Finite Group Databasebeta

← #13085774

Subgroups — #13085774

Order 1440.

292 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D3×D60C211yesmaximal, characteristic, complemented
2C3×#6769C211yesmaximal, characteristic, complemented
3#10623822C211yesmaximal, characteristic, complemented
4#10623799C211yesmaximal, characteristic, complemented
5C5×#3711C211yesmaximal, characteristic, complemented
6#10623763C211yesmaximal, characteristic, complemented
7C3×#6658C211yesmaximal, characteristic, complemented
8#91301—31nomaximal
9#91253—31nomaximal
10C2×D3×D15—21no—
11C4⋊(C3⋊D15)C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×D60C2211yescharacteristic, complemented
14C3×C4×C5×D3C2211yescharacteristic
15C32×Dic10C2211yescharacteristic, complemented
16#67151—21no—
17C3×#1203—21no—
18C3×#1200—21no—
19C5×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63939—51nomaximal, Hall
22C2×D60—31no—
23C3×#709—31no—
24D3×D20—31no—
25#6769D311yescharacteristic, complemented
26D120—31no—
27C5×#208—31no—
28C5×ΓL(1,𝔽25)—31no—
29C3×#677—31no—
30#6658—31no—
31#6658—31no—
32#6658—61no—
33#6658D311yescharacteristic, complemented
34#6653—31no—
35#6653—31no—
36#6653—31no—
37C2×C3⋊D15—21no—
38C2×C3×D15—21no—
39C2×C3×D15—21no—
40C2×C3×C5×D3D411yescharacteristic
41D3×D15—42no—
42C32×C4×C5C2311yescharacteristic
43C3×C5×Dic3D411yescharacteristic
44C32×Dic5—21no—
45#4054—91noHall
46C3×#239—51no—
47D3×D12—51no—
48#3755—51no—
49C3×#215—51no—
50#3714—51no—
51#3713—51no—
52#3711D511yescharacteristic, complemented
53C22×D15—61no—
54C2×D3×D5—61no—
55C2×C3×C4×C5—31no—
56D60—31no—
57D60—31no—
58D60—61no—
59D60—61no—
60D60C2×D311yescharacteristic
61D60C2×D311yescharacteristic, complemented
62C4×C5×D3C2×D311yescharacteristic
63C3×C22⋊D5—61no—
64C3×D20—31no—
65C3×D20—31no—
66C3×C4×D5—61no—
67C3×Dic10—21no—
68C3×Dic10C2×D311yescharacteristic, complemented
69C3×Dic10C2×D311yescharacteristic, complemented
70#1203—21no—
71#1202—61no—
72#1200—21no—
73C3×C5×C8—31no—
74C5×C3⋊C8—31no—
75C5×C3⋊C8—31no—
76C5×C3⋊C8—61no—
77C5×C3⋊C8C2×D311yescharacteristic, complemented
78#949—151no—
79#914—151no—
80C2×C32×C5C2×D411yescharacteristic
81C3⋊D15—41no—
82C3×D15—41no—
83C3×D15—41no—
84C3×C5×D3—21no—
85#709—31no—
86C2×D20—91no—
87C5×M16—91no—
88D40—91no—
89D40—91no—
90#677—31no—
91#677—91no—
92C2×D32—101no—
93C32×Q8—51no—
94C4⋊(C3⋊D3)—51no—
95C3×D12—51no—
96C3×D12—51no—
97C3×D12—101no—
98C3×C4×D3—101no—
99C3×C4×D3C2×D511yescharacteristic
100#626—101no—
101C3⋊(C3⋊C8)C2×D511yescharacteristic, complemented
102C3×C3⋊C8C2×D511yescharacteristic, complemented
103C22×C3×C5—31no—
104C2×D15—21no—
105C2×D15—21no—
106C2×D15—61no—
107C2×D15—61no—
108C2×D15—121no—
109C2×D15—122no—
110C2×C5×D3#6711yescharacteristic
111C2×C3×D5—61no—
112C2×C3×D5—61no—
113D3×D5—122no—
114C3×C4×C5—21no—
115C3×C4×C5—31no—
116C3×C4×C5C22×D311yescharacteristic
117C3×C4×C5C22×D311yescharacteristic
118C3×Dic5—21no—
119C3×Dic5—21no—
120C3×Dic5—41no—
121C5×Dic3#6711yescharacteristic
122C3×#41—151no—
123#239—51no—
124D3×D4—151no—
125C2×D12—151no—
126C3×SD16—151no—
127#215—51no—
128#215—151no—
129#215—151no—
130#215—301no—
131#213—151no—
132#213—151no—
133#213—151no—
134#208—31no—
135D24—151no—
136ΓL(1,𝔽25)—31no—
137C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
138C22×D5—181no—
139C2×C4×C5—31no—
140C22⋊D5—61no—
141D20—31no—
142D20—31no—
143D20—91no—
144D20—181no—
145C4×D5—61no—
146Dic10D3211yescharacteristic, complemented
147C5×C8—31no—
148C5×C8—91no—
149C2×C3⋊D3—101no—
150C2×C3×D3—101no—
151C2×C3×D3—101no—
