JSFiddle - React, Tailwind, and code Playground

HTML

<ul id="menu">
    <li>
        <a href="index.htm">
            <img src="http://placehold.it/140x15" alt="" />
        </a>
    </li>
    <li>
        <a href="TTUgalleries.html">
            <img src="http://placehold.it/140x15" alt="" />
        </a>
    </li>
    <li>
        <a href="STATEgalleries.html">
            <img src="http://placehold.it/140x15" alt="" />
        </a>
    </li>
    <li>
        <a nohref="#">
            <img src="http://placehold.it/140x15" alt=""  />
        </a>
        <ul class="sub-menu">
            <li>
                <a href="classes.html" id="demargpadLink"><img src="http://placehold.it/140x15" alt="" /></a>
            </li>
            <li>
                <a href="mats.html"><img src="http://placehold.it/140x15" alt="" /></a>
            </li>
        </ul>
    </li>
    <li>
        <a href="newsletter.html">
            <img src="http://placehold.it/140x15" alt="" />
        </a>
    </li>
    <li>
        <a href="artiststatement.html">
            <img src="http://placehold.it/140x15" alt="" />
        </a>
    </li>
    <li>
        <a href="contact.html">
            <img src="http://placehold.it/140x15" alt="" />
        </a>
    </li>
</ul>

CSS

#menu {
    float: left;
    position: relative;
    margin-left: 10px;
    margin-top: 10px;
    z-index:15;
    padding-bottom: 0px;

}
a {
    text-decoration: none;
    color: #838383;

}
a:hover {
    color: black;

}
#menu a {
    display: block;
    width: 140px;

}
#menu ul {
    list-style-type: none;
    padding-top: 10px;

}
#menu li {
    display:block;
    position: relative;
    margin-left: 1px;
    text-align: center;

}
#menu li ul.sub-menu {
    display: none;
    position: absolute;
    top: 0;
    left: 100%;
    padding: 10px;
    z-index: 90;
    background:#000;

}
#menu li ul.sub-menu li {
    text-align: left;

}
#menu li:hover ul.sub-menu {
    display: block;

}
#menu li:hover ul.sub-menu a {
    margin-top: 4px;
    margin-bottom: 0;
    padding: 0;

}