Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 147 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 | #127 |
| 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×C4⋊(C3⋊D15) | C2 | semidirect |
| 4. C4×C3⋊Dic15 | C2 | semidirect |
| 14. C2×C3×C5×D4 | D3 | semidirect |
| 23. C32×C4×C5 | D4 | semidirect |
| 24. C3⋊Dic15 | D4 | semidirect |
| 26. C2×C32×D4 | D5 | semidirect |
| 42. C2×C5×D4 | C3⋊D3 | semidirect |
| 58. C3×C4×C5 | #67 | semidirect |
| 60. C2×C3×D4 | D15 | semidirect |
| 64. C32×C5 | #127 | semidirect |
| 77. C32×C4 | C22⋊D5 | semidirect |
| 96. C4×C5 | #638 | semidirect |
| 104. C2×D4 | C3⋊D15 | semidirect |
| 106. C3×C5 | #940 | semidirect |
| 112. C3×C4 | #1220 | semidirect |
| 118. C32 | #4086 | semidirect |
| 130. C5 | #64149 | semidirect |
| 137. C4 | #67184 | semidirect |
| 138. C3 | #91829 | 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 |
| C2×C4⋊(C3⋊D15) | 2 |
| C4×C3⋊Dic15 | 2 |
| #91829 | 3 |
| #64149 | 5 |