Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | #120 |
| commutator | C42 | C22×C4×C79 |
| Frattini, cosocle | C2×C42 | C23×C79 |
| prime radical | C2×#127×C79 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C2×C42×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#2382 | C2 | semidirect |
| 4. C2×#330×C79 | C2 | semidirect |
| 5. C79×#1295 | C2 | semidirect |
| 9. #490×C79 | C4 | semidirect |
| 129. #9002 | C79 | direct (N × H) |
| 137. #2382 | C2×C79 | semidirect |
| 139. C2×#330 | C2×C79 | semidirect |
| 140. #1295 | C2×C79 | semidirect |
| 141. C79 | #9002 | direct (N × H) |
| 145. #490 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#490×C79 | 2 |
| C79×#2382 | 2 |
| C79×#1961 | 2 |
| C2×#330×C79 | 2 |
| C79×#1295 | 2 |
| #9002 | 79 |