How to effectively group a whole bunch of Sharepoint lists

I'm still learning Sharepoint and all of its various concepts, so apologies in advance for my ignorance. Here's what's going on – my company is moving a whole bunch of forms from another application into Sharepoint as InfoPath forms. Each InfoPath form is a Sharepoint list. So, we've got something like 300 different lists representing these forms.

My task is to put these lists on a page in some kind of reasonable format, meaning we need to present them in more reasonably-sized groups. Essentially, what I think I need is a list of lists. I've seen a few discussions here on this topic, all of which end with "Sharepoint doesn't provide a list of lists you need to do it yourself". I attempted to use a Content Query web part, but that only could get me the items inside each list, which in this case isn't what I want – I want the Sharepoint list itself.

From what I've read, it sounds like some custom code can build what I want. Is there any other way for me to group these lists?

Edit for more information: Part of the problem we have is that we aren't sure how to group the lists. I believe what Tom says below, that it's pretty easy to get a list of all the lists. But somehow, we still have a need to get the lists into the appropriate buckets.

For example, let's say there are 10 lists, and we want to group them by department. The first three belong to HR, lists 4-7 belong to IT, and lists 8-10 are Executives. Even with a custom code solution, we still need to make that connection, and I'm not sure how to do that (easily). If that's going to be a manual process anyway, it seems like a master list like @strongopinions suggests will be easier than a custom code solution?