Are secondary education programs considered part of CEHD or part of the subject's major?

Colleges and Universities A-Z University of Minnesota
1

For example, is math education part of CSE or CEHD? Is english education part of CLA or CEHD?

2

Most seem to be via the dept. of curriculum and instruction, in CEHD:

http://www.cehd.umn.edu/ci/Academic-Programs/default.html

The Math department, however, also has a special program (joint with C&I) where you can earn an MS in Math with special emphasis in Math Education:

http://www.math.umn.edu/grad/mathed.shtml

Note that all these are post-baccalaureate programs culminating in the secondary ed. licensure.