For about 10 minutes Tuesday, the House District Committee, in its first meeting of the 96th Congress, had something that often eludes it -- a quorum.

But it was in session long enough to name its former chairman, convicted Rep. Charles C. Diggs Jr. (D -- Mich.) to a subcommittee that has power over criminal code revision, confirmation of judges and reorganization of the court system.

Rep. Donald V. Dellums (D-Calif.), who moved up to the chairmanship following Diggs' conviction for misuse of Congressional funds, has reduced the membership of the committee in hopes in making it easier to get a quorum than it has been in recent years.

The streamlined committee, reduced from 20 to 14 members, attracted all nine of its Democrats but only one of its five Republicans to its organizations session Tuesday.

That didn't last long. After 10 minutes, one of the committe's five new members, Rep. Anthony Toby Moffett (D-Conn.) walked out, followed a minute later by freshman Rep. William H. Gray III (D-P.).

But most of the work was accomplished in the closed caucus that preceded the open meeting. It was behind those closed doors that Diggs was named to the subcommittee on judiciary, manpower and education, under ther chairmanship of Rep. Romano L. Mazzoli (D-Ky.). Other subcommittee chairmen selected were Dellums for fiscal affairs and health; Rep. Fortney H. Stark (D-Calif.) for metropolitan affairs, and D.C. Del. Walter E. Fauntroy for government affairs and budget.