Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
876 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C3⋊D15 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C32×C5×#41 | C2 |
| hypercenter | #41 | C3⋊D15 |
| hypocenter | C32×C5 | 2−1+4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5×#41 | C2 | semidirect |
| 2. Q8×C3⋊D15 | C2 | semidirect |
| 3. #10624285 | C2 | semidirect |
| 4. #10624283 | C2 | semidirect |
| 5. C2×#67180 | C2 | semidirect |
| 17. C3×C5×#41 | D3 | semidirect |
| 28. C32×#41 | D5 | semidirect |
| 46. C5×#41 | C3⋊D3 | semidirect |
| 65. C3×#41 | D15 | semidirect |
| 70. C32×C5 | 2−1+4 | semidirect |
| 108. #41 | C3⋊D15 | semidirect |
| 111. C3×C5 | #1010 | semidirect |
| 120. C32 | #4150 | semidirect |
| 133. C5 | #64367 | semidirect |
| 139. C3 | #92101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| Q8×C3⋊D15 | 2 |
| #10624285 | 2 |
| #10624283 | 2 |
| C2×#67180 | 2 |
| #92101 | 3 |
| #64367 | 5 |