Finite Group Databasebeta

← D95⋊(C3⋊D15) #30685916

Subgroups — D95⋊(C3⋊D15) #30685916

Order 17100.

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
1C19×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
2C5×C3⋊D285C211yesmaximal, characteristic, complemented
3C32×C5×D95C211yesmaximal, characteristic, complemented
4D95⋊D15—34nomaximal
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6D95⋊(C3⋊D3)—51nomaximal
7D19×C3⋊D15—51nomaximal
8C19×C3⋊(C5⋊D5)—34no—
9C5×D285—34no—
10C3×C5×D95D314yescomplemented
11(C5⋊D5)⋊D19—91noHall
12C3⋊D285D511yescharacteristic, complemented
13C19×C3⋊D15—51no—
14C19×C3⋊D15—51no—
15C19×C3⋊D15—102no—
16C5×C3⋊D57—51no—
17C32×D95D511yescharacteristic, complemented
18C32×C5×D19—51no—
19C3×C52×C19C2×D314yescomplemented
20D15⋊D19—154no—
21D15×D19—154no—
22C19×C5⋊D5—91no—
23C5×D95—91no—
24C5×D95C3⋊D311yescharacteristic, complemented
25D5×C3⋊D15—191nomaximal, Hall
26C32×C5×C19—22no—
27C32×C5×C19C2×D511yescharacteristic, complemented
28C32×C5×C19C2×D511yescharacteristic, complemented
29C3⋊D3×D19—251noHall
30D285—34no—
31C19×D15—154no—
32C19×D15—154no—
33C19×D15—308no—
34C5×D57—154no—
35C3×D95D1514yescomplemented
36C3×C5×D19—54no—
37C52×C19C2×C3⋊D311yescharacteristic, complemented, Hall
38C3⋊(C3⋊(C5⋊D5))D1911yescharacteristic, complemented
39C5×C3⋊D15—191no—
40C32×C5×D5—191no—
41D5×D19—451no—
42D5×D19—451no—
43C3⋊D57—51no—
44C3⋊D3×C19—251no—
45C32×D19—51no—
46D5×D15—574no—
47C3×C5×C19—28no—
48C3×C5×C19D3×D514yescomplemented
49C3×C5×C19C2×D1514yescomplemented
50D3×D19—754no—
51C32×C52C2×D1911yescharacteristic, complemented, Hall
52D95—91no—
53D95C3⋊D1511yescharacteristic, complemented
54C5×D19—51no—
55C5×D19—451no—
56D5×C19—451no—
57D5×C19—451no—
58D5×C19—902no—
59C2×C3⋊D15—951no—
60D5×C3⋊D3—951no—
61C32×C19D5211yescharacteristic, complemented, Hall
62C3⋊(C5⋊D5)—34no—
63C5×D15—574no—
64C3×C5×D5—194no—
65D57—154no—
66C3×D19—54no—
67D3×C19—754no—
68D52—1711noHall
69C5×C19—22no—
70C5×C19D5×C3⋊D311yescharacteristic, complemented
71C5×C19C2×C3⋊D1511yescharacteristic, complemented
72C2×C32×C5—951no—
73C3⋊D15—51no—
74C3⋊D15—51no—
75C3⋊D15—102no—
76C3⋊D15—191no—
77C5×C3⋊D3—951no—
78C32×D5—191no—
79C2×D19—2251noHall
80C3×C52D3×D1914yescomplemented
81C2×D15—2854no—
82D3×D5—2854no—
83C3×C19D5×D1514yescomplemented
84C5⋊D5—91no—
85C5×D5—191no—
86C5×D5—1711no—
87C32×C5—22no—
88C32×C5D5×D1911yescharacteristic, complemented
89C32×C5D5×D1911yescharacteristic, complemented
90C2×C19—2251no—
91D19—51no—
92D19—451no—
93C2×C3⋊D3—4751noHall
94C2×C3×C5—954no—
95D15—154no—
96D15—154no—
97D15—308no—
98D15—574no—
99C3×D5—194no—
100C5×D3—2854no—
101C52C3⋊D3×D1911yescharacteristic, complemented, Sylow
102C2×D5—8551no—
103C2×D5—8551no—
104C19D5×C3⋊D1511yescharacteristic, complemented, Sylow
105C2×C32—951no—
106C3⋊D3—251no—
107C3⋊D3—951no—
108C3×C5—28no—
109C3×C5D15×D1914yescomplemented
110C3×C5D15⋊D1914yescomplemented
111C2×D3—14254no—
112C2×C5—8551no—
113C2×C5—951no—
114D5—191no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5—1711no—
119C32(C5⋊D5)⋊D1911yescharacteristic, complemented, Sylow
120C2×C3—954no—
121D3—2854no—
122D3—754no—
123C5—22no—
124C5D19×C3⋊D1511yescharacteristic, complemented
125C5D95⋊(C3⋊D3)11yescharacteristic, complemented
126C22—42751noSylow
127C3D95⋊D1514yescomplemented
128C2—8551no—
129C2—951no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C19C22
LCSG ▷ C32×C52×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C19×C3⋊(C3⋊(C5⋊D5))C2semidirect
2. C5×C3⋊D285C2semidirect
3. C32×C5×D95C2semidirect
5. C32×C52×C19C22semidirect
10. C3×C5×D95D3semidirect
12. C3⋊D285D5semidirect
17. C32×D95D5semidirect
19. C3×C52×C19C2×D3semidirect
24. C5×D95C3⋊D3semidirect
27. C32×C5×C19C2×D5semidirect
28. C32×C5×C19C2×D5semidirect
35. C3×D95D15semidirect
37. C52×C19C2×C3⋊D3semidirect
38. C3⋊(C3⋊(C5⋊D5))D19semidirect
48. C3×C5×C19D3×D5semidirect
49. C3×C5×C19C2×D15semidirect
51. C32×C52C2×D19semidirect
53. D95C3⋊D15semidirect
61. C32×C19D52semidirect
70. C5×C19D5×C3⋊D3semidirect
71. C5×C19C2×C3⋊D15semidirect
80. C3×C52D3×D19semidirect
83. C3×C19D5×D15semidirect
88. C32×C5D5×D19semidirect
89. C32×C5D5×D19semidirect
101. C52C3⋊D3×D19semidirect
104. C19D5×C3⋊D15semidirect
109. C3×C5D15×D19semidirect
110. C3×C5D15⋊D19semidirect
119. C32(C5⋊D5)⋊D19semidirect
124. C5D19×C3⋊D15semidirect
125. C5D95⋊(C3⋊D3)semidirect
127. C3D95⋊D15semidirect

Maximal subgroups

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

subgroupindex
C19×C3⋊(C3⋊(C5⋊D5))2
C5×C3⋊D2852
C32×C5×D952
D95⋊D153
D95⋊(C3⋊D3)5
D19×C3⋊D155
D5×C3⋊D1519