Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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×Q8×D5 | C2 | semidirect |
| 3. #10623912 | C2 | semidirect |
| 4. C5×#3755 | C2 | semidirect |
| 5. #10623767 | C2 | semidirect |
| 6. #10623761 | C2 | semidirect |
| 7. #10623754 | C2 | semidirect |
| 21. C3×Q8×D5 | D3 | semidirect |
| 41. #3755 | D5 | semidirect |
| 58. Q8×D5 | C3⋊D3 | semidirect |
| 90. C32×C5 | #137 | semidirect |
| 141. C3×C5 | #942 | semidirect |
| 152. C32 | #4061 | semidirect |
| 167. C5 | #64151 | semidirect |
| 175. C3 | #91513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×D5 | 2 |
| #10624155 | 2 |
| #10623912 | 2 |
| C5×#3755 | 2 |
| #10623767 | 2 |
| #10623761 | 2 |
| #10623754 | 2 |
| #91513 | 3 |
| #64151 | 5 |