Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
291 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11716847 | C2 | semidirect |
| 4. C4⋊#6032 | C2 | semidirect |
| 24. C4×C5×D5 | C8 | semidirect |
| 42. C4×C52 | C2×C8 | semidirect |
| 44. C5×Dic5 | C2×C8 | semidirect |
| 70. C5×D5 | C4⋊C8 | semidirect |
| 93. C4×D5 | #168 | semidirect |
| 102. C52 | C2×C4⋊C8 | semidirect |
| 121. C4×C5 | C2×#168 | semidirect |
| 123. C4×C5 | D5⋊C8 | semidirect |
| 126. Dic5 | C2×#168 | semidirect |
| 148. D5 | C4⋊#168 | semidirect |
| 162. C5 | C2×C4⋊#168 | semidirect |
| 163. C5 | D5⋊(C4⋊C8) | semidirect |
| 173. C4 | D5⋊#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C42×C5×D5 | 2 |
| #11716847 | 2 |
| C4⋊#6032 | 2 |
| D5⋊(C4⋊C8) | 5 |
| C2×C4⋊#168 | 5 |