Subgroups — #27211366

Order 13364.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₂₅₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#11759967	—	13	1	no	maximal, Hall
4	D₂₅₇	D₁₃	1	1	yes	characteristic
5	C₂₅₇	Dic₁₃	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₃	—	257	1	no	maximal, Hall
7	C₂×C₁₃	—	257	1	no	—
8	C₁₃	#11759967	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	3341	1	no	Sylow
10	C₂	—	257	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₂₅₇	C₄
prime radical, cosocle	C₁₃×D₂₅₇	C₂
LCS	G ▷ C₁₃×C₂₅₇
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.