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Oceanus (probable father), Cocytus (father in some myths)
Acheron, Cocytus (in some myths), Styx, Lethe, and other river gods (presumably)
River Phlegethon, Underworld
Phlegethon (most commonly known as Pyriphlegethon meaning 'fiery') was the Underworld potamoi or river god of fire, probable sons of Oceanus (Titan of water), and one of the infernal rivers of the realm of Hades, along with his probable siblings: Styx (Hatred), Cocytus (Lamentation), Lethe (Oblivion/Forgetfulness) and Acheron (Pain). Phlegethon punished the souls of the wicked with his fire, so that they can endure the torments of the Fields of Punishment. In some legends, the River Phlegethon is the "River of Healing".
The Phlegethon falls into a vast region burning with a great fire and makes a lake larger than the Mediterranean sea, boiling with water and mud. Thence it flows in a circle, turbid and muddy, and comes in its winding course, among other places, to the edge of the Acheronian Lake, but does not mingle with its water. Then, after winding about many times underground, it flows into Tartarus at a lower level. This is the river which is called Pyriphlegethon, and the streams of lava which spout up at various places on earth are offshoots from it.
As Phlegethon was also a god, he presumably has the following powers:
Possesses the standard powers of a god.
The ability to control his domain, the River Phlegethon.
The ability to control fire, for he was the god of the river of fire.
Heal anyone who drinks from his river (in some legends).
"More dreadful things have I, Theseus, seen in the underworld which Phlegethon bids imprisoned sinners suffer, compassing them about with his stream of fire; what punishment waits for me, and what place, I know."