In Greek mythology, Agave was a princess of Thebes, daughter of Cadmus and Harmonia, wife of the Spartos Echion, and mother of king Pentheus. Driven mad by Dionysus, she led the Maenads on Mount Cithaeron and tore her own son apart, mistaking him for a wild beast—a central episode of Euripides' Bacchae.
Adapted from Wikipedia, "Agave (daughter of Cadmus)" · CC BY-SA 4.0
I.Theban house
Agave was the eldest daughter of Cadmus and Harmonia, sister of Autonoë, Ino, Semele, and Polydorus. By Echion she bore Pentheus, who succeeded to the Theban kingship, and in some notices a child Epirus.
After Semele's death, Agave and her sisters denied that Zeus was the father of Dionysus, treating Semele's claim as a cover for a mortal love affair. Dionysus returned to Thebes to vindicate his mother and prove his divinity.
II.The Bacchae
Dionysus maddened the Theban women and drove them to Cithaeron as Maenads. Pentheus forbade the rites; disguised by the god, he spied on the revels from a tree. The Maenads, led by Agave, pulled him down and dismembered him.
Agave carried Pentheus' head into Thebes believing it a lion's trophy until Cadmus restored her sanity. Later notices exile her to Illyria; Hyginus' sequel in which she kills a king for Cadmus is often judged a misplaced or secondary tale.