Finite Group Databasebeta

← C₃×C₂₃×ΓL(1,𝔽₃₂) #24924120

Subgroups — C₃×C₂₃×ΓL(1,𝔽₃₂) #24924120

Order 10695.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₃×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₃×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₃×ΓL(1,𝔽₃₂)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₃	—	31	1	no	maximal, Hall
6	ΓL(1,𝔽₃₂)	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₂₃	—	31	1	no	Hall
8	C₃×C₃₁	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₂₃	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
10	C₃₁	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
11	C₂₃	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	—	31	1	no	Hall
13	C₅	—	31	1	no	Sylow
14	C₃	C₂₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×ΓL(1,𝔽₃₂)	C₃	direct (N × H)
2. C₃×C₂₃×C₃₁	C₅	semidirect
3. C₂₃×C₃₁	C₃×C₅	semidirect
4. C₃×ΓL(1,𝔽₃₂)	C₂₃	direct (N × H)
6. ΓL(1,𝔽₃₂)	C₃×C₂₃	direct (N × H)
8. C₃×C₃₁	C₅×C₂₃	semidirect
9. C₃×C₂₃	ΓL(1,𝔽₃₂)	direct (N × H)
10. C₃₁	C₃×C₅×C₂₃	semidirect
11. C₂₃	C₃×ΓL(1,𝔽₃₂)	direct (N × H)
14. C₃	C₂₃×ΓL(1,𝔽₃₂)	direct (N × H)