Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 608 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×#137 | C2 | semidirect |
| 3. #11717267 | C2 | semidirect |
| 4. #11717262 | C2 | semidirect |
| 5. #11716704 | C2 | semidirect |
| 6. #11716692 | C2 | semidirect |
| 7. #11716690 | C2 | semidirect |
| 9. C2×C52×Q8 | C22 | semidirect |
| 19. C52×M16 | C22 | semidirect |
| 23. C4×#1039 | C22 | semidirect |
| 24. #87804 | C22 | semidirect |
| 49. C5×#137 | D5 | semidirect |
| 68. C2×C5×Q8 | C2×D5 | semidirect |
| 78. C5×M16 | C2×D5 | semidirect |
| 114. #137 | C5⋊D5 | semidirect |
| 119. C52 | #455 | semidirect |
| 136. C2×Q8 | C2×C5⋊D5 | semidirect |
| 146. M16 | C2×C5⋊D5 | semidirect |
| 176. C5 | #65491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717522 | 2 |
| C52×#137 | 2 |
| #11717267 | 2 |
| #11717262 | 2 |
| #11716704 | 2 |
| #11716692 | 2 |
| #11716690 | 2 |
| #65491 | 5 |