The term "Subject Races" is used a few times in H. G. Wells's novel The War in the Air. I have been looking around but only found a paper called "The Treatment of Subject Races", is this related?
In a nutshell, "subject races" means people of colour who were subjects of the British Empire. Wells uses the term ironically.
There is a passage near the beginning of Chapter 4 that makes this clear:
Instead of the sturdy establishment in prejudice of Bert's grandfather, to whom the word “Frenchified” was the ultimate term of contempt, there flowed through Bert's brain a squittering succession of thinly violent ideas about German competition, about the Yellow Danger, about the Black Peril, about the White Man's Burthen—that is to say, Bert's preposterous right to muddle further the naturally very muddled politics of the entirely similar little cads to himself (except for a smear of brown) who smoked cigarettes and rode bicycles in Buluwayo, Kingston (Jamaica), or Bombay. These were Bert's “Subject Races,” and he was ready to die—by proxy in the person of any one who cared to enlist—to maintain his hold upon that right. It kept him awake at nights to think that he might lose it.
People from what is now Zambabwe, from Jamaica, from India: then all parts of the British Empire, all thought of by the Berts of the Empire as being inferior. The reference to cigarette cards is interesting: it would be nice to find the particular series Wells was referring to.