Jeff,
At this time, there is not an option to disable notifications by group or type. It is on the list to add to the web portal. I will ask for an update as to when we can expect to see this implemented.
Currently all Arming/Disarming, Troubles, and Alarms are set via notifications.
With the user login via the web portal, the user can select and or add who gets Notifications and which format the notifications are sent in. They can choose from Push, Email, or Text. They can also disable all of them from here as well.
Thanks,
Mike