Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×C3×C4×C52 | C2 | semidirect |
| 2. C5×#1220 | C2 | semidirect |
| 3. C5×D60 | C2 | semidirect |
| 4. C4×C5×D15 | C2 | semidirect |
| 5. C5×Dic30 | C2 | semidirect |
| 12. #6817 | C5 | direct (N × H) |
| 14. C2×C4×C52 | D3 | semidirect |
| 23. C2×C3×C4×C5 | D5 | semidirect |
| 24. C2×C3×C4×C5 | C2×C5 | semidirect |
| 25. #1220 | C2×C5 | semidirect |
| 26. D60 | C2×C5 | semidirect |
| 27. C4×D15 | C2×C5 | semidirect |
| 28. Dic30 | C2×C5 | semidirect |
| 40. C3×C52 | #41 | semidirect |
| 63. C2×C4×C5 | C5×D3 | semidirect |
| 64. C2×C4×C5 | D15 | semidirect |
| 77. C52 | #235 | semidirect |
| 78. C2×C3×C4 | C5×D5 | semidirect |
| 98. C3×C5 | #709 | semidirect |
| 99. C3×C5 | C5×#41 | semidirect |
| 117. C2×C4 | C5×D15 | semidirect |
| 122. C5 | C5×#235 | semidirect |
| 123. C5 | #6817 | direct (N × H) |
| 129. C3 | C5×#709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C52 | 2 |
| C5×#1220 | 2 |
| C5×D60 | 2 |
| C4×C5×D15 | 2 |
| C5×Dic30 | 2 |
| C5×#709 | 3 |
| #6817 | 5 |
| C5×#235 | 5 |