Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
440 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C52×M16 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. C5×#3955 | C2 | direct (N × H) |
| 14. C52×M16 | C22 | semidirect |
| 17. C5×#681 | C22 | semidirect |
| 20. C2×#3955 | C5 | direct (N × H) |
| 42. C2×C5×M16 | D5 | semidirect |
| 43. C2×C5×M16 | C2×C5 | semidirect |
| 44. C2×#681 | C2×C5 | semidirect |
| 46. #3955 | C2×C5 | direct (N × H) |
| 82. C5×M16 | C2×D5 | semidirect |
| 83. C5×M16 | C22×C5 | semidirect |
| 89. #681 | C22×C5 | semidirect |
| 94. C2×C52 | #100 | semidirect |
| 141. C2×M16 | C5×D5 | semidirect |
| 143. C52 | C2×#100 | semidirect |
| 187. M16 | C2×C5×D5 | semidirect |
| 199. C2×C5 | #3955 | direct (N × H) |
| 200. C2×C5 | C5×#100 | semidirect |
| 222. C5 | C2×#3955 | direct (N × H) |
| 223. C5 | C2×C5×#100 | semidirect |
| 239. C2 | C5×#3955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C2×C52×M16 | 2 |
| C2×C5×#681 | 2 |
| C5×#3955 | 2 |
| C2×C5×#100 | 5 |
| C2×#3955 | 5 |