def unique_dimkeys(obj, default_dim='Frame'):
    """
    Finds all common dimension keys in the object including subsets of
    dimensions. If there are is no common subset of dimensions, None
    is returned.

    Returns the list of dimensions followed by the list of unique
    keys.
    """
    from .ndmapping import NdMapping, item_check
    from .spaces import HoloMap
    key_dims = obj.traverse(lambda x: (tuple(x.kdims),
                                       list(x.data.keys())), (HoloMap,))
    if not key_dims:
        return [Dimension(default_dim)], [(0,)]
    dim_groups, keys = zip(*sorted(key_dims, key=lambda x: -len(x[0])))
    dgroups = [frozenset(d.name for d in dg) for dg in dim_groups]
    subset = all(g1 <= g2 or g1 >= g2 for g1 in dgroups for g2 in dgroups)
    # Find unique keys
    if subset:
        dims = merge_dimensions(dim_groups)
        all_dims = sorted(dims, key=lambda x: dim_groups[0].index(x))
    else:
        # Handle condition when HoloMap/DynamicMap dimensions do not overlap
        hmaps = obj.traverse(lambda x: x, ['HoloMap'])
        if hmaps:
            raise ValueError('When combining HoloMaps into a composite plot '
                             'their dimensions must be subsets of each other.')
        dimensions = merge_dimensions(dim_groups)
        dim_keys = {}
        for dims, keys in key_dims:
            for key in keys:
                for d, k in zip(dims, key):
                    dim_keys[d.name] = k
        if dim_keys:
            keys = [tuple(dim_keys.get(dim.name) for dim in dimensions)]
        else:
            keys = []
        return merge_dimensions(dim_groups), keys

    ndims = len(all_dims)
    unique_keys = []
    for group, keys in zip(dim_groups, keys):
        dim_idxs = [all_dims.index(dim) for dim in group]
        for key in keys:
            padded_key = create_ndkey(ndims, dim_idxs, key)
            matches = [item for item in unique_keys
                       if padded_key == tuple(k if k is None else i
                                              for i, k in zip(item, padded_key))]
            if not matches:
                unique_keys.append(padded_key)

    with item_check(False):
        sorted_keys = NdMapping({key: None for key in unique_keys},
                                kdims=all_dims).data.keys()
    return all_dims, list(sorted_keys)