Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1602 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 3. #21424173 | C2 | semidirect |
| 4. #21424171 | C2 | semidirect |
| 5. #21424169 | C2 | semidirect |
| 6. #342×D59 | C2 | semidirect |
| 7. C59×#1820 | C2 | semidirect |
| 10. C2×C4×D236 | C4 | semidirect |
| 11. C2×#14273689 | C4 | semidirect |
| 32. C22×C4×D59 | C2×C4 | semidirect |
| 36. C2×C4⋊Dic59 | C2×C4 | semidirect |
| 42. C2×(C2×D59)⋊C4 | C2×C4 | semidirect |
| 46. C2×C4×Dic59 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C59 | C2×C4 | semidirect |
| 53. C2×C42×C59 | C2×C4 | semidirect |
| 157. #1820 | D59 | semidirect |
| 182. C59 | #20689 | semidirect |
| 198. C2×C4⋊C4 | C4×D59 | semidirect |
| 211. C2×C42 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837876 | 2 |
| #21426673 | 2 |
| #21424173 | 2 |
| #21424171 | 2 |
| #21424169 | 2 |
| #342×D59 | 2 |
| C59×#1820 | 2 |
| #20689 | 59 |