The "T" on its back should really be a 4" "y". From the pic it looks like 3".
and the cleanout should not even be there. You should always have a clean sweep when doing underground drains. You have the potential to have drain cleaning problems.
If you remove the cleanout and the "T" , you can replace them with a 4" "y' on the horizontal and 45 and a branch "Y" to your laundry facilities. You can use a "T" vertically but not horizontally unless you are using it as a back vented "T".
I hope that made sense
Sheesh, I almost confused myself