GROUP BY is a little different; it's used when you are using aggregate functions (e.g. MIN, COUNT, etc) and want a subtotal produced within like groups of data.
If all you want is the raw columns in a particular order, just use ORDER BY.
For example, to simply list the individual votes by state and county, say:
select state, county, votes from election order by state, city;
But if you want a subtotal for each state, say:
select state, sum(votes) from election group by state;