Finite Group Databasebeta

← #13085802

Subgroups — #13085802

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#10624227C211yesmaximal, characteristic, complemented
2C5×#3796C211yesmaximal, characteristic, complemented
3#10623801C211yesmaximal, characteristic, complemented
4#10623798C211yesmaximal, characteristic, complemented
5#10623755C211yesmaximal, characteristic, complemented
6C3×#6660C211yesmaximal, characteristic, complemented
7C3×#6654C211yesmaximal, characteristic, complemented
8#91504—31nomaximal
9#91480—31nomaximal
10C2×(C3⋊D3)⋊D5—21no—
11C4×C5×C3⋊D3C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×D60C2211yescharacteristic
14C3×C5×D12C2211yescharacteristic, complemented
15C3×C5×Dic6C2211yescharacteristic, complemented
16#67157—21no—
17C5×#626—21no—
18C5×D3×Dic3—21no—
19C3⋊(C3⋊#168)C2211yescharacteristic, complemented
20C32×#168C2211yescharacteristic, complemented
21#63798—51nomaximal, Hall
22C5×#239—31no—
23C5×#237—31no—
24D3×D20—31no—
25D3×D20—31no—
26#6717—31no—
27#6715—31no—
28C3×#688—31no—
29C3×#686—31no—
30#6660D311yescharacteristic, complemented
31#6655—31no—
32#6654D311yescharacteristic, complemented
33#6652—31no—
34#6650—31no—
35#6650—31no—
36#6650—61no—
37C2×C5×C3⋊D3D411yescharacteristic
38C2×C3×D15—21no—
39C2×C3×D15—21no—
40C2×C3×C5×D3—21no—
41(C3⋊D3)⋊D5—42no—
42C32×C4×C5C2311yescharacteristic
43C5×C3⋊Dic3D411yescharacteristic
44C3×C5×Dic3—21no—
45#4095—91noHall
46#3802—51no—
47#3796D511yescharacteristic, complemented
48#3743—51no—
49C3×D24—51no—
50C3×#204—51no—
51#3715—51no—
52#3713—51no—
53C2×D3×D5—61no—
54C2×D3×D5—61no—
55C3×C5×Q8—31no—
56C3×C5×D4—31no—
57D60C2×D311yescharacteristic
58D60C2×D311yescharacteristic
59C5×#67—61no—
60C2×C5×Dic3—61no—
61C5×D12—61no—
62C5×D12C2×D311yescharacteristic, complemented
63C4×C5×D3—31no—
64C4×C5×D3—31no—
65C4×C5×D3—61no—
66C4×C5×D3—61no—
67C5×Dic6C2×D311yescharacteristic, complemented
68C3×D20—31no—
69C3×D20—31no—
70#1202—61no—
71#1202—61no—
72C3⋊#168—31no—
73C3⋊#168—31no—
74C3⋊#168—61no—
75C3×#168—21no—
76C3×#168C2×D311yescharacteristic, complemented
77C3×#168C2×D311yescharacteristic, complemented
78#914—151no—
79#911—151no—
80C2×C32×C5C2×D411yescharacteristic
81C5×C3⋊D3—21no—
82C3×D15—41no—
83C3×D15—41no—
84C3×C5×D3—41no—
85C5×#41—91no—
86C2×D20—91no—
87#688—31no—
88#688—91no—
89#686—31no—
90#686—91no—
91#681—91no—
92C2×D32—101no—
93C4×C3⋊D3C2×D511yescharacteristic
94C3×D12—51no—
95C3×D12—51no—
96C3×D12C2×D511yescharacteristic, complemented
97C3×Dic6C2×D511yescharacteristic, complemented
98#626—21no—
99#625—101no—
100D3×Dic3—21no—
101C32×C8—51no—
102C3⋊(C3⋊C8)—51no—
103C22×C3×C5—61no—
104C2×D15—21no—
105C2×D15—21no—
106C2×C5×D3—21no—
107C2×C5×D3—31no—
108C2×C5×D3—31no—
109C2×C5×D3—61no—
110C2×C3×D5—61no—
111C2×C3×D5—61no—
112D3×D5—122no—
113D3×D5—122no—
114C3×C4×C5—21no—
115C3×C4×C5—61no—
116C3×C4×C5C22×D311yescharacteristic
117C3×C4×C5C22×D311yescharacteristic
118C5×Dic3—21no—
119C5×Dic3—31no—
120C5×Dic3—31no—
121C5×Dic3—61no—
122#239—31no—
123#237—31no—
124D3×D4—151no—
125D3×D4—151no—
126C3×SD16—151no—
127C3×D8—151no—
128#215—151no—
129#214—151no—
130#213—151no—
131#213—151no—
132D24—51no—
133#204—51no—
134ΓL(1,𝔽25)—151no—
135ΓL(1,𝔽25)—151no—
136ΓL(1,𝔽25)—301no—
137C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
138C22×D5—181no—
139C5×Q8—31no—
140C5×D4—31no—
141C5×D4—181no—
142C2×C4×C5—91no—
143C2×C4×C5—181no—
144D20—31no—
145D20—31no—
146D20—181no—
147#168—91no—
148#168D3211yescharacteristic, complemented
149C2×C3⋊D3C22⋊D511yescharacteristic
150C2×C3×D3—21no—
