Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
810 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #1782 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C22×D4 | C23×C5 |
| prime radical | C5×#3508 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C23×C5 ◁ C5×#518 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2127 | C2 | semidirect |
| 3. C2×C5×#353 | C2 | semidirect |
| 4. C5×#1828 | C2 | semidirect |
| 9. C5×#535 | C4 | semidirect |
| 11. C5×#533 | C4 | semidirect |
| 14. C5×#518 | C4 | semidirect |
| 16. C4×C5×#41 | C4 | semidirect |
| 23. #12727 | C5 | direct (N × H) |
| 70. #2127 | C2×C5 | semidirect |
| 71. C2×#353 | C2×C5 | semidirect |
| 72. #1828 | C2×C5 | semidirect |
| 127. #535 | C4×C5 | semidirect |
| 129. #533 | C4×C5 | semidirect |
| 132. #518 | C4×C5 | semidirect |
| 134. C4×#41 | C4×C5 | semidirect |
| 334. C5 | #12727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3508 | 2 |
| C5×#2127 | 2 |
| C2×C5×#353 | 2 |
| C5×#1828 | 2 |
| #12727 | 5 |