Finite Group Databasebeta

← #13087726

Subgroups — #13087726

Order 1440.

326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C3×D4×D15C211yesmaximal, characteristic, complemented
2#10624226C211yesmaximal, characteristic, complemented
3C5×#3753C211yesmaximal, characteristic, complemented
4C3×#6715C211yesmaximal, characteristic, complemented
5#10623822C211yesmaximal, characteristic, complemented
6#10623821C211yesmaximal, characteristic, complemented
7#10623817C211yesmaximal, characteristic, complemented
8#91481—31nomaximal
9D5×#213—31nomaximal
10C22×C3×D15—21no—
11C2×(C3⋊D3)⋊D5—21no—
12C32×C5×D4C2211yescharacteristic, complemented
13C5×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
14C3×#1220—21no—
15C3×D60C2211yescharacteristic, complemented
16C3×D60C2211yescharacteristic, complemented
17C3×C4×D15C2211yescharacteristic
18#67156—21no—
19C5×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C3×C3⋊#168C2211yescharacteristic, complemented
21D3×#213—51nomaximal, Hall
22D4×D15D311yescharacteristic, complemented
23C3×D4×D5—31no—
24#6777—31no—
25D5×D12—31no—
26#6715D311yescharacteristic, complemented
27C5×#213—31no—
28C5×#213—31no—
29C5×#213—61no—
30C3×#686—31no—
31#6654—31no—
32#6653—31no—
33#6653—31no—
34#6652—31no—
35#6648—31no—
36D5×C3⋊C8—31no—
37C22×C32×C5—21no—
38C2×C5×C3⋊D3—21no—
39C2×C3×D15—21no—
40C2×C3×D15—21no—
41C2×C3×D15—42no—
42C2×C3×D15D411yescharacteristic
43(C3⋊D3)⋊D5—42no—
44C32×C4×C5C2311yescharacteristic
45C3×Dic15D411yescharacteristic
46D5×D8—91noHall
47C3×D3×D4—51no—
48D3×D12—51no—
49#3753D511yescharacteristic, complemented
50C3×#213—51no—
51#3714—51no—
52#3713—51no—
53D3×C3⋊C8—51no—
54C22×D15—21no—
55C22×C3×D5—61no—
56C2×D3×D5—61no—
57C2×D3×D5—61no—
58C3×C5×D4—21no—
59C3×C5×D4C2×D311yescharacteristic, complemented
60C3×C5×D4C2×D311yescharacteristic, complemented
61#1220—21no—
62D60C2×D311yescharacteristic, complemented
63D60C2×D311yescharacteristic, complemented
64C4×D15C2×D311yescharacteristic
65C5×D12—31no—
66C5×D12—31no—
67C5×D12—61no—
68C3×C22⋊D5—61no—
69C3×D20—31no—
70C3×D20—31no—
71C3×C4×D5—31no—
72#1203—61no—
73#1201—61no—
74C3⋊#168C2×D311yescharacteristic, complemented
75C3×#168—31no—
76C5×C3⋊C8—31no—
77C5×C3⋊C8—31no—
78C5×C3⋊C8—61no—
79C2×#213—151no—
80D3×D8—151no—
81C2×C32×C5—41no—
82C2×C32×C5C2×D411yescharacteristic
83C5×C3⋊D3—41no—
84C3×D15—41no—
85C3×D15—41no—
86C3×D15D812yescomplemented
87D4×D5—31no—
88D4×D5—91no—
89C5×D8—91no—
90#686—31no—
91#686—91no—
92D40—91no—
93C8×D5—91no—
94C22×C3×D3—101no—
95C2×D32—101no—
96C32×D4C2×D511yescharacteristic, complemented
97C4⋊(C3⋊D3)C2×D511yescharacteristic, complemented
98C3×#67—101no—
99C3×D12—51no—
100C3×D12—51no—
101C3×C4×D3—51no—
102#626—101no—
103C3⋊(C3⋊C8)C2×D511yescharacteristic, complemented
104C3×C3⋊C8—51no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C22×C3×C5—41no—
108C2×D15—21no—
109C2×D15—21no—
110C2×D15—42no—
111C2×D15#6711yescharacteristic
112C2×C5×D3—61no—
113C2×C5×D3—61no—
114C2×C5×D3—121no—
115C2×C3×D5—31no—
116C2×C3×D5—61no—
117C2×C3×D5—61no—
118C2×C3×D5—122no—
119D3×D5—122no—
120D3×D5—122no—
121C3×C4×C5—21no—
122C3×C4×C5C22×D311yescharacteristic
123C3×C4×C5C22×D311yescharacteristic
124Dic15#6711yescharacteristic
125C3×Dic5—31no—
126C2×C3×D4—151no—
127D3×D4—51no—
128D3×D4—151no—
129C2×D12—151no—
130C3×D8—151no—
131#213—31no—
132#213—31no—
133#213—51no—
134#213—61no—
135#213—151no—
136#213—151no—
137#213—151no—
138C2×C3⋊C8—151no—
139D24—151no—
140D3×C8—151no—
141C32×C5C2×D811yescharacteristic, complemented, Hall
142C22×D5—61no—
143C22×D5—181no—
144C5×D4—91no—
145C5×D4D3211yescharacteristic, complemented
146C22⋊D5—61no—
147C22⋊D5—181no—
148D20—31no—
149D20—31no—
150C4×D5—31no—
151C5×C8—91no—
152#168—31no—
153C22×C32—21no—
154C2×C3⋊D3—21no—
155C2×C3×D3—51no—
156C2×C3×D3—101no—
157C2×C3×D3—101no—
158C2×C3×D3—202no—
159D32—202no—
160C32×C4C22×D511yescharacteristic
161C3×Dic3—51no—
162C2×D8—451noSylow
163C2×C3×C5—21no—
