Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. C3×C5×#510 | C2 | semidirect |
| 3. #11751290 | C2 | semidirect |
| 4. #11751280 | C2 | semidirect |
| 5. #11746387 | C2 | semidirect |
| 6. #11746339 | C2 | semidirect |
| 7. #11746335 | C2 | semidirect |
| 11. C2×C3×C5×Q16 | C22 | semidirect |
| 22. C3×C5×M32 | C22 | semidirect |
| 26. #91101 | C22 | semidirect |
| 27. #91096 | C22 | semidirect |
| 30. C5×#510 | D3 | semidirect |
| 70. C3×#510 | D5 | semidirect |
| 78. C2×C5×Q16 | C2×D3 | semidirect |
| 89. C5×M32 | C2×D3 | semidirect |
| 126. C2×C3×Q16 | C2×D5 | semidirect |
| 137. C3×M32 | C2×D5 | semidirect |
| 178. #510 | D15 | semidirect |
| 265. C2×Q16 | C2×D15 | semidirect |
| 273. M32 | C2×D15 | semidirect |
| 355. C3×C5 | #2191 | semidirect |
| 407. C5 | #71522 | semidirect |
| 421. C3 | #10602315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756527 | 2 |
| C3×C5×#510 | 2 |
| #11751290 | 2 |
| #11751280 | 2 |
| #11746387 | 2 |
| #11746339 | 2 |
| #11746335 | 2 |
| #10602315 | 3 |
| #71522 | 5 |