Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
262 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 262 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 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C5 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ C5×C8×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2246 | C2 | semidirect |
| 2. C5×#2169 | C2 | semidirect |
| 3. C5×#1667 | C2 | semidirect |
| 4. C5×#1372 | C2 | semidirect |
| 5. C5×#1361 | C2 | semidirect |
| 17. #12433 | C5 | direct (N × H) |
| 35. #2246 | C2×C5 | semidirect |
| 36. #2169 | C2×C5 | semidirect |
| 37. #1667 | C2×C5 | semidirect |
| 38. #1372 | C2×C5 | semidirect |
| 39. #1361 | C2×C5 | semidirect |
| 60. C5×C16 | D8 | semidirect |
| 140. C16 | C5×D8 | semidirect |
| 165. C5 | #12433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2246 | 2 |
| C5×#2169 | 2 |
| C5×#1667 | 2 |
| C5×#1372 | 2 |
| C5×#1361 | 2 |
| #12433 | 5 |