On isotopies, parastrophies, and orthogonality of quasigroups

In V. D. Belousov's papers, some properties of parastrophes were studied and some relations between parastrophes of a given quasigroup were obtained. Also some invariants of a parastrophy were found. This article continues our paper with V. V. Gushan, in which minimal sets of parastrophe systems for quasigroups of order $6$ were obtained and some questions about orthogonality of parastrophes of a given quasigroup were studied as well.