Finite Group Databasebeta

← C32×#4095 #13087874

Subgroups — C32×#4095 #13087874

Order 1440.

408 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 174 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×#41C211yesmaximal, characteristic, complemented
2C2×C32×D20C211yesmaximal, characteristic, complemented
3C32×#688C212yesmaximal, complemented
4C32×#686C212yesmaximal, complemented
5C32×#681C211yesmaximal, characteristic, complemented
6C3×#4095C314yesmaximal, direct product factor
7C22×C32×D5—21no—
8C32×C5×Q8C2211yescharacteristic, complemented
9C32×C5×D4—21no—
10C32×C5×D4C2211yescharacteristic, complemented
11C2×C32×C4×C5—21no—
12C2×C32×C4×C5C2211yescharacteristic
13C32×D20—21no—
14C32×D20C2212yes—
15C32×#168C2212yescomplemented
16C32×AGL(1,ℤ/8)—51nomaximal, Hall
17C3×C5×#41C2×C314yescomplemented
18C2×C3×D20C2×C314yescomplemented
19C3×#688C2×C318yescomplemented
20C3×#686C2×C318yescomplemented
21C3×#681C2×C314yescomplemented
22C22×C32×C5—21no—
23C22×C32×C5D411yescharacteristic
24C2×C32×D5—22no—
25C2×C32×D5—42no—
26C32×C4×C5—21no—
27C32×C4×C5D411yescharacteristic
28C32×C4×C5C2311yescharacteristic
29#4095C3211yescharacteristic, direct product factor, Hall
30C32×#41D511yescharacteristic, complemented
31C2×C32×D4—51no—
32C32×SD16—52no—
33C32×D8—52no—
34C32×M16—51no—
35C22×C3×D5—24no—
36C3×C5×Q8C22×C314yescomplemented
37C3×C5×D4—24no—
38C3×C5×D4C22×C314yescomplemented
39C2×C3×C4×C5—24no—
40C2×C3×C4×C5C22×C314yes—
41C3×D20—24no—
42C3×D20C22×C318yes—
43C3×#168C22×C318yescomplemented
44C3×AGL(1,ℤ/8)—54no—
45C2×C32×C5—21no—
46C2×C32×C5—41no—
47C2×C32×C5C2×D411yescharacteristic
48C32×D5—42no—
49C5×#41C2×C3211yescharacteristic, complemented
50C2×D20C2×C3211yescharacteristic, complemented
51#688C2×C3212yescomplemented
52#686C2×C3212yescomplemented
53#681C2×C3211yescharacteristic, complemented
54C23×C32—101no—
55C32×Q8C2×D511yescharacteristic, complemented
56C32×D4—21no—
57C32×D4—52no—
58C32×D4—101no—
59C32×D4C2×D511yescharacteristic, complemented
60C2×C32×C4—21no—
61C2×C32×C4C2×D511yescharacteristic
62C32×C8—52no—
63C22×C3×C5—24no—
64C22×C3×C5C3×D414yes—
65C2×C3×D5—28no—
66C2×C3×D5—48no—
67C3×C4×C5—24no—
68C3×C4×C5C3×D414yes—
69C3×C4×C5C23×C314yes—
70C3×#41C3×D514yescomplemented
71C2×C3×D4—54no—
72C3×SD16—58no—
73C3×D8—58no—
74C3×M16—54no—
75C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
76C22×D5—21no—
77C5×Q8C22×C3211yescharacteristic, complemented
78C5×D4—21no—
79C5×D4C22×C3211yescharacteristic, complemented
80C2×C4×C5—21no—
81C2×C4×C5C22×C3211yescharacteristic
82D20—21no—
83D20C22×C3212yes—
84#168C22×C3212yescomplemented
85C22×C32—21no—
86C22×C32—102no—
87C22×C32—202no—
88C22×C32C22⋊D511yescharacteristic
89C32×C4—21no—
90C32×C4C22⋊D511yescharacteristic
91C32×C4C22×D511yescharacteristic
92AGL(1,ℤ/8)—51noSylow
93C2×C3×C5—24no—
94C2×C3×C5—44no—
95C2×C3×C5C2×C3×D414yes—
96C3×D5—48no—
97C23×C3—104no—
98C3×Q8C2×C3×D514yescomplemented
99C3×D4—24no—
100C3×D4—58no—
101C3×D4—104no—
102C3×D4C2×C3×D514yescomplemented
103C2×C3×C4—24no—
104C2×C3×C4C2×C3×D514yes—
105C3×C8—58no—
106C22×C5—21no—
107C22×C5C32×D411yescharacteristic
108C2×D5—22no—
109C2×D5—42no—
110C4×C5—21no—
111C4×C5C32×D411yescharacteristic
112C4×C5C23×C3211yescharacteristic
113C2×C32—21no—
114C2×C32—41no—
115C2×C32—202no—
116C2×C32C2×C22⋊D511yescharacteristic
117#41C32×D511yescharacteristic, complemented
118C2×D4—51no—
119SD16—52no—
120D8—52no—
121M16—51no—
122C3×C5C3×AGL(1,ℤ/8)14yescomplemented
123C22×C3—24no—
124C22×C3—108no—
125C22×C3—208no—
126C22×C3C3×C22⋊D514yes—
127C3×C4—24no—
128C3×C4C3×C22⋊D514yes—
129C3×C4C22×C3×D514yes—
130C2×C5—21no—
131C2×C5—41no—
132C2×C5C2×C32×D411yescharacteristic
133D5—42no—
134C32#409511yescharacteristic, direct product factor, Sylow
135C23—101no—
136Q8C2×C32×D511yescharacteristic, complemented
137D4—21no—
138D4—52no—
139D4—101no—
140D4C2×C32×D511yescharacteristic, complemented
141C2×C4—21no—
142C2×C4C2×C32×D511yescharacteristic
143C8—52no—
144C2×C3—24no—
145C2×C3—44no—
146C2×C3—208no—
147C2×C3C2×C3×C22⋊D514yes—
148C5C32×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
149C22—21no—
150C22—102no—
151C22—202no—
152C22C32×C22⋊D511yescharacteristic
153C4—21no—
154C4C32×C22⋊D511yescharacteristic
155C4C22×C32×D511yescharacteristic
156C3C3×#409514yesdirect product factor
157C2—21no—
158C2—41no—
159C2—202no—
160C2C2×C32×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C32C2×C22⋊D5
commutator, cosocleC4×C5C23×C32
FrattiniC4C22×C32×D5
FittingC32×C5×#41C2
socleC2×C32×C5C2×D4
hypercenterC32×#41D5
hypocenterC5C32×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C32×#41

