C-type asteroid
The largest unequivocally C-type asteroid is 10 Hygiea, although the SMASS classification places the largest asteroid, 1 Ceres, here as well, because that scheme lacks a G-type.
M-type asteroid
16 Psyche is the largest M-type asteroid, and does appear to be metallic. 21 Lutetia, an anomalous, probably non-metallic body, was the first M-type asteroid to be imaged by a spacecraft when the Rosetta space probe visited it on July 10, 2010. Another M-type asteroid, 216 Kleopatra, was imaged by radar by the Arecibo Observatory in Puerto Rico, and has a dog bone-like shape.