Finite Group Databasebeta

← #13087573

Subgroups — #13087573

Order 1440.

574 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 98 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×C3×D15C211yesmaximal, characteristic, complemented
2C2×#67184C211yesmaximal, characteristic, complemented
3C2×#67151C212yesmaximal, complemented
4C3×C5×#217C211yesmaximal, characteristic, complemented
5#10623811C212yesmaximal, complemented
6#91771—31nomaximal
7#91564—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3⋊D15C2211yescharacteristic, complemented
10C22×C3×D15—22no—
11C22×C3×D15—24no—
12C22×C3×D15C2212yes—
13#67184—22no—
14C2×C3⋊Dic15C2211yescharacteristic, complemented
15C2×C3×C5×Dic3C2212yescomplemented
16#67151—24no—
17#63977—51nomaximal, Hall
18C23×D15D311yescharacteristic, complemented
19C23×C3×D5—31no—
20C2×#1220—31no—
21C2×#1220—31no—
22C2×#1220—61no—
23C2×D60—32no—
24C2×#1202—32no—
25C3×C5×C22⋊C4—31no—
26#6714—32no—
27C5×#217D311yescharacteristic, complemented
28#6665—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C3⋊D15—21no—
33C2×C3⋊D15—22no—
34C2×C3×D15—28no—
35C2×C3×D15—22no—
36C2×C3×D15—22no—
37C2×C3×D15D414yescomplemented
38C3⋊Dic15—21no—
39C3×C5×Dic3—22no—
40#4028—91noHall
41C23×C3×D3—51no—
42C2×#638—51no—
43C2×#626—52no—
44C3×#217D511yescharacteristic, complemented
45(C2×D3)⋊Dic3—52no—
46C23×C3×C5—21no—
47C23×C3×C5C2×D311yescharacteristic
48C23×C3×C5C2×D311yescharacteristic
49C22×D15—22no—
50C22×D15—24no—
51C22×D15—31no—
52C22×D15—31no—
53C22×D15—61no—
54C22×D15C2×D312yes—
55C22×C3×D5—32no—
56C22×C3×D5—64no—
57C22×C3×D5—62no—
58C2×C3×C4×C5—32no—
59#1220—64no—
60#1220—62no—
61#1220—62no—
62C2×Dic15—31no—
63C2×Dic15—31no—
64C2×Dic15—61no—
65D60—64no—
66C2×C5×Dic3C2×D312yescomplemented
67#1202—64no—
68#953—151no—
69#882—151no—
70C2×C32×C5—22no—
71C2×C32×C5C2×D411yescharacteristic
72C2×C32×C5C2×D412yes—
73C3⋊D15—41no—
74C3×D15—24no—
75C23×D5—31no—
76C2×C22⋊D5—91no—
77C2×D20—92no—
78C5×C22⋊C4—31no—
79#685—92no—
80C23×C32C2×D511yescharacteristic
81C22×C3⋊D3—51no—
82C22×C3×D3—52no—
83C22×C3×D3—104no—
84C22×C3×D3—102no—
85#638—102no—
86C2×C3⋊Dic3—51no—
87C2×C3×Dic3C2×D512yescomplemented
88#626—104no—
89C22×C3×C5—22no—
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—21no—
93C22×C3×C5—42no—
94C22×C3×C5D1212yescomplemented
95C22×C3×C5#6712yescomplemented
96C22×C3×C5C22×D311yescharacteristic
97C22×C3×C5C22×D311yescharacteristic
98C2×D15—28no—
99C2×D15—22no—
100C2×D15—22no—
101C2×D15—62no—
102C2×D15—61no—
103C2×D15—62no—
104C2×D15—62no—
105C2×D15—61no—
106C2×D15—122no—
107C2×D15#6714yescomplemented
108C2×C3×D5—34no—
109C2×C3×D5—68no—
110C2×C3×D5—62no—
111C2×C3×D5—62no—
112C3×C4×C5—62no—
113Dic15—62no—
114Dic15—61no—
115Dic15—61no—
116C5×Dic3—22no—
117C24×C3—151no—
118C23×D3—51no—
119C2×#67—151no—
120C2×#67—151no—
121C2×#67—152no—
122C2×#67—301no—
123C2×D12—152no—
124C3×C22⋊C4—31no—
125#217—152no—
126#217D1511yescharacteristic, complemented
127(C2×D3)⋊C4—152no—
128C32×C5#12011yescharacteristic, complemented, Hall
129C23×C5D3211yescharacteristic
130C22×D5—32no—
131C22×D5—64no—
132C22×D5—62no—
133C22×D5—91no—
134C2×C4×C5—32no—
135C22⋊D5—182no—
136C2×Dic5—91no—
137D20—184no—
138C22×C32—22no—
139C22×C32D2012yescomplemented
140C22×C32C22×D511yescharacteristic
141C2×C3⋊D3—101no—
142C2×C3⋊D3—102no—
143C2×C3×D3—54no—
144C2×C3×D3—108no—
145C2×C3×D3—102no—
146C2×C3×D3—102no—
147C3⋊Dic3—101no—
148C3×Dic3—22no—
149#120—451noSylow
150C2×C3×C5—22no—
151C2×C3×C5—22no—
152C2×C3×C5—21no—
153C2×C3×C5—22no—
154C2×C3×C5—42no—
155C2×C3×C5C2×D1211yescharacteristic
156C2×C3×C5D3×D412yes—
157C2×C3×C5C2×#6711yescharacteristic
