Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
792 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 224 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. C2×D5×C3⋊Dic3 | C2 | semidirect |
| 3. #10623913 | C2 | semidirect |
| 4. C5×#3757 | C2 | semidirect |
| 5. #10623770 | C2 | semidirect |
| 9. C22×C32×D5 | C4 | semidirect |
| 12. C2×C3⋊Dic15 | C22 | semidirect |
| 13. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 22. C22×C32×C5 | C2×C4 | semidirect |
| 27. C2×C32×D5 | C2×C4 | semidirect |
| 36. #3757 | D5 | direct (N × H) |
| 39. C22×C3×D5 | Dic3 | semidirect |
| 50. C32×D5 | C22⋊C4 | semidirect |
| 63. C2×C3⋊Dic3 | C2×D5 | semidirect |
| 65. C22×C3×C5 | C2×Dic3 | semidirect |
| 70. C2×C3×D5 | C2×Dic3 | semidirect |
| 79. C32×C5 | C2×C22⋊C4 | semidirect |
| 82. C22×D5 | C3⋊Dic3 | semidirect |
| 94. C22×C32 | C4×D5 | semidirect |
| 103. C3×D5 | #217 | semidirect |
| 113. C22×C5 | C2×C3⋊Dic3 | semidirect |
| 118. C2×D5 | C2×C3⋊Dic3 | semidirect |
| 132. C3×C5 | C2×#217 | semidirect |
| 139. C22×C3 | D5×Dic3 | semidirect |
| 147. D5 | #3757 | direct (N × H) |
| 148. C32 | D5×C22⋊C4 | semidirect |
| 162. C5 | C2×#3757 | semidirect |
| 169. C22 | D5×C3⋊Dic3 | semidirect |
| 173. C3 | D5×#217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×D5 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| #10623913 | 2 |
| C5×#3757 | 2 |
| #10623770 | 2 |
| D5×#217 | 3 |
| C2×#3757 | 5 |