Finite Group Databasebeta

← C23×C3×D40 #14509643

Subgroups — C23×C3×D40 #14509643

Order 1920.

3952 conjugacy classes of subgroups; only the 1290 normal subgroups are shown.

normal subgroups only

This group has 3952 conjugacy classes of subgroups — too many to draw. Only its 1290 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
1C23×C3×D20C212yesmaximal, complemented
2C23×C3×C5×C8C211yesmaximal, characteristic, complemented
3C22×C3×D40C2128yesmaximal, direct product factor
4C23×D40C311yesmaximal, characteristic, direct product factor, Hall
5C24×C3×D5—22no—
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×D20—214no—
8C22×C3×D20C22128yescomplemented
9C22×C3×C5×C8C22114yescomplemented
10C2×C3×D40C221112yesdirect product factor
11C23×C3×D8—51nomaximal, Hall
12C23×D20C2×C312yescomplemented
13C23×C5×C8C2×C311yescharacteristic, complemented
14C22×D40C2×C3128yesdirect product factor
15C24×C3×C5D411yescharacteristic
16C23×C3×D5—228no—
17C23×C3×D5—416no—
18C22×C3×C4×C5D417yes—
19C22×C3×C4×C5C2317yes—
20C2×C3×D20—284no—
21C2×C3×D20C23156yescomplemented
22C2×C3×C5×C8C23128yescomplemented
23C3×D40C23164yesdirect product factor
24C23×C3×D4—52no—
25C22×C3×D8—528no—
26C23×C3×C8D511yescharacteristic, complemented
27C24×D5—22no—
28C23×C4×C5C22×C311yescharacteristic
29C22×D20—214no—
30C22×D20C22×C3128yescomplemented
31C22×C5×C8C22×C3114yescomplemented
32C2×D40C22×C31112yesdirect product factor
33C23×D8—51noSylow
34C23×C3×C5D818yescomplemented
35C23×C3×C5C2×D417yes—
36C22×C3×D5—256no—
37C22×C3×D5—4112no—
38C2×C3×C4×C5C2×D4121yes—
39C2×C3×C4×C5C2417yes—
40C3×D20—256no—
41C3×D20C24116yescomplemented
42C3×C5×C8C2418yescomplemented
43C25×C3—102no—
44C22×C3×D4—528no—
45C22×C3×D4—1014no—
46C23×C3×C4C2×D511yescharacteristic
47C2×C3×D8—5112no—
48C22×C3×C8C2×D5114yescomplemented
49C24×C5C3×D411yescharacteristic
50C23×D5—228no—
51C23×D5—416no—
52C22×C4×C5C3×D417yes—
53C22×C4×C5C23×C317yes—
54C2×D20—284no—
55C2×D20C23×C3156yescomplemented
56C2×C5×C8C23×C3128yescomplemented
57D40C23×C3164yesdirect product factor
58C23×D4—52no—
59C22×D8—528no—
60C23×C8C3×D511yescharacteristic, complemented
61C22×C3×C5C2×D8128yescomplemented
62C22×C3×C5C22×D417yes—
63C2×C3×D5—216no—
64C2×C3×D5—4112no—
65C3×C4×C5C22×D417yes—
66C3×C4×C5C2511yescharacteristic
67C24×C3—1028no—
68C24×C3—2016no—
69C24×C3D2011yescharacteristic
70C2×C3×D4—556no—
71C2×C3×D4—1084no—
72C22×C3×C4D2017yes—
73C22×C3×C4C22×D517yes—
74C3×D8—564no—
75C2×C3×C8C22×D5128yescomplemented
76C23×C5C3×D818yescomplemented
77C23×C5C2×C3×D417yes—
78C22×D5—256no—
79C22×D5—4112no—
80C2×C4×C5C2×C3×D4121yes—
81C2×C4×C5C24×C317yes—
82D20—256no—
83D20C24×C3116yescomplemented
84C5×C8C24×C318yescomplemented
85C25—102no—
86C22×D4—528no—
87C22×D4—1014no—
88C23×C4C2×C3×D511yescharacteristic
89C2×D8—5112no—
90C22×C8C2×C3×D5114yescomplemented
91C2×C3×C5C22×D8114yescomplemented
92C2×C3×C5C23×D411yescharacteristic
93C3×D5—416no—
94C23×C3—1056no—
95C23×C3—20112no—
96C23×C3D4018yesdirect product factor
97C23×C3C2×D2017yes—
98C3×D4—516no—
99C3×D4—1056no—
100C2×C3×C4C2×D20121yes—
101C2×C3×C4C23×D517yes—
102C3×C8C23×D518yescomplemented
103C22×C5C2×C3×D8128yescomplemented
104C22×C5C22×C3×D417yes—
105C2×D5—216no—
106C2×D5—4112no—
107C4×C5C22×C3×D417yes—
108C4×C5C25×C311yescharacteristic
109C24—1028no—
110C24—2016no—
111C24C3×D2011yescharacteristic
112C2×D4—556no—
113C2×D4—1084no—
114C22×C4C3×D2017yes—
115C22×C4C22×C3×D517yes—
116D8—564no—
117C2×C8C22×C3×D5128yescomplemented
118C3×C5C23×D811yescharacteristic, complemented, Hall
119C22×C3—1016no—
120C22×C3—20112no—
121C22×C3C2×D40128yesdirect product factor
122C22×C3C22×D2017yes—
123C3×C4C22×D2017yes—
124C3×C4C24×D511yescharacteristic
125C2×C5C22×C3×D8114yescomplemented
126C2×C5C23×C3×D411yescharacteristic
127D5—416no—
128C23—1056no—
129C23—20112no—
130C23C3×D4018yesdirect product factor
131C23C2×C3×D2017yes—
132D4—516no—
133D4—1056no—
134C2×C4C2×C3×D20121yes—
135C2×C4C23×C3×D517yes—
136C8C23×C3×D518yescomplemented
137C2×C3—2016no—
138C2×C3C22×D40114yesdirect product factor
139C2×C3C23×D2011yescharacteristic
140C5C23×C3×D811yescharacteristic, complemented, Sylow
141C22—1016no—
142C22—20112no—
143C22C2×C3×D40128yesdirect product factor
144C22C22×C3×D2017yes—
145C4C22×C3×D2017yes—
146C4C24×C3×D511yescharacteristic
147C3C23×D4011yescharacteristic, direct product factor, Sylow
148C2—2016no—
149C2C22×C3×D40114yesdirect product factor
150C2C23×C3×D2011yescharacteristic
subgroupG/H
centerC24×C3D20
commutator, cosocleC4×C5C25×C3
FrattiniC4C24×C3×D5
FittingC23×C3×C5×C8C2
socleC24×C3×C5D4
hypercenterC23×C3×C8D5
hypocenterC5C23×C3×D8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C23×C3×C4 ◁ C23×C3×C8