158C2×C3×C5C2×#6712yes—
159D15—24no—
160D15—122no—
161D15—121no—
162D15—121no—
163C3×D5—64no—
164C23×C3—21no—
165C23×C3—152no—
166C23×C3—304no—
167C23×C3—302no—
168C23×C3D3×D511yescharacteristic
169C23×C3C2×D1511yescharacteristic
170C22×D3—52no—
171C22×D3—104no—
172C22×D3—102no—
173C22×D3—151no—
174C22×D3—151no—
175C22×D3—301no—
176C2×C3×C4—32no—
177#67—304no—
178#67—304no—
179#67—302no—
180#67—302no—
181C2×Dic3—151no—
182C2×Dic3—151no—
183C2×Dic3—301no—
184C2×Dic3C2×D1512yescomplemented
185D12—304no—
186C22×C5—22no—
187C22×C5#62612yescomplemented
188C22×C5C2×D3211yescharacteristic
189C2×D5—34no—
190C2×D5—68no—
191C2×D5—62no—
192C2×D5—62no—
193C2×D5—181no—
194C2×D5—182no—
195C4×C5—62no—
196Dic5—181no—
197C2×C32—22no—
198C2×C32C2×D2011yescharacteristic
199C2×C32D4×D512yes—
200C3⋊D3—201no—
201C3×D3—104no—
202C24—151no—
203C2×D4—452no—
204C2×D4—451no—
205C22⋊C4—31no—
206C22⋊C4—452no—
207C3×C5—21no—
208C3×C5#88211yescharacteristic, complemented
209C3×C5#95311yescharacteristic, complemented
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—21no—
214C22×C3—42no—
215C22×C3—154no—
216C22×C3—308no—
217C22×C3—302no—
218C22×C3—302no—
219C22×C3#120212yescomplemented
220C22×C3D6012yescomplemented
221C22×C3C2×D3×D511yescharacteristic
222C22×C3C22×D1511yescharacteristic
223C2×D3—54no—
224C2×D3—108no—
225C2×D3—102no—
226C2×D3—102no—
227C2×D3—302no—
228C2×D3—301no—
229C2×D3—302no—
230C2×D3—301no—
231C2×D3—302no—
232C2×D3—602no—
233C3×C4—62no—
234Dic3—22no—
235Dic3—302no—
236Dic3—301no—
237Dic3—301no—
238C2×C5—22no—
239C2×C5C2×#62611yescharacteristic
240C2×C5D3×#6712yes—
241D5—64no—
242D5—361no—
243C32#402811yescharacteristic, complemented, Sylow
244C23—152no—
245C23—304no—
246C23—302no—
247C23—451no—
248C23D3×D1511yescharacteristic
249D4—904no—
250D4—902no—
251C2×C4—32no—
252C2×C4—451no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—21no—
256C2×C3—22no—
257C2×C3—42no—
258C2×C3—304no—
259C2×C3C2×#120211yescharacteristic
260C2×C3D5×#6712yes—
261C2×C3C2×D6011yescharacteristic
262C2×C3D4×D1512yes—
263D3—104no—
264D3—602no—
265D3—601no—
266D3—601no—
267C5#6397711yescharacteristic, complemented, Sylow
268C22—22no—
269C22—154no—
270C22—308no—
271C22—302no—
272C22—302no—
273C22—901no—
274C22—902no—
275C22#6715112yescomplemented
276C22C2×D3×D1511yescharacteristic
277C4—62no—
278C4—901no—
279C3—21no—
280C3#9156411yescharacteristic, complemented
281C3#9177111yescharacteristic, complemented
282C2—22no—
283C2—304no—
284C2—1801no—
285C2C2×#6715111yescharacteristic
286C2#67×D1512yes—
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D3×D15
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C3×D15C2semidirect
2. C2×#67184C2semidirect
3. C2×#67151C2semidirect
4. C3×C5×#217C2semidirect
5. #10623811C2semidirect
9. C22×C3⋊D15C22semidirect
14. C2×C3⋊Dic15C22semidirect
15. C2×C3×C5×Dic3C22semidirect
18. C23×D15D3semidirect
27. C5×#217D3semidirect
30. C22×C32×C5D4semidirect
37. C2×C3×D15D4semidirect
44. C3×#217D5semidirect
66. C2×C5×Dic3C2×D3semidirect
87. C2×C3×Dic3C2×D5semidirect
94. C22×C3×C5D12semidirect
95. C22×C3×C5#67semidirect
107. C2×D15#67semidirect
126. #217D15semidirect
128. C32×C5#120semidirect
139. C22×C32D20semidirect
184. C2×Dic3C2×D15semidirect
187. C22×C5#626semidirect
208. C3×C5#882semidirect
209. C3×C5#953semidirect
219. C22×C3#1202semidirect
220. C22×C3D60semidirect
243. C32#4028semidirect
267. C5#63977semidirect
275. C22#67151semidirect
280. C3#91564semidirect
281. C3#91771semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D152
C2×#671842
C2×#671512
C3×C5×#2172
#106238112
#917713
#915643
#639775