Here's another interesting calculation.
Hogwarts has 12 subjects. (Plus some minor extra stuff like Flying and apparition.) 7 are mandatory (Defense, Charms, Transfiguration, Potions, Herbology, History, Astronomy), and 5 are up for for choice up from year three (Runes, Arithmancy, Muggle studies, Care for Creatures, Divination). Harry chooses only the last two. (Which is a pretty hilariously bad choice when you think about it.)
If all subjects have 4 periods per week, then you're at 48. You can fit 10 periods in a day if you start at 9:00 in the morning and end with dinner at 18:00. So students shouldn't need time turners.
However, teachers will actually have a tough time! A teacher like MgGonnagirl should have 22 different courses: 4*5 with four houses times 5 years, plus two for the last two years, where every subject is optional and they throw all houses together. So that would be 88 periods per week if each course has 4. That's not possible.
I therefore conclude that not mixing houses for mandatory subjects is a plot hole. Every mandatory subject should always take place with 2 houses at once. Then we get back to a barely manageable number. Unless the teachers all use time turners, but man they don't.
In the books, Potions takes place with the Slytherins, but Transfiguration is Gryffindor only, and so is defense