Final answer:
The dominant party between 1800 and 1860 was the Democratic Party, but they split into three factions in the election of 1860. The Republicans won one out of the 15 elections during this period.
Step-by-step explanation:
The dominant party in the period between 1800 and 1860 was the Democratic Party. However, it is important to note that the Democratic Party itself split into three factions in the election of 1860. This division allowed the Republican Party, led by Abraham Lincoln, to win the presidency. Out of the 15 elections during this period, the Republicans won one election, which was the election of 1860.