Conjugate-comparable not implies normal

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., conjugate-comparable subgroup) need not satisfy the second subgroup property (i.e., normal subgroup)
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Proof

Example of the Baumslag-Solitar group

Further information: Baumslag-Solitar group:BS(1,2)