  The interplay between strongly correlated liquid and crystal phases for
two-dimensional electrons exposed to a high transverse magnetic field is of
fundamental interest. Through the non-perturbative fixed phase diffusion Monte
Carlo method, we determine the phase diagram of the Wigner crystal in the
$\nu-\kappa$ plane, where $\nu$ is the filling factor and $\kappa$ is the
strength of Landau level mixing. The phase boundary is seen to exhibit a
striking $\nu$ dependence, with the states away from the magic filling factors
$\nu=n/(2pn+1)$ being much more susceptible to crystallization due to Landau
level mixing than those at $\nu=n/(2pn+1)$. Our results explain the qualitative
difference between the experimental behaviors observed in n-doped and p-doped
GaAs quantum wells, and, in particular, the existence of an insulating state
for $\nu<1/3$ and also for $1/3 <\nu< 2/5$ in low density p-doped systems. We
predict that in the vicinity of $\nu=1/5$ and $\nu=2/9$, increasing LL mixing
causes a transition not into an ordinary electron Wigner crystal but rather
into a strongly correlated crystal of composite fermions carrying two vortices.
