Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 136 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×C32×D20 | C2 | semidirect |
| 3. C2×#67139 | C2 | semidirect |
| 4. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 15. C2×C3×D20 | D3 | semidirect |
| 23. C32×C4×C5 | D4 | semidirect |
| 24. C5×C3⋊Dic3 | D4 | semidirect |
| 29. C4×C3⋊Dic3 | D5 | semidirect |
| 44. C2×D20 | C3⋊D3 | semidirect |
| 58. C3×C4×C5 | #67 | semidirect |
| 64. C32×C5 | #127 | semidirect |
| 77. C32×C4 | D20 | semidirect |
| 78. C3⋊Dic3 | D20 | semidirect |
| 97. C4×C5 | #638 | semidirect |
| 106. C3×C5 | #940 | semidirect |
| 112. C3×C4 | #1202 | semidirect |
| 118. C32 | #4020 | semidirect |
| 130. C5 | #64149 | semidirect |
| 137. C4 | #67139 | semidirect |
| 138. C3 | #91458 | 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×C32×D20 | 2 |
| C2×#67139 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| #91458 | 3 |
| #64149 | 5 |