Finite Group Databasebeta

← C3×C5×#940 #13087944

Subgroups — C3×C5×#940 #13087944

Order 1440.

486 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 148 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
1C2×C32×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×C5×#67C214yesmaximal, complemented
3C2×C3×C5×D12C211yesmaximal, characteristic, complemented
4C3×C4×C5×Dic3C211yesmaximal, characteristic, complemented
5C3×C5×#127—31nomaximal
6C5×#940C311yesmaximal, characteristic, direct product factor
7C23×C32×C5C2212yes—
8C22×C3×C5×D3C2212yes—
9C32×C5×D4—22no—
10C2×C32×C4×C5C2211yescharacteristic
11C3×C5×#67—28no—
12C2×C3×C5×Dic3C2212yes—
13C3×C5×D12—22no—
14C3×#940C511yesmaximal, characteristic, direct product factor, Hall
15C2×C3×C5×D4—21no—
16C2×C3×C5×D4—34no—
17C2×C3×C5×D4—31no—
18C2×C3×C5×D4D311yescharacteristic, complemented
19C2×C3×C5×D4C2×C311yescharacteristic, complemented
20C2×C5×#67C2×C314yescomplemented
21C2×C5×D12C2×C311yescharacteristic, complemented
22C3×C42×C5—31no—
23C4×C5×Dic3C2×C311yescharacteristic, complemented
24C22×C32×C5—22no—
25C22×C32×C5—24no—
26C22×C32×C5C2311yescharacteristic
27C2×C3×C5×D3—22no—
28C2×C3×C5×D3—24no—
29C32×C4×C5D412yescomplemented
30C3×C5×Dic3D414yescomplemented
31C5×#127—31noHall
32C2×C32×D4C2×C511yescharacteristic, complemented
33C2×C3×#67C2×C514yescomplemented
34C2×C3×D12C2×C511yescharacteristic, complemented
35C3×C4×Dic3C2×C511yescharacteristic, complemented
36C23×C3×C5—22no—
37C23×C3×C5—32no—
38C23×C3×C5C2×D312yes—
39C23×C3×C5C22×C312yes—
40C22×C5×D3C22×C312yes—
41C3×C5×D4—24no—
42C3×C5×D4—22no—
43C3×C5×D4—22no—
44C3×C5×D4—68no—
45C3×C5×D4—62no—
46C2×C3×C4×C5—21no—
47C2×C3×C4×C5—32no—
48C2×C3×C4×C5C2×D311yescharacteristic
49C2×C3×C4×C5C22×C311yescharacteristic
50C5×#67—28no—
51C2×C5×Dic3C22×C312yes—
52C5×D12—22no—
53C3×#127—31no—
54#940C3×C511yescharacteristic, direct product factor
55C2×C32×C5—42no—
56C2×C32×C5C2×D412yes—
57C2×C32×C5C2×D411yescharacteristic
58C3×C5×D3—42no—
59C2×C5×D4—34no—
60C2×C5×D4—31no—
61C2×C5×D4C3×D311yescharacteristic, complemented
62C42×C5—31no—
63C23×C32C22×C512yes—
64C22×C3×D3C22×C512yes—
65C32×D4—22no—
66C2×C32×C4C22×C511yescharacteristic
67C3×#67—28no—
68C2×C3×Dic3C22×C512yes—
69C3×D12—22no—
70C22×C3×C5—24no—
71C22×C3×C5—24no—
72C22×C3×C5—22no—
73C22×C3×C5—24no—
74C22×C3×C5—22no—
75C22×C3×C5—21no—
76C22×C3×C5—44no—
77C22×C3×C5—64no—
78C22×C3×C5—62no—
79C22×C3×C5C22×D311yescharacteristic
80C22×C3×C5C23×C311yescharacteristic
81C2×C5×D3—22no—
82C2×C5×D3—24no—
83C3×C4×C5—22no—
84C3×C4×C5—34no—
85C3×C4×C5#6712yescomplemented
86C3×C4×C5C3×D412yescomplemented
87C5×Dic3C3×D414yescomplemented
88C2×C3×D4—21no—
89C2×C3×D4—34no—
90C2×C3×D4—31no—
91C2×C3×D4C5×D311yescharacteristic, complemented
92C2×C3×D4C2×C3×C511yescharacteristic, complemented
93C2×#67C2×C3×C514yescomplemented
94C2×D12C2×C3×C511yescharacteristic, complemented
95C3×C42—31no—
96C4×Dic3C2×C3×C511yescharacteristic, complemented
97C32×C5#12711yescharacteristic, complemented, Hall
98C23×C5—32no—
99C23×C5C2×C3×D312yes—
100C5×D4—22no—
101C5×D4—68no—
102C5×D4—62no—
103C2×C4×C5—32no—
104C2×C4×C5C2×C3×D311yescharacteristic
105C22×C32—22no—
106C22×C32—24no—
107C22×C32C23×C511yescharacteristic
108C2×C3×D3—22no—
109C2×C3×D3—24no—
110C32×C4C5×D412yescomplemented
111C3×Dic3C5×D414yescomplemented
112#127—31noSylow
113C2×C3×C5—22no—
114C2×C3×C5—21no—
115C2×C3×C5—44no—
116C2×C3×C5—42no—
117C2×C3×C5—42no—
118C2×C3×C5—122no—
119C2×C3×C5D3×D412yes—
120C2×C3×C5C2×#6711yescharacteristic
121C2×C3×C5C2×C3×D412yes—
122C2×C3×C5C2×C3×D411yescharacteristic
123C5×D3—42no—
124C23×C3—22no—
125C23×C3—32no—
126C23×C3C2×C5×D312yes—
