  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 non-unimodular. 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.
