Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #120 |
| commutator | C42 | C22×C4×C5 |
| Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C22×C5×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1993 | C2 | semidirect |
| 5. C5×#1295 | C2 | semidirect |
| 11. C5×#497 | C4 | semidirect |
| 22. #9003 | C5 | direct (N × H) |
| 37. C5×C4⋊Q8 | C2×C4 | semidirect |
| 53. C5×#97 | C2×C4 | semidirect |
| 59. #1993 | C2×C5 | semidirect |
| 61. #1295 | C2×C5 | semidirect |
| 111. #497 | C4×C5 | semidirect |
| 173. C4⋊Q8 | C2×C4×C5 | semidirect |
| 189. #97 | C2×C4×C5 | semidirect |
| 298. C5 | #9003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#497 | 2 |
| C5×#2379 | 2 |
| C5×#1993 | 2 |
| C2×C5×#329 | 2 |
| C5×#1295 | 2 |
| #9003 | 5 |