Vertical convection, often also called lateral convection, is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity. In this numerical study, we consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O($10^8$). This flow consists of two plume motions near the boundaries and a linear stable temperature stratification in the interior. As a function of the Prandtl number, $Pr$, and the height-to-width aspect ratio of the domain, $A$, the base flow (steady state) of each case is computed and linear simulations are used to obtain the properties of the leading linear mode of instability. The flow regimes show a rich variation with Prandtl number and aspect ratio. These regimes depend on whether the plumes generate a circulation in the entire cavity, detach from the horizontal boundaries or the corner regions, and further on whether the oscillation frequency of the instability is slower (or faster) than the buoyancy frequency of the stratification in the interior, and allows for the presence of internal waves (or not), Accordingly, the regime is called slow or fast, respectively. Internal wave allow for the coupling between the top and bottom plumes, and their absence implies asymmetry in part of the regimes. Six essentially different flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$.