Finite Group DatabasebetaFinite Group DatabasebetaOrder 34645.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C41×C169 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C13×C41⋊C5 | C13 | 1 | 1 | yes | maximal, characteristic |
| 3 | C5×C169 | — | 41 | 1 | no | maximal, Hall |
| 4 | C13×C41 | C5×C13 | 1 | 1 | yes | characteristic |
| 5 | C41⋊C5 | C169 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 6 | C169 | C41⋊C5 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 7 | C5×C13 | — | 41 | 1 | no | — |
| 8 | C41 | C5×C169 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C13 | C13×C41⋊C5 | 1 | 1 | yes | characteristic |
| 10 | C5 | — | 41 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | C41⋊C5 |
| commutator, hypocenter | C41 | C5×C169 |
| Frattini | C13 | C13×C41⋊C5 |
| Fitting | C41×C169 | C5 |
| socle, cosocle | C13×C41 | C5×C13 |
| prime radical | C13×C41⋊C5 | C13 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C169 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×C169 | C5 | semidirect |
| 5. C41⋊C5 | C169 | direct (N × H) |
| 6. C169 | C41⋊C5 | direct (N × H) |
| 8. C41 | C5×C169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×C169 | 5 |
| C13×C41⋊C5 | 13 |
| C5×C169 | 41 |