Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C79 | #354 |
| commutator | C42 | C22×C4×C79 |
| Frattini, cosocle | #127 | C23×C79 |
| socle | C2×C79 | C2×#354 |
| prime radical | #532×C79 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C79 ◁ C2×C4×C79 ◁ C22×C4×C79 ◁ #532×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C79×#1412 | C2 | semidirect |
| 4. #533×C79 | C4 | semidirect |
| 6. #491×C79 | C4 | semidirect |
| 11. C2×#97×C79 | C4 | semidirect |
| 93. #13594 | C79 | direct (N × H) |
| 100. #1412 | C2×C79 | semidirect |
| 101. C79 | #13594 | direct (N × H) |
| 102. #533 | C4×C79 | semidirect |
| 104. #491 | C4×C79 | semidirect |
| 109. C2×#97 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3135 | 2 |
| C79×#2126 | 2 |
| C79×#1412 | 2 |
| #13594 | 79 |