Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
844 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C2×#99 |
| commutator | C24 | C22×C4×C5 |
| Frattini, cosocle | C22×D4 | C23×C5 |
| prime radical | C5×#2408 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×AΣL(1,𝔽16) | C2 | semidirect |
| 3. C5×#1800 | C2 | semidirect |
| 4. C4×C5×#99 | C2 | semidirect |
| 5. C23×C5×D4 | C4 | semidirect |
| 15. C5×#380 | C4 | semidirect |
| 16. C5×#379 | C4 | semidirect |
| 21. #13221 | C5 | direct (N × H) |
| 53. C5×#99 | D4 | semidirect |
| 57. C2×AΣL(1,𝔽16) | C2×C5 | semidirect |
| 58. #1800 | C2×C5 | semidirect |
| 59. C4×#99 | C2×C5 | semidirect |
| 114. C23×D4 | C4×C5 | semidirect |
| 124. #380 | C4×C5 | semidirect |
| 125. #379 | C4×C5 | semidirect |
| 215. #99 | C5×D4 | semidirect |
| 250. C4×C5 | AΣL(1,𝔽16) | semidirect |
| 367. C5 | #13221 | direct (N × H) |
| 400. C4 | C5×AΣL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2408 | 2 |
| C2×C5×AΣL(1,𝔽16) | 2 |
| C5×#1800 | 2 |
| C4×C5×#99 | 2 |
| #13221 | 5 |