Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| prime radical | C5×#3186 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2232 | C2 | semidirect |
| 3. C5×#2075 | C2 | semidirect |
| 4. C5×#1347 | C2 | semidirect |
| 5. C5×#1314 | C2 | semidirect |
| 11. C2×C5×#107 | C22 | semidirect |
| 16. C5×C22⋊C16 | C22 | semidirect |
| 18. C5×#340 | C22 | semidirect |
| 19. #12278 | C5 | direct (N × H) |
| 45. #2232 | C2×C5 | semidirect |
| 46. #2075 | C2×C5 | semidirect |
| 47. #1347 | C2×C5 | semidirect |
| 48. #1314 | C2×C5 | semidirect |
| 89. C2×#107 | C22×C5 | semidirect |
| 94. C22⋊C16 | C22×C5 | semidirect |
| 96. #340 | C22×C5 | semidirect |
| 254. C5 | #12278 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3186 | 2 |
| C5×#2232 | 2 |
| C5×#2075 | 2 |
| C5×#1347 | 2 |
| C5×#1314 | 2 |
| #12278 | 5 |