We study the influence of the surface field on lamellar morphologies that form in a diblock copolymer melt confined in a cylindrical nanopore, using self-consistent mean-field theory. By varying the pore diameter and surface field strength and by introducing a slight composition asymmetry, we systematically explore the stability regions of parallel and perpendicular lamellar phases and accurately compute the phase boundaries. When the surface field is weak, or the natural period of the lamellae is incommensurate with the pore size, lamellae perpendicular to the pore wall are preferred. A strong surface preference and/or a small composition asymmetry can lead to the formation of concentric parallel lamellae. In narrow pores, we find that complex structures can exist as equilibrium phases between regions of parallel and perpendicular lamellae. When we reduce the volume fraction of the block preferred by the pore wall, this composition asymmetry competes with the Surface preference and call lead to the formation of perpendicular lamellae. This suggests a route to produce perpendicular lamellar phases in the common experimental situation where a surface preference is present. This competition also enables us to characterize the strength of the surface field in the theory.