The groups that claim to have set off two downtown explosions yesterday may be new to the Washington area, but they are well known along the gaily painted of streets of Miami's Little Havana.

Authorities said the Pedro Luis Boitel Commando group, which telephoned a 5-minute warning of the second blast, emerged last May 25 from the ever-shifting maze of splinter groups that make up Miami's Cuban refugee community.

Three Miami incidents, plus the Washington bombings, are part of a pattern of terrorist acts by various groups aimed at overthrowing Cuban Premier Fidel Castro and discouraging anyone from befriending or even dealing with the Castro government.

At this time, the Justice Department does not believe the Boitel Commando group is connected to the Letelier bombing. The group is named after an anti-Castro Cuban student leader who died in 1972 in a Cuban jail on the 59th day of a hunger strike.

Later in the day a Miami group, calling itself "El Condor", also claimed responsibility for the early morning Washington bombings.

The anti-Castro groups have centered in Miami where there are roughly 450,000 Cubans, most of them rapidly anti-Castro. A U.S. grand jury has been hearing evidence there since November on made-in-Miami terrorism, and local authorities maintain special refugee-oriented anticrime and investigation units.

In contrast, Washington's Cuban community numbers between 10,000 and 20,000 persons, whom community leaders and local officials say are well integrated into the general society.

Both Justice Department and Federal Bureau of Investigation spokesmen said they knew of no pending investigations involving Washington's Cuban community. They added they had never heard of the Boitel Commandos before yesterday.

Even in Miami the rise of a new group means little. "We've pretty much accepted that the Boitel group is just another name for the same group of people, another faction...maybe CORU or somebody else," said Assistant U.S. Attorney Jerome Sanford in Miami. CORU, the United Revolutionary Organizations Command, is an umbrella organization for a variety of anti-Castro groups.

The Boitel Commandos first appeared May 25, when they claimed responsibility for a bomb at the Ft. Lauderdale office of Mackey International airlines. The small company promptly canceled its plans to begin regular flights to Cuba.

The commandos next said they were the ones who threw a small bomb over a fence at a Venezuelan DC-9 parked at the Miami International Airport. That their communique said, Orlando Bosch, a flamboyant Cuban exiled physician jailed in Caracas since October. He claims to be the leader of CORU, and is charged in an Oct. 6 bombing that killed 83 persons aboard a Cuban Airlines jet.

The first group to claim responsibility for that bombing called itself "El Condor," which was the same name used by the group that joined the Boitel Commandos in claiming responsibility for yesterday's Washington bombings.

Although El Condor means little to Washington, it refers in Miami to the defendant in two much-publicized bombing trials last year, Rolando Otero, and to one or more splinter groups that appeared during and after the trial.

They could be different groups using the same name to throw off law enforcement. . .or to make some little group of one or two sound like a big group," said a federal official in Miami. He added that often more than one group will claim a bombing, as in the Washington case, although they may have had nothing to do with it.

Neither the Boitel nor the Condor group has ever acted outside Miami before, according to officials there and in Washington. The most recent incident involving either took place Friday in Miami, when a caller alleging ties to the Boitel Commandos warned of a series of bombs set to go for along U.S. Rte. 1 between Homestead and Key West, Fla.

Authorities mounted a large-scale search in the area but no bombs were found. The only terrorist incidents in the Miami area this year have been the two claimed by the Boitel group. There were 95 such events between 1974 and 1976.

"There are indications there may now be an attempt . . . to become more active," said Sgt. Paul Janosky of the Dade County Organized Crime Bureau's terrorism unit. Three boats loaded with uniforms, guns and ammunition were seized Aug. 15 bu U.S. Customs officials, who arrested one man and broke up what appeared to be a planned commando raid on Cuba.

Shortly afterward, federal authorities received reports that Cuban exiles might be planning retaliation for the State Department's Aug. 3 admission "that we have exchanged information with the Cuban government on possible terrorist acts." Exile community leaders escalated their criticism of the Carter administration and its cordiality to Castro, and internal memos have alerted federal authorities against U.S. installations or individuals.

Cuban leaders in Washington say the community here is less politically active than the Miami enclave. About 5,000 Cubans from up and down the East Coast came to Washington last Sunday, according to the Rev. Armando Jimenez of St. James Church, for the consecration of a new statue of Nuestra Senora de la Caribad (Our Lady of Charity), the Cuban patron saint.

"It was a very beautiful thing, and nobody noticed it because it was peaceful," said Padre Jimenez.