Finite Group Databasebeta

← C32×#4076 #13087855

Subgroups — C32×#4076 #13087855

Order 1440.

564 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 222 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
1C22×C32×C4×C5C211yesmaximal, characteristic, complemented
2C2×C32×C22⋊D5C212yesmaximal, complemented
3C2×C32×D20C211yesmaximal, characteristic, complemented
4C32×#685C212yesmaximal, complemented
5C32×C4⋊Dic5C211yesmaximal, characteristic, complemented
6C3×#4076C314yesmaximal, direct product factor
7C23×C32×C5C2211yescharacteristic
8C22×C32×D5C2212yes—
9C2×C32×C4×C5—22no—
10C2×C32×C4×C5C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C32×C22⋊D5—24no—
13C2×C32×Dic5C2212yes—
14C32×D20—22no—
15C32×#121—51nomaximal, Hall
16C22×C3×C4×C5C2×C314yescomplemented
17C2×C3×C22⋊D5C2×C318yescomplemented
18C2×C3×D20C2×C314yescomplemented
19C3×#685C2×C318yescomplemented
20C3×C4⋊Dic5C2×C314yescomplemented
21C22×C32×C5—21no—
22C22×C32×C5—21no—
23C22×C32×C5D412yescomplemented
24C22×C32×C5C2311yescharacteristic
25C2×C32×D5—22no—
26C2×C32×D5—22no—
27C2×C32×D5—22no—
28C32×C4×C5—21no—
29C32×C4×C5D412yescomplemented
30C32×Dic5—22no—
31#4076C3211yescharacteristic, direct product factor, Hall
32C2×C32×D4—52no—
33C2×C32×D4—51no—
34C22×C32×C4D511yescharacteristic, complemented
35C32×C4⋊C4—51no—
36C32×C22⋊C4—52no—
37C23×C3×C5C22×C314yes—
38C22×C3×D5C22×C318yes—
39C2×C3×C4×C5—28no—
40C2×C3×C4×C5C22×C314yes—
41C2×C3×C4×C5C22×C314yes—
42C3×C22⋊D5—216no—
43C2×C3×Dic5C22×C318yes—
44C3×D20—28no—
45C3×#121—54no—
46C2×C32×C5—22no—
47C2×C32×C5C2×D411yescharacteristic
48C2×C32×C5C2×D411yescharacteristic
49C2×C32×C5#4111yescharacteristic
50C32×D5—42no—
51C22×C4×C5C2×C3211yescharacteristic, complemented
52C2×C22⋊D5C2×C3212yescomplemented
53C2×D20C2×C3211yescharacteristic, complemented
54#685C2×C3212yescomplemented
55C4⋊Dic5C2×C3211yescharacteristic, complemented
56C23×C32—52no—
57C23×C32C2×D511yescharacteristic
58C32×D4—104no—
59C32×D4—102no—
60C2×C32×C4—22no—
61C2×C32×C4—52no—
62C2×C32×C4C2×D511yescharacteristic
63C2×C32×C4C2×D511yescharacteristic
64C22×C3×C5—24no—
65C22×C3×C5—24no—
66C22×C3×C5C3×D418yescomplemented
67C22×C3×C5C23×C314yes—
68C2×C3×D5—28no—
69C2×C3×D5—28no—
70C2×C3×D5—28no—
71C3×C4×C5—24no—
72C3×C4×C5C3×D418yescomplemented
73C3×Dic5—28no—
74C2×C3×D4—58no—
75C2×C3×D4—54no—
76C22×C3×C4C3×D514yescomplemented
77C3×C4⋊C4—54no—
78C3×C22⋊C4—58no—
79C32×C5#12111yescharacteristic, complemented, Hall
80C23×C5C22×C3211yescharacteristic
81C22×D5C22×C3212yes—
82C2×C4×C5—22no—
83C2×C4×C5C22×C3211yescharacteristic
84C2×C4×C5C22×C3211yescharacteristic
85C22⋊D5—24no—
86C2×Dic5C22×C3212yes—
87D20—22no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—102no—
91C22×C32—102no—
92C22×C32—102no—
93C22×C32D2012yescomplemented
94C22×C32C22×D511yescharacteristic
95C32×C4—21no—
96C32×C4—102no—
97C32×C4C22⋊D512yescomplemented
98#121—51noSylow
99C2×C3×C5—28no—
100C2×C3×C5C2×C3×D414yes—
101C2×C3×C5C2×C3×D414yes—
102C2×C3×C5C3×#4114yes—
103C3×D5—48no—
104C23×C3—58no—
105C23×C3C2×C3×D514yes—
106C3×D4—1016no—
107C3×D4—108no—
108C2×C3×C4—28no—
109C2×C3×C4—58no—
