Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
880 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D52 |
| commutator, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting, prime radical | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#6039 | C2 | semidirect |
| 4. #11717100 | C2 | direct (N × H) |
| 5. C2×#87781 | C2 | semidirect |
| 6. C2×#87780 | C2 | semidirect |
| 15. C2×#6039 | C22 | semidirect |
| 17. #87781 | C22 | semidirect |
| 18. #87780 | C22 | semidirect |
| 22. C23×C52 | Q8 | semidirect |
| 49. C22×C52 | C2×Q8 | semidirect |
| 79. C2×C52 | C22⋊Q8 | semidirect |
| 90. C23×C5 | Dic10 | semidirect |
| 118. C52 | C2×C22⋊Q8 | semidirect |
| 131. C22×C5 | C2×Dic10 | semidirect |
| 161. C2×C5 | #4024 | semidirect |
| 167. C23 | #6039 | semidirect |
| 181. C5 | C2×#4024 | semidirect |
| 187. C22 | C2×#6039 | semidirect |
| 195. C2 | #11717100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C22×#6039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| #11717100 | 2 |
| C2×#87781 | 2 |
| C2×#87780 | 2 |
| C2×#4024 | 5 |