Finite Group Databasebeta

← #13085797

Subgroups — #13085797

Order 1440.

292 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 58 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
1#10624226C211yesmaximal, characteristic, complemented
2#10624200C211yesmaximal, characteristic, complemented
3#10623803C211yesmaximal, characteristic, complemented
4C5×#3714C211yesmaximal, characteristic, complemented
5#10623764C211yesmaximal, characteristic, complemented
6C3×#6654C211yesmaximal, characteristic, complemented
7C3×#6651C211yesmaximal, characteristic, complemented
8#91482—31nomaximal
9#91250—31nomaximal
10C2×(C3⋊D3)⋊D5—21no—
11#67180C2211yescharacteristic, complemented
12C5×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×D60C2211yescharacteristic
14C3×C4×D15C2211yescharacteristic
15C3×C5×D12C2211yescharacteristic, complemented
16#67156—21no—
17#67150—21no—
18D3×Dic15—21no—
19C3×C5×C3⋊C8C2211yescharacteristic, complemented
20C32×#168C2211yescharacteristic, complemented
21#63795—51nomaximal, Hall
22#6819—31no—
23#6777—31no—
24D5×D12—31no—
25#6772—31no—
26#6706—31no—
27C5×#213—31no—
28C5×D24—31no—
29C3×#686—31no—
30C3×#676—31no—
31#6659—31no—
32#6659—31no—
33#6659—61no—
34#6657—31no—
35#6654D311yescharacteristic, complemented
36#6651D311yescharacteristic, complemented
37C2×C5×C3⋊D3—21no—
38C2×C3×D15—21no—
39C2×C3×D15D411yescharacteristic
40C2×C3×C5×D3—21no—
41(C3⋊D3)⋊D5—42no—
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15—21no—
44C3×Dic15D411yescharacteristic
45#4057—91noHall
46D3×D12—51no—
47#3795—51no—
48#3744—51no—
49C3×D24—51no—
50C3×ΓL(1,𝔽25)—51no—
51#3716—51no—
52#3714D511yescharacteristic, complemented
53C2×D3×D5—61no—
54C2×D3×D5—61no—
55C3×C5×D4—31no—
56#1220—61no—
57C2×Dic15—61no—
58D60C2×D311yescharacteristic
59C4×D15C2×D311yescharacteristic
60Dic30—31no—
61Dic30—31no—
62Dic30—61no—
63C5×D12—31no—
64C5×D12—31no—
65C5×D12—61no—
66C5×D12C2×D311yescharacteristic, complemented
67C3×D20—31no—
68C3×C4×D5—31no—
69#1203—61no—
70#1201—61no—
71#1201—61no—
72D3×Dic5—61no—
73C3×C5×C8—31no—
74C3×#168—21no—
75C3×#168C2×D311yescharacteristic, complemented
76C3×#168C2×D311yescharacteristic, complemented
77C5×C3⋊C8C2×D311yescharacteristic, complemented
78#911—151no—
79#908—151no—
80C2×C32×C5C2×D411yescharacteristic
81C5×C3⋊D3—41no—
82C3×D15—21no—
83C3×D15—41no—
84C3×C5×D3—41no—
85#711—91no—
86D4×D5—91no—
87C5×D8—91no—
88#687—91no—
89#686—31no—
90#677—91no—
91#676—31no—
92C2×D32—101no—
93C4⋊(C3⋊D3)C2×D511yescharacteristic
94#634—51no—
95C3×D12—51no—
96C3×D12C2×D511yescharacteristic, complemented
97C3×C4×D3—51no—
98#626—101no—
99#625—101no—
100D3×Dic3—101no—
101C32×C8—51no—
102C3×C3⋊C8C2×D511yescharacteristic, complemented
103C22×C3×C5—61no—
104C2×D15—21no—
105C2×D15D1211yescharacteristic
106C2×C5×D3—21no—
107C2×C5×D3—61no—
108C2×C5×D3—61no—
109C2×C5×D3—121no—
110C2×C3×D5—31no—
111C2×C3×D5—61no—
112D3×D5—122no—
113D3×D5—122no—
114C3×C4×C5—21no—
115C3×C4×C5C22×D311yescharacteristic
116C3×C4×C5C22×D311yescharacteristic
117Dic15—61no—
118Dic15—61no—
119Dic15—121no—
120Dic15D1211yescharacteristic
121C3×Dic5—31no—
122#237—151no—
123D3×D4—151no—
124#235—151no—
125C2×D12—151no—
126C3×D8—151no—
127C3×M16—151no—
128#214—151no—
129#213—31no—
130D24—31no—
131D24—51no—
132#204—151no—
133#204—151no—
134#204—151no—
135#204—301no—
136ΓL(1,𝔽25)—51no—
137C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
138C22×D5—181no—
139C5×D4—31no—
140C5×D4—91no—
141C22⋊D5—181no—
142C22⋊D5—181no—
143C2×Dic5—181no—
144D20—31no—
145C4×D5—31no—
146Dic10—91no—
147C5×C8—31no—
148#168D3211yescharacteristic, complemented
149C2×C3⋊D3—21no—
