Finite Group Databasebeta

← #13087511

Subgroups — #13087511

Order 1440.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#10624194C211yesmaximal, characteristic, complemented
3C3×#6715C211yesmaximal, characteristic, complemented
4C3×C5×#214C211yesmaximal, characteristic, complemented
5#10623806C211yesmaximal, characteristic, complemented
6#10623799C211yesmaximal, characteristic, complemented
7#10623797C211yesmaximal, characteristic, complemented
8#91803—31nomaximal
9#91498—31nomaximal
10C22×C3⋊D15—21no—
11C32×C5×D4C2211yescharacteristic
12#67184—21no—
13C4⋊(C3⋊D15)C2211yescharacteristic
14C4×C3⋊D15C2211yescharacteristic
15C3×D60C2211yescharacteristic, complemented
16C3×C5×Dic6C2211yescharacteristic, complemented
17#67151—21no—
18Dic3×D15—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63937—51nomaximal, Hall
22#6821—31no—
23D4×D15—31no—
24D4×D15—31no—
25D4×D15—61no—
26#6766—31no—
27C3×C5×SD16—31no—
28#6717—31no—
29#6715D311yescharacteristic, complemented
30D120—31no—
31#6705—31no—
32C5×#214D311yescharacteristic, complemented
33C3×#686—31no—
34#6660—31no—
35#6653—31no—
36#6651—31no—
37C22×C32×C5—21no—
38C2×C3⋊D15—21no—
39C2×C3⋊D15—42no—
40C2×C3⋊D15D411yescharacteristic
41C2×C3×D15—21no—
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15D411yescharacteristic
44C3×C5×Dic3—21no—
45#4060—91noHall
46D4×C3⋊D3—51no—
47#3796—51no—
48C3×#214D511yescharacteristic, complemented
49C3×#213—51no—
50#3717—51no—
51#3714—51no—
52#3712—51no—
53C22×D15—61no—
54C22×D15—61no—
55C22×D15—62no—
56C3×C5×Q8—31no—
57C3×C5×D4—21no—
58C3×C5×D4C2×D311yescharacteristic
59C3×C5×D4C2×D311yescharacteristic
60#1220—61no—
61#1220—61no—
62#1220—62no—
63D60—31no—
64D60—31no—
65D60—61no—
66D60—61no—
67D60C2×D311yescharacteristic, complemented
68C4×D15—31no—
69C4×D15—31no—
70C4×D15—61no—
71C4×D15—61no—
72C5×Dic6C2×D311yescharacteristic, complemented
73C3×D20—31no—
74#1202—61no—
75D5×Dic3—61no—
76C3×C5×C8—31no—
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C5×C3⋊C8C2×D311yescharacteristic, complemented
80#914—151no—
81#911—151no—
82C2×C32×C5—41no—
83C2×C32×C5C2×D411yescharacteristic
84C3⋊D15—21no—
85C3⋊D15—41no—
86C3×D15—41no—
87#713—91no—
88D4×D5—91no—
89C5×SD16—31no—
90#688—91no—
91#686—31no—
92D40—91no—
93#676—91no—
94C22×C3⋊D3—101no—
95C32×D4C2×D511yescharacteristic
96#638—101no—
97C4⋊(C3⋊D3)—51no—
98C4×C3⋊D3—51no—
99C3×D12—51no—
100C3×Dic6C2×D511yescharacteristic, complemented
101#626—101no—
102D3×Dic3—101no—
103C3×C3⋊C8—51no—
104C3×C3⋊C8C2×D511yescharacteristic, complemented
105C22×C3×C5—22no—
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C2×D15—21no—
109C2×D15—31no—
110C2×D15—31no—
111C2×D15—61no—
112C2×D15—62no—
113C2×D15—61no—
114C2×D15—61no—
115C2×D15—124no—
116C2×D15—122no—
117C2×D15—122no—
118C2×C3×D5—61no—
119C3×C4×C5—21no—
120C3×C4×C5—61no—
121C3×C4×C5C22×D311yescharacteristic
122C3×C4×C5C22×D311yescharacteristic
123Dic15—31no—
124Dic15—31no—
125Dic15—61no—
126C5×Dic3—21no—
127#239—151no—
128#237—151no—
129D3×D4—151no—
130D3×D4—151no—
131D3×D4—301no—
132C3×SD16—31no—
133C3×D8—151no—
134#215—151no—
135#214D1511yescharacteristic, complemented
136#213—51no—
137#213—151no—
138D24—151no—
139#204—151no—
140ΓL(1,𝔽25)—151no—
141ΓL(1,𝔽25)—151no—
142C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
143C22×D5—181no—
144C5×Q8—31no—
145C5×D4D3211yescharacteristic
146C22⋊D5—181no—
147D20—31no—
148D20—91no—
149D20—181no—
150C4×D5—91no—
151C4×D5—181no—
152C5×C8—31no—
153#168—31no—
154C22×C32—21no—
155C2×C3⋊D3—51no—
156C2×C3⋊D3—101no—
157C2×C3⋊D3—202no—
158C2×C3×D3—101no—
159C32×C4C22×D511yescharacteristic
160C3⋊Dic3—51no—
161C3×Dic3—21no—
