Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
678 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #547 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87874 | C2 | semidirect |
| 2. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C4×C5×D20 | C2 | semidirect |
| 4. C5×#4015 | C2 | semidirect |
| 5. #11717034 | C2 | semidirect |
| 6. #11717018 | C2 | semidirect |
| 7. #11716974 | C2 | semidirect |
| 8. #11716972 | C2 | semidirect |
| 34. C4⋊(C5⋊D5) | D4 | semidirect |
| 58. C4×D20 | D5 | semidirect |
| 59. #4015 | D5 | semidirect |
| 69. C4×C52 | #41 | semidirect |
| 163. C52 | #547 | semidirect |
| 189. C4×C5 | #709 | semidirect |
| 192. C4×C5 | #713 | semidirect |
| 245. C5 | #65885 | semidirect |
| 246. C5 | #66060 | semidirect |
| 258. C4 | #87874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C4×C5×D20 | 2 |
| C5×#4015 | 2 |
| #11717034 | 2 |
| #11717018 | 2 |
| #11716974 | 2 |
| #11716972 | 2 |
| #66060 | 5 |
| #65885 | 5 |