Summary: Small telescopes will not show any visual detail in a galaxy. The website What Can You See With Different Telescopes is a good reference. (Thanks to JamesK for referencing this website in a comment to Is the Celestron astromaster 130 EQ Model able to see nebulas and galaxies?) Keep in mind that observing an object visually is much different than photos you may have seen. A camera can take a long exposure to "build up" an image of a faint galaxy. The eye does not behave this way.
Most galaxies are faint when viewed visually. Therefore, details can be difficult to see. (In some cases, it is more a matter of "barely detecting" some detail compared to being able to easily "see" some detail.) For some amateur astronomers, being able to locate an object and see it is a victory. Being able to see some detail in a galaxy is a dream (for a larger telescope).
Here are some of the factors that will affect how much detail you can see in a galaxy:
- How large is the telescope? The main purpose of a telescope is to collect light. The more light that is collected, the brighter the object will appear. A 60 mm telescope (2.4 inch, the size of the objective) is small and will not gather much light. Therefore, only the brightest portion of a galaxy will be visible. Fainter details will not be visible. (Perhaps the dust lane in M64 or M104 will be visible if the sky is really dark.)
- How dark is the sky? Since galaxies are faint, seeing them well requires a dark sky. Can you see clouds at night because they reflect light? If the answer is no, you can only "see" the clouds because you notice that "stars are missing", then you have a dark sky. If the outline of the clouds are easily visible due to nearby light pollution, then seeing details in "faint fuzzies" will be impossible. What is the magnitude (the brightness) of the faintest star that can be seen? Both of those questions will help to judge how dark or bright the night sky is at your location.
- Experience. Experienced observers can see more detail than inexperienced observers. Part is the difference is knowing to take time to study an object instead of viewing it for 5 seconds and saying "oh well".
- Does the galaxy have any detail to be seen? (This factor should be obvious but is a good reminder.) Some galaxies are featureless blobs, such as elliptical galaxies. Other galaxies that theoretically have detail may be seen from an angle that makes the detail hard to see, such as a spiral galaxy seen from edge on. Spiral arms can be faint and may be indistinguishable even though the galaxy can be seen due to the combined light of the nucleus and arms.