Finite Group DatabasebetaFinite Group DatabasebetaOrder 10050.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C25×C67⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D25×C67 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | D5×C67⋊C3 | — | 5 | 1 | no | maximal |
| 4 | C25×C67 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C5×C67⋊C3 | D5 | 1 | 1 | yes | characteristic |
| 6 | D5×C67 | — | 5 | 1 | no | — |
| 7 | C2×C67⋊C3 | — | 25 | 1 | no | Hall |
| 8 | C5×C67 | C3×D5 | 1 | 1 | yes | characteristic |
| 9 | C67⋊C3 | D25 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 10 | C3×D25 | — | 67 | 1 | no | maximal, Hall |
| 11 | C2×C67 | — | 25 | 1 | no | Hall |
| 12 | C3×C25 | — | 67 | 1 | no | Hall |
| 13 | C67 | C3×D25 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | D25 | C67⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 15 | C3×D5 | — | 335 | 1 | no | — |
| 16 | C25 | C2×C67⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | C3×C5 | — | 67 | 1 | no | — |
| 18 | D5 | — | 5 | 1 | no | — |
| 19 | C2×C3 | — | 1675 | 1 | no | Hall |
| 20 | C5 | D5×C67⋊C3 | 1 | 1 | yes | characteristic |
| 21 | C3 | — | 67 | 1 | no | Sylow |
| 22 | C2 | — | 25 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C67 | C2×C3 |
| Frattini | C5 | D5×C67⋊C3 |
| socle | C5×C67 | C3×D5 |
| LCS | G ▷ C25×C67 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C67⋊C3 | C2 | semidirect |
| 2. D25×C67 | C3 | semidirect |
| 4. C25×C67 | C2×C3 | semidirect |
| 9. C67⋊C3 | D25 | direct (N × H) |
| 13. C67 | C3×D25 | semidirect |
| 14. D25 | C67⋊C3 | direct (N × H) |
| 16. C25 | C2×C67⋊C3 | semidirect |