JSFiddle - React, Tailwind, and code Playground
HTML
<script src="http://code.jquery.com/ui/1.9.1/jquery-ui.js"></script>
<div id="ctl00_mainContentPlaceHolder_ctl00_mainContentPlaceHolder_lvwGalleryThumbsPanel" style="display: block; width: 100px ">
<fieldset style="float: left;">
<table>
<tbody><tr>
<td>
<a href="#"><img src="http://images.wikia.com/reddithistory/images/1/10/3-rage-face.png" style="border-color:#DDDDDD;border-width:2px;border-style:solid;width:50px;margin-left: 10px"></a>
</td>
<td>
<a href="#"><img src="http://profile.ak.fbcdn.net/hprofile-ak-prn1/162000_59402216532_1218556484_q.jpg" style="border-color:White;border-width:2px;border-style:solid;width:50px;margin-left: 10px"></a>
</td>
<td>
<a href="#"><img src="http://l.yimg.com/a/i/identity2/profile_16a.png" style="border-color:White;border-width:2px;border-style:solid;width:50px;margin-left: 10px"></a>
</td>
<td>
<a href="#"><img src="http://www.gravatar.com/avatar/9270737ce9487fbaabc328f0dfccee29?s=32&d=identicon&r=PG" style="border-color:White;border-width:2px;border-style:solid;width:50px;margin-left: 10px"></a>
</td>
</tr>
</tbody></table>
</fieldset>
<fieldset style="float: left;">
<table>
...
JavaScript
$( "#ctl00_mainContentPlaceHolder_ctl00_mainContentPlaceHolder_lvwGalleryThumbsPanel tr" ).sortable({
connectWith: "#ctl00_mainContentPlaceHolder_ctl00_mainContentPlaceHolder_lvwGalleryThumbsPanel tr"
});