Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
472 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 4. #11716685 | C2 | semidirect |
| 5. #11716684 | C2 | semidirect |
| 8. C52×M16 | C4 | semidirect |
| 26. C52×C8 | C2×C4 | semidirect |
| 44. C5×M16 | Dic5 | semidirect |
| 66. C5×C8 | C2×Dic5 | semidirect |
| 72. C52 | #428 | semidirect |
| 85. M16 | #1039 | semidirect |
| 106. C8 | C2×#1039 | semidirect |
| 107. C5 | #65410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| #11717246 | 2 |
| C2×C4⋊#1039 | 2 |
| #11716685 | 2 |
| #11716684 | 2 |
| #65410 | 5 |