Subgroups — #72244717

Order 6591.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	13₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₁₃×C₁₃⋊C₃	—	13	1	no	maximal
3	C₁₆₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃²	C₁₃⋊C₃	1	1	yes	characteristic
5	C₁₆₉	—	3	4	no	—
6	C₁₆₉	C₃×C₁₃	1	1	yes	characteristic, complemented
7	C₃×C₁₃	—	169	1	no	—
8	C₁₃⋊C₃	—	13	1	no	—
9	C₁₃	—	39	1	no	—
10	C₁₃	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic
11	C₃	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₆₉	C₃×C₁₃
Frattini, socle	C₁₃	C₁₃×C₁₃⋊C₃
Fitting	13₋¹⁺²	C₃
LCS	G ▷ C₁₆₉
UCS	C₁

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.