Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×C32×Dic10 | C2 | semidirect |
| 3. #10623906 | C2 | semidirect |
| 5. #10623775 | C2 | semidirect |
| 6. #10623773 | C2 | semidirect |
| 19. C2×C3×Dic10 | D3 | semidirect |
| 29. C2×C5×C3⋊D3 | Q8 | semidirect |
| 59. C2×Dic10 | C3⋊D3 | semidirect |
| 91. C32×C5 | C22⋊Q8 | semidirect |
| 104. C2×C3⋊D3 | Dic10 | semidirect |
| 146. C3×C5 | #946 | semidirect |
| 161. C32 | #4024 | semidirect |
| 175. C5 | #64155 | semidirect |
| 186. C3 | #91410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic10 | 2 |
| C2×C3⋊D3×Dic5 | 2 |
| #10623906 | 2 |
| C5×#3752 | 2 |
| #10623775 | 2 |
| #10623773 | 2 |
| #10623771 | 2 |
| #91410 | 3 |
| #64155 | 5 |