Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#91084 | C2 | semidirect |
| 3. #11747943 | C2 | semidirect |
| 4. C2×#90944 | C2 | semidirect |
| 5. C5×#4509 | C2 | semidirect |
| 6. C3×#64727 | C2 | semidirect |
| 7. #11745896 | C2 | semidirect |
| 10. C2×Dic60 | C22 | semidirect |
| 18. C2×C3×C5×C16 | C22 | semidirect |
| 20. C5×#818 | C22 | semidirect |
| 21. C2×C3×#672 | C22 | semidirect |
| 30. #64727 | D3 | semidirect |
| 62. #4509 | D5 | semidirect |
| 72. C2×C5×C16 | C2×D3 | semidirect |
| 75. C2×#672 | C2×D3 | semidirect |
| 111. C2×C3×C16 | C2×D5 | semidirect |
| 112. #818 | C2×D5 | semidirect |
| 156. C2×C3×D5 | SD32 | semidirect |
| 221. C2×C16 | D3×D5 | semidirect |
| 262. C2×D5 | #800 | semidirect |
| 292. C3×C5 | #2187 | semidirect |
| 343. C5 | #69110 | semidirect |
| 360. C3 | #10599986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D24 | 2 |
| C2×#91084 | 2 |
| #11747943 | 2 |
| C2×#90944 | 2 |
| C5×#4509 | 2 |
| C3×#64727 | 2 |
| #11745896 | 2 |
| #10599986 | 3 |
| #69110 | 5 |