Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C5 |
| prime radical | C5×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3216 | C2 | semidirect |
| 3. C5×#3135 | C2 | semidirect |
| 4. C5×#1659 | C2 | semidirect |
| 5. C5×#1536 | C2 | semidirect |
| 6. C5×#1530 | C2 | semidirect |
| 14. C5×#533 | C22 | semidirect |
| 17. C5×#497 | C22 | semidirect |
| 20. C5×#489 | C22 | semidirect |
| 21. C5×#489 | C22 | semidirect |
| 25. C5×#432 | C22 | semidirect |
| 27. C2×C5×#97 | C22 | semidirect |
| 28. C5×#329 | C22 | semidirect |
| 29. C5×#329 | C22 | semidirect |
| 30. #19056 | C5 | direct (N × H) |
| 77. #3216 | C2×C5 | semidirect |
| 78. #3135 | C2×C5 | semidirect |
| 79. #1659 | C2×C5 | semidirect |
| 80. #1536 | C2×C5 | semidirect |
| 81. #1530 | C2×C5 | semidirect |
| 132. #533 | C22×C5 | semidirect |
| 135. #497 | C22×C5 | semidirect |
| 138. #489 | C22×C5 | semidirect |
| 139. #489 | C22×C5 | semidirect |
| 143. #432 | C22×C5 | semidirect |
| 145. C2×#97 | C22×C5 | semidirect |
| 146. #329 | C22×C5 | semidirect |
| 147. #329 | C22×C5 | semidirect |
| 319. C5 | #19056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3549 | 2 |
| C5×#3216 | 2 |
| C5×#3135 | 2 |
| C5×#1659 | 2 |
| C5×#1536 | 2 |
| C5×#1530 | 2 |
| #19056 | 5 |