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 P_1={ 1ox | x\in H}, where 1\in H is the right scalar identity. If the size of H is 5, then P_1 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) P_1 ={{1}, {2, 3}, {4}, {5}}; b) P_1 ={{1}, {2,3}, {4, 5}}. In these cases, P_1 is a partition of H and the equivalence relation associated to it is a regular equivalence on H. We find that, apart of isomorphisms, there are exactly 41 hypergroups in case a), and 56 hypergroup in case b).