Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#408 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3199 | C2 | semidirect |
| 2. C5×#2184 | C2 | semidirect |
| 3. C5×#2018 | C2 | semidirect |
| 4. C5×#1349 | C2 | semidirect |
| 5. C5×#1315 | C2 | semidirect |
| 7. C22×C5×D8 | C22 | semidirect |
| 17. C5×C22⋊C16 | C22 | semidirect |
| 18. C5×#341 | C22 | semidirect |
| 19. #12108 | C5 | direct (N × H) |
| 49. #3199 | C2×C5 | semidirect |
| 50. #2184 | C2×C5 | semidirect |
| 51. #2018 | C2×C5 | semidirect |
| 52. #1349 | C2×C5 | semidirect |
| 53. #1315 | C2×C5 | semidirect |
| 95. C22×D8 | C22×C5 | semidirect |
| 105. C22⋊C16 | C22×C5 | semidirect |
| 106. #341 | C22×C5 | semidirect |
| 264. C5 | #12108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3199 | 2 |
| C5×#2184 | 2 |
| C5×#2018 | 2 |
| C5×#1349 | 2 |
| C5×#1315 | 2 |
| #12108 | 5 |