  We consider factorizations of a finite group $G$ into conjugate subgroups,
$G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$,
where $A$ is nilpotent or solvable. First we exploit the split $BN$-pair
structure of finite simple groups of Lie type to give a unified self-contained
proof that every such group is a product of four or three unipotent Sylow
subgroups. Then we derive an upper bound on the minimal length of a solvable
conjugate factorization of a general finite group. Finally, using conjugate
factorizations of a general finite solvable group by any of its Carter
subgroups, we obtain an upper bound on the minimal length of a nilpotent
conjugate factorization of a general finite group.
