Federal authorities investigating suspected Islamic State supporters in all 50 states have found no clear pattern to the type of American inspired to try to join the militant group, complicating efforts to thwart terror recruiting.

Some common threads exist, such as the fact that would-be recruits are often in their teens or early 20s and use social media to express support for Islamic State, also known as ISIS or ISIL. But overall, the group is broad, covering people who were raised Muslim and those who converted, married...