Finite Group Databasebeta

← C₁₁×C₁₃×D₁₀₉ #44529910

Subgroups — C₁₁×C₁₃×D₁₀₉ #44529910

Order 31174.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₀₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×D₁₀₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₁₀₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₁₀₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₁×C₁₃	—	109	1	no	maximal, Hall
7	D₁₀₉	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×C₁₃	D₁₀₉	1	1	yes	characteristic, direct product factor, Hall
9	C₁₀₉	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₃	—	109	1	no	Hall
11	C₂×C₁₁	—	109	1	no	Hall
12	C₁₃	C₁₁×D₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₁₃×D₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	109	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₁₀₉
commutator, cosocle, hypocenter	C₁₀₉	C₂×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₁₀₉	C₂
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×C₁₀₉	C₂	semidirect
2. C₁₃×D₁₀₉	C₁₁	direct (N × H)
3. C₁₁×D₁₀₉	C₁₃	direct (N × H)
4. C₁₃×C₁₀₉	C₂×C₁₁	semidirect
5. C₁₁×C₁₀₉	C₂×C₁₃	semidirect
7. D₁₀₉	C₁₁×C₁₃	direct (N × H)
8. C₁₁×C₁₃	D₁₀₉	direct (N × H)
9. C₁₀₉	C₂×C₁₁×C₁₃	semidirect
12. C₁₃	C₁₁×D₁₀₉	direct (N × H)
13. C₁₁	C₁₃×D₁₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×C₁₀₉	2
C₁₃×D₁₀₉	11
C₁₁×D₁₀₉	13
C₂×C₁₁×C₁₃	109