Not sure I entirely understand… but, you could use the permalinks to groups. You would have to disable the category drop down filter and use the enhanced categories addon instead so as not to create conflicts.
Navigate to the Connections Settings admin page and click the Advanced tab. Here you will find the Permalinks section. The only one enabled by default is the Name option. You can enable the others that will be relevant for your needs.
I recommend switching to the cMap template because it’ll make viewing these permalinks easier since the date is displayed by default.
You can copy/paste these permalinks as needed to create menu items / buttons. After you are setup like you want, switch to your desired template.
Hope this helps get you on your way. Let me know if you have any further questions.