  Suppose that $G$ is a finite, transitive, solvable permutation group acting
on a set $S$ with $n$ elements. Let $G_0$ be the stabilizer of a point $\alpha
\in \Omega$. Define the rank of a permutation group, denoted $r(G),$ as the
number of distinct orbits of $G_0$ in $S$ (including the trivial orbit
$\{\alpha\}$). Huppert \cite{Huppert} and Foulser \cite{Foulser} classified all
finite, solvable, permutation groups of rank two and three respectively, and
Foulser restricted the rank four groups to a small list of possibilities. This
paper completes the classification of all groups of rank less than $5$ by
explicitly confirming these past results and computationally constructing the
groups of rank $4$.
