Mexico City
There was no "Republican Party" in 1820; the Republican Party in the United States was founded in the 1840s on an anti-slavery policy.
It became a Republic.
The Federalist party first became a factor in the 1796 presidential election. The political views that motivated this party were around when the Constitution was being drawn up some 10 years earlier.
Federalists were a prominent political party that died by 1820. With the federalists gone it left only the republican party in the United States.
All though party strength was difficult to judge and not properly recorded prior to the general election of 1830 (only 56% of MPs in 1820 belonged firmly to a party group), the UK general election of 1820 resulted in a working majority for the Tory Party - the spiritual precursor to the modern Conservative Party.
They expanded its territory and power by buying them for big money, forcing them to give it to them, & by voting it out.
What was the main crops in the south during 1820 and 1865?
Emprasarios.
1820 miles
Henry Clay
Trough attrition. The US has had a larger population than Mexico since the 1820's and as you may notice, if two countries have an even technological advance, the one that wins is usually the one with the larger population.