150C2×C3×D3—21no—
151C2×C3×D3—51no—
152C2×C3×D3—101no—
153D32—202no—
154C32×C4C22×D511yescharacteristic
155C3⋊Dic3—101no—
156C3×Dic3—51no—
157AGL(1,ℤ/8)—451noSylow
158C2×C3×C5—21no—
159C2×C3×C5—121no—
160C2×C3×C5C2×D1211yescharacteristic
161C2×C3×C5D3×D411yescharacteristic
162D15—21no—
163D15—41no—
164C3×D5—61no—
165C3×D5—121no—
166C5×D3—41no—
167C5×D3—121no—
168C5×D3—121no—
169C5×D3—241no—
170C22×D3—301no—
171C22×D3—301no—
172C3×D4—31no—
173C3×D4—151no—
174C2×C3×C4—151no—
175#67—301no—
176#67—301no—
177#67—301no—
178C2×Dic3—301no—
179D12—31no—
180D12—31no—
181D12—51no—
182D12—61no—
183D12—301no—
184D12D3×D511yescharacteristic, complemented
185C4×D3—51no—
186C4×D3—301no—
187Dic6—151no—
188Dic6—151no—
189Dic6—301no—
190C3×C8—31no—
191C3×C8—51no—
192C3×C8—51no—
193C3×C8—101no—
194C3⋊C8D3×D511yescharacteristic, complemented
195C22×C5—61no—
196C22×C5—181no—
197C2×D5—31no—
198C2×D5—61no—
199C2×D5—362no—
200C4×C5C2×D3211yescharacteristic
201Dic5—31no—
202Dic5—181no—
203C2×C32D4×D511yescharacteristic
204C3⋊D3—41no—
205C3×D3—41no—
206C3×D3—101no—
207C3×D3—201no—
208#41—451no—
209C2×D4—451no—
210SD16—451no—
211SD16—451no—
212D8—91no—
213D8—151no—
214M16—151no—
215C3×C5—21no—
216C3×C5#90811yescharacteristic, complemented
217C3×C5#91111yescharacteristic, complemented
218C22×C3—61no—
219C22×C3—151no—
220C22×C3—301no—
221C2×D3—21no—
222C2×D3—51no—
223C2×D3—61no—
224C2×D3—61no—
225C2×D3—101no—
226C2×D3—121no—
227C2×D3—602no—
228C2×D3—602no—
229C3×C4—21no—
230C3×C4—151no—
231C3×C4C2×D3×D511yescharacteristic
232C3×C4C2×D3×D511yescharacteristic
233Dic3—51no—
234Dic3—301no—
235Dic3—301no—
236Dic3—601no—
237C2×C5—121no—
238C2×C5—361no—
239C2×C5D3×D1211yescharacteristic
240D5—61no—
241D5—121no—
242C32#405711yescharacteristic, complemented, Sylow
243C23—901no—
244Q8—451no—
245D4—31no—
246D4—91no—
247D4—151no—
248D4—901no—
249D4—901no—
250C2×C4—151no—
251C2×C4—901no—
252C8—31no—
253C8—51no—
254C2×C3—21no—
255C2×C3—121no—
256C2×C3—301no—
257C2×C3—601no—
258C2×C3D5×D1211yescharacteristic
259C2×C3#679011yescharacteristic
260D3—41no—
261D3—101no—
262D3—121no—
263D3—121no—
264D3—201no—
265D3—241no—
266C5#6379511yescharacteristic, complemented, Sylow
267C22—61no—
268C22—151no—
269C22—181no—
270C22—301no—
271C22—1802no—
272C4—151no—
273C4—901no—
274C4D32×D511yescharacteristic
275C3—21no—
276C3#9125011yescharacteristic, complemented
277C3#9148211yescharacteristic, complemented
278C2—121no—
279C2—301no—
280C2—361no—
281C2—601no—
282C2#1062403311yescharacteristic
subgroupG/H
centerC2#10624033
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5AGL(1,ℤ/8)
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #10624226C2semidirect
2. #10624200C2semidirect
3. #10623803C2semidirect
4. C5×#3714C2semidirect
5. #10623764C2semidirect
6. C3×#6654C2semidirect
7. C3×#6651C2semidirect
11. #67180C22semidirect
15. C3×C5×D12C22semidirect
19. C3×C5×C3⋊C8C22semidirect
20. C32×#168C22semidirect
35. #6654D3semidirect
36. #6651D3semidirect
52. #3714D5semidirect
66. C5×D12C2×D3semidirect
75. C3×#168C2×D3semidirect
76. C3×#168C2×D3semidirect
77. C5×C3⋊C8C2×D3semidirect
96. C3×D12C2×D5semidirect
102. C3×C3⋊C8C2×D5semidirect
137. C32×C5AGL(1,ℤ/8)semidirect
148. #168D32semidirect
184. D12D3×D5semidirect
194. C3⋊C8D3×D5semidirect
216. C3×C5#908semidirect
217. C3×C5#911semidirect
242. C32#4057semidirect
266. C5#63795semidirect
276. C3#91250semidirect
277. C3#91482semidirect

Maximal subgroups

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

subgroupindex
#106242262
#106242002
#106238032
C5×#37142
#106237642
C3×#66542
C3×#66512
#914823
#912503
#637955