Subgroups — #10621721

Order 676.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₉	C₂	1	1	yes	maximal, characteristic
2	C₁₆₉	C₄	1	1	yes	characteristic, complemented, Sylow
3	#261	—	13	1	no	maximal
4	D₁₃	—	13	1	no	—
5	C₁₃	#261	1	1	yes	characteristic
6	C₄	—	169	1	no	Sylow
7	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₁₆₉	C₄
Frattini, socle	C₁₃	#261
prime radical, cosocle	D₁₆₉	C₂
LCS	G ▷ C₁₆₉
UCS	C₁

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

N	H ≅ G/N	type
2. C₁₆₉	C₄	semidirect

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

subgroup	index
D₁₆₉	2
#261	13