Finite Group Databasebeta

← C22×D32×D5 #13089607

Subgroups — C22×D32×D5 #13089607

Order 1440.

3126 conjugacy classes of subgroups; only the 628 normal subgroups are shown.

normal subgroups only

This group has 3126 conjugacy classes of subgroups — too many to draw. Only its 628 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×(C3⋊D3)⋊D5C211yesmaximal, characteristic, complemented
2C22×D3×D15C212yesmaximal, complemented
3C22×C5×D32C211yesmaximal, characteristic, complemented
4C22×D5×C3⋊D3C211yesmaximal, characteristic, complemented
5C22×C3×D3×D5C212yesmaximal, complemented
6C2×D32×D5C2124yesmaximal, direct product factor
7C23×D3×D5—32nomaximal
8C22×C3⋊D15C2211yescharacteristic, complemented
9C22×C5×C3⋊D3C2211yescharacteristic, complemented
10C22×C3×D15C2212yescomplemented
11C22×C3×C5×D3C2212yescomplemented
12C22×C32×D5C2211yescharacteristic, complemented
13C2×(C3⋊D3)⋊D5C22112yescomplemented
14C2×D3×D15C22124yescomplemented
15C2×C5×D32C22112yescomplemented
16C2×D5×C3⋊D3C22112yescomplemented
17C2×C3×D3×D5C22124yescomplemented
18D32×D5C22164yesdirect product factor
19C23×D32—51nomaximal, Hall
20C23×D15—32no—
21C23×C5×D3—32no—
22C23×C3×D5—32no—
23C22×D3×D5—32no—
24C22×D3×D5—32no—
25C22×D3×D5—32no—
26C22×D3×D5—348no—
27C22×D3×D5—61no—
28C22×D3×D5D312yesdirect product factor
29C22×C32×C5C2311yescharacteristic, complemented
30C2×C3⋊D15C2316yescomplemented
31C2×C5×C3⋊D3C2316yescomplemented
32C2×C3×D15C23112yescomplemented
33C2×C3×C5×D3C23112yescomplemented
34C2×C32×D5C2316yescomplemented
35(C3⋊D3)⋊D5C23116yescomplemented
36D3×D15C23132yescomplemented
37C5×D32C23116yescomplemented
38D5×C3⋊D3C23116yescomplemented
39C3×D3×D5C23132yescomplemented
40C24×D5—91noHall
41C23×C3⋊D3—51no—
42C23×C3×D3—52no—
43C22×D32—51no—
44C22×D32—52no—
45C22×D32—524no—
46C22×D32D511yescharacteristic, direct product factor
47C23×C3×C5—32no—
48C22×D15—32no—
49C22×D15—324no—
50C22×D15—61no—
51C22×D15C2×D312yescomplemented
52C22×C5×D3—32no—
53C22×C5×D3—324no—
54C22×C5×D3—61no—
55C22×C5×D3C2×D312yescomplemented
56C22×C3×D5—21no—
57C22×C3×D5—32no—
58C22×C3×D5—324no—
59C22×C3×D5C2×D312yescomplemented
60C2×D3×D5—324no—
61C2×D3×D5—324no—
62C2×D3×D5—324no—
63C2×D3×D5—3128no—
64C2×D3×D5—612no—
65C2×D3×D5C2×D3124yesdirect product factor
66C24×D3—152no—
67C2×C32×C5C2413yescomplemented
68C3⋊D15C2414yescomplemented
69C5×C3⋊D3C2414yescomplemented
70C3×D15C2418yescomplemented
71C3×C5×D3C2418yescomplemented
72C32×D5C2414yescomplemented
73C24×C5—91no—
74C23×D5—32no—
75C23×D5—91no—
76C23×D5—924no—
77C23×D5—92no—
78C23×D5—91no—
79C23×C32—51no—
80C22×C3⋊D3—51no—
81C22×C3⋊D3—512no—
82C22×C3⋊D3C2×D511yescharacteristic, complemented
83C22×C3×D3—52no—
84C22×C3×D3—524no—
85C22×C3×D3C2×D512yescomplemented
86C2×D32—512no—
87C2×D32—524no—
88C2×D32—564no—
89C2×D32C2×D5112yesdirect product factor
90C22×C3×C5—21no—
91C22×C3×C5—312no—
92C22×C3×C5C22×D312yescomplemented
93C2×D15—312no—
94C2×D15—332no—
95C2×D15—66no—
96C2×D15C22×D3112yescomplemented
