Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
314 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C24 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C23×C4 |
| prime radical | C23×C41 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#446 | C2 | semidirect |
| 47. #2987 | C41 | direct (N × H) |
| 52. #446 | C2×C41 | semidirect |
| 55. C41 | #2987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#533 | 2 |
| C41×#446 | 2 |
| C41×#433 | 2 |
| C41×#432 | 2 |
| #2987 | 41 |