Finite Group Databasebeta

← D5×#11925898 #27130922

Subgroups — D5×#11925898 #27130922

Order 12100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#10597244C211yesmaximal, characteristic, complemented
2C5⋊#11925898C211yesmaximal, characteristic, complemented
3C5×#11925898C211yesmaximal, characteristic, complemented
4C5×#10597244C2211yescharacteristic, complemented, Hall
5D5×C11×D11C511yesmaximal, characteristic, complemented
6C2×#11925898—51nomaximal
7C11×D55C2×C511yescharacteristic, complemented
8D5×C112C2×C511yescharacteristic, complemented
9C5×C11×D11C2×C511yescharacteristic, complemented
10C2×#10597244—51no—
11#11925898—22no—
12#11925898—51no—
13#11925898D511yescharacteristic, direct product factor
14C2×D5×C11⋊C5—111nomaximal
15D5×AGL(1,𝔽11)—111nomaximal
16C5×C112C22×C511yescharacteristic, complemented
17#10597244—22no—
18#10597244C2×D511yescharacteristic, complemented
19C2×C5×C11⋊C5—111no—
20C5⋊AGL(1,𝔽11)—111no—
21D5×C11⋊C5—111no—
22D5×C11⋊C5—111no—
23D5×C11⋊C5—111no—
24C5×AGL(1,𝔽11)—111no—
25C2×C11×D11—51noHall
26C5×C11⋊C5—111no—
27C5×C11⋊C5—111no—
28C2×C112—51no—
29C11×D11—51no—
30C11×D11C5×D511yescharacteristic, complemented
31C2×D5×C11—111no—
32D5×D11C11⋊C511yescharacteristic, complemented
33C22×C11⋊C5—551no—
34C2×AGL(1,𝔽11)—551no—
35C112C2×C5×D511yescharacteristic, complemented, Sylow
36C2×C5×C11—111no—
37D55C2×C11⋊C511yescharacteristic, complemented
38C5×D11C2×C11⋊C511yescharacteristic, complemented
39D5×C11—101no—
40D5×C11—111no—
41D5×C11AGL(1,𝔽11)11yescharacteristic, complemented
42D5×C11C2×C11⋊C511yescharacteristic, complemented
43C2×C11⋊C5—111no—
44C2×C11⋊C5—222no—
45C2×C11⋊C5—551no—
46C2×C11⋊C5—551no—
47C2×C11⋊C5—551no—
48AGL(1,𝔽11)—111no—
49AGL(1,𝔽11)—222no—
50AGL(1,𝔽11)—551no—
51C2×C5×D5—1211noHall
52C5×C11—101no—
53C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
54C5×C11C22×C11⋊C511yescharacteristic, complemented
55C11⋊C5—111no—
56C11⋊C5—111no—
57C11⋊C5—222no—
58C11⋊C5—222no—
59C2×C52—1211no—
60C5×D5—1211no—
61C5×D5—1211no—
62C22×C11—551no—
63C2×D11—51no—
64C52—1211noSylow
65C2×C11—51no—
66C2×C11—51no—
67C2×C11—111no—
68C2×C11—501no—
69C2×C11—551no—
70D11—51no—
71D11D5×C11⋊C511yescharacteristic, complemented
72C22×C5—6051no—
73C2×D5—111no—
74C11—101no—
75C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
76C11C2×D5×C11⋊C511yescharacteristic, complemented
77C2×C5—111no—
78C2×C5—6051no—
79C2×C5—6051no—
80C2×C5—1211no—
81C2×C5—2422no—
82D5—111no—
83D5#1192589811yescharacteristic, direct product factor
84C5—1211no—
85C5—2422no—
86C5C2×#1192589811yescharacteristic, complemented
87C22—551noSylow
88C2—51no—
89C2—111no—
90C2—551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C112C22×C5
LCSG ▷ C5×C112
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D5×#10597244C2semidirect
2. C5⋊#11925898C2semidirect
3. C5×#11925898C2semidirect
4. C5×#10597244C22semidirect
5. D5×C11×D11C5semidirect
7. C11×D55C2×C5semidirect
8. D5×C112C2×C5semidirect
9. C5×C11×D11C2×C5semidirect
13. #11925898D5direct (N × H)
16. C5×C112C22×C5semidirect
18. #10597244C2×D5semidirect
30. C11×D11C5×D5semidirect
32. D5×D11C11⋊C5semidirect
35. C112C2×C5×D5semidirect
37. D55C2×C11⋊C5semidirect
38. C5×D11C2×C11⋊C5semidirect
41. D5×C11AGL(1,𝔽11)semidirect
42. D5×C11C2×C11⋊C5semidirect
53. C5×C11C2×AGL(1,𝔽11)semidirect
54. C5×C11C22×C11⋊C5semidirect
71. D11D5×C11⋊C5semidirect
75. C11D5×AGL(1,𝔽11)semidirect
76. C11C2×D5×C11⋊C5semidirect
83. D5#11925898direct (N × H)
86. C5C2×#11925898semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D5×#105972442
C5⋊#119258982
C5×#119258982
D5×C11×D115
C2×#119258985
C2×D5×C11⋊C511
D5×AGL(1,𝔽11)11