What were the social inequalities of classical Rome?
Rome was a hierarchical and sexist society dependent on slave labor. Slaves comprised about 10–15% of the population across the Roman Empire overall and about 35–40% of the population in the wealthy area of Italy, the heart of the empire. Slaves did not have legal status as persons, though they did have a few rights.
Above the slaves were plebians, free Roman citizens. Above them was the patrician class, which had its own graduations. About 1.5% of Romans were very wealthy patricians who owned much of the land.
Women could be Roman citizens, but beyond that, they had few rights. The cornerstone of social organization was the paterfamilias or head of the household. This was the oldest male in the household, who was given complete power over the members of his household, including his wife, children, extended family, and slaves. By giving one male power over all the individuals living with him, the Romans believed they could achieve social order.
This clearly was a winner-take-all society where a few males at the top, usually of hereditary wealth and status (though the society had some fluidity) had a preponderance of power.
On a legal and political basis, women were systematically denied equality in classical Rome. They were completely excluded from the realm of politics—though many women did play an important role behind the scenes—as this was deemed to be an exclusively male preserve.
Right throughout the whole of their lives, women were regarded by the law as subordinate to their menfolk. In practice, once a Roman woman was married, the absolute control over her life that had previously been exercised by her father passed to her husband. Technically, however, a woman's father still continued to exercise what was called patria potestas over her, the power that the father held as head of the family.
Nonetheless, Roman women had property rights, and if a woman's father died without making a will, then his property would be divided up equally between his children, both male and female.
Classical Rome was in many ways founded on a social inequality. Essentially, Roman society, at least free people, was fundamentally divided between plebeians and patricians.
Plebeians were common people who were initially denied political voice in republican Rome. "Plebs" contained many variations, and were by definition free, but they lacked the social status of patricians, who inherited their positions through their family line. Eventually, class tensions between the plebs and patricians led to the establishment of plebeian officers, the most senior of which were tribunes.
Patricians, on the other hand, were aristocrats, representing a much smaller percentage of Roman society (probably about 10 percent.) While their status did not necessarily depend on their wealth, they did tend to be large landowners. More importantly, they controlled politics in Rome, and used their power to get policies, such as taxation and debt laws, to benefit them.
There were many different classes of people in the Roman Empire.
Namely (from lowest to highest)
4. Equestrian class
5. Senatorial class
Women were also highly unimportant figures in Roman society. There is no existing text found that was written by a woman which proves this. However there were a few exceptions. For example, in Pompeii, the cloth workers guild (a major and large business) was run by a woman.
This is of course just a vague outline of the classes. rrteacher's answer holds more detail.