To move the custom record from Custom to another subtab, please follow these steps:
- Go to Setup > Customization > Record Types.
- Select the record type in question.
- Under the Fields tab, click the field where you have "Record is Parent" = Checked.
- On the Edit Custom Field page > Display subtab, look for the "Parent Subtab".
- Assign the name of the tab to where you want to display the custom record sublist or to move it from Custom to another subtab.
The above worked. Initially I was doing the above but was setting the "Subtab" option. What needed set was the "Parent Subtab" in the right hand column. A screenshot has been provided for your benefit.