Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
608 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. #11716874 | C3 | direct (N × H) |
| 7. C2×C3×#1043 | C4 | semidirect |
| 8. C2×C3×C4×C52 | C4 | semidirect |
| 9. C2×C3×#1039 | C4 | semidirect |
| 27. C2×#1043 | C3×C4 | semidirect |
| 28. C2×C4×C52 | C3×C4 | semidirect |
| 29. C2×#1039 | C3×C4 | semidirect |
| 41. C2×C3×C4×C5 | AGL(1,𝔽5) | semidirect |
| 55. C3×C52 | #95 | semidirect |
| 75. C2×C4×C5 | C3×AGL(1,𝔽5) | semidirect |
| 84. C52 | C3×#95 | semidirect |
| 91. C2×C3×C4 | #1043 | semidirect |
| 102. C3×C5 | (C2×AGL(1,𝔽5))⋊C4 | semidirect |
| 122. C2×C4 | C3×#1043 | semidirect |
| 128. C5 | C3×(C2×AGL(1,𝔽5))⋊C4 | semidirect |
| 137. C3 | #11716874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#1043 | 2 |
| C2×C3×C4×C5⋊D5 | 2 |
| #11716874 | 3 |
| C3×(C2×AGL(1,𝔽5))⋊C4 | 5 |