Finite Group Databasebeta

← C₁₁×C₁₃×C₅²⋊C₃ #24924335

Subgroups — C₁₁×C₁₃×C₅²⋊C₃ #24924335

Order 10725.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅²⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₅²⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₁₃	—	3	2	no	—
5	C₃×C₁₁×C₁₃	—	25	1	no	maximal, Hall
6	C₅²×C₁₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₅²×C₁₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₁₃	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅²⋊C₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₁₃	—	3	2	no	—
11	C₅×C₁₁	—	3	2	no	—
12	C₃×C₁₃	—	25	1	no	Hall
13	C₃×C₁₁	—	25	1	no	Hall
14	C₅²	C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
15	C₁₃	C₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₁₁	C₁₃×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₅	—	3	2	no	—
18	C₃	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₃	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₁×C₁₃	C₃	semidirect
2. C₁₃×C₅²⋊C₃	C₁₁	direct (N × H)
3. C₁₁×C₅²⋊C₃	C₁₃	direct (N × H)
6. C₅²×C₁₃	C₃×C₁₁	semidirect
7. C₅²×C₁₁	C₃×C₁₃	semidirect
8. C₁₁×C₁₃	C₅²⋊C₃	direct (N × H)
9. C₅²⋊C₃	C₁₁×C₁₃	direct (N × H)
14. C₅²	C₃×C₁₁×C₁₃	semidirect
15. C₁₃	C₁₁×C₅²⋊C₃	direct (N × H)
16. C₁₁	C₁₃×C₅²⋊C₃	direct (N × H)