Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D79 |
| commutator | C2×C4×C79 | C23 |
| Frattini | C2×C4 | C22×D79 |
| Fitting | #102×C79 | C2 |
| socle | C22×C79 | C2×D4 |
| hypercenter | #102 | D79 |
| hypocenter | C79 | #490 |
| LCS | G ▷ C2×C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14579152 | C2 | semidirect |
| 3. #14579083 | C2 | semidirect |
| 4. #14579082 | C2 | semidirect |
| 5. #14579081 | C2 | semidirect |
| 6. #14579071 | C2 | semidirect |
| 7. #102×C79 | C2 | semidirect |
| 52. C79 | #490 | semidirect |
| 59. #102 | D79 | semidirect |