Finite Group Databasebeta

← C₂₃⋊(D₅₃⋊C₁₃) #44540139

Subgroups — C₂₃⋊(D₅₃⋊C₁₃) #44540139

Order 31694.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₅₃⋊C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₂₁₉	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₅₃⋊C₁₃	—	23	1	no	maximal, Hall
4	C₂₃×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₅₃⋊C₁₃	D₂₃	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₂₃	—	53	1	no	maximal, Hall
7	C₁₃×C₂₃	—	53	1	no	Hall
8	D₅₃	—	23	1	no	Hall
9	C₅₃	C₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
10	D₂₃	—	53	1	no	Hall
11	C₂×C₁₃	—	1219	1	no	Hall
12	C₂₃	D₅₃⋊C₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	—	53	1	no	Sylow
14	C₂	—	1219	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₃×C₅₃	C₂×C₁₃
LCS	G ▷ C₂₃×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₅₃⋊C₁₃	C₂	semidirect
2. D₁₂₁₉	C₁₃	semidirect
4. C₂₃×C₅₃	C₂×C₁₃	semidirect
5. C₅₃⋊C₁₃	D₂₃	semidirect
9. C₅₃	C₁₃×D₂₃	semidirect
12. C₂₃	D₅₃⋊C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×C₅₃⋊C₁₃	2
D₁₂₁₉	13
D₅₃⋊C₁₃	23
C₁₃×D₂₃	53