On irreducible sextics with non-abelian fundamental group

We calculate the fundamental groups $\pi ={\pi }_1(P^2\setminus B)$ for all irreducible plane sextics $B\subset {\mathrm{\P }}^2$ with simple singularities for which $\pi$ is known to admit a dihedral quotient $D_{10}$. All groups found are shown to be finite, two of them being of large order: 960 and 21600.