I have just been to Germany for a few days and spent the weekend in Frankfurt. Following the advice of a friend, I went to Heidelberg, for which I took a train.
At Frankfurt Hauptbahnhof I checked the price of the trip in the machines and the price with ICE was 196 euros for all of us, four people (49 euros per person). From another trip to Germany I remembered that there was a special ticket for groups up to 5 people. So, I asked and they told me that it doesn't apply to ICE tickets.
By chance, a very kind person at the railways station suggested to try with regional trains instead of ICE. The time was just 20-25 minutes more and there was no change (direct train Frankfurt-Heidelberg). When I checked it, I was shocked because the price was 36 euros (for the entire group!). So, we saved 160 euros!!
I just wanted to leave this comment because maybe it is useful for other people too.
Regards from Spain,
Francisco Marin