  Let $PL_0(I)$ represent the group of orientation-preserving piecewise-linear
homeomorphisms of the unit interval which admit finitely many breaks in slope,
under the operation of composition. We find a non-solvable group $W$ and show
that $W$ embeds in every non-solvable subgroup of $PL_0(I)$. We find mild
conditions under which other non-solvable subgroups ($B$,
$(\wr\Z\wr)^{\infty}$, $(\Z\wr)^{\infty}$, and $^{\infty}(\wr\Z)$) embed in
subgroups of $PL_0(I)$. We show that all solvable subgroups of $PL_0(I)$ embed
in all non-solvable subgroups of $PL_0(I)$. These results continue to apply if
we replace $PL_0(I)$ by any generalized R. Thompson group $F_n$.
