Answer :

#1 - Fluffy the dog in Harry Potter and the Philosopher's Stone is relevent to the guard dog of the underworld called Cerberus.
#2 - The scar on Harry Potter's forehead resembles the Greek god Zeus.
#3 - Fluffy and Cerberus both fell asleep due to music.
#4 - Hermione has the same name as the Greek daughter of King Menelaus of Sparta and Helen of Troy.
#5 - The hippocampus does show up in Harry Potter and Greek mythology pulling the greek god Poseidon's chariot.
#6 - Argus, the caretaker of Hogwarts, has the same name as the Hundred-eyed one, who is also named Argus.
#7 - Greek gods have a nimbus, not a broom, but a cloud
#8 - Harry meets a sphinx in the Goblet of Fire, and answers it's riddle, Oedipus solved a sphinxes riddle in greek mythology.
#9 - Minerva McGonagall's first name is the same as Greek goddess Athena's roman name.
#10 - Centaurs are top-half human and bottom-half horse, and they show up in Harry Potter (In the Forbidden Forest) and in Greek mythology.

There you go... You now have ten things that are connections between Harry Potter and Greek mythology. 

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