Finite Group DatabasebetaFinite Group DatabasebetaOrder 17775.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C52⋊(C79⋊C3) | C3 | 1 | 3 | yes | maximal, direct product factor |
| 2 | C3×C52×C79 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C52×C79 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3×C5×C79 | — | 3 | 2 | no | — |
| 5 | C3×C79⋊C3 | — | 25 | 1 | no | maximal, Hall |
| 6 | C5×C79 | — | 3 | 2 | no | — |
| 7 | C3×C79 | C52⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | C79⋊C3 | — | 25 | 3 | no | — |
| 9 | C3×C52⋊C3 | — | 79 | 1 | no | maximal, Hall |
| 10 | C79 | C3×C52⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C3×C52 | C79⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C52⋊C3 | — | 79 | 3 | no | — |
| 13 | C52 | C3×C79⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C3×C5 | — | 3 | 2 | no | — |
| 15 | C32 | — | 1975 | 1 | no | Sylow |
| 16 | C5 | — | 3 | 2 | no | — |
| 17 | C3 | — | 1975 | 3 | no | — |
| 18 | C3 | C52⋊(C79⋊C3) | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C52⋊(C79⋊C3) |
| commutator, cosocle, hypocenter | C52×C79 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C79 | C3 |
| LCS | G ▷ C52×C79 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52⋊(C79⋊C3) | C3 | direct (N × H) |
| 2. C3×C52×C79 | C3 | semidirect |
| 3. C52×C79 | C32 | semidirect |
| 7. C3×C79 | C52⋊C3 | semidirect |
| 10. C79 | C3×C52⋊C3 | semidirect |
| 11. C3×C52 | C79⋊C3 | semidirect |
| 13. C52 | C3×C79⋊C3 | semidirect |
| 18. C3 | C52⋊(C79⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52⋊(C79⋊C3) | 3 |
| C3×C52×C79 | 3 |
| C3×C79⋊C3 | 25 |
| C3×C52⋊C3 | 79 |