Finite Group Databasebeta

← C2×C3×#14519615 #26043696

Subgroups — C2×C3×#14519615 #26043696

Order 11700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13⋊(C52⋊C3)C211yesmaximal, characteristic, complemented
2C3×#14519615C212yesmaximal, direct product factor
3C2×C3×C5⋊D65C311yesmaximal, characteristic, complemented
4C2×#14519615C313yesmaximal, direct product factor
5C3×C13⋊(C52⋊C3)C2211yescharacteristic, complemented, Hall
6C2×C3×C52×C13C2×C311yescharacteristic, complemented
7C3×C5⋊D65C2×C312yescomplemented
8C2×C13⋊(C52⋊C3)C2×C313yescomplemented
9#14519615C2×C316yesdirect product factor
10C2×C5⋊D65C3211yescharacteristic, complemented, Hall
11C3×C52×C13C22×C311yescharacteristic, complemented
12C13⋊(C52⋊C3)C22×C313yescomplemented
13C2×C3×(C5⋊D5)⋊C3—131nomaximal, Hall
14C2×C3×D65—152no—
15C2×C52×C13C2×C3211yescharacteristic, complemented
16C5⋊D65C2×C3212yescomplemented
17C2×C3×D13⋊C3—251nomaximal, Hall
18C2×C3×C52⋊C3—131no—
19C3×(C5⋊D5)⋊C3—132no—
20C2×C3×C5×C13—32no—
21C3×D65—154no—
22C52×C13C22×C3211yescharacteristic, complemented, Hall
23C2×C3×C5⋊D5—131no—
24C2×(C5⋊D5)⋊C3—133no—
25C2×D65—152no—
26C2×C3×C13⋊C3—251no—
27C3×D13⋊C3—252no—
28C3×C52⋊C3—131noHall
29C3×C5×C13—32no—
30C2×C3×D13—251no—
31C2×D13⋊C3—253no—
32C2×C3×C52D13⋊C311yescharacteristic, complemented
33C3×C5⋊D5—132no—
34C2×C52⋊C3—133no—
35(C5⋊D5)⋊C3—136no—
36C2×C5×C13—32no—
37D65—154no—
38C3×C13⋊C3—251noHall
39C2×C5⋊D5—131noHall
40C2×C3×C13(C5⋊D5)⋊C311yescharacteristic, complemented
41C3×D13—252no—
42C2×C13⋊C3—253no—
43D13⋊C3—256no—
44C3×C52C2×D13⋊C311yescharacteristic, complemented
45C52⋊C3—133no—
46C5×C13—32no—
47C2×C3×D5—1952no—
48C2×D13—251noHall
49C2×C52C3×D13⋊C311yescharacteristic, complemented
50C5⋊D5—132no—
51C3×C13C2×(C5⋊D5)⋊C311yescharacteristic, complemented
52C13⋊C3—253no—
53C22×C32—3251noHall
54C2×C3×C5—32no—
55C3×D5—1954no—
56C2×C13C3×(C5⋊D5)⋊C311yescharacteristic, complemented
57D13—252no—
58C52C2×C3×D13⋊C311yescharacteristic, complemented, Sylow
59C2×D5—1952no—
60C2×C32—3252no—
61C2×C32—3251no—
62C3×C5—32no—
63C13C2×C3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
64C22×C3—3253no—
65C22×C3—3251no—
66C2×C5—32no—
67D5—1954no—
68C32—3251noSylow
69C2×C3—3256no—
70C2×C3—3252no—
71C2×C3—3253no—
72C2×C3#1451961511yescharacteristic, direct product factor
73C5—32no—
74C22—3251noSylow
75C3—3253no—
76C3C2×#1451961511yescharacteristic, direct product factor
77C2—3252no—
78C2C3×#1451961511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3#14519615
commutator, cosocle, hypocenterC52×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C52×C13C2×C3
LCSG ▷ C52×C13
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C13⋊(C52⋊C3)C2semidirect
2. C3×#14519615C2direct (N × H)
3. C2×C3×C5⋊D65C3semidirect
4. C2×#14519615C3direct (N × H)
5. C3×C13⋊(C52⋊C3)C22semidirect
6. C2×C3×C52×C13C2×C3semidirect
7. C3×C5⋊D65C2×C3semidirect
8. C2×C13⋊(C52⋊C3)C2×C3semidirect
9. #14519615C2×C3direct (N × H)
10. C2×C5⋊D65C32semidirect
11. C3×C52×C13C22×C3semidirect
12. C13⋊(C52⋊C3)C22×C3semidirect
15. C2×C52×C13C2×C32semidirect
16. C5⋊D65C2×C32semidirect
22. C52×C13C22×C32semidirect
32. C2×C3×C52D13⋊C3semidirect
40. C2×C3×C13(C5⋊D5)⋊C3semidirect
44. C3×C52C2×D13⋊C3semidirect
49. C2×C52C3×D13⋊C3semidirect
51. C3×C13C2×(C5⋊D5)⋊C3semidirect
56. C2×C13C3×(C5⋊D5)⋊C3semidirect
58. C52C2×C3×D13⋊C3semidirect
63. C13C2×C3×(C5⋊D5)⋊C3semidirect
72. C2×C3#14519615direct (N × H)
76. C3C2×#14519615direct (N × H)
78. C2C3×#14519615direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C13⋊(C52⋊C3)2
C3×#145196152
C2×C3×C5⋊D653
C2×#145196153
C2×C3×(C5⋊D5)⋊C313
C2×C3×D13⋊C325