Finite Group Databasebeta

← C3⋊D15×D65 #26043807

Subgroups — C3⋊D15×D65 #26043807

Order 11700.

288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C3⋊(C3⋊(C5⋊D65))C211yesmaximal, characteristic, complemented
2C5×C13×C3⋊D15C211yesmaximal, characteristic, complemented
3C32×C5×D65C211yesmaximal, characteristic, complemented
4D15×D65—34nomaximal
5C32×C52×C13C2211yescharacteristic, complemented, Hall
6C3⋊D3×D65—51nomaximal
7D13×C3⋊D15—51nomaximal
8C3⋊(C5⋊D65)—34no—
9C5×C13×D15—34no—
10C3×C5×D65D314yescomplemented
11D5×D65—91noHall
12C3⋊D195—51no—
13C3⋊D195—51no—
14C3⋊D195—102no—
15C13×C3⋊D15D511yescharacteristic, complemented
16C5×C13×C3⋊D3—51no—
17C32×D65D511yescharacteristic, complemented
18C32×C5×D13—51no—
19C3×C52×C13C2×D314yescomplemented
20D5×C3⋊D15—131nomaximal, Hall
21D3×D65—154no—
22D13×D15—154no—
23C5⋊D65—91no—
24C5×D65C3⋊D311yescharacteristic, complemented
25C5×D5×C13—91no—
26C32×C5×C13—22no—
27C32×C5×C13C2×D511yescharacteristic, complemented
28C32×C5×C13C2×D511yescharacteristic, complemented
29C3⋊D3×D13—251noHall
30C3⋊(C3⋊(C5⋊D5))—131no—
31C5×C3⋊D15D1311yescharacteristic, complemented
32C32×C5×D5—131no—
33D195—154no—
34D195—154no—
35D195—308no—
36C13×D15—34no—
37C5×D3×C13—154no—
38C3×D65D1514yescomplemented
39C3×C5×D13—54no—
40C52×C13C2×C3⋊D311yescharacteristic, complemented, Hall
41D5×D15—394no—
42C2×D65—451no—
43D5×D13—451no—
44C3⋊D39—251no—
45C13×C3⋊D3—51no—
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)—394no—
55C5×D15—34no—
56C3×C5×D5—134no—
57C2×C5×C13—451no—
58D65—451no—
59D65—451no—
60D65—902no—
61D65C3⋊D1511yescharacteristic, direct product factor
62C5×D13—51no—
63D5×C13—91no—
64C32×C13D5211yescharacteristic, complemented, Hall
65D52—1171noHall
66C2×C32×C5—651no—
67C3⋊D15—651no—
68C3⋊D15—651no—
69C3⋊D15—1302no—
70C3⋊D15D6511yescharacteristic, direct product factor
71C5×C3⋊D3—51no—
72C32×D5—131no—
73D39—754no—
74C3×D13—54no—
75D3×C13—154no—
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—1171no—
84C5×D5—91no—
85C5×D5—131no—
86C32×C5—22no—
87C32×C5D5×D1311yescharacteristic, complemented
88C32×C5C2×D6511yescharacteristic, complemented
89C3×C13D5×D1514yescomplemented
90C2×C3⋊D3—3251noHall
91C2×C3×C5—654no—
92D15—34no—
93D15—3908no—
94D15—1954no—
95D15—1954no—
96C3×D5—134no—
97C5×D3—154no—
98C2×C13—451no—
99D13—51no—
100D13—2251no—
101C52C3⋊D3×D1311yescharacteristic, complemented, Sylow
102C2×D5—5851no—
103C2×D5—5851no—
104C2×C32—651no—
105C3⋊D3—51no—
106C3⋊D3—3251no—
107C3×C5—28no—
108C3×C5D13×D1514yescomplemented
109C3×C5D3×D6514yescomplemented
110C13D5×C3⋊D1511yescharacteristic, complemented, Sylow
111C2×D3—9754no—
112C2×C5—451no—
113C2×C5—651no—
114D5—91no—
115D5—131no—
116D5—5851no—
117D5—5851no—
118D5—11702no—
119C32D5×D6511yescharacteristic, complemented, Sylow
120C2×C3—654no—
121D3—154no—
122D3—9754no—
123C5—22no—
124C5D13×C3⋊D1511yescharacteristic, complemented
125C5C3⋊D3×D6511yescharacteristic, complemented
126C22—29251noSylow
127C3D15×D6514yescomplemented
128C2—451no—
129C2—651no—
130C2—29251no—
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. C3⋊(C3⋊(C5⋊D65))C2semidirect
2. C5×C13×C3⋊D15C2semidirect
3. C32×C5×D65C2semidirect
5. C32×C52×C13C22semidirect
10. C3×C5×D65D3semidirect
15. C13×C3⋊D15D5semidirect
17. C32×D65D5semidirect
19. C3×C52×C13C2×D3semidirect
24. C5×D65C3⋊D3semidirect
27. C32×C5×C13C2×D5semidirect
28. C32×C5×C13C2×D5semidirect
31. C5×C3⋊D15D13semidirect
38. C3×D65D15semidirect
40. C52×C13C2×C3⋊D3semidirect
47. C32×C52C2×D13semidirect
49. C3×C5×C13D3×D5semidirect
50. C3×C5×C13C2×D15semidirect
61. D65C3⋊D15direct (N × H)
64. C32×C13D52semidirect
70. C3⋊D15D65direct (N × H)
76. C3×C52D3×D13semidirect
78. C5×C13D5×C3⋊D3semidirect
79. C5×C13C2×C3⋊D15semidirect
87. C32×C5D5×D13semidirect
88. C32×C5C2×D65semidirect
89. C3×C13D5×D15semidirect
101. C52C3⋊D3×D13semidirect
108. C3×C5D13×D15semidirect
109. C3×C5D3×D65semidirect
110. C13D5×C3⋊D15semidirect
119. C32D5×D65semidirect
124. C5D13×C3⋊D15semidirect
125. C5C3⋊D3×D65semidirect
127. C3D15×D65semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D65))2
C5×C13×C3⋊D152
C32×C5×D652
D15×D653
C3⋊D3×D655
D13×C3⋊D155
D5×C3⋊D1513