Subgroups — C₁₃×D₁₂₂₃ #44541213

Order 31798.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₂₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₂₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₃	—	1223	1	no	maximal, Hall
5	C₁₃	D₁₂₂₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	1223	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₁₂₂₃
commutator, cosocle, hypocenter	C₁₂₂₃	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₂₂₃	C₂
LCS	G ▷ C₁₂₂₃
UCS	C₁ ◁ C₁₃

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.