Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
6046 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 6046 conjugacy classes of subgroups — too many to draw. Only its 1539 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C24×C5×Q8 | C2 |
| socle, prime radical | C25×C5 | C23 |
| hypercenter | C24×Q8 | D5 |
| hypocenter | C5 | C22×#395 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C25 ◁ C24×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#65518 | C2 | direct (N × H) |
| 12. #65518 | C22 | direct (N × H) |
| 25. C23×Dic5 | Q8 | semidirect |
| 50. C22×Dic5 | C2×Q8 | semidirect |
| 79. C2×Dic5 | C22×Q8 | semidirect |
| 96. C22×C5 | #395 | semidirect |
| 125. C2×C5 | C2×#395 | semidirect |
| 146. C5 | C22×#395 | semidirect |
| 147. C22 | #65518 | direct (N × H) |
| 157. C2 | C2×#65518 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×Q8 | 2 |
| C23×#683 | 2 |
| C2×#65518 | 2 |
| C22×#3963 | 2 |
| C22×#395 | 5 |