Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
824 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 824 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 | #380×C79 | C2 |
| hypercenter | #380 | D79 |
| hypocenter | C79 | #2617 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579135 | C2 | semidirect |
| 2. C2×#14579131 | C2 | semidirect |
| 3. C22×(C2×D79)⋊C4 | C2 | semidirect |
| 4. #19098490 | C2 | semidirect |
| 5. #19098480 | C2 | semidirect |
| 6. #19098473 | C2 | semidirect |
| 7. #19098440 | C2 | semidirect |
| 8. #380×C79 | C2 | semidirect |
| 11. C22×D316 | C22 | semidirect |
| 16. C2×C4⋊Dic79 | C22 | semidirect |
| 21. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 22. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 23. C79⋊#95 | C22 | semidirect |
| 25. C2×C4⋊C4×C79 | C22 | semidirect |
| 27. #95×C79 | C22 | semidirect |
| 32. C23×D79 | D4 | semidirect |
| 55. C22×C4×C79 | D4 | semidirect |
| 134. C79 | #2617 | semidirect |
| 142. #380 | D79 | semidirect |
| 152. C2×C4⋊C4 | C2×D79 | semidirect |
| 161. #95 | C2×D79 | semidirect |
| 183. C22×C4 | D316 | semidirect |