Which parts of the cerebral cortex don't belong to the neocortex?

Question

In the Wikipedia article on the cerebral cortex one reads:

»Most of the cerebral cortex consists of the six-layered neocortex.«

Accordingly, in the Wikipedia list of regions in the human brain, one finds "cerebral cortex" and "neocortex" as almost synonyms.

But assuming that they are not perfect synonyms – but that there are some parts of the cerebral cortex that are not part of the neocortex – I wonder which parts this might specifically be.

To make my question specific, I list here all parts of the cerebral cortex as listed at Wikipedia:

Cerebral cortex (neocortex)
Frontal lobe
    Primary motor cortex
    Supplementary motor cortex
    Premotor cortex
    Prefrontal cortex
    Orbitofrontal cortex
    Dorsolateral prefrontal cortex
    Superior frontal gyrus
    Middle frontal gyrus
    Inf. frontal gyrus
    Brodmann areas
Parietal lobe
    Primary somatosensory cortex (S1)
    Secondary somatosensory cortex (S2)
    Posterior parietal cortex
    Postcentral gyrus (Primary somesthetic area)
    Precuneus
    Brodmann areas
Occipital lobe
    Primary visual cortex (V1)
    V2
    V3
    V4
    V5/MT
    Lateral occipital gyrus
    Cuneus
    Brodmann areas
Temporal lobe
    Primary auditory cortex (A1)
    secondary auditory cortex (A2)
    Inf. temporal cortex
    Posterior Inf. temporal cortex
    Superior temporal gyrus
    Middle temporal gyrus
    Inf. temporal gyrus
    Entorhinal cortex
    Perirhinal cortex
    Parahippocampal gyrus
    Fusiform gyrus
    Brodmann areas
    Medial superior temporal area (MST)
Insular cortex
Cingulate cortex
    Anterior cingulate
    Posterior cingulate
    Retrosplenial cortex
    Indusium griseum
    Subgenual area 25
    Brodmann areas

If there are parts of the cerebral cortex missing here, a hint would be welcome!

Answer 1

The hippocampus is considered archicortex rather than neocortex. Sometimes hippocampus is considered "sub-cortical" but I think this is only really fair if you really mean "sub-neocortical"; it's common for "cortical" to be used as a shorthand for neocortex in human neurobiology. Writers will be more specific when necessary.

The piriform cortex and related olfactory structures are considered paleocortex.

Some also delineate an in-between periallocortex that includes entorhinal cortex and limbic structures around the hippocampus.

Neocortex is mostly a six-layered structure and found only in mammals. The other, non-neocortical types of cortex have fewer layers, and are shared by an older common ancestor that includes other vertebrates.