Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 259 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. #11716683 | C2 | direct (N × H) |
| 10. C2×#6045 | C4 | semidirect |
| 28. #6045 | C2×C4 | semidirect |
| 55. C2×C52 | #103 | semidirect |
| 76. C52 | C2×#103 | semidirect |
| 97. C2×C5 | #3948 | semidirect |
| 114. C5 | C2×#3948 | semidirect |
| 124. C2 | #11716683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C22×C52×C8 | 2 |
| C2×C4⋊#1039 | 2 |
| #11716683 | 2 |
| C2×#3948 | 5 |