Finite Group Databasebeta

← C₁₃×C₄₁×D₂₃ #37589207

Subgroups — C₁₃×C₄₁×D₂₃ #37589207

Order 24518.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₃×C₄₁	—	23	1	no	maximal, Hall
4	C₂₃×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₂₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₁	D₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₁₃×C₂₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₁	—	23	1	no	Hall
9	D₂₃	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄₁	C₁₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₃	—	23	1	no	Hall
12	C₂₃	C₂×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	C₄₁×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₄₁	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₁₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₂₃×C₄₁	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₁₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂₃×C₄₁	C₂	semidirect
2. C₄₁×D₂₃	C₁₃	direct (N × H)
4. C₂₃×C₄₁	C₂×C₁₃	semidirect
5. C₁₃×D₂₃	C₄₁	direct (N × H)
6. C₁₃×C₄₁	D₂₃	direct (N × H)
7. C₁₃×C₂₃	C₂×C₄₁	semidirect
9. D₂₃	C₁₃×C₄₁	direct (N × H)
10. C₄₁	C₁₃×D₂₃	direct (N × H)
12. C₂₃	C₂×C₁₃×C₄₁	semidirect
13. C₁₃	C₄₁×D₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₂₃×C₄₁	2
C₄₁×D₂₃	13
C₂×C₁₃×C₄₁	23
C₁₃×D₂₃	41