Here is a simple example with navigate buttons.
HTML
<ul>
<li>1 <a class='up' href='#'>up</a> <a class='down' href='#'>down</a></li>
<li>2 <a class='up' href='#'>up</a> <a class='down' href='#'>down</a></li>
<li>3 <a class='up' href='#'>up</a> <a class='down' href='#'>down</a></li>
<li>4 <a class='up' href='#'>up</a> <a class='down' href='#'>down</a></li>
<li>5 <a class='up' href='#'>up</a> <a class='down' href='#'>down</a></li>
<li>6 <a class='up' href='#'>up</a> <a class='down' href='#'>down</a></li>
</ul>
Javascript with JQuery
$('.up').on('click', function(e) {
var wrapper = $(this).closest('li')
wrapper.insertBefore(wrapper.prev())
})
$('.down').on('click', function(e) {
var wrapper = $(this).closest('li')
wrapper.insertAfter(wrapper.next())
})
Try it here: https://jsfiddle.net/nguyenvuloc/vd105gst