The Plebs were all the rest – they were not simply low class – they included Senators and Equestrians, some of the richest men in Rome as well as the poorest. Patricians could be poor – they constituded the original ruling class, not an economic distinction.
The initial political setup of the Republic after final expulsion of the kings left power in the hands of the Patricians – they filled the magistracies and the Priesthood – the office bearers who controlled the business of the state. The people in general could only vote in the assembly under arms in their centuries called the Centuriate Assembly or in the Tribal Assembly. Both were stacked so that the votes of the upper classes counted more than those of the lower classes.
This control of power was progressively eroded as the Plebs withdrew support at critical times – if the Centuriate Assembly did not vote for war, the state could neither be defended nor could enemy be invaded to steal their land, and so on. As a result, the Patricians reluctantly progressively shared the magistracies with the Plebs.
A further major advance was the establishment of a Plebeian Assembly which gained power by producing its own laws, overcoming reliance on a Senate dominated by Patricians. The institution and election of 10 Tribunes of the Plebs by the Plebeian Assembly put further power in the hands of that Assembly. Tribunes of the Plebs had personal immunity, could veto laws in the Senate, and also introduce laws in the Senate; they became Senators at the end of their term, each year further diluting the Patrician contol of the Senate. This, added to the sharing of magistracies progressively forced on the Patricians – Praetor, then finally Consul, between Patrician and Plebeian candidates, progressed further power to the Plebs, so manipulation by both sides became critical.
The civil wars of the 1st Century BCE brought an end to the Patrician-Plebeian divide. Death in war, and the proscriptions in which victorious sides had opponents killed to seize their property, so wasted the Patricians that they ceased to be a defined power bloc, and it became merely a social honorific. So the Patrician-Plebs conflict ceased to exist. It came down to simple manipulation of the three Assemblies – Centuriate, Tribal and Plebeian.
Augustus’ settlement of the constitution after his victory in the civil wars over, first the killers of his adoptive father Julius Caesar, then Mark Antony, rested principally on his assumption of lifetime powers of a Tribune of the Plebs. He didn’t take on the office, just the powers, which meant he didn’t have to be elected annually. This gave him immunity from prosecution, a veto over laws and the ability to introduce laws. Very clever. And by this move, and gaining personal control of the legions by allocating to himself the provinces which had legions, he was able to eliminate the power of the Centuriate and Plebeian Assemblies. His ‘restoration of the Republic’ in 27 BCE was in reality elimination of the mechanisms of the Republic, and set the progressive roadmap of imperial control, which culminated by the 3rd Century CE in despotism.