Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
732 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #1790 |
| commutator | C2×Q8 | C22×C4×C79 |
| Frattini, cosocle | C2×#41 | C23×C79 |
| prime radical | #532×C79 | C22 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×C4×C79 ◁ C2×#41×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#2129 | C2 | semidirect |
| 4. C79×#1909 | C2 | semidirect |
| 8. #563×C79 | C4 | semidirect |
| 10. Q82×C79 | C4 | semidirect |
| 187. #12779 | C79 | direct (N × H) |
| 194. #2129 | C2×C79 | semidirect |
| 196. #1909 | C2×C79 | semidirect |
| 198. C79 | #12779 | direct (N × H) |
| 201. #563 | C4×C79 | semidirect |
| 203. Q82 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3550 | 2 |
| C79×#2129 | 2 |
| C79×#2126 | 2 |
| C79×#1909 | 2 |
| C79×#1884 | 2 |
| #12779 | 79 |