Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
782 conjugacy classes of subgroups.
The subgroup lattice has 606 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #21422216 | C2 | direct (N × H) |
| 5. C22×#11745664 | C4 | semidirect |
| 6. C23×C59⋊C8 | C4 | semidirect |
| 10. #16837376 | C4 | semidirect |
| 13. C2×#14273642 | C4 | semidirect |
| 16. #16837369 | C4 | semidirect |
| 24. C59×#410 | C4 | semidirect |
| 27. C2×#99×C59 | C4 | semidirect |
| 31. C2×#11745664 | C2×C4 | semidirect |
| 37. C22×C59⋊C8 | C2×C4 | semidirect |
| 48. #14273642 | C2×C4 | semidirect |
| 82. #99×C59 | C2×C4 | semidirect |
| 305. C2×C59 | #1391 | semidirect |
| 318. #410 | Dic59 | semidirect |
| 323. C2×#99 | Dic59 | semidirect |
| 330. C59 | C2×#1391 | semidirect |
| 381. #99 | C2×Dic59 | semidirect |
| 603. C2 | #21422216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837376 | 2 |
| C2×#16837369 | 2 |
| #21422216 | 2 |
| C2×C59×#410 | 2 |
| C2×#1391 | 59 |