A classless society is theoretically obtainable in communism. This is because communism is an economic and political system where all property and resources are collectively owned by the people, and the means of production are controlled by the state. In such a system, there is no private ownership of property, and everyone works for the common good.
The idea behind communism is that there will be no social classes, and everyone will be equal. However, in practice, most attempts at communism have resulted in the creation of a ruling class of government officials who have all the power and wealth, while the general population remains poor and oppressed.
Feudalism, plutocracy, and capitalism all have social classes and class divisions built into their systems. Feudalism is a system of land ownership and labor where there are lords and serfs, and social mobility is extremely limited. Plutocracy is a government by the wealthy, where the wealthy class holds all the power and resources. Capitalism is an economic system where private individuals or companies own the means of production, and there is a large wealth gap between the rich and the poor.
In summary, while a classless society is theoretically possible in communism, it has yet to be achieved in practice.