Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
298 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 90 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, prime radical, cosocle | C22×C32×C5 | C23 |
| hypocenter | C32×C5 | C4⋊Q8 |
| 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 |
|---|---|---|
| 37. C5×C3⋊Dic3 | Q8 | semidirect |
| 41. C3×C5×Dic3 | Q8 | semidirect |
| 111. C5×Dic3 | Dic6 | semidirect |
| 128. C32×C5 | C4⋊Q8 | semidirect |
| 141. C3⋊Dic3 | Dic10 | semidirect |
| 144. C3×Dic3 | Dic10 | semidirect |
| 196. C3×C5 | #888 | semidirect |
| 197. C3×C5 | #944 | semidirect |
| 217. Dic3 | #1204 | semidirect |
| 221. C32 | #4015 | semidirect |
| 240. C5 | #63839 | semidirect |
| 250. C3 | #91389 | semidirect |
| 251. C3 | #91469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67153 | 2 |
| C2×C3×#1204 | 2 |
| #10623832 | 2 |
| Dic3⋊Dic15 | 2 |
| C5×Dic32 | 2 |
| #10623775 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| #91469 | 3 |
| #91389 | 3 |
| #63839 | 5 |