Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
296 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #11716685 | C2 | semidirect |
| 4. C5×#3950 | C2 | semidirect |
| 5. #11716616 | C2 | semidirect |
| 12. C5×C8×D5 | C4 | semidirect |
| 24. C52×C8 | C2×C4 | semidirect |
| 25. C5×#168 | C2×C4 | semidirect |
| 35. #3950 | D5 | direct (N × H) |
| 63. C8×D5 | Dic5 | semidirect |
| 68. C5×D5 | #107 | semidirect |
| 89. C5×C8 | C4×D5 | semidirect |
| 90. C5×C8 | C2×Dic5 | semidirect |
| 91. #168 | C2×Dic5 | semidirect |
| 97. C52 | C2×#107 | semidirect |
| 138. D5 | #3950 | direct (N × H) |
| 148. C8 | D5×Dic5 | semidirect |
| 150. C5 | D5×#107 | semidirect |
| 151. C5 | C2×#3950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×D5 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11716685 | 2 |
| C5×#3950 | 2 |
| #11716616 | 2 |
| C2×#3950 | 5 |
| D5×#107 | 5 |