Finite Group Databasebeta

← C32×D5×D95 #30685866

Subgroups — C32×D5×D95 #30685866

Order 17100.

288 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 96 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⋊D95C211yesmaximal, characteristic, complemented
2C32×C5×D95C211yesmaximal, characteristic, complemented
3C32×C5×D5×C19C211yesmaximal, characteristic, complemented
4C3×D5×D95C314yesmaximal, direct product factor
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6C2×C32×D95—51nomaximal
7C32×D5×D19—51nomaximal
8C3×C5⋊D95C2×C314yescomplemented
9C3×C5×D95C2×C314yescomplemented
10C3×C5×D5×C19C2×C314yescomplemented
11D5×D95C3211yescharacteristic, direct product factor, Hall
12C2×C32×C5×C19—51no—
13C32×D95—51no—
14C32×D95—51no—
15C32×D95—102no—
16C32×D95D511yescharacteristic, direct product factor
17C32×D5×C19D511yescharacteristic, complemented
18C32×C5×D19—51no—
19C3×C52×C19C22×C314yescomplemented
20C2×C3×D95—54no—
21C3×D5×D19—54no—
22C5⋊D95C2×C3211yescharacteristic, complemented
23C5×D95C2×C3211yescharacteristic, complemented
24C5×D5×C19C2×C3211yescharacteristic, complemented
25C32×D52—191nomaximal, Hall
26C32×C5×C19—22no—
27C32×C5×C19C2×D511yescharacteristic, complemented
28C32×C5×C19C2×D511yescharacteristic, complemented
29C2×C32×D19—251noHall
30C2×C3×C5×C19—54no—
31C3×D95—54no—
32C3×D95—54no—
33C3×D95—108no—
34C3×D95C3×D514yesdirect product factor
35C3×D5×C19C3×D514yescomplemented
36C3×C5×D19—54no—
37C52×C19C22×C3211yescharacteristic, complemented, Hall
38C32×C5⋊D5—191no—
39C32×C5×D5—191no—
40C32×C5×D5D1911yescharacteristic, complemented
41C2×D95—51no—
42D5×D19—51no—
43C2×C32×C19—51no—
44C32×D19—51no—
45C32×D19—251no—
46C3×D52—194no—
47C3×C5×C19—28no—
48C3×C5×C19C2×C3×D514yescomplemented
49C3×C5×C19C2×C3×D514yescomplemented
50C2×C3×D19—254no—
51C32×C52C2×D1911yescharacteristic, complemented, Hall
52C2×C5×C19—51no—
53D95—51no—
54D95—51no—
55D95—102no—
56D95C32×D511yescharacteristic, direct product factor
57C5×D19—51no—
58D5×C19C32×D511yescharacteristic, complemented
59C2×C32×D5—951no—
60C2×C32×D5—951no—
61C32×C19D5211yescharacteristic, complemented, Hall
62C3×C5⋊D5—194no—
63C3×C5×D5—194no—
64C3×C5×D5C3×D1914yescomplemented
65C2×C3×C19—54no—
66C3×D19—54no—
67C3×D19—254no—
68D52—191noHall
69C5×C19—22no—
70C5×C19C2×C32×D511yescharacteristic, complemented
71C5×C19C2×C32×D511yescharacteristic, complemented
72C2×C32×C5—51no—
73C2×C32×C5—951no—
74C32×D5—191no—
75C32×D5—951no—
76C32×D5—951no—
77C32×D5—1902no—
78C32×D5D9511yescharacteristic, direct product factor
79C2×D19—251noHall
80C3×C52C2×C3×D1914yescomplemented
81C2×C3×D5—954no—
82C2×C3×D5—954no—
83C3×C19C3×D5214yescomplemented
84C5⋊D5—191no—
85C5×D5—191no—
86C5×D5C32×D1911yescharacteristic, complemented
