Isomorphism classes of the hypergroups of type UU on the right of size five

By means of a blend of theoretical arguments and computer algebra techniques, we prove that the number of isomorphism classes of hypergroups of type UU on the right of order five, having a scalar (bilateral) identity, is 14 751. In this way, we complete the classification of hypergroups of type UU on the right of order five, started in our preceding papers [M. De Salvo, D. Freni, G. Lo Faro, A new family of hypergroups and hypergroups of type UU on the right of size five, Far East J. Math. Sci. 26(2) (2007) 393–418; M. De Salvo, D. Freni, G. Lo Faro, A new family of hypergroups and hypergroups of type UU on the right of size five Part two, Mathematicki Vesnik 60 (2008) 23–45; M. De Salvo, D. Freni, G. Lo Faro, On the hypergroups of type UU on the right of size five, with scalar identity (submitted for publication)]. In particular, we obtain that the number of isomorphism classes of such hypergroups is 14 865.