Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3006 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#16837164 | C2 | direct (N × H) |
| 8. C23×C59⋊C8 | C4 | semidirect |
| 12. C22×C4⋊Dic59 | C4 | semidirect |
| 14. #16837164 | C22 | direct (N × H) |
| 19. C22×C4⋊C4×C59 | C4 | semidirect |
| 28. C22×C59⋊C8 | C2×C4 | semidirect |
| 33. C2×C4⋊Dic59 | C2×C4 | semidirect |
| 51. C2×C4⋊C4×C59 | C2×C4 | semidirect |
| 88. C4⋊C4×C59 | C22×C4 | semidirect |
| 91. C4⋊Dic59 | C22×C4 | semidirect |
| 95. C2×C59⋊C8 | C22×C4 | semidirect |
| 135. C22×C59 | #340 | semidirect |
| 161. C2×C59 | C2×#340 | semidirect |
| 182. C22×C4⋊C4 | Dic59 | semidirect |
| 185. C59 | C22×#340 | semidirect |
| 216. C2×C4⋊C4 | C2×Dic59 | semidirect |
| 260. C4⋊C4 | C22×Dic59 | semidirect |
| 299. C22 | #16837164 | direct (N × H) |
| 321. C2 | C2×#16837164 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C59⋊C8 | 2 |
| C23×C4⋊Dic59 | 2 |
| C2×#16837164 | 2 |
| C23×C4⋊C4×C59 | 2 |
| C22×#340 | 59 |