Of course, as the Greek culture was based on the premise that men were far more important than women, generally in Greek life as a guide, women were thought to be rather insignificant. However, this approach was actually belied by the major role that women had in a number of Greek tragedies, where women often were the most important characters, which yields very interesting thoughts about the position of women in this society.
You might like to consider the character of Clytemnestra in the play of Agamemnon, the infamous villainess who killed her husband and his concubine. She is shown to be a very bloodthirsty and savage character who is described as "a woman with a man's heart." In addition, consider Antigone in the play bearing her name by Sophocles. Although she committs suicide, she is the character that the play focuses on and Sophocles uses her to bring into focus the main conflict of the play, which is whether we acknowledge the laws of the gods or the laws of our government when the two are in opposition to each other. Finally, think of Medea, the wife of Jason who is infamous again for killing both his new wife and her children as a form of revenge against Jason because of the depth of love for him. Although we are tempted to dismiss her as just a nastly character, when we consider how she was maltreated by Jason, she becomes very complex.
So we can see from these three examples that women characters in Greek Drama were actually fascinatingly diverse and complicated, which is interesting because the plays emerged from a patriarchal culture where the rights of women were severely curtailed.