Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
580 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 580 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 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C5 |
| Frattini, cosocle | C22×D4 | C23×C5 |
| prime radical | C2×C5×#127 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#1867 | C2 | semidirect |
| 5. C5×#1390 | C2 | semidirect |
| 17. C5×#353 | C4 | semidirect |
| 20. #12966 | C5 | direct (N × H) |
| 43. C5×#99 | C2×C4 | semidirect |
| 52. #1867 | C2×C5 | semidirect |
| 53. #1390 | C2×C5 | semidirect |
| 65. C2×C5×D4 | C4⋊C4 | semidirect |
| 95. C42×C5 | C4⋊C4 | semidirect |
| 107. #353 | C4×C5 | semidirect |
| 173. #99 | C2×C4×C5 | semidirect |
| 213. C2×D4 | C5×C4⋊C4 | semidirect |
| 243. C42 | C5×C4⋊C4 | semidirect |
| 292. C5 | #12966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2380 | 2 |
| C2×C5×#353 | 2 |
| C5×#1887 | 2 |
| C5×#1867 | 2 |
| C5×#1390 | 2 |
| #12966 | 5 |