Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21426693 | C2 | semidirect |
| 3. #21422664 | C2 | semidirect |
| 4. C2×#16837125 | C2 | semidirect |
| 5. #21421964 | C2 | semidirect |
| 6. #21421963 | C2 | semidirect |
| 7. C59×#1519 | C2 | semidirect |
| 11. #16837328 | C4 | semidirect |
| 13. #16837310 | C4 | semidirect |
| 53. C59⋊#95 | D4 | semidirect |
| 68. #95×C59 | D4 | semidirect |
| 243. #1519 | D59 | semidirect |
| 277. C59 | #9205 | semidirect |
| 319. #95 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429832 | 2 |
| #21426693 | 2 |
| #21422664 | 2 |
| C2×#16837125 | 2 |
| #21421964 | 2 |
| #21421963 | 2 |
| C59×#1519 | 2 |
| #9205 | 59 |