Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2062 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #99 |
| commutator | C2×C4 | C23×C4×C5 |
| Frattini, cosocle | C2×D4 | C24×C5 |
| prime radical | C22×C5×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C24×C5 ◁ C23×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C5×#99 | C2 | semidirect |
| 3. C2×C5×#353 | C2 | direct (N × H) |
| 5. C23×C5×D4 | C4 | semidirect |
| 8. C2×C5×#127 | C4 | semidirect |
| 11. C22×C42×C5 | C4 | semidirect |
| 13. C2×C5×#99 | C22 | semidirect |
| 14. C5×#353 | C22 | direct (N × H) |
| 15. C22×#353 | C5 | direct (N × H) |
| 27. C22×C5×D4 | C2×C4 | semidirect |
| 35. C5×#127 | C2×C4 | semidirect |
| 40. C2×C42×C5 | C2×C4 | semidirect |
| 42. C5×#99 | C23 | semidirect |
| 44. C22×#99 | C2×C5 | semidirect |
| 45. C2×#353 | C2×C5 | direct (N × H) |
| 73. C2×C5×D4 | C22×C4 | semidirect |
| 87. C42×C5 | C22×C4 | semidirect |
| 89. C23×D4 | C4×C5 | semidirect |
| 92. C2×#127 | C4×C5 | semidirect |
| 95. C22×C42 | C4×C5 | semidirect |
| 97. C2×#99 | C22×C5 | semidirect |
| 98. #353 | C22×C5 | direct (N × H) |
| 148. C22×D4 | C2×C4×C5 | semidirect |
| 156. #127 | C2×C4×C5 | semidirect |
| 161. C2×C42 | C2×C4×C5 | semidirect |
| 163. #99 | C23×C5 | semidirect |
| 178. C22×C5 | #353 | direct (N × H) |
| 213. C2×D4 | C22×C4×C5 | semidirect |
| 227. C42 | C22×C4×C5 | semidirect |
| 233. C2×C5 | C2×#353 | direct (N × H) |
| 273. C5 | C22×#353 | direct (N × H) |
| 288. C22 | C5×#353 | direct (N × H) |
| 301. C2 | C2×C5×#353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#127 | 2 |
| C22×C5×#99 | 2 |
| C2×C5×#353 | 2 |
| C22×#353 | 5 |