Finite Group Databasebeta

← #13087579

Subgroups — #13087579

Order 1440.

574 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 106 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×C5×D3C211yesmaximal, characteristic, complemented
2C2×#67184C211yesmaximal, characteristic, complemented
3C2×#67152C212yesmaximal, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic15C212yesmaximal, complemented
6#91842—31nomaximal
7#91570—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3⋊D15C2211yescharacteristic, complemented
10C22×C3×C5×D3—22no—
11C22×C3×C5×D3—24no—
12C22×C3×C5×D3C2212yes—
13#67184—22no—
14C2×C3⋊Dic15C2211yescharacteristic, complemented
15C2×C3×Dic15C2212yescomplemented
16#67152—24no—
17#63977—51nomaximal, Hall
18C24×C3×C5—31no—
19C23×C5×D3D311yescharacteristic, complemented
20C2×#1220—31no—
21C2×#1220—31no—
22C2×#1220—32no—
23C2×#1220—61no—
24C2×#1203—32no—
25#6719—32no—
26#6719D311yescharacteristic, complemented
27C3×C22⋊Dic5—31no—
28(C2×D3)⋊Dic5—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C3⋊D15—21no—
33C2×C3⋊D15—22no—
34C2×C3×C5×D3—28no—
35C2×C3×C5×D3—22no—
36C2×C3×C5×D3—22no—
37C2×C3×C5×D3D414yescomplemented
38C3⋊Dic15—21no—
39C3×Dic15—22no—
40#4099—91noHall
41C23×C3×D3D511yescharacteristic, complemented
42C2×#638—51no—
43C2×#626—52no—
44C3×#217—51no—
45(C2×D3)⋊Dic3—52no—
46C23×C3×C5—21no—
47C23×C3×C5—32no—
48C23×C3×C5—64no—
49C23×C3×C5—62no—
50C23×C3×C5C2×D311yescharacteristic
51C23×C3×C5C2×D311yescharacteristic
52C22×D15—31no—
53C22×D15—31no—
54C22×D15—61no—
55C22×C5×D3—22no—
56C22×C5×D3—24no—
57C22×C5×D3C2×D312yes—
58#1220—64no—
59#1220—64no—
60#1220—62no—
61#1220—62no—
62C2×Dic15—31no—
63C2×Dic15—31no—
64C2×Dic15—61no—
65C2×Dic15C2×D312yescomplemented
66C2×C3×Dic5—32no—
67#1203—64no—
68#953—151no—
69#882—151no—
70C2×C32×C5—22no—
71C2×C32×C5C2×D411yescharacteristic
72C2×C32×C5C2×D412yes—
73C3⋊D15—41no—
74C3×C5×D3—24no—
75C24×C5—31no—
76C2×C22⋊D5—92no—
77C2×C22⋊D5—91no—
78C22⋊Dic5—31no—
79C22⋊Dic5—92no—
80C23×C32C2×D511yescharacteristic
81C22×C3⋊D3—51no—
82C22×C3×D3—22no—
83C22×C3×D3—24no—
84C22×C3×D3C2×D512yes—
85#638—102no—
86C2×C3⋊Dic3—51no—
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—34no—
94C22×C3×C5—42no—
95C22×C3×C5—68no—
96C22×C3×C5—62no—
97C22×C3×C5—62no—
98C22×C3×C5D1212yescomplemented
99C22×C3×C5#6712yescomplemented
100C22×C3×C5C22×D311yescharacteristic
101C22×C3×C5C22×D311yescharacteristic
102C2×D15—62no—
103C2×D15—61no—
104C2×D15—62no—
105C2×D15—62no—
106C2×D15—61no—
107C2×D15—122no—
108C2×C5×D3—28no—
109C2×C5×D3—22no—
110C2×C5×D3—22no—
111C2×C5×D3#6714yescomplemented
112Dic15—22no—
113Dic15—62no—
114Dic15—61no—
115Dic15—61no—
116C3×Dic5—62no—
117C24×C3—31no—
118C23×D3D1511yescharacteristic, complemented
119C2×#67—152no—
120C2×#67—151no—
121C2×#67—151no—
122C2×#67—301no—
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—32no—
130C23×C5—64no—
131C23×C5—62no—
132C23×C5D3211yescharacteristic
133C22×D5—91no—
134C22⋊D5—184no—
135C22⋊D5—182no—
136C2×Dic5—32no—
137C2×Dic5—91no—
138C22×C32—22no—
139C22×C32C22⋊D512yescomplemented
140C22×C32C22×D511yescharacteristic
141C2×C3⋊D3—101no—
142C2×C3⋊D3—102no—
143C2×C3×D3—28no—
144C2×C3×D3—22no—
145C2×C3×D3—22no—
146C2×C3×D3C22⋊D514yescomplemented
147C3⋊Dic3—101no—
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×C5—64no—
156C2×C3×C5C2×D1211yescharacteristic
157C2×C3×C5D3×D412yes—
158C2×C3×C5C2×#6711yescharacteristic
