Finite Group Databasebeta

← #13087773

Subgroups — #13087773

Order 1440.

574 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 95 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×C5×#638C211yesmaximal, characteristic, complemented
3C2×#67156C212yesmaximal, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5#10623829C212yesmaximal, complemented
6#91573—31nomaximal
7#91563—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C5×C3⋊D3C2211yescharacteristic, complemented
10C22×C3×D15—22no—
11C22×C3×D15—24no—
12C22×C3×D15C2212yes—
13C5×#638—22no—
14C2×C5×C3⋊Dic3C2211yescharacteristic, complemented
15C2×C3×Dic15C2212yescomplemented
16#67156—24no—
17#63977—51nomaximal, Hall
18C23×D15D311yescharacteristic, complemented
19C23×C3×D5—31no—
20C2×C5×#67—31no—
21C2×C5×#67—31no—
22C2×C5×#67—61no—
23C2×#1203—32no—
24C2×#1201—32no—
25#6719D311yescharacteristic, complemented
26C3×C22⋊Dic5—31no—
27#6667—32no—
28#6665—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C5×C3⋊D3—21no—
33C2×C5×C3⋊D3—22no—
34C2×C3×D15—28no—
35C2×C3×D15—22no—
36C2×C3×D15—22no—
37C2×C3×D15D414yescomplemented
38C5×C3⋊Dic3—21no—
39C3×Dic15—22no—
40#4083—91noHall
41C23×C3×D3—51no—
42C2×#638D511yescharacteristic, complemented
43C2×#626—52no—
44C3×#217—51no—
45(C2×D3)⋊Dic3—52no—
46C23×C3×C5—21no—
47C23×C3×C5C2×D311yescharacteristic
48C23×C3×C5C2×D311yescharacteristic
49C22×D15—22no—
50C22×D15—24no—
51C22×D15C2×D312yes—
52C22×C5×D3—31no—
53C22×C5×D3—31no—
54C22×C5×D3—61no—
55C22×C3×D5—32no—
56C22×C3×D5—64no—
57C22×C3×D5—62no—
58C2×Dic15C2×D312yescomplemented
59C5×#67—64no—
60C5×#67—62no—
61C5×#67—62no—
62C2×C5×Dic3—31no—
63C2×C5×Dic3—31no—
64C2×C5×Dic3—61no—
65C2×C3×Dic5—32no—
66#1203—64no—
67#1201—64no—
68#953—151no—
69#882—151no—
70C2×C32×C5—22no—
71C2×C32×C5C2×D412yes—
72C2×C32×C5C2×D411yescharacteristic
73C5×C3⋊D3—41no—
74C3×D15—24no—
75C23×D5—31no—
76C2×C5×D4—91no—
77C2×C22⋊D5—92no—
78C22⋊Dic5—31no—
79#685—92no—
80C23×C32C2×D511yescharacteristic
81C22×C3⋊D3C2×D511yescharacteristic, complemented
82C22×C3×D3—52no—
83C22×C3×D3—104no—
84C22×C3×D3—102no—
85#638—22no—
86C2×C3⋊Dic3C2×D511yescharacteristic, complemented
87C2×C3×Dic3—52no—
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#6714yescomplemented
102C2×C5×D3—62no—
103C2×C5×D3—61no—
104C2×C5×D3—62no—
105C2×C5×D3—62no—
106C2×C5×D3—61no—
107C2×C5×D3—122no—
108C2×C3×D5—34no—
109C2×C3×D5—68no—
110C2×C3×D5—62no—
111C2×C3×D5—62no—
112Dic15—22no—
113C3×Dic5—62no—
114C5×Dic3—62no—
115C5×Dic3—61no—
116C5×Dic3—61no—
117C24×C3—151no—
118C23×D3—51no—
119C2×#67—31no—
120C2×#67—31no—
121C2×#67—61no—
122C2×#67—152no—
123C2×D12—152no—
124C3×C22⋊C4—151no—
125#217—51no—
126#217—152no—
127(C2×D3)⋊C4—152no—
128C32×C5#12011yescharacteristic, complemented, Hall
129C23×C5—91no—
130C23×C5D3211yescharacteristic
131C22×D5—32no—
132C22×D5—64no—
133C22×D5—62no—
134C5×D4—182no—
135C2×C4×C5—91no—
136C22⋊D5—184no—
137C2×Dic5—32no—
138C22×C32—22no—
139C22×C32C22⋊D512yescomplemented
140C22×C32C22×D511yescharacteristic
141C2×C3⋊D3—21no—
142C2×C3⋊D3—22no—
143C2×C3×D3—54no—
144C2×C3×D3—108no—
145C2×C3×D3—102no—
146C2×C3×D3—102no—
147C3⋊Dic3—21no—
148C3×Dic3—102no—
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—
160C3×D5—64no—
161C5×D3—122no—
162C5×D3—121no—
