Actually, there never was a Type C, but that name is sometimes used as shorthand for the official "Type 53C" and "Type 53/54C" nomenclatures.
The Type 53C is a dual-trace plugin for 500-series scopes. It was introduced along with the 531 and 535 mainframes in 1954. In those scopes (Tek never documented its performance in the 540's), its bandwidth is 8.5MHz, and like most letter-series plugins, its maximum vertical sensitivity is 50mV/div. Unlike Type A and Type B, Type C had the ability to invert the signal before display.
At 15 tubes, the Type 53/54C and Type CA have the highest tube count of any letter-series plugin. Each channel consists of a 6AK5 cathode-follower driving a 12AU6 differential pair which drives a 6AU6 differential pair. The two channels converge on a 12AT7 cross-coupled cathode-follower. Four more tubes, a 6AL5 and three 12AT7's, comprise a logic circuit which determines which channel drives the output at any given moment. The options are A, B, CHOPPED, or ALT.