Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1000 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 | #390×C79 | C2 |
| hypercenter | #390 | D79 |
| hypocenter | C79 | #2679 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579131 | C2 | semidirect |
| 2. C2×#14579129 | C2 | semidirect |
| 3. #19098480 | C2 | semidirect |
| 4. #19098479 | C2 | semidirect |
| 5. #19098465 | C2 | semidirect |
| 6. #390×C79 | C2 | semidirect |
| 7. C24×D79 | C22 | semidirect |
| 13. C2×C4⋊Dic79 | C22 | semidirect |
| 14. C2×C22⋊Dic79 | C22 | semidirect |
| 15. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 16. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 17. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 18. C79⋊#95 | C22 | semidirect |
| 20. C2×C4⋊C4×C79 | C22 | semidirect |
| 21. C2×C22⋊C4×C79 | C22 | semidirect |
| 22. C2×C42×C79 | C22 | semidirect |
| 33. C2×D316 | D4 | semidirect |
| 46. C2×D4×C79 | D4 | semidirect |
| 116. C79 | #2679 | semidirect |
| 122. #390 | D79 | semidirect |
| 131. C2×C4⋊C4 | C2×D79 | semidirect |
| 136. C2×C22⋊C4 | C2×D79 | semidirect |
| 137. C2×C42 | C2×D79 | semidirect |
| 156. C2×D4 | D316 | semidirect |