There are many systems of galaxy classification beyond galaxy morphological classification systems of the Hubble sequence and the de Vaucouleurs system.
Abolutely note that most (really almost all) galaxies fall into multiple classes: the classes overlap.
For reference, we give a large, but NOT exhaustive, listing of galaxy types from various systems of galaxy classification and of the systems themselves linked to their descriptions:
active galaxy, brightest cluster galaxies (BCGs), blue compact dwarf galaxy (BCD), cD or supergiant elliptical galaxy, de Vaucouleurs system, dark galaxy, dwarf galaxy, dwarf elliptical galaxy, dwarf irregular galaxies (dIrrs), dwarf spheriodal galaxy (dSph), early-type galaxies, elliptical galaxy (cD or supergiant elliptical galaxy, dwarf elliptical galaxy), extremely metal-deficient dwarf galaxies (XMDs), flocculent spiral galaxy, galaxy, galaxy color-magnitude diagram (red sequence galaxy, blue cloud galaxy, green valley galaxy), galaxy colors (blue galaxies, green galaxies, red galaxies), grand design spiral galaxy, green bean galaxy, green pea galaxy (I kid you NOT), Hubble sequence (Hubble sequence galaxy types, early type galaxies, late type galaxies), irregular galaxy, interacting galaxy, jellyfish galaxy, L* galaxies, late-type galaxies, lenticular (SO or SB0), LINER galaxy, little red dot galaxies or Little Red Dots (LRDs), low-surface brightness galaxy, luminous infrared galaxy (LIRG), Lyman-alpha emitter (LAE) galaxy, Magellanic spiral galaxies, merged galaxy, multi-arm spiral galaxy, peculiar galaxy, polar-ring galaxy, prolate rotator galaxy, protogalaxy, quenched galaxy, radio galaxy, red geyser galaxy, red nugget galaxies, satellite galaxy, Seyfert galaxy, spiral galaxy (barred spiral galaxy, flocculent spiral galaxy, grand design spiral galaxy, intermediate spiral galaxy, multi-arm spiral galaxy, unbarred spiral galaxy), starburst galaxy, super early galaxies (z ≥ 10), tidal dwarf galaxies, ultra compact dwarf galaxy (UCD), ultra diffuse galaxy (UDG), ultra faint dwarf galaxy (UFD), ultraluminous infrared galaxy (ULIRG), void galaxy---enough, enough.