Problem: A giant group in your on-premises Active Directory does not sync through Azure Active Directory Sync
Source: Azure / O365 has a limit in the Azure AD Sync (AAD Sync) such that it ignores groups that are over 50k - I even found groups really close to this limit acted weird
Resolution: Script a solution that will take your on-prem group and create mirror groups with a maximum number of users in each so that all the miniature groups will sync and auto-add/remove users from the mirror groups, and you can use these groups in Azure.
Update 2019-06-17 - I have moved this script to a github repository to make updates easier. DO NOT WORRY - it is not some crazy-looking developer page...just a list of scripts from this site. Here is the url to my repository: https://github.com/hornerit/powershell/blob/master/ActiveDirectory-SplitAndSyncGroups-Public.ps1