Unterseeboot 413 (U-413) was a Type VIIC submarine of the Kriegsmarine. Her keel was laid down on April 25, 1941 by Danziger Werft, of Danzig. She was commissioned June 3, 1942, with Oberleutnant zur See Gustav Poel in command. Poel commanded her (receiving a promotion to Kapitänleutnant) until April 19, 1944, when he was relieved by Oblt. Dietrich Sachse who commanded her until her loss.
U-413 conducted eight patrols, sinking six ships totaling of 37,985 tons.
On November 19, 1942, U-413 was attacked by a British Lockheed Hudson aircraft with five bombs and was damaged so severely that she had to return to base.
U-413 did not suffer any casualties until August 20, 1944, when she was sunk in the English Channel by depth charges from the British escort destroyer HMS Wensleydale and the destroyers HMS Forester and Vidette. 45 of her crew were killed; there was one survivor.
Neal Stephenson's novel Cryptonomicon features a fictitious U-413, a milchcow. It is possible that Stephenson picked the number of the boat not for historical accuracy but rather because it is the product of two primes, 7 and 59.