Finite Group Databasebeta

← #13087494

Subgroups — #13087494

Order 1440.

358 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D4×C3⋊D15C211yesmaximal, characteristic, complemented
2#10624205C211yesmaximal, characteristic, complemented
3C3×#6715C211yesmaximal, characteristic, complemented
4C3×C5×#213C211yesmaximal, characteristic, complemented
5#10623800C211yesmaximal, characteristic, complemented
6#10623799C211yesmaximal, characteristic, complemented
7#10623794C211yesmaximal, characteristic, complemented
8D8×D15—31nomaximal
9#91481—31nomaximal
10C22×C3⋊D15—21no—
11C2×D3×D15—21no—
12C32×C5×D4C2211yescharacteristic, complemented
13#67184—21no—
14C4⋊(C3⋊D15)C2211yescharacteristic, complemented
15C4×C3⋊D15C2211yescharacteristic
16C3×D60C2211yescharacteristic, complemented
17C3×C5×D12C2211yescharacteristic, complemented
18#67150—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63926—51nomaximal, Hall
22D4×D15—31no—
23D4×D15—31no—
24D4×D15—31no—
25D4×D15—61no—
26#6777—31no—
27C3×C5×D8—31no—
28#6715—31no—
29#6715D311yescharacteristic, complemented
30D120—31no—
31C8×D15—31no—
32C5×#213D311yescharacteristic, complemented
33C3×#686—31no—
34#6654—31no—
35#6653—31no—
36#6648—31no—
37C22×C32×C5—21no—
38C2×C3⋊D15—21no—
39C2×C3⋊D15—42no—
40C2×C3⋊D15D411yescharacteristic
41C2×C3×D15—21no—
42C2×C3×C5×D3—21no—
43D3×D15—42no—
44C32×C4×C5C2311yescharacteristic
45C3⋊Dic15D411yescharacteristic
46D5×D8—91noHall
47D4×C3⋊D3—51no—
48#3802—51no—
49C3×#213—51no—
50C3×#213D511yescharacteristic, complemented
51#3714—51no—
52#3714—51no—
53#3710—51no—
54C22×D15—61no—
55C22×D15—61no—
56C22×D15—61no—
57C22×D15—62no—
58C2×D3×D5—61no—
59C3×C5×D4—21no—
60C3×C5×D4—31no—
61C3×C5×D4C2×D311yescharacteristic, complemented
62C3×C5×D4C2×D311yescharacteristic, complemented
63#1220—61no—
64#1220—61no—
65#1220—61no—
66#1220—62no—
67D60—31no—
68D60—31no—
69D60—61no—
70D60C2×D311yescharacteristic, complemented
71C4×D15—31no—
72C4×D15—31no—
73C4×D15—61no—
74C5×D12C2×D311yescharacteristic, complemented
75C3×D20—31no—
76#1201—61no—
77C3×C5×C8—31no—
78C3⋊#168C2×D311yescharacteristic, complemented
79C3×#168—31no—
80C5×C3⋊C8C2×D311yescharacteristic, complemented
81D3×D8—151no—
82D3×D8—151no—
83C2×C32×C5—41no—
84C2×C32×C5C2×D411yescharacteristic
85C3⋊D15—41no—
86C3⋊D15D812yescomplemented
87C3×D15—41no—
88C3×C5×D3—41no—
89D4×D5—91no—
90D4×D5—91no—
91C5×D8—31no—
92#686—31no—
93#686—91no—
94D40—91no—
95C8×D5—91no—
96C22×C3⋊D3—101no—
97C2×D32—101no—
98C32×D4C2×D511yescharacteristic, complemented
99#638—101no—
100C4⋊(C3⋊D3)—51no—
101C4×C3⋊D3—51no—
102C3×D12—51no—
103C3×D12C2×D511yescharacteristic, complemented
104#625—101no—
