Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 80 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×#66091 | C2 | semidirect |
| 2. C2×C5×#826 | C2 | semidirect |
| 3. #11748081 | C2 | semidirect |
| 4. #11747540 | C2 | semidirect |
| 5. #11746384 | C2 | semidirect |
| 6. #11745904 | C2 | semidirect |
| 7. #11745886 | C2 | semidirect |
| 11. C2×C5×D24 | C22 | semidirect |
| 19. #91103 | C22 | semidirect |
| 20. #91096 | C22 | semidirect |
| 22. C2×C5×C3⋊C16 | C22 | semidirect |
| 27. #66091 | D3 | semidirect |
| 63. C2×#826 | D5 | semidirect |
| 118. C2×D24 | C2×D5 | semidirect |
| 125. C2×C3⋊C16 | C2×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #72122 | semidirect |
| 368. C3 | #10602264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66091 | 2 |
| C2×C5×#826 | 2 |
| #11748081 | 2 |
| #11747540 | 2 |
| #11746384 | 2 |
| #11745904 | 2 |
| #11745886 | 2 |
| #10602264 | 3 |
| #72122 | 5 |