A judge says it is constitutional for New York City to require groups of 50 people on bicycles to get a parade permit from the police department.

Judge Lewis Kaplan’s ruling Tuesday came in a clash between cyclists and police that began when more than 260 bicyclists were arrested during the 2004 Republican National Convention.

Kaplan said he is sympathetic to cyclists’ concerns. He said he was not persuaded by the argument that the 50-person threshold is arbitrary and lower than necessary to achieve “the city’s substantial interests in safety, efficiency and traffic flow.”

In ruling, Kaplan tossed out the lawsuit brought by the Five Borough Bicycle Club and interested bicycle enthusiasts.

A message left with the bike riders’ lawyers was not immediately returned.