basement toilet vent problems

[flick]

I have a toilet in the basement ,it is on a lateral 15ft from the main drain and the stack is 20 ft back from where it ties in. Is there a toilet that will work for me ? I do have a sink and shower next to the toilet they work, and there is a floor drain on lateral before the bathroom I had to plug it though.
Best I can describe it.
outside
toilet,snk. shwr I
10FT I
plgdflr drn---15ft--------Y-----------12FT------------MAIN
I
I
20FT
I
I
STACK

 

[Cass]

Not sure I understand the question. If you have 3" DWV pipe that is vented and is pitched right any toilet that flushes will work.