Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
752 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
| prime radical | C2×#14579157 | C2 |
| hypercenter | #390 | D79 |
| hypocenter | C79 | #2858 |
| 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×#14579160 | C2 | semidirect |
| 3. C2×#14579147 | C2 | semidirect |
| 4. #19098466 | C2 | semidirect |
| 5. #19098465 | C2 | semidirect |
| 6. #19098464 | C2 | semidirect |
| 7. #19098463 | C2 | semidirect |
| 8. C42×Dic79 | C2 | semidirect |
| 9. #390×C79 | C2 | semidirect |
| 52. C4×Dic79 | D4 | semidirect |
| 113. C4×C79 | #124 | semidirect |
| 116. Dic79 | #124 | semidirect |
| 126. C79 | #2858 | semidirect |
| 134. #390 | D79 | semidirect |
| 243. C4 | #14579147 | semidirect |