Finite Group Databasebeta

← C2×C5×#3795 #13089308

Subgroups — C2×C5×#3795 #13089308

Order 1440.

694 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#634C211yesmaximal, characteristic, complemented
2C2×C3×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×C4×C5×D3C211yesmaximal, characteristic, complemented
4C2×C5×#625C212yesmaximal, complemented
5C2×C5×D3×Dic3C212yesmaximal, complemented
6C5×#3795C218yesmaximal, direct product factor
7C2×C5×#237—31nomaximal
8C2×C5×#235—31nomaximal
9C22×C3×C5×D3C2212yes—
10C22×C3×C5×D3C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C5×C3⋊Dic3C2212yes—
13C5×#634C2214yescomplemented
14C2×C3×C5×Dic3C2211yescharacteristic
15C3×C5×D12C2214yescomplemented
16C3×C4×C5×D3C2214yescomplemented
17C5×#625C2218yescomplemented
18C5×D3×Dic3C2218yescomplemented
19C2×#3795C511yesmaximal, characteristic, direct product factor, Hall
20C2×C3×C5×D4—31no—
21C22×C3×C4×C5—31no—
22C2×C5×#67—32no—
23C2×C5×#67—32no—
24C22×C5×Dic3—32no—
25C5×#237—38no—
26C5×#235—38no—
27C2×C5×D12D311yescharacteristic, complemented
28C2×C4×C5×D3—32no—
29C2×C4×C5×D3D311yescharacteristic, complemented
30C2×C5×Dic6—31no—
31C2×C5×Dic6—31no—
32C2×C5×Dic6—61no—
33C22×C32×C5C2311yescharacteristic
34C2×C3×C5×D3—22no—
35C2×C3×C5×D3—24no—
36C2×C3×C5×D3C2314yes—
37C2×C3×C5×D3C2312yes—
38C32×C4×C5C2312yes—
39C5×C3⋊Dic3C2314yes—
40C3×C5×Dic3C2312yes—
41C2×C5×#41—91noHall
42C2×#634C2×C511yescharacteristic, complemented
43C2×C3×D12C2×C511yescharacteristic, complemented
44C2×C3×C4×D3C2×C511yescharacteristic, complemented
45C2×#625C2×C512yescomplemented
46C2×D3×Dic3C2×C512yescomplemented
47#3795C2×C518yesdirect product factor
48C23×C3×C5—32no—
49C23×C3×C5—31no—
50C22×C5×D3C2×D312yes—
51C22×C5×D3C2×D311yescharacteristic
52C3×C5×D4—34no—
53C2×C3×C4×C5—21no—
54C2×C3×C4×C5—31no—
55C2×C3×C4×C5—34no—
56C2×C3×C4×C5C2×D311yescharacteristic
57C2×C3×C4×C5C2×D311yescharacteristic
58C5×#67—38no—
59C5×#67—38no—
60C2×C5×Dic3—32no—
61C2×C5×Dic3—32no—
62C2×C5×Dic3—38no—
63C2×C5×Dic3—62no—
64C2×C5×Dic3C2×D311yescharacteristic
65C5×D12C2×D314yescomplemented
66C4×C5×D3—38no—
67C4×C5×D3C2×D314yescomplemented
68C5×Dic6—34no—
69C5×Dic6—34no—
70C5×Dic6—64no—
71C2×#237—31no—
72C2×#235—31no—
73C2×C32×C5#4112yescomplemented
74C2×C32×C5C2411yescharacteristic
75C3×C5×D3—22no—
76C3×C5×D3—24no—
77C5×#41—98no—
78C2×C5×Q8—91no—
79C2×C5×D4—31no—
80C2×C5×D4—92no—
81C22×C4×C5—31no—
82C22×C4×C5—92no—
83C22×C3×D3C22×C512yes—
84C22×C3×D3C22×C511yescharacteristic
85C2×C32×C4C22×C511yescharacteristic
86C2×C3⋊Dic3C22×C512yes—
87#634C22×C514yescomplemented
88C2×C3×Dic3C22×C511yescharacteristic
89C3×D12C22×C514yescomplemented
90C3×C4×D3C22×C514yescomplemented
91#625C22×C518yescomplemented