110C2×C3×C4C2×C3×D514yes—
111C2×C3×C4C2×C3×D514yes—
112C22×C5—21no—
113C22×C5—21no—
114C22×C5C32×D412yescomplemented
115C22×C5C23×C3211yescharacteristic
116C2×D5—22no—
117C2×D5—22no—
118C2×D5—22no—
119C4×C5—21no—
120C4×C5C32×D412yescomplemented
121Dic5—22no—
122C2×C32—22no—
123C2×C32—202no—
124C2×C32C2×D2011yescharacteristic
125C2×C32#70911yescharacteristic
126C2×C32C2×C22⋊D511yescharacteristic
127C2×D4—52no—
128C2×D4—51no—
129C22×C4C32×D511yescharacteristic, complemented
130C4⋊C4—51no—
131C22⋊C4—52no—
132C3×C5C3×#12114yescomplemented
133C22×C3—24no—
134C22×C3—24no—
135C22×C3—108no—
136C22×C3—108no—
137C22×C3—108no—
138C22×C3C3×D2018yescomplemented
139C22×C3C22×C3×D514yes—
140C3×C4—24no—
141C3×C4—108no—
142C3×C4C3×C22⋊D518yescomplemented
143C2×C5—22no—
144C2×C5C2×C32×D411yescharacteristic
145C2×C5C2×C32×D411yescharacteristic
146C2×C5C32×#4111yescharacteristic
147D5—42no—
148C32#407611yescharacteristic, direct product factor, Sylow
149C23—52no—
150C23C2×C32×D511yescharacteristic
151D4—104no—
152D4—102no—
153C2×C4—22no—
154C2×C4—52no—
155C2×C4C2×C32×D511yescharacteristic
156C2×C4C2×C32×D511yescharacteristic
157C2×C3—28no—
158C2×C3—208no—
159C2×C3C2×C3×D2014yes—
160C2×C3C3×#70914yes—
161C2×C3C2×C3×C22⋊D514yes—
162C5C32×#12111yescharacteristic, complemented, Sylow
163C22—21no—
164C22—21no—
165C22—102no—
166C22—102no—
167C22—102no—
168C22C32×D2012yescomplemented
169C22C22×C32×D511yescharacteristic
170C4—21no—
171C4—102no—
172C4C32×C22⋊D512yescomplemented
173C3C3×#407614yesdirect product factor
174C2—22no—
175C2—202no—
176C2C2×C32×D2011yescharacteristic
177C2C32×#70911yescharacteristic
178C2C2×C32×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C32C22×D5
commutator, cosocleC22×C5C23×C32
FrattiniC22C22×C32×D5
FittingC22×C32×C4×C5C2
socleC22×C32×C5C23
hypercenterC22×C32×C4D5
hypocenterC5C32×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C22×C32×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×C5C2semidirect
2. C2×C32×C22⋊D5C2semidirect
3. C2×C32×D20C2semidirect
4. C32×#685C2semidirect
5. C32×C4⋊Dic5C2semidirect
6. C3×#4076C3direct (N × H)
16. C22×C3×C4×C5C2×C3semidirect
17. C2×C3×C22⋊D5C2×C3semidirect
18. C2×C3×D20C2×C3semidirect
19. C3×#685C2×C3semidirect
20. C3×C4⋊Dic5C2×C3semidirect
23. C22×C32×C5D4semidirect
29. C32×C4×C5D4semidirect
31. #4076C32direct (N × H)
34. C22×C32×C4D5semidirect
51. C22×C4×C5C2×C32semidirect
52. C2×C22⋊D5C2×C32semidirect
53. C2×D20C2×C32semidirect
54. #685C2×C32semidirect
55. C4⋊Dic5C2×C32semidirect
66. C22×C3×C5C3×D4semidirect
72. C3×C4×C5C3×D4semidirect
76. C22×C3×C4C3×D5semidirect
79. C32×C5#121semidirect
93. C22×C32D20semidirect
97. C32×C4C22⋊D5semidirect
114. C22×C5C32×D4semidirect
120. C4×C5C32×D4semidirect
129. C22×C4C32×D5semidirect
132. C3×C5C3×#121semidirect
138. C22×C3C3×D20semidirect
142. C3×C4C3×C22⋊D5semidirect
148. C32#4076direct (N × H)
162. C5C32×#121semidirect
168. C22C32×D20semidirect
172. C4C32×C22⋊D5semidirect
173. C3C3×#4076direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4×C52
C2×C32×C22⋊D52
C2×C32×D202
C32×#6852
C32×C4⋊Dic52
C3×#40763
C32×#1215