No Republic was destroyed in 1860/61, it split apart just like it did three score and sixteen years before. From 1787 to 1790 there were two Republics, one under the United States Constitution and another under the Articles of Confederation. Between 1776 and 1860 independent Republics of Vermont, Texas, California, and West Florida were created and all were later annexed into the United States.
In 1860 there were several Republics, Haiti, Dominican, Peru, Chile, Guatemala, Costa Rica etc.
This is outside of the time period but worth mentioning; Hawaii was the last Republic annexed into the United States.
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David Upton