164C2×C3×C5—41no—
165C2×C3×C5—41no—
166C2×C3×C5—81no—
167C2×C3×C5D3×D411yescharacteristic
168C2×C3×C5C2×#6711yescharacteristic
169D15—41no—
170D15—41no—
171D15#21312yescomplemented
172C3×D5—32no—
173C3×D5—121no—
174C3×D5—121no—
175C5×D3—121no—
176C5×D3—121no—
177C5×D3—241no—
178C23×C3—301no—
179C22×D3—101no—
180C22×D3—301no—
181C22×D3—301no—
182C3×D4—21no—
183C3×D4—151no—
184C3×D4—151no—
185C3×D4—301no—
186C3×D4D3×D511yescharacteristic, complemented
187C3×D4D3×D511yescharacteristic, complemented
188C2×C3×C4—151no—
189#67—101no—
190#67—301no—
191D12—31no—
192D12—31no—
193D12—51no—
194D12—51no—
195D12—61no—
196D12—301no—
197C4×D3—51no—
198C3×C8—151no—
199C3⋊C8—31no—
200C3⋊C8—31no—
201C3⋊C8—51no—
202C3⋊C8—61no—
203C22×C5—21no—
204C22×C5—181no—
205C2×D5—31no—
206C2×D5—61no—
207C2×D5—61no—
208C2×D5—122no—
209C2×D5—362no—
210C4×C5C2×D3211yescharacteristic
211Dic5—31no—
212C2×C32—41no—
213C2×C32D4×D511yescharacteristic
214C3⋊D3—41no—
215C3×D3—52no—
216C3×D3—201no—
217C3×D3—201no—
218C2×D4—151no—
219C2×D4—451no—
220D8—91no—
221D8—151no—
222D8—451no—
223D8—451no—
224C2×C8—451no—
225C3×C5—21no—
226C3×C5D3×D811yescharacteristic, complemented
227C3×C5C2×#21311yescharacteristic, complemented
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—41no—
231C22×C3—151no—
232C22×C3—301no—
233C22×C3—301no—
234C22×C3—602no—
235C2×D3—51no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—101no—
239C2×D3—101no—
240C2×D3—121no—
241C2×D3—202no—
242C2×D3—602no—
243C2×D3—602no—
244C3×C4—21no—
245C3×C4—151no—
246C3×C4C2×D3×D511yescharacteristic
247C3×C4C2×D3×D511yescharacteristic
248Dic3—51no—
249C2×C5—41no—
250C2×C5—361no—
251C2×C5D3×#6711yescharacteristic
252D5—32no—
253D5—121no—
254D5—121no—
255C32D5×D811yescharacteristic, complemented, Sylow
256C23—301no—
257C23—901no—
258D4—91no—
259D4—151no—
260D4—151no—
261D4—301no—
262D4—901no—
263D4(C3⋊D3)⋊D511yescharacteristic, complemented
264C2×C4—151no—
265C8—91no—
266C8—151no—
267C2×C3—21no—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3—81no—
271C2×C3—152no—
272C2×C3—601no—
273C2×C3—601no—
274C2×C3D5×#6711yescharacteristic
275C2×C3#679011yescharacteristic
276D3—52no—
277D3—121no—
278D3—121no—
279D3—201no—
280D3—201no—
281D3—241no—
282C5D3×#21311yescharacteristic, complemented, Sylow
283C22—21no—
284C22—151no—
285C22—181no—
286C22—301no—
287C22—301no—
288C22—602no—
289C22—1802no—
290C4—151no—
291C4C2×(C3⋊D3)⋊D511yescharacteristic
292C3—21no—
293C3D5×#21311yescharacteristic, complemented
294C3#9148111yescharacteristic, complemented
295C2—41no—
296C2—152no—
297C2—361no—
298C2—601no—
299C2—601no—
300C2#1062423511yescharacteristic
subgroupG/H
centerC2#10624235
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×(C3⋊D3)⋊D5
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4(C3⋊D3)⋊D5
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. C3×D4×D15C2semidirect
2. #10624226C2semidirect
3. C5×#3753C2semidirect
4. C3×#6715C2semidirect
5. #10623822C2semidirect
6. #10623821C2semidirect
7. #10623817C2semidirect
12. C32×C5×D4C22semidirect
13. C5×C4⋊(C3⋊D3)C22semidirect
15. C3×D60C22semidirect
16. C3×D60C22semidirect
19. C5×C3⋊(C3⋊C8)C22semidirect
20. C3×C3⋊#168C22semidirect
22. D4×D15D3semidirect
26. #6715D3semidirect
49. #3753D5semidirect
59. C3×C5×D4C2×D3semidirect
60. C3×C5×D4C2×D3semidirect
62. D60C2×D3semidirect
63. D60C2×D3semidirect
74. C3⋊#168C2×D3semidirect
86. C3×D15D8semidirect
96. C32×D4C2×D5semidirect
97. C4⋊(C3⋊D3)C2×D5semidirect
103. C3⋊(C3⋊C8)C2×D5semidirect
141. C32×C5C2×D8semidirect
145. C5×D4D32semidirect
171. D15#213semidirect
186. C3×D4D3×D5semidirect
187. C3×D4D3×D5semidirect
226. C3×C5D3×D8semidirect
227. C3×C5C2×#213semidirect
255. C32D5×D8semidirect
263. D4(C3⋊D3)⋊D5semidirect
282. C5D3×#213semidirect
293. C3D5×#213semidirect
294. C3#91481semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D152
#106242262
C5×#37532
C3×#67152
#106238222
#106238212
#106238172
#914813
D5×#2133
D3×#2135