Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
656 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C22⋊#1044 | C2 | semidirect |
| 3. #11716904 | C2 | direct (N × H) |
| 4. C24×C52 | C4 | semidirect |
| 9. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 11. C22×#1039 | C4 | semidirect |
| 13. C22⋊#1044 | C22 | semidirect |
| 19. C23×C52 | C2×C4 | semidirect |
| 31. C2×#1039 | C2×C4 | semidirect |
| 53. C24×C5 | AGL(1,𝔽5) | semidirect |
| 73. C2×C52 | #99 | semidirect |
| 86. C23×C5 | C2×AGL(1,𝔽5) | semidirect |
| 112. C52 | C2×#99 | semidirect |
| 145. C24 | #1044 | semidirect |
| 162. C2×C5 | #4011 | semidirect |
| 177. C23 | C2×#1044 | semidirect |
| 186. C5 | C2×#4011 | semidirect |
| 208. C2 | #11716904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C2×C22⋊#1044 | 2 |
| #11716904 | 2 |
| C2×#4011 | 5 |