Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D79 |
| commutator, socle | C22×C79 | C24 |
| Fitting | #121×C79 | C2 |
| hypercenter | #121 | D79 |
| hypocenter | C79 | #525 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11929623 | C2 | semidirect |
| 2. C22×C4×D79 | C2 | semidirect |
| 3. #14579143 | C2 | semidirect |
| 4. #14579141 | C2 | semidirect |
| 5. #14579140 | C2 | semidirect |
| 6. #14579132 | C2 | semidirect |
| 7. #14579129 | C2 | semidirect |
| 8. D4×Dic79 | C2 | semidirect |
| 9. (C22⋊D79)⋊C4 | C2 | semidirect |
| 10. #14579119 | C2 | semidirect |
| 11. #121×C79 | C2 | semidirect |
| 14. C2×Dic158 | C22 | semidirect |
| 18. C22×Dic79 | C22 | semidirect |
| 24. C4⋊Dic79 | C22 | semidirect |
| 25. C4⋊Dic79 | C22 | semidirect |
| 26. Dic79⋊C4 | C22 | semidirect |
| 28. C22⋊Dic79 | C22 | semidirect |
| 31. C4×Dic79 | C22 | semidirect |
| 33. C2×D4×C79 | C22 | semidirect |
| 35. C4⋊C4×C79 | C22 | semidirect |
| 36. C22⋊C4×C79 | C22 | semidirect |
| 61. C4×D79 | D4 | semidirect |
| 68. C22×C79 | #41 | semidirect |
| 76. C2×D79 | #41 | semidirect |
| 91. C79 | #525 | semidirect |
| 99. #121 | D79 | semidirect |
| 110. C2×D4 | C2×D79 | semidirect |
| 122. C4⋊C4 | C2×D79 | semidirect |
| 127. C22⋊C4 | C2×D79 | semidirect |
| 167. C22 | #11929623 | semidirect |