Finite Group Databasebeta

← C₂×C₁₁⋊C₅×C₁₃₉ #29504199

Subgroups — C₂×C₁₁⋊C₅×C₁₃₉ #29504199

Order 15290.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×C₁₃₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₁₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₃₉	—	11	1	no	maximal, Hall
5	C₅×C₁₃₉	—	11	1	no	Hall
6	C₂×C₁₃₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₁₃₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₁₁⋊C₅	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₁⋊C₅	C₂×C₁₃₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁	C₅×C₁₃₉	1	1	yes	characteristic, complemented, Hall
11	C₁₁	C₂×C₅×C₁₃₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	11	1	no	Hall
13	C₅	—	11	1	no	Sylow
14	C₂	C₁₁⋊C₅×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₃₉	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₁₃₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃₉	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₃₉

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×C₁₃₉	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃₉	C₅	semidirect
3. C₁₁×C₁₃₉	C₂×C₅	semidirect
6. C₂×C₁₃₉	C₁₁⋊C₅	direct (N × H)
7. C₁₃₉	C₂×C₁₁⋊C₅	direct (N × H)
8. C₂×C₁₁⋊C₅	C₁₃₉	direct (N × H)
9. C₁₁⋊C₅	C₂×C₁₃₉	direct (N × H)
10. C₂×C₁₁	C₅×C₁₃₉	semidirect
11. C₁₁	C₂×C₅×C₁₃₉	semidirect
14. C₂	C₁₁⋊C₅×C₁₃₉	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⋊C₅×C₁₃₉	2
C₂×C₁₁×C₁₃₉	5
C₂×C₅×C₁₃₉	11
C₂×C₁₁⋊C₅	139