Subgroups — C₂×C₉×C₃₁⋊C₂₅ #28358367

Order 13950.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₃₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₉×C₃₁	C₅	1	1	yes	maximal, characteristic
4	C₃×C₃₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic
5	C₂×C₃₁⋊C₂₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₂×C₃×C₅×C₃₁	C₃×C₅	1	1	yes	characteristic
8	C₃₁⋊C₂₅	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₉×C₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
11	C₂×C₉×C₂₅	—	31	1	no	maximal, Hall
12	C₂×C₅×C₃₁	C₅×C₉	1	1	yes	characteristic
13	C₉×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
14	C₉×C₂₅	—	31	1	no	Hall
15	C₂×C₃×C₃₁	C₃×C₂₅	1	1	yes	characteristic
16	C₅×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic
17	C₂×C₃×C₂₅	—	31	1	no	—
18	C₃×C₃₁	C₂×C₃×C₂₅	1	1	yes	characteristic
19	C₂×C₅×C₉	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
20	C₃×C₂₅	—	31	1	no	—
21	C₂×C₃₁	C₉×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₂₅	—	31	1	no	Hall
23	C₅×C₉	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
24	C₃₁	C₂×C₉×C₂₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₅	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
26	C₂₅	—	31	1	no	Sylow
27	C₂×C₉	C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₂×C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
29	C₂×C₅	C₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
30	C₉	C₂×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₃₁⋊C₂₅	1	1	yes	characteristic
32	C₅	C₂×C₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
33	C₃	C₂×C₃×C₃₁⋊C₂₅	1	1	yes	characteristic
34	C₂	C₉×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉	ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃₁	C₂×C₉×C₂₅
Frattini	C₃×C₅	C₂×C₃×ΓL(1,𝔽₃₂)
Fitting	C₂×C₅×C₉×C₃₁	C₅
socle, prime radical	C₂×C₃×C₅×C₃₁	C₃×C₅
cosocle	C₃×C₅×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₃₁⋊C₂₅	C₂	direct (N × H)
5. C₂×C₃₁⋊C₂₅	C₉	direct (N × H)
8. C₃₁⋊C₂₅	C₂×C₉	direct (N × H)
9. C₂×C₉×C₃₁	C₂₅	semidirect
13. C₉×C₃₁	C₂×C₂₅	semidirect
21. C₂×C₃₁	C₉×C₂₅	semidirect
24. C₃₁	C₂×C₉×C₂₅	semidirect
27. C₂×C₉	C₃₁⋊C₂₅	direct (N × H)
30. C₉	C₂×C₃₁⋊C₂₅	direct (N × H)
34. C₂	C₉×C₃₁⋊C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₃₁⋊C₂₅	2
C₂×C₃×C₃₁⋊C₂₅	3
C₂×C₅×C₉×C₃₁	5
C₂×C₉×C₂₅	31

Subgroups — C2×C9×C31⋊C25 #28358367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃₁⋊C₂₅ #28358367