Finite Group Databasebeta

← C3⋊D15×D95 #30685915

Subgroups — C3⋊D15×D95 #30685915

Order 17100.

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⋊D95))C211yesmaximal, characteristic, complemented
2C5×C19×C3⋊D15C211yesmaximal, characteristic, complemented
3C32×C5×D95C211yesmaximal, characteristic, complemented
4D15×D95—34nomaximal
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6C3⋊D3×D95—51nomaximal
7D19×C3⋊D15—51nomaximal
8C3⋊(C5⋊D95)—34no—
9C5×C19×D15—34no—
10C3×C5×D95D314yescomplemented
11D5×D95—91noHall
12C3⋊D285—51no—
13C3⋊D285—51no—
14C3⋊D285—102no—
15C19×C3⋊D15D511yescharacteristic, complemented
16C5×C3⋊D3×C19—51no—
17C32×D95D511yescharacteristic, complemented
18C32×C5×D19—51no—
19C3×C52×C19C2×D314yescomplemented
20D3×D95—154no—
21D15×D19—154no—
22C5⋊D95—91no—
23C5×D95C3⋊D311yescharacteristic, complemented
24C5×D5×C19—91no—
25D5×C3⋊D15—191nomaximal, Hall
26C32×C5×C19—22no—
27C32×C5×C19C2×D511yescharacteristic, complemented
28C32×C5×C19C2×D511yescharacteristic, complemented
29C3⋊D3×D19—251noHall
30D285—154no—
31D285—154no—
32D285—308no—
33C19×D15—34no—
34C5×D3×C19—154no—
35C3×D95D1514yescomplemented
36C3×C5×D19—54no—
37C52×C19C2×C3⋊D311yescharacteristic, complemented, Hall
38C3⋊(C3⋊(C5⋊D5))—191no—
39C5×C3⋊D15D1911yescharacteristic, complemented
40C32×C5×D5—191no—
41C2×D95—451no—
42D5×D19—451no—
43C3⋊D57—251no—
44C3⋊D3×C19—51no—
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
52C2×C5×C19—451no—
53D95—451no—
54D95—451no—
55D95—902no—
56D95C3⋊D1511yescharacteristic, direct product factor
57C5×D19—51no—
58D5×C19—91no—
59C2×C3⋊D15—951no—
60D5×C3⋊D3—951no—
61C32×C19D5211yescharacteristic, complemented, Hall
62C3⋊(C5⋊D5)—574no—
63C5×D15—34no—
64C3×C5×D5—194no—
65D57—754no—
66C3×D19—54no—
67D3×C19—154no—
68D52—1711noHall
69C5×C19—22no—
70C5×C19D5×C3⋊D311yescharacteristic, complemented
71C5×C19C2×C3⋊D1511yescharacteristic, complemented
72C2×C32×C5—951no—
73C3⋊D15—951no—
74C3⋊D15—951no—
75C3⋊D15—1902no—
76C3⋊D15D9511yescharacteristic, direct product factor
77C5×C3⋊D3—51no—
78C32×D5—191no—
79C2×D19—2251noHall
80C3×C52D3×D1914yescomplemented
81C2×D15—2854no—
82D3×D5—2854no—
83C3×C19D5×D1514yescomplemented
84C5⋊D5—1711no—
85C5×D5—91no—
86C5×D5—191no—
87C32×C5—22no—
88C32×C5D5×D1911yescharacteristic, complemented
89C32×C5C2×D9511yescharacteristic, complemented
90C2×C19—451no—
91D19—51no—
92D19—2251no—
93C2×C3⋊D3—4751noHall
94C2×C3×C5—954no—
95D15—34no—
96D15—2854no—
97D15—2854no—
98D15—5708no—
99C3×D5—194no—
100C5×D3—154no—
101C52C3⋊D3×D1911yescharacteristic, complemented, Sylow
102C2×D5—8551no—
103C2×D5—8551no—
104C19D5×C3⋊D1511yescharacteristic, complemented, Sylow
105C2×C32—951no—
106C3⋊D3—51no—
107C3⋊D3—4751no—
108C3×C5—28no—
109C3×C5D15×D1914yescomplemented
110C3×C5D3×D9514yescomplemented
111C2×D3—14254no—
112C2×C5—451no—
113C2×C5—951no—
114D5—91no—
115D5—191no—
116D5—8551no—
117D5—8551no—
118D5—17102no—
119C32D5×D9511yescharacteristic, complemented, Sylow
120C2×C3—954no—
121D3—154no—
122D3—14254no—
123C5—22no—
124C5D19×C3⋊D1511yescharacteristic, complemented
125C5C3⋊D3×D9511yescharacteristic, complemented
126C22—42751noSylow
127C3D15×D9514yescomplemented
128C2—451no—
129C2—951no—
130C2—42751no—
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. C3⋊(C3⋊(C5⋊D95))C2semidirect
2. C5×C19×C3⋊D15C2semidirect
3. C32×C5×D95C2semidirect
5. C32×C52×C19C22semidirect
10. C3×C5×D95D3semidirect
15. C19×C3⋊D15D5semidirect
17. C32×D95D5semidirect
19. C3×C52×C19C2×D3semidirect
23. C5×D95C3⋊D3semidirect
27. C32×C5×C19C2×D5semidirect
28. C32×C5×C19C2×D5semidirect
35. C3×D95D15semidirect
37. C52×C19C2×C3⋊D3semidirect
39. C5×C3⋊D15D19semidirect
48. C3×C5×C19D3×D5semidirect
49. C3×C5×C19C2×D15semidirect
51. C32×C52C2×D19semidirect
56. D95C3⋊D15direct (N × H)
61. C32×C19D52semidirect
70. C5×C19D5×C3⋊D3semidirect
71. C5×C19C2×C3⋊D15semidirect
76. C3⋊D15D95direct (N × H)
80. C3×C52D3×D19semidirect
83. C3×C19D5×D15semidirect
88. C32×C5D5×D19semidirect
89. C32×C5C2×D95semidirect
101. C52C3⋊D3×D19semidirect
104. C19D5×C3⋊D15semidirect
109. C3×C5D15×D19semidirect
110. C3×C5D3×D95semidirect
119. C32D5×D95semidirect
124. C5D19×C3⋊D15semidirect
125. C5C3⋊D3×D95semidirect
127. C3D15×D95semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D95))2
C5×C19×C3⋊D152
C32×C5×D952
D15×D953
C3⋊D3×D955
D19×C3⋊D155
D5×C3⋊D1519