Is it a lobster number?
Python 3, 155, 126, 124, 123, 120 116, 113 bytes

Yes! First python answer!
Saved 21 bytes due to a suggestion by Dominic van Essen to remove the for loop!
Saved 8 bytes because I realized I could use t*=True/False instead of t+=[True/False].
Saved another 2 bytes right after I finished editing because I realized t could simply be set to the same value as i and l!
Saved 1 byte based off Danis's python 2 comment.
Saved another 3 bytes based off Tipping Octopus's comment.
Saved another 4 bytes due to Tipping Octopus again!
Saved another 3 bytes thanks to Dominic's suggestion to remove the t variable.
New Answer
x=input()
n=int(x)
i=l=2
while~-n:
 if n%i:i+=1
 else:n//=i;l+=1;j=iter(x);l*=2*all(c in j for c in str(i))
print(l&gt;4)

How it works
The while loop computes the prime factors of the input. If a prime factor is found, it checks if it is a subsequence of the input. l is multiplied by whether or not this is True. This takes advantage of the fact that python's True and False values act like 1s and 0s when you multiply by them. This means that instead of appending True/False to t and checking whether all(t) is True like in my old answer, I can just multiply l by 2*True/False and check its value in the print statement. The print statement prints True if l&gt;4.
Try it online!
Old Answer
x=n=int(input())
l=[]
i=2
while i&lt;=n:
 if n%i:i+=1
 else:n/=i;l+=[i]
t=[]
for p in l:i=iter(str(x));t+=[all(c in i for c in str(p))]
print(all(t)*len(l)&gt;1)

Try it online!