Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D32×D5 |
| commutator, socle | C2×C32×C5 | C22×C4 |
| Fitting, cosocle | C32×C4×C5 | C23 |
| prime radical | #10624223 | C2 |
| hypocenter | C32×C5 | #131 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10623795 | C2 | semidirect |
| 3. C3⋊C8×D15 | C2 | semidirect |
| 4. C5×#3710 | C2 | semidirect |
| 5. #10623755 | C2 | semidirect |
| 6. C3×#6651 | C2 | semidirect |
| 7. C3×#6648 | C2 | semidirect |
| 30. #6651 | D3 | semidirect |
| 35. #6648 | D3 | semidirect |
| 50. #3710 | D5 | semidirect |
| 133. C32×C5 | #131 | semidirect |
| 207. C3×C5 | #901 | semidirect |
| 208. C3×C5 | #907 | semidirect |
| 230. C32 | #4047 | semidirect |
| 252. C5 | #63804 | semidirect |
| 261. C3 | #91265 | semidirect |
| 262. C3 | #91267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624223 | 2 |
| #10623795 | 2 |
| C3⋊C8×D15 | 2 |
| C5×#3710 | 2 |
| #10623755 | 2 |
| C3×#6651 | 2 |
| C3×#6648 | 2 |
| #91267 | 3 |
| #91265 | 3 |
| #63804 | 5 |