Finite Group Databasebeta

← D5×C13×C3⋊D15 #26043805

Subgroups — D5×C13×C3⋊D15 #26043805

Order 11700.

288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 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×C13×C3⋊D15C211yesmaximal, characteristic, complemented
3C32×C5×D5×C13C211yesmaximal, characteristic, complemented
4D5×C13×D15—34nomaximal
5C32×C52×C13C2211yescharacteristic, complemented, Hall
6C2×C13×C3⋊D15—51nomaximal
7D5×C13×C3⋊D3—51nomaximal
8C13×C3⋊(C5⋊D5)—34no—
9C5×C13×D15—34no—
10C3×C5×D5×C13D314yescomplemented
11D52×C13—91noHall
12C2×C32×C5×C13—51no—
13C13×C3⋊D15—51no—
14C13×C3⋊D15—51no—
15C13×C3⋊D15—102no—
16C13×C3⋊D15D511yescharacteristic, direct product factor
17C5×C13×C3⋊D3—51no—
18C32×D5×C13D511yescharacteristic, complemented
19C3×C52×C13C2×D314yescomplemented
20D5×C3⋊D15C1311yesmaximal, characteristic, direct product factor, Hall
21C2×C13×D15—154no—
22D3×D5×C13—154no—
23C13×C5⋊D5—91no—
24C5×D5×C13—91no—
25C5×D5×C13C3⋊D311yescharacteristic, complemented
26C32×C5×C13—22no—
27C32×C5×C13C2×D511yescharacteristic, complemented
28C32×C5×C13C2×D511yescharacteristic, complemented
29C2×C13×C3⋊D3—251noHall
30C3⋊(C3⋊(C5⋊D5))C2×C1311yescharacteristic, complemented
31C5×C3⋊D15C2×C1311yescharacteristic, complemented
32C32×C5×D5C2×C1311yescharacteristic, complemented
33C2×C3×C5×C13—54no—
34C13×D15—34no—
35C13×D15—154no—
36C13×D15—154no—
37C13×D15—308no—
38C5×D3×C13—154no—
39C3×D5×C13D1514yescomplemented
40C52×C13C2×C3⋊D311yescharacteristic, complemented, Hall
41D5×D15—34no—
42C2×D5×C13—451no—
43C2×D5×C13—451no—
44C2×C32×C13—51no—
45C13×C3⋊D3—51no—
46C13×C3⋊D3—251no—
47C32×C52C22×C1311yescharacteristic, complemented, Hall
48C3×C5×C13—28no—
49C3×C5×C13D3×D514yescomplemented
50C3×C5×C13C2×D1514yescomplemented
51C2×C3⋊D15—51no—
52D5×C3⋊D3—51no—
53C2×D3×C13—754no—
54C3⋊(C5⋊D5)—34no—
55C5×D15—34no—
56C3×C5×D5D3×C1314yescomplemented
57C2×C5×C13—51no—
58C2×C5×C13—451no—
59D5×C13—91no—
60D5×C13—451no—
61D5×C13—451no—
62D5×C13—902no—
63D5×C13C3⋊D1511yescharacteristic, direct product factor
64C32×C13D5211yescharacteristic, complemented, Hall
65D52—91noHall
66C2×C32×C5—51no—
67C3⋊D15—51no—
68C3⋊D15—51no—
69C3⋊D15—102no—
70C3⋊D15D5×C1311yescharacteristic, direct product factor
71C5×C3⋊D3—51no—
72C32×D5D5×C1311yescharacteristic, complemented
73C2×C3×C13—54no—
74D3×C13—154no—
75D3×C13—754no—
76C3×C52C2×D3×C1314yescomplemented
77C5×C13—22no—
78C5×C13D5×C3⋊D311yescharacteristic, complemented
79C5×C13C2×C3⋊D1511yescharacteristic, complemented
80C2×D15—154no—
81D3×D5—154no—
82C22×C13—2251noHall
83C5⋊D5—91no—
84C5×D5—91no—
85C5×D5C13×C3⋊D311yescharacteristic, complemented
86C32×C5—22no—
