Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21433225 | C2 | semidirect |
| 3. #21424937 | C2 | semidirect |
| 4. #21422533 | C2 | semidirect |
| 5. C59⋊#1309 | C2 | semidirect |
| 6. #21421987 | C2 | semidirect |
| 7. C59×#1545 | C2 | semidirect |
| 166. Dic118 | #100 | semidirect |
| 200. #1545 | D59 | semidirect |
| 233. C59 | #9360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433572 | 2 |
| #21433225 | 2 |
| #21424937 | 2 |
| #21422533 | 2 |
| C59⋊#1309 | 2 |
| #21421987 | 2 |
| C59×#1545 | 2 |
| #9360 | 59 |