Subgroups — C₂₂₃×C₂₅₇ #65291237

Order 57311.

4 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅₇	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂₂₃	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow

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

N	H ≅ G/N	type
1. C₂₅₇	C₂₂₃	direct (N × H)
2. C₂₂₃	C₂₅₇	direct (N × H)

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

subgroup	index
C₂₅₇	223
C₂₂₃	257