Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 98 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, Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C22×C5×D4 | D4 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ 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×#2084 | C2 | semidirect |
| 4. C5×#2083 | C2 | semidirect |
| 5. C5×#1271 | C2 | semidirect |
| 6. C5×#1271 | C2 | semidirect |
| 27. #7793 | C5 | direct (N × H) |
| 63. #2084 | C2×C5 | semidirect |
| 64. #2083 | C2×C5 | semidirect |
| 65. #1271 | C2×C5 | semidirect |
| 66. #1271 | C2×C5 | semidirect |
| 344. C5 | #7793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2727 | 2 |
| C5×#2093 | 2 |
| C5×#2084 | 2 |
| C5×#2083 | 2 |
| C5×#1271 | 2 |
| C5×#1270 | 2 |
| #7793 | 5 |