Immediate email push notifications account + app combos?

Which accounts (e.g. @gmail.com, @outlook.com, @icloud.com, etc.) paired with which apps (e.g. Mail, Gmail, Outlook, etc.) will give me immediate push notifications for any email received? I'm looking for those combinations that generate a push notification within 5 seconds. For example, imagine if when Outlook is paired with a Gmail account, it uses 15 minute polling to determine when a new message arrives. This would not satisfy my requirement above. On the other hand, imagine you use the built-in mail app with an @icloud.com account, and you enable Push in the settings. This should send immediate push notifications, satisfying the requirement above. I'm looking for several solutions, not just one so that I can have multiple "inboxes" or workflows.