Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. C32×C5×#41 | C2 | semidirect |
| 2. #10624283 | C2 | semidirect |
| 3. #10623912 | C2 | semidirect |
| 4. #10623911 | C2 | semidirect |
| 5. #10623910 | C2 | semidirect |
| 6. #10623909 | C2 | semidirect |
| 7. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 21. C3×C5×#41 | D3 | semidirect |
| 36. C32×#41 | D5 | semidirect |
| 59. C5×#41 | C3⋊D3 | semidirect |
| 84. C3×#41 | D15 | semidirect |
| 91. C32×C5 | #135 | semidirect |
| 138. #41 | C3⋊D15 | semidirect |
| 144. C3×C5 | #950 | semidirect |
| 156. C32 | #4096 | semidirect |
| 172. C5 | #64159 | semidirect |
| 180. C3 | #91839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| #10624283 | 2 |
| #10623912 | 2 |
| #10623911 | 2 |
| #10623910 | 2 |
| #10623909 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| #91839 | 3 |
| #64159 | 5 |