Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
932 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 157 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, socle, cosocle | C23×C79 | C24 |
| Fitting | C2×#127×C79 | C2 |
| hypercenter | C2×#127 | D79 |
| hypocenter | C79 | #2669 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579133 | C2 | semidirect |
| 2. C2×#14579129 | C2 | semidirect |
| 3. C2×#14579129 | C2 | semidirect |
| 4. #19098477 | C2 | semidirect |
| 5. #19098471 | C2 | semidirect |
| 6. #19098471 | C2 | semidirect |
| 7. #19098454 | C2 | semidirect |
| 8. #19098443 | C2 | semidirect |
| 9. C2×#127×C79 | C2 | semidirect |
| 14. C23×Dic79 | C22 | semidirect |
| 18. C2×Dic79⋊C4 | C22 | semidirect |
| 21. C2×C22⋊Dic79 | C22 | semidirect |
| 22. C2×C22⋊Dic79 | C22 | semidirect |
| 23. C2×C22⋊Dic79 | C22 | semidirect |
| 27. C79⋊#95 | C22 | semidirect |
| 28. C79⋊#95 | C22 | semidirect |
| 31. C22×D4×C79 | C22 | semidirect |
| 32. C22×D4×C79 | C22 | semidirect |
| 34. C2×C42×C79 | C22 | semidirect |
| 63. (C2×D79)⋊C4 | D4 | semidirect |
| 78. C2×D4×C79 | D4 | semidirect |
| 180. C79 | #2669 | semidirect |
| 181. C2×#127 | D79 | semidirect |
| 196. C22×D4 | C2×D79 | semidirect |
| 197. C22×D4 | C2×D79 | semidirect |
| 212. C2×C42 | C2×D79 | semidirect |
| 244. C2×D4 | C22⋊D79 | semidirect |