Finite Group DatabasebetaFinite Group DatabasebetaOrder 32305.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C13×C71⋊C7 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C13×C71⋊C5 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | (C71⋊C5)⋊C7 | C13 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C13×C71 | C5×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C71⋊C7 | C5×C13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C5×C7×C13 | — | 71 | 1 | no | maximal, Hall |
| 7 | C71⋊C5 | C7×C13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C7×C13 | — | 71 | 1 | no | Hall |
| 9 | C71 | C5×C7×C13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C5×C13 | — | 71 | 1 | no | Hall |
| 11 | C5×C7 | — | 71 | 1 | no | Hall |
| 12 | C13 | (C71⋊C5)⋊C7 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 13 | C7 | — | 71 | 1 | no | Sylow |
| 14 | C5 | — | 71 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | (C71⋊C5)⋊C7 |
| commutator, cosocle, hypocenter | C71 | C5×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C71 | C5×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C13 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×C71⋊C7 | C5 | semidirect |
| 2. C13×C71⋊C5 | C7 | semidirect |
| 3. (C71⋊C5)⋊C7 | C13 | direct (N × H) |
| 4. C13×C71 | C5×C7 | semidirect |
| 5. C71⋊C7 | C5×C13 | semidirect |
| 7. C71⋊C5 | C7×C13 | semidirect |
| 9. C71 | C5×C7×C13 | semidirect |
| 12. C13 | (C71⋊C5)⋊C7 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×C71⋊C7 | 5 |
| C13×C71⋊C5 | 7 |
| (C71⋊C5)⋊C7 | 13 |
| C5×C7×C13 | 71 |