Which two important groups pressed for change in america society?

The two main groups that lead the push for change in American society are: 

The Suffrage Movement (Women's rights movement)

The Abolitionist Movement (Anti-Slavery Movement)

The suffrage movement pushed for women's rights starting around the very late 1800's and early 1900's. Through persistence they were able to get their full rights like voting, same wage as men, all collages etc. 

The abolitionist movement has been around since slavery started in America. People helped slaves escape and get to free land through a network called the Underground Railroad. Slavery was finally ended on January 31st.

Hope this helps!