Finite Group Databasebeta

← C2×D32×Dic5 #13088981

Subgroups — C2×D32×Dic5 #13088981

Order 1440.

998 conjugacy classes of subgroups; only the 284 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 284 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×C5×D32C211yesmaximal, characteristic
2C2×#67155C211yesmaximal, characteristic, complemented
3C2×D3×Dic15C212yesmaximal, complemented
4C2×C3⋊D3×Dic5C211yesmaximal, characteristic, complemented
5C2×C3×D3×Dic5C212yesmaximal, complemented
6D32×Dic5C218yesmaximal, direct product factor
7C22×D3×Dic5—32nomaximal
8C22×C5×C3⋊D3C2211yescharacteristic
9C22×C3×C5×D3C2212yes—
10C2×C5×D32C418yescomplemented
11C2×C5×D32C2214yes—
12C2×C3⋊Dic15C2211yescharacteristic, complemented
13C2×C3×Dic15C2212yescomplemented
14C2×C32×Dic5C2211yescharacteristic, complemented
15#67155C2214yescomplemented
16D3×Dic15C2218yescomplemented
17C3⋊D3×Dic5C2214yescomplemented
18C3×D3×Dic5C2218yescomplemented
19C2×C4×D32—51nomaximal, Hall
20C23×C5×D3—32no—
21C22×Dic15—32no—
22C22×C3×Dic5—32no—
23C2×D3×Dic5—32no—
24C2×D3×Dic5—32no—
25C2×D3×Dic5—32no—
26C2×D3×Dic5—316no—
27C2×D3×Dic5—61no—
28C2×D3×Dic5D312yesdirect product factor
29C22×C32×C5C2311yescharacteristic
30C2×C5×C3⋊D3C2×C414yescomplemented
31C2×C5×C3⋊D3C2312yes—
32C2×C3×C5×D3C2×C418yescomplemented
33C2×C3×C5×D3C2314yes—
34C5×D32C2×C4116yescomplemented
35C3⋊Dic15C2312yescomplemented
36C3×Dic15C2314yescomplemented
37C32×Dic5C2312yescomplemented
38C23×Dic5—91noHall
39C22×D32D511yescharacteristic
40C2×C4×C3⋊D3—51no—
41C2×C3×C4×D3—52no—
42C2×#624—51no—
43C2×D3×Dic3—52no—
44C4×D32—58no—
45C23×C3×C5—32no—
46C22×C5×D3—32no—
47C22×C5×D3—316no—
48C22×C5×D3—38no—
49C22×C5×D3—61no—
50C22×C5×D3C2×D312yes—
51C2×Dic15—32no—
52C2×Dic15—38no—
53C2×Dic15—61no—
54C2×Dic15C2×D312yescomplemented
55C2×C3×Dic5—21no—
56C2×C3×Dic5—32no—
57C2×C3×Dic5—38no—
58C2×C3×Dic5C2×D312yescomplemented
59D3×Dic5—38no—
60D3×Dic5—38no—
61D3×Dic5—38no—
62D3×Dic5—64no—
63D3×Dic5C2×D318yesdirect product factor
64C22×C4×D3—152no—
65C2×C32×C5C22×C412yescomplemented
66C2×C32×C5C2411yescharacteristic
67C5×C3⋊D3C22×C414yescomplemented
68C3×C5×D3C22×C418yescomplemented
69C24×C5—91no—
70C22×Dic5—32no—
71C22×Dic5—91no—
72C22×Dic5—98no—
73C22×Dic5—92no—
74C22×Dic5—91no—
75C22×C3⋊D3C2×D511yescharacteristic
76C22×C3×D3C2×D512yes—
77C2×D32Dic518yesdirect product factor
78C2×D32C2×D514yes—
79C2×C32×C4—51no—
80C2×C3⋊Dic3—51no—
81C4×C3⋊D3—54no—
82C2×C3×Dic3—52no—
83C3×C4×D3—58no—
84#624—54no—
85D3×Dic3—58no—
