Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
704 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D52 |
| commutator | C22×C52 | C22×C4 |
| Fitting, prime radical | C24×C52 | C22 |
| socle, cosocle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #385 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#87780 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 14. C5×C22⋊Dic5 | C4 | semidirect |
| 34. C2×C5×Dic5 | C2×C4 | semidirect |
| 50. C22×C52 | C4⋊C4 | semidirect |
| 81. C22⋊Dic5 | Dic5 | semidirect |
| 134. C2×Dic5 | C2×Dic5 | semidirect |
| 140. C52 | #385 | semidirect |
| 159. C22×C5 | #683 | semidirect |
| 160. C22×C5 | C4⋊Dic5 | semidirect |
| 226. C5 | #65235 | semidirect |
| 227. C5 | #65239 | semidirect |
| 232. C22 | #87780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×#87780 | 2 |
| #11716620 | 2 |
| #65239 | 5 |
| #65235 | 5 |