Finite Group Databasebeta

← D145⋊(C3⋊D15) #39908203

Subgroups — D145⋊(C3⋊D15) #39908203

Order 26100.

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
1C32×C5×D145C211yesmaximal, characteristic, complemented
2C5×C3⋊D435C211yesmaximal, characteristic, complemented
3C29×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4D145⋊D15—34nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6D145⋊(C3⋊D3)—51nomaximal
7D29×C3⋊D15—51nomaximal
8C29×C3⋊(C5⋊D5)—34no—
9C5×D435—34no—
10C3×C5×D145D314yescomplemented
11(C5⋊D5)⋊D29—91noHall
12C3⋊D435D511yescharacteristic, complemented
13C29×C3⋊D15—51no—
14C29×C3⋊D15—51no—
15C29×C3⋊D15—102no—
16C5×C3⋊D87—51no—
17C32×D145D511yescharacteristic, complemented
18C32×C5×D29—51no—
19C3×C52×C29C2×D314yescomplemented
20D15⋊D29—154no—
21D15×D29—154no—
22C29×C5⋊D5—91no—
23C5×D145—91no—
24C5×D145C3⋊D311yescharacteristic, complemented
25C32×C5×C29—22no—
26C32×C5×C29C2×D511yescharacteristic, complemented
27C32×C5×C29C2×D511yescharacteristic, complemented
28C3⋊D3×D29—251noHall
29D5×C3⋊D15—291nomaximal, Hall
30D435—34no—
31C29×D15—154no—
32C29×D15—154no—
33C29×D15—308no—
34C5×D87—154no—
35C3×D145D1514yescomplemented
36C3×C5×D29—54no—
37C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
38D5×D29—451no—
39D5×D29—451no—
40C3⋊D87—51no—
41C3⋊D3×C29—251no—
42C32×D29—51no—
43C3⋊(C3⋊(C5⋊D5))D2911yescharacteristic, complemented
44C5×C3⋊D15—291no—
45C32×C5×D5—291no—
46C3×C5×C29—28no—
47C3×C5×C29D3×D514yescomplemented
48C3×C5×C29C2×D1514yescomplemented
49D3×D29—754no—
50D5×D15—874no—
51D145—91no—
52D145C3⋊D1511yescharacteristic, complemented
53C5×D29—51no—
54C5×D29—451no—
55D5×C29—451no—
56D5×C29—451no—
57D5×C29—902no—
58C32×C29D5211yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60C2×C3⋊D15—1451no—
61D5×C3⋊D3—1451no—
62D87—154no—
63C3×D29—54no—
64D3×C29—754no—
65C3⋊(C5⋊D5)—34no—
66C5×D15—874no—
67C3×C5×D5—294no—
68C5×C29—22no—
69C5×C29D5×C3⋊D311yescharacteristic, complemented
70C5×C29C2×C3⋊D1511yescharacteristic, complemented
71C2×D29—2251noHall
72D52—2611noHall
73C2×C32×C5—1451no—
74C3⋊D15—51no—
75C3⋊D15—51no—
76C3⋊D15—102no—
77C3⋊D15—291no—
78C5×C3⋊D3—1451no—
79C32×D5—291no—
80C3×C29D5×D1514yescomplemented
81C3×C52D3×D2914yescomplemented
82C2×D15—4354no—
83D3×D5—4354no—
84C2×C29—2251no—
85D29—51no—
86D29—451no—
87C5⋊D5—91no—
88C5×D5—2611no—
89C5×D5—291no—
90C32×C5—22no—
91C32×C5D5×D2911yescharacteristic, complemented
92C32×C5D5×D2911yescharacteristic, complemented
93C2×C3⋊D3—7251noHall
94C2×C3×C5—1454no—
95D15—154no—
96D15—154no—
97D15—308no—
98D15—874no—
99C3×D5—294no—
100C5×D3—4354no—
101C29D5×C3⋊D1511yescharacteristic, complemented, Sylow
102C52C3⋊D3×D2911yescharacteristic, complemented, Sylow
103C2×D5—13051no—
104C2×D5—13051no—
105C2×C32—1451no—
106C3⋊D3—251no—
107C3⋊D3—1451no—
108C3×C5—28no—
109C3×C5D15×D2914yescomplemented
110C3×C5D15⋊D2914yescomplemented
111C2×D3—21754no—
112C2×C5—13051no—
113C2×C5—1451no—
114D5—2611no—
115D5—291no—
116D5—451no—
117D5—451no—
118D5—902no—
119C32(C5⋊D5)⋊D2911yescharacteristic, complemented, Sylow
120C2×C3—1454no—
121D3—754no—
122D3—4354no—
123C5—22no—
124C5D29×C3⋊D1511yescharacteristic, complemented
125C5D145⋊(C3⋊D3)11yescharacteristic, complemented
126C22—65251noSylow
127C3D145⋊D1514yescomplemented
128C2—13051no—
129C2—1451no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C29C22
LCSG ▷ C32×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×D145C2semidirect
2. C5×C3⋊D435C2semidirect
3. C29×C3⋊(C3⋊(C5⋊D5))C2semidirect
5. C32×C52×C29C22semidirect
10. C3×C5×D145D3semidirect
12. C3⋊D435D5semidirect
17. C32×D145D5semidirect
19. C3×C52×C29C2×D3semidirect
24. C5×D145C3⋊D3semidirect
26. C32×C5×C29C2×D5semidirect
27. C32×C5×C29C2×D5semidirect
35. C3×D145D15semidirect
37. C52×C29C2×C3⋊D3semidirect
43. C3⋊(C3⋊(C5⋊D5))D29semidirect
47. C3×C5×C29D3×D5semidirect
48. C3×C5×C29C2×D15semidirect
52. D145C3⋊D15semidirect
58. C32×C29D52semidirect
59. C32×C52C2×D29semidirect
69. C5×C29D5×C3⋊D3semidirect
70. C5×C29C2×C3⋊D15semidirect
80. C3×C29D5×D15semidirect
81. C3×C52D3×D29semidirect
91. C32×C5D5×D29semidirect
92. C32×C5D5×D29semidirect
101. C29D5×C3⋊D15semidirect
102. C52C3⋊D3×D29semidirect
109. C3×C5D15×D29semidirect
110. C3×C5D15⋊D29semidirect
119. C32(C5⋊D5)⋊D29semidirect
124. C5D29×C3⋊D15semidirect
125. C5D145⋊(C3⋊D3)semidirect
127. C3D145⋊D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1452
C5×C3⋊D4352
C29×C3⋊(C3⋊(C5⋊D5))2
D145⋊D153
D145⋊(C3⋊D3)5
D29×C3⋊D155
D5×C3⋊D1529