Hippies - A counterculture movement gained momentum in which the younger generation began to define itself as a class that aimed to create a new kind of society in 1967.
Feminism - The role of women as full-time homemakers in industrial society was challenged giving momentum to the women's movement and influencing the second wave of feminism.
The Lesbian, Gay, Bisexual, and Transgender community (commonly abbreviated as the "LGBT" community) fits the definition a countercultural movement as "a cultural group whose values and norms of behavior run counter to those of the social mainstream of the day."
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Countercultures are a kind of subculture that deliberately opposes certain aspects of the larger society. Examples of this would be the hippies of the 60's, anarchists, the KKK, Neo-Nazi's, most gangs, as well as MLK Jr. and his followers (in their time at least, they would have been grouped as a kind of counterculture, going against the norms of the American society at the time.)