CHICAGO — United Airlines will pay more than $1 million in fines for stranding passengers on 13 planes for more than three hours on the tarmac during a stormy day last year at Chicago’s O’Hare International Airport, federal officials said Friday.

The $1.1 million fine is the largest levied against an airline since 2010, when new rules took effect that bar airlines from stranding passengers on the tarmac for longer than three hours without giving them the opportunity to leave the plane, according to the U.S. Department of Transportation.

The delays involved 13 United and United Express planes on July 13, 2012, a day when severe thunderstorms and lightning had caused several ramp closures and disrupted the movement of aircraft at O’Hare, the nation’s second largest airport. Toilets weren’t working on two of those planes.

“It is unacceptable for passengers to be stranded in planes on the tarmac for hours on end,” U.S. Transportation Secretary Anthony Foxx said. “We will continue to require airlines to adopt workable plans to protect passengers from lengthy tarmac delays and carry out these plans when necessary.”

The airline exceeded the three-hour limit by as much as an hour and 17 minutes, and didn’t contact airport personnel or other airlines for help, according to the department.

United will pay the government $475,000, while $185,000 will be used to compensate affected passengers. It will use $440,000 for a surveillance system to monitor the location of each of its planes on the airfield.