Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. #10598665 | C3 | direct (N × H) |
| 8. C3×#3996 | C4 | semidirect |
| 12. C2×C3×C5×C16 | C4 | semidirect |
| 13. C2×C3×#672 | C4 | semidirect |
| 41. #3996 | C3×C4 | semidirect |
| 45. C2×C5×C16 | C3×C4 | semidirect |
| 46. C2×#672 | C3×C4 | semidirect |
| 69. C2×C3×C16 | AGL(1,𝔽5) | semidirect |
| 135. C2×C16 | C3×AGL(1,𝔽5) | semidirect |
| 181. C3×C5 | #1382 | semidirect |
| 212. C5 | C3×#1382 | semidirect |
| 222. C3 | #10598665 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5⋊#108 | 2 |
| C3×#65721 | 2 |
| C2×C3×D5×C16 | 2 |
| #10598665 | 3 |
| C3×#1382 | 5 |