Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
186 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C4⋊Dic79 | C2 | 1 | 6 | yes | maximal |
| 2 | C2×C42×C79 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C22×Dic79 | C22 | 1 | 4 | yes | — |
| 4 | C4⋊Dic79 | — | 2 | 12 | no | — |
| 5 | C22×C4×C79 | C22 | 1 | 3 | yes | — |
| 6 | C42×C79 | C4 | 1 | 4 | yes | complemented |
| 7 | C23×C79 | C23 | 1 | 1 | yes | characteristic |
| 8 | C2×C4×C79 | C2×C4 | 1 | 6 | yes | — |
| 9 | C2×C4×C79 | D4 | 1 | 6 | yes | — |
| 10 | C2×C4×C79 | Q8 | 1 | 6 | yes | — |
| 11 | C2×Dic79 | — | 2 | 12 | no | — |
| 12 | C22×C79 | C22×C4 | 1 | 1 | yes | characteristic |
| 13 | C22×C79 | C2×D4 | 1 | 3 | yes | — |
| 14 | C22×C79 | C2×Q8 | 1 | 3 | yes | — |
| 15 | C4×C79 | C4⋊C4 | 1 | 12 | yes | complemented |
| 16 | Dic79 | — | 4 | 4 | no | — |
| 17 | C2×C79 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 18 | C2×C79 | #127 | 1 | 1 | yes | characteristic |
| 19 | C2×C79 | C4⋊Q8 | 1 | 3 | yes | — |
| 20 | C79 | #384 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | #384 | — | 79 | 1 | no | maximal, Sylow |
| 22 | C2×C4⋊C4 | — | 79 | 6 | no | — |
| 23 | C2×C42 | D79 | 1 | 1 | yes | characteristic |
| 24 | C22×C4 | — | 79 | 4 | no | — |
| 25 | C22×C4 | C2×D79 | 1 | 3 | yes | — |
| 26 | C4⋊C4 | — | 158 | 12 | no | — |
| 27 | C42 | Dic79 | 1 | 4 | yes | complemented |
| 28 | C23 | C22×D79 | 1 | 1 | yes | characteristic |
| 29 | C2×C4 | — | 158 | 12 | no | — |
| 30 | C2×C4 | Dic158 | 1 | 6 | yes | — |
| 31 | C2×C4 | D316 | 1 | 6 | yes | — |
| 32 | C2×C4 | C2×Dic79 | 1 | 6 | yes | — |
| 33 | C22 | C22×Dic79 | 1 | 1 | yes | characteristic |
| 34 | C22 | C2×D316 | 1 | 3 | yes | — |
| 35 | C22 | C2×Dic158 | 1 | 3 | yes | — |
| 36 | C4 | — | 316 | 4 | no | — |
| 37 | C4 | C4⋊Dic79 | 1 | 12 | yes | complemented |
| 38 | C2 | C2×C4⋊Dic79 | 1 | 3 | yes | — |
| 39 | C2 | #14579158 | 1 | 1 | yes | characteristic |
| 40 | C2 | #14579161 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D79 |
| commutator | C22×C79 | C22×C4 |
| Fitting | C2×C42×C79 | C2 |
| socle | C23×C79 | C23 |
| hypercenter | C2×C42 | D79 |
| hypocenter | C79 | #384 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C42×C79 | C4 | semidirect |
| 15. C4×C79 | C4⋊C4 | semidirect |
| 20. C79 | #384 | semidirect |
| 27. C42 | Dic79 | semidirect |
| 37. C4 | C4⋊Dic79 | semidirect |