105C3×C3⋊C8—51no—
106C3×C3⋊C8C2×D511yescharacteristic, complemented
107C22×C3×C5—22no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5—61no—
111C2×D15—21no—
112C2×D15—31no—
113C2×D15—31no—
114C2×D15—61no—
115C2×D15—62no—
116C2×D15—61no—
117C2×D15—61no—
118C2×D15—122no—
119C2×D15—122no—
120C2×D15—122no—
121C2×D15—124no—
122C2×C5×D3—21no—
123C2×C3×D5—61no—
124D3×D5—122no—
125C3×C4×C5—21no—
126C3×C4×C5C22×D311yescharacteristic
127C3×C4×C5C22×D311yescharacteristic
128Dic15—31no—
129Dic15—31no—
130Dic15—61no—
131D3×D4—151no—
132D3×D4—151no—
133D3×D4—151no—
134D3×D4—151no—
135D3×D4—301no—
136C3×D8—31no—
137C3×D8—151no—
138#213—51no—
139#213—151no—
140#213—151no—
141#213D1511yescharacteristic, complemented
142D24—151no—
143D24—151no—
144D3×C8—151no—
145D3×C8—151no—
146C32×C5C2×D811yescharacteristic, complemented, Hall
147C22×D5—181no—
148C22×D5—181no—
149C5×D4—31no—
150C5×D4D3211yescharacteristic, complemented
151C22⋊D5—181no—
152C22⋊D5—181no—
153D20—31no—
154D20—91no—
155C4×D5—91no—
156C5×C8—31no—
157#168—31no—
158C22×C32—21no—
159C2×C3⋊D3—51no—
160C2×C3⋊D3—101no—
161C2×C3⋊D3—202no—
162C2×C3×D3—21no—
163C2×C3×D3—101no—
164D32—202no—
165C32×C4C22×D511yescharacteristic
166C3⋊Dic3—51no—
167C2×D8—451noSylow
168C2×C3×C5—21no—
169C2×C3×C5—42no—
170C2×C3×C5—41no—
171C2×C3×C5—41no—
172C2×C3×C5—121no—
173C2×C3×C5D3×D411yescharacteristic
174C2×C3×C5D3×D411yescharacteristic
175D15—32no—
176D15—32no—
177D15—41no—
178D15—62no—
179D15—122no—
180D15—121no—
181D15—121no—
182C3×D5—121no—
183C5×D3—41no—
184C22×D3—301no—
185C22×D3—301no—
186C22×D3—301no—
187C22×D3—301no—
188C22×D3—302no—
189C3×D4—21no—
190C3×D4—31no—
191C3×D4—151no—
192C3×D4D3×D511yescharacteristic, complemented
193C3×D4C2×D1511yescharacteristic, complemented
194#67—301no—
195#67—301no—
196#67—301no—
197#67—301no—
198#67—302no—
199D12—51no—
200D12—151no—
201D12—151no—
202D12—301no—
203D12C2×D1511yescharacteristic, complemented
204C4×D3—151no—
205C4×D3—151no—
206C4×D3—301no—
207C3×C8—31no—
208C3×C8—151no—
209C3⋊C8—51no—
210C3⋊C8C2×D1511yescharacteristic, complemented
211C22×C5—21no—
212C22×C5—61no—
213C2×D5—61no—
214C2×D5—91no—
215C2×D5—181no—
216C2×D5—362no—
217C2×D5—362no—
218C4×C5C2×D3211yescharacteristic
219Dic5—91no—
220C2×C32—41no—
221C2×C32D4×D511yescharacteristic
222C3⋊D3—52no—
223C3⋊D3—201no—
224C3×D3—41no—
225C3×D3—201no—
226C2×D4—451no—
227C2×D4—451no—
228D8—31no—
229D8—151no—
230D8—451no—
231D8—451no—
232C2×C8—451no—
233C3×C5—21no—
234C3×C5D3×D811yescharacteristic, complemented
235C3×C5D3×D811yescharacteristic, complemented
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—61no—
240C22×C3—301no—
241C2×D3—21no—
242C2×D3—101no—
