What were a group of hard-shelled animals that lived 65 million to 500 million years ago and are used as index fossils?

The group of hard-shelled animals you are referring to is likely trilobites. These marine arthropods thrived between approximately 500 million and 250 million years ago, with a peak diversity during the Cambrian and Ordovician periods. Due to their widespread presence and rapid evolutionary changes, trilobites are commonly used as index fossils to help date and correlate rock layers in the fossil record.