Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1232 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1232 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 | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C2×#127 |
| 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. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 2. C22×C5×C22⋊D5 | C2 | semidirect |
| 3. C22×#6038 | C2 | semidirect |
| 4. C22×#6037 | C2 | semidirect |
| 5. #11717097 | C2 | direct (N × H) |
| 6. C2×Dic52 | C2 | semidirect |
| 11. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 14. C2×C5×C22⋊D5 | C22 | semidirect |
| 17. C2×#6038 | C22 | semidirect |
| 19. C2×#6037 | C22 | semidirect |
| 20. Dic52 | C22 | semidirect |
| 34. C2×#1039 | D4 | semidirect |
| 37. C2×C5×Dic5 | D4 | semidirect |
| 46. C22×C22⋊D5 | D5 | semidirect |
| 63. #1039 | C2×D4 | semidirect |
| 64. C5×Dic5 | C2×D4 | semidirect |
| 83. C2×C22⋊D5 | C2×D5 | semidirect |
| 92. C2×C52 | #127 | semidirect |
| 133. C2×Dic5 | C22⋊D5 | semidirect |
| 142. C52 | C2×#127 | semidirect |
| 175. Dic5 | C2×C22⋊D5 | semidirect |
| 196. C2×C5 | #4086 | semidirect |
| 223. C5 | C2×#4086 | semidirect |
| 242. C2 | #11717097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C22×C5×C22⋊D5 | 2 |
| C22×#6038 | 2 |
| C22×#6037 | 2 |
| #11717097 | 2 |
| C2×Dic52 | 2 |
| C2×#4086 | 5 |