Custom Post type URLs

Hello,

First attempt at Custom Post Types and Taxonomies. Seems to be having a URL issue.

My CPT is “Properties” and my Taxonomy is “Property Types”. All seems to be fine on Admin dashboard and I added two proerty types;

1. Land for Sale
2. Farms for Sale

I can see these ok on front end but the URLs are not what I was hoping.

The actual property listing can be viewed here: http://noeloconnor.com/property/castleroberts-adare-limerick/

I would like it to appear as http://noeloconnor.com/property/farms-for-sale/castleroberts-adare-limerick/

What I was hoping would be its parent page can be seen here: http://noeloconnor.com/property_types/farms-for-sale/

I would like the parent page to appear as http://noeloconnor.com/property/farms-for-sale/ if possible

It just seems to be that from an SEO point of view it is not correct. I was hoping to have the URL structure similar to how the regular domainname/categoryname/postname structure

Below is the Custom Post Type code I entered in my functions.php code for my child theme;

// Custom Post Type for Property

add_action( 'init', 'register_cpt_property' );

function register_cpt_property() {

    $labels = array(
        'name' => _x( 'Properties', 'property' ),
        'singular_name' => _x( 'Property', 'property' ),
        'add_new' => _x( 'Add New', 'property' ),
        'all_items' => _x( 'Properties', 'property' ),
        'add_new_item' => _x( 'Add New Property', 'property' ),
        'edit_item' => _x( 'Edit Property', 'property' ),
        'new_item' => _x( 'New Property', 'property' ),
        'view_item' => _x( 'View Property', 'property' ),
        'search_items' => _x( 'Search Properties', 'property' ),
        'not_found' => _x( 'No properties found', 'property' ),
        'not_found_in_trash' => _x( 'No properties found in Trash', 'property' ),
        'parent_item_colon' => _x( 'Parent Property:', 'property' ),
        'menu_name' => _x( 'Properties', 'property' ),
    );

    $args = array(
        'labels' => $labels,
        'hierarchical' => false,
        'public' => true,
        'show_ui' => true,
        'show_in_menu' => true
    );

    register_post_type( 'property', $args );
}

Below is the Taxonomy code I entered in my functions.php code for my child theme;

// Taxonomy for Property Types

add_action( 'init', 'register_taxonomy_property_types' );

function register_taxonomy_property_types() {

    $labels = array(
        'name' => _x( 'Property Types', 'property_types' ),
        'singular_name' => _x( 'Property Type', 'property_types' ),
        'search_items' => _x( 'Search Property Types', 'property_types' ),
        'popular_items' => _x( 'Popular Property Types', 'property_types' ),
        'all_items' => _x( 'All Property Types', 'property_types' ),
        'parent_item' => _x( 'Parent Property Type', 'property_types' ),
        'parent_item_colon' => _x( 'Parent Property Type:', 'property_types' ),
        'edit_item' => _x( 'Edit Property Type', 'property_types' ),
        'update_item' => _x( 'Update Property Type', 'property_types' ),
        'add_new_item' => _x( 'Add New Property Type', 'property_types' ),
        'new_item_name' => _x( 'New Property Type', 'property_types' ),
        'separate_items_with_commas' => _x( 'Separate property types with commas', 'property_types' ),
        'add_or_remove_items' => _x( 'Add or remove property types', 'property_types' ),
        'choose_from_most_used' => _x( 'Choose from the most used property types', 'property_types' ),
        'menu_name' => _x( 'Property Types', 'property_types' ),
    );

    $args = array(
        'labels' => $labels,
        'public' => true,
        'show_in_nav_menus' => true,
        'show_ui' => true,
        'show_tagcloud' => false,
        'show_admin_column' => false,
        'hierarchical' => true,

        'rewrite' => true,
        'query_var' => true
    );

    register_taxonomy( 'property_types', array('property'), $args );
}

Any help would be so much appreciated.