Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
788 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 140 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×D4 | C22 |
| hypercenter | C2×D4 | D52 |
| hypocenter | C52 | #550 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87902 | C2 | semidirect |
| 2. C2×#87870 | C2 | semidirect |
| 3. C5×#4086 | C2 | semidirect |
| 4. C5×#4084 | C2 | semidirect |
| 5. #11717098 | C2 | semidirect |
| 6. #11717097 | C2 | semidirect |
| 7. #11717091 | C2 | semidirect |
| 8. #11717089 | C2 | semidirect |
| 9. #11717034 | C2 | semidirect |
| 10. C4×#6038 | C2 | semidirect |
| 11. #11716962 | C2 | semidirect |
| 50. #6045 | D4 | semidirect |
| 73. #4086 | D5 | semidirect |
| 78. #4084 | D5 | semidirect |
| 106. C5×Dic5 | #41 | semidirect |
| 242. C52 | #550 | semidirect |
| 292. Dic5 | #711 | semidirect |
| 363. C5 | #65933 | semidirect |
| 364. C5 | #66052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| C2×#87870 | 2 |
| C5×#4086 | 2 |
| C5×#4084 | 2 |
| #11717098 | 2 |
| #11717097 | 2 |
| #11717091 | 2 |
| #11717089 | 2 |
| #11717034 | 2 |
| C4×#6038 | 2 |
| #11716962 | 2 |
| #66052 | 5 |
| #65933 | 5 |