Parent Group Layers

Parent Layers to Group

Parents all layers, contained in a group, to its group header (Win: Shift+J, Mac: no default shortcut).
Layers parented to its Group Header
When enabling group parenting, all layers that have no parent or parents outside of the group will be parented to its group header. Parents within the group, however, are allowed. If a group has sub-groups, all layers, contained in the sub-group, will be parented to the sub-group header. (If you try to unparent one of those sub-groups, they will be parented again.) If layers are moved into a parented group and Refresh Layout is executed, they will be parented as well.
If you want to have layers with parents outside of the group or no parent within a parented group, you need to set a Parent Exception Layer (see below).

Set Parent Exception Layer

Turns the selected layers into Parent Exception Layers (Win: Shift+K, Mac: no default shortcut).
A Parent Exception Layer, as indicated by the x Icon
A Parent Exception Layer won't be parented to a group header when the group has Parent Layers to Group enabled. You can either set no parent or a parent outside of the group.
Parent Exception Layers are also excluded from being parented when a Prime Clone has Precomp Transforms enabled.
Precomp Clones, Matte Merge Layers as well as Linked and Matted Adjustment Layers are all Parent Exception Layers by default since they're fit to the comp size and their contents (the individual clone layers in a Precomp Clone, for example) are already parented to the group header (in case it has parenting enabled).