Finite Group Databasebeta

← #13087046

Subgroups — #13087046

Order 1440.

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

normal subgroups only

This group has 648 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
1C2×#67184C211yesmaximal, characteristic, complemented
2C2×C5×#638C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×#67140C211yesmaximal, characteristic, complemented
5C2×#67139C211yesmaximal, characteristic, complemented
6C2×#67138C211yesmaximal, characteristic, complemented
7Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#91567—34nomaximal
9C23×C32×C5C2211yescharacteristic
10C22×C3⋊D15C2211yescharacteristic
11C22×C5×C3⋊D3C2211yescharacteristic
12C22×C32×D5C2211yescharacteristic
13#67184—22no—
14C2×C3⋊Dic15C2211yescharacteristic
15C5×#638—22no—
16C2×C5×C3⋊Dic3C2211yescharacteristic
17C32×C22⋊D5—22no—
18C2×C32×Dic5C2211yescharacteristic
19#67140—22no—
20#67139—22no—
21#67138—22no—
22#64149—51nomaximal, Hall
23C2×#1220—34no—
24C2×C5×#67—34no—
25C2×C3×C22⋊D5D314yescomplemented
26C2×#1203—34no—
27C2×#1202—34no—
28C2×#1201—34no—
29Dic3×Dic5—34no—
30C22×C32×C5—21no—
31C22×C32×C5—21no—
32C22×C32×C5—21no—
33C22×C32×C5C2311yescharacteristic
34C2×C3⋊D15—21no—
35C2×C3⋊D15—21no—
36C2×C3⋊D15—21no—
37C2×C5×C3⋊D3—21no—
38C2×C5×C3⋊D3—21no—
39C2×C5×C3⋊D3—21no—
40C2×C32×D5—21no—
41C2×C32×D5—21no—
42C2×C32×D5—21no—
43C3⋊Dic15D412yescomplemented
44C5×C3⋊Dic3D412yescomplemented
45C32×Dic5D412yescomplemented
46#4086—91noHall
47C2×C32×D4—51no—
48C2×#638—51no—
49C2×#638—51no—
50C2×#638—51no—
51C2×#638D511yescharacteristic, complemented
52C2×C4⋊(C3⋊D3)—51no—
53C4×C3⋊Dic3—51no—
54C23×C3×C5C2×D314yes—
55C22×D15—34no—
56C22×C5×D3—34no—
57C22×C3×D5C2×D314yes—
58#1220—68no—
59C2×Dic15—34no—
60C5×#67—68no—
61C2×C5×Dic3—34no—
62C3×C22⋊D5—28no—
63C2×C3×Dic5C2×D314yes—
64#1203—68no—
65#1202—68no—
66#1201—68no—
67#940—154no—
68C2×C32×C5—41no—
69C2×C32×C5C2×D411yescharacteristic
70C2×C32×C5C2×D411yescharacteristic
71C2×C32×C5C2×D411yescharacteristic
72C3⋊D15—41no—
73C5×C3⋊D3—41no—
74C32×D5—41no—
75C2×C5×D4—91no—
76C2×C22⋊D5—91no—
77C2×C22⋊D5—91no—
78C2×C22⋊D5—91no—
79C2×C22⋊D5C3⋊D311yescharacteristic, complemented
80C2×D20—91no—
81C4×Dic5—91no—
82C23×C32—51no—
83C23×C32C2×D511yescharacteristic
84C22×C3⋊D3—51no—
85C22×C3⋊D3C2×D511yescharacteristic
86C32×D4—102no—
87C2×C32×C4—51no—
88#638—22no—
89#638—102no—
90#638—102no—
91#638—102no—
92C2×C3⋊Dic3—51no—
93C2×C3⋊Dic3C2×D511yescharacteristic
94C4⋊(C3⋊D3)—102no—
95C22×C3×C5—24no—
96C22×C3×C5—24no—
97C22×C3×C5—24no—
98C22×C3×C5C22×D314yes—
99C2×D15—64no—
100C2×D15—64no—
101C2×D15—64no—
102C2×C5×D3—64no—
103C2×C5×D3—64no—
104C2×C5×D3—64no—
105C2×C3×D5—24no—
106C2×C3×D5—24no—
107C2×C3×D5—24no—
108Dic15—38no—
109C3×Dic5#6718yescomplemented
110C5×Dic3—38no—
111C2×C3×D4—54no—
112C2×#67—34no—
113C2×#67—154no—
114C2×#67—154no—
115C2×#67—154no—
116C2×D12—154no—
117C4×Dic3—154no—
118C32×C5#12711yescharacteristic, complemented, Hall
119C23×C5—91no—
120C23×C5C2×C3⋊D311yescharacteristic
121C22×D5—91no—
122C22×D5C2×C3⋊D311yescharacteristic
123C5×D4—182no—
124C2×C4×C5—91no—
125C22⋊D5—22no—
126C22⋊D5—182no—
127C22⋊D5—182no—
128C22⋊D5—182no—
129C2×Dic5—91no—
130C2×Dic5C2×C3⋊D311yescharacteristic
131D20—182no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—101no—
136C22×C32—101no—
