Visa had the most former Congressional officials, with 37 lobbyists; it was followed closely by other financial powerhouses like Goldman Sachs, Prudential, Citigroup and the American Bankers Association, according to the analysis from Public Citizen, an advocacy group that has pushed for tougher lobbying restrictions.

The case of Peter S. Roberson, whose hiring by a derivatives clearinghouse drew the ire of Mr. Frank, is the most extreme, and it points to holes in the rules governing lobbying by former aides.

As a senior aide to Mr. Frank on the House financial services committee, Mr. Roberson helped draft legislation last year on regulating the over-the-counter derivatives market, which played a big part in the 2008 market collapse. After leaving his Congressional post in January, he began working as a lobbyist for IntercontinentalExchange, the world’s leading clearinghouse for derivatives.

Mr. Roberson, who was paid $124,416 last year as a senior aide, is banned from contacting or lobbying his former colleagues on the committee. But that will not stop him from lobbying, if he chooses to do so. Indeed, he is opening the Washington lobbying office of the exchange.

He is allowed to contact other committees that will be considering the derivatives part of the legislation, like the agriculture committee, as well as anyone in the Senate, where the debate has now shifted. The House has already approved the legislation written by Mr. Frank.

IntercontinentalExchange, known as ICE, said that Mr. Roberson would not be available for an interview and declined to say who had initiated the job discussions. In a statement, Johnathan Short, general counsel for the company, said, “ICE is aware of and has respectfully followed all requirements under House ethics rules governing contact between members, current and former staff. We hired Peter with a full and complete understanding of existing ethics rules and the chairman’s purview in administering the same.”

In an interview last week, Mr. Frank said that he was incensed when Mr. Roberson informed him several months ago that he was in job discussions with the exchange. “In this case, what made it particularly egregious was that he had been working specifically on legislation that was relevant to the company — he had been working on derivatives,” Mr. Frank said.