Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
784 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 784 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 | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #532 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×#87871 | C2 | semidirect |
| 3. C5×#4093 | C2 | semidirect |
| 4. C5×#4090 | C2 | semidirect |
| 5. #11717029 | C2 | semidirect |
| 6. #11717028 | C2 | semidirect |
| 7. C4×#6036 | C2 | semidirect |
| 8. #11716999 | C2 | semidirect |
| 9. #11716982 | C2 | semidirect |
| 41. C4×C5⋊D5 | D4 | semidirect |
| 59. #4093 | D5 | semidirect |
| 60. #4090 | D5 | semidirect |
| 82. C5×Dic5 | #41 | semidirect |
| 192. C52 | #532 | semidirect |
| 226. Dic5 | #713 | semidirect |
| 281. C5 | #66002 | semidirect |
| 282. C5 | #66059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×#87871 | 2 |
| C5×#4093 | 2 |
| C5×#4090 | 2 |
| #11717029 | 2 |
| #11717028 | 2 |
| C4×#6036 | 2 |
| #11716999 | 2 |
| #11716982 | 2 |
| #66059 | 5 |
| #66002 | 5 |