Finite Group Databasebeta

← C11×D45⋊D13 #38787907

Subgroups — C11×D45⋊D13 #38787907

Order 25740.

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C13×D45C211yesmaximal, characteristic, complemented
2C5×C11×D117C211yesmaximal, characteristic, complemented
3C9×C11×D65C211yesmaximal, characteristic, complemented
4C11×D15⋊D13—31nomaximal
5C5×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C11×D9×D13—51nomaximal, Hall
7C11×C13×D15—31no—
8C5×C11×D39—31no—
9C3×C11×D65D311yescharacteristic
10D5×C11×D13—91noHall
11C11×D117D511yescharacteristic, complemented
12C11×C13×D9—51no—
13C9×C11×D13—51no—
14D45⋊D13C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C2×D311yescharacteristic
16D5×C11×D9—131nomaximal, Hall
17D3×C11×D13—151no—
18C11×D65D911yescharacteristic, complemented
19D5×C11×C13—91no—
20C5×C11×D13—91no—
21C9×C11×C13C2×D511yescharacteristic, complemented, Hall
22C13×D45C2×C1111yescharacteristic, complemented
23C5×D117C2×C1111yescharacteristic, complemented
24C9×D65C2×C1111yescharacteristic, complemented
25C11×D45D1311yescharacteristic, complemented
26C5×C11×D9—131no—
27C9×D5×C11—131no—
28C11×D39—31no—
29D3×C11×C13—151no—
30C3×C11×D13—51no—
31D15⋊D13—31no—
32C5×C11×C13C2×D911yescharacteristic, complemented, Hall
33D3×D5×C11—391no—
34C5×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C2×C11×D13—451noHall
36C5×C9×C11C2×D1311yescharacteristic, complemented, Hall
37D9×D13—51noHall
38C3×C11×C13D3×D511yescharacteristic
39C2×C11×D9—651noHall
40C13×D15—31no—
41C5×D39—31no—
42C3×D65D3×C1111yescharacteristic
43C11×D15—31no—
44C5×D3×C11—391no—
45C3×D5×C11—131no—
46C2×C11×C13—451no—
47C11×D13—51no—
48C11×D13—91no—
49D5×D13—91noHall
50D117D5×C1111yescharacteristic, complemented
51C9×D13—51no—
52C13×D9—51no—
53C2×D5×C11—1171noHall
54C2×C9×C11—651no—
55C11×D9—51no—
56C11×D9—131no—
57C3×C5×C13C2×D3×C1111yescharacteristic
58D5×D9—131noHall
59C3×C5×C11D3×D1311yescharacteristic
60D3×D13—151no—
61C11×C13D5×D911yescharacteristic, complemented, Hall
62C2×D3×C11—1951no—
63D65C11×D911yescharacteristic, complemented
64C5×D13—91no—
65D5×C13—91no—
66C9×C13C2×D5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—1171no—
68D5×C11—91no—
69D5×C11—131no—
70C9×C11D5×D1311yescharacteristic, complemented, Hall
71D45C11×D1311yescharacteristic, complemented
72C9×D5—131no—
73C5×D9—131no—
74D39—31no—
75C3×D13—51no—
76D3×C13—151no—
77C2×C3×C11—651no—
78D3×C11—151no—
79D3×C11—391no—
80C5×C13C2×C11×D911yescharacteristic, complemented, Hall
81D3×D5—391no—
82C5×C11D9×D1311yescharacteristic, complemented, Hall
83C2×D13—451noHall
84C5×C9C2×C11×D1311yescharacteristic, complemented, Hall
85C22×C11—5851noHall
86C3×C13D3×D5×C1111yescharacteristic
87C2×D9—651noHall
88C3×C11D15⋊D1311yescharacteristic
89D15—31no—
90C3×D5—131no—
91C5×D3—391no—
92C2×C13—451no—
93D13—51no—
94D13—91no—
95C2×C11—451no—
96C2×C11—651no—
97C2×C11—1171no—
98C2×D5—1171noHall
99C2×C9—651no—
100D9—51no—
101D9—131no—
102C3×C5D3×C11×D1311yescharacteristic
103C13D5×C11×D911yescharacteristic, complemented, Sylow
104C2×D3—1951no—
105C11D45⋊D1311yescharacteristic, direct product factor, Sylow
106C2×C5—1171no—
107D5—91no—
108D5—131no—
109C9D5×C11×D1311yescharacteristic, complemented, Sylow
110C2×C3—651no—
111D3—151no—
112D3—391no—
113C5C11×D9×D1311yescharacteristic, complemented, Sylow
114C22—5851noSylow
115C3C11×D15⋊D1311yescharacteristic
116C2—451no—
117C2—651no—
118C2—1171no—
subgroupG/H
center, hypercenterC11D45⋊D13
commutator, cosocle, hypocenterC5×C9×C13C22×C11
FrattiniC3C11×D15⋊D13
FittingC5×C9×C11×C13C22
socleC3×C5×C11×C13C2×D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C13×D45C2semidirect
2. C5×C11×D117C2semidirect
3. C9×C11×D65C2semidirect
5. C5×C9×C11×C13C22semidirect
11. C11×D117D5semidirect
14. D45⋊D13C11direct (N × H)
18. C11×D65D9semidirect
21. C9×C11×C13C2×D5semidirect
22. C13×D45C2×C11semidirect
23. C5×D117C2×C11semidirect
24. C9×D65C2×C11semidirect
25. C11×D45D13semidirect
32. C5×C11×C13C2×D9semidirect
34. C5×C9×C13C22×C11semidirect
36. C5×C9×C11C2×D13semidirect
50. D117D5×C11semidirect
61. C11×C13D5×D9semidirect
63. D65C11×D9semidirect
66. C9×C13C2×D5×C11semidirect
70. C9×C11D5×D13semidirect
71. D45C11×D13semidirect
80. C5×C13C2×C11×D9semidirect
82. C5×C11D9×D13semidirect
84. C5×C9C2×C11×D13semidirect
103. C13D5×C11×D9semidirect
105. C11D45⋊D13direct (N × H)
109. C9D5×C11×D13semidirect
113. C5C11×D9×D13semidirect

Maximal subgroups

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

subgroupindex
C11×C13×D452
C5×C11×D1172
C9×C11×D652
C11×D15⋊D133
C11×D9×D135
D45⋊D1311
D5×C11×D913