Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11748072 | C2 | semidirect |
| 3. #11746323 | C2 | semidirect |
| 4. C3×#64726 | C2 | semidirect |
| 5. #11745905 | C2 | semidirect |
| 12. C5×Dic24 | C4 | semidirect |
| 13. C5×#800 | C4 | semidirect |
| 14. C5×D48 | C4 | semidirect |
| 21. #64726 | D3 | semidirect |
| 69. Dic24 | Dic5 | semidirect |
| 70. #800 | Dic5 | semidirect |
| 71. D48 | Dic5 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #69358 | semidirect |
| 191. C3 | #10602305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4904 | 2 |
| #11748072 | 2 |
| #11746323 | 2 |
| C3×#64726 | 2 |
| #11745905 | 2 |
| #10602305 | 3 |
| #69358 | 5 |