Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 103 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. C3×C5×#358 | C2 | semidirect |
| 5. #11746385 | C2 | semidirect |
| 6. #11746324 | C2 | semidirect |
| 7. #11746313 | C2 | semidirect |
| 13. Q16×D15 | C4 | semidirect |
| 27. C5×#358 | D3 | semidirect |
| 56. C3×#358 | D5 | semidirect |
| 135. #358 | D15 | semidirect |
| 256. C3×C5 | #2141 | semidirect |
| 294. C5 | #69222 | 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×Q16×D15 | 2 |
| C2×#91082 | 2 |
| #11750981 | 2 |
| C3×C5×#358 | 2 |
| #11746385 | 2 |
| #11746324 | 2 |
| #11746313 | 2 |
| #10600015 | 3 |
| #69222 | 5 |