Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
958 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 238 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 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C5 |
| prime radical | C2×C5×#562 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#491 | C2 | semidirect |
| 3. C2×C5×#489 | C2 | semidirect |
| 4. C5×#1662 | C2 | direct (N × H) |
| 5. C2×C5×#330 | C2 | semidirect |
| 6. C2×C5×#329 | C2 | semidirect |
| 17. C5×#491 | C22 | semidirect |
| 19. C5×#489 | C22 | semidirect |
| 25. C5×#330 | C22 | semidirect |
| 26. C5×#329 | C22 | semidirect |
| 27. C2×#1662 | C5 | direct (N × H) |
| 67. C2×#491 | C2×C5 | semidirect |
| 68. C2×#489 | C2×C5 | semidirect |
| 69. #1662 | C2×C5 | direct (N × H) |
| 70. C2×#330 | C2×C5 | semidirect |
| 71. C2×#329 | C2×C5 | semidirect |
| 120. #491 | C22×C5 | semidirect |
| 122. #489 | C22×C5 | semidirect |
| 128. #330 | C22×C5 | semidirect |
| 129. #329 | C22×C5 | semidirect |
| 248. C2×C5 | #1662 | direct (N × H) |
| 278. C5 | C2×#1662 | direct (N × H) |
| 294. C2 | C5×#1662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#562 | 2 |
| C2×C5×#491 | 2 |
| C2×C5×#489 | 2 |
| C5×#1662 | 2 |
| C2×C5×#330 | 2 |
| C2×C5×#329 | 2 |
| C2×#1662 | 5 |