# Questions tagged [groups-enumeration]

Number and enumeration of all finite groups of a given order

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### How many (non-isomorphic) groups of order 315 are there?

Show that all such groups are a direct product of a group of order 5 with the semi direct product of a group of order 7 with a group of order 9. Please help me fix my solution! Help appreciated. The ...
159 views

### Conjectures around number of subgroups of symmetric group [closed]

I am asking if you know unsolved or recently solved conjectures around numbers of subgroups in symmetric or alternating groups. In fact, is there a formula depending of $n$ to count subgroups of order ...
103 views

### How to approximate the number of groups?

How can I find a reasonable approximation for the number of groups upto isomorphism of some higher order $\ n\$ with relatively large exponents in the prime factorization without excessive ...
595 views

### Classify the groups of order $88$ up to isomorphism.

Classify the groups of order $88$ up to isomorphism. Here is what I have so far (I'm aware that there are $12$ groups, but I don't know which ones I'm missing as well as why the $3$ groups are ...
164 views

### Classify all groups of order $375$

According to A000001, the number of groups of order $375$ is $7$. How to figure them out? $5$ groups can be found in this way: Because the number of $125$-order groups is $5$, we can make the direct ...
292 views

### Find all the groups of order 28

I've seen there is a similar question, but it looks for something more specific. I'll write what I thought. I've rapidly seen that every group of order 28 has a unique normal subgroup of order 7. ...
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