97C2×C5×D3—312no—
98C2×C5×D3—332no—
99C2×C5×D3—66no—
100C2×C5×D3C22×D3112yescomplemented
101C2×C3×D5—26no—
102C2×C3×D5—312no—
103C2×C3×D5—332no—
104C2×C3×D5C22×D3112yescomplemented
105D3×D5—332no—
106D3×D5—332no—
107D3×D5—332no—
108D3×D5—616no—
109D3×D5C22×D3132yesdirect product factor
110C24×C3—152no—
111C23×D3—32no—
112C23×D3—52no—
113C23×D3—152no—
114C23×D3—1548no—
115C23×D3—152no—
116C23×D3—152no—
117C23×D3—152no—
118C23×D3—301no—
119C32×C5C2511yescharacteristic, complemented, Hall
120C23×C5—32no—
121C23×C5—912no—
122C23×C5—91no—
123C22×D5—32no—
124C22×D5—324no—
125C22×D5—912no—
126C22×D5—964no—
127C22×D5—924no—
128C22×D5—91no—
129C22×D5—912no—
130C22×D5D3211yescharacteristic, direct product factor
131C22×C32—56no—
132C22×C32C22×D511yescharacteristic, complemented
133C2×C3⋊D3—56no—
134C2×C3⋊D3—516no—
135C2×C3⋊D3C22×D516yescomplemented
136C2×C3×D3—512no—
137C2×C3×D3—532no—
138C2×C3×D3C22×D5112yescomplemented
139D32—516no—
140D32—532no—
141D32C22×D5116yesdirect product factor
142C25—451noSylow
143C2×C3×C5—23no—
144C2×C3×C5—38no—
145C2×C3×C5C23×D316yescomplemented
146D15—38no—
147D15—64no—
148D15C23×D318yescomplemented
149C3×D5—24no—
150C3×D5—38no—
151C3×D5C23×D318yescomplemented
152C5×D3—38no—
153C5×D3—64no—
154C5×D3C23×D318yescomplemented
155C23×C3—32no—
156C23×C3—52no—
157C23×C3—101no—
158C23×C3—1524no—
159C23×C3—152no—
160C22×D3—32no—
161C22×D3—324no—
162C22×D3—52no—
163C22×D3—524no—
164C22×D3—61no—
165C22×D3—1524no—
166C22×D3—15128no—
167C22×D3—1524no—
168C22×D3—1524no—
169C22×D3—152no—
170C22×D3—1524no—
171C22×D3—3012no—
172C22×D3—301no—
173C22×D3D3×D512yesdirect product factor
174C22×C5—312no—
175C22×C5—916no—
176C22×C5—96no—
177C22×C5C2×D3211yescharacteristic, complemented
178C2×D5—312no—
179C2×D5—332no—
180C2×D5—916no—
181C2×D5—932no—
182C2×D5—96no—
183C2×D5—916no—
184C2×D5C2×D3216yesdirect product factor
185C2×C32—54no—
186C2×C32C23×D513yescomplemented
187C3⋊D3—54no—
188C3⋊D3C23×D514yescomplemented
189C3×D3—58no—
190C3×D3C23×D518yescomplemented
191C24—91no—
192C24—152no—
193C24—452no—
194C24—451no—
195C24—4524no—
196C24—451no—
197C3×C5—21no—
198C3×C5C24×D312yescomplemented
199C22×C3—21no—
200C22×C3—312no—
201C22×C3—512no—
202C22×C3—106no—
203C22×C3—1532no—
204C22×C3—1512no—
205C22×C3C2×D3×D512yescomplemented
206C2×D3—312no—
207C2×D3—332no—
208C2×D3—512no—
209C2×D3—532no—
210C2×D3—66no—
211C2×D3—1532no—
212C2×D3—1532no—
213C2×D3—1532no—
214C2×D3—1512no—
215C2×D3—1532no—
216C2×D3—3016no—
217C2×D3—306no—
218C2×D3C2×D3×D5112yesdirect product factor
219C2×C5—38no—
220C2×C5—94no—
221C2×C5C22×D3213yescomplemented
222D5—38no—
223D5—94no—
224D5C22×D3214yesdirect product factor
225C32C24×D511yescharacteristic, complemented, Sylow
226C23—32no—
227C23—51no—
228C23—912no—
229C23—91no—
230C23—1524no—
231C23—152no—
232C23—4524no—
233C23—4512no—
234C23—4564no—
235C23—4512no—
236C23—451no—
237C2×C3—23no—
238C2×C3—38no—
239C2×C3—58no—
240C2×C3—104no—
241C2×C3—158no—
242C2×C3C22×D3×D516yescomplemented
