Horrible nested if statement for changing CSS based on RadioButton selection

I'm writing away for this website, and I've come into a problem. I need to display only one td based on the corresponding radio button pressed. However, there are two 'master' radio buttons that dictate how many radio buttons are shown, and after that, which are selected. - if that makes any sense!

Now, I am only showing a very small snippet of what I actually have at the moment - this nested if statement goes on 5 more times. So, as you can probably imagine, it looks horrendous. And I'm not sure if there is a better way, maybe there is a way to create functions that can be called? What do you all think?

$('input:radio').change(function () {
                if (this.id == prodMoveRadio) {
                    if ($("#ExtIdTd").is(":visible") === true) {
                        $("#ExtIdTd").css({ visibility: "hidden" });
                        $("#LocIdTd").css({ visibility: "visible" });
                        $("#" + locIdRadio).prop("checked", true);
                        $("#ExtIdTr").css({ visibility: "hidden" });
                    }
                    else {
                        $("#MainContent_DetailsPanel").css({ visibility: "hidden" });
                        $("#ExtIdTr").css({ visibility: "hidden" });
                        $("#LocIdTd").css({ visibility: "visible" });
                        $("#" + locIdRadio).prop("checked", true);
                    }
                }
                else if (this.id == opMoveRadio) {
                    if ($("#ExtIdTd").is(":visible") === false) {
                        $("#ExtIdTr").css({ visibility: "visible" });
                        $("#ExtIdTd").css({ visibility: "visible" });
                    }
                    else {
                        $("#MainContent_DetailsPanel").css({ visibility: "visible" });
                        $("#" + extIdRadio).prop("checked", true);
                        $("#ExtIdTr").css({ visibility: "visible" });
                        $("#ExtIdTd").css({ visibility: "visible" });
                        $("#LocIdTd").css({ visibility: "hidden" });
                    }
                }

Edit

Would it be 'clean' to put a class onto the td's I need to hide, and hide that whole class then set only the visibility to visible on the td I require? Thoughts?