Subgroups — #34040176

Order 19071.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₆₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₁₆₃	C₉	1	1	yes	characteristic, complemented, Hall
3	#13091814	—	13	1	no	maximal, Hall
4	C₁₆₃⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic
5	C₁₆₃	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
6	C₁₃⋊C₉	—	163	1	no	maximal, Hall
7	C₃×C₁₃	—	163	1	no	—
8	C₁₃	#13091814	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	2119	1	no	Sylow
10	C₃	—	163	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₆₃	C₉
prime radical, cosocle	C₁₃×C₁₆₃⋊C₃	C₃
LCS	G ▷ C₁₃×C₁₆₃
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.