Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
840 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 251 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⋊#1039 | C2 | semidirect |
| 3. #11716701 | C2 | direct (N × H) |
| 4. C24×C52 | C4 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 10. C22×C4×C52 | C4 | semidirect |
| 13. C22⋊#1039 | C22 | semidirect |
| 21. C23×C52 | C2×C4 | semidirect |
| 29. C2×C4×C52 | C2×C4 | semidirect |
| 51. C24×C5 | Dic5 | semidirect |
| 55. C2×C5×D4 | Dic5 | semidirect |
| 57. C22×C4×C5 | Dic5 | semidirect |
| 67. C2×C52 | #99 | semidirect |
| 75. C23×C5 | C2×Dic5 | semidirect |
| 83. C2×C4×C5 | C2×Dic5 | semidirect |
| 89. C52 | C2×#99 | semidirect |
| 106. C24 | #1039 | semidirect |
| 110. C2×D4 | #1039 | semidirect |
| 113. C22×C4 | #1039 | semidirect |
| 121. C2×C5 | #3966 | semidirect |
| 129. C23 | C2×#1039 | semidirect |
| 139. C2×C4 | C2×#1039 | semidirect |
| 140. C5 | C2×#3966 | semidirect |
| 162. C2 | #11716701 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C22⋊#1039 | 2 |
| #11716701 | 2 |
| C2×#3966 | 5 |