Seven transatlantic shipping lines were fined a total of $5.45 million and 13 shipping executives $650,000 yesterday after they pleaded no contest to federal charges that they illegally conspired to fix shipping rates on routes between Europe and America.

The fines, imposed by U.S. District Court Judge June L. Green based on recommendations by Justice Department prosecutors, were the largest ever levied in a criminal case brought under the regulations of the 89-year-old Sherman Antitrust Act.

A grand jury had indicted the shippers and their top executives just a week ago yesterday, but Elliott M. Seiden, chief of Justice's transportation section, said that plea bargaining in the case had begun about two weeks earlier.

"It's a good disposition for the government," said Justice trial attorney Janet C. Hall. "The fines are substantial." She said that if the case had gone to trial, some attorneys familiar with the charges predicted it might have lasted as long as eight months.

Price-fixing activities by shipping firms are usually immunized from antitrust prosecution by the Federal Maritime Commission. But the conspiracy indictments against the shipping lines and the executives alleged that they went beyond the commission-sanctioned procedures, set their own rates and then filed tariffs with the commission that "were the product of the combination and conspiracy."

The result, the indictment charged, was the freight rates between Europe and the United States were "fixed, raised, maintained or stabilized at artificial and non-competitive levels" and people who shipped freight were "deprived of the benefits of competition."

Four companies were fined the maximum $1 million - Atlantic Container Line Ltd., a commission-approved consortium of firms from Sweden, Holland, France and the United Kingdom; Sea-Land Service, Inc., of Menlo Park, NJ..; Hapag-Lloyd Aktiengesellschft, a German firm with headquarters in Hamburg; and United States Lines, Inc., of New York.

Dart Containerline Co. Ltd., a commission-sanctioned consortium of firms from Belgium, the United Kingdom and Honk Kong, was fined $800,000, while Seatrain Lines, Inc., of New York was fined $450,000 and American Export Lines, Inc., was fined $200,000.

Seiden said that the varying fines reflected how much each of the companies cooperated with the Justice Department investigation, the companies' degree of culpability in the conspiracy and their current financial status.

Atlantic, Dart, Sea-Land and United States Lines were given six months to pay their fines, but Hapag-Lloyd and American Export were given until Dec. 31 and Seatrain two years.

The 13 executives were all fined the maximum $50,000 after entering their no-contest pleas to the misdemeanor conspiracy charges. The companies pleaded no contest to a felony conspiracy charge.

The executives were Edward J. Heine Jr., president of United States Lines, and the company's executive vice president, Donald G. Aldridge; Hapag's North American managing director, Wolfgang Bohle, and the firm's North Atlantic chief executive, Karl-Heinz Sager; Atlantic Container's chairman, Philip E. Bates, and its managing director, Arne G. M. Koch; Dart's chief executive officer, Daniel du Bois, and its depty chief executive, David B. Hall; Sea-Land's president, Paul F. Richardson, and its marketing senior vice president, J. Scott Morrison; Seatrain's president, Arthur C. Novacek; and Manuel Diaz, executive director of the Associated North Atlantic Freight Conferences, and the conferences' attorney, Howard A. Levy.

All of the executives were given six months to pay their fines with the exception of Morrison, who was given a year.

According to the indictment, the conspiracy covered the period between 1971 and 1975. In that period, the shipping lines reportedly had about 60 percent of the $1 billion-a-year trade in the transatlantic market.