Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
710 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C5 |
| prime radical | C5×#3027 | C2 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3200 | C2 | semidirect |
| 2. C5×#3028 | C2 | semidirect |
| 4. C5×#2129 | C2 | semidirect |
| 5. C5×#2128 | C2 | semidirect |
| 6. C5×#1794 | C2 | semidirect |
| 7. C5×#1391 | C2 | semidirect |
| 33. #13351 | C5 | direct (N × H) |
| 45. C22×C5×Q8 | D4 | semidirect |
| 49. C2×C5×M16 | D4 | semidirect |
| 50. C22×C5×C8 | D4 | semidirect |
| 75. C5×#117 | D4 | semidirect |
| 92. C5×#99 | D4 | semidirect |
| 95. #3200 | C2×C5 | semidirect |
| 96. #3028 | C2×C5 | semidirect |
| 98. #2129 | C2×C5 | semidirect |
| 99. #2128 | C2×C5 | semidirect |
| 100. #1794 | C2×C5 | semidirect |
| 101. #1391 | C2×C5 | semidirect |
| 280. C22×Q8 | C5×D4 | semidirect |
| 284. C2×M16 | C5×D4 | semidirect |
| 285. C22×C8 | C5×D4 | semidirect |
| 310. #117 | C5×D4 | semidirect |
| 327. #99 | C5×D4 | semidirect |
| 506. C5 | #13351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3200 | 2 |
| C5×#3028 | 2 |
| C5×#3027 | 2 |
| C5×#2129 | 2 |
| C5×#2128 | 2 |
| C5×#1794 | 2 |
| C5×#1391 | 2 |
| #13351 | 5 |