87C32×C5C2×D5×C1311yescharacteristic, complemented
88C32×C5C2×D5×C1311yescharacteristic, complemented
89C3×C13D5×D1514yescomplemented
90C2×C3⋊D3—251noHall
91C2×C3×C5—54no—
92D15—34no—
93D15—154no—
94D15—154no—
95D15—308no—
96C3×D5C13×D1514yescomplemented
97C5×D3—154no—
98C2×C13—51no—
99C2×C13—451no—
100C2×C13—2251no—
101C52C2×C13×C3⋊D311yescharacteristic, complemented, Sylow
102C2×D5—451no—
103C2×D5—451no—
104C2×C32—51no—
105C3⋊D3—51no—
106C3⋊D3—251no—
107C3×C5—28no—
108C3×C5D3×D5×C1314yescomplemented
109C3×C5C2×C13×D1514yescomplemented
110C13D5×C3⋊D1511yescharacteristic, direct product factor, Sylow
111C2×D3—754no—
112C2×C5—51no—
113C2×C5—451no—
114D5—91no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5C13×C3⋊D1511yescharacteristic, direct product factor
119C32D52×C1311yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—154no—
122D3—754no—
123C5—22no—
124C5D5×C13×C3⋊D311yescharacteristic, complemented
125C5C2×C13×C3⋊D1511yescharacteristic, complemented
126C22—2251noSylow
127C3D5×C13×D1514yescomplemented
128C2—51no—
129C2—451no—
130C2—2251no—
subgroupG/H
center, hypercenterC13D5×C3⋊D15
commutator, cosocle, hypocenterC32×C52C22×C13
FrattiniC1G
Fitting, socleC32×C52×C13C22
LCSG ▷ C32×C52
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C13×C3⋊(C3⋊(C5⋊D5))C2semidirect
2. C5×C13×C3⋊D15C2semidirect
3. C32×C5×D5×C13C2semidirect
5. C32×C52×C13C22semidirect
10. C3×C5×D5×C13D3semidirect
16. C13×C3⋊D15D5direct (N × H)
18. C32×D5×C13D5semidirect
19. C3×C52×C13C2×D3semidirect
20. D5×C3⋊D15C13direct (N × H)
25. C5×D5×C13C3⋊D3semidirect
27. C32×C5×C13C2×D5semidirect
28. C32×C5×C13C2×D5semidirect
30. C3⋊(C3⋊(C5⋊D5))C2×C13semidirect
31. C5×C3⋊D15C2×C13semidirect
32. C32×C5×D5C2×C13semidirect
39. C3×D5×C13D15semidirect
40. C52×C13C2×C3⋊D3semidirect
47. C32×C52C22×C13semidirect
49. C3×C5×C13D3×D5semidirect
50. C3×C5×C13C2×D15semidirect
56. C3×C5×D5D3×C13semidirect
63. D5×C13C3⋊D15direct (N × H)
64. C32×C13D52semidirect
70. C3⋊D15D5×C13direct (N × H)
72. C32×D5D5×C13semidirect
76. C3×C52C2×D3×C13semidirect
78. C5×C13D5×C3⋊D3semidirect
79. C5×C13C2×C3⋊D15semidirect
85. C5×D5C13×C3⋊D3semidirect
87. C32×C5C2×D5×C13semidirect
88. C32×C5C2×D5×C13semidirect
89. C3×C13D5×D15semidirect
96. C3×D5C13×D15semidirect
101. C52C2×C13×C3⋊D3semidirect
108. C3×C5D3×D5×C13semidirect
109. C3×C5C2×C13×D15semidirect
110. C13D5×C3⋊D15direct (N × H)
118. D5C13×C3⋊D15direct (N × H)
119. C32D52×C13semidirect
124. C5D5×C13×C3⋊D3semidirect
125. C5C2×C13×C3⋊D15semidirect
127. C3D5×C13×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×C13×C3⋊D152
C32×C5×D5×C132
D5×C13×D153
C2×C13×C3⋊D155
D5×C13×C3⋊D35
D5×C3⋊D1513