Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
13856 conjugacy classes of subgroups; only the 678 normal subgroups are shown.
This group has 13856 conjugacy classes of subgroups — too many to draw. Only its 678 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 |
|---|---|---|
| 2. C22×C22⋊#1043 | C2 | semidirect |
| 3. #13104812 | C2 | direct (N × H) |
| 4. C25×C52 | C4 | semidirect |
| 6. C24×C5⋊D5 | C4 | semidirect |
| 7. C24×C5⋊D5 | C4 | semidirect |
| 10. C23×#1043 | C22 | semidirect |
| 12. C2×C22⋊#1043 | C22 | semidirect |
| 16. C24×C52 | C2×C4 | semidirect |
| 25. C23×C5⋊D5 | C2×C4 | semidirect |
| 30. C22×#1043 | C23 | semidirect |
| 38. C23×C52 | C22⋊C4 | semidirect |
| 50. C22×C5⋊D5 | C22⋊C4 | semidirect |
| 51. C22×C5⋊D5 | C22⋊C4 | semidirect |
| 59. C25×C5 | AGL(1,𝔽5) | semidirect |
| 73. C22×C52 | C2×C22⋊C4 | semidirect |
| 81. C2×C5⋊D5 | C2×C22⋊C4 | semidirect |
| 87. C24×C5 | C2×AGL(1,𝔽5) | semidirect |
| 107. C2×C52 | #379 | semidirect |
| 110. C5⋊D5 | #379 | semidirect |
| 115. C23×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 141. C25 | #1043 | semidirect |
| 145. C52 | C2×#379 | semidirect |
| 150. C22×C5 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 176. C24 | C2×#1043 | semidirect |
| 181. C2×C5 | #65800 | semidirect |
| 205. C23 | C22⋊#1043 | semidirect |
| 210. C5 | C2×#65800 | semidirect |
| 224. C22 | C2×C22⋊#1043 | semidirect |
| 231. C2 | #13104812 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C5⋊D5 | 2 |
| C22×C22⋊#1043 | 2 |
| #13104812 | 2 |
| C2×#65800 | 5 |