Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C3⋊D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C5×D4 | C2 |
| hypercenter | C2×D4 | C3⋊D15 |
| hypocenter | C32×C5 | #121 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×C5×D4 | C2 | semidirect |
| 2. C2×#67184 | C2 | semidirect |
| 3. C2×#67184 | C2 | semidirect |
| 4. C22×C3⋊Dic15 | C2 | semidirect |
| 5. #10623913 | C2 | semidirect |
| 6. #10623908 | C2 | semidirect |
| 7. #10623906 | C2 | semidirect |
| 21. C2×C3×C5×D4 | D3 | semidirect |
| 33. C22×C32×C5 | D4 | semidirect |
| 41. C3⋊Dic15 | D4 | semidirect |
| 43. C2×C32×D4 | D5 | semidirect |
| 68. C2×C5×D4 | C3⋊D3 | semidirect |
| 91. C22×C3×C5 | #67 | semidirect |
| 100. C2×C3×D4 | D15 | semidirect |
| 107. C32×C5 | #121 | semidirect |
| 124. C22×C32 | C22⋊D5 | semidirect |
| 156. C22×C5 | #638 | semidirect |
| 173. C2×D4 | C3⋊D15 | semidirect |
| 178. C3×C5 | #939 | semidirect |
| 184. C22×C3 | #1220 | semidirect |
| 199. C32 | #4085 | semidirect |
| 217. C5 | #64148 | semidirect |
| 226. C22 | #67184 | semidirect |
| 232. C3 | #91828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×#67184 | 2 |
| C22×C3⋊Dic15 | 2 |
| #10623913 | 2 |
| #10623908 | 2 |
| #10623906 | 2 |
| #91828 | 3 |
| #64148 | 5 |