A neo-Nazi couple who named their baby son after Adolf Hitler and made their home a “shrine to extreme racism” have been jailed for membership of a terrorist group.

Adam Thomas was pictured cradling his son while wearing the hooded robes of the Ku Klux Klan. His partner, Claudia Patatas, believed “all Jews must be put to death”, a trial at Birmingham crown court heard.

The pair had a long history of violent racist beliefs, said the judge, Melbourne Inman QC, and both had claimed they were “willing to murder a mixed-race child” to further their neo-Nazi agenda.

“These are not idle words,” the judge said. “The vile regime you and Thomas worship, and which you wish to impose on this country, did – and would do – exactly that.”

Thomas, 22, and Patatas, 38, cried and held hands in the dock as they were jailed for six years and six months, and five years respectively. The couple, from Banbury in Oxfordshire, were last week found guilty of being members of the far-right organisation National Action, which was banned in 2016.

Their friend Darren Fletcher, who admitted National Action membership before the trial, was jailed for five years for the same offence. In all, six people were sentenced on Tuesday for being members of the group, which the judge described as having horrific goals.

“Its aims and objectives are the overthrow of democracy in this country by serious violence and murder, and the imposition of a Nazi-style state which would eradicate whole sections of society by such violence and mass murder,” he said. “The eradication of those who you consider to be inferior because of no more than the colour of their skin or their religion.”

During the trial the court heard Fletcher, 28, of Wolverhampton, had taught his daughter to do a Nazi salute, and sent a message to Patatas saying: “Finally got her to do it.”

The jury was told that Thomas and Patatas gave their child the middle name “Adolf”, which Thomas said was in “admiration” of Hitler, and the couple had swastika cushions in their home.

In conversation with another National Action member, Patatas said “all Jews must be put to death”, while Thomas had once told his partner he found “all non-whites intolerable”.

Thomas, a former Amazon security guard and twice-failed army applicant, was also convicted on a majority verdict of having a terrorist manual – a copy of the bomb-making guide known as the Anarchist’s Cookbook. Patatas, a wedding photographer originally from Portugal, had also said she wanted to “bring back concentration camps”.

The couple had both been involved in what the judge described as the desecration of war memorials, including one in Warwickshire, and were “equally extreme” in their views and actions.

The judge told Thomas: “Your home with Patatas was a veritable shrine to extreme racism.”

He said Thomas’s views had been so extreme that his only recourse had been to claim to jurors he had “deliberately exaggerated, to shock. That was rightly rejected by the jury.”

Daniel Bogunovic, 27, from Leicester, was sentenced to six years and four months’ jail having being convicted of membership of National Action after standing trial with Patatas and Thomas. He was described by prosecutors as a “committed National Action leader, propagandist and strategist” within the group’s Midlands cell.

Two other men, Joel Wilmore, 24, a cyber-security worker and National Action Midlands cell “banker”, and Nathan Pryke, 26, a van driver described as the group’s “security enforcer”, were also jailed. Wilmore, of Stockport, Greater Manchester, and Pryke, 26, of March, Cambridgeshire, admitted membership of the banned group prior to the trial, along with Fletcher. Pryke was jailed for five years and five months, and Wilmore was jailed for five years and 10 months.