The nuclear aircraft carrier Enterprise, The Big E, ran aground in San Francisco harbor yesterday after sailing under the Golden Gate Bridge on its way home. Tugs wrestled the 90,000-ton ship off a sand bar, with a heavy assist from a rising tide, after a five-hour struggle during which hundreds of wives, children and sweethearts of the Enterprise's crew could only stand by and wait.

No one was hurt, the Navy said, and it did not appear that the carrier was damaged, but divers will check the hull to make sure.

The helmsman apparently lost control of the ship after the farthest out of its two starboard propellers stopped churning, causing the two port-side propellers to exert more lateral force than the rudder could overcome before the giant ship went aground, Navy officials said.

Eyewitnesses said the Enterprise listed at a 10-degree angle when it first stuck at the edge of the 400-yard-wide channel, a most embarrassing sight for the Navy in general and hardly helpful for the career of the captain. The Navy yesterday did not lay blame on the skipper, Capt. R.J. Kelley, or anyone else, pending an investigation.

An official of the San Francisco Bar Pilots Association said a civilian pilot had been at the carrier's helm as it sailed under the Golden Gate but he turned over the wheel to a Navy pilot just before the ship went aground, according to the Associated Press.

At one point during the Enterprise's grounding, witnesses said, crew members were ordered to gather in one part of the ship, in hopes that their weight would tilt the carrier enough to make it slide off the mud or would correct the listing. Both unofficial explanations were offered at the scene.

The carrier was returning from an eight-month deployment in the western Pacific. Its bow was pushed by the uneven force of the propellers out of the 400-yard-wide channel about 9:30 a.m. PDT, according to Navy officials, in full sight of the families and friends of the 4,500-man crew. The Big E got stuck only 3,000 feet from the pier.

"I keep waiting and waiting," said Debbie Harris, 21, of Show Low, Ariz., as she gazed at the stuck ship, longer than three football fields. "The anticipation is getting really thick. It's awful hard being able to see him but not see him," she said of her husband, Petty Officer Kenneth Harris.

The Harrises were married two years ago and had not seen each other for nine months.

Old Navy hands said yesterday that the Enterprise's plight reminded them of the time the battleship Missouri went aground on Jan. 17, 1950, on a mud bank in the Chesapeake Bay two miles off Old Point Comfort, Va. After three days of trying, tugs could not budge "Old Mo." A high tide finally did the trick. Legend has it that an Air Force transport flew over the stuck ship, dropping canoe paddles.