I remember someone already mentioned that having "child" may not be appropriate (due to children in the common sense outliving their parents in general). Could the term subtask be considered instead? The sub/super relation is already present in the language. From the mathematical standpoint alone, it reminds to sub/supersets, which is appropriate in this context: a subset cannot overrun its superset as much a subtask cannot overrun its supertask.
It's also apt from the common parlance point of view: if you mark a task consisting of various subtasks as completed, that means that you've generally completed/handled all said subtasks.
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