Quiz:Subgroup structure of alternating group:A5

See subgroup structure of alternating group:A5 for background information.

Basic stuff
Review a summary of the subgroup structure:

{For which of the following divisors of 60 does there exist a subgroup of the alternating group of degree five with that as index? - 2 - 3 - 4 + 5
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{What is the smallest possible order of a group that is not isomorphic to any subgroup of the alternating group of degree five? - 2 - 3 + 4 - 5 - 6
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{For which of the following pairs of primes does the alternating group of degree five have a Hall subgroup corresponding to that pair of primes? - All pairs of primes, i.e., (2,3), (2,5), and (3,5) - (2,3) and (2,5) only + (2,3) only - (2,3) and (3,5) only - (3,5) only - (2,5) only
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{The alternating group of degree five has a maximal subgroup whose index is not a prime number. What is the best description of this subgroup? - Cyclic of order five + Dihedral of order ten, degree five - Cyclic of order ten - Alternating of degree four - Cyclic of order fifteen
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{The alternating group of degree five can be expressed as a product of two subgroups $$HK$$ where $$H,K$$ are permutable complements. What are the orders of these subgroups? - 2 and 30 - 3 and 10 - 4 and 15 + 5 and 12 - 6 and 10
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