87C32×C5—22no—
88C32×C5D5×D1911yescharacteristic, complemented
89C32×C5C2×D9511yescharacteristic, complemented
90C2×C19—51no—
91D19—51no—
92D19—251no—
93C22×C32—4751noHall
94C2×C3×C5—54no—
95C2×C3×C5—954no—
96C3×D5—194no—
97C3×D5—954no—
98C3×D5—954no—
99C3×D5—1908no—
100C3×D5C3×D9514yesdirect product factor
101C52C2×C32×D1911yescharacteristic, complemented, Sylow
102C2×D5—951no—
103C2×D5—951no—
104C19C32×D5211yescharacteristic, complemented, Sylow
105C2×C32—51no—
106C2×C32—951no—
107C2×C32—4751no—
108C3×C5—28no—
109C3×C5C3×D5×D1914yescomplemented
110C3×C5C2×C3×D9514yescomplemented
111C22×C3—4754no—
112C2×C5—51no—
113C2×C5—951no—
114D5—191no—
115D5—951no—
116D5—951no—
117D5—1902no—
118D5C32×D9511yescharacteristic, direct product factor
119C32D5×D9511yescharacteristic, direct product factor, Sylow
120C2×C3—54no—
121C2×C3—954no—
122C2×C3—4754no—
123C5—22no—
124C5C32×D5×D1911yescharacteristic, complemented
125C5C2×C32×D9511yescharacteristic, complemented
126C22—4751noSylow
127C3C3×D5×D9514yesdirect product factor
128C2—51no—
129C2—951no—
130C2—4751no—
subgroupG/H
center, hypercenterC32D5×D95
commutator, cosocle, hypocenterC52×C19C22×C32
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C52×C19
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊D95C2semidirect
2. C32×C5×D95C2semidirect
3. C32×C5×D5×C19C2semidirect
4. C3×D5×D95C3direct (N × H)
5. C32×C52×C19C22semidirect
8. C3×C5⋊D95C2×C3semidirect
9. C3×C5×D95C2×C3semidirect
10. C3×C5×D5×C19C2×C3semidirect
11. D5×D95C32direct (N × H)
16. C32×D95D5direct (N × H)
17. C32×D5×C19D5semidirect
19. C3×C52×C19C22×C3semidirect
22. C5⋊D95C2×C32semidirect
23. C5×D95C2×C32semidirect
24. C5×D5×C19C2×C32semidirect
27. C32×C5×C19C2×D5semidirect
28. C32×C5×C19C2×D5semidirect
34. C3×D95C3×D5direct (N × H)
35. C3×D5×C19C3×D5semidirect
37. C52×C19C22×C32semidirect
40. C32×C5×D5D19semidirect
48. C3×C5×C19C2×C3×D5semidirect
49. C3×C5×C19C2×C3×D5semidirect
51. C32×C52C2×D19semidirect
56. D95C32×D5direct (N × H)
58. D5×C19C32×D5semidirect
61. C32×C19D52semidirect
64. C3×C5×D5C3×D19semidirect
70. C5×C19C2×C32×D5semidirect
71. C5×C19C2×C32×D5semidirect
78. C32×D5D95direct (N × H)
80. C3×C52C2×C3×D19semidirect
83. C3×C19C3×D52semidirect
86. C5×D5C32×D19semidirect
88. C32×C5D5×D19semidirect
89. C32×C5C2×D95semidirect
100. C3×D5C3×D95direct (N × H)
101. C52C2×C32×D19semidirect
104. C19C32×D52semidirect
109. C3×C5C3×D5×D19semidirect
110. C3×C5C2×C3×D95semidirect
118. D5C32×D95direct (N × H)
119. C32D5×D95direct (N × H)
124. C5C32×D5×D19semidirect
125. C5C2×C32×D95semidirect
127. C3C3×D5×D95direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5⋊D952
C32×C5×D952
C32×C5×D5×C192
C3×D5×D953
C2×C32×D955
C32×D5×D195
C32×D5219