Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
808 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 808 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 | C24×C52 | C22 |
| socle, cosocle | C23×C52 | C23 |
| prime radical | C22×C5×C22⋊D5 | C2 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #386 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#1039 | C2 | semidirect |
| 3. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 4. C2×#87778 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 13. C2×C5×C22⋊D5 | C4 | semidirect |
| 30. C22×C5×D5 | C2×C4 | semidirect |
| 34. C2×#1039 | D4 | semidirect |
| 41. C2×C5×Dic5 | C2×C4 | semidirect |
| 49. C2×C22⋊Dic5 | D5 | semidirect |
| 57. C22×C52 | C22⋊C4 | semidirect |
| 83. C2×C22⋊D5 | Dic5 | semidirect |
| 134. C22×D5 | C2×Dic5 | semidirect |
| 160. C2×Dic5 | C2×Dic5 | semidirect |
| 166. C52 | #386 | semidirect |
| 190. C22×C5 | #685 | semidirect |
| 191. C22×C5 | C22⋊Dic5 | semidirect |
| 269. C5 | #65247 | semidirect |
| 270. C5 | #65509 | semidirect |
| 280. C22 | #87778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C22×C5×C22⋊D5 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×#87778 | 2 |
| #11716620 | 2 |
| #65509 | 5 |
| #65247 | 5 |