No, carbon steel pans are not dishwasher safe, as they can rust in moist environments. Instead, carbon steel frying pans should be hand-washed with warm water and a soft-bristle brush or non-scouring sponge.
How to clean: scrub with a plastic brush, which won't scratch. Before cooking, rub 1/2 teaspoon oil inside to safeguard the nonstick surface.
Here are two recommended nonstick skillets from CR’s tests.