We report measurements of the de Haas-van Alphen effect on a series of compounds, LaMIn5 (M=Co,Rh,Ir). The results show that each of the Co and Ir Fermi surfaces (FSs) exhibits some portions that are two dimensional and some portions that are three dimensional. The most two-dimensional character is exhibited in LaCoIn5, less two-dimensional behavior is seen in LaIrIn5, and no part of Fermi surface of LaRhIn5 is found to have a two-dimensional character. Thus the two dimensionality of portions of the FSs is largely determined by the d character of the energy bands while all of the effective masses remain <= 1.2. This fact has implications for the causes of the heavy fermion nature of superconductivity and magnetism in the Ce-based compounds having similar composition and structure.