Finite Group Databasebeta

← C₁₃×C₁₉₃⋊C₃ #21419087

Subgroups — C₁₃×C₁₉₃⋊C₃ #21419087

Order 7527.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉₃	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₁₃	—	193	1	no	maximal, Hall
5	C₁₃	C₁₉₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	193	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₁₉₃⋊C₃
commutator, hypocenter	C₁₉₃	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉₃	C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉₃	C₃	semidirect
2. C₁₉₃⋊C₃	C₁₃	direct (N × H)
3. C₁₉₃	C₃×C₁₃	semidirect
5. C₁₃	C₁₉₃⋊C₃	direct (N × H)