Corporal Mikko Vehvilainen, a veteran of the Afghan conflict, was jailed for eight years.
National Action is an extreme right-wing organisation which glorifies Hitler and the Third Reich, and was banned in 2016 by the Home Office.
Claudia Patatas and Adam Thomas were found guilty of being members of banned group National Action.
The four males and a woman were all detained in coordinated counter-terrorism raids carried out across the country.
The neo-Nazi was convicted of membership of the banned group but cleared of encouraging Jack Renshaw in a plot to murder MP Rosie Cooper.
Jack Renshaw, 23, is one of several defendants to deny membership of the banned far-right group.
Counter-terror chief warns neo-Nazis pose a "significant" terror threat as he calls for a "whole society" effort to combat extremism.
Five men and a woman will appear at Westminster Magistrates Court charged with belonging to banned far-right terror group National Action.