Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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. C5×#5078 | C2 | semidirect |
| 3. C3×#65381 | C2 | semidirect |
| 5. #11746962 | C2 | semidirect |
| 7. #11745831 | C2 | semidirect |
| 24. #65381 | D3 | semidirect |
| 52. #5078 | D5 | semidirect |
| 228. C3×C5 | #1722 | semidirect |
| 263. C5 | #71301 | semidirect |
| 274. C3 | #10602159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751189 | 2 |
| C5×#5078 | 2 |
| C3×#65381 | 2 |
| #11747067 | 2 |
| #11746962 | 2 |
| #11746910 | 2 |
| #11745831 | 2 |
| #10602159 | 3 |
| #71301 | 5 |