Primark Corp. of McLean, in a bid to expand its varied holdings in the nation's service industry, has agreed to a $130-million buyout of the Aviation Group Inc. of North Carolina, spokesmen for both companies announced yesterday.

Primark will pay $23 a share for the Aviation Group's 5.6 million outstanding shares of common stock in a tender offer that will begin on Tuesday, the company spokesmen said.

Primark had $2 billion in sales for calendar 1984 and $1.3 billion in the first nine months of this year. Net earnings for 1984 amounted to $49.5 billion ($2.63 per share). The company earned $1.3 billion ($1.96) in the first three quarters of 1985.

Primark, a publicly traded holding company, has had consecutive annual revenue increases since its founding in 1981. Some of the company's current properties include Michigan Consolidated Gas Co., a natural-gas distribution company serving about 1 million residential and commercial customers in Michigan; Hospital Satellite Network Inc., a telecommunications and information service for the health-care industry, and Primark Financial Services Inc., a banking and insurance business.

The acquisition of the Aviation Group, which services the overnight air freight-delivery industry, is compatible with Primark's longterm growth strategy, said John J. Lewis, Primark's director of investor relations.