Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 272 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. #10598627 | C3 | direct (N × H) |
| 12. C3×D5⋊C16 | C4 | semidirect |
| 13. C3×C5×#108 | C4 | semidirect |
| 15. C3×#3951 | C4 | semidirect |
| 45. D5⋊C16 | C3×C4 | semidirect |
| 46. C5×#108 | C3×C4 | semidirect |
| 48. #3951 | C3×C4 | semidirect |
| 73. C3×#108 | AGL(1,𝔽5) | semidirect |
| 141. #108 | C3×AGL(1,𝔽5) | semidirect |
| 187. C3×C5 | #1383 | semidirect |
| 220. C5 | C3×#1383 | semidirect |
| 230. C3 | #10598627 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3993 | 2 |
| C3×D5⋊M32 | 2 |
| C3×D5×#108 | 2 |
| #10598627 | 3 |
| C3×#1383 | 5 |