We examine light trapping in thin silicon nanostructures for solar cell applications. Using group theory, we design surface nanostructures with an absorptance exceeding the Lambertian limit over a broad band at normal incidence. Further, we demonstrate that the absorptance of nanorod arrays closely follows the Lambertian limit for isotropic incident radiation. These effects correspond to a reduction in silicon mass by 2 orders of magnitude, pointing to the promising future of thin crystalline silicon solar cells.