Hypergroups of type U on the right of size five Part two

The hypergroups H of type U on the right can be classified in terms of the family P1 ={1◦x/xϵH}, where 1 ϵ H is the right scalar identity. If the size of H is 5, then P1 can assume only 6 possible values, three of which have been studied in [3]. In this paper, we completely describe other two of the remaining possible cases: a) P1 ={{1},{2,3},{4},{5}}; b) P1 ={{1},{2,3},{4,5}}. In these cases, P1 is a partition of H and the equivalence relation associated to it is a regular equivalence on H. We find that, apart of somorphisms, there are exactly 41 hypergroups in case a), and 56 hypergroups in case b).