Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
428 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 81 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×D5⋊ΓL(1,𝔽16) | C2 | semidirect |
| 3. C4×C3⋊#1044 | C2 | semidirect |
| 4. C4⋊(C3⋊#1043) | C2 | semidirect |
| 5. #11925350 | C2 | semidirect |
| 13. C3×C5×D20 | C4 | semidirect |
| 14. C3×#6037 | C4 | semidirect |
| 22. C2×C3×C5×D5 | C2×C4 | semidirect |
| 26. C3⋊#1044 | D4 | semidirect |
| 28. C3×C4×C52 | C2×C4 | semidirect |
| 29. C3×#1039 | C2×C4 | semidirect |
| 42. C5×D20 | Dic3 | semidirect |
| 43. #6037 | Dic3 | semidirect |
| 57. C3×D20 | AGL(1,𝔽5) | semidirect |
| 61. C2×C5×D5 | C2×Dic3 | semidirect |
| 67. C4×C52 | C2×Dic3 | semidirect |
| 68. #1039 | C2×Dic3 | semidirect |
| 76. C3×C52 | C4×D4 | semidirect |
| 82. C2×C3×D5 | C2×AGL(1,𝔽5) | semidirect |
| 88. C3×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 108. D20 | ΓL(1,𝔽16) | semidirect |
| 120. C52 | D4×Dic3 | semidirect |
| 134. C2×D5 | C2×ΓL(1,𝔽16) | semidirect |
| 140. C4×C5 | C2×ΓL(1,𝔽16) | semidirect |
| 149. C3×C5 | D4×AGL(1,𝔽5) | semidirect |
| 155. C3×C4 | D5⋊AGL(1,𝔽5) | semidirect |
| 180. C5 | D4×ΓL(1,𝔽16) | semidirect |
| 189. C4 | D5⋊ΓL(1,𝔽16) | semidirect |
| 190. C3 | #11717365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊ΓL(1,𝔽16) | 2 |
| C3×#87877 | 2 |
| C4×C3⋊#1044 | 2 |
| C4⋊(C3⋊#1043) | 2 |
| #11925350 | 2 |
| #11717365 | 3 |
| D4×ΓL(1,𝔽16) | 5 |