Finite Group DatabasebetaFinite Group DatabasebetaOrder 5150.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C52×C103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D515 | — | 5 | 6 | no | maximal |
| 3 | C5×C103 | D5 | 1 | 6 | yes | complemented |
| 4 | D103 | — | 25 | 1 | no | Hall |
| 5 | C103 | C5⋊D5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C5⋊D5 | — | 103 | 1 | no | maximal, Hall |
| 7 | C52 | D103 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | D5 | — | 515 | 6 | no | — |
| 9 | C5 | D515 | 1 | 6 | yes | complemented |
| 10 | C2 | — | 2575 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C103 | C2 |
| LCS | G ▷ C52×C103 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C103 | C2 | semidirect |
| 3. C5×C103 | D5 | semidirect |
| 5. C103 | C5⋊D5 | semidirect |
| 7. C52 | D103 | semidirect |
| 9. C5 | D515 | semidirect |