Finite Group DatabasebetaFinite Group DatabasebetaOrder 10408.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×C1301 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Dic1301 | C2 | 1 | 2 | yes | maximal |
| 3 | C2×C1301 | C22 | 1 | 1 | yes | characteristic |
| 4 | C1301 | Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | Q8 | — | 1301 | 1 | no | maximal, Sylow |
| 6 | C4 | — | 1301 | 2 | no | — |
| 7 | C4 | D1301 | 1 | 1 | yes | characteristic |
| 8 | C2 | C2×D1301 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1301 |
| commutator, socle, prime radical, cosocle | C2×C1301 | C22 |
| Fitting | C4×C1301 | C2 |
| hypercenter | C4 | D1301 |
| hypocenter | C1301 | Q8 |
| LCS | G ▷ C2×C1301 ▷ C1301 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C1301 | Q8 | semidirect |