Finite Group Databasebeta

← C₃×C₄₁×ΓL(1,𝔽₃₂) #34040113

Subgroups — C₃×C₄₁×ΓL(1,𝔽₃₂) #34040113

Order 19065.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₃₁×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁×C₄₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₄₁	—	31	1	no	maximal, Hall
5	C₃×ΓL(1,𝔽₃₂)	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₄₁	—	31	1	no	Hall
7	ΓL(1,𝔽₃₂)	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₄₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₃₁	C₅×C₄₁	1	1	yes	characteristic, complemented, Hall
10	C₄₁	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₃×C₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₅	—	31	1	no	Hall
13	C₅	—	31	1	no	Sylow
14	C₃	C₄₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₁	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₃×C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₄₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×ΓL(1,𝔽₃₂)	C₃	direct (N × H)
2. C₃×C₃₁×C₄₁	C₅	semidirect
3. C₃₁×C₄₁	C₃×C₅	semidirect
5. C₃×ΓL(1,𝔽₃₂)	C₄₁	direct (N × H)
7. ΓL(1,𝔽₃₂)	C₃×C₄₁	direct (N × H)
8. C₃×C₄₁	ΓL(1,𝔽₃₂)	direct (N × H)
9. C₃×C₃₁	C₅×C₄₁	semidirect
10. C₄₁	C₃×ΓL(1,𝔽₃₂)	direct (N × H)
11. C₃₁	C₃×C₅×C₄₁	semidirect
14. C₃	C₄₁×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
C₄₁×ΓL(1,𝔽₃₂)	3
C₃×C₃₁×C₄₁	5
C₃×C₅×C₄₁	31
C₃×ΓL(1,𝔽₃₂)	41