NEW YORK CITY — A rare and operational Nazi Enigma machine sold for $365,000 to a private collector at Bonhams on October 21, setting a new record at auction.

The M4 machine, which was builtbetween 1943 and 1945, is one of around 150 to have survived from an estimated 1,500 that were built as Nazi Germany fought to fend off the Allies.

The M4, with four rotors, is the rarest of all Enigma encryption machines and was used on naval submarines.

Its manufacture was ordered by German Admiral Karl Donitz due to concerns that the three-rotor Enigma machine had been compromised following the capture of a U-boat in August 1941.

The model was made rarer still by the sinking of 70 percent of German U-boats in the later stages of World War II, in part due to the breaking of the Enigma code, Bonhams said.

Of the 50 Enigma machines on display in museums around the world, only seven are M4s, taken from captured U-boats.

For information, www.bonhams.com or 212-644-9001.