Finite Group DatabasebetaFinite Group DatabasebetaOrder 33255.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C5×C739 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20268985 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C5×C739 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3×C739 | C3×C5 | 1 | 1 | yes | characteristic |
| 5 | C739 | C5×C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C5×C9 | — | 739 | 1 | no | maximal, Hall |
| 7 | C3×C5 | C739⋊C3 | 1 | 1 | yes | characteristic |
| 8 | C9 | — | 739 | 1 | no | Sylow |
| 9 | C5 | #20268985 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 10 | C3 | C5×C739⋊C3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C739⋊C3 |
| commutator, hypocenter | C739 | C5×C9 |
| Frattini | C3 | C5×C739⋊C3 |
| Fitting, socle, prime radical | C3×C5×C739 | C3 |
| cosocle | C3×C739 | C3×C5 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C3×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20268985 | C5 | direct (N × H) |
| 3. C5×C739 | C9 | semidirect |
| 5. C739 | C5×C9 | semidirect |
| 9. C5 | #20268985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C739 | 3 |
| #20268985 | 5 |
| C5×C9 | 739 |