	C₅×D₃	1	1	yes	characteristic
11	D₉×C₂₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₃₁	—	9	1	no	—
13	C₉×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
14	C₉×C₂₅	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
15	D₃×C₃₁	—	3	1	no	—
16	C₅×C₃₁	C₅×D₉	1	1	yes	characteristic
17	D₃×C₂₅	—	3	1	no	—
18	C₃×C₃₁	D₃×C₂₅	1	1	yes	characteristic
19	C₅×D₉	C₅×C₃₁	1	1	yes	characteristic
20	C₃×C₂₅	D₃×C₃₁	1	1	yes	characteristic
21	C₂×C₃₁	—	9	1	no	Hall
22	C₂×C₂₅	—	9	1	no	Hall
23	C₅×C₉	C₂×C₅×C₃₁	1	1	yes	characteristic
24	C₃₁	D₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×D₃	—	3	1	no	—
26	C₂₅	D₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
27	D₉	C₂₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₅×D₃×C₃₁	1	1	yes	characteristic
29	C₂×C₅	—	9	1	no	—
30	C₉	C₂×C₂₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	1	no	—
32	C₅	C₅×D₉×C₃₁	1	1	yes	characteristic
33	C₃	D₃×C₂₅×C₃₁	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅×C₃₁	D₉
commutator, hypocenter	C₉	C₂×C₂₅×C₃₁
Frattini	C₃×C₅	C₅×D₃×C₃₁
Fitting	C₉×C₂₅×C₃₁	C₂
socle	C₃×C₅×C₃₁	C₅×D₃
prime radical	C₅×D₉×C₃₁	C₅
cosocle	C₅×C₉	C₂×C₅×C₃₁
LCS	G ▷ C₉
UCS	C₁ ◁ C₂₅×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₂₅×C₃₁	C₂	semidirect
8. C₂₅×C₃₁	D₉	direct (N × H)
9. D₉×C₃₁	C₂₅	direct (N × H)
11. D₉×C₂₅	C₃₁	direct (N × H)
13. C₉×C₃₁	C₂×C₂₅	semidirect
14. C₉×C₂₅	C₂×C₃₁	semidirect
24. C₃₁	D₉×C₂₅	direct (N × H)
26. C₂₅	D₉×C₃₁	direct (N × H)
27. D₉	C₂₅×C₃₁	direct (N × H)
30. C₉	C₂×C₂₅×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₂₅×C₃₁	2
D₃×C₂₅×C₃₁	3
C₅×D₉×C₃₁	5
D₉×C₂₅	31

Subgroups — D9×C25×C31 #28358372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₂₅×C₃₁ #28358372