Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C22×#6045 | C2 | semidirect |
| 3. C2×#87800 | C2 | semidirect |
| 4. C52×C22⋊C8 | C2 | semidirect |
| 5. #11716683 | C2 | semidirect |
| 30. #6045 | D4 | semidirect |
| 35. C5×C22⋊C8 | D5 | semidirect |
| 39. C22×C52 | SD16 | semidirect |
| 83. C22⋊C8 | C5⋊D5 | semidirect |
| 84. C52 | #448 | semidirect |
| 87. C22×C5 | #677 | semidirect |
| 126. C5 | #65027 | semidirect |
| 132. C22 | #87800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| #11717250 | 2 |
| C2×#87800 | 2 |
| C52×C22⋊C8 | 2 |
| #11716683 | 2 |
| #65027 | 5 |