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.
Near-Earth object
Two of the biggest Near-Earth objects 433 Eros and 1036 Ganymed, were also some the earliest to be detected. 1036 Ganymed is about 20 miles in diameter. As bigger asteroids they reflected more light. One way around simply finding the NEOs that reflect the most visible light, is to use infrared telescopes that observe the objects heat emissions.