Finite Group Databasebeta

← C₂×C₂₃×C₅₃⋊C₁₃ #44540129

Subgroups — C₂×C₂₃×C₅₃⋊C₁₃ #44540129

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, direct product factor, Hall
2	C₂×C₂₃×C₅₃	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅₃⋊C₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂₃×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₅₃⋊C₁₃	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₃×C₂₃	—	53	1	no	maximal, Hall
7	C₁₃×C₂₃	—	53	1	no	Hall
8	C₂×C₅₃	C₁₃×C₂₃	1	1	yes	characteristic, complemented, Hall
9	C₅₃	C₂×C₁₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₂₃	C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₃	—	53	1	no	Hall
12	C₂₃	C₂×C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	—	53	1	no	Sylow
14	C₂	C₂₃×C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₅₃⋊C₁₃	C₂	direct (N × H)
2. C₂×C₂₃×C₅₃	C₁₃	semidirect
3. C₂×C₅₃⋊C₁₃	C₂₃	direct (N × H)
4. C₂₃×C₅₃	C₂×C₁₃	semidirect
5. C₅₃⋊C₁₃	C₂×C₂₃	direct (N × H)
8. C₂×C₅₃	C₁₃×C₂₃	semidirect
9. C₅₃	C₂×C₁₃×C₂₃	semidirect
10. C₂×C₂₃	C₅₃⋊C₁₃	direct (N × H)
12. C₂₃	C₂×C₅₃⋊C₁₃	direct (N × H)
14. C₂	C₂₃×C₅₃⋊C₁₃	direct (N × H)

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
C₂×C₂₃×C₅₃	13
C₂×C₅₃⋊C₁₃	23
C₂×C₁₃×C₂₃	53