A semifield plane of odd order admitting an autotopism subgroup isomorphic to $A_5$

We develop an approach to constructing and classifying semifield projective planes with the use of a spread set. The famous conjecture is discussed on the solvability of the full collineation group of a finite semifield nondesarguesian plane. We construct a matrix representation of a spread set of a semifield plane of odd order admitting an autotopism subgroup isomorphic to the alternating group $A_5$ and find a series of semifield planes of odd order not admitting $A_5$.