Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
102 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 27 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⋊#1035 | C2 | semidirect |
| 3. C2×C3×#1035 | C2 | semidirect |
| 5. C2×D75 | C4 | semidirect |
| 6. C2×D3×C25 | C4 | semidirect |
| 15. C2×#1035 | D3 | semidirect |
| 32. C3×C25 | C22⋊C4 | semidirect |
| 54. C25 | (C2×D3)⋊C4 | semidirect |
| 71. C2×D3 | #1035 | semidirect |
| 95. C3 | C22⋊#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D25 | 2 |
| C2×C3⋊#1035 | 2 |
| C2×C3×#1035 | 2 |
| C22⋊#1035 | 3 |
| (C2×D3)⋊AGL(1,𝔽5) | 5 |