Finite Group Databasebeta

← #13087571

Subgroups — #13087571

Order 1440.

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

normal subgroups only

This group has 554 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×C3×C5×#67C211yesmaximal, characteristic, complemented
3C2×#67150C212yesmaximal, complemented
4#10623913C211yesmaximal, characteristic, complemented
5#10623811C212yesmaximal, complemented
6#91826—31nomaximal
7#91563—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3×D15—22no—
10C22×C3×D15—24no—
11C22×C3×D15C2212yes—
12C22×C3×C5×D3C2211yescharacteristic, complemented
13C2×C3⋊Dic15C2212yescomplemented
14C3×C5×#67—22no—
15C2×C3×C5×Dic3C2211yescharacteristic, complemented
16#67150—24no—
17#63976—51nomaximal, Hall
18C23×D15D311yescharacteristic, complemented
19C23×C3×D5—31no—
20C2×C3×C5×D4—31no—
21C2×#1220—32no—
22C2×C5×#67D311yescharacteristic, complemented
23C2×#1201—32no—
24#6719—31no—
25#6719—31no—
26#6719—61no—
27#6714—32no—
28#6665—32no—
29C22×C32×C5—22no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C3×D15—28no—
33C2×C3×D15—22no—
34C2×C3×D15—22no—
35C2×C3×D15D414yescomplemented
36C2×C3×C5×D3—22no—
37C2×C3×C5×D3—21no—
38C3⋊Dic15—22no—
39C3×C5×Dic3—21no—
40#4083—91noHall
41C23×C3×D3—51no—
42C2×C3×#67D511yescharacteristic, complemented
43C2×#625—52no—
44#3757—51no—
45(C2×D3)⋊Dic3—52no—
46C23×C3×C5—21no—
47C23×C3×C5—31no—
48C23×C3×C5C2×D311yescharacteristic
49C23×C3×C5C2×D311yescharacteristic
50C22×D15—22no—
51C22×D15—24no—
52C22×D15C2×D312yes—
53C22×C5×D3C2×D311yescharacteristic, complemented
54C22×C3×D5—32no—
55C22×C3×D5—64no—
56C22×C3×D5—62no—
57C3×C5×D4—62no—
58C2×C3×C4×C5—31no—
59#1220—64no—
60C2×Dic15—32no—
61C2×Dic15—32no—
62C2×Dic15—62no—
63C5×#67—22no—
64C2×C5×Dic3C2×D311yescharacteristic, complemented
65#1201—64no—
66#953—151no—
67#937—151no—
68C2×C32×C5—22no—
69C2×C32×C5C2×D412yes—
70C2×C32×C5C2×D411yescharacteristic
71C3×D15—24no—
72C3×C5×D3—41no—
73C23×D5—31no—
74C2×C5×D4—31no—
75C2×C22⋊D5—92no—
76C22⋊Dic5—91no—
77#685—92no—
78C23×C32C2×D511yescharacteristic
79C22×C3×D3—52no—
80C22×C3×D3—104no—
81C22×C3×D3—102no—
82C22×C3×D3C2×D511yescharacteristic, complemented
83C2×C3⋊Dic3—52no—
84C3×#67—22no—
85C2×C3×Dic3C2×D511yescharacteristic, complemented
86#625—104no—
87C22×C3×C5—22no—
88C22×C3×C5—22no—
89C22×C3×C5—22no—
90C22×C3×C5—21no—
91C22×C3×C5—42no—
92C22×C3×C5—62no—
93C22×C3×C5—61no—
94C22×C3×C5#6712yescomplemented
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—22no—
103C2×C5×D3—21no—
104C2×C3×D5—34no—
105C2×C3×D5—68no—
106C2×C3×D5—62no—
107C2×C3×D5—62no—
108C3×C4×C5—61no—
109Dic15—62no—
110Dic15—62no—
111Dic15—122no—
112C5×Dic3—21no—
113C24×C3—151no—
114C23×D3—51no—
115C2×C3×D4—31no—
116C2×#67—152no—
117C2×#67—152no—
118C2×#67D1511yescharacteristic, complemented
119#217—151no—
120#217—151no—
121#217—152no—
122#217—301no—
123(C2×D3)⋊C4—152no—
124C32×C5#12011yescharacteristic, complemented, Hall
125C23×C5—31no—
126C23×C5D3211yescharacteristic
127C22×D5—32no—
128C22×D5—64no—
129C22×D5—62no—
130C5×D4—62no—
131C2×C4×C5—31no—
132C22⋊D5—184no—
133C2×Dic5—92no—
134C22×C32—22no—
135C22×C32C22⋊D512yescomplemented
136C22×C32C22×D511yescharacteristic
137C2×C3×D3—22no—
138C2×C3×D3—21no—
139C2×C3×D3—54no—
140C2×C3×D3—108no—
141C2×C3×D3—102no—
142C2×C3×D3—102no—
143C3⋊Dic3—102no—
144C3×Dic3—21no—
145#120—451noSylow
146C2×C3×C5—22no—
147C2×C3×C5—22no—
148C2×C3×C5—21no—
149C2×C3×C5—22no—
150C2×C3×C5—42no—
151C2×C3×C5—121no—
152C2×C3×C5D3×D412yes—
153C2×C3×C5C2×#6711yescharacteristic
154C2×C3×C5C2×#6712yes—
