Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3169 | C2 | semidirect |
| 2. C5×#2224 | C2 | semidirect |
| 3. C5×#2215 | C2 | semidirect |
| 4. C5×#2206 | C2 | semidirect |
| 5. C2×C5×C4⋊C16 | C2 | semidirect |
| 20. #33811 | C5 | direct (N × H) |
| 43. #3169 | C2×C5 | semidirect |
| 44. #2224 | C2×C5 | semidirect |
| 45. #2215 | C2×C5 | semidirect |
| 46. #2206 | C2×C5 | semidirect |
| 47. C2×C4⋊C16 | C2×C5 | semidirect |
| 101. C2×C4×C5 | D16 | semidirect |
| 189. C2×C4 | C5×D16 | semidirect |
| 198. C5 | #33811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3169 | 2 |
| C5×#2224 | 2 |
| C5×#2215 | 2 |
| C5×#2206 | 2 |
| C2×C5×C4⋊C16 | 2 |
| #33811 | 5 |