Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
326 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 1. C4×#6045 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 4. C5×C4⋊#168 | C2 | semidirect |
| 5. #11716604 | C2 | semidirect |
| 25. #6045 | D4 | semidirect |
| 41. C4⋊#168 | D5 | semidirect |
| 47. C4×C52 | SD16 | semidirect |
| 120. C52 | #460 | semidirect |
| 136. C4×C5 | #677 | semidirect |
| 137. C4×C5 | #687 | semidirect |
| 183. C5 | #65137 | semidirect |
| 184. C5 | #65364 | semidirect |
| 192. C4 | #87773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C5×#4020 | 2 |
| C2×#87773 | 2 |
| C5×C4⋊#168 | 2 |
| #11716604 | 2 |
| #65364 | 5 |
| #65137 | 5 |