Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
236 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 86 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×#64678 | C2 | semidirect |
| 4. #10598051 | C3 | direct (N × H) |
| 13. C5×C4⋊C16 | C2×C3 | semidirect |
| 14. #64678 | C2×C3 | semidirect |
| 27. C3×C4⋊C16 | D5 | semidirect |
| 67. C4⋊C16 | C3×D5 | semidirect |
| 145. C3×C5 | #1361 | semidirect |
| 176. C5 | C3×#1361 | semidirect |
| 186. C3 | #10598051 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64984 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C3×#64678 | 2 |
| #10598051 | 3 |
| C3×#1361 | 5 |