162AGL(1,ℤ/8)—451noSylow
163C2×C3×C5—21no—
164C2×C3×C5—42no—
165C2×C3×C5—41no—
166C2×C3×C5—41no—
167C2×C3×C5D3×D411yescharacteristic
168C2×C3×C5D3×D411yescharacteristic
169D15—41no—
170D15—62no—
171D15—61no—
172D15—61no—
173D15—122no—
174D15—121no—
175D15—121no—
176C3×D5—121no—
177C22×D3—301no—
178C22×D3—301no—
179C22×D3—302no—
180C3×Q8—31no—
181C3×D4—21no—
182C3×D4—151no—
183C3×D4D3×D511yescharacteristic
184C3×D4C2×D1511yescharacteristic
185#67—301no—
186#67—301no—
187#67—301no—
188#67—302no—
189C2×Dic3—301no—
190D12—51no—
191D12—151no—
192D12—151no—
193D12—301no—
194D12—301no—
195C4×D3—151no—
196C4×D3—151no—
197C4×D3—301no—
198C4×D3—301no—
199Dic6C2×D1511yescharacteristic, complemented
200C3×C8—31no—
201C3×C8—151no—
202C3⋊C8—51no—
203C3⋊C8C2×D1511yescharacteristic, complemented
204C22×C5—21no—
205C2×D5—61no—
206C2×D5—91no—
207C2×D5—181no—
208C2×D5—362no—
209C4×C5—61no—
210C4×C5C2×D3211yescharacteristic
211Dic5—91no—
212C2×C32—41no—
213C2×C32D4×D511yescharacteristic
214C3⋊D3—101no—
215C3⋊D3—201no—
216C3×D3—201no—
217#41—451no—
218C2×D4—451no—
219SD16—31no—
220SD16—451no—
221D8—151no—
222D8—451no—
223M16—451no—
224C3×C5—21no—
225C3×C5#91111yescharacteristic, complemented
226C3×C5#91411yescharacteristic, complemented
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—301no—
231C2×D3—101no—
232C2×D3—151no—
233C2×D3—151no—
234C2×D3—301no—
235C2×D3—302no—
236C2×D3—301no—
237C2×D3—301no—
238C2×D3—604no—
239C2×D3—602no—
240C2×D3—602no—
241C3×C4—21no—
242C3×C4—61no—
243C3×C4C2×D3×D511yescharacteristic
244C3×C4C22×D1511yescharacteristic
245Dic3—21no—
246Dic3—151no—
247Dic3—151no—
248Dic3—301no—
249C2×C5—41no—
250C2×C5#381111yescharacteristic
251D5—121no—
252D5—181no—
253D5—361no—
254C32#406011yescharacteristic, complemented, Sylow
255C23—901no—
256Q8—31no—
257D4—151no—
258D4—451no—
259D4—901no—
260D4—901no—
261D4D3×D1511yescharacteristic
262C2×C4—451no—
263C2×C4—901no—
264C8—31no—
265C8—151no—
266C2×C3—21no—
267C2×C3—42no—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3—601no—
271C2×C3#679011yescharacteristic
272C2×C3D4×D1511yescharacteristic
273D3—201no—
274D3—302no—
275D3—301no—
276D3—301no—
277D3—602no—
278D3—601no—
279D3—601no—
280C5#6393711yescharacteristic, complemented, Sylow
281C22—21no—
282C22—301no—
283C22—451no—
284C22—901no—
285C22—1802no—
286C4—61no—
287C4—451no—
288C4C2×D3×D1511yescharacteristic
289C3—21no—
290C3#9149811yescharacteristic, complemented
291C3#9180311yescharacteristic, complemented
292C2—41no—
293C2—601no—
294C2—901no—
295C2—1801no—
296C2#1062421811yescharacteristic
subgroupG/H
centerC2#10624218
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4D3×D15
hypocenterC32×C5AGL(1,ℤ/8)
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. #10624194C2semidirect
3. C3×#6715C2semidirect
4. C3×C5×#214C2semidirect
5. #10623806C2semidirect
6. #10623799C2semidirect
7. #10623797C2semidirect
15. C3×D60C22semidirect
16. C3×C5×Dic6C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C5×C3⋊C8C22semidirect
29. #6715D3semidirect
32. C5×#214D3semidirect
48. C3×#214D5semidirect
67. D60C2×D3semidirect
72. C5×Dic6C2×D3semidirect
77. C3⋊#168C2×D3semidirect
79. C5×C3⋊C8C2×D3semidirect
100. C3×Dic6C2×D5semidirect
104. C3×C3⋊C8C2×D5semidirect
135. #214D15semidirect
142. C32×C5AGL(1,ℤ/8)semidirect
199. Dic6C2×D15semidirect
203. C3⋊C8C2×D15semidirect
225. C3×C5#911semidirect
226. C3×C5#914semidirect
254. C32#4060semidirect
280. C5#63937semidirect
290. C3#91498semidirect
291. C3#91803semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊D152
#106241942
C3×#67152
C3×C5×#2142
#106238062
#106237992
#106237972
#918033
#914983
#639375