Finite Group Databasebeta

← C₃×C₄₁×D₂₃ #19150830

Subgroups — C₃×C₄₁×D₂₃ #19150830

Order 5658.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₄₁	—	23	1	no	maximal, Hall
5	C₃×D₂₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₄₁	D₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₄₁	—	23	1	no	Hall
8	C₃×C₂₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
9	D₂₃	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄₁	C₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	23	1	no	Hall
13	C₃	C₄₁×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₂₃
commutator, hypocenter	C₂₃	C₂×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₄₁	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×C₄₁	C₂	semidirect
2. C₄₁×D₂₃	C₃	direct (N × H)
3. C₂₃×C₄₁	C₂×C₃	semidirect
5. C₃×D₂₃	C₄₁	direct (N × H)
6. C₃×C₄₁	D₂₃	direct (N × H)
8. C₃×C₂₃	C₂×C₄₁	semidirect
9. D₂₃	C₃×C₄₁	direct (N × H)
10. C₄₁	C₃×D₂₃	direct (N × H)
11. C₂₃	C₂×C₃×C₄₁	semidirect
13. C₃	C₄₁×D₂₃	direct (N × H)