Controlling task notifications

Summary

Would like a task notification to go to only user, but also need to assign task to large group

Content

Has anyone found a workaround to a task notification going only to an individual rather than a group. For example, I have a task set up that is assigned to our functional role of corp health. This role consists of 20 people, however, I want to restrict the notification of this task to only go to one email address/user, instead of all 20 users. 

I tried seperating the notification as it's own task , but then of course the task URL doesn't work as it's not connected to the actual task, so users are being directed only to a listing of all tasks which is confusing.