Finite Group Databasebeta

← C₁₁×C₁₇×C₁₁⋊C₅ #23779807

Subgroups — C₁₁×C₁₇×C₁₁⋊C₅ #23779807

Order 10285.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₁₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×C₁₇	—	11	1	no	maximal
3	C₁₇×C₁₁⋊C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
4	C₁₁×C₁₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁×C₁₇	—	5	2	no	—
6	C₁₁×C₁₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
7	C₁₁×C₁₇	C₅×C₁₁	1	1	yes	characteristic, complemented
8	C₁₁²	C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₇	—	11	1	no	Hall
10	C₅×C₁₁	—	11	1	no	—
11	C₁₁⋊C₅	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor
12	C₁₇	C₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	—	5	2	no	—
14	C₁₁	C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
15	C₁₁	C₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented
16	C₅	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₅×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₁²×C₁₇	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₁₇	C₅	semidirect
3. C₁₇×C₁₁⋊C₅	C₁₁	direct (N × H)
4. C₁₁×C₁₁⋊C₅	C₁₇	direct (N × H)
6. C₁₁×C₁₇	C₁₁⋊C₅	direct (N × H)
7. C₁₁×C₁₇	C₅×C₁₁	semidirect
8. C₁₁²	C₅×C₁₇	semidirect
11. C₁₁⋊C₅	C₁₁×C₁₇	direct (N × H)
12. C₁₇	C₁₁×C₁₁⋊C₅	direct (N × H)
14. C₁₁	C₁₇×C₁₁⋊C₅	direct (N × H)
15. C₁₁	C₅×C₁₁×C₁₇	semidirect