Everyone is immigrants (except native Americans). But certain groups came here in large numbers, settled the country in large homogenous groups, and shaped the country from the ground-up. Our legal and political structure is entirely Anglo. The culture of large swaths of the country can be traced directly back to different subgroups from different parts of England: https://www.barnesandnoble.com/w/albions-seed-david-h-fische....

Germans, Dutch, Norwegians, and Swedes settled the midwest, which was a key to the development of American society and government. They were a backbone of the Republican Party during the Civil War. Iowa, full of recent German immigrants at the time, contributed more soldiers per capita to the union than any other state. To this day, midwestern speech patterns are full of German or Norwegian influences. There's 50 million German Americans--more than half as many as in Germany.

Italians and Irish had major impacts on the culture and politics of the nation's largest cities. They changed the course of the 20th century by supporting the Democratic Party by large margins from FDR until Reagan, which took the country in a very different direction from the original vision created by the British founders. There's more Irish people in America than in Ireland.

Other European immigrant groups had localized impacts, but never shaped the country the way these other groups did.