Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
406 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 406 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 | C4×C8 | C23×C5 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#436 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3273 | C2 | semidirect |
| 2. C5×#2250 | C2 | semidirect |
| 3. C5×#2206 | C2 | semidirect |
| 4. C5×#1687 | C2 | semidirect |
| 5. C5×#1360 | C2 | semidirect |
| 6. C5×#1333 | C2 | semidirect |
| 7. C5×#1330 | C2 | semidirect |
| 14. C5×#493 | C22 | semidirect |
| 22. C5×C4⋊C16 | C22 | semidirect |
| 24. C5×#346 | C22 | semidirect |
| 25. C5×#334 | C22 | semidirect |
| 27. #12324 | C5 | direct (N × H) |
| 66. #3273 | C2×C5 | semidirect |
| 67. #2250 | C2×C5 | semidirect |
| 68. #2206 | C2×C5 | semidirect |
| 69. #1687 | C2×C5 | semidirect |
| 70. #1360 | C2×C5 | semidirect |
| 71. #1333 | C2×C5 | semidirect |
| 72. #1330 | C2×C5 | semidirect |
| 103. C5×D8 | D8 | semidirect |
| 128. #493 | C22×C5 | semidirect |
| 136. C4⋊C16 | C22×C5 | semidirect |
| 138. #346 | C22×C5 | semidirect |
| 139. #334 | C22×C5 | semidirect |
| 267. D8 | C5×D8 | semidirect |
| 330. C5 | #12324 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3273 | 2 |
| C5×#2250 | 2 |
| C5×#2206 | 2 |
| C5×#1687 | 2 |
| C5×#1360 | 2 |
| C5×#1333 | 2 |
| C5×#1330 | 2 |
| #12324 | 5 |