Finite group subschemes of abelian varieties over finite fields

Let $A$ be an abelian variety over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by the Weil polynomial $f_A$. We assume that $f_A$ is separable. For a given prime number $\mathrm{\ell }\mathrm{\ne }\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}k$ we give a classification of group schemes $B[\mathrm{\ell }]$, where $B$ runs through the isogeny class, in terms of certain Newton polygons associated to $f_A$. As an application we classify zeta functions of Kummer surfaces over $k$.