Finite Group Databasebeta

← #13086958

Subgroups — #13086958

Order 1440.

780 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 122 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×D5×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C5×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×#67140C211yesmaximal, characteristic, complemented
4C2×#67138C211yesmaximal, characteristic, complemented
5#10623908C211yesmaximal, characteristic, complemented
6C32×#685C211yesmaximal, characteristic, complemented
7#10623771C211yesmaximal, characteristic, complemented
8#91475—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C5×C3⋊D3C2211yescharacteristic, complemented
12C22×C32×D5C2211yescharacteristic
13C2×D5×C3⋊D3—22no—
14C2×D5×C3⋊D3—22no—
15C2×D5×C3⋊D3—22no—
16C2×C32×C4×C5C2211yescharacteristic, complemented
17C2×C3⋊Dic15C2211yescharacteristic, complemented
18C5×C4⋊(C3⋊D3)—22no—
19C2×C32×Dic5C2211yescharacteristic, complemented
20#67140—22no—
21#67138—22no—
22#64091—51nomaximal, Hall
23C22×D3×D5—34no—
24C2×C5×D12—34no—
25C2×#1203—34no—
26C2×#1201—34no—
27#6714—34no—
28C3×#685D314yescomplemented
29(C2×D3)⋊Dic5—34no—
30C22×C32×C5C2311yescharacteristic
31C2×C3⋊D15—21no—
32C2×C3⋊D15—21no—
33C2×C3⋊D15D412yescomplemented
34C2×C5×C3⋊D3—21no—
35C2×C5×C3⋊D3—21no—
36C2×C5×C3⋊D3—21no—
37C2×C5×C3⋊D3—21no—
38C2×C5×C3⋊D3—21no—
39C2×C5×C3⋊D3D412yescomplemented
40C2×C32×D5—21no—
41C2×C32×D5—21no—
42C2×C32×D5D412yescomplemented
43D5×C3⋊D3—28no—
44C32×C4×C5—21no—
45C3⋊Dic15—21no—
46C32×Dic5—21no—
47#4083—91noHall
48C23×C3⋊D3—51no—
49C2×#638—51no—
50C2×C4⋊(C3⋊D3)—51no—
51C2×C4⋊(C3⋊D3)D511yescharacteristic, complemented
52C32×C22⋊C4—51no—
53#3752—51no—
54#3752—51no—
55C22×D15—34no—
56C22×C5×D3—34no—
57C22×C5×D3—34no—
58C22×C3×D5C2×D314yes—
59C2×D3×D5—68no—
60C2×D3×D5—68no—
61C2×D3×D5—68no—
62C2×C3×C4×C5C2×D314yescomplemented
63C2×Dic15—34no—
64C5×D12—68no—
65C2×C3×Dic5C2×D314yescomplemented
66#1203—68no—
67#1201—68no—
68#882—154no—
69C2×C32×C5C2×D411yescharacteristic
70C2×C32×C5C2×D411yescharacteristic
71C2×C32×C5C2×D411yescharacteristic
72C3⋊D15—22no—
73C5×C3⋊D3—22no—
74C5×C3⋊D3—41no—
75C32×D5—22no—
76C23×D5—91no—
77C2×C5×D4—91no—
78C2×C22⋊D5—91no—
79C2×C22⋊D5—91no—
80C22⋊Dic5—91no—
81#685—91no—
82#685C3⋊D311yescharacteristic, complemented
83C23×C32—51no—
84C22×C3⋊D3—51no—
85C22×C3⋊D3—102no—
86C22×C3⋊D3—102no—
87C22×C3⋊D3—102no—
88C22×C3⋊D3C2×D511yescharacteristic
89C22×C3⋊D3C2×D511yescharacteristic, complemented
90C2×C32×C4—51no—
91C2×C32×C4C2×D511yescharacteristic, complemented
92#638—102no—
93C2×C3⋊Dic3—51no—
94C4⋊(C3⋊D3)—22no—
95C4⋊(C3⋊D3)—102no—
96C22×C3×C5C22×D314yes—
97C2×D15—38no—
98C2×D15—64no—
99C2×D15—64no—
100C2×C5×D3—38no—
101C2×C5×D3—64no—
102C2×C5×D3—64no—
103C2×C5×D3—64no—
104C2×C5×D3—64no—
105C2×C5×D3—64no—
106C2×C3×D5—24no—
107C2×C3×D5—24no—
108C2×C3×D5D1218yescomplemented
109D3×D5—632no—
110C3×C4×C5—24no—
111Dic15—64no—
112C3×Dic5—24no—
113C23×D3—154no—
114C2×#67—154no—
115C2×D12—34no—
116C2×D12—154no—
117C3×C22⋊C4—54no—
118(C2×D3)⋊C4—154no—
119(C2×D3)⋊C4—154no—
120C32×C5#12011yescharacteristic, complemented, Hall
121C23×C5—91no—
122C23×C5—91no—
123C22×D5—91no—
124C22×D5—182no—
125C22×D5—182no—
126C22×D5—182no—
127C22×D5C2×C3⋊D311yescharacteristic
128C5×D4—182no—
129C2×C4×C5C2×C3⋊D311yescharacteristic, complemented
130C22⋊D5—182no—
131C22⋊D5—182no—
132C2×Dic5—91no—
133C2×Dic5C2×C3⋊D311yescharacteristic, complemented
134C22×C32—52no—
135C22×C32—101no—
136C22×C32—101no—
137C22×C32C22×D511yescharacteristic
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—52no—
144C2×C3⋊D3—108no—