151C2×C3×D3—101no—
152C2×C3×D3—101no—
153D32—202no—
154C32×C4C22×D511yescharacteristic
155C3⋊Dic3C22⋊D511yescharacteristic
156C3×Dic3—21no—
157AGL(1,ℤ/8)—451noSylow
158C2×C3×C5—21no—
159C2×C3×C5—121no—
160C2×C3×C5D3×D411yescharacteristic
161C2×C3×C5D3×D411yescharacteristic
162D15—41no—
163D15—41no—
164C3×D5—121no—
165C3×D5—121no—
166C5×D3—41no—
167C5×D3—61no—
168C5×D3—61no—
169C5×D3—121no—
170C22×D3—301no—
171C22×D3—301no—
172C3×Q8—31no—
173C3×D4—31no—
174C3×D4—151no—
175C3×D4—151no—
176#67—61no—
177#67—301no—
178#67—301no—
179C2×Dic3—61no—
180D12—51no—
181D12—51no—
182D12—61no—
183D12D3×D511yescharacteristic, complemented
184C4×D3—31no—
185C4×D3—31no—
186C4×D3—61no—
187C4×D3—61no—
188Dic6D3×D511yescharacteristic, complemented
189C3×C8—51no—
190C3×C8—51no—
191C3×C8—101no—
192C3⋊C8—151no—
193C3⋊C8—151no—
194C3⋊C8—301no—
195C22×C5—61no—
196C22×C5—91no—
197C2×D5—61no—
198C2×D5—61no—
199C2×D5—362no—
200C4×C5—61no—
201C4×C5—91no—
202C4×C5C2×D3211yescharacteristic
203C2×C32C2×C22⋊D511yescharacteristic
204C3⋊D3—21no—
205C3×D3—41no—
206C3×D3—201no—
207C3×D3—201no—
208#41—91no—
209C2×D4—451no—
210SD16—151no—
211SD16—451no—
212D8—151no—
213D8—451no—
214M16—451no—
215C3×C5—21no—
216C3×C5#91111yescharacteristic, complemented
217C3×C5#91411yescharacteristic, complemented
218C22×C3—61no—
219C22×C3—301no—
220C22×C3—301no—
221C2×D3—21no—
222C2×D3—31no—
223C2×D3—31no—
224C2×D3—61no—
225C2×D3—101no—
226C2×D3—101no—
227C2×D3—602no—
228C2×D3—602no—
229C3×C4—21no—
230C3×C4—61no—
231C3×C4C2×D3×D511yescharacteristic
232C3×C4C2×D3×D511yescharacteristic
233Dic3—21no—
234Dic3—31no—
235Dic3—31no—
236Dic3—61no—
237C2×C5—121no—
238C2×C5—181no—
239C2×C5#380211yescharacteristic
240D5—121no—
241D5—121no—
242C32#409511yescharacteristic, complemented, Sylow
243C23—901no—
244Q8—31no—
245D4—31no—
246D4—151no—
247D4—151no—
248D4—181no—
249D4—901no—
250C2×C4—91no—
251C2×C4—181no—
252C8—51no—
253C8—451no—
254C2×C3—21no—
255C2×C3—121no—
256C2×C3—601no—
257C2×C3—601no—
258C2×C3D3×C22⋊D511yescharacteristic
259C2×C3D3×C22⋊D511yescharacteristic
260D3—41no—
261D3—61no—
262D3—61no—
263D3—121no—
264D3—201no—
265D3—201no—
266C5#6379811yescharacteristic, complemented, Sylow
267C22—61no—
268C22—91no—
269C22—301no—
270C22—301no—
271C22—1802no—
272C4—61no—
273C4—91no—
274C4D32×D511yescharacteristic
275C3—21no—
276C3#9148011yescharacteristic, complemented
277C3#9150411yescharacteristic, complemented
278C2—121no—
279C2—181no—
280C2—601no—
281C2—601no—
282C2#1062403411yescharacteristic
subgroupG/H
centerC2#10624034
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. #10624227C2semidirect
2. C5×#3796C2semidirect
3. #10623801C2semidirect
4. #10623798C2semidirect
5. #10623755C2semidirect
6. C3×#6660C2semidirect
7. C3×#6654C2semidirect
14. C3×C5×D12C22semidirect
15. C3×C5×Dic6C22semidirect
19. C3⋊(C3⋊#168)C22semidirect
20. C32×#168C22semidirect
30. #6660D3semidirect
32. #6654D3semidirect
47. #3796D5semidirect
62. C5×D12C2×D3semidirect
67. C5×Dic6C2×D3semidirect
76. C3×#168C2×D3semidirect
77. C3×#168C2×D3semidirect
96. C3×D12C2×D5semidirect
97. C3×Dic6C2×D5semidirect
137. C32×C5AGL(1,ℤ/8)semidirect
148. #168D32semidirect
183. D12D3×D5semidirect
188. Dic6D3×D5semidirect
216. C3×C5#911semidirect
217. C3×C5#914semidirect
242. C32#4095semidirect
266. C5#63798semidirect
276. C3#91480semidirect
277. C3#91504semidirect

Maximal subgroups

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

subgroupindex
#106242272
C5×#37962
#106238012
#106237982
#106237552
C3×#66602
C3×#66542
#915043
#914803
#637985