Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #386 |
| commutator | C42 | C22×C4×C5 |
| Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C2×C5×#127 | C22 |
| 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 |
|---|---|---|
| 4. C5×#1515 | C2 | semidirect |
| 5. C5×#1288 | C2 | semidirect |
| 9. C5×#486 | C4 | semidirect |
| 18. #9425 | C5 | direct (N × H) |
| 23. C5×C4⋊Q8 | C2×C4 | semidirect |
| 39. C4×C5×C8 | C2×C4 | semidirect |
| 46. #1515 | C2×C5 | semidirect |
| 47. #1288 | C2×C5 | semidirect |
| 79. #486 | C4×C5 | semidirect |
| 115. C4⋊Q8 | C2×C4×C5 | semidirect |
| 131. C4×C8 | C2×C4×C5 | semidirect |
| 204. C5 | #9425 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3138 | 2 |
| C5×#2380 | 2 |
| C5×#1555 | 2 |
| C5×#1515 | 2 |
| C5×#1288 | 2 |
| #9425 | 5 |