243C2×D3—151no—
244C2×D3—151no—
245C2×D3—301no—
246C2×D3—302no—
247C2×D3—301no—
248C2×D3—301no—
249C2×D3—602no—
250C2×D3—602no—
251C2×D3—602no—
252C2×D3—602no—
253C2×D3—604no—
254C3×C4—21no—
255C3×C4C2×D3×D511yescharacteristic
256C3×C4C22×D1511yescharacteristic
257Dic3—151no—
258Dic3—151no—
259Dic3—301no—
260C2×C5—41no—
261C2×C5—121no—
262C2×C5#381111yescharacteristic
263D5—92no—
264D5—121no—
265D5—361no—
266C32D5×D811yescharacteristic, complemented, Sylow
267C23—901no—
268C23—901no—
269D4—31no—
270D4—151no—
271D4—451no—
272D4—901no—
273D4—901no—
274D4D3×D1511yescharacteristic, complemented
275C2×C4—451no—
276C8—31no—
277C8—151no—
278C2×C3—21no—
279C2×C3—42no—
280C2×C3—41no—
281C2×C3—41no—
282C2×C3—121no—
283C2×C3—601no—
284C2×C3#679011yescharacteristic
285C2×C3D4×D1511yescharacteristic
286D3—41no—
287D3—152no—
288D3—152no—
289D3—201no—
290D3—302no—
291D3—602no—
292D3—601no—
293D3—601no—
294C5#6392611yescharacteristic, complemented, Sylow
295C22—21no—
296C22—61no—
297C22—301no—
298C22—451no—
299C22—901no—
300C22—1802no—
301C22—1802no—
302C4—451no—
303C4C2×D3×D1511yescharacteristic
304C3—21no—
305C3#9148111yescharacteristic, complemented
306C3D8×D1511yescharacteristic, complemented
307C2—41no—
308C2—121no—
309C2—452no—
310C2—601no—
311C2—1801no—
312C2#1062421811yescharacteristic
subgroupG/H
centerC2#10624218
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4D3×D15
hypocenterC32×C5C2×D8
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×C3⋊D15C2semidirect
2. #10624205C2semidirect
3. C3×#6715C2semidirect
4. C3×C5×#213C2semidirect
5. #10623800C2semidirect
6. #10623799C2semidirect
7. #10623794C2semidirect
12. C32×C5×D4C22semidirect
14. C4⋊(C3⋊D15)C22semidirect
16. C3×D60C22semidirect
17. C3×C5×D12C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C5×C3⋊C8C22semidirect
29. #6715D3semidirect
32. C5×#213D3semidirect
50. C3×#213D5semidirect
61. C3×C5×D4C2×D3semidirect
62. C3×C5×D4C2×D3semidirect
70. D60C2×D3semidirect
74. C5×D12C2×D3semidirect
78. C3⋊#168C2×D3semidirect
80. C5×C3⋊C8C2×D3semidirect
86. C3⋊D15D8semidirect
98. C32×D4C2×D5semidirect
103. C3×D12C2×D5semidirect
106. C3×C3⋊C8C2×D5semidirect
141. #213D15semidirect
146. C32×C5C2×D8semidirect
150. C5×D4D32semidirect
192. C3×D4D3×D5semidirect
193. C3×D4C2×D15semidirect
203. D12C2×D15semidirect
210. C3⋊C8C2×D15semidirect
234. C3×C5D3×D8semidirect
235. C3×C5D3×D8semidirect
266. C32D5×D8semidirect
274. D4D3×D15semidirect
294. C5#63926semidirect
305. C3#91481semidirect
306. C3D8×D15semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊D152
#106242052
C3×#67152
C3×C5×#2132
#106238002
#106237992
#106237942
D8×D153
#914813
#639265