A novel maize variety designated PH410P and seed, plants and plant parts thereof are provided. Methods for producing a maize plant comprise crossing maize variety PH410P with another maize plant are provided. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PH410P through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby are provided. Hybrid maize seed, plants or plant parts are produced by crossing the variety PH410P or a locus conversion of PH410P with another maize variety.