Finite Group Databasebeta

← D₁₃×C₃₄₉ #22583751

Subgroups — D₁₃×C₃₄₉ #22583751

Order 9074.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₄₉	—	13	1	no	maximal, Hall
3	C₃₄₉	D₁₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₁₃	C₃₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃	C₂×C₃₄₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₄₉	D₁₃
commutator, hypocenter	C₁₃	C₂×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₄₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃₄₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₄₉	C₂	semidirect
3. C₃₄₉	D₁₃	direct (N × H)
4. D₁₃	C₃₄₉	direct (N × H)
5. C₁₃	C₂×C₃₄₉	semidirect