Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C22×C5×#41 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2817 | C2 | semidirect |
| 4. C5×#1511 | C2 | semidirect |
| 5. C5×#1306 | C2 | semidirect |
| 21. #9982 | C5 | direct (N × H) |
| 55. #2817 | C2×C5 | semidirect |
| 57. #1511 | C2×C5 | semidirect |
| 58. #1306 | C2×C5 | semidirect |
| 289. C5 | #9982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3007 | 2 |
| C5×#2817 | 2 |
| C5×#1782 | 2 |
| C5×#1511 | 2 |
| C5×#1306 | 2 |
| #9982 | 5 |