Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3342 conjugacy classes of subgroups; only the 739 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 739 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D5 |
| commutator | C23×C5 | C23×C4 |
| Fitting | C2×C43×C5 | C2 |
| socle, cosocle | C24×C5 | C24 |
| prime radical | C22×#4020 | C2 |
| hypercenter | C2×C43 | D5 |
| hypocenter | C5 | #14713 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C43×C5 | C2 | semidirect |
| 3. C2×#65228 | C2 | semidirect |
| 4. C2×#65224 | C2 | semidirect |
| 12. C2×#4020 | C4 | semidirect |
| 31. C2×C42×C5 | D4 | semidirect |
| 39. C2×C43 | D5 | semidirect |
| 62. C42×C5 | C22⋊C4 | semidirect |
| 95. C2×C4×C5 | #127 | semidirect |
| 116. C2×C42 | D20 | semidirect |
| 131. C4×C5 | #390 | semidirect |
| 157. C42 | #685 | semidirect |
| 183. C2×C4 | #4020 | semidirect |
| 187. C5 | #14713 | semidirect |
| 202. C4 | #65228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4020 | 2 |
| C2×C43×C5 | 2 |
| C2×#65228 | 2 |
| C2×#65224 | 2 |
| #14713 | 5 |