Does F603 govern the speed of the extruder “E” in a line of gcode like this?
G1 X174.202 Y156.200 E1.7413 F603
Print speeds are different than extruder speeds so I’m wondering how to read the extrusion speed in lines like that which group them all together?
Breaking this down, the values for that line say "using printhead g1, move from where the printhead is currently over to x174.202 and y156.2 (units, probably milimeters) and once there feed 1.7413 units worth of filament into the hotend (again most likely in milimeters) at a feed rate of 603 units per minute.
I’m not an expert at reading g-code, but here’s the definition of the G1 command:
http://reprap.org/wiki/G-code#G0_.26_G1:_Move
Fnnn is the feedrate (which is the speed of the print head movement)
Ex.xxxx is the amount of extrusion (mm)
So in your example, it basically says:
“Move to X174.202 Y156.200, extrude 1.7413mm and move the print head at a speed of 603 mm/s”
Fnnn looks constant until set by another G1/G0 command.
The E value is probably derived from the flow rate (multiplier), extrusion width, layer height, nozzle diameter, filament diameter… and probably other factors listed in the slicer settings.
EDIT: Dammit, piercet beat me to the answer… as I was typing/researching. 
You gotta watch him, he’s sneaky like that sometimes!
In the world of CNC commands which stay in effect until changed are known as modal commands.
http://www.cnctrainingcentre.com/cnc-programming/modal-nonmodal-g-codes/