Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11751297 | C2 | semidirect |
| 3. #11748072 | C2 | semidirect |
| 4. C3×#64787 | C2 | semidirect |
| 5. #11745947 | C2 | semidirect |
| 6. #11745906 | C2 | semidirect |
| 7. #11745875 | C2 | semidirect |
| 16. C5×#829 | C4 | semidirect |
| 17. C5×#828 | C4 | semidirect |
| 18. C5×#827 | C4 | semidirect |
| 19. C5×#826 | C4 | semidirect |
| 29. #64787 | D3 | semidirect |
| 98. #829 | Dic5 | semidirect |
| 99. #828 | Dic5 | semidirect |
| 100. #827 | Dic5 | semidirect |
| 101. #826 | Dic5 | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #69239 | semidirect |
| 282. C3 | #10602305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751297 | 2 |
| C5×#5194 | 2 |
| #11748072 | 2 |
| C3×#64787 | 2 |
| #11745947 | 2 |
| #11745906 | 2 |
| #11745875 | 2 |
| #10602305 | 3 |
| #69239 | 5 |