Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 167 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 | C22×C32×C4×C5 | C2 |
| hypercenter | C22×C4 | C3⋊D15 |
| hypocenter | C32×C5 | #121 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×C4×C5 | C2 | semidirect |
| 2. C2×#67184 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊D15) | C2 | semidirect |
| 4. #10623908 | C2 | semidirect |
| 5. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 16. C22×C3×C4×C5 | D3 | semidirect |
| 23. C22×C32×C5 | D4 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 32. C22×C32×C4 | D5 | semidirect |
| 51. C22×C4×C5 | C3⋊D3 | semidirect |
| 66. C22×C3×C5 | D12 | semidirect |
| 72. C3×C4×C5 | #67 | semidirect |
| 74. C22×C3×C4 | D15 | semidirect |
| 79. C32×C5 | #121 | semidirect |
| 90. C22×C32 | D20 | semidirect |
| 96. C32×C4 | C22⋊D5 | semidirect |
| 114. C22×C5 | C4⋊(C3⋊D3) | semidirect |
| 120. C4×C5 | #638 | semidirect |
| 129. C22×C4 | C3⋊D15 | semidirect |
| 132. C3×C5 | #930 | semidirect |
| 135. C22×C3 | D60 | semidirect |
| 141. C3×C4 | #1220 | semidirect |
| 148. C32 | #4076 | semidirect |
| 162. C5 | #64139 | semidirect |
| 168. C22 | C4⋊(C3⋊D15) | semidirect |
| 172. C4 | #67184 | semidirect |
| 173. C3 | #91819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C2×#67184 | 2 |
| C2×C4⋊(C3⋊D15) | 2 |
| #10623908 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| #91819 | 3 |
| #64139 | 5 |