Finite Group DatabasebetaFinite Group DatabasebetaOrder 4970.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | (C71⋊C5)⋊C7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D71⋊C7 | C5 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | D71⋊C5 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C71⋊C7 | C2×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C71⋊C5 | C2×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D71 | C5×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C71 | C2×C5×C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C2×C5×C7 | — | 71 | 1 | no | maximal, Hall |
| 9 | C5×C7 | — | 71 | 1 | no | Hall |
| 10 | C2×C7 | — | 71 | 1 | no | Hall |
| 11 | C2×C5 | — | 71 | 1 | no | Hall |
| 12 | C7 | — | 71 | 1 | no | Sylow |
| 13 | C5 | — | 71 | 1 | no | Sylow |
| 14 | C2 | — | 71 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C71 | C2×C5×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. (C71⋊C5)⋊C7 | C2 | semidirect |
| 2. D71⋊C7 | C5 | semidirect |
| 3. D71⋊C5 | C7 | semidirect |
| 4. C71⋊C7 | C2×C5 | semidirect |
| 5. C71⋊C5 | C2×C7 | semidirect |
| 6. D71 | C5×C7 | semidirect |
| 7. C71 | C2×C5×C7 | semidirect |