First thing you have to understand is that, even though they were entirely written and acted by men, it didn’t stop the good playwrights in the fifth century BC from writing decent female characters (even strong in some cases). Writing humans as humans is something at which fifth-century tragedians were adept.

The basic rules for tragedy are different than the rules for comedy; in tragedy, you had to follow a set myth (e.g. the Oedipus cycle), or the known course of historical events (e.g. Aeschylus’ Persians). In comedy, the rule was kind of that there were no rules, and all the fifth-century Attic comedy we have is pretty much Aristophanes, and was mostly presented at the Lenaia (an Athenian festival) rather than the panhellenic Dionysia. So you could, as a comic playwright, step directly out and talk to the audience (Aristophanes was a character in one of his own plays), so that affects the types of characters you’re allowed to portray.

Some big female non-choral archetypes are (1) goddess/harpy/what have you, (2) sister/daughter, (3) wife/mother, and sometimes (1) acts like (2) or (3). Hera tends to fall into the third category if she’s mentioned (because matrimonial deity), but Athena is pretty much in the first category only. There are good examples and bad examples of the latter two, and plenty of disagreement among scholars as to the interpretation of which is which. I’ll give a few examples of each, but this is by no means exhaustive.

For the sister/daughter, you’ve got examples in Antigone and Oedipus at Colonus (both Sophocles) of a daughter (Antigone) doing her duty by her exiled family after Oedipus blinds himself and is thrown out of Thebes by Creon. Throughout Oedipus at Colonus, Antigone acts as support both physical and emotional for her dying father. Later, in Antigone, she buries the brother who’s betrayed Thebes (in Seven against Thebes, an earlier Aeschylean play) even though Creon, the king, specifically forbids it. All that stuff is done by Antigone, Oedipus’s daughter, and her sister Ismene tries to help, fails, and pretty much fades into obscurity. She attempts to take the blame for her sister’s crime after the fact, but breaks no laws herself; she is the middle ground between Antigone and Creon, and faces no backlash for her actions.

For the mother, you have Tecmessa in Ajax (Sophocles) and Atossa in Persians (Aeschylus); Tecmessa is Ajax’s spearwife and Atossa is Xerxes’s mom. Their whole thing is remaining cool and collected in the face of tragedy, and they’re contrasted with men in context, where the sister/daughter tends to be assisting men. Mothers/wives are foils for the male characters, for the most part, but there’s a kind of dichotomy in mother/wife characters—on the one hand you have Atossa and Tecmessa, but on the other you have Jocasta (Oedipus’s mom) and Medea (Jason’s spurned lover, who had his kids and killed them when he cheated on her). They tend to be the most realistic, I think, because there are shades of gray like Pentheus’s mom Agave in Bacchae, who’s basically a pawn for Dionysus but ends up killing her son anyway.

Mother figures in particular are usually portrayed as either wise, levelheaded leaders, or the exact opposite; in Aeschylus’ Persians, for example, Xerxes’ mother Atossa is the center of the majority of the “action,” and is repeatedly focused on in her dialogue with the messenger as a foil for the absent Xerxes—he is young where she is old, he’s male where she’s female, she’s experienced where he’s a bit green. Faced with the overwhelming loss of the Persians against the Athenians, Atossa maintains her composure while worrying for her son’s life, and she embodies those left behind when the Persians went to fight (mothers, sisters, daughters, wives).

In Sophocles’ Ajax, you have Ajax’s spear wife Tecmessa, who is the mother to Ajax’s son. When Ajax is contemplating suicide, Tecmessa is one of the strongest voices attempting to persuade him otherwise—she appeals to his emotions as a father, a son, and as a husband. She assists with the burial, as was customary, after Ajax’s suicide, which (like Antigone’s actions in another Sophocles play) flies in the face of Menelaus’ direct edict that Ajax not receive burial rites because he was plotting Menelaus’ murder.

On the other hand, you have Jocasta and Medea, one in Sophocles and the other in Euripides, who are less-than-stellar mothers. Jocasta probably doesn’t bear much more explaining, as she’s the mother of Oedipus—his father, Laius, received a prophecy that, should he and Jocasta bear children, that son would grow up to kill his father and marry (and father children) by his mother. Her main sin is ignorance—she thinks her son is dead and that Laius was killed by a band of thieves, but when she finds out the truth of Oedipus’ parentage, she hangs herself without telling him:

JOCASTA Ah mayst thou ne'er discover who thou art!

OEDIPUS Go, fetch me here the herd, and leave yon woman To glory in her pride of ancestry.

JOCASTA O woe is thee, poor wretch! With that last word I leave thee, henceforth silent evermore. Exit JOCASTA.

Oedipus is stuck thinking she was ashamed of his newly revealed lowborn heritage (because he was adopted by peasants), but he figures the real situation out soon enough and then blinds himself with the pins from her clothing.

Speaking of excellent parenting, you have Euripides’ Medea, the very same one who had Jason’s kids. When Jason decides to marry Creon’s (King of Corinth) daughter, Medea goes through the stages of grief in the wrong order, settles on anger, and decides to kill both Glauce (the new wife) and her own children, as well as Creon, who wants to exile her from Corinth. Medea is, in the play, a force of “no chill,” and her filicide is a bit of a departure from traditional myth, which has the Corinthians killing her children after she escapes to Athens. Medea has a lot of monologues about what it’s like to be a woman in a patriarchal society, and her barbarian nature was off-putting enough to knock Euripides down a few places when it was presented at the Dionysia.

Then, finally and most briefly, there are goddesses, who mostly work as forces of nature and/or justice and as advisors to male protags (I’m thinking of Athena guiding Odysseus specifically). They tend to enact justice or advise the protags; Athena in particular shows up to drive the plot of plays, but mostly stays out of the action herself.

If you have any followup questions about comedy, or further examples of each type in tragedy, I’m happy to answer them! Aristophanes’ Lysistrata is an interesting one to study for that, as it’s about a group of women taking control of Athens, and so is Thesmophoriazusae, which is about a group of women who are angry at Euripides for portraying them as crazy, depraved, and murderous. Which, okay, he wrote Medea, but I liked Medea. Female characters given agency goes against the Athenian social norm, on a final note; in a society driven by men, calling attention to the plights of the women who bear the shared weight of men’s decisions is a pretty big deal.

Tl;dr lots of women, lots of plays, lots of names

Sources (translators available upon request):

• Euripides, Medea

• Aeschylus, Persians

• Sophocles, Oedipus Rex

• Sophocles, Ajax

• Sophocles, Oedipus at Colonus

• Euripides, Bacchae