Capitalize subsidiaries and use lowercase for internal elements of an organization

I have consulted AP Stylebook, CP Stylebook and Chicago Manual of Style to ascertain if the departments and divisions within a company are capitalized. All of these reference books state to capitalize subsidiaries and use lowercase for internal elements of an organization, but I don't know if that applies to the name of a specific department or division of a company. Could you help with this?

I say 'lowercase' to the departments below (generic references). Am I correct?

I contacted the loss prevention department to report the incident.
I will contact the human resources department.
I contacted the benefits department for an answer.
I will get in touch with the supply division.
Kayla works in the meat department at the supermarket.
Amy works in both the deli department and seafood department.

Thank you kindly.