All the spirals have spiral arms, but some have arms so tightly wound around the central core they appear almost like elliptical galaxies, which have no spiral arms. There are four basic types of lenticular spirals, as shown in this illustration.

click to enlarge
There are actually two subtypes of SOs
• S01—lenticular with no visible spiral arms.
• S03—lenticular with a lot of light absorbing dust.
• Sa—tightly wound, smooth arms.
• Sb—more defined arms.
• Sc—more loosely wound, clearly defined arms.
And there is one more type of lenticular:
• Sd—very loose arms; the arms are much brighter than the core.
Very often, from ground based telescopes, only the arms can be seen, and this type appears to a viewer as another type of galaxy.
Then there are the barred spirals.
These do not have the central bulge, but rather have a line of stars through the middle. They do exhibit a center swelling however, and most show distinct spiral arms. They are designated SBx, where x is a sub type designation. The sub types are:
• SB01—a barred galaxy with no visible spiral arms.
• SB03—barred with very tightly wound arms.
• SBa—tight but distinct arms.
• SBb—well defined loosely wound arms.
• SBc—very loosely wound arms, and dim core.
One aspect of all spirals that is intriguing is that the spiral arms are logarithmic in form—that is, they are described by the natural logarithm e, 2.71828. All things in nature are formed by this force. A nautilus' shell, for example, is described by e.

click to enlarge
.