We report on a wide variety of magnetic states in Co/Cu multilayered nanocylinders grown by electrodeposition with different thicknesses of both elements. The remnant magnetic states in individual Co layers have quantitatively been determined at the nanoscale by micromagnetic reconstruction of the magnetic phase shift image obtained by electron holography. We demonstrate that the magnetization in the Co layers can present either uniform or vortex states. Also, different magnetic configurations can be observed within the same nanocylinder. In the case of vortices, the direction of the core can rotate almost at 90° from the nanocylinder axis for layers with aspect ratio close to 1. We show that the occurrence of each magnetic configuration depends on the aspect ratio of the layers, the direction of magnetocrystalline anisotropy and in some cases on the interlayer dipolar coupling. Such a wide variety of magnetic states are observed due to lower values of the Co magnetic constants (magnetization, exchange, anisotropy) with respect to bulk, typical of electrodeposition process in a single bath, and to the local geometrical variation of the layers. We also calculated the phase diagram of the remnant magnetic states in a single layer for various amplitudes and orientations of the magnetocrystalline anisotropy and different directions of the saturation field. In particular cases, these phase diagrams in addition to statistics of occurrence of each kind of magnetic configurations in the multilayer and the application of a saturation field in different directions allows recovering information on the preferential orientation of the crystalline anisotropy.