← (C2×AGL(1,𝔽5))⋊AGL(1,𝔽5) #11717298
Order 800.
160 conjugacy classes of subgroups.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×D5⋊AGL(1,𝔽5) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×D5×AGL(1,𝔽5) | C2 | 1 | 2 | yes | maximal |
| 3 | C2×D52 | C22 | 1 | 1 | yes | characteristic |
| 4 | C2×#1044 | C4 | 1 | 1 | yes | characteristic, complemented |
| 5 | C2×#1043 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C2×#1042 | C4 | 1 | 2 | yes | complemented |
| 7 | C2×C5×AGL(1,𝔽5) | C4 | 1 | 2 | yes | complemented |
| 8 | D5⋊AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 9 | D5×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 10 | D5×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 11 | (C2×AGL(1,𝔽5))⋊C4 | — | 5 | 2 | no | maximal |
| 12 | C2×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 13 | C2×C5×D5 | C2×C4 | 1 | 2 | yes | — |
| 14 | D52 | D4 | 1 | 2 | yes | — |
| 15 | D52 | D4 | 1 | 1 | yes | characteristic |
| 16 | D52 | Q8 | 1 | 1 | yes | characteristic |
| 17 | #1044 | — | 2 | 1 | no | — |
| 18 | #1043 | — | 2 | 1 | no | — |
| 19 | #1042 | — | 2 | 2 | no | — |
| 20 | C5×AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 21 | C22×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 22 | C22×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 23 | C2×C4×D5 | — | 5 | 2 | no | — |
| 24 | C2×C52 | C42 | 1 | 1 | yes | characteristic |
| 25 | C5⋊D5 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 26 | C5⋊D5 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 27 | C5×D5 | C22⋊C4 | 1 | 2 | yes | — |
| 28 | C5×D5 | C4⋊C4 | 1 | 2 | yes | — |
| 29 | C22×D5 | — | 5 | 2 | no | — |
| 30 | C2×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 31 | C2×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 32 | C2×AGL(1,𝔽5) | — | 5 | 2 | no | — |
| 33 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 34 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 35 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 36 | C2×AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 37 | C2×AGL(1,𝔽5) | — | 20 | 1 | no | — |
| 38 | C2×AGL(1,𝔽5) | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 39 | C2×C4×C5 | — | 5 | 2 | no | — |
| 40 | C2×Dic5 | — | 5 | 2 | no | — |
| 41 | C4×D5 | — | 10 | 2 | no | — |
| 42 | C4×D5 | — | 10 | 2 | no | — |
| 43 | #95 | — | 25 | 1 | no | Sylow |
| 44 | C52 | #95 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 45 | C22×C5 | — | 5 | 2 | no | — |
| 46 | C2×D5 | — | 5 | 2 | no | — |
| 47 | C2×D5 | — | 5 | 2 | no | — |
| 48 | C2×D5 | — | 5 | 2 | no | — |
| 49 | C2×D5 | — | 5 | 2 | no | — |
| 50 | C2×D5 | — | 5 | 2 | no | — |
| 51 | C2×D5 | — | 20 | 1 | no | — |
| 52 | C2×D5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 53 | AGL(1,𝔽5) | — | 2 | 2 | no | — |
| 54 | AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 55 | AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 56 | AGL(1,𝔽5) | — | 10 | 2 | no | — |
| 57 | AGL(1,𝔽5) | — | 20 | 2 | no | — |
| 58 | C4×C5 | — | 10 | 2 | no | — |
| 59 | Dic5 | — | 10 | 2 | no | — |
| 60 | C22×C4 | — | 25 | 2 | no | — |
| 61 | C22×C4 | — | 25 | 1 | no | — |
| 62 | C2×C5 | — | 4 | 1 | no | — |
| 63 | C2×C5 | — | 5 | 2 | no | — |
| 64 | C2×C5 | — | 5 | 2 | no | — |
| 65 | C2×C5 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 66 | D5 | — | 5 | 2 | no | — |
| 67 | D5 | — | 5 | 2 | no | — |
| 68 | D5 | — | 20 | 1 | no | — |
| 69 | D5 | — | 20 | 1 | no | — |
| 70 | D5 | C4⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 71 | D5 | C22⋊AGL(1,𝔽5) | 1 | 2 | yes | — |
| 72 | C23 | — | 25 | 1 | no | — |
| 73 | C2×C4 | — | 5 | 2 | no | — |
| 74 | C2×C4 | — | 25 | 2 | no | — |
| 75 | C2×C4 | — | 25 | 1 | no | — |
| 76 | C2×C4 | — | 25 | 1 | no | — |
| 77 | C2×C4 | — | 50 | 2 | no | — |
| 78 | C2×C4 | — | 50 | 2 | no | — |
| 79 | C2×C4 | — | 50 | 2 | no | — |
| 80 | C5 | — | 4 | 1 | no | — |
| 81 | C5 | (C2×AGL(1,𝔽5))⋊C4 | 1 | 2 | yes | complemented |
| 82 | C22 | — | 5 | 2 | no | — |
| 83 | C22 | — | 25 | 1 | no | — |
| 84 | C22 | — | 25 | 2 | no | — |
| 85 | C22 | — | 25 | 1 | no | — |
| 86 | C22 | — | 25 | 1 | no | — |
| 87 | C4 | — | 10 | 2 | no | — |
| 88 | C4 | — | 50 | 2 | no | — |
| 89 | C4 | — | 50 | 1 | no | — |
| 90 | C4 | — | 50 | 1 | no | — |
| 91 | C2 | — | 5 | 2 | no | — |
| 92 | C2 | — | 5 | 2 | no | — |
| 93 | C2 | — | 25 | 1 | no | — |
| 94 | C2 | — | 25 | 1 | no | — |
| 95 | C2 | AGL(1,𝔽5)2 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta