Finite Group DatabasebetaFinite Group DatabasebetaOrder 10506.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C17×C103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D1751 | — | 3 | 1 | no | maximal, Hall |
| 3 | C17×C103 | D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D309 | — | 17 | 1 | no | maximal, Hall |
| 5 | C3×C103 | D17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D103 | — | 51 | 1 | no | Hall |
| 7 | C103 | D51 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | D51 | — | 103 | 1 | no | maximal, Hall |
| 9 | C3×C17 | D103 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D17 | — | 309 | 1 | no | Hall |
| 11 | C17 | D309 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D3 | — | 1751 | 1 | no | Hall |
| 13 | C3 | D1751 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 5253 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C103 | C2 |
| LCS | G ▷ C3×C17×C103 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C17×C103 | C2 | semidirect |
| 3. C17×C103 | D3 | semidirect |
| 5. C3×C103 | D17 | semidirect |
| 7. C103 | D51 | semidirect |
| 9. C3×C17 | D103 | semidirect |
| 11. C17 | D309 | semidirect |
| 13. C3 | D1751 | semidirect |