One person in this group was banished to Rhodes after accidentally killing his great uncle Licymnius and led the forces of Rhodes in the Trojan War.  Another one was told by an oracle to look for a man with three eyes, and found a one-eyed man riding a two-eyed horse in Oxylus. In addition to Tlepolemus and Temenus, this group included Aristomachus, who was struck by lightning and had his fleet destroyed due to Hippotes' 
One person in this group was banished to Rhodes after accidentally killing his great uncle Licymnius and led the forces of Rhodes in the Trojan War.  Another one was told by an oracle to look for a man with three eyes, and found a one-eyed man riding a two-eyed horse in Oxylus. In addition to Tlepolemus and Temenus, this group included Aristomachus, who was struck by lightning and had his fleet destroyed due to Hippotes' slaying of a soothsayer. After being adopted by King Aegimius, one of these people was slain in single combat by Echemus while leading an expedition against Atreus. Macaria was sacrificed for the protection of these people, who were taken in by Demophon and saved when their elderly guardian had his youth restored by Hebe. Their conquest of the Peloponnesus is a mythological variation of the Dorian invasion. This group, first led by Hyllus, are defended by Iolaus and hounded by Eurystheus in a Euripides play. FTP, name this group of heroes, who were the sons of the dude who slayed the Hydra. 
One person in this group was banished to Rhodes after accidentally killing his great uncle Licymnius and led the forces of Rhodes in the Trojan War.  
the Heracleidae [or the Children of Heracles]