92D3×Dic3C22×C518yescomplemented
93C22×C3×C5—21no—
94C22×C3×C5—34no—
95C22×C3×C5—32no—
96C22×C3×C5—64no—
97C22×C3×C5—62no—
98C22×C3×C5C22×D311yescharacteristic
99C22×C3×C5C22×D311yescharacteristic
100C2×C5×D3—22no—
101C2×C5×D3—24no—
102C2×C5×D3C22×D314yes—
103C2×C5×D3C22×D312yes—
104C3×C4×C5—22no—
105C3×C4×C5—32no—
106C3×C4×C5C22×D312yes—
107C3×C4×C5C22×D312yes—
108C5×Dic3—34no—
109C5×Dic3—34no—
110C5×Dic3—64no—
111C5×Dic3C22×D312yes—
112C2×C3×D4—31no—
113C22×C3×C4—31no—
114C2×#67—32no—
115C2×#67—32no—
116C22×Dic3—32no—
117#237—38no—
118#235—38no—
119C2×D12C5×D311yescharacteristic, complemented
120C2×C4×D3—32no—
121C2×C4×D3C5×D311yescharacteristic, complemented
122C2×Dic6—31no—
123C2×Dic6—31no—
124C2×Dic6—61no—
125C32×C5C2×#4111yescharacteristic, complemented, Hall
126C23×C5—31no—
127C23×C5—32no—
128C5×Q8—94no—
129C5×D4—34no—
130C5×D4—98no—
131C2×C4×C5—31no—
132C2×C4×C5—34no—
133C2×C4×C5—98no—
134C2×C4×C5—92no—
135C2×C4×C5D3211yescharacteristic
136C22×C32C23×C511yescharacteristic
137C2×C3×D3—22no—
138C2×C3×D3—24no—
139C2×C3×D3C23×C514yes—
140C2×C3×D3C23×C512yes—
141C32×C4C23×C512yes—
142C3⋊Dic3C23×C514yes—
143C3×Dic3C23×C512yes—
144C2×#41—91noSylow
145C2×C3×C5—21no—
146C2×C3×C5—22no—
147C2×C3×C5—64no—
148C2×C3×C5—62no—
149C2×C3×C5#23512yescomplemented
150C2×C3×C5#23712yescomplemented
151C2×C3×C5C23×D311yescharacteristic
152C2×C3×C5C23×D311yescharacteristic
153C5×D3—22no—
154C5×D3—24no—
155C23×C3—32no—
156C23×C3—31no—
157C22×D3C2×C5×D312yes—
158C22×D3C2×C5×D311yescharacteristic
159C3×D4—34no—
160C2×C3×C4—21no—
161C2×C3×C4—31no—
162C2×C3×C4—34no—
163C2×C3×C4C2×C5×D311yescharacteristic
164C2×C3×C4C2×C5×D311yescharacteristic
165#67—38no—
166#67—38no—
167C2×Dic3—32no—
168C2×Dic3—32no—
169C2×Dic3—38no—
170C2×Dic3—62no—
171C2×Dic3C2×C5×D311yescharacteristic
172D12C2×C5×D314yescomplemented
173C4×D3—38no—
174C4×D3C2×C5×D314yescomplemented
175Dic6—34no—
176Dic6—34no—
177Dic6—64no—
178C22×C5—32no—
179C22×C5—34no—
180C22×C5—62no—
181C22×C5—64no—
182C22×C5C2×D3211yescharacteristic
183C4×C5—32no—
184C4×C5—94no—
185C4×C5C2×D3212yes—
186C2×C32C5×#4112yescomplemented
187C2×C32C24×C511yescharacteristic
188C3×D3—22no—
189C3×D3—24no—
190#41—98no—
191C2×Q8—91no—
192C2×D4—31no—
193C2×D4—92no—
194C22×C4—31no—
195C22×C4—92no—
196C3×C5—21no—
197C3×C5C2×#23511yescharacteristic, complemented
198C3×C5C2×#23711yescharacteristic, complemented
199C22×C3—21no—
200C22×C3—34no—
201C22×C3—32no—
202C22×C3—64no—
203C22×C3—62no—
204C22×C3C22×C5×D311yescharacteristic
205C22×C3C22×C5×D311yescharacteristic
206C2×D3—22no—
207C2×D3—24no—
208C2×D3C22×C5×D314yes—
209C2×D3C22×C5×D312yes—
210C3×C4—22no—
211C3×C4—32no—
212C3×C4C22×C5×D312yes—
213C3×C4C22×C5×D312yes—
214Dic3—34no—
215Dic3—34no—
216Dic3—64no—
217Dic3C22×C5×D312yes—
218C2×C5—62no—
219C2×C5—64no—
220C2×C5#379512yesdirect product factor
221C2×C5C22×D3211yescharacteristic
222C32C2×C5×#4111yescharacteristic, complemented, Sylow
223C23—31no—
224C23—32no—
225Q8—94no—
226D4—34no—
227D4—98no—
228C2×C4—31no—
229C2×C4—34no—
230C2×C4—98no—
231C2×C4—92no—
232C2×C4C5×D3211yescharacteristic
233C2×C3—21no—
234C2×C3—22no—
235C2×C3—64no—
236C2×C3—62no—
237C2×C3C5×#23512yescomplemented
238C2×C3C5×#23712yescomplemented
239C2×C3C23×C5×D311yescharacteristic
240C2×C3C23×C5×D311yescharacteristic
241D3—22no—
242D3—24no—
243C5C2×#379511yescharacteristic, direct product factor, Sylow
244C22—32no—
245C22—34no—
246C22—62no—
247C22—64no—
248C22C2×C5×D3211yescharacteristic
249C4—32no—
250C4—94no—
251C4C2×C5×D3212yes—
252C3—21no—
253C3C2×C5×#23511yescharacteristic, complemented
254C3C2×C5×#23711yescharacteristic, complemented
255C2—62no—
256C2—64no—
257C2C5×#379512yesdirect product factor
258C2C22×C5×D3211yescharacteristic
subgroupG/H
centerC22×C5C2×D32
commutator, cosocleC2×C32C24×C5
FrattiniC2C22×C5×D32
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
hypercenterC2×C4×C5D32
hypocenterC32C2×C5×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C2×C4×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#634C2semidirect
2. C2×C3×C5×D12C2semidirect
3. C2×C3×C4×C5×D3C2semidirect
4. C2×C5×#625C2semidirect
5. C2×C5×D3×Dic3C2semidirect
6. C5×#3795C2direct (N × H)
13. C5×#634C22semidirect
15. C3×C5×D12C22semidirect
16. C3×C4×C5×D3C22semidirect
17. C5×#625C22semidirect
18. C5×D3×Dic3C22semidirect
19. C2×#3795C5direct (N × H)
27. C2×C5×D12D3semidirect
29. C2×C4×C5×D3D3semidirect
42. C2×#634C2×C5semidirect
43. C2×C3×D12C2×C5semidirect
44. C2×C3×C4×D3C2×C5semidirect
45. C2×#625C2×C5semidirect
46. C2×D3×Dic3C2×C5semidirect
47. #3795C2×C5direct (N × H)
65. C5×D12C2×D3semidirect
67. C4×C5×D3C2×D3semidirect
73. C2×C32×C5#41semidirect
87. #634C22×C5semidirect
89. C3×D12C22×C5semidirect
90. C3×C4×D3C22×C5semidirect
91. #625C22×C5semidirect
92. D3×Dic3C22×C5semidirect
119. C2×D12C5×D3semidirect
121. C2×C4×D3C5×D3semidirect
125. C32×C5C2×#41semidirect
149. C2×C3×C5#235semidirect
150. C2×C3×C5#237semidirect
172. D12C2×C5×D3semidirect
174. C4×D3C2×C5×D3semidirect
186. C2×C32C5×#41semidirect
197. C3×C5C2×#235semidirect
198. C3×C5C2×#237semidirect
220. C2×C5#3795direct (N × H)
222. C32C2×C5×#41semidirect
237. C2×C3C5×#235semidirect
238. C2×C3C5×#237semidirect
243. C5C2×#3795direct (N × H)
253. C3C2×C5×#235semidirect
254. C3C2×C5×#237semidirect
257. C2C5×#3795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#6342
C2×C3×C5×D122
C2×C3×C4×C5×D32
C2×C5×#6252
C2×C5×D3×Dic32
C5×#37952
C2×C5×#2373
C2×C5×#2353
C2×#37955