Commands for Dropdown Menu Buttons

I am trying to move some of the buttons on the Insert tab in LiveContent Create over to Home tab. I was able to successfully move the Image and Hyperlink buttons. However, this isn't the case with the Symbol and Table buttons. Can you please provide the commands for these as well as MoveUp, MoveDown, and Delete buttons? I inspected the HTML with the developer tools in the browser. I tried InsertSymbolCommand and InsertTableCommand. Those didn't work at all. I have also tried InsertSymbolMenuCommand and InsertTableMenuCommand. Those commands display the correct text under the buttons. However the buttons have no images on them and do not function. I'm not sure if this has something to do with the buttons being dropdowns. Here is the configuration used in dita-config-custom.xml:

<x:overlay xmlns="">

   <!-- Symbols button -->
   <ribbon-bigbutton id="InsertSymbolMenuButton" available="false" />
   <ribbon-bigbutton id="CustomInsertSymbolMenuButton" after="MoveFlowGroup" command="InsertSymbolMenuCommand" />

   <!-- Table button -->
   <ribbon-bigbutton id="InsertTableMenuButton" available="false" />
   <ribbon-bigbutton id="CustomInsertTableMenuButton" after="MoveFlowGroup" command="InsertTableMenuCommand" />

   <!-- Reuse Content buttons -->
   <ribbon-bigbutton id="ToggleLibraryButton" available="false"/>
   <ribbon-bigbutton id="NewImageButton" after="MoveFlowGroup" command="ToggleLibraryCommand" property="showImageLibrary"/>
   <ribbon-bigbutton id="NewLinkButton" after="MoveFlowGroup" command="ToggleLibraryCommand" property="showLinkLibrary"/>