Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
640 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 111 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. C52×#123 | C2 | semidirect |
| 3. #11717249 | C2 | semidirect |
| 4. #11716701 | C2 | semidirect |
| 5. #11716673 | C2 | semidirect |
| 7. C22×C4×C52 | C22 | semidirect |
| 15. C52×C22⋊C4 | C22 | semidirect |
| 16. C22⋊#1039 | C22 | semidirect |
| 39. C5×#123 | D5 | semidirect |
| 57. C22×C4×C5 | C2×D5 | semidirect |
| 65. C5×C22⋊C4 | C2×D5 | semidirect |
| 95. #123 | C5⋊D5 | semidirect |
| 98. C52 | #458 | semidirect |
| 118. C22×C4 | C2×C5⋊D5 | semidirect |
| 124. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 148. C5 | #65342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717517 | 2 |
| C52×#123 | 2 |
| #11717249 | 2 |
| #11716701 | 2 |
| #11716673 | 2 |
| #65342 | 5 |