Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the
sense that their isometry groups contain the isometry groups of any other
left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily
nonunimodular. In this work we consider unimodular solvable Lie groups and prove
that there is always some metric with maximal symmetry. Further, if the group at
hand admits a Ricci soliton, then it is the isometry group of the Ricci soliton which is
maximal.