Complements

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

NH ≅ G/Ntype
1. C23×C3×D20C2semidirect
2. C23×C3×C5×C8C2semidirect
3. C22×C3×D40C2direct (N × H)
4. C23×D40C3direct (N × H)
8. C22×C3×D20C22semidirect
9. C22×C3×C5×C8C22semidirect
10. C2×C3×D40C22direct (N × H)
12. C23×D20C2×C3semidirect
13. C23×C5×C8C2×C3semidirect
14. C22×D40C2×C3direct (N × H)
21. C2×C3×D20C23semidirect
22. C2×C3×C5×C8C23semidirect
23. C3×D40C23direct (N × H)
26. C23×C3×C8D5semidirect
30. C22×D20C22×C3semidirect
31. C22×C5×C8C22×C3semidirect
32. C2×D40C22×C3direct (N × H)
34. C23×C3×C5D8semidirect
41. C3×D20C24semidirect
42. C3×C5×C8C24semidirect
48. C22×C3×C8C2×D5semidirect
55. C2×D20C23×C3semidirect
56. C2×C5×C8C23×C3semidirect
57. D40C23×C3direct (N × H)
60. C23×C8C3×D5semidirect
61. C22×C3×C5C2×D8semidirect
75. C2×C3×C8C22×D5semidirect
76. C23×C5C3×D8semidirect
83. D20C24×C3semidirect
84. C5×C8C24×C3semidirect
90. C22×C8C2×C3×D5semidirect
91. C2×C3×C5C22×D8semidirect
96. C23×C3D40direct (N × H)
102. C3×C8C23×D5semidirect
103. C22×C5C2×C3×D8semidirect
117. C2×C8C22×C3×D5semidirect
118. C3×C5C23×D8semidirect
121. C22×C3C2×D40direct (N × H)
125. C2×C5C22×C3×D8semidirect
130. C23C3×D40direct (N × H)
136. C8C23×C3×D5semidirect
138. C2×C3C22×D40direct (N × H)
140. C5C23×C3×D8semidirect
143. C22C2×C3×D40direct (N × H)
147. C3C23×D40direct (N × H)
149. C2C22×C3×D40direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D202
C23×C3×C5×C82
C22×C3×D402
C23×D403
C23×C3×D85