Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
484 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 87 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. C22×C3⋊#1044 | C2 | semidirect |
| 3. #11925540 | C2 | semidirect |
| 4. C4⋊(C3⋊#1044) | C2 | semidirect |
| 5. C4×C3⋊#1044 | C2 | semidirect |
| 12. C3×C52×D4 | C4 | semidirect |
| 13. C3×C22⋊(C5⋊D5) | C4 | semidirect |
| 14. C3×C4⋊(C5⋊D5) | C4 | semidirect |
| 22. C22×C3×C52 | C2×C4 | semidirect |
| 25. C2×C3×C5⋊D5 | C2×C4 | semidirect |
| 29. C3⋊#1044 | D4 | direct (N × H) |
| 30. C3×C4×C52 | C2×C4 | semidirect |
| 31. C3×#1039 | C2×C4 | semidirect |
| 43. C52×D4 | Dic3 | semidirect |
| 44. C22⋊(C5⋊D5) | Dic3 | semidirect |
| 45. C4⋊(C5⋊D5) | Dic3 | semidirect |
| 60. C3×C5×D4 | AGL(1,𝔽5) | semidirect |
| 67. C22×C52 | C2×Dic3 | semidirect |
| 70. C2×C5⋊D5 | C2×Dic3 | semidirect |
| 75. C4×C52 | C2×Dic3 | semidirect |
| 76. #1039 | C2×Dic3 | semidirect |
| 84. C3×C52 | C4×D4 | semidirect |
| 86. C22×C3×C5 | C2×AGL(1,𝔽5) | semidirect |
| 99. C3×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 119. C5×D4 | ΓL(1,𝔽16) | semidirect |
| 137. C52 | D4×Dic3 | semidirect |
| 141. C3×D4 | #1044 | semidirect |
| 148. C22×C5 | C2×ΓL(1,𝔽16) | semidirect |
| 161. C4×C5 | C2×ΓL(1,𝔽16) | semidirect |
| 170. C3×C5 | D4×AGL(1,𝔽5) | semidirect |
| 175. C22×C3 | C2×#1044 | semidirect |
| 177. C3×C4 | C2×#1044 | semidirect |
| 194. D4 | C3⋊#1044 | direct (N × H) |
| 206. C5 | D4×ΓL(1,𝔽16) | semidirect |
| 211. C22 | C2×C3⋊#1044 | semidirect |
| 216. C4 | C2×C3⋊#1044 | semidirect |
| 217. C3 | D4×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#1044 | 2 |
| C3×D4×C5⋊D5 | 2 |
| #11925540 | 2 |
| C4⋊(C3⋊#1044) | 2 |
| C4×C3⋊#1044 | 2 |
| D4×#1044 | 3 |
| D4×ΓL(1,𝔽16) | 5 |