Finite Group Databasebeta

← D13×#11925895 #44538176

Subgroups — D13×#11925895 #44538176

Order 31460.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#10597243C211yesmaximal, characteristic, complemented
2C13⋊#11925895C211yesmaximal, characteristic, complemented
3C13×#11925895C211yesmaximal, characteristic, complemented
4C13×#10597243C2211yescharacteristic, complemented, Hall
5C11×D11×D13C511yesmaximal, characteristic, complemented, Hall
6C11×D143C2×C511yescharacteristic, complemented
7C11×C13×D11C2×C511yescharacteristic, complemented
8C112×D13C2×C511yescharacteristic, complemented
9C2×D13×C11⋊C5—111nomaximal
10D13×AGL(1,𝔽11)—111nomaximal
11C2×#11925895—131nomaximal, Hall
12C112×C13C22×C511yescharacteristic, complemented, Hall
13C2×C13×C11⋊C5—111no—
14C13⋊AGL(1,𝔽11)—111no—
15C13×AGL(1,𝔽11)—111no—
16D13×C11⋊C5—111no—
17D13×C11⋊C5—111no—
18D13×C11⋊C5—111no—
19D13×C11⋊C5—225no—
20C2×#10597243—131no—
21#11925895—131no—
22#11925895D1311yescharacteristic, direct product factor
23C13×C11⋊C5—111no—
24C13×C11⋊C5—111no—
25C13×C11⋊C5—225no—
26#10597243C2×D1311yescharacteristic, complemented, Hall
27C2×C11×D13—111no—
28D11×D13C11⋊C511yescharacteristic, complemented
29C2×C11×D11—131noHall
30C2×C11×C13—111no—
31D143C2×C11⋊C511yescharacteristic, complemented
32C11×D13—25no—
33C11×D13—111no—
34C11×D13AGL(1,𝔽11)11yescharacteristic, complemented
35C11×D13C2×C11⋊C511yescharacteristic, complemented
36C13×D11C2×C11⋊C511yescharacteristic, complemented
37C2×C5×D13—1211noHall
38C2×C112—131no—
39C11×D11—131no—
40C11×D11C5×D1311yescharacteristic, complemented
41C22×C11⋊C5—1431no—
42C2×AGL(1,𝔽11)—1431no—
43C11×C13—25no—
44C11×C13C2×AGL(1,𝔽11)11yescharacteristic, complemented
45C11×C13C22×C11⋊C511yescharacteristic, complemented
46C2×C5×C13—1211no—
47C5×D13—1211no—
48C5×D13—1211no—
49C112C2×C5×D1311yescharacteristic, complemented, Sylow
50C2×C11⋊C5—111no—
51C2×C11⋊C5—2865no—
52C2×C11⋊C5—1431no—
53C2×C11⋊C5—1431no—
54C2×C11⋊C5—1431no—
55AGL(1,𝔽11)—111no—
56AGL(1,𝔽11)—1431no—
57C5×C13—1211noHall
58C11⋊C5—111no—
59C11⋊C5—111no—
60C11⋊C5—225no—
61C2×D13—111noHall
62C22×C11—1431no—
63C2×D11—131no—
64C2×C13—111no—
65D13—111no—
66D13#1192589511yescharacteristic, direct product factor
67C2×C11—111no—
68C2×C11—131no—
69C2×C11—131no—
70C2×C11—265no—
71C2×C11—1431no—
72D11—131no—
73D11D13×C11⋊C511yescharacteristic, complemented
74C22×C5—15731noHall
75C13C2×#1192589511yescharacteristic, complemented, Sylow
76C11—25no—
77C11D13×AGL(1,𝔽11)11yescharacteristic, complemented
78C11C2×D13×C11⋊C511yescharacteristic, complemented
79C2×C5—15731no—
80C2×C5—15731no—
81C2×C5—1211no—
82C5—1211noSylow
83C22—1431noSylow
84C2—111no—
85C2—131no—
86C2—1431no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC112×C13C22×C5
LCSG ▷ C112×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D13×#10597243C2semidirect
2. C13⋊#11925895C2semidirect
3. C13×#11925895C2semidirect
4. C13×#10597243C22semidirect
5. C11×D11×D13C5semidirect
6. C11×D143C2×C5semidirect
7. C11×C13×D11C2×C5semidirect
8. C112×D13C2×C5semidirect
12. C112×C13C22×C5semidirect
22. #11925895D13direct (N × H)
26. #10597243C2×D13semidirect
28. D11×D13C11⋊C5semidirect
31. D143C2×C11⋊C5semidirect
34. C11×D13AGL(1,𝔽11)semidirect
35. C11×D13C2×C11⋊C5semidirect
36. C13×D11C2×C11⋊C5semidirect
40. C11×D11C5×D13semidirect
44. C11×C13C2×AGL(1,𝔽11)semidirect
45. C11×C13C22×C11⋊C5semidirect
49. C112C2×C5×D13semidirect
66. D13#11925895direct (N × H)
73. D11D13×C11⋊C5semidirect
75. C13C2×#11925895semidirect
77. C11D13×AGL(1,𝔽11)semidirect
78. C11C2×D13×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
D13×#105972432
C13⋊#119258952
C13×#119258952
C11×D11×D135
C2×D13×C11⋊C511
D13×AGL(1,𝔽11)11
C2×#1192589513