Finite Group Databasebeta

← C₁₁×C₁₉×C₅²⋊C₃ #30627872

Subgroups — C₁₁×C₁₉×C₅²⋊C₃ #30627872

Order 15675.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₅²⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₁×C₁₉	—	3	2	no	—
4	C₁₁×C₅²⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₁₉	—	25	1	no	maximal, Hall
6	C₅²×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₅²×C₁₁	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₉	—	3	2	no	—
10	C₅²⋊C₃	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₁₉	—	25	1	no	Hall
12	C₅×C₁₁	—	3	2	no	—
13	C₃×C₁₁	—	25	1	no	Hall
14	C₅²	C₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
15	C₁₉	C₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₁₁	C₁₉×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×C₁₉	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₉	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₁×C₁₉	C₃	semidirect
2. C₁₉×C₅²⋊C₃	C₁₁	direct (N × H)
4. C₁₁×C₅²⋊C₃	C₁₉	direct (N × H)
6. C₅²×C₁₉	C₃×C₁₁	semidirect
7. C₅²×C₁₁	C₃×C₁₉	semidirect
8. C₁₁×C₁₉	C₅²⋊C₃	direct (N × H)
10. C₅²⋊C₃	C₁₁×C₁₉	direct (N × H)
14. C₅²	C₃×C₁₁×C₁₉	semidirect
15. C₁₉	C₁₁×C₅²⋊C₃	direct (N × H)
16. C₁₁	C₁₉×C₅²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₁₁×C₁₉	3
C₁₉×C₅²⋊C₃	11
C₁₁×C₅²⋊C₃	19
C₃×C₁₁×C₁₉	25