155C2×C3×C5C2×#6711yescharacteristic
156D15—24no—
157C3×D5—64no—
158C5×D3—41no—
159C23×C3—21no—
160C23×C3—31no—
161C23×C3—152no—
162C23×C3—304no—
163C23×C3—302no—
164C23×C3D3×D511yescharacteristic
165C23×C3C2×D1511yescharacteristic
166C22×D3—52no—
167C22×D3—104no—
168C22×D3—102no—
169C22×D3C2×D1511yescharacteristic, complemented
170C3×D4—62no—
171C2×C3×C4—31no—
172#67—22no—
173#67—304no—
174#67—304no—
175C2×Dic3—152no—
176C2×Dic3—152no—
177C2×Dic3—302no—
178C2×Dic3C2×D1511yescharacteristic, complemented
179C22×C5—22no—
180C22×C5—61no—
181C22×C5—62no—
182C22×C5#62512yescomplemented
183C22×C5C2×D3211yescharacteristic
184C2×D5—34no—
185C2×D5—68no—
186C2×D5—62no—
187C2×D5—62no—
188C4×C5—61no—
189Dic5—182no—
190C2×C32—22no—
191C2×C32D4×D512yes—
192C2×C32C2×C22⋊D511yescharacteristic
193C3×D3—41no—
194C3×D3—104no—
195C24—151no—
196C2×D4—31no—
197C2×D4—452no—
198C22⋊C4—452no—
199C22⋊C4—451no—
200C3×C5—21no—
201C3×C5#93711yescharacteristic, complemented
202C3×C5#95311yescharacteristic, complemented
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—42no—
208C22×C3—61no—
209C22×C3—62no—
210C22×C3—154no—
211C22×C3—308no—
212C22×C3—302no—
213C22×C3—302no—
214C22×C3#120112yescomplemented
215C22×C3#122012yescomplemented
216C22×C3C2×D3×D511yescharacteristic
217C22×C3C22×D1511yescharacteristic
218C2×D3—22no—
219C2×D3—21no—
220C2×D3—54no—
221C2×D3—108no—
222C2×D3—102no—
223C2×D3—102no—
224C3×C4—61no—
225Dic3—21no—
226Dic3—302no—
227Dic3—302no—
228Dic3—602no—
229C2×C5—22no—
230C2×C5—121no—
231C2×C5C2×#62511yescharacteristic
232C2×C5D3×#6712yes—
233D5—64no—
234C32#408311yescharacteristic, complemented, Sylow
235C23—31no—
236C23—152no—
237C23—304no—
238C23—302no—
239C23D3×D1511yescharacteristic
240D4—62no—
241D4—904no—
242C2×C4—31no—
243C2×C4—452no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—21no—
247C2×C3—22no—
248C2×C3—42no—
249C2×C3—121no—
250C2×C3—304no—
251C2×C3C2×#120111yescharacteristic
252C2×C3D5×#6712yes—
253C2×C3D4×D1512yes—
254C2×C3C2×#122011yescharacteristic
255D3—41no—
256D3—104no—
257C5#6397611yescharacteristic, complemented, Sylow
258C22—22no—
259C22—61no—
260C22—62no—
261C22—154no—
262C22—308no—
263C22—302no—
264C22—302no—
265C22#6715012yescomplemented
266C22C2×D3×D1511yescharacteristic
267C4—61no—
268C4—902no—
269C3—21no—
270C3#9156311yescharacteristic, complemented
271C3#9182611yescharacteristic, complemented
272C2—22no—
273C2—121no—
274C2—304no—
275C2C2×#6715011yescharacteristic
276C2#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×C3×C5×#67C2semidirect
3. C2×#67150C2semidirect
4. #10623913C2semidirect
5. #10623811C2semidirect
12. C22×C3×C5×D3C22semidirect
13. C2×C3⋊Dic15C22semidirect
15. C2×C3×C5×Dic3C22semidirect
18. C23×D15D3semidirect
22. C2×C5×#67D3semidirect
30. C22×C32×C5D4semidirect
35. C2×C3×D15D4semidirect
42. C2×C3×#67D5semidirect
53. C22×C5×D3C2×D3semidirect
64. C2×C5×Dic3C2×D3semidirect
82. C22×C3×D3C2×D5semidirect
85. C2×C3×Dic3C2×D5semidirect
94. C22×C3×C5#67semidirect
95. C22×C3×C5#67semidirect
101. C2×D15#67semidirect
118. C2×#67D15semidirect
124. C32×C5#120semidirect
135. C22×C32C22⋊D5semidirect
169. C22×D3C2×D15semidirect
178. C2×Dic3C2×D15semidirect
182. C22×C5#625semidirect
201. C3×C5#937semidirect
202. C3×C5#953semidirect
214. C22×C3#1201semidirect
215. C22×C3#1220semidirect
234. C32#4083semidirect
257. C5#63976semidirect
265. C22#67150semidirect
270. C3#91563semidirect
271. C3#91826semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D152
C2×C3×C5×#672
C2×#671502
#106239132
#106238112
#918263
#915633
#639765