In this paper, we prove various inclusion relationships among different classes of algebraic structures and hyperstructures of type U on the right of finite size. In particular, we consider in detail the inclusion properties Gn⊆PURn⊆HURn⊆SURn between the classes of groups Gn, polygroups PURn, hypergroups HURn and semihypergroups SURn of type U on the right of size n and provide conditions such that the equality holds. As a particular result, we prove that every polygroup of type U on the right is a group.
