Finite Group Databasebeta

← C₁₉×C₃₁×C₁₁⋊C₅ #44569288

Subgroups — C₁₉×C₃₁×C₁₁⋊C₅ #44569288

Order 32395.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉×C₃₁	—	11	1	no	maximal, Hall
3	C₃₁×C₁₁⋊C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₁₁⋊C₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉×C₃₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₁₁×C₃₁	C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₁₉	C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₃₁	—	11	1	no	Hall
9	C₅×C₁₉	—	11	1	no	Hall
10	C₁₁⋊C₅	C₁₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃₁	C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₉	C₃₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₅×C₁₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
14	C₅	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₃₁	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₅×C₁₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₃₁	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₉×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₃₁	C₅	semidirect
3. C₃₁×C₁₁⋊C₅	C₁₉	direct (N × H)
4. C₁₉×C₁₁⋊C₅	C₃₁	direct (N × H)
5. C₁₉×C₃₁	C₁₁⋊C₅	direct (N × H)
6. C₁₁×C₃₁	C₅×C₁₉	semidirect
7. C₁₁×C₁₉	C₅×C₃₁	semidirect
10. C₁₁⋊C₅	C₁₉×C₃₁	direct (N × H)
11. C₃₁	C₁₉×C₁₁⋊C₅	direct (N × H)
12. C₁₉	C₃₁×C₁₁⋊C₅	direct (N × H)
13. C₁₁	C₅×C₁₉×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₃₁	5
C₅×C₁₉×C₃₁	11
C₃₁×C₁₁⋊C₅	19
C₁₉×C₁₁⋊C₅	31