Can I create subtasks?

Subtasks can be added to your cards as checklist items.
From an open task view, you can add your checklist items at the top, using + Add checklist

Each of the items can be assigned to someone, and the assignee will receive email notifications on that assignment, just as they do for a task card assignment.

To assign a checklist item to a team member, to edit, delete or move it up or down the list, hover your mouse pointer over the item, and the respective options will show up.

You can add more granularity to the checklists, by creating hierarchical sub-levels of checklists. When a checklist item gets its own list added, it changes into a list heading, with a distinct look. The list heading will mark as complete automatically, after all of its sub-list elements are done.

To reference related tasks inside a checklist item, please type # to open the global search window:

You may also be interested in trying Task Dependencies - a simple way to connect separate tasks into a tree-like hierarchy.