Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C2 | D32×AGL(1,𝔽5) |
| commutator, Fitting, socle | C2×C32×C5 | C22×C4 |
| prime radical | #10624049 | C2 |
| cosocle | C32×Dic5 | C23 |
| hypocenter | C32×C5 | #131 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10623980 | C2 | semidirect |
| 3. #10623976 | C2 | semidirect |
| 4. D3×C3⋊#170 | C2 | semidirect |
| 5. #10623968 | C2 | semidirect |
| 6. C3×#6739 | C2 | semidirect |
| 7. C3×#6738 | C2 | semidirect |
| 32. #6739 | D3 | semidirect |
| 33. #6738 | D3 | semidirect |
| 133. C32×C5 | #131 | semidirect |
| 207. C3×C5 | #901 | semidirect |
| 208. C3×C5 | #907 | semidirect |
| 230. C32 | #4131 | semidirect |
| 252. C5 | #63804 | semidirect |
| 261. C3 | #91911 | semidirect |
| 262. C3 | #91929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624049 | 2 |
| #10623980 | 2 |
| #10623976 | 2 |
| D3×C3⋊#170 | 2 |
| #10623968 | 2 |
| C3×#6739 | 2 |
| C3×#6738 | 2 |
| #91929 | 3 |
| #91911 | 3 |
| #63804 | 5 |