127C23×C3C22×C3×C512yes—
128C22×D3C22×C3×C512yes—
129C3×D4—24no—
130C3×D4—22no—
131C3×D4—22no—
132C3×D4—68no—
133C3×D4—62no—
134C2×C3×C4—21no—
135C2×C3×C4—32no—
136C2×C3×C4C2×C5×D311yescharacteristic
137C2×C3×C4C22×C3×C511yescharacteristic
138#67—28no—
139C2×Dic3C22×C3×C512yes—
140D12—22no—
141C22×C5—24no—
142C22×C5—22no—
143C22×C5—64no—
144C22×C5—62no—
145C22×C5C22×C3×D311yescharacteristic
146C4×C5—34no—
147C4×C5C3×#6712yescomplemented
148C2×C32—42no—
149C2×C32C2×C5×D412yes—
150C2×C32C2×C5×D411yescharacteristic
151C3×D3—42no—
152C2×D4—34no—
153C2×D4—31no—
154C2×D4C3×C5×D311yescharacteristic, complemented
155C42—31no—
156C3×C5—21no—
157C3×C5#94011yescharacteristic, direct product factor
158C3×C5C3×#12711yescharacteristic, complemented
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—22no—
162C22×C3—24no—
163C22×C3—22no—
164C22×C3—21no—
165C22×C3—44no—
166C22×C3—64no—
167C22×C3—62no—
168C22×C3C22×C5×D311yescharacteristic
169C22×C3C23×C3×C511yescharacteristic
170C2×D3—22no—
171C2×D3—24no—
172C3×C4—22no—
173C3×C4—34no—
174C3×C4C5×#6712yescomplemented
175C3×C4C3×C5×D412yescomplemented
176Dic3C3×C5×D414yescomplemented
177C2×C5—42no—
178C2×C5—122no—
179C2×C5C3×D3×D412yes—
180C2×C5C2×C3×#6711yescharacteristic
181C32C5×#12711yescharacteristic, complemented, Sylow
182C23—32no—
183C23C2×C3×C5×D312yes—
184D4—22no—
185D4—68no—
186D4—62no—
187C2×C4—32no—
188C2×C4C2×C3×C5×D311yescharacteristic
189C2×C3—21no—
190C2×C3—22no—
191C2×C3—44no—
192C2×C3—42no—
193C2×C3—42no—
194C2×C3—122no—
195C2×C3C5×D3×D412yes—
196C2×C3C2×C5×#6711yescharacteristic
197C2×C3C2×C3×C5×D411yescharacteristic
198C2×C3C2×C3×C5×D412yes—
199D3—42no—
200C5C3×#94011yescharacteristic, direct product factor, Sylow
201C22—22no—
202C22—24no—
203C22—62no—
204C22—64no—
205C22C22×C3×C5×D311yescharacteristic
206C4—34no—
207C4C3×C5×#6712yescomplemented
208C3—21no—
209C3C5×#94011yescharacteristic, direct product factor
210C3C3×C5×#12711yescharacteristic, complemented
211C2—42no—
212C2—122no—
213C2C3×C5×D3×D412yes—
214C2C2×C3×C5×#6711yescharacteristic
subgroupG/H
centerC22×C3×C5C22×D3
commutator, cosocleC22×C3C23×C3×C5
FrattiniC22C22×C3×C5×D3
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C3×C5×D4D3
hypocenterC3C3×C5×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C5 ◁ C2×C3×C5×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×C3×C5×#67C2semidirect
3. C2×C3×C5×D12C2semidirect
4. C3×C4×C5×Dic3C2semidirect
6. C5×#940C3direct (N × H)
14. C3×#940C5direct (N × H)
18. C2×C3×C5×D4D3semidirect
19. C2×C3×C5×D4C2×C3semidirect
20. C2×C5×#67C2×C3semidirect
21. C2×C5×D12C2×C3semidirect
23. C4×C5×Dic3C2×C3semidirect
29. C32×C4×C5D4semidirect
30. C3×C5×Dic3D4semidirect
32. C2×C32×D4C2×C5semidirect
33. C2×C3×#67C2×C5semidirect
34. C2×C3×D12C2×C5semidirect
35. C3×C4×Dic3C2×C5semidirect
54. #940C3×C5direct (N × H)
61. C2×C5×D4C3×D3semidirect
85. C3×C4×C5#67semidirect
86. C3×C4×C5C3×D4semidirect
87. C5×Dic3C3×D4semidirect
91. C2×C3×D4C5×D3semidirect
92. C2×C3×D4C2×C3×C5semidirect
93. C2×#67C2×C3×C5semidirect
94. C2×D12C2×C3×C5semidirect
96. C4×Dic3C2×C3×C5semidirect
97. C32×C5#127semidirect
110. C32×C4C5×D4semidirect
111. C3×Dic3C5×D4semidirect
147. C4×C5C3×#67semidirect
154. C2×D4C3×C5×D3semidirect
157. C3×C5#940direct (N × H)
158. C3×C5C3×#127semidirect
174. C3×C4C5×#67semidirect
175. C3×C4C3×C5×D4semidirect
176. Dic3C3×C5×D4semidirect
181. C32C5×#127semidirect
200. C5C3×#940direct (N × H)
207. C4C3×C5×#67semidirect
209. C3C5×#940direct (N × H)
210. C3C3×C5×#127semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×C3×C5×#672
C2×C3×C5×D122
C3×C4×C5×Dic32
C3×C5×#1273
C5×#9403
C3×#9405