Nevermind, figured it out. Made the following changes:
add_settings_section( 'cp_required_info', null, array($this, 'cp_required_info'), 'cp-settings-group' );
add_settings_section( 'cp_sync_info', null, array($this, 'cp_sync_info'), 'cp-settings-group' );
register_setting( 'cp-settings-group', 'cp_admin_options', array( $this, 'sanitize' ) );
<?php settings_fields( 'cp-settings-group' );
do_settings_sections( 'cp-settings-group' );
do_settings_fields( 'cp-settings', 'cp_required_info' );?>
<!--Some HTML goes here-->
<?php
do_settings_fields( 'cp-settings', 'cp_sync_info' );?>
?>