Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator | C22×C79 | C23×C4 |
| Fitting | #380×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C24×D79 | C22 |
| hypercenter | #380 | D79 |
| hypocenter | C79 | #2315 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #19098437 | C2 | semidirect |
| 4. #19098434 | C2 | semidirect |
| 5. #19098423 | C2 | semidirect |
| 6. #19098421 | C2 | semidirect |
| 7. #380×C79 | C2 | semidirect |
| 11. C2×C4⋊Dic79 | C22 | semidirect |
| 12. C2×Dic79⋊C4 | C22 | semidirect |
| 14. C2×(C2×D79)⋊C4 | C4 | semidirect |
| 19. C79⋊#95 | C22 | semidirect |
| 20. C79⋊#95 | C22 | semidirect |
| 22. C2×C4⋊C4×C79 | C22 | semidirect |
| 24. #95×C79 | C22 | semidirect |
| 32. C22×Dic79 | C2×C4 | semidirect |
| 42. (C2×D79)⋊C4 | C2×C4 | semidirect |
| 43. (C2×D79)⋊C4 | C2×C4 | semidirect |
| 46. C22×C4×C79 | C2×C4 | semidirect |
| 64. C22×D79 | C4⋊C4 | semidirect |
| 112. C79 | #2315 | semidirect |
| 119. #380 | D79 | semidirect |
| 126. C2×C4⋊C4 | C2×D79 | semidirect |
| 136. #95 | C2×D79 | semidirect |
| 152. C22×C4 | C4×D79 | semidirect |