Finite Group Databasebeta

← C₁₉×C₃₁×C₁₃⋊C₃ #37525849

Subgroups — C₁₉×C₃₁×C₁₃⋊C₃ #37525849

Order 22971.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×C₃₁	—	13	1	no	maximal, Hall
3	C₃₁×C₁₃⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₁₃⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₁₃×C₃₁	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₁₉	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
8	C₃×C₃₁	—	13	1	no	Hall
9	C₃×C₁₉	—	13	1	no	Hall
10	C₁₃⋊C₃	C₁₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃₁	C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₉	C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	C₃×C₁₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
14	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₃₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₁₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉×C₃₁	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₉×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₃₁	C₃	semidirect
3. C₃₁×C₁₃⋊C₃	C₁₉	direct (N × H)
4. C₁₉×C₁₃⋊C₃	C₃₁	direct (N × H)
5. C₁₉×C₃₁	C₁₃⋊C₃	direct (N × H)
6. C₁₃×C₃₁	C₃×C₁₉	semidirect
7. C₁₃×C₁₉	C₃×C₃₁	semidirect
10. C₁₃⋊C₃	C₁₉×C₃₁	direct (N × H)
11. C₃₁	C₁₉×C₁₃⋊C₃	direct (N × H)
12. C₁₉	C₃₁×C₁₃⋊C₃	direct (N × H)
13. C₁₃	C₃×C₁₉×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₃₁	3
C₃×C₁₉×C₃₁	13
C₃₁×C₁₃⋊C₃	19
C₁₉×C₁₃⋊C₃	31