Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
226 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 226 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C52 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical | C2×C3×D52 | C2 |
| cosocle | C3×C5×D5 | C23 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊#1042 | C2 | semidirect |
| 3. C2×C5×ΓL(1,𝔽16) | C2 | semidirect |
| 4. D5×ΓL(1,𝔽16) | C2 | direct (N × H) |
| 6. C2×C3×C5⋊D5 | C4 | semidirect |
| 7. C2×C3×C5×D5 | C4 | semidirect |
| 9. C3×D52 | C4 | semidirect |
| 11. C3⋊#1042 | C22 | semidirect |
| 12. C5×ΓL(1,𝔽16) | C22 | semidirect |
| 19. C2×C3×C52 | C2×C4 | semidirect |
| 20. C3×C5⋊D5 | C2×C4 | semidirect |
| 21. C3×C5×D5 | C2×C4 | semidirect |
| 22. C3×C5×D5 | C2×C4 | semidirect |
| 28. C2×ΓL(1,𝔽16) | D5 | direct (N × H) |
| 32. C2×C5⋊D5 | Dic3 | semidirect |
| 33. C2×C5×D5 | Dic3 | semidirect |
| 35. D52 | Dic3 | semidirect |
| 41. C3×C52 | C22×C4 | semidirect |
| 51. C2×C3×D5 | AGL(1,𝔽5) | semidirect |
| 54. ΓL(1,𝔽16) | C2×D5 | direct (N × H) |
| 57. C2×C52 | C2×Dic3 | semidirect |
| 58. C5⋊D5 | C2×Dic3 | semidirect |
| 59. C5×D5 | C2×Dic3 | semidirect |
| 60. C5×D5 | C2×Dic3 | semidirect |
| 75. C2×C3×C5 | C4×D5 | semidirect |
| 76. C2×C3×C5 | C2×AGL(1,𝔽5) | semidirect |
| 80. C3×D5 | C4×D5 | semidirect |
| 81. C3×D5 | C2×AGL(1,𝔽5) | semidirect |
| 83. C52 | C22×Dic3 | semidirect |
| 97. C2×D5 | ΓL(1,𝔽16) | direct (N × H) |
| 105. C3×C5 | C2×C4×D5 | semidirect |
| 106. C3×C5 | C22×AGL(1,𝔽5) | semidirect |
| 118. C2×C5 | D5×Dic3 | semidirect |
| 119. C2×C5 | C2×ΓL(1,𝔽16) | semidirect |
| 123. D5 | D5×Dic3 | semidirect |
| 124. D5 | C2×ΓL(1,𝔽16) | direct (N × H) |
| 134. C2×C3 | D5×AGL(1,𝔽5) | semidirect |
| 136. C5 | C2×D5×Dic3 | semidirect |
| 137. C5 | C22×ΓL(1,𝔽16) | semidirect |
| 145. C3 | C2×D5×AGL(1,𝔽5) | semidirect |
| 150. C2 | D5×ΓL(1,𝔽16) | 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⋊#1042 | 2 |
| C2×C5×ΓL(1,𝔽16) | 2 |
| D5×ΓL(1,𝔽16) | 2 |
| C2×D5×AGL(1,𝔽5) | 3 |
| C22×ΓL(1,𝔽16) | 5 |
| C2×D5×Dic3 | 5 |