Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 108 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×#4682 | C2 | semidirect |
| 3. #11747096 | C2 | semidirect |
| 5. #11746955 | C2 | semidirect |
| 7. C3×#64674 | C2 | semidirect |
| 29. #64674 | D3 | semidirect |
| 53. #4682 | D5 | semidirect |
| 228. C3×C5 | #1722 | semidirect |
| 263. C5 | #68098 | semidirect |
| 274. C3 | #10602159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750795 | 2 |
| C5×#4682 | 2 |
| #11747096 | 2 |
| #11747067 | 2 |
| #11746955 | 2 |
| #11746912 | 2 |
| C3×#64674 | 2 |
| #10602159 | 3 |
| #68098 | 5 |