LONDON — A couple who named their child after Hitler have been sentenced to more than 10 years total in prison after they were convicted of being members of a banned neo-Nazi group that had sought to start a race war in Britain, the police said.

A judge in Birmingham Crown Court, in northwest England, sentenced the couple, Adam Thomas, 22, and Claudia Patatas, 38, on Tuesday, along with four other members, for being members of the violent National Action group after they were convicted last month. Mr. Thomas received six years and six months in prison, and Ms. Patatas five years.

The six were active members of the group, which has been banned under British antiterrorism law since 2016. But Mr. Thomas, a former security guard, and Ms. Patatas, a wedding photographer, stood out: The couple gave their child the middle name Adolf out of admiration for Hitler, the BBC reported.

In one image released by the West Midlands Police, the couple were photographed holding their baby alongside a flag emblazoned with a swastika. In another, Mr. Thomas is shown in a white robe reminiscent of those worn by the Ku Klux Klan while cradling a baby also dressed in white.