Finite Group Databasebeta

← #13085803

Subgroups — #13085803

Order 1440.

292 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 56 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#10624205C211yesmaximal, characteristic, complemented
2#10624196C211yesmaximal, characteristic, complemented
3#10623825C211yesmaximal, characteristic, complemented
4C5×#3713C211yesmaximal, characteristic, complemented
5#10623756C211yesmaximal, characteristic, complemented
6C3×#6659C211yesmaximal, characteristic, complemented
7C3×#6654C211yesmaximal, characteristic, complemented
8#91500—31nomaximal
9#91482—31nomaximal
10C2×D3×D15—21no—
11C4×C3⋊D15C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×Dic30C2211yescharacteristic, complemented
14C3×C5×D12C2211yescharacteristic
15C3×C5×D12C2211yescharacteristic, complemented
16#67152—21no—
17#67150—21no—
18D3×Dic15—21no—
19C5×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C32×#168C2211yescharacteristic, complemented
21#63798—51nomaximal, Hall
22#6819—31no—
23D4×D15—31no—
24#6777—31no—
25#6768—31no—
26C5×#213—31no—
27C5×#213—31no—
28C3×#687—31no—
29C3×#686—31no—
30#6659D311yescharacteristic, complemented
31#6658—31no—
32#6657—31no—
33#6654D311yescharacteristic, complemented
34#6651—31no—
35#6651—31no—
36#6651—61no—
37C2×C3⋊D15D411yescharacteristic
38C2×C3×D15—21no—
39C2×C3×C5×D3—21no—
40C2×C3×C5×D3—21no—
41D3×D15—42no—
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15D411yescharacteristic
44C3×Dic15—21no—
45#4057—91noHall
46#3802—51no—
47#3796—51no—
48#3743—51no—
49C3×D24—51no—
50C3×#204—51no—
51#3715—51no—
52#3713D511yescharacteristic, complemented
53C22×D15—61no—
54C2×D3×D5—61no—
55C3×C5×D4—31no—
56C3×C5×D4—31no—
57#1220—61no—
58#1220—61no—
59C2×Dic15—61no—
60D60C2×D311yescharacteristic
61C4×D15—31no—
62C4×D15—31no—
63C4×D15—61no—
64Dic30C2×D311yescharacteristic, complemented
65C5×D12C2×D311yescharacteristic
66C5×D12C2×D311yescharacteristic, complemented
67C3×D20—31no—
68C3×Dic10—31no—
69#1203—61no—
70#1201—61no—
71D3×Dic5—61no—
72C3×#168—21no—
73C3×#168C2×D311yescharacteristic, complemented
74C3×#168C2×D311yescharacteristic, complemented
75C5×C3⋊C8—31no—
76C5×C3⋊C8—31no—
77C5×C3⋊C8—61no—
78#914—151no—
79#911—151no—
80C2×C32×C5C2×D411yescharacteristic
81C3⋊D15—21no—
82C3×D15—41no—
83C3×C5×D3—41no—
84C3×C5×D3—41no—
85#711—91no—
86D4×D5—91no—
87C5×D8—91no—
88#687—31no—
89#686—31no—
90#677—91no—
91#676—91no—
92C2×D32—101no—
93C4×C3⋊D3—51no—
94C3×D12—51no—
95C3×D12C2×D511yescharacteristic
96C3×D12C2×D511yescharacteristic, complemented
97C3×Dic6—51no—
98#626—101no—
99#625—101no—
100D3×Dic3—101no—
101C32×C8—51no—
102C3⋊(C3⋊C8)C2×D511yescharacteristic, complemented
103C22×C3×C5—61no—
104C22×C3×C5—61no—
105C2×D15—21no—
106C2×D15—31no—
107C2×D15—31no—
108C2×D15—61no—
109C2×D15—122no—
110C2×C5×D3—21no—
111C2×C5×D3—21no—
112C2×C3×D5—61no—
113D3×D5—122no—
114C3×C4×C5—21no—
115C3×C4×C5C22×D311yescharacteristic
116C3×C4×C5C22×D311yescharacteristic
117Dic15—21no—
118Dic15—31no—
119Dic15—31no—
120Dic15—61no—
121C3×Dic5—61no—
122#239—151no—
123#237—151no—
124D3×D4—151no—
125D3×D4—151no—
126C3×SD16—151no—
127C3×D8—151no—
128#215—151no—
129#214—151no—
130#213—31no—
131#213—31no—
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×D4—31no—
140C5×D4—31no—
141C22⋊D5—181no—
142C22⋊D5—181no—
143C2×Dic5—181no—
144D20—31no—
145C4×D5—91no—
146Dic10—31no—
147C5×C8—91no—
148#168D3211yescharacteristic, complemented
149C2×C3⋊D3—51no—
150C2×C3×D3—21no—
