Subgroups — #44545596

Order 32097.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₈₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₈₂₃⋊C₃	—	13	1	no	maximal, Hall
3	C₈₂₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
4	C₁₃⋊C₃	—	823	1	no	maximal, Hall
5	C₁₃	C₈₂₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	10699	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₈₂₃	C₃
LCS	G ▷ C₁₃×C₈₂₃
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.