Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #121 |
| 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×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×#67138 | C2 | semidirect |
| 3. C2×#67138 | C2 | semidirect |
| 4. C2×C3⋊D3×Dic5 | C2 | semidirect |
| 5. #10623906 | C2 | semidirect |
| 6. C32×#685 | C2 | semidirect |
| 7. #10623771 | C2 | semidirect |
| 26. C3×#685 | D3 | semidirect |
| 34. C2×C5×C3⋊D3 | D4 | semidirect |
| 40. C3⋊Dic15 | D4 | semidirect |
| 45. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 73. #685 | C3⋊D3 | semidirect |
| 107. C32×C5 | #121 | semidirect |
| 128. C2×C3⋊D3 | C22⋊D5 | semidirect |
| 178. C3×C5 | #884 | semidirect |
| 199. C32 | #4085 | semidirect |
| 217. C5 | #64093 | semidirect |
| 232. C3 | #91453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×#67138 | 2 |
| C2×C3⋊D3×Dic5 | 2 |
| #10623906 | 2 |
| C32×#685 | 2 |
| #10623771 | 2 |
| #91453 | 3 |
| #64093 | 5 |