Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. #11751193 | C2 | semidirect |
| 2. C5×#5078 | C2 | semidirect |
| 5. #11746955 | C2 | semidirect |
| 7. #11745833 | C2 | semidirect |
| 50. #5078 | D5 | semidirect |
| 228. C3×C5 | #1722 | semidirect |
| 263. C5 | #71195 | semidirect |
| 274. C3 | #10602159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751193 | 2 |
| C5×#5078 | 2 |
| C3×#65377 | 2 |
| #11747079 | 2 |
| #11746955 | 2 |
| #11746890 | 2 |
| #11745833 | 2 |
| #10602159 | 3 |
| #71195 | 5 |