Letter group puzzles; What do these letters have in common?

BCDGJKPQTVWYZ are the letters whose English names do not begin with a vowel (but do end in a vowel).

FHLMNRSX are the letters whose English names begin with a vowel but end in a consonant.  The remaining groups of letters are arranged by how they rhyme:

AJK
BCDEGPTVZ
IY
O
QUW

BCEGKMQSW are letters in prime position, DFHIJLNOPRTUVXYZ are composites.

BDO have no "spokes", P has 1, ACGLMNQRSUVWZ have 2, EFJTY have 3, and HIKX have 4.

CEFGHIJKLMNSTUVWXYZ have no loops, ADOPQR have one loop, and B has two loops.

BEJQXYZ begin no state names;
DFGHLPRU begin 1 state name each:
    Delaware, Florida, Georgia, Hawaii, Louisiana, Pennsylvania, Rhode Island and Utah.
KSTV begin 2 state names each:
    Kansas, Kentucky; South Carolina, South Dakota; Tennessee, Texas; Vermont, Virginia.
CO begin 3 state names each:
    California, Colorado, Connecticut; Ohio, Oklahoma, Oregon.
AIW begin 4 state names each:
    Alabama, Alaska, Arizona and Arkansas; Idaho, Illinois, Indiana, Iowa;
    Washington, West Virginia, Wisconsin, Wyoming.
MN begin 8 state names each:
    Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana;
    Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, New York, North Carolina, North Dakota.

ABEHIKMNOPTXZ look like Greek letters, while
CDFGJLQRSUVWY do not look like Greek letters.

AEFHIKLMNTVWXYZ have no curves; Of non-curved letters, EFHILT have no slanted lines, while AKMNVWXYZ have slanted lines.
BCDGJOPQRSU have curves; Of curved letters, CGJSU have no loops while BDOPQR have loops.