Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 82 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 | C5×#3798 | 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. #10623820 | C2 | semidirect |
| 3. #10623796 | C2 | semidirect |
| 4. C3⋊D3×#168 | C2 | semidirect |
| 5. C3×D3×#168 | C2 | semidirect |
| 23. D3×#168 | D3 | semidirect |
| 84. C32×C5 | #131 | semidirect |
| 133. C3×C5 | #901 | semidirect |
| 147. C32 | #4094 | semidirect |
| 162. C5 | #63803 | semidirect |
| 169. C3 | #91286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3798 | 2 |
| #10623820 | 2 |
| #10623796 | 2 |
| C3⋊D3×#168 | 2 |
| C3×D3×#168 | 2 |
| #91286 | 3 |
| #63803 | 5 |