The plaintiffs say the missing people vanished after being arrested by Russian servicemen. They also accused the Russian authorities of failing to effectively investigate the cases.
The Strasbourg court ruled that the Russian authorities had violated a number of articles of the European Convention on Human Rights, including the right to life, a ban on torture and humiliation, the right to freedom and security and the right to effective legal protection.
The sum includes 475,000 euros in moral damages, 47,000 euros for material damages and 29,600 euros to cover court expenses.
Chechnya saw two brutal separatist wars in the 1990s and early 2000s. Militant attacks remain fairly common in the troubled republic.
Russia has lost the majority of cases brought against it in the Strasbourg court. In 2008, the court ruled against Russia 245 times. Overall, around 20% of all complaints made to the court in the past decade have involved Russia.