Subgroups — D₁₃×C₁₂₁₃ #44538679

Order 31538.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₂₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₂₁₃	—	13	1	no	maximal, Hall
3	C₁₂₁₃	D₁₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₁₃	C₁₂₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃	C₂×C₁₂₁₃	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₂₁₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₂₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₂₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₂₁₃

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

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