Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10624027 |
| commutator, Fitting, cosocle | C32×C4×C5 | C23 |
| Frattini, hypercenter | C4 | D32×D5 |
| socle | C2×C32×C5 | C2×D4 |
| hypocenter | C32×C5 | #135 |
| LCS | G ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624200 | C2 | semidirect |
| 2. C3×#6768 | C2 | semidirect |
| 3. #10623817 | C2 | semidirect |
| 4. #10623805 | C2 | semidirect |
| 5. C5×#3713 | C2 | semidirect |
| 6. #10623767 | C2 | semidirect |
| 7. C3×#6656 | C2 | semidirect |
| 25. #6768 | D3 | semidirect |
| 34. #6656 | D3 | semidirect |
| 50. #3713 | D5 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 206. C3×C5 | #916 | semidirect |
| 207. C3×C5 | #950 | semidirect |
| 229. C32 | #4058 | semidirect |
| 250. C5 | #63947 | semidirect |
| 259. C3 | #91490 | semidirect |
| 260. C3 | #91499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624200 | 2 |
| C3×#6768 | 2 |
| #10623817 | 2 |
| #10623805 | 2 |
| C5×#3713 | 2 |
| #10623767 | 2 |
| C3×#6656 | 2 |
| #91499 | 3 |
| #91490 | 3 |
| #63947 | 5 |