Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
756 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| prime radical | C2×H(5,𝔽2)×C41 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×#41×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#568 | C2 | semidirect |
| 3. C41×#413 | C2 | semidirect |
| 4. C2×#100×C41 | C2 | semidirect |
| 12. C2×M16×C41 | C22 | semidirect |
| 13. #101×C41 | C22 | semidirect |
| 14. #100×C41 | C22 | semidirect |
| 57. #2888 | C41 | direct (N × H) |
| 63. #568 | C2×C41 | semidirect |
| 64. #413 | C2×C41 | semidirect |
| 65. C2×#100 | C2×C41 | semidirect |
| 66. C41 | #2888 | direct (N × H) |
| 74. C2×M16 | C22×C41 | semidirect |
| 75. #101 | C22×C41 | semidirect |
| 76. #100 | C22×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×H(5,𝔽2)×C41 | 2 |
| C41×#568 | 2 |
| C41×#413 | 2 |
| C2×#100×C41 | 2 |
| #2888 | 41 |