Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1240 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 267 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#127 | C2 |
| hypercenter | #127 | C5⋊D5 |
| hypocenter | C52 | #532 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87902 | C2 | semidirect |
| 2. C52×#127 | C2 | semidirect |
| 3. #11717258 | C2 | semidirect |
| 4. #11717256 | C2 | semidirect |
| 5. D4×#1039 | C2 | semidirect |
| 6. C42×C5⋊D5 | C2 | semidirect |
| 7. #11717189 | C2 | semidirect |
| 34. C4×C5⋊D5 | D4 | semidirect |
| 37. C5×#127 | D5 | semidirect |
| 49. C4×C52 | #41 | semidirect |
| 87. #127 | C5⋊D5 | semidirect |
| 92. C52 | #532 | semidirect |
| 99. C4×C5 | #711 | semidirect |
| 134. C5 | #66050 | semidirect |
| 144. C4 | #87902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| C52×#127 | 2 |
| #11717258 | 2 |
| #11717256 | 2 |
| D4×#1039 | 2 |
| C42×C5⋊D5 | 2 |
| #11717189 | 2 |
| #66050 | 5 |