There are several synonyms for the phrase "were subordinate to." Some of the common synonyms include subservient to, secondary to, inferior to, subject to, and under the authority of. "Subservient to" implies a willingness to obey or serve, while "secondary to" denotes a lower rank or importance. "Inferior to" is used when one entity is of lesser quality or value compared to another. "Subject to" indicates that one is subject to the control or influence of another. "Under the authority of" implies that one is subordinate to someone who has power or control over them. All these synonyms indicate a state of being lower in rank, power or importance, compared to someone or something else.