Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 4. #11746385 | C2 | semidirect |
| 5. C5×#4564 | C2 | semidirect |
| 6. #11745898 | C2 | semidirect |
| 7. #11745897 | C2 | semidirect |
| 13. C3×D5×Q16 | C4 | semidirect |
| 59. #4564 | D5 | semidirect |
| 64. D5×Q16 | Dic3 | semidirect |
| 256. C3×C5 | #2141 | semidirect |
| 294. C5 | #72061 | semidirect |
| 306. C3 | #10600015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D5×Q16 | 2 |
| #11747672 | 2 |
| C2×#90934 | 2 |
| #11746385 | 2 |
| C5×#4564 | 2 |
| #11745898 | 2 |
| #11745897 | 2 |
| #10600015 | 3 |
| #72061 | 5 |