Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 127 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×C8 | C22×D5 |
| commutator, socle, prime radical | C23×C5 | C22×C8 |
| Fitting | C5×#1374 | C2 |
| cosocle | C22×C5×C8 | C23 |
| hypercenter | #1374 | D5 |
| hypocenter | C5 | #12895 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C8 ◁ #1374 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 188. C5 | #12895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600542 | 2 |
| C5×#1374 | 2 |
| #10598295 | 2 |
| #10598148 | 2 |
| #12895 | 5 |