From time to time I see references to Roman Catholics who object to (part? all?) of Vatican II. Most commonly I see ads in my local newspaper for traditional Latin masses, but I understand the objections to be more than vernacular versus Latin worship. I've also heard (as a Jew) that not all Roman Catholics accept nostra aetate, the Vatican II declaration that Jews have a valid covenant with God and don't need to be sought as converts, but I don't know if the anti-NA folks overlap the Latin-mass folks and what other beliefs they share. Do certain groups object to the whole thing or just parts of it?
I tried to find an answer on Google and it led me to this page at Catholic Answers (no idea how authoritative that is), which in turn led me to the name "Society of Saint Pius X". This page on their site lists key concerns of: modernism, religious liberty, ecumenism, collegiality, and liturgical abuses (their wording, not mine), but I can't tell if that's all based on Vatican II or if it's something broader. I also can't tell if SSPX comprises the Catholics who object to Vatican II or if they are just one such group. (I don't remember seeing that name in the aforementioned newspaper ads.) I found this C.SE question about whether SSPX is schismatic, which is helpful but doesn't answer my question, which is about the broader platform, not one specific organization.
So: is there a (denomination? ideology?) that describes objectors to Vatican II, or do such objections come from scattered groups or individuals with no over-riding ideology? If there is an ideology beyond specific people/groups, does it have a name? And what specifically do they object to -- everything decided at that council or just certain things?