152C2×C3×D3D2011yescharacteristic
153D32—202no—
154C32×C4—101no—
155C32×C4C22×D511yescharacteristic
156C3×Dic3D2011yescharacteristic
157AGL(1,ℤ/8)—451noSylow
158C2×C3×C5—21no—
159C2×C3×C5—61no—
160C2×C3×C5D3×D411yescharacteristic
161C2×C3×C5C2×#6711yescharacteristic
162D15—41no—
163D15—41no—
164D15—121no—
165D15—121no—
166D15—241no—
167C3×D5—121no—
168C3×D5—121no—
169C5×D3—21no—
170C22×D3—301no—
171C22×D3—301no—
172C3×Q8—51no—
173C3×Q8—51no—
174C3×Q8—101no—
175C3×D4—151no—
176C3×D4—151no—
177C3×D4—301no—
178C2×C3×C4—31no—
179C2×C3×C4—301no—
180#67—301no—
181D12—51no—
182D12—51no—
183D12—101no—
184D12—151no—
185D12—151no—
186D12—301no—
187D12—301no—
188C4×D3—101no—
189C4×D3D3×D511yescharacteristic
190C3×C8—31no—
191C3⋊C8—31no—
192C3⋊C8—31no—
193C3⋊C8—61no—
194C3⋊C8D3×D511yescharacteristic, complemented
195C22×C5—31no—
196C2×D5—61no—
197C2×D5—61no—
198C2×D5—181no—
199C2×D5—362no—
200C4×C5—31no—
201C4×C5C2×D3211yescharacteristic
202Dic5—21no—
203C2×C32C2×D2011yescharacteristic
204C3⋊D3—201no—
205C3×D3—21no—
206C3×D3—201no—
207C3×D3—201no—
208#41—151no—
209C2×D4—451no—
210SD16—151no—
211SD16—451no—
212D8—451no—
213D8—451no—
214M16—91no—
215C3×C5—21no—
216C3×C5#91411yescharacteristic, complemented
217C3×C5#94911yescharacteristic, complemented
218C22×C3—31no—
219C22×C3—301no—
220C22×C3—301no—
221C2×D3—101no—
222C2×D3—101no—
223C2×D3—301no—
224C2×D3—301no—
225C2×D3—601no—
226C2×D3—602no—
227C2×D3—602no—
228C2×D3#120211yescharacteristic
229C3×C4—21no—
230C3×C4—31no—
231C3×C4—101no—
232C3×C4—101no—
233C3×C4—201no—
234C3×C4C2×D3×D511yescharacteristic
235C3×C4C2×D3×D511yescharacteristic
236Dic3#120211yescharacteristic
237C2×C5—61no—
238C2×C5D3×#6711yescharacteristic
239D5—121no—
240D5—121no—
241D5—361no—
242C32#405411yescharacteristic, complemented, Sylow
243C23—901no—
244Q8—51no—
245D4—151no—
246D4—151no—
247D4—301no—
248D4—451no—
249D4—901no—
250C2×C4—31no—
251C2×C4—301no—
252C8—31no—
253C8—91no—
254C2×C3—21no—
255C2×C3—61no—
256C2×C3—601no—
257C2×C3—601no—
258C2×C3D3×D2011yescharacteristic
259C2×C3C2×#120211yescharacteristic
260D3—21no—
261D3—201no—
262D3—201no—
263D3—601no—
264D3—601no—
265D3—1201no—
266C5#6393911yescharacteristic, complemented, Sylow
267C22—31no—
268C22—301no—
269C22—301no—
270C22—901no—
271C22—1802no—
272C4—31no—
273C4—101no—
274C4D32×D511yescharacteristic
275C3—21no—
276C3#9125311yescharacteristic, complemented
277C3#9130111yescharacteristic, complemented
278C2—61no—
279C2—601no—
280C2—601no—
281C2—1801no—
282C2D3×#120211yescharacteristic
subgroupG/H
centerC2D3×#1202
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. D3×D60C2semidirect
2. C3×#6769C2semidirect
3. #10623822C2semidirect
4. #10623799C2semidirect
5. C5×#3711C2semidirect
6. #10623763C2semidirect
7. C3×#6658C2semidirect
13. C3×D60C22semidirect
15. C32×Dic10C22semidirect
19. C5×C3⋊(C3⋊C8)C22semidirect
20. C3×C5×C3⋊C8C22semidirect
25. #6769D3semidirect
33. #6658D3semidirect
52. #3711D5semidirect
61. D60C2×D3semidirect
68. C3×Dic10C2×D3semidirect
69. C3×Dic10C2×D3semidirect
77. C5×C3⋊C8C2×D3semidirect
101. C3⋊(C3⋊C8)C2×D5semidirect
102. C3×C3⋊C8C2×D5semidirect
137. C32×C5AGL(1,ℤ/8)semidirect
146. Dic10D32semidirect
194. C3⋊C8D3×D5semidirect
216. C3×C5#914semidirect
217. C3×C5#949semidirect
242. C32#4054semidirect
266. C5#63939semidirect
276. C3#91253semidirect
277. C3#91301semidirect

Maximal subgroups

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

subgroupindex
D3×D602
C3×#67692
#106238222
#106237992
C5×#37112
#106237632
C3×#66582
#913013
#912533
#639395