243D3—38no—
244D3—58no—
245D3—64no—
246D3—158no—
247D3—304no—
248D3C22×D3×D518yesdirect product factor
249C5C23×D3211yescharacteristic, complemented, Sylow
250C22—312no—
251C22—56no—
252C22—916no—
253C22—96no—
254C22—1532no—
255C22—1512no—
256C22—4532no—
257C22—4516no—
258C22—4516no—
259C22—456no—
260C22D32×D511yescharacteristic, direct product factor
261C3—21no—
262C3C23×D3×D512yescomplemented
263C2—38no—
264C2—54no—
265C2—94no—
266C2—158no—
267C2—454no—
268C2C2×D32×D513yesdirect product factor
subgroupG/H
center, hypercenterC22D32×D5
commutator, cosocle, hypocenterC32×C5C25
FrattiniC1G
Fitting, socleC22×C32×C5C23
LCSG ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×(C3⋊D3)⋊D5C2semidirect
2. C22×D3×D15C2semidirect
3. C22×C5×D32C2semidirect
4. C22×D5×C3⋊D3C2semidirect
5. C22×C3×D3×D5C2semidirect
6. C2×D32×D5C2direct (N × H)
8. C22×C3⋊D15C22semidirect
9. C22×C5×C3⋊D3C22semidirect
10. C22×C3×D15C22semidirect
11. C22×C3×C5×D3C22semidirect
12. C22×C32×D5C22semidirect
13. C2×(C3⋊D3)⋊D5C22semidirect
14. C2×D3×D15C22semidirect
15. C2×C5×D32C22semidirect
16. C2×D5×C3⋊D3C22semidirect
17. C2×C3×D3×D5C22semidirect
18. D32×D5C22direct (N × H)
28. C22×D3×D5D3direct (N × H)
29. C22×C32×C5C23semidirect
30. C2×C3⋊D15C23semidirect
31. C2×C5×C3⋊D3C23semidirect
32. C2×C3×D15C23semidirect
33. C2×C3×C5×D3C23semidirect
34. C2×C32×D5C23semidirect
35. (C3⋊D3)⋊D5C23semidirect
36. D3×D15C23semidirect
37. C5×D32C23semidirect
38. D5×C3⋊D3C23semidirect
39. C3×D3×D5C23semidirect
46. C22×D32D5direct (N × H)
51. C22×D15C2×D3semidirect
55. C22×C5×D3C2×D3semidirect
59. C22×C3×D5C2×D3semidirect
65. C2×D3×D5C2×D3direct (N × H)
67. C2×C32×C5C24semidirect
68. C3⋊D15C24semidirect
69. C5×C3⋊D3C24semidirect
70. C3×D15C24semidirect
71. C3×C5×D3C24semidirect
72. C32×D5C24semidirect
82. C22×C3⋊D3C2×D5semidirect
85. C22×C3×D3C2×D5semidirect
89. C2×D32C2×D5direct (N × H)
92. C22×C3×C5C22×D3semidirect
96. C2×D15C22×D3semidirect
100. C2×C5×D3C22×D3semidirect
104. C2×C3×D5C22×D3semidirect
109. D3×D5C22×D3direct (N × H)
119. C32×C5C25semidirect
130. C22×D5D32direct (N × H)
132. C22×C32C22×D5semidirect
135. C2×C3⋊D3C22×D5semidirect
138. C2×C3×D3C22×D5semidirect
141. D32C22×D5direct (N × H)
145. C2×C3×C5C23×D3semidirect
148. D15C23×D3semidirect
151. C3×D5C23×D3semidirect
154. C5×D3C23×D3semidirect
173. C22×D3D3×D5direct (N × H)
177. C22×C5C2×D32semidirect
184. C2×D5C2×D32direct (N × H)
186. C2×C32C23×D5semidirect
188. C3⋊D3C23×D5semidirect
190. C3×D3C23×D5semidirect
198. C3×C5C24×D3semidirect
205. C22×C3C2×D3×D5semidirect
218. C2×D3C2×D3×D5direct (N × H)
221. C2×C5C22×D32semidirect
224. D5C22×D32direct (N × H)
225. C32C24×D5semidirect
242. C2×C3C22×D3×D5semidirect
248. D3C22×D3×D5direct (N × H)
249. C5C23×D32semidirect
260. C22D32×D5direct (N × H)
262. C3C23×D3×D5semidirect
268. C2C2×D32×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C3⋊D3)⋊D52
C22×D3×D152
C22×C5×D322
C22×D5×C3⋊D32
C22×C3×D3×D52
C2×D32×D52
C23×D3×D53
C23×D325