163C5×D3—121no—
164C23×C3—21no—
165C23×C3—152no—
166C23×C3—304no—
167C23×C3—302no—
168C23×C3D3×D511yescharacteristic
169C23×C3D3×D511yescharacteristic
170C22×D3—31no—
171C22×D3—31no—
172C22×D3—52no—
173C22×D3—61no—
174C22×D3—104no—
175C22×D3—102no—
176C2×C3×C4—152no—
177#67—64no—
178#67—62no—
179#67—62no—
180#67—304no—
181C2×Dic3—31no—
182C2×Dic3—31no—
183C2×Dic3—52no—
184C2×Dic3—61no—
185D12—304no—
186C22×C5—22no—
187C22×C5—181no—
188C22×C5—182no—
189C22×C5#62612yescomplemented
190C22×C5C2×D3211yescharacteristic
191C2×D5—34no—
192C2×D5—68no—
193C2×D5—62no—
194C2×D5—62no—
195C4×C5—181no—
196Dic5—62no—
197C2×C32—22no—
198C2×C32D4×D512yes—
199C2×C32C2×C22⋊D511yescharacteristic
200C3⋊D3—41no—
201C3×D3—104no—
202C24—151no—
203C2×D4—91no—
204C2×D4—452no—
205C22⋊C4—151no—
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#120112yescomplemented
220C22×C3#120312yescomplemented
221C22×C3C2×D3×D511yescharacteristic
222C22×C3C2×D3×D511yescharacteristic
223C2×D3—54no—
224C2×D3—62no—
225C2×D3—61no—
226C2×D3—61no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—108no—
230C2×D3—102no—
231C2×D3—102no—
232C2×D3—122no—
233C3×C4—302no—
234Dic3—62no—
235Dic3—61no—
236Dic3—61no—
237Dic3—102no—
238C2×C5—22no—
239C2×C5—361no—
240C2×C5C2×#62611yescharacteristic
241C2×C5D3×#6712yes—
242D5—64no—
243C32#408311yescharacteristic, complemented, Sylow
244C23—91no—
245C23—152no—
246C23—304no—
247C23—302no—
248C23(C3⋊D3)⋊D511yescharacteristic
249D4—182no—
250D4—904no—
251C2×C4—91no—
252C2×C4—152no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—21no—
256C2×C3—22no—
257C2×C3—42no—
258C2×C3—304no—
259C2×C3C2×#120111yescharacteristic
260C2×C3C2×#120311yescharacteristic
261C2×C3D5×#6712yes—
262C2×C3#679012yes—
263D3—104no—
264D3—122no—
265D3—121no—
266D3—121no—
267C5#6397711yescharacteristic, complemented, Sylow
268C22—22no—
269C22—154no—
270C22—181no—
271C22—182no—
272C22—308no—
273C22—302no—
274C22—302no—
275C22#6715612yescomplemented
276C22C2×(C3⋊D3)⋊D511yescharacteristic
277C4—181no—
278C4—302no—
279C3—21no—
280C3#9156311yescharacteristic, complemented
281C3#9157311yescharacteristic, complemented
282C2—22no—
283C2—304no—
284C2—361no—
285C2C2×#6715611yescharacteristic
286C2#1062423512yes—
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23(C3⋊D3)⋊D5
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×C5×#638C2semidirect
3. C2×#67156C2semidirect
4. C3×#6719C2semidirect
5. #10623829C2semidirect
9. C22×C5×C3⋊D3C22semidirect
14. C2×C5×C3⋊Dic3C22semidirect
15. C2×C3×Dic15C22semidirect
18. C23×D15D3semidirect
25. #6719D3semidirect
30. C22×C32×C5D4semidirect
37. C2×C3×D15D4semidirect
42. C2×#638D5semidirect
58. C2×Dic15C2×D3semidirect
81. C22×C3⋊D3C2×D5semidirect
86. C2×C3⋊Dic3C2×D5semidirect
94. C22×C3×C5D12semidirect
95. C22×C3×C5#67semidirect
101. C2×D15#67semidirect
128. C32×C5#120semidirect
139. C22×C32C22⋊D5semidirect
189. C22×C5#626semidirect
208. C3×C5#882semidirect
209. C3×C5#953semidirect
219. C22×C3#1201semidirect
220. C22×C3#1203semidirect
243. C32#4083semidirect
267. C5#63977semidirect
275. C22#67156semidirect
280. C3#91563semidirect
281. C3#91573semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D152
C2×C5×#6382
C2×#671562
C3×#67192
#106238292
#915733
#915633
#639775