Finite Group Databasebeta

← C₁₃⋊C₃×C₁₉₃ #21419086

Subgroups — C₁₃⋊C₃×C₁₉₃ #21419086

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	C₃×C₁₉₃	—	13	1	no	maximal, Hall
3	C₁₉₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₁₃⋊C₃	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃	C₃×C₁₉₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	13	1	no	Sylow

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

Complements

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

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