Finite Group Databasebeta

← D65⋊(C3⋊D15) #26043808

Subgroups — D65⋊(C3⋊D15) #26043808

Order 11700.

288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C13×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
2C5×C3⋊D195C211yesmaximal, characteristic, complemented
3C32×C5×D65C211yesmaximal, characteristic, complemented
4D65⋊D15—34nomaximal
5C32×C52×C13C2211yescharacteristic, complemented, Hall
6D65⋊(C3⋊D3)—51nomaximal
7D13×C3⋊D15—51nomaximal
8C13×C3⋊(C5⋊D5)—34no—
9C5×D195—34no—
10C3×C5×D65D314yescomplemented
11(C5⋊D5)⋊D13—91noHall
12C3⋊D195D511yescharacteristic, complemented
13C13×C3⋊D15—51no—
14C13×C3⋊D15—51no—
15C13×C3⋊D15—102no—
16C5×C3⋊D39—51no—
17C32×D65D511yescharacteristic, complemented
18C32×C5×D13—51no—
19C3×C52×C13C2×D314yescomplemented
20D5×C3⋊D15—131nomaximal, Hall
21D15⋊D13—154no—
22D13×D15—154no—
23C13×C5⋊D5—91no—
24C5×D65—91no—
25C5×D65C3⋊D311yescharacteristic, complemented
26C32×C5×C13—22no—
27C32×C5×C13C2×D511yescharacteristic, complemented
28C32×C5×C13C2×D511yescharacteristic, complemented
29C3⋊D3×D13—251noHall
30C3⋊(C3⋊(C5⋊D5))D1311yescharacteristic, complemented
31C5×C3⋊D15—131no—
32C32×C5×D5—131no—
33D195—34no—
34C13×D15—154no—
35C13×D15—154no—
36C13×D15—308no—
37C5×D39—154no—
38C3×D65D1514yescomplemented
39C3×C5×D13—54no—
40C52×C13C2×C3⋊D311yescharacteristic, complemented, Hall
41D5×D15—394no—
42D5×D13—451no—
43D5×D13—451no—
44C3⋊D39—51no—
45C13×C3⋊D3—251no—
46C32×D13—51no—
47C32×C52C2×D1311yescharacteristic, complemented, Hall
48C3×C5×C13—28no—
49C3×C5×C13D3×D514yescomplemented
50C3×C5×C13C2×D1514yescomplemented
51C2×C3⋊D15—651no—
52D5×C3⋊D3—651no—
53D3×D13—754no—
54C3⋊(C5⋊D5)—34no—
55C5×D15—394no—
56C3×C5×D5—134no—
57D65—91no—
58D65C3⋊D1511yescharacteristic, complemented
59C5×D13—51no—
60C5×D13—451no—
61D5×C13—451no—
62D5×C13—451no—
63D5×C13—902no—
64C32×C13D5211yescharacteristic, complemented, Hall
65D52—1171noHall
66C2×C32×C5—651no—
67C3⋊D15—51no—
68C3⋊D15—51no—
69C3⋊D15—102no—
70C3⋊D15—131no—
71C5×C3⋊D3—651no—
72C32×D5—131no—
73D39—154no—
74C3×D13—54no—
75D3×C13—754no—
76C3×C52D3×D1314yescomplemented
77C5×C13—22no—
78C5×C13D5×C3⋊D311yescharacteristic, complemented
79C5×C13C2×C3⋊D1511yescharacteristic, complemented
80C2×D15—1954no—
81D3×D5—1954no—
82C2×D13—2251noHall
83C5⋊D5—91no—
84C5×D5—131no—
85C5×D5—1171no—
86C32×C5—22no—
87C32×C5D5×D1311yescharacteristic, complemented
88C32×C5D5×D1311yescharacteristic, complemented
89C3×C13D5×D1514yescomplemented
90C2×C3⋊D3—3251noHall
91C2×C3×C5—654no—
92D15—154no—
93D15—154no—
94D15—308no—
95D15—394no—
96C3×D5—134no—
97C5×D3—1954no—
98C2×C13—2251no—
99D13—51no—
100D13—451no—
101C52C3⋊D3×D1311yescharacteristic, complemented, Sylow
102C2×D5—5851no—
103C2×D5—5851no—
104C2×C32—651no—
105C3⋊D3—251no—
106C3⋊D3—651no—
107C3×C5—28no—
108C3×C5D13×D1514yescomplemented
109C3×C5D15⋊D1314yescomplemented
110C13D5×C3⋊D1511yescharacteristic, complemented, Sylow
111C2×D3—9754no—
112C2×C5—651no—
113C2×C5—5851no—
114D5—131no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5—1171no—
119C32(C5⋊D5)⋊D1311yescharacteristic, complemented, Sylow
120C2×C3—654no—
121D3—754no—
122D3—1954no—
123C5—22no—
124C5D13×C3⋊D1511yescharacteristic, complemented
125C5D65⋊(C3⋊D3)11yescharacteristic, complemented
126C22—29251noSylow
127C3D65⋊D1514yescomplemented
128C2—651no—
129C2—5851no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C13C22
LCSG ▷ C32×C52×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13×C3⋊(C3⋊(C5⋊D5))C2semidirect
2. C5×C3⋊D195C2semidirect
3. C32×C5×D65C2semidirect
5. C32×C52×C13C22semidirect
10. C3×C5×D65D3semidirect
12. C3⋊D195D5semidirect
17. C32×D65D5semidirect
19. C3×C52×C13C2×D3semidirect
25. C5×D65C3⋊D3semidirect
27. C32×C5×C13C2×D5semidirect
28. C32×C5×C13C2×D5semidirect
30. C3⋊(C3⋊(C5⋊D5))D13semidirect
38. C3×D65D15semidirect
40. C52×C13C2×C3⋊D3semidirect
47. C32×C52C2×D13semidirect
49. C3×C5×C13D3×D5semidirect
50. C3×C5×C13C2×D15semidirect
58. D65C3⋊D15semidirect
64. C32×C13D52semidirect
76. C3×C52D3×D13semidirect
78. C5×C13D5×C3⋊D3semidirect
79. C5×C13C2×C3⋊D15semidirect
87. C32×C5D5×D13semidirect
88. C32×C5D5×D13semidirect
89. C3×C13D5×D15semidirect
101. C52C3⋊D3×D13semidirect
108. C3×C5D13×D15semidirect
109. C3×C5D15⋊D13semidirect
110. C13D5×C3⋊D15semidirect
119. C32(C5⋊D5)⋊D13semidirect
124. C5D13×C3⋊D15semidirect
125. C5D65⋊(C3⋊D3)semidirect
127. C3D65⋊D15semidirect

Maximal subgroups

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

subgroupindex
C13×C3⋊(C3⋊(C5⋊D5))2
C5×C3⋊D1952
C32×C5×D652
D65⋊D153
D65⋊(C3⋊D3)5
D13×C3⋊D155
D5×C3⋊D1513