Finite Group DatabasebetaFinite Group DatabasebetaOrder 1925.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×C7×C11 | C5 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×C11⋊C5 | C5 | 1 | 5 | yes | maximal, direct product factor |
| 3 | C5×C11⋊C5 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C52×C7 | — | 11 | 1 | no | maximal, Hall |
| 5 | C7×C11 | C52 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C5×C11 | C5×C7 | 1 | 1 | yes | characteristic, complemented |
| 7 | C11⋊C5 | C5×C7 | 1 | 5 | yes | direct product factor |
| 8 | C5×C7 | — | 11 | 5 | no | — |
| 9 | C5×C7 | C11⋊C5 | 1 | 1 | yes | characteristic, direct product factor |
| 10 | C52 | — | 11 | 1 | no | Sylow |
| 11 | C11 | C52×C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C7 | C5×C11⋊C5 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 13 | C5 | — | 11 | 5 | no | — |
| 14 | C5 | C7×C11⋊C5 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C7×C11 | C5 | semidirect |
| 2. C7×C11⋊C5 | C5 | direct (N × H) |
| 3. C5×C11⋊C5 | C7 | direct (N × H) |
| 5. C7×C11 | C52 | semidirect |
| 6. C5×C11 | C5×C7 | semidirect |
| 7. C11⋊C5 | C5×C7 | direct (N × H) |
| 9. C5×C7 | C11⋊C5 | direct (N × H) |
| 11. C11 | C52×C7 | semidirect |
| 12. C7 | C5×C11⋊C5 | direct (N × H) |
| 14. C5 | C7×C11⋊C5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×C11 | 5 |
| C7×C11⋊C5 | 5 |
| C5×C11⋊C5 | 7 |
| C52×C7 | 11 |