Finite Group DatabasebetaFinite Group DatabasebetaOrder 10730.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×C29×C37 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C2×C29×C37 | — | 5 | 1 | no | maximal, Hall |
| 3 | C29×C37 | D5 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 4 | D5×C37 | C29 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | D5×C29 | C37 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C5×C37 | C2×C29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C5×C29 | C2×C37 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C2×C37 | — | 5 | 1 | no | Hall |
| 9 | C2×C29 | — | 5 | 1 | no | Hall |
| 10 | C37 | D5×C29 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 11 | C29 | D5×C37 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 12 | D5 | C29×C37 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 13 | C5 | C2×C29×C37 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 5 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29×C37 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C29×C37 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C37 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C29×C37 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C29×C37 | C2 | semidirect |
| 3. C29×C37 | D5 | direct (N × H) |
| 4. D5×C37 | C29 | direct (N × H) |
| 5. D5×C29 | C37 | direct (N × H) |
| 6. C5×C37 | C2×C29 | semidirect |
| 7. C5×C29 | C2×C37 | semidirect |
| 10. C37 | D5×C29 | direct (N × H) |
| 11. C29 | D5×C37 | direct (N × H) |
| 12. D5 | C29×C37 | direct (N × H) |
| 13. C5 | C2×C29×C37 | semidirect |