Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
346 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C22 | D32×D5 |
| commutator, Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C2×#67156 | C2 |
| hypocenter | C32×C5 | #123 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#624 | C2 | semidirect |
| 3. #10623815 | C2 | semidirect |
| 4. #10623811 | C2 | semidirect |
| 5. #10623771 | C2 | semidirect |
| 6. C3×#6668 | C2 | semidirect |
| 7. C3×#6667 | C2 | semidirect |
| 29. #6668 | D3 | semidirect |
| 30. #6667 | D3 | semidirect |
| 49. C2×#624 | D5 | semidirect |
| 144. C32×C5 | #123 | semidirect |
| 227. C3×C5 | #883 | semidirect |
| 228. C3×C5 | #894 | semidirect |
| 264. C32 | #4075 | semidirect |
| 288. C5 | #63854 | semidirect |
| 302. C3 | #91351 | semidirect |
| 303. C3 | #91452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67156 | 2 |
| C2×C5×#624 | 2 |
| #10623815 | 2 |
| #10623811 | 2 |
| #10623771 | 2 |
| C3×#6668 | 2 |
| C3×#6667 | 2 |
| #91452 | 3 |
| #91351 | 3 |
| #63854 | 5 |