As members of the Oath Keepers paramilitary group shouldered their way through the mob and up the steps to the U.S. Capitol, their plans for Jan. 6 were clear, authorities say. "Arrest this assembly, we have probable cause for acts of treason, election fraud," someone commanded over an encrypted messaging app some extremists used to communicate during the siege.

A little while earlier, Proud Boys carrying two-way radios and wearing earpieces spread out and tried to blend in with the crowd as they invaded the Capitol led by a man assigned "war powers" to oversee the group's attack, prosecutors say.

These two extremist groups that travelled to Washington along with thousands of other Trump supporters weren't whipped into an impulsive frenzy by President Donald Trump that day, officials say. They'd been laying attack plans. And their internal communications and other evidence emerging in court papers and in hearings show how authorities are trying to build a case that small cells hidden within the masses mounted an organized, military-style assault on the heart of American democracy.

"This was not simply a march. This was an incredible attack on our institutions of government," Assistant U.S. Attorney Jason McCullough said during a recent hearing.

The Proud Boys and Oath Keepers make up a fraction of the more than 300 Trump supporters charged so far in the siege that led to Trump's second impeachment and resulted in the deaths of five people, including a police officer. But several of their leaders, members and associates have become the central targets of the Justice Department's sprawling investigation.

It could mean more serious criminal charges for some rioters. On the other hand, mounting evidence of advance planning could also fuel Trump's and his supporters' claims that the Republican former president did not incite the riot and therefore should not be liable for it.

Defence attorneys have accused prosecutors of distorting their clients' words and actions to falsely portray the attack as a premeditated, orchestrated insurrection instead of a spontaneous outpouring of election-fueled rage to stop Congress' certification of Trump's defeat by Democrat Joe Biden.

And prosecutors' case against a man described as a leader in the Proud Boys' attack took a hit last week when a judge ordered him released while he awaits trial, calling some of the evidence against him "weak to say the least."

The Oath Keepers began readying for violence as early as November, authorities say. Communications show the group discussing logistics, weapons and training, including "2 days of wargames."

"I need you fighting fit" by the inauguration, one Ohio member, Jessica Watkins, told a recruit in November, according to court documents. "If Biden becomes president our way of life as we know it is over. Our Republic would be over. Then it is our duty as Americans to fight, kill and die for our rights," she said in another message later that month.

As the mob swarmed the Capitol, Stewart Rhodes, the leader of the Oath Keepers, was communicating with some of the alleged rioters.

"All I see Trump doing is complaining. I see no intent by him to do anything. So the patriots are taking it into their own hands. They've had enough," he said in a Signal message to a group around 1:40 p.m., authorities say. A little later, Rhodes, who has not been charged in the attack, instructed the group to "come to South Side of Capitol on steps."

Around 2:40 p.m., members of a military-style "stack" who moved up Capitol stairs in a line entered the building through a door on the east side, authorities say. Lawmakers and Vice-President Mike Pence had been evacuated from the House and Senate chambers just about 20 minutes earlier.

"We are in the mezzanine. We are in the main dome right now. We are rocking it. They are throwing grenades, they are fricking shooting people with paint balls. But we are in here," Watkins declared over a channel called Stop the Steal J6 on the walkie-talkie app Zello, prosecutors say.

The Proud Boys met at the Washington Monument and were already at the Capitol before Trump finished addressing thousands of supporters near the White House. Listening to the president's speech wasn't part of their plan, prosecutors say.

Ethan Nordean led the way with a bullhorn while they wore headgear marked with orange tape. Dominic Pezzola appeared to have an earpiece in his right ear. Joseph Biggs had what looked like a walkie-talkie device on his chest.

Nordean was spotted having a brief exchange near the Capitol with Robert Gieswein, a bat-wielding Colorado man. Proud Boys planning for Jan. 6 had discussed using non-members, or "normies," like Gieswein to "burn that city to ash" and "smash some pigs to dust," prosecutors said.

Nine people linked to the Oath Keepers have been indicted on charges that they planned and co-ordinated with one another in the siege. At least 11 leaders, members or associates of the Proud Boys charged in the riots are accused by the Justice Department of participating in a co-ordinated attack.

Several from both groups remain in federal custody while awaiting trial.

In testimony to Congress, the acting Capitol Police chief said officers had worked to intercept "the radio frequency used by some demonstration groups and monitoring the communications of those groups," though it's unclear if those groups included the Proud Boys or the Oath Keepers.

Their defence attorneys claim prosecutors have painted a misleading account of the day's events based on shaky evidence. Other lawyers for those charged with storming the Capitol have tried to pin the blame on Trump for inciting the rioters.

Nordean's lawyers said prosecutors haven't presented any evidence that he used encrypted communications to lead a group's attack on the Capitol.

"The government has made repeated claims about Ethan's activities and then backed away from them without providing any support," said one of his attorneys, Nicholas Smith.