Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1502 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C5 | C22⋊C4 |
| commutator | C2×C4 | C23×C4×C5 |
| Frattini, cosocle | C42 | C24×C5 |
| prime radical | C23×C5×D4 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ C22×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C5×#97 | C2 | semidirect |
| 3. C2×C5×#329 | C2 | direct (N × H) |
| 13. C2×C5×#97 | C22 | semidirect |
| 14. C5×#329 | C22 | direct (N × H) |
| 15. C22×#329 | C5 | direct (N × H) |
| 38. C5×#97 | C23 | semidirect |
| 40. C22×#97 | C2×C5 | semidirect |
| 41. C2×#329 | C2×C5 | direct (N × H) |
| 79. C2×#97 | C22×C5 | semidirect |
| 80. #329 | C22×C5 | direct (N × H) |
| 125. #97 | C23×C5 | semidirect |
| 129. C22×C5 | #329 | direct (N × H) |
| 167. C2×C5 | C2×#329 | direct (N × H) |
| 192. C5 | C22×#329 | direct (N × H) |
| 196. C22 | C5×#329 | direct (N × H) |
| 206. C2 | C2×C5×#329 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#124 | 2 |
| C22×C5×#97 | 2 |
| C2×C5×#329 | 2 |
| C22×#329 | 5 |