Finite Group Databasebeta

← (C13⋊C3)⋊AGL(1,𝔽31) #49136554

Subgroups — (C13⋊C3)⋊AGL(1,𝔽31) #49136554

Order 36270.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13⋊C3×(C31⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2#14559031⋊C5C311yesmaximal, characteristic, complemented
3#14559030⋊C5C311yesmaximal, characteristic, complemented
4(C13⋊C3)⋊(D31⋊C5)C311yesmaximal, characteristic, complemented
5((C31⋊C3)⋊C5)⋊D13C311yesmaximal, characteristic, complemented
6(C13⋊C3)⋊(D31⋊C3)C511yesmaximal, characteristic, complemented, Hall
7#11925881⋊C5C2×C311yescharacteristic, complemented
8#11925882⋊C5C2×C311yescharacteristic, complemented
9C13⋊C3×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
10C13×(C31⋊C3)⋊C5C2×C311yescharacteristic, complemented
11C13⋊(D31⋊C5)C3211yescharacteristic, complemented, Hall
12C13⋊C3×C31⋊C3C2×C511yescharacteristic, complemented, Hall
13C3×AGL(1,𝔽31)—131nomaximal, Hall
14#14559031C3×C511yescharacteristic, complemented
15#14559030C3×C511yescharacteristic, complemented
16(C13⋊C3)⋊D31C3×C511yescharacteristic, complemented
17(C31⋊C3)⋊D13C3×C511yescharacteristic, complemented
18C13×ΓL(1,𝔽32)C2×C3211yescharacteristic, complemented, Hall
19C3×(C31⋊C3)⋊C5—131noHall
20#11925882C2×C3×C511yescharacteristic, complemented
21#11925881C2×C3×C511yescharacteristic, complemented
22C13×C31⋊C3C2×C3×C511yescharacteristic, complemented
23C31×C13⋊C3C2×C3×C511yescharacteristic, complemented
24C3×C5×D13⋊C3—311nomaximal, Hall
25C3×D31⋊C5—131no—
26AGL(1,𝔽31)—131no—
27AGL(1,𝔽31)—131no—
28AGL(1,𝔽31)—131no—
29D403C32×C511yescharacteristic, complemented, Hall
30C3×C5×C13⋊C3—311noHall
31C3×D31⋊C3—131noHall
32C3×ΓL(1,𝔽32)—131no—
33(C31⋊C3)⋊C5—131no—
34(C31⋊C3)⋊C5—131no—
35(C31⋊C3)⋊C5D13⋊C311yescharacteristic, complemented
36C13×C31C2×C32×C511yescharacteristic, complemented, Hall
37C3×C5×D13—311no—
38C5×D13⋊C3—311no—
39C5×D13⋊C3—311no—
40C5×D13⋊C3—311no—
41D31⋊C5—131noHall
42C3×C31⋊C3—131noHall
43C3×D13⋊C3—311noHall
44C3×C5×C13—311no—
45C5×C13⋊C3—311no—
46C5×C13⋊C3—311no—
47C5×C13⋊C3—311no—
48C3×D31—131no—
49D31⋊C3—131no—
50D31⋊C3—131no—
51D31⋊C3—131no—
52ΓL(1,𝔽32)C3×D13⋊C311yescharacteristic, complemented, Hall
53C5×D13—311noHall
54C3×C13⋊C3—311noHall
55C3×C31—131no—
56C31⋊C3—131no—
57C31⋊C3—131no—
58C31⋊C3C5×D13⋊C311yescharacteristic, complemented
59C2×C32×C5—4031noHall
60C3×D13—311no—
61D13⋊C3—311no—
62D13⋊C3—311no—
63D13⋊C3—311no—
64C5×C13—311noHall
65D31—131noHall
66C32×C5—4031noHall
67C3×C13—311no—
68C13⋊C3—311no—
69C13⋊C3—311no—
70C13⋊C3AGL(1,𝔽31)11yescharacteristic, complemented
71C31C3×C5×D13⋊C311yescharacteristic, complemented, Sylow
72C2×C3×C5—4031no—
73C2×C3×C5—4031no—
74C2×C3×C5—4031no—
75C2×C3×C5—4031no—
76D13—311noHall
77C2×C32—4031noHall
78C3×C5—311no—
79C3×C5—4031no—
80C3×C5—4031no—
81C3×C5—4031no—
82C13C3×AGL(1,𝔽31)11yescharacteristic, complemented, Sylow
83C2×C5—4031noHall
84C32—4031noSylow
85C2×C3—4031no—
86C2×C3—4031no—
87C2×C3—4031no—
88C2×C3—4031no—
89C5—311noSylow
90C3—131no—
91C3—311no—
92C3—4031no—
93C3—4031no—
94C2—4031noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C31C2×C32×C5
LCSG ▷ C13×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×(C31⋊C3)⋊C5C2semidirect
2. #14559031⋊C5C3semidirect
3. #14559030⋊C5C3semidirect
4. (C13⋊C3)⋊(D31⋊C5)C3semidirect
5. ((C31⋊C3)⋊C5)⋊D13C3semidirect
6. (C13⋊C3)⋊(D31⋊C3)C5semidirect
7. #11925881⋊C5C2×C3semidirect
8. #11925882⋊C5C2×C3semidirect
9. C13⋊C3×ΓL(1,𝔽32)C2×C3semidirect
10. C13×(C31⋊C3)⋊C5C2×C3semidirect
11. C13⋊(D31⋊C5)C32semidirect
12. C13⋊C3×C31⋊C3C2×C5semidirect
14. #14559031C3×C5semidirect
15. #14559030C3×C5semidirect
16. (C13⋊C3)⋊D31C3×C5semidirect
17. (C31⋊C3)⋊D13C3×C5semidirect
18. C13×ΓL(1,𝔽32)C2×C32semidirect
20. #11925882C2×C3×C5semidirect
21. #11925881C2×C3×C5semidirect
22. C13×C31⋊C3C2×C3×C5semidirect
23. C31×C13⋊C3C2×C3×C5semidirect
29. D403C32×C5semidirect
35. (C31⋊C3)⋊C5D13⋊C3semidirect
36. C13×C31C2×C32×C5semidirect
52. ΓL(1,𝔽32)C3×D13⋊C3semidirect
58. C31⋊C3C5×D13⋊C3semidirect
70. C13⋊C3AGL(1,𝔽31)semidirect
71. C31C3×C5×D13⋊C3semidirect
82. C13C3×AGL(1,𝔽31)semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×(C31⋊C3)⋊C52
#14559031⋊C53
#14559030⋊C53
(C13⋊C3)⋊(D31⋊C5)3
((C31⋊C3)⋊C5)⋊D133
(C13⋊C3)⋊(D31⋊C3)5
C3×AGL(1,𝔽31)13
C3×C5×D13⋊C331