Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 12. C4⋊(C3⋊#170) | C4 | semidirect |
| 13. C3×C5×#97 | C4 | semidirect |
| 15. C3×#3935 | C4 | semidirect |
| 44. C5×#97 | Dic3 | semidirect |
| 46. #3935 | Dic3 | semidirect |
| 68. C3×#97 | AGL(1,𝔽5) | semidirect |
| 138. #97 | ΓL(1,𝔽16) | semidirect |
| 186. C3×C5 | #1300 | semidirect |
| 222. C5 | #67665 | semidirect |
| 234. C3 | #10598543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752345 | 2 |
| #11752342 | 2 |
| C3×#64996 | 2 |
| #10598543 | 3 |
| #67665 | 5 |