Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
652 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 152 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×#87870 | C2 | semidirect |
| 2. #11717189 | C2 | semidirect |
| 3. C4×C5×D20 | C2 | semidirect |
| 4. C4×C5×D20 | C2 | semidirect |
| 5. #11717026 | C2 | semidirect |
| 6. D5×C4⋊Dic5 | C2 | semidirect |
| 7. #11717003 | C2 | semidirect |
| 8. #11716975 | C2 | semidirect |
| 38. C5×D20 | D4 | semidirect |
| 55. C4×D20 | D5 | semidirect |
| 56. C4×D20 | D5 | semidirect |
| 69. C4×C52 | #41 | semidirect |
| 145. D20 | D20 | semidirect |
| 160. C52 | #547 | semidirect |
| 184. C4×C5 | #709 | semidirect |
| 186. C4×C5 | #711 | semidirect |
| 238. C5 | #65885 | semidirect |
| 239. C5 | #65889 | semidirect |
| 251. C4 | #87870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| #11717189 | 2 |
| C4×C5×D20 | 2 |
| #11717026 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11717003 | 2 |
| #11716975 | 2 |
| #65889 | 5 |
| #65885 | 5 |