Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. C4×C3⋊#1044 | C2 | semidirect |
| 3. C4×C3⋊#1043 | C2 | semidirect |
| 4. #11925351 | C2 | semidirect |
| 11. C3×C4×C5×D5 | C4 | semidirect |
| 13. C3×D5×Dic5 | C4 | semidirect |
| 38. C4×C5×D5 | Dic3 | semidirect |
| 40. D5×Dic5 | Dic3 | semidirect |
| 55. C3×C4×D5 | AGL(1,𝔽5) | semidirect |
| 71. C3×C52 | #117 | semidirect |
| 105. C4×D5 | ΓL(1,𝔽16) | semidirect |
| 113. C52 | #926 | semidirect |
| 142. C3×C5 | #4130 | semidirect |
| 168. C5 | #91989 | semidirect |
| 177. C3 | #11717356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D52 | 2 |
| C4×C3⋊#1044 | 2 |
| C4×C3⋊#1043 | 2 |
| #11925351 | 2 |
| #11925350 | 2 |
| #11717356 | 3 |
| #91989 | 5 |