Subgroups — C₁₃₁×C₃₄₉ #56089705

Order 45719.

4 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₄₉	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₁₃₁	C₃₄₉	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. C₃₄₉	C₁₃₁	direct (N × H)
2. C₁₃₁	C₃₄₉	direct (N × H)

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

subgroup	index
C₃₄₉	131
C₁₃₁	349