Finite Group Databasebeta

← D5×C29×C3⋊D15 #39908200

Subgroups — D5×C29×C3⋊D15 #39908200

Order 26100.

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
1C32×C5×D5×C29C211yesmaximal, characteristic, complemented
2C5×C29×C3⋊D15C211yesmaximal, characteristic, complemented
3C29×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4D5×C29×D15—34nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6C2×C29×C3⋊D15—51nomaximal
7D5×C3⋊D3×C29—51nomaximal
8C29×C3⋊(C5⋊D5)—34no—
9C5×C29×D15—34no—
10C3×C5×D5×C29D314yescomplemented
11D52×C29—91noHall
12C29×C3⋊D15—51no—
13C29×C3⋊D15—51no—
14C29×C3⋊D15—102no—
15C29×C3⋊D15D511yescharacteristic, direct product factor
16C5×C3⋊D3×C29—51no—
17C32×D5×C29D511yescharacteristic, complemented
18C2×C32×C5×C29—51no—
19C3×C52×C29C2×D314yescomplemented
20C2×C29×D15—154no—
21D3×D5×C29—154no—
22C29×C5⋊D5—91no—
23C5×D5×C29—91no—
24C5×D5×C29C3⋊D311yescharacteristic, complemented
25C32×C5×C29—22no—
26C32×C5×C29C2×D511yescharacteristic, complemented
27C32×C5×C29C2×D511yescharacteristic, complemented
28C2×C3⋊D3×C29—251noHall
29D5×C3⋊D15C2911yesmaximal, characteristic, direct product factor, Hall
30C2×C3×C5×C29—54no—
31C29×D15—34no—
32C29×D15—154no—
33C29×D15—154no—
34C29×D15—308no—
35C5×D3×C29—154no—
36C3×D5×C29D1514yescomplemented
37C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×D5×C29—451no—
39C2×D5×C29—451no—
40C2×C32×C29—51no—
41C3⋊D3×C29—51no—
42C3⋊D3×C29—251no—
43C3⋊(C3⋊(C5⋊D5))C2×C2911yescharacteristic, complemented
44C5×C3⋊D15C2×C2911yescharacteristic, complemented
45C32×C5×D5C2×C2911yescharacteristic, complemented
46C3×C5×C29—28no—
47C3×C5×C29D3×D514yescomplemented
48C3×C5×C29C2×D1514yescomplemented
49C2×D3×C29—754no—
50D5×D15—34no—
51C2×C5×C29—51no—
52C2×C5×C29—451no—
53D5×C29—91no—
54D5×C29—451no—
55D5×C29—451no—
56D5×C29—902no—
57D5×C29C3⋊D1511yescharacteristic, direct product factor
58C32×C29D5211yescharacteristic, complemented, Hall
59C32×C52C22×C2911yescharacteristic, complemented, Hall
60C2×C3⋊D15—51no—
61D5×C3⋊D3—51no—
62C2×C3×C29—54no—
63D3×C29—154no—
64D3×C29—754no—
65C3⋊(C5⋊D5)—34no—
66C5×D15—34no—
67C3×C5×D5D3×C2914yescomplemented
68C5×C29—22no—
69C5×C29D5×C3⋊D311yescharacteristic, complemented
70C5×C29C2×C3⋊D1511yescharacteristic, complemented
71C22×C29—2251noHall
72D52—91noHall
73C2×C32×C5—51no—
74C3⋊D15—51no—
75C3⋊D15—51no—
76C3⋊D15—102no—
77C3⋊D15D5×C2911yescharacteristic, direct product factor
78C5×C3⋊D3—51no—
79C32×D5D5×C2911yescharacteristic, complemented
80C3×C29D5×D1514yescomplemented
81C3×C52C2×D3×C2914yescomplemented
82C2×D15—154no—
83D3×D5—154no—
84C2×C29—51no—
85C2×C29—451no—
86C2×C29—2251no—
87C5⋊D5—91no—
88C5×D5—91no—
