Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C79 |
| Frattini, cosocle | C22×D4 | C23×C79 |
| prime radical | C22×D4×C79 | C23 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C23×C79 ◁ C22×D4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. #354×C79 | C4 | semidirect |
| 54. C2×Q8×C79 | C4⋊C4 | semidirect |
| 90. C42×C79 | C4⋊C4 | semidirect |
| 150. #12967 | C79 | direct (N × H) |
| 163. C79 | #12967 | direct (N × H) |
| 175. #354 | C4×C79 | semidirect |
| 212. C2×Q8 | C4⋊C4×C79 | semidirect |
| 248. C42 | C4⋊C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#2379 | 2 |
| C2×#354×C79 | 2 |
| C79×#1885 | 2 |
| C79×#1867 | 2 |
| C79×#1390 | 2 |
| #12967 | 79 |