Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| prime radical | C5×#3191 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2236 | C2 | semidirect |
| 3. C5×#2233 | C2 | semidirect |
| 4. C5×#2076 | C2 | semidirect |
| 5. C5×#1348 | C2 | semidirect |
| 6. C5×#1347 | C2 | semidirect |
| 7. C5×#1314 | C2 | semidirect |
| 27. #12283 | C5 | direct (N × H) |
| 62. #2236 | C2×C5 | semidirect |
| 63. #2233 | C2×C5 | semidirect |
| 64. #2076 | C2×C5 | semidirect |
| 65. #1348 | C2×C5 | semidirect |
| 66. #1347 | C2×C5 | semidirect |
| 67. #1314 | C2×C5 | semidirect |
| 307. C5 | #12283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3191 | 2 |
| C5×#2236 | 2 |
| C5×#2233 | 2 |
| C5×#2076 | 2 |
| C5×#1348 | 2 |
| C5×#1347 | 2 |
| C5×#1314 | 2 |
| #12283 | 5 |