Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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 | C2×D5×C3⋊D3 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | D5×C3⋊D3 |
| hypocenter | C32×C5 | #127 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×#67140 | C2 | semidirect |
| 4. C32×C4×Dic5 | C2 | semidirect |
| 17. C3×C4×Dic5 | D3 | semidirect |
| 23. C32×C4×C5 | D4 | semidirect |
| 24. C32×Dic5 | D4 | semidirect |
| 28. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 45. C4×Dic5 | C3⋊D3 | semidirect |
| 58. C3×C4×C5 | D12 | semidirect |
| 59. C3×Dic5 | D12 | semidirect |
| 64. C32×C5 | #127 | semidirect |
| 78. C32×C4 | C22⋊D5 | semidirect |
| 96. C4×C5 | C4⋊(C3⋊D3) | semidirect |
| 97. Dic5 | C4⋊(C3⋊D3) | semidirect |
| 106. C3×C5 | #874 | semidirect |
| 113. C3×C4 | #1203 | semidirect |
| 118. C32 | #4086 | semidirect |
| 130. C5 | #64083 | semidirect |
| 137. C4 | #67140 | semidirect |
| 138. C3 | #91451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D15) | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×#67140 | 2 |
| C32×C4×Dic5 | 2 |
| #91451 | 3 |
| #64083 | 5 |