Hertz Corp., the nation's largest car-rental company, was sold yesterday for $1.3 billion to Ford Motor Co. and a group of Hertz executives by Allegis Corp., the Chicago travel conglomerate.

The sale of Hertz followed by just four days the sale of its chief rival, Avis, to that company's employes. Both major car rental agencies have changed hands several times in recent years, and two smaller competitors, National Car Rental and Budget Rent-a-Car, were sold last year.

Ford will put up more than $1.2 billion of the purchase price, although officials of the automobile maker said they hoped eventually to reduce Ford's interest in Hertz to a minority stake.

More than half of Hertz' 350,000 rental cars are Ford products, and the company began in 1918 as a rental agency for Ford Model T cars.

Ford's comptroller, David McCammon, said he expects Hertz' reliance on Ford cars to increase somewhat in the future. "Ford has assisted Hertz management with the acquisition in order to retain our long-term relationship with Hertz," he said.

McCammon said several other parties had been interested in joining the purchasing group, which is called Park Ridge Corp., but arrangements could not be made in time to complete the bid that was submitted to Allegis. So Ford agreed to put up most of the financing and then sell pieces of Hertz to the other interests later. "This you might view as a financial transaction in the meantime, until the ownership base can be broadened," McCammon said.

Eventually, he added, stock in Hertz likely will be sold to the public.

By selling Hertz, Allegis took one more step in its efforts to concentrate on its original business, United Airlines. Under former Chairman Richard Ferris, Allegis had attempted to become a full-service travel company, with the Westin and Hilton International hotel chains in addition to the airline and rental car operations.

But the strategy proved more troublesome and less profitable than Ferris had hoped, and he was ousted last spring when the company's woes made it a takeover target. The new management has announced the sale of the Hilton International chain to Ladbroke PLC, a British hotel company, for $1.1 billion, and plans to sell Westin soon.

The management team that is joining with Ford to buy Hertz includes Frank Olson, who has been acting chairman of Allegis since Ferris' ouster.

An Allegis spokesman said Olson, a longtime Hertz executive, would step down as Allegis chairman when a replacement is found. A committee of Allegis directors has been searching for a new chairman since mid-summer, and while no timetable for an appointment has been set, a company spokesman indicated the job would be filled before the scheduled closing of the Hertz deal in mid-November.

Allegis, which had been criticized for paying too much when it bought Hertz from RCA Corp. two years ago for $587.5 million, made a hefty profit on the deal. The transaction includes $1 billion worth of Hertz debt, which will be assumed by its new owners.

Analysts have attributed the high turnover of ownership in the rental car industry to a variety of factors, including upheaval and strategy changes at the companies that have owned Hertz and Avis. For instance, RCA, which owned Hertz for more than 20 years, sold it to Allegis -- then known as UAL Inc. -- in 1985 because RCA decided to concentrate on its technology and broadcasting businesses.

Avis has had an even more tumultuous ownership history. It has been sold four times in the past five years.

On Monday, an employe stock-ownership plan set up by the 11,000 Avis employes bought the company for $1.75 billion from Wesray Capital Corp., an investment firm. Wesray, which said it made a $740 million profit on the sale, had purchased Avis last year for $265 million and the assumption of $1.3 billion in debt from Beatrice Cos. Beatrice put Avis on the market after the food conglomerate was taken private in a leveraged buyout and had to shed assets to pay debt.

Beatrice had acquired Avis in its takeover of Esmark Inc., which in turn had acquired Avis in a takeover of Norton Simon Inc. And Norton Simon bought Avis in 1977 from a federal trustee, who took control of the company after International Telephone & Telegraph Inc. divested Avis to settle federal charges stemming from an antitrust case.

Last year, Household International Inc. sold National Car Rental System Inc., ranked third in the industry, to a private investor group for $459 million, and Transamerica Corp. sold Budget Rent-A-Car to an investor group for $205 million. Both of those sales were prompted by strategy changes at the parent corporations.