Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11925361 | C2 | semidirect |
| 5. #11925359 | C2 | semidirect |
| 10. C2×C5×Dic15 | C4 | semidirect |
| 11. #10597126 | C4 | semidirect |
| 51. C2×Dic15 | AGL(1,𝔽5) | semidirect |
| 72. C3×C52 | #117 | semidirect |
| 117. C52 | #877 | semidirect |
| 146. C3×C5 | #4130 | semidirect |
| 175. C5 | #91923 | semidirect |
| 184. C3 | #11717367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597126 | 2 |
| #11925533 | 2 |
| C3×C22⋊#1044 | 2 |
| #11925361 | 2 |
| #11925359 | 2 |
| #11717367 | 3 |
| #91923 | 5 |