89C5×D5C3⋊D3×C2911yescharacteristic, complemented
90C32×C5—22no—
91C32×C5C2×D5×C2911yescharacteristic, complemented
92C32×C5C2×D5×C2911yescharacteristic, complemented
93C2×C3⋊D3—251noHall
94C2×C3×C5—54no—
95D15—34no—
96D15—154no—
97D15—154no—
98D15—308no—
99C3×D5C29×D1514yescomplemented
100C5×D3—154no—
101C29D5×C3⋊D1511yescharacteristic, direct product factor, Sylow
102C52C2×C3⋊D3×C2911yescharacteristic, complemented, Sylow
103C2×D5—451no—
104C2×D5—451no—
105C2×C32—51no—
106C3⋊D3—51no—
107C3⋊D3—251no—
108C3×C5—28no—
109C3×C5D3×D5×C2914yescomplemented
110C3×C5C2×C29×D1514yescomplemented
111C2×D3—754no—
112C2×C5—51no—
113C2×C5—451no—
114D5—91no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5C29×C3⋊D1511yescharacteristic, direct product factor
119C32D52×C2911yescharacteristic, complemented, Sylow
120C2×C3—54no—
121D3—154no—
122D3—754no—
123C5—22no—
124C5D5×C3⋊D3×C2911yescharacteristic, complemented
125C5C2×C29×C3⋊D1511yescharacteristic, complemented
126C22—2251noSylow
127C3D5×C29×D1514yescomplemented
128C2—51no—
129C2—451no—
130C2—2251no—
subgroupG/H
center, hypercenterC29D5×C3⋊D15
commutator, cosocle, hypocenterC32×C52C22×C29
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C32×C52
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C29C2semidirect
2. C5×C29×C3⋊D15C2semidirect
3. C29×C3⋊(C3⋊(C5⋊D5))C2semidirect
5. C32×C52×C29C22semidirect
10. C3×C5×D5×C29D3semidirect
15. C29×C3⋊D15D5direct (N × H)
17. C32×D5×C29D5semidirect
19. C3×C52×C29C2×D3semidirect
24. C5×D5×C29C3⋊D3semidirect
26. C32×C5×C29C2×D5semidirect
27. C32×C5×C29C2×D5semidirect
29. D5×C3⋊D15C29direct (N × H)
36. C3×D5×C29D15semidirect
37. C52×C29C2×C3⋊D3semidirect
43. C3⋊(C3⋊(C5⋊D5))C2×C29semidirect
44. C5×C3⋊D15C2×C29semidirect
45. C32×C5×D5C2×C29semidirect
47. C3×C5×C29D3×D5semidirect
48. C3×C5×C29C2×D15semidirect
57. D5×C29C3⋊D15direct (N × H)
58. C32×C29D52semidirect
59. C32×C52C22×C29semidirect
67. C3×C5×D5D3×C29semidirect
69. C5×C29D5×C3⋊D3semidirect
70. C5×C29C2×C3⋊D15semidirect
77. C3⋊D15D5×C29direct (N × H)
79. C32×D5D5×C29semidirect
80. C3×C29D5×D15semidirect
81. C3×C52C2×D3×C29semidirect
89. C5×D5C3⋊D3×C29semidirect
91. C32×C5C2×D5×C29semidirect
92. C32×C5C2×D5×C29semidirect
99. C3×D5C29×D15semidirect
101. C29D5×C3⋊D15direct (N × H)
102. C52C2×C3⋊D3×C29semidirect
109. C3×C5D3×D5×C29semidirect
110. C3×C5C2×C29×D15semidirect
118. D5C29×C3⋊D15direct (N × H)
119. C32D52×C29semidirect
124. C5D5×C3⋊D3×C29semidirect
125. C5C2×C29×C3⋊D15semidirect
127. C3D5×C29×D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D5×C292
C5×C29×C3⋊D152
C29×C3⋊(C3⋊(C5⋊D5))2
D5×C29×D153
C2×C29×C3⋊D155
D5×C3⋊D3×C295
D5×C3⋊D1529