Button inside Update Panel is not triggered, in as

<asp:ModalPopupExtender ID="MPE_EditGroup" runat="server" TargetControlID="btnShowPopup" PopupControlID="pnlpopup" CancelControlID="btnCancel" />
<asp:ToolkitScriptManager ID="ScriptManager1" runat="server" />
<asp:UpdatePanel ID="UpdatePanel1" runat="server" UpdateMode="Conditional" ChildrenAsTriggers="false">
    <ContentTemplate>
        <asp:Panel ID="pnlpopup" runat="server">
            <asp:ListBox ID="lst_allmembers" DataValueField="FirstName" runat="server" />                       
            <asp:Button ID="btn_Add" runat="server" Text="Add" OnClick="btn_Add_Click" /><asp:ListBox ID="lst_grpmembers" runat="server" />
            <asp:Button ID="btn_remove" runat="server" Text="Remove" />
            <asp:Button ID="btnUpdate" CommandName="Update" runat="server" Text="Update" OnClick="btnUpdate_Click" />
            <asp:Button ID="btnCancel" runat="server" Text="Cancel" /></asp:Panel>
    </ContentTemplate>
</asp:UpdatePanel>

The add button has a event OnClick="btn_Add_Click"

  protected void btn_Add_Click(object sender, EventArgs e)
  {
        lst_grpmembers.Items.Add(lst_allmembers.SelectedItem.Text);
             }

The event is not triggered and when I click the add button nothing happens. And the Update Button was working fine before I added the update panel now only the cancel button closes the popup no other button works inside the pop up How to trigger the event.

Change the UpdatePanel's ChildrenAsTriggers property to true. This will cause any postbacks triggered by the UpdatePanel's child elements to update its content.

EDIT: Just realized that btn_Add is a nested control, so you will have to explicitly call it out as an UpdatePanel Trigger. Add the following to your UpdatePanel markup, after the ContentTemplate:

<Triggers>
    <asp:AsyncPostBackTrigger ControlID="btn_Add" /> 
</Triggers>

EDIT #2: To keep your modal popup from closing when an async postback occurs, move the UpdatePanel inside the panel specified by ModalPopupExtender's PopupControlID:

<asp:Panel ID="pnlpopup" runat="server">
    <asp:UpdatePanel ID="UpdatePanel1" runat="server" UpdateMode="Conditional" ChildrenAsTriggers="true">
        <ContentTemplate>
            <asp:ListBox ID="lst_allmembers" DataValueField="FirstName" runat="server" />
            <asp:Button ID="btn_Add" runat="server" Text="Add" OnClick="btn_Add_Click" />
            <asp:ListBox ID="lst_grpmembers" runat="server" />
            <asp:Button ID="btn_remove" runat="server" Text="Remove" />
            <asp:Button ID="btnUpdate" CommandName="Update" runat="server" Text="Update" OnClick="btnUpdate_Click" />
             <asp:Button ID="btnCancel" runat="server" Text="Cancel" />
        </ContentTemplate>
    </asp:UpdatePanel>
</asp:Panel>