Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
200 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×C5×C4⋊C16 | C2 | semidirect |
| 3. C3×#64681 | C2 | semidirect |
| 4. #10598048 | C3 | direct (N × H) |
| 14. C5×C4⋊C16 | C2×C3 | semidirect |
| 15. #64681 | C2×C3 | semidirect |
| 29. C3×C4⋊C16 | D5 | semidirect |
| 71. C4⋊C16 | C3×D5 | semidirect |
| 150. C3×C5 | #1330 | semidirect |
| 180. C5 | C3×#1330 | semidirect |
| 190. C3 | #10598048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64977 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C3×#64681 | 2 |
| #10598048 | 3 |
| C3×#1330 | 5 |