137C22×C32—101no—
138C22×C32C22×D511yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—101no—
143C2×C3⋊D3—101no—
144C2×C3⋊D3—101no—
145C32×C4—52no—
146C3⋊Dic3—52no—
147C3⋊Dic3C22⋊D512yescomplemented
148#127—451noSylow
149C2×C3×C5—44no—
150C2×C3×C5D3×D414yes—
151C2×C3×C5D3×D414yes—
152C2×C3×C5C2×#6714yes—
153D15—124no—
154C3×D5—44no—
155C5×D3—124no—
156C23×C3—54no—
157C23×C3D3×D514yes—
158C22×D3—34no—
159C22×D3—154no—
160C3×D4—108no—
161C2×C3×C4—54no—
162#67—68no—
163#67—308no—
164#67—308no—
165#67—308no—
166C2×Dic3—34no—
167C2×Dic3—154no—
168D12—308no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—181no—
173C22×C5—181no—
174C22×C5—181no—
175C22×C5C22×C3⋊D311yescharacteristic
176C2×D5—21no—
177C2×D5—21no—
178C2×D5—21no—
179C2×D5—181no—
180C2×D5—181no—
181C2×D5—181no—
182C4×C5—92no—
183Dic5—92no—
184Dic5#63812yescomplemented
185C2×C32—41no—
186C2×C32—201no—
187C2×C32D4×D511yescharacteristic
188C2×C32D4×D511yescharacteristic
189C2×C32C2×C22⋊D511yescharacteristic
190C3⋊D3—41no—
191C3⋊D3—201no—
192C2×D4—51no—
193C2×D4—91no—
194C2×D4—451no—
195C2×D4—451no—
196C2×D4—451no—
197C2×D4—451no—
198C42—451no—
199C3×C5#94014yescomplemented
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—24no—
203C22×C3—104no—
204C22×C3—104no—
205C22×C3—104no—
206C22×C3C2×D3×D514yes—
207C2×D3—64no—
208C2×D3—64no—
209C2×D3—64no—
210C2×D3—304no—
211C2×D3—304no—
212C2×D3—304no—
213C3×C4—58no—
214Dic3—38no—
215Dic3—158no—
216C2×C5—41no—
217C2×C5—361no—
218C2×C5D4×C3⋊D311yescharacteristic
219C2×C5D4×C3⋊D311yescharacteristic
220C2×C5C2×#63811yescharacteristic
221D5—41no—
222D5—361no—
223C32#408611yescharacteristic, complemented, Sylow
224C23—51no—
225C23—91no—
226C23—451no—
227C23D5×C3⋊D311yescharacteristic
228D4—102no—
229D4—182no—
230D4—902no—
231D4—902no—
232D4—902no—
233D4—902no—
234C2×C4—51no—
235C2×C4—91no—
236C2×C4—451no—
237C2×C3—44no—
238C2×C3—204no—
239C2×C3D5×#6714yes—
240C2×C3D3×C22⋊D514yes—
241C2×C3#679014yes—
242D3—124no—
243D3—604no—
244C5#6414911yescharacteristic, complemented, Sylow
245C22—21no—
246C22—21no—
247C22—21no—
248C22—101no—
249C22—101no—
250C22—101no—
251C22—181no—
252C22—181no—
253C22—181no—
254C22—901no—
255C22—901no—
256C22—901no—
257C22C2×D5×C3⋊D311yescharacteristic
258C4—52no—
259C4—92no—
260C4—452no—
261C3#9156714yescomplemented
262C2—41no—
263C2—201no—
264C2—361no—
265C2—1801no—
266C2D5×#63811yescharacteristic
267C2C3⋊D3×C22⋊D511yescharacteristic
268C2#1062417311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D5×C3⋊D3
hypocenterC32×C5#127
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#67184C2semidirect
2. C2×C5×#638C2semidirect
3. C2×C32×C22⋊D5C2semidirect
4. C2×#67140C2semidirect
5. C2×#67139C2semidirect
6. C2×#67138C2semidirect
7. Dic5×C3⋊Dic3C2semidirect
25. C2×C3×C22⋊D5D3semidirect
43. C3⋊Dic15D4semidirect
44. C5×C3⋊Dic3D4semidirect
45. C32×Dic5D4semidirect
51. C2×#638D5semidirect
79. C2×C22⋊D5C3⋊D3semidirect
109. C3×Dic5#67semidirect
118. C32×C5#127semidirect
147. C3⋊Dic3C22⋊D5semidirect
184. Dic5#638semidirect
199. C3×C5#940semidirect
223. C32#4086semidirect
244. C5#64149semidirect
261. C3#91567semidirect

Maximal subgroups

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

subgroupindex
C2×#671842
C2×C5×#6382
C2×C32×C22⋊D52
C2×#671402
C2×#671392
C2×#671382
Dic5×C3⋊Dic32
#915673
#641495