When asked to condemn “white supremacists and militia groups” during his debate with Joe Biden this week, President Trump gave a largely garbled answer, asking for definitions and caveats, attempting to misdirect attention to leftist violence, and repeatedly interrupting the moderator. One part of his answer, however, was crystal clear. “Proud Boys, stand back and stand by,” Mr. Trump said.

Rather than condemn white power groups, Mr. Trump instead issued an unambiguous call to them to be ready.

Watchdog groups and analysts have debated about how to classify the Proud Boys. Its members explicitly disavow white supremacy in a bid for respectability, but its ideology is clearly white supremacist: Photographs of members flashing the white power sign, the presence of members at white power events and at rallies and expert analyses of the group’s online content make this clear.

They should be seen as fellow travelers with white power groups and activists. Names and tactics vary, but the white power movement is united in ideology and intent. Its adherents include propagandists calling for the end of non-European immigration, those who carry out attacks mislabeled “lone wolf” violence in places like El Paso, Pittsburgh, Charleston, S.C., and Christchurch, New Zealand, and groups that train secretly for war, like the Base, and even for nuclear war, like Atomwaffen Division.

It also includes members of the Ku Klux Klan, neo-Nazi and racist skinhead groups, and large segments of the Boogaloo Boys and extralegal militias. This is why it is a mistake to understand Mr. Trump’s statement as directed solely to the Proud Boys — which had, before the night was over, incorporated “Stand Back, Stand By” into a badge logo. Other groups aligned with the white power movement will certainly interpret Mr. Trump’s message as including them. This complex web has worked exactly this way since the late 1970s, with disastrous results.

The white power movement is, in many ways, an incredibly diverse array of activists. I found in my research that though it is a fringe movement, its supporters represent a cross-section of American life: rich and poor and middle class; religious leaders and felons; men and women and children; people in cities and suburbs and rural areas.

What binds these disparate groups is that they espouse the violent defense of white supremacy. They see the white race as under attack — from immigration, from the rise of the nonwhite population, and from the acceptance of multiculturalism by much of the nation.