Complements

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

NH ≅ G/Ntype
1. C32×C5×#41C2semidirect
2. C2×C32×D20C2semidirect
3. C32×#688C2semidirect
4. C32×#686C2semidirect
5. C32×#681C2semidirect
6. C3×#4095C3direct (N × H)
8. C32×C5×Q8C22semidirect
10. C32×C5×D4C22semidirect
15. C32×#168C22semidirect
17. C3×C5×#41C2×C3semidirect
18. C2×C3×D20C2×C3semidirect
19. C3×#688C2×C3semidirect
20. C3×#686C2×C3semidirect
21. C3×#681C2×C3semidirect
29. #4095C32direct (N × H)
30. C32×#41D5semidirect
36. C3×C5×Q8C22×C3semidirect
38. C3×C5×D4C22×C3semidirect
43. C3×#168C22×C3semidirect
49. C5×#41C2×C32semidirect
50. C2×D20C2×C32semidirect
51. #688C2×C32semidirect
52. #686C2×C32semidirect
53. #681C2×C32semidirect
55. C32×Q8C2×D5semidirect
59. C32×D4C2×D5semidirect
70. C3×#41C3×D5semidirect
75. C32×C5AGL(1,ℤ/8)semidirect
77. C5×Q8C22×C32semidirect
79. C5×D4C22×C32semidirect
84. #168C22×C32semidirect
98. C3×Q8C2×C3×D5semidirect
102. C3×D4C2×C3×D5semidirect
117. #41C32×D5semidirect
122. C3×C5C3×AGL(1,ℤ/8)semidirect
134. C32#4095direct (N × H)
136. Q8C2×C32×D5semidirect
140. D4C2×C32×D5semidirect
148. C5C32×AGL(1,ℤ/8)semidirect
156. C3C3×#4095direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×#412
C2×C32×D202
C32×#6882
C32×#6862
C32×#6812
C3×#40953
C32×AGL(1,ℤ/8)5