How can I sort a list of file names by some substring of the name?

How can I sort a list of file names by some substring of the name?

I have a number of files with names like:
beginning_num1_734_num2_1.363e+12_num3_800.pdf
beginning_num1_735_num2_7.453e+13_num3_800.pdf
beginning_num1_1007_num2_9.453e+12_num3_1200.pdf
I'd like to be able to sort a list of these filenames by the various nums,
and pass the sorted list to various command line utilities. For example,
if I were sorting by num2, I'd want the order:
beginning_num1_734_num2_1.363e+12_num3_800.pdf
beginning_num1_1007_num2_9.453e+12_num3_1200.pdf
beginning_num1_735_num2_7.453e+13_num3_800.pdf
I have a python script to do this, but it seems like it should be possible
with nothing but filters like sed and sort.
Is there any easy way to sort by parts of a file name, using only common
command line filters?