Subgroups — 13₋¹⁺² #14555587

Order 2197.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²	C₁₃	1	1	yes	maximal, characteristic
2	C₁₆₉	C₁₃	1	13	yes	maximal, complemented
3	C₁₃	—	13	1	no	—
4	C₁₃	C₁₃²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₁₃	C₁₃²
prime radical	C₁₃²	C₁₃
LCS	G ▷ C₁₃ ▷ C₁
UCS	C₁ ◁ C₁₃ ◁ G
LECS	G ▷ C₁₃ ▷ C₁

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

N	H ≅ G/N	type
2. C₁₆₉	C₁₃	semidirect

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

subgroup	index
C₁₃²	13
C₁₆₉	13