151C2×C3×D3—21no—
152C2×C3×D3—101no—
153D32—202no—
154C32×C4C22×D511yescharacteristic
155C3⋊Dic3—51no—
156C3×Dic3—101no—
157AGL(1,ℤ/8)—451noSylow
158C2×C3×C5—21no—
159C2×C3×C5—121no—
160C2×C3×C5—121no—
161C2×C3×C5D3×D411yescharacteristic
162C2×C3×C5D3×D411yescharacteristic
163D15—41no—
164D15—61no—
165D15—61no—
166D15—121no—
167C3×D5—121no—
168C5×D3—41no—
169C5×D3—41no—
170C22×D3—301no—
171C22×D3—301no—
172C3×Q8—151no—
173C3×D4—31no—
174C3×D4—31no—
175C3×D4—151no—
176#67—301no—
177#67—301no—
178#67—301no—
179C2×Dic3—301no—
180D12—51no—
181D12—301no—
182D12D3×D511yescharacteristic
183D12D3×D511yescharacteristic, complemented
184C4×D3—151no—
185C4×D3—151no—
186C4×D3—301no—
187C4×D3—301no—
188Dic6—51no—
189C3×C8—51no—
190C3×C8—51no—
191C3×C8—101no—
192C3⋊C8—31no—
193C3⋊C8—31no—
194C3⋊C8—61no—
195C22×C5—61no—
196C22×C5—61no—
197C2×D5—61no—
198C2×D5—91no—
199C2×D5—362no—
200C4×C5C2×D3211yescharacteristic
201Dic5—61no—
202Dic5—91no—
203C2×C32D4×D511yescharacteristic
204C3⋊D3—101no—
205C3×D3—41no—
206C3×D3—41no—
207C3×D3—201no—
208#41—451no—
209C2×D4—451no—
210SD16—151no—
211SD16—451no—
212D8—91no—
213D8—151no—
214M16—451no—
215C3×C5—21no—
216C3×C5#91111yescharacteristic, complemented
217C3×C5#91411yescharacteristic, complemented
218C22×C3—61no—
219C22×C3—61no—
220C22×C3—301no—
221C2×D3—21no—
222C2×D3—21no—
223C2×D3—101no—
224C2×D3—151no—
225C2×D3—151no—
226C2×D3—301no—
227C2×D3—602no—
228C2×D3—602no—
229C3×C4—21no—
230C3×C4—301no—
231C3×C4C2×D3×D511yescharacteristic
232C3×C4C2×D3×D511yescharacteristic
233Dic3—101no—
234Dic3—151no—
235Dic3—151no—
236Dic3—301no—
237C2×C5—121no—
238C2×C5—121no—
239C2×C5#380211yescharacteristic
240D5—121no—
241D5—181no—
242C32#405711yescharacteristic, complemented, Sylow
243C23—901no—
244Q8—151no—
245D4—31no—
246D4—31no—
247D4—151no—
248D4—901no—
249D4—901no—
250C2×C4—451no—
251C2×C4—901no—
252C8—51no—
253C8—91no—
254C2×C3—21no—
255C2×C3—121no—
256C2×C3—121no—
257C2×C3—601no—
258C2×C3#679011yescharacteristic
259C2×C3#679011yescharacteristic
260D3—41no—
261D3—41no—
262D3—201no—
263D3—301no—
264D3—301no—
265D3—601no—
266C5#6379811yescharacteristic, complemented, Sylow
267C22—61no—
268C22—61no—
269C22—301no—
270C22—451no—
271C22—1802no—
272C4—301no—
273C4—451no—
274C4D32×D511yescharacteristic
275C3—21no—
276C3#9148211yescharacteristic, complemented
277C3#9150011yescharacteristic, complemented
278C2—121no—
279C2—121no—
280C2—601no—
281C2—901no—
282C2#1062403511yescharacteristic
subgroupG/H
centerC2#10624035
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. #10624205C2semidirect
2. #10624196C2semidirect
3. #10623825C2semidirect
4. C5×#3713C2semidirect
5. #10623756C2semidirect
6. C3×#6659C2semidirect
7. C3×#6654C2semidirect
13. C3×Dic30C22semidirect
15. C3×C5×D12C22semidirect
19. C5×C3⋊(C3⋊C8)C22semidirect
20. C32×#168C22semidirect
30. #6659D3semidirect
33. #6654D3semidirect
52. #3713D5semidirect
64. Dic30C2×D3semidirect
66. C5×D12C2×D3semidirect
73. C3×#168C2×D3semidirect
74. C3×#168C2×D3semidirect
96. C3×D12C2×D5semidirect
102. C3⋊(C3⋊C8)C2×D5semidirect
137. C32×C5AGL(1,ℤ/8)semidirect
148. #168D32semidirect
183. D12D3×D5semidirect
216. C3×C5#911semidirect
217. C3×C5#914semidirect
242. C32#4057semidirect
266. C5#63798semidirect
276. C3#91482semidirect
277. C3#91500semidirect

Maximal subgroups

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

subgroupindex
#106242052
#106241962
#106238252
C5×#37132
#106237562
C3×#66592
C3×#66542
#915003
#914823
#637985