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Let $G$ be a group of collineations of a finite thick generalised quadrangle$\Gamma$. Suppose that $G$ acts primitively on the point set $\mathcal{P}$ of$\Gamma$, and transitively on the lines of $\Gamma$. We show that the primitiveaction of $G$ on $\mathcal{P}$ cannot be of holomorph simple or holomorphcompound type. In joint work with Glasby, we have previously classified theexamples $\Gamma$ for which the action of $G$ on $\mathcal{P}$ is of affinetype. The problem of classifying generalised quadrangles with apoint-primitive, line-transitive collineation group is therefore reduced to thecase where there is a unique minimal normal subgroup $M$ and $M$ isnon-Abelian.

Point-primitive, line-transitive generalised quadrangles of holomorph type