No. JIRA doesn't have that type of heirarchy. All projects are equal.
You could try the Structure add-on if you want something more complex than Category, Project, Issue, Sub-task. But I'd take a look at Portfolio - it doesn't really do what you describe here, but it does offer functionality which helps you work as though it did.
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG