Finite Group Databasebeta

← C2×C5×#3811 #13089342

Subgroups — C2×C5×#3811 #13089342

Order 1440.

1078 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 248 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×C5×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C5×D32C211yesmaximal, characteristic, complemented
3C2×C3×C5×#67C212yesmaximal, complemented
4C5×#3811C218yesmaximal, direct product factor
5C2×C5×#626C212yesmaximal, complemented
6C2×C5×#624C211yesmaximal, characteristic, complemented
7C2×C5×D3×D4—32nomaximal
8C23×C32×C5C2211yescharacteristic, complemented
9C22×C5×C3⋊D3—24no—
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C5×C3⋊D3C2214yescomplemented
12C22×C5×C3⋊D3C2211yescharacteristic, complemented
13C22×C3×C5×D3C2212yescomplemented
14C2×C5×D32—24no—
15C2×C5×D32C2214yescomplemented
16C3×C5×#67C2218yescomplemented
17C2×C3×C5×Dic3C2212yescomplemented
18C5×#626C2218yescomplemented
19C5×#624C2214yescomplemented
20C2×#3811C511yesmaximal, characteristic, direct product factor, Hall
21C23×C5×D3—32no—
22C23×C5×D3—32no—
23C23×C5×D3—61no—
24C2×C3×C5×D4—32no—
25C2×C5×#67—32no—
26C2×C5×#67D312yescomplemented
27C5×D3×D4—316no—
28C2×C5×D12—32no—
29C2×C4×C5×D3—32no—
30C22×C32×C5—22no—
31C22×C32×C5C2311yescharacteristic
32C22×C32×C5C2312yescomplemented
33C2×C5×C3⋊D3—22no—
34C2×C5×C3⋊D3—28no—
35C2×C5×C3⋊D3D414yescomplemented
36C2×C5×C3⋊D3C2312yes—
37C2×C5×C3⋊D3C2312yescomplemented
38C2×C3×C5×D3—24no—
39C2×C3×C5×D3C2314yescomplemented
40C5×D32—28no—
41C3×C5×Dic3C2314yescomplemented
42C22×C5×D4—91noHall
43C23×C3⋊D3C2×C511yescharacteristic, complemented
44C22×D32C2×C511yescharacteristic, complemented
45C2×C3×#67C2×C512yescomplemented
46#3811C2×C518yesdirect product factor
47C2×#626C2×C512yescomplemented
48C2×#624C2×C511yescharacteristic, complemented
49C23×C3×C5—21no—
50C23×C3×C5—32no—
51C23×C3×C5C2×D312yescomplemented
52C22×C5×D3—32no—
53C22×C5×D3—32no—
54C22×C5×D3—38no—
55C22×C5×D3—38no—
56C22×C5×D3—68no—
57C22×C5×D3—68no—
58C22×C5×D3—61no—
59C22×C5×D3—64no—
60C22×C5×D3—61no—
61C22×C5×D3—68no—
62C22×C5×D3C2×D312yescomplemented
63C3×C5×D4—38no—
64C2×C3×C4×C5—32no—
65C5×#67—38no—
66C5×#67C2×D318yescomplemented
67C2×C5×Dic3C2×D312yescomplemented
68C5×D12—38no—
69C4×C5×D3—38no—
70C2×D3×D4—32no—
71C2×C32×C5—22no—
72C2×C32×C5C2×D412yescomplemented
73C2×C32×C5C2411yescharacteristic
74C5×C3⋊D3—22no—
75C5×C3⋊D3C2×D414yescomplemented
76C3×C5×D3—24no—
77C24×C5—91no—
78C24×C5—91no—
79C2×C5×D4—32no—
80C2×C5×D4—92no—
81C2×C5×D4—98no—
82C22×C4×C5—91no—
83C23×C32C22×C511yescharacteristic, complemented
84C22×C3⋊D3—24no—
85C22×C3⋊D3C22×C511yescharacteristic
86C22×C3⋊D3C22×C514yescomplemented
87C22×C3⋊D3C22×C511yescharacteristic, complemented
88C22×C3×D3C22×C512yescomplemented
89C2×D32—24no—
90C2×D32C22×C514yescomplemented
91C3×#67C22×C518yescomplemented
92C2×C3×Dic3C22×C512yescomplemented
93#626C22×C518yescomplemented
94#624C22×C514yescomplemented
95C22×C3×C5—24no—
96C22×C3×C5—24no—
97C22×C3×C5—21no—
98C22×C3×C5—22no—
99C22×C3×C5—34no—
100C22×C3×C5—64no—
101C22×C3×C5C22×D312yes—
102C22×C3×C5C22×D314yescomplemented
103C2×C5×D3—24no—
104C2×C5×D3—38no—
105C2×C5×D3—34no—
106C2×C5×D3—34no—
107C2×C5×D3—64no—
108C2×C5×D3—62no—
109C2×C5×D3—62no—
110C2×C5×D3—616no—
111C2×C5×D3—616no—
112C2×C5×D3—616no—
113C2×C5×D3—64no—
114C2×C5×D3—64no—
115C2×C5×D3C22×D314yescomplemented
116C3×C4×C5—34no—
117C5×Dic3C22×D314yescomplemented
118C23×D3—32no—
119C23×D3—32no—
120C23×D3—61no—
121C2×C3×D4—32no—
122C2×#67—32no—
123C2×#67C5×D312yescomplemented
124D3×D4—316no—
125C2×D12—32no—
126C2×C4×D3—32no—
127C32×C5C22×D411yescharacteristic, complemented, Hall
128C23×C5—32no—
129C23×C5—94no—
130C23×C5—91no—
131C23×C5—91no—
132C23×C5—94no—
133C23×C5—184no—
134C23×C5—184no—
135C23×C5D3211yescharacteristic, complemented
136C5×D4—38no—
137C5×D4—98no—
138C2×C4×C5—32no—
139C2×C4×C5—94no—
140C22×C32—22no—
141C22×C32C23×C511yescharacteristic
142C22×C32C23×C512yescomplemented
143C2×C3⋊D3—22no—
144C2×C3⋊D3—28no—
145C2×C3⋊D3C5×D414yescomplemented
146C2×C3⋊D3C23×C512yes—
147C2×C3⋊D3C23×C512yescomplemented
148C2×C3×D3—24no—
149C2×C3×D3C23×C514yescomplemented
150D32—28no—
151C3×Dic3C23×C514yescomplemented
152C22×D4—91noSylow
153C2×C3×C5—24no—
154C2×C3×C5—24no—
155C2×C3×C5—21no—
156C2×C3×C5—22no—
157C2×C3×C5—64no—
158C2×C3×C5D3×D414yescomplemented
159C2×C3×C5C23×D312yes—
160C5×D3—24no—
161C5×D3—38no—
162C5×D3—64no—
163C5×D3—64no—
164C5×D3—64no—
165C23×C3—21no—
166C23×C3—32no—
167C23×C3C2×C5×D312yescomplemented
168C22×D3—32no—
169C22×D3—32no—
170C22×D3—38no—
171C22×D3—38no—
172C22×D3—61no—
173C22×D3—61no—
174C22×D3—64no—
175C22×D3—68no—
176C22×D3—68no—
177C22×D3—68no—
178C22×D3C2×C5×D312yescomplemented
179C3×D4—38no—
180C2×C3×C4—32no—
181#67—38no—
182#67C2×C5×D318yescomplemented
183C2×Dic3C2×C5×D312yescomplemented
184D12—38no—
185C4×D3—38no—
186C22×C5—22no—
187C22×C5—34no—
188C22×C5—64no—
189C22×C5—92no—
190C22×C5—94no—
191C22×C5—92no—
192C22×C5—188no—
193C22×C5—188no—
194C22×C5—182no—
195C22×C5C2×D3211yescharacteristic
196C22×C5C2×D3212yescomplemented
197C4×C5—34no—
198C2×C32—22no—
199C2×C32C2×C5×D412yescomplemented
200C2×C32C24×C511yescharacteristic
201C3⋊D3—22no—
202C3⋊D3C2×C5×D414yescomplemented
203C3×D3—24no—
204C24—91no—
205C24—91no—
206C2×D4—32no—
207C2×D4—92no—
208C2×D4—98no—
209C22×C4—91no—
210C3×C5—21no—
211C3×C5C2×D3×D412yescomplemented
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—21no—
215C22×C3—22no—
216C22×C3—34no—
217C22×C3—64no—
218C22×C3C22×C5×D312yes—
219C22×C3C22×C5×D314yescomplemented
220C2×D3—24no—
221C2×D3—38no—
222C2×D3—34no—
223C2×D3—34no—
224C2×D3—64no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—616no—
228C2×D3—616no—
229C2×D3—616no—
230C2×D3—64no—
231C2×D3—64no—
232C2×D3C22×C5×D314yescomplemented
233C3×C4—34no—
234Dic3C22×C5×D314yescomplemented
235C2×C5—22no—
236C2×C5—64no—
237C2×C5—94no—
238C2×C5—182no—
239C2×C5#381112yesdirect product factor
240C2×C5C22×D3211yescharacteristic
241C32C22×C5×D411yescharacteristic, complemented, Sylow
242C23—32no—
243C23—94no—
244C23—91no—
245C23—91no—
246C23—94no—
247C23—184no—
248C23—184no—
249C23C5×D3211yescharacteristic, complemented
250D4—38no—
251D4—98no—
252C2×C4—32no—
253C2×C4—94no—
254C2×C3—24no—
255C2×C3—24no—
256C2×C3—21no—
257C2×C3—22no—
258C2×C3—64no—
259C2×C3C5×D3×D414yescomplemented
260C2×C3C23×C5×D312yes—
261D3—24no—
262D3—38no—
263D3—64no—
264D3—64no—
265D3—64no—
266C5C2×#381111yescharacteristic, direct product factor, Sylow
267C22—22no—
268C22—34no—
269C22—64no—
270C22—92no—
271C22—94no—
272C22—92no—
273C22—188no—
274C22—188no—
275C22—182no—
276C22C2×C5×D3211yescharacteristic
277C22C2×C5×D3212yescomplemented
278C4—34no—
279C3—21no—
280C3C2×C5×D3×D412yescomplemented
281C2—22no—
282C2—64no—
283C2—94no—
284C2—182no—
285C2C5×#381112yesdirect product factor
286C2C22×C5×D3211yescharacteristic
subgroupG/H
centerC22×C5C2×D32
commutator, cosocleC2×C32C24×C5
FrattiniC2C22×C5×D32
FittingC23×C32×C5C22
socleC22×C32×C5C23
hypercenterC23×C5D32
hypocenterC32C22×C5×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C23×C5

Complements

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

NH ≅ G/Ntype
1. C23×C5×C3⋊D3C2semidirect
2. C22×C5×D32C2semidirect
3. C2×C3×C5×#67C2semidirect
4. C5×#3811C2direct (N × H)
5. C2×C5×#626C2semidirect
6. C2×C5×#624C2semidirect
8. C23×C32×C5C22semidirect
11. C22×C5×C3⋊D3C22semidirect
12. C22×C5×C3⋊D3C22semidirect
13. C22×C3×C5×D3C22semidirect
15. C2×C5×D32C22semidirect
16. C3×C5×#67C22semidirect
17. C2×C3×C5×Dic3C22semidirect
18. C5×#626C22semidirect
19. C5×#624C22semidirect
20. C2×#3811C5direct (N × H)
26. C2×C5×#67D3semidirect
32. C22×C32×C5C23semidirect
35. C2×C5×C3⋊D3D4semidirect
37. C2×C5×C3⋊D3C23semidirect
39. C2×C3×C5×D3C23semidirect
41. C3×C5×Dic3C23semidirect
43. C23×C3⋊D3C2×C5semidirect
44. C22×D32C2×C5semidirect
45. C2×C3×#67C2×C5semidirect
46. #3811C2×C5direct (N × H)
47. C2×#626C2×C5semidirect
48. C2×#624C2×C5semidirect
51. C23×C3×C5C2×D3semidirect
62. C22×C5×D3C2×D3semidirect
66. C5×#67C2×D3semidirect
67. C2×C5×Dic3C2×D3semidirect
72. C2×C32×C5C2×D4semidirect
75. C5×C3⋊D3C2×D4semidirect
83. C23×C32C22×C5semidirect
86. C22×C3⋊D3C22×C5semidirect
87. C22×C3⋊D3C22×C5semidirect
88. C22×C3×D3C22×C5semidirect
90. C2×D32C22×C5semidirect
91. C3×#67C22×C5semidirect
92. C2×C3×Dic3C22×C5semidirect
93. #626C22×C5semidirect
94. #624C22×C5semidirect
102. C22×C3×C5C22×D3semidirect
115. C2×C5×D3C22×D3semidirect
117. C5×Dic3C22×D3semidirect
123. C2×#67C5×D3semidirect
127. C32×C5C22×D4semidirect
135. C23×C5D32semidirect
142. C22×C32C23×C5semidirect
145. C2×C3⋊D3C5×D4semidirect
147. C2×C3⋊D3C23×C5semidirect
149. C2×C3×D3C23×C5semidirect
151. C3×Dic3C23×C5semidirect
158. C2×C3×C5D3×D4semidirect
167. C23×C3C2×C5×D3semidirect
178. C22×D3C2×C5×D3semidirect
182. #67C2×C5×D3semidirect
183. C2×Dic3C2×C5×D3semidirect
196. C22×C5C2×D32semidirect
199. C2×C32C2×C5×D4semidirect
202. C3⋊D3C2×C5×D4semidirect
211. C3×C5C2×D3×D4semidirect
219. C22×C3C22×C5×D3semidirect
232. C2×D3C22×C5×D3semidirect
234. Dic3C22×C5×D3semidirect
239. C2×C5#3811direct (N × H)
241. C32C22×C5×D4semidirect
249. C23C5×D32semidirect
259. C2×C3C5×D3×D4semidirect
266. C5C2×#3811direct (N × H)
277. C22C2×C5×D32semidirect
280. C3C2×C5×D3×D4semidirect
285. C2C5×#3811direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C22×C5×D322
C2×C3×C5×#672
C5×#38112
C2×C5×#6262
C2×C5×#6242
C2×C5×D3×D43
C2×#38115