Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
222 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C2×D8 |
| commutator | C8 | C22×C5×C8 |
| Frattini, cosocle | C4×C8 | C23×C5 |
| socle, prime radical | C22×C5 | C4×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ C5×C82 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. #12044 | C5 | direct (N × H) |
| 19. C5×Q32 | C8 | semidirect |
| 76. Q32 | C5×C8 | semidirect |
| 126. C5 | #12044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q32 | 2 |
| C5×C8×Q16 | 2 |
| C5×#1372 | 2 |
| C5×#1332 | 2 |
| C5×#1311 | 2 |
| #12044 | 5 |