Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
168 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 38 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. C2×C3×#1044 | C2 | semidirect |
| 3. C2×C3×#1043 | C2 | semidirect |
| 4. #87831 | C3 | direct (N × H) |
| 6. C2×C3×C5×D5 | C4 | semidirect |
| 13. C2×#1044 | C2×C3 | semidirect |
| 14. C2×#1043 | C2×C3 | semidirect |
| 24. C2×C5×D5 | C3×C4 | semidirect |
| 30. C3×C52 | C22⋊C4 | semidirect |
| 36. C2×C3×D5 | AGL(1,𝔽5) | semidirect |
| 57. C52 | C3×C22⋊C4 | semidirect |
| 66. C2×D5 | C3×AGL(1,𝔽5) | semidirect |
| 72. C3×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 95. C5 | C3×C22⋊AGL(1,𝔽5) | semidirect |
| 102. C3 | #87831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D52 | 2 |
| C2×C3×#1044 | 2 |
| C2×C3×#1043 | 2 |
| #87831 | 3 |
| C3×C22⋊AGL(1,𝔽5) | 5 |