86C22×C3×C5—21no—
87C22×C3×C5—38no—
88C22×C3×C5—34no—
89C22×C3×C5C22×D312yes—
90C2×C5×D3—38no—
91C2×C5×D3—34no—
92C2×C5×D3—332no—
93C2×C5×D3—64no—
94C2×C5×D3—62no—
95C2×C5×D3C4×D318yescomplemented
96C2×C5×D3C22×D314yes—
97Dic15—34no—
98Dic15—62no—
99Dic15C22×D314yescomplemented
100C3×Dic5—22no—
101C3×Dic5—34no—
102C3×Dic5C22×D314yescomplemented
103C23×D3—32no—
104C22×C3×C4—152no—
105C22×Dic3—152no—
106C2×C4×D3—52no—
107C2×C4×D3—1516no—
108C2×C4×D3—152no—
109C2×C4×D3—152no—
110C2×C4×D3—152no—
111C2×C4×D3—301no—
112C32×C5C23×C411yescharacteristic, complemented, Hall
113C23×C5—32no—
114C23×C5—94no—
115C23×C5—98no—
116C23×C5—91no—
117C2×Dic5—32no—
118C2×Dic5—38no—
119C2×Dic5—94no—
120C2×Dic5—98no—
121C2×Dic5—91no—
122C2×Dic5—94no—
123C2×Dic5D3211yescharacteristic, direct product factor
124C22×C32C22×D511yescharacteristic
125C2×C3⋊D3C2×Dic514yescomplemented
126C2×C3⋊D3C22×D512yes—
127C2×C3×D3C2×Dic518yescomplemented
128C2×C3×D3C22×D514yes—
129D32C2×Dic5116yesdirect product factor
130C32×C4—52no—
131C3⋊Dic3—52no—
132C3×Dic3—54no—
133C23×C4—451noSylow
134C2×C3×C5—21no—
135C2×C3×C5—22no—
136C2×C3×C5—38no—
137C2×C3×C5C2×C4×D314yescomplemented
138C2×C3×C5C23×D312yes—
139C5×D3—38no—
140C5×D3—64no—
141C5×D3C2×C4×D318yescomplemented
142C23×C3—32no—
143C22×D3—32no—
144C22×D3—316no—
145C22×D3—38no—
146C22×D3—61no—
147C22×D3D3×D512yes—
148C2×C3×C4—52no—
149C2×C3×C4—101no—
150C2×C3×C4—158no—
151C2×C3×C4—152no—
152C2×Dic3—52no—
153C2×Dic3—158no—
154C2×Dic3—152no—
155C2×Dic3—301no—
156C4×D3—58no—
157C4×D3—158no—
158C4×D3—158no—
159C4×D3—158no—
160C4×D3—304no—
161C22×C5—34no—
162C22×C5—38no—
163C22×C5—916no—
164C22×C5—92no—
165C22×C5—94no—
166C22×C5C2×D3211yescharacteristic
167Dic5—34no—
168Dic5—92no—
169Dic5C2×D3212yesdirect product factor
170C2×C32C22×Dic512yescomplemented
171C2×C32C23×D511yescharacteristic
172C3⋊D3C22×Dic514yescomplemented
173C3×D3C22×Dic518yescomplemented
174C24—91no—
175C22×C4—152no—
176C22×C4—451no—
177C22×C4—458no—
178C22×C4—451no—
179C22×C4—452no—
180C3×C5—21no—
181C3×C5C22×C4×D312yescomplemented
182C22×C3—21no—
183C22×C3—38no—
184C22×C3—34no—
185C22×C3C2×D3×D512yes—
186C2×D3—38no—
187C2×D3—34no—
188C2×D3—332no—
189C2×D3—62no—
190C2×D3—64no—
191C2×D3D3×Dic518yesdirect product factor
192C2×D3C2×D3×D514yes—
193C3×C4—54no—
194C3×C4—102no—
195C3×C4—154no—
196Dic3—54no—
197Dic3—154no—
198Dic3—302no—
199C2×C5—38no—
200C2×C5—94no—
201C2×C5C4×D3212yescomplemented
202C2×C5C22×D3211yescharacteristic
203C32C23×Dic511yescharacteristic, complemented, Sylow
