Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D15⋊D5 |
| commutator, hypocenter | C3×C52 | C22×C4 |
| Frattini | C2 | C2×D15⋊D5 |
| Fitting, socle | C22×C3×C52 | C22 |
| prime radical | C22×C5×D15 | C2 |
| cosocle | C2×C3×C52 | C23 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×Dic15 | C2 | semidirect |
| 3. C2×C3×#1039 | C2 | semidirect |
| 4. #10597125 | C2 | direct (N × H) |
| 7. C2×C5×D15 | C4 | semidirect |
| 9. C5×Dic15 | C22 | semidirect |
| 10. C3×#1039 | C22 | semidirect |
| 14. C2×#1039 | D3 | semidirect |
| 17. C2×C3×C52 | C2×C4 | semidirect |
| 19. C5×D15 | C2×C4 | semidirect |
| 22. C2×Dic15 | D5 | semidirect |
| 32. #1039 | C2×D3 | semidirect |
| 36. C3×C52 | C22×C4 | semidirect |
| 40. C2×D15 | Dic5 | semidirect |
| 44. Dic15 | C2×D5 | semidirect |
| 49. C2×C52 | C4×D3 | semidirect |
| 64. C2×C3×C5 | C4×D5 | semidirect |
| 65. C2×C3×C5 | C2×Dic5 | semidirect |
| 68. D15 | C2×Dic5 | semidirect |
| 70. C52 | C2×C4×D3 | semidirect |
| 89. C3×C5 | C2×C4×D5 | semidirect |
| 90. C3×C5 | C22×Dic5 | semidirect |
| 99. C2×C5 | D3×Dic5 | semidirect |
| 100. C2×C5 | #1200 | semidirect |
| 108. C2×C3 | D5×Dic5 | semidirect |
| 112. C5 | C2×D3×Dic5 | semidirect |
| 113. C5 | C2×#1200 | semidirect |
| 119. C3 | C2×D5×Dic5 | semidirect |
| 121. C2 | #10597125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D15 | 2 |
| C2×C5×Dic15 | 2 |
| C2×C3×#1039 | 2 |
| #10597125 | 2 |
| C2×D5×Dic5 | 3 |
| C2×#1200 | 5 |
| C2×D3×Dic5 | 5 |