Subgroups — C₁₃⋊D₁₃ #66764

Order 338.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₁₃	—	13	14	no	maximal
3	C₁₃	D₁₃	1	14	yes	complemented
4	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²	C₂
LCS	G ▷ C₁₃²
UCS	C₁

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

N	H ≅ G/N	type
1. C₁₃²	C₂	semidirect
3. C₁₃	D₁₃	semidirect

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

subgroup	index
C₁₃²	2
D₁₃	13