Finite Group Databasebeta

← C13×C3⋊(C7⋊(C7⋊AGL(1,𝔽5))) #50304423

Subgroups — C13×C3⋊(C7⋊(C7⋊AGL(1,𝔽5))) #50304423

Order 38220.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×D5×C13C211yesmaximal, characteristic
2C13×C7⋊(C7⋊AGL(1,𝔽5))—31nomaximal, Hall
3C3×C5×C72×C13C411yescharacteristic, complemented, Hall
4C13×C3⋊(C7⋊Dic7)—51nomaximal, Hall
5C72×D5×C13D311yescharacteristic
6C13×C3⋊(C7⋊AGL(1,𝔽5))—78nomaximal
7C2×C3×C72×C13—51no—
8C5×C72×C13Dic311yescharacteristic, complemented, Hall
9C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))C1311yesmaximal, characteristic, direct product factor, Hall
10C3×C7×D5×C13D718yes—
11C13×C7⋊Dic7—151noHall
12C3×C72×C13AGL(1,𝔽5)11yescharacteristic, complemented, Hall
13C13×C7⋊AGL(1,𝔽5)—218no—
14C3×C72×D5C2×C1311yescharacteristic
15C3×C5×C7×C13Dic718yescomplemented
16C2×C72×C13—51no—
17C13×Dic21—358no—
18C7⋊(C7⋊AGL(1,𝔽5))—31noHall
19C7×D5×C13D2118yes—
20C13×ΓL(1,𝔽16)—491noHall
21C3×C5×C72C4×C1311yescharacteristic, complemented, Hall
22C72×C13ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
23C3⋊(C7⋊Dic7)—51noHall
24C2×C3×C7×C13—58no—
25C72×D5D3×C1311yescharacteristic
26C5×C7×C13Dic2118yescomplemented
27C3⋊(C7⋊AGL(1,𝔽5))—78no—
28C3×D5×C13C7⋊D711yescharacteristic
29C13×Dic7—1058no—
30C2×C3×C72—51no—
31C3×C7×C13C7⋊AGL(1,𝔽5)18yescomplemented
32C13×AGL(1,𝔽5)—1471noHall
33C5×C72Dic3×C1311yescharacteristic, complemented, Hall
34C3×C7×D5C13×D718yes—
35C7⋊Dic7—151noHall
36C3×C5×C13C7⋊Dic711yescharacteristic, complemented, Hall
37C2×C7×C13—58no—
38Dic3×C13—2451noHall
39C3×C72C13×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
40C7⋊AGL(1,𝔽5)—218no—
41D5×C13C3⋊(C7⋊D7)11yescharacteristic
42C3×C5×C7C13×Dic718yescomplemented
43C2×C72—51no—
44C7×C13C3⋊(C7⋊AGL(1,𝔽5))18yescomplemented
45Dic21—358no—
46C2×C3×C13—51no—
47C7×D5C13×D2118yes—
48C5×C13C3⋊(C7⋊Dic7)11yescharacteristic, complemented, Hall
49ΓL(1,𝔽16)—491noHall
50C4×C13—7351noHall
51C72C13×ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
52C2×C3×C7—58no—
53C3×C13C7⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Hall
54C5×C7C13×Dic2118yescomplemented
55C3×D5C13×C7⋊D711yescharacteristic
56Dic7—1058no—
57C2×C13—51no—
58C3×C7C13×C7⋊AGL(1,𝔽5)18yescomplemented
59AGL(1,𝔽5)—1471noHall
60C3×C5C13×C7⋊Dic711yescharacteristic, complemented, Hall
61C2×C7—58no—
62C13C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))11yescharacteristic, direct product factor, Sylow
63Dic3—2451noHall
64D5C13×C3⋊(C7⋊D7)11yescharacteristic
65C7C13×C3⋊(C7⋊AGL(1,𝔽5))18yescomplemented
66C2×C3—51no—
67C5C13×C3⋊(C7⋊Dic7)11yescharacteristic, complemented, Sylow
68C4—7351noSylow
69C3C13×C7⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
70C2—51no—
subgroupG/H
center, hypercenterC13C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))
commutator, hypocenterC3×C5×C72C4×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C72×D5×C13C2
cosocleC3×C72×D5C2×C13
LCSG ▷ C3×C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
3. C3×C5×C72×C13C4semidirect
8. C5×C72×C13Dic3semidirect
9. C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))C13direct (N × H)
12. C3×C72×C13AGL(1,𝔽5)semidirect
15. C3×C5×C7×C13Dic7semidirect
21. C3×C5×C72C4×C13semidirect
22. C72×C13ΓL(1,𝔽16)semidirect
26. C5×C7×C13Dic21semidirect
31. C3×C7×C13C7⋊AGL(1,𝔽5)semidirect
33. C5×C72Dic3×C13semidirect
36. C3×C5×C13C7⋊Dic7semidirect
39. C3×C72C13×AGL(1,𝔽5)semidirect
42. C3×C5×C7C13×Dic7semidirect
44. C7×C13C3⋊(C7⋊AGL(1,𝔽5))semidirect
48. C5×C13C3⋊(C7⋊Dic7)semidirect
51. C72C13×ΓL(1,𝔽16)semidirect
53. C3×C13C7⋊(C7⋊AGL(1,𝔽5))semidirect
54. C5×C7C13×Dic21semidirect
58. C3×C7C13×C7⋊AGL(1,𝔽5)semidirect
60. C3×C5C13×C7⋊Dic7semidirect
62. C13C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))direct (N × H)
65. C7C13×C3⋊(C7⋊AGL(1,𝔽5))semidirect
67. C5C13×C3⋊(C7⋊Dic7)semidirect
69. C3C13×C7⋊(C7⋊AGL(1,𝔽5))semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D5×C132
C13×C7⋊(C7⋊AGL(1,𝔽5))3
C13×C3⋊(C7⋊Dic7)5
C13×C3⋊(C7⋊AGL(1,𝔽5))7
C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))13