The holy roman empire. It is neither holy, nor roman, nor an empire. How about the theistic german kingdom?
The word 'sacrum' ("holy") was not used till about 200 years after the first Roman 'emperor' was crowned, so there's that. Definition of 'empire': An empire is a state with politico-military dominion of populations who are culturally and ethnically distinct from the imperial (ruling) ethnic group and its culture. Definitely an empire.