Jack Fischer

There are numerous plugins for emailing or otherwise notifying administrators when users log into WordPress. However, this is not desirable for installations with hundreds or thousands of users. Admin Login Monitor provides more managable email alerts, just for administrator accounts.
Example alert email,
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Hello Alice,
The account ‘bob’ just logged into example.com
User Login ‘bob’ 
User Display Name ‘Bob’ 
User Email bob@example.com 
User ID ‘8’ 
User Registered 2019-08-25 19:33:18
Forwarded IP Address 96.224.58.71 (HTTP_X_FORWARDED_FOR) 
Connected IP Address 96.224.58.71 (possibly a CDN or proxy)
Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/15.5 Safari/605.1.15
This notification is generated by the WordPress Admin Login Monitor plugin installed on example.com 
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For convenience investigating IP addresses, email notifications link to Ipinfo.io (https://ipinfo.io/). 
Ipinfo.io Terms of Service: https://ipinfo.io/terms-of-service 
Ipinfo.io Privacy Policy: https://ipinfo.io/privacy-policy

Admin Login Monitor

Email site administrators about all administrator logins.

prouptime

Prouptime is service that monitors your wordpress blog or site. Prouptime checks your site every minute (or every five minutes) from its servers. If your site returns an error or is unreachable, prouptime will send you an email-alert.
You’ll also get statistics about your uptime and site-speed that you can view in your wordpress backend. You’ll also get these statistics by email once a week.

Prouptime – Uptime Monitoring & Alerts

Prouptime monitors your wordpress site and alerts you when it is unreachable or returns an error.

Admin Login Monitor vs Prouptime – Uptime Monitoring & Alerts