145C2×C3⋊D3—101no—
146C2×C3⋊D3—101no—
147C2×C3⋊D3C22⋊D512yescomplemented
148C32×C4—21no—
149C32×C4—101no—
150C3⋊Dic3—101no—
151#120—451noSylow
152C2×C3×C5C2×D1214yes—
153C2×C3×C5D3×D414yes—
154C2×C3×C5D3×D414yes—
155D15—68no—
156C3×D5—28no—
157C5×D3—68no—
158C5×D3—124no—
159C23×C3—54no—
160C22×D3—34no—
161C22×D3—34no—
162C22×D3—154no—
163C22×D3—308no—
164C22×D3—308no—
165C22×D3—308no—
166C2×C3×C4—54no—
167C2×C3×C4D3×D514yescomplemented
168#67—308no—
169C2×Dic3—154no—
170D12—68no—
171D12—308no—
172C22×C5—92no—
173C22×C5—181no—
174C22×C5—181no—
175C22×C5—181no—
176C22×C5—181no—
177C22×C5—181no—
178C22×C5C22×C3⋊D311yescharacteristic
179C2×D5—21no—
180C2×D5—21no—
181C2×D5—92no—
182C2×D5—188no—
183C2×D5—181no—
184C2×D5—181no—
185C2×D5C4⋊(C3⋊D3)12yescomplemented
186C4×C5—21no—
187Dic5—21no—
188Dic5—181no—
189C2×C32—102no—
190C2×C32D4×D511yescharacteristic
191C2×C32D4×D511yescharacteristic
192C2×C32C2×C22⋊D511yescharacteristic
193C3⋊D3—22no—
194C3⋊D3—41no—
195C3⋊D3—102no—
196C24—451no—
197C2×D4—91no—
198C2×D4—451no—
199C2×D4—451no—
200C22⋊C4—51no—
201C22⋊C4—451no—
202C22⋊C4—451no—
203C3×C5#88214yescomplemented
204C22×C3—58no—
205C22×C3—104no—
206C22×C3—104no—
207C22×C3C2×D3×D514yes—
208C2×D3—38no—
209C2×D3—64no—
210C2×D3—64no—
211C2×D3—64no—
212C2×D3—64no—
213C2×D3—64no—
214C2×D3—158no—
215C2×D3—3032no—
216C2×D3—304no—
217C2×D3—304no—
218C3×C4—24no—
219C3×C4—104no—
220Dic3—304no—
221C2×C5—182no—
222C2×C5—361no—
223C2×C5C2×C4⋊(C3⋊D3)11yescharacteristic
224C2×C5D4×C3⋊D311yescharacteristic
225C2×C5D4×C3⋊D311yescharacteristic
226D5—22no—
227D5—182no—
228C32#408311yescharacteristic, complemented, Sylow
229C23—51no—
230C23—91no—
231C23—91no—
232C23—451no—
233C23—902no—
234C23—902no—
235C23—902no—
236D4—182no—
237D4—902no—
238D4—902no—
239C2×C4—51no—
240C2×C4—451no—
241C2×C4D5×C3⋊D311yescharacteristic, complemented
242C2×C3—108no—
243C2×C3D5×D1214yes—
244C2×C3#677714yes—
245C2×C3D3×C22⋊D514yes—
246D3—68no—
247D3—124no—
248D3—308no—
249C5#6409111yescharacteristic, complemented, Sylow
250C22—52no—
251C22—92no—
252C22—101no—
253C22—101no—
254C22—181no—
255C22—181no—
256C22—181no—
257C22—181no—
258C22—181no—
259C22—452no—
260C22—908no—
261C22—901no—
262C22—901no—
263C22C2×D5×C3⋊D311yescharacteristic
264C4—21no—
265C4—101no—
266C4—901no—
267C3#9147514yescomplemented
268C2—102no—
269C2—182no—
270C2—361no—
271C2—902no—
272C2D5×C4⋊(C3⋊D3)11yescharacteristic
273C2#1062416011yescharacteristic
274C2C3⋊D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×C3⋊D3C2semidirect
2. C2×C5×C4⋊(C3⋊D3)C2semidirect
3. C2×#67140C2semidirect
4. C2×#67138C2semidirect
5. #10623908C2semidirect
6. C32×#685C2semidirect
7. #10623771C2semidirect
11. C22×C5×C3⋊D3C22semidirect
16. C2×C32×C4×C5C22semidirect
17. C2×C3⋊Dic15C22semidirect
19. C2×C32×Dic5C22semidirect
28. C3×#685D3semidirect
33. C2×C3⋊D15D4semidirect
39. C2×C5×C3⋊D3D4semidirect
42. C2×C32×D5D4semidirect
51. C2×C4⋊(C3⋊D3)D5semidirect
62. C2×C3×C4×C5C2×D3semidirect
65. C2×C3×Dic5C2×D3semidirect
82. #685C3⋊D3semidirect
89. C22×C3⋊D3C2×D5semidirect
91. C2×C32×C4C2×D5semidirect
108. C2×C3×D5D12semidirect
120. C32×C5#120semidirect
129. C2×C4×C5C2×C3⋊D3semidirect
133. C2×Dic5C2×C3⋊D3semidirect
147. C2×C3⋊D3C22⋊D5semidirect
167. C2×C3×C4D3×D5semidirect
185. C2×D5C4⋊(C3⋊D3)semidirect
203. C3×C5#882semidirect
228. C32#4083semidirect
241. C2×C4D5×C3⋊D3semidirect
249. C5#64091semidirect
267. C3#91475semidirect

Maximal subgroups

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

subgroupindex
C22×D5×C3⋊D32
C2×C5×C4⋊(C3⋊D3)2
C2×#671402
C2×#671382
#106239082
C32×#6852
#106237712
#914753
#640915