Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
778 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C5 |
| prime radical | C5×#2404 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#342 | C2 | semidirect |
| 3. C5×#1462 | C2 | semidirect |
| 4. C5×#1351 | C2 | semidirect |
| 5. C5×#1343 | C2 | semidirect |
| 6. C22×C5×#41 | C4 | semidirect |
| 11. C5×#393 | C4 | semidirect |
| 13. C5×#392 | C4 | semidirect |
| 18. C5×#381 | C4 | semidirect |
| 23. #11753 | C5 | direct (N × H) |
| 28. C22×C5×Q8 | C2×C4 | semidirect |
| 32. C22×C5×D4 | C2×C4 | semidirect |
| 59. C5×#95 | C2×C4 | semidirect |
| 60. C5×#95 | C2×C4 | semidirect |
| 62. C2×#342 | C2×C5 | semidirect |
| 63. #1462 | C2×C5 | semidirect |
| 64. #1351 | C2×C5 | semidirect |
| 65. #1343 | C2×C5 | semidirect |
| 130. C22×#41 | C4×C5 | semidirect |
| 135. #393 | C4×C5 | semidirect |
| 137. #392 | C4×C5 | semidirect |
| 142. #381 | C4×C5 | semidirect |
| 223. C22×Q8 | C2×C4×C5 | semidirect |
| 227. C22×D4 | C2×C4×C5 | semidirect |
| 254. #95 | C2×C4×C5 | semidirect |
| 255. #95 | C2×C4×C5 | semidirect |
| 447. C5 | #11753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2404 | 2 |
| C2×C5×#342 | 2 |
| C5×#1462 | 2 |
| C5×#1351 | 2 |
| C5×#1343 | 2 |
| #11753 | 5 |