As a security measure, the Google Groups for Business service has limits for message activity, group size, invitations, and membership. If you reach one of the limits, your activity is temporarily restricted. The restriction typically lasts an hour but can last as long as 24 hours.

These restrictions may apply to a single group, sender, member, or to all UW-Madison Google Groups.

The maximum number of members you can add to a Google Group is 50,000. The maximum number of external members you can add to a Google Group is 20,000. These limits are in place to prevent mail delivery issues caused by reaching per-group and per-organization sending limits.

Those wishing to distribute email to groups larger than allowed in Google Groups are advised to use an email marketing tool, such as Eloqua.

Review all policies and limits here: https://support.google.com/a/answer/6099642.