Finite Group DatabasebetaFinite Group DatabasebetaOrder 5056.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic632 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C79⋊C32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q32×C79 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic316 | — | 2 | 1 | no | — |
| 5 | Q16×C79 | — | 2 | 1 | no | — |
| 6 | C16×C79 | C22 | 1 | 1 | yes | characteristic |
| 7 | Q8×C79 | — | 4 | 1 | no | — |
| 8 | Dic158 | — | 4 | 1 | no | — |
| 9 | C8×C79 | D4 | 1 | 1 | yes | characteristic |
| 10 | C4×C79 | — | 8 | 1 | no | — |
| 11 | C4×C79 | D8 | 1 | 1 | yes | characteristic |
| 12 | Dic79 | — | 8 | 1 | no | — |
| 13 | C2×C79 | D16 | 1 | 1 | yes | characteristic |
| 14 | C79 | Q64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | Q64 | — | 79 | 1 | no | maximal, Sylow |
| 16 | Q32 | — | 79 | 1 | no | — |
| 17 | Q32 | D79 | 1 | 1 | yes | characteristic |
| 18 | C32 | — | 79 | 1 | no | — |
| 19 | Q16 | — | 2 | 1 | no | — |
| 20 | Q16 | — | 158 | 1 | no | — |
| 21 | C16 | C2×D79 | 1 | 1 | yes | characteristic |
| 22 | Q8 | — | 4 | 1 | no | — |
| 23 | Q8 | — | 316 | 1 | no | — |
| 24 | C8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 25 | C4 | — | 8 | 1 | no | — |
| 26 | C4 | — | 632 | 1 | no | — |
| 27 | C4 | #11929609 | 1 | 1 | yes | characteristic |
| 28 | C2 | #14579102 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14579102 |
| commutator | C16×C79 | C22 |
| Frattini | C16 | C2×D79 |
| Fitting | Q32×C79 | C2 |
| socle | C2×C79 | D16 |
| hypercenter | Q32 | D79 |
| hypocenter | C79 | Q64 |
| LCS | G ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C79 | Q64 | semidirect |