Finite Group Databasebeta

← C2×#14559026⋊C5 #37563791

Subgroups — C2×#14559026⋊C5 #37563791

Order 24180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14559026⋊C5C211yesmaximal, characteristic, direct product factor
2#14559026⋊C5C211yesmaximal, characteristic, direct product factor
3C2×#11925882⋊C5C211yesmaximal, characteristic, complemented
4C2×D13×ΓL(1,𝔽32)C311yesmaximal, characteristic, complemented, Hall
5#11925882⋊C5C2211yescharacteristic, complemented, Hall
6C2×#14559026C511yesmaximal, characteristic, complemented, Hall
7D13×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
8D13×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
9C2×C13×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
10#14559026C2×C511yescharacteristic, complemented
11#14559026C2×C511yescharacteristic, complemented
12C2×#11925882C2×C511yescharacteristic, complemented
13C13×ΓL(1,𝔽32)C22×C311yescharacteristic, complemented, Hall
14C22×(C31⋊C3)⋊C5—131nomaximal, Hall
15C2×D13×C31C3×C511yescharacteristic, complemented, Hall
16#11925882C22×C511yescharacteristic, complemented, Hall
17C2×(C31⋊C3)⋊C5—131no—
18C2×(C31⋊C3)⋊C5—131no—
19C2×(C31⋊C3)⋊C5—131no—
20C2×C13×C31C2×C3×C511yescharacteristic, complemented
21D13×C31C2×C3×C511yescharacteristic, complemented
22D13×C31C2×C3×C511yescharacteristic, complemented
23C2×C5×D13⋊C3—311nomaximal, Hall
24C22×ΓL(1,𝔽32)—131noHall
25(C31⋊C3)⋊C5—131noHall
26C13×C31C22×C3×C511yescharacteristic, complemented, Hall
27C2×C5×C13⋊C3—311no—
28C5×D13⋊C3—311no—
29C5×D13⋊C3—311no—
30C22×C31⋊C3—131noHall
31C2×ΓL(1,𝔽32)—131no—
32C2×ΓL(1,𝔽32)—131no—
33C2×ΓL(1,𝔽32)D13⋊C311yescharacteristic, complemented
34C2×C5×D13—311noHall
35C5×C13⋊C3—311noHall
36C2×C31⋊C3—131no—
37C2×C31⋊C3—131no—
38C2×C31⋊C3—131no—
39C2×D13⋊C3—1551noHall
40ΓL(1,𝔽32)C2×D13⋊C311yescharacteristic, complemented, Hall
41C2×C5×C13—311no—
42C5×D13—311no—
43C5×D13—311no—
44C22×C31—131noHall
45C31⋊C3—131noHall
46C2×C13⋊C3—311no—
47D13⋊C3—1551no—
48D13⋊C3—1551no—
49C5×C13—311noHall
50C2×C31—131no—
51C2×C31—131no—
52C2×C31C5×D13⋊C311yescharacteristic, complemented
53C22×C3×C5—4031noHall
54C2×D13(C31⋊C3)⋊C511yescharacteristic, complemented, Hall
55C13⋊C3—1551noHall
56C31C2×C5×D13⋊C311yescharacteristic, complemented, Sylow
57C2×C3×C5—4031no—
58C2×C3×C5—4031no—
59C2×C3×C5—4031no—
60C2×C13C2×(C31⋊C3)⋊C511yescharacteristic, complemented
61D13C2×(C31⋊C3)⋊C511yescharacteristic, complemented
62D13C2×(C31⋊C3)⋊C511yescharacteristic, complemented
63C22×C5—4031noHall
64C3×C5—4031noHall
65C13C22×(C31⋊C3)⋊C511yescharacteristic, complemented, Sylow
66C22×C3—20151noHall
67C2×C5—311no—
68C2×C5—4031no—
69C2×C5—4031no—
70C2×C3—4031no—
71C2×C3—20151no—
72C2×C3—20151no—
73C5—311noSylow
74C22—131noSylow
75C3—20151noSylow
76C2—131no—
77C2—131no—
78C2#14559026⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#14559026⋊C5
commutator, cosocle, hypocenterC13×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #14559026⋊C5C2direct (N × H)
2. #14559026⋊C5C2direct (N × H)
3. C2×#11925882⋊C5C2semidirect
4. C2×D13×ΓL(1,𝔽32)C3semidirect
5. #11925882⋊C5C22semidirect
6. C2×#14559026C5semidirect
7. D13×ΓL(1,𝔽32)C2×C3semidirect
8. D13×ΓL(1,𝔽32)C2×C3semidirect
9. C2×C13×ΓL(1,𝔽32)C2×C3semidirect
10. #14559026C2×C5semidirect
11. #14559026C2×C5semidirect
12. C2×#11925882C2×C5semidirect
13. C13×ΓL(1,𝔽32)C22×C3semidirect
15. C2×D13×C31C3×C5semidirect
16. #11925882C22×C5semidirect
20. C2×C13×C31C2×C3×C5semidirect
21. D13×C31C2×C3×C5semidirect
22. D13×C31C2×C3×C5semidirect
26. C13×C31C22×C3×C5semidirect
33. C2×ΓL(1,𝔽32)D13⋊C3semidirect
40. ΓL(1,𝔽32)C2×D13⋊C3semidirect
52. C2×C31C5×D13⋊C3semidirect
54. C2×D13(C31⋊C3)⋊C5semidirect
56. C31C2×C5×D13⋊C3semidirect
60. C2×C13C2×(C31⋊C3)⋊C5semidirect
61. D13C2×(C31⋊C3)⋊C5semidirect
62. D13C2×(C31⋊C3)⋊C5semidirect
65. C13C22×(C31⋊C3)⋊C5semidirect
78. C2#14559026⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
#14559026⋊C52
C2×#11925882⋊C52
C2×D13×ΓL(1,𝔽32)3
C2×#145590265
C22×(C31⋊C3)⋊C513
C2×C5×D13⋊C331