Finite Group DatabasebetaFinite Group DatabasebetaOrder 9006.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C19×C79⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D19×C79 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C19×C79 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C79⋊C3 | — | 19 | 1 | no | maximal, Hall |
| 5 | C79⋊C3 | D19 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 6 | C2×C79 | — | 19 | 1 | no | Hall |
| 7 | C3×D19 | — | 79 | 1 | no | maximal, Hall |
| 8 | C79 | C3×D19 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C3×C19 | — | 79 | 1 | no | Hall |
| 10 | D19 | C79⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 11 | C19 | C2×C79⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C3 | — | 1501 | 1 | no | Hall |
| 13 | C3 | — | 79 | 1 | no | Sylow |
| 14 | C2 | — | 19 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C79 | C2×C3 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C79⋊C3 | C2 | semidirect |
| 2. D19×C79 | C3 | semidirect |
| 3. C19×C79 | C2×C3 | semidirect |
| 5. C79⋊C3 | D19 | direct (N × H) |
| 8. C79 | C3×D19 | semidirect |
| 10. D19 | C79⋊C3 | direct (N × H) |
| 11. C19 | C2×C79⋊C3 | semidirect |