Convert Sparsely-Populated XML List to HTML Table Using XSL

I'm trying to convert an XML file into a nice-looking HTML table using XSL, and I can't for the life of me figure out how to get the columns all lined up properly. I found a similar question (Convert XML List to HTML Table Using XSL), which was informative (I'm pretty new to XSL in general so every little bit helps), but my XML is structured a bit more... irregularly:

<?xml version="1.0"?>
<root>
    <Group>
        <Type>Type1</Type>
        <Desc>Desc1</Desc>
        <Name>Name1</Name>
    </Group>
    <Group>
        <Type>Type2</Type>
        <Name>Name2</Name>
        <State>State2</State>
    </Group>
    <Group>
        <Type>Type3</Type>
        <State>State3</State>
        <Country>Country4</Country>
    </Group>
</root>

Is there a good way to turn this into a well-formatted table? I'd prefer if it worked on the XML as it is like this, as if we ever add a new field to one of the Group elements, I don't want them to have to add the same tag to every other element (though if there's alternately a good way to automatically add all the missing children to a Group element that are present in other Group elements, that would be good too, maybe using a second XSLT that can run first). There's no backing schema for this XML, but one could be made if it helps.

Sorry if this has been answered before, I couldn't find anything closer besides the mentioned question and nothing about how to add the missing children to an element.

Here is my attempt at an XSLT 2.0 solution:

<xsl:transform xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="2.0">
    <xsl:output method="html" version="5.0" encoding="UTF-8" indent="yes" />

    <xsl:variable name="col-names" select="distinct-values(root/Group/*/node-name(.))"/>

    <xsl:template match="root">
        <table>
            <thead>
                <tr>
                    <xsl:for-each select="$col-names">
                        <th>
                            <xsl:value-of select="."/>
                        </th>
                    </xsl:for-each>
                </tr>
            </thead>
            <tbody>
                <xsl:apply-templates select="Group"/>                
            </tbody>
        </table>
    </xsl:template>

    <xsl:template match="Group">
        <tr>
            <xsl:variable name="this" select="."/>
            <xsl:for-each select="$col-names">
                <td>
                    <xsl:value-of select="$this/*[node-name(.) eq current()]"/>
                </td>
            </xsl:for-each>
        </tr>
    </xsl:template>
</xsl:transform>