Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 150 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×C4×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C32×C4×D5 | C2 | semidirect |
| 4. C4×C3⋊Dic15 | C2 | semidirect |
| 5. #10623774 | C2 | semidirect |
| 6. #10623771 | C2 | semidirect |
| 7. #10623770 | C2 | semidirect |
| 18. #67138 | C4 | direct (N × H) |
| 21. C2×C3×C4×D5 | D3 | semidirect |
| 30. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 33. C2×C32×D5 | C2×C4 | semidirect |
| 34. C32×C4×C5 | D4 | semidirect |
| 36. C3⋊Dic15 | C2×C4 | semidirect |
| 42. C2×C4×C3⋊D3 | D5 | semidirect |
| 65. C2×C4×D5 | C3⋊D3 | semidirect |
| 86. C2×C3×D5 | C4×D3 | semidirect |
| 87. C3×C4×C5 | #67 | semidirect |
| 99. C32×C5 | C4×D4 | semidirect |
| 116. C2×C3⋊D3 | C4×D5 | semidirect |
| 118. C32×C4 | C22⋊D5 | semidirect |
| 144. C2×D5 | C4×C3⋊D3 | semidirect |
| 146. C4×C5 | #638 | semidirect |
| 162. C3×C5 | C4×#67 | semidirect |
| 171. C3×C4 | #1201 | semidirect |
| 180. C32 | C4×C22⋊D5 | semidirect |
| 196. C5 | C4×#638 | semidirect |
| 208. C4 | #67138 | direct (N × H) |
| 209. C3 | C4×#1201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C32×C4×D5 | 2 |
| C2×#67138 | 2 |
| C4×C3⋊Dic15 | 2 |
| #10623774 | 2 |
| #10623771 | 2 |
| #10623770 | 2 |
| C4×#1201 | 3 |
| C4×#638 | 5 |