Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
426 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D79 |
| commutator | C22×C79 | C24 |
| Frattini | C22 | C23×D79 |
| Fitting | C23×C4×C79 | C2 |
| socle | C23×C79 | C23 |
| hypercenter | C23×C4 | D79 |
| hypocenter | C79 | C2×#121 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D316 | C2 | semidirect |
| 2. C22×C22⋊D79 | C2 | semidirect |
| 3. #14579135 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic79 | C2 | semidirect |
| 5. C2×(C2×D79)⋊C4 | C2 | semidirect |
| 6. C23×C4×C79 | C2 | semidirect |
| 9. C2×D316 | C22 | semidirect |
| 11. C2×C22⋊D79 | C22 | semidirect |
| 13. C4⋊Dic79 | C22 | semidirect |
| 14. (C2×D79)⋊C4 | C22 | semidirect |
| 19. C22×C4×C79 | C22 | semidirect |
| 22. C23×C79 | D4 | semidirect |
| 31. C2×C4×C79 | D4 | semidirect |
| 43. C22×C79 | C2×D4 | semidirect |
| 51. C4×C79 | C2×D4 | semidirect |
| 54. C2×C79 | #121 | semidirect |
| 59. C79 | C2×#121 | semidirect |
| 63. C23×C4 | D79 | semidirect |
| 77. C22×C4 | C2×D79 | semidirect |
| 86. C23 | D316 | semidirect |
| 95. C2×C4 | C22⋊D79 | semidirect |
| 107. C22 | C2×D316 | semidirect |
| 112. C4 | C2×C22⋊D79 | semidirect |
| 115. C2 | #14579135 | direct (N × H) |