Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
476 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11925351 | C2 | direct (N × H) |
| 11. C2×C3×C5×Dic5 | C4 | semidirect |
| 12. C3×#6036 | C4 | semidirect |
| 26. C3×C5×Dic5 | C2×C4 | semidirect |
| 37. C2×C5×Dic5 | Dic3 | semidirect |
| 38. #6036 | Dic3 | semidirect |
| 41. C2×C3×C52 | C4⋊C4 | semidirect |
| 43. C3×C5⋊D5 | C4⋊C4 | semidirect |
| 55. C2×C3×Dic5 | AGL(1,𝔽5) | semidirect |
| 65. C5×Dic5 | C2×Dic3 | semidirect |
| 72. C3×C52 | C2×C4⋊C4 | semidirect |
| 87. C3×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 88. C2×C52 | C4⋊Dic3 | semidirect |
| 90. C5⋊D5 | C4⋊Dic3 | semidirect |
| 106. C2×Dic5 | ΓL(1,𝔽16) | semidirect |
| 112. C2×C3×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 120. C52 | C2×C4⋊Dic3 | semidirect |
| 143. Dic5 | C2×ΓL(1,𝔽16) | semidirect |
| 149. C3×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 160. C2×C5 | C4⋊ΓL(1,𝔽16) | semidirect |
| 179. C2×C3 | #87832 | semidirect |
| 182. C5 | C2×C4⋊ΓL(1,𝔽16) | semidirect |
| 191. C3 | C2×#87832 | semidirect |
| 195. C2 | #11925351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#1044 | 2 |
| C22×C3⋊#1043 | 2 |
| C2×C3×#6036 | 2 |
| #11925351 | 2 |
| C2×#87832 | 3 |
| C2×C4⋊ΓL(1,𝔽16) | 5 |