Finite Group Databasebeta

← C₁₁×C₁₉×ΓL(1,𝔽₃₂) #44569287

Subgroups — C₁₁×C₁₉×ΓL(1,𝔽₃₂) #44569287

Order 32395.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×ΓL(1,𝔽₃₂)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×ΓL(1,𝔽₃₂)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₁₉	—	31	1	no	maximal, Hall
5	C₁₉×C₃₁	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₃₁	C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₁₉	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
8	ΓL(1,𝔽₃₂)	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₉	—	31	1	no	Hall
10	C₅×C₁₁	—	31	1	no	Hall
11	C₃₁	C₅×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
12	C₁₉	C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₁₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
14	C₅	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₅×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₃₁	C₅	semidirect
2. C₁₉×ΓL(1,𝔽₃₂)	C₁₁	direct (N × H)
3. C₁₁×ΓL(1,𝔽₃₂)	C₁₉	direct (N × H)
5. C₁₉×C₃₁	C₅×C₁₁	semidirect
6. C₁₁×C₃₁	C₅×C₁₉	semidirect
7. C₁₁×C₁₉	ΓL(1,𝔽₃₂)	direct (N × H)
8. ΓL(1,𝔽₃₂)	C₁₁×C₁₉	direct (N × H)
11. C₃₁	C₅×C₁₁×C₁₉	semidirect
12. C₁₉	C₁₁×ΓL(1,𝔽₃₂)	direct (N × H)
13. C₁₁	C₁₉×ΓL(1,𝔽₃₂)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₃₁	5
C₁₉×ΓL(1,𝔽₃₂)	11
C₁₁×ΓL(1,𝔽₃₂)	19
C₅×C₁₁×C₁₉	31