Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C3×C5×#499 | C2 | semidirect |
| 5. #11746311 | C2 | semidirect |
| 6. #11746310 | C2 | semidirect |
| 7. C4⋊(C3⋊#672) | C2 | semidirect |
| 21. C5×#499 | D3 | semidirect |
| 43. C3×#499 | D5 | semidirect |
| 101. #499 | D15 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | #71356 | semidirect |
| 246. C3 | #10602149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#499 | 2 |
| C4×D120 | 2 |
| #11746312 | 2 |
| #11746311 | 2 |
| #11746310 | 2 |
| C4⋊(C3⋊#672) | 2 |
| #10602149 | 3 |
| #71356 | 5 |