159C2×C3×C5C2×#6712yes—
160D15—122no—
161D15—121no—
162D15—121no—
163C5×D3—24no—
164C23×C3—21no—
165C23×C3—32no—
166C23×C3—64no—
167C23×C3—62no—
168C23×C3D3×D511yescharacteristic
169C23×C3C2×D1511yescharacteristic
170C22×D3—22no—
171C22×D3—24no—
172C22×D3—151no—
173C22×D3—151no—
174C22×D3—301no—
175C22×D3C2×D1512yes—
176C2×C3×C4—152no—
177#67—304no—
178#67—304no—
179#67—302no—
180#67—302no—
181C2×Dic3—52no—
182C2×Dic3—151no—
183C2×Dic3—151no—
184C2×Dic3—301no—
185D12—304no—
186C22×C5—22no—
187C22×C5—34no—
188C22×C5—68no—
189C22×C5—62no—
190C22×C5—62no—
191C22×C5#62612yescomplemented
192C22×C5C2×D3211yescharacteristic
193C2×D5—181no—
194C2×D5—182no—
195Dic5—62no—
196Dic5—181no—
197C2×C32—22no—
198C2×C32C2×C22⋊D511yescharacteristic
199C2×C32C2×C22⋊D512yes—
200C3⋊D3—201no—
201C3×D3—24no—
202C24—31no—
203C2×D4—452no—
204C2×D4—451no—
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—34no—
215C22×C3—42no—
216C22×C3—68no—
217C22×C3—62no—
218C22×C3—62no—
219C22×C3#120312yescomplemented
220C22×C3#122012yescomplemented
221C22×C3C2×D3×D511yescharacteristic
222C22×C3C22×D1511yescharacteristic
223C2×D3—28no—
224C2×D3—22no—
225C2×D3—22no—
226C2×D3—302no—
227C2×D3—301no—
228C2×D3—302no—
229C2×D3—302no—
230C2×D3—301no—
231C2×D3—602no—
232C2×D3#122014yescomplemented
233C3×C4—302no—
234Dic3—102no—
235Dic3—302no—
236Dic3—301no—
237Dic3—301no—
238C2×C5—22no—
239C2×C5—64no—
240C2×C5C2×#62611yescharacteristic
241C2×C5D3×#6712yes—
242D5—361no—
243C32#409911yescharacteristic, complemented, Sylow
244C23—32no—
245C23—64no—
246C23—62no—
247C23—451no—
248C23D3×D1511yescharacteristic
249D4—904no—
250D4—902no—
251C2×C4—152no—
252C2×C4—451no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—21no—
256C2×C3—22no—
257C2×C3—42no—
258C2×C3—64no—
259C2×C3C2×#120311yescharacteristic
260C2×C3D3×C22⋊D512yes—
261C2×C3C2×#122011yescharacteristic
262C2×C3C2×#122012yes—
263D3—24no—
264D3—602no—
265D3—601no—
266D3—601no—
267C5#6397711yescharacteristic, complemented, Sylow
268C22—22no—
269C22—34no—
270C22—68no—
271C22—62no—
272C22—62no—
273C22—901no—
274C22—902no—
275C22#6715212yescomplemented
276C22C2×D3×D1511yescharacteristic
277C4—302no—
278C4—901no—
279C3—21no—
280C3#9157011yescharacteristic, complemented
281C3#9184211yescharacteristic, complemented
282C2—22no—
283C2—64no—
284C2—1801no—
285C2C2×#6715211yescharacteristic
286C2D3×#122012yes—
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×C5×D3C2semidirect
2. C2×#67184C2semidirect
3. C2×#67152C2semidirect
4. C3×#6719C2semidirect
5. (C2×D3)⋊Dic15C2semidirect
9. C22×C3⋊D15C22semidirect
14. C2×C3⋊Dic15C22semidirect
15. C2×C3×Dic15C22semidirect
19. C23×C5×D3D3semidirect
26. #6719D3semidirect
30. C22×C32×C5D4semidirect
37. C2×C3×C5×D3D4semidirect
41. C23×C3×D3D5semidirect
65. C2×Dic15C2×D3semidirect
98. C22×C3×C5D12semidirect
99. C22×C3×C5#67semidirect
111. C2×C5×D3#67semidirect
118. C23×D3D15semidirect
128. C32×C5#120semidirect
139. C22×C32C22⋊D5semidirect
146. C2×C3×D3C22⋊D5semidirect
191. C22×C5#626semidirect
208. C3×C5#882semidirect
209. C3×C5#953semidirect
219. C22×C3#1203semidirect
220. C22×C3#1220semidirect
232. C2×D3#1220semidirect
243. C32#4099semidirect
267. C5#63977semidirect
275. C22#67152semidirect
280. C3#91570semidirect
281. C3#91842semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C5×D32
C2×#671842
C2×#671522
C3×#67192
(C2×D3)⋊Dic152
#918423
#915703
#639775