Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
688 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 159 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. #13102753 | C2 | semidirect |
| 3. C52×#367 | C2 | semidirect |
| 4. #13099536 | C2 | semidirect |
| 5. #13099525 | C2 | semidirect |
| 13. #11716666 | C4 | semidirect |
| 23. #87801 | C2×C4 | semidirect |
| 24. C52×C16 | C2×C4 | semidirect |
| 28. C5×#367 | D5 | semidirect |
| 67. C5×C16 | C4×D5 | semidirect |
| 71. #367 | C5⋊D5 | semidirect |
| 95. C52 | #2177 | semidirect |
| 114. C16 | C4×C5⋊D5 | semidirect |
| 128. C5 | #10600132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716666 | 2 |
| #13102753 | 2 |
| C52×#367 | 2 |
| #13099536 | 2 |
| #13099525 | 2 |
| #10600132 | 5 |