204C23—32no—
205C23—94no—
206C23—98no—
207C23—91no—
208C2×C4—51no—
209C2×C4—158no—
210C2×C4—152no—
211C2×C4—454no—
212C2×C4—454no—
213C2×C4—458no—
214C2×C4—451no—
215C2×C3—22no—
216C2×C3—21no—
217C2×C3—38no—
218C2×C3C2×D3×Dic514yescomplemented
219C2×C3C22×D3×D512yes—
220D3—38no—
221D3—64no—
222D3C2×D3×Dic518yesdirect product factor
223C5C2×C4×D3211yescharacteristic, complemented, Sylow
224C22—38no—
225C22—34no—
226C22—916no—
227C22—94no—
228C22—92no—
229C22D32×D511yescharacteristic
230C4—52no—
231C4—154no—
232C4—452no—
233C3—21no—
234C3C22×D3×Dic512yescomplemented
235C2—38no—
236C2—94no—
237C2D32×Dic512yesdirect product factor
238C2C2×D32×D511yescharacteristic
subgroupG/H
center, hypercenterC22D32×D5
commutator, hypocenterC32×C5C23×C4
FrattiniC2C2×D32×D5
Fitting, socleC22×C32×C5C23
prime radicalC22×C5×D32C2
cosocleC2×C32×C5C24
LCSG ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×#67155C2semidirect
3. C2×D3×Dic15C2semidirect
4. C2×C3⋊D3×Dic5C2semidirect
5. C2×C3×D3×Dic5C2semidirect
6. D32×Dic5C2direct (N × H)
10. C2×C5×D32C4semidirect
12. C2×C3⋊Dic15C22semidirect
13. C2×C3×Dic15C22semidirect
14. C2×C32×Dic5C22semidirect
15. #67155C22semidirect
16. D3×Dic15C22semidirect
17. C3⋊D3×Dic5C22semidirect
18. C3×D3×Dic5C22semidirect
28. C2×D3×Dic5D3direct (N × H)
30. C2×C5×C3⋊D3C2×C4semidirect
32. C2×C3×C5×D3C2×C4semidirect
34. C5×D32C2×C4semidirect
35. C3⋊Dic15C23semidirect
36. C3×Dic15C23semidirect
37. C32×Dic5C23semidirect
54. C2×Dic15C2×D3semidirect
58. C2×C3×Dic5C2×D3semidirect
63. D3×Dic5C2×D3direct (N × H)
65. C2×C32×C5C22×C4semidirect
67. C5×C3⋊D3C22×C4semidirect
68. C3×C5×D3C22×C4semidirect
77. C2×D32Dic5direct (N × H)
95. C2×C5×D3C4×D3semidirect
99. Dic15C22×D3semidirect
102. C3×Dic5C22×D3semidirect
112. C32×C5C23×C4semidirect
123. C2×Dic5D32direct (N × H)
125. C2×C3⋊D3C2×Dic5semidirect
127. C2×C3×D3C2×Dic5semidirect
129. D32C2×Dic5direct (N × H)
137. C2×C3×C5C2×C4×D3semidirect
141. C5×D3C2×C4×D3semidirect
169. Dic5C2×D32direct (N × H)
170. C2×C32C22×Dic5semidirect
172. C3⋊D3C22×Dic5semidirect
173. C3×D3C22×Dic5semidirect
181. C3×C5C22×C4×D3semidirect
191. C2×D3D3×Dic5direct (N × H)
201. C2×C5C4×D32semidirect
203. C32C23×Dic5semidirect
218. C2×C3C2×D3×Dic5semidirect
222. D3C2×D3×Dic5direct (N × H)
223. C5C2×C4×D32semidirect
234. C3C22×D3×Dic5semidirect
237. C2D32×Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×D322
C2×#671552
C2×D3×Dic152
C2×C3⋊D3×Dic52
C2×C3×D3×Dic52
D32×Dic52
C22×D3×Dic53
C2×C4×D325