Finite Group Databasebeta

← #13085798

Subgroups — #13085798

Order 1440.

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

normal subgroups only

This group has 294 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#10624224C211yesmaximal, characteristic, complemented
2D12×D15C211yesmaximal, characteristic, complemented
3#10623804C211yesmaximal, characteristic, complemented
4C5×#3714C211yesmaximal, characteristic, complemented
5#10623759C211yesmaximal, characteristic, complemented
6C3×#6659C211yesmaximal, characteristic, complemented
7C3×#6651C211yesmaximal, characteristic, complemented
8#91500—31nomaximal
9#91250—31nomaximal
10C2×D3×D15—21no—
11C4⋊(C3⋊D15)C2211yescharacteristic
12C5×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
13C3×C4×D15C2211yescharacteristic
14C3×Dic30C2211yescharacteristic, complemented
15C3×C5×D12C2211yescharacteristic
16#67156—21no—
17#67155—21no—
18#67152—21no—
19C3×C5×C3⋊C8C2211yescharacteristic, complemented
20C32×#168C2211yescharacteristic, complemented
21#63794—51nomaximal, Hall
22D4×D15—31no—
23D5×D12—31no—
24#6772—31no—
25#6768—31no—
26#6706—31no—
27C5×#213—31no—
28C5×D24—31no—
29C3×#687—31no—
30C3×#676—31no—
31#6659D311yescharacteristic, complemented
32#6658—31no—
33#6654—31no—
34#6654—31no—
35#6654—61no—
36#6651D311yescharacteristic, complemented
37C2×C3⋊D15—21no—
38C2×C5×C3⋊D3—21no—
39C2×C3×D15D411yescharacteristic
40C2×C3×C5×D3—21no—
41D3×D15—42no—
42C32×C4×C5C2311yescharacteristic
43C3×Dic15—21no—
44C3×Dic15D411yescharacteristic
45#4057—91noHall
46D3×D12—51no—
47#3799—51no—
48#3745—51no—
49C3×#204—51no—
50C3×ΓL(1,𝔽25)—51no—
51#3717—51no—
52#3714D511yescharacteristic, complemented
53C22×D15—61no—
54C2×D3×D5—61no—
55C3×C5×D4—31no—
56#1220—61no—
57D60—31no—
58D60—31no—
59D60—61no—
60C4×D15C2×D311yescharacteristic
61Dic30C2×D311yescharacteristic, complemented
62C5×D12—31no—
63C5×D12—31no—
64C5×D12—61no—
65C5×D12C2×D311yescharacteristic
66C3×C4×D5—31no—
67C3×Dic10—31no—
68#1203—61no—
69#1203—61no—
70#1201—61no—
71D3×Dic5—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#914—151no—
79#908—151no—
80C2×C32×C5C2×D411yescharacteristic
81C3⋊D15—41no—
82C5×C3⋊D3—41no—
83C3×D15—21no—
84C3×C5×D3—41no—
85#711—91no—
86D4×D5—91no—
87C5×D8—91no—
88#687—31no—
89#686—91no—
90#677—91no—
91#676—31no—
92C2×D32—101no—
93C4⋊(C3⋊D3)—51no—
94C4⋊(C3⋊D3)C2×D511yescharacteristic, complemented
95C3×D12C2×D511yescharacteristic
96C3×C4×D3—51no—
97C3×Dic6—51no—
98#626—101no—
99#626—101no—
100#624—101no—
101C32×C8—51no—
102C3×C3⋊C8C2×D511yescharacteristic, complemented
103C22×C3×C5—61no—
104C2×D15—61no—
105C2×D15—61no—
106C2×D15—121no—
107C2×D15—122no—
108C2×D15D1211yescharacteristic
109C2×C5×D3—21no—
110C2×C5×D3—61no—
111C2×C5×D3—61no—
112C2×C5×D3—121no—
113C2×C3×D5—31no—
114D3×D5—122no—
115C3×C4×C5—21no—
116C3×C4×C5C22×D311yescharacteristic
117C3×C4×C5C22×D311yescharacteristic
118Dic15—21no—
119Dic15D1211yescharacteristic
120C3×Dic5—31no—
121C3×Dic5—61no—
122#239—151no—
123D3×D4—151no—
124#235—151no—
125C2×D12—151no—
126C3×SD16—151no—
127C3×M16—151no—
128#215—151no—
129#213—31no—
130D24—31no—
131D24—151no—
132D24—151no—
133D24—301no—
134#204—51no—
135#204—151no—
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—91no—
145C4×D5—31no—
146Dic10—31no—
147C5×C8—31no—
148#168D3211yescharacteristic, complemented
149C2×C3⋊D3—21no—
150C2×C3⋊D3—101no—
151C2×C3×D3—21no—
152C2×C3×D3—51no—
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×C5C2×D1211yescharacteristic
161C2×C3×C5D3×D411yescharacteristic
162D15—21no—
163D15—121no—
164D15—121no—
165D15—241no—
166C3×D5—61no—
167C5×D3—41no—
168C5×D3—121no—
169C5×D3—121no—
170C5×D3—241no—
171C22×D3—301no—
172C22×D3—301no—
173C3×Q8—151no—
174C3×D4—31no—
175C2×C3×C4—151no—
176#67—301no—
177#67—301no—
178D12—31no—
179D12—31no—
180D12—61no—
181D12—151no—
182D12—151no—
183D12—301no—
184D12—301no—
185D12—301no—
186D12D3×D511yescharacteristic
187C4×D3—51no—
188C4×D3—301no—
189C4×D3—301no—
190Dic6—51no—
191C3×C8—31no—
192C3×C8—51no—
193C3×C8—51no—
194C3×C8—101no—
195C3⋊C8D3×D511yescharacteristic, complemented
196C22×C5—61no—
197C22×C5—181no—
198C2×D5—31no—
199C2×D5—181no—
200C2×D5—362no—
201C4×C5C2×D3211yescharacteristic
202Dic5—31no—
203Dic5—61no—
204C2×C32D4×D511yescharacteristic
205C3⋊D3—41no—
206C3⋊D3—201no—
207C3×D3—41no—
208C3×D3—101no—
209#41—451no—
210C2×D4—451no—
211SD16—151no—
212SD16—451no—
213D8—91no—
214D8—451no—
215M16—151no—
216C3×C5—21no—
217C3×C5#90811yescharacteristic, complemented
218C3×C5#91411yescharacteristic, complemented
219C22×C3—61no—
220C22×C3—151no—
221C2×D3—21no—
222C2×D3—51no—
223C2×D3—61no—
224C2×D3—61no—
225C2×D3—121no—
226C2×D3—301no—
227C2×D3—301no—
228C2×D3—601no—
229C2×D3—602no—
230C2×D3—602no—
231C3×C4—21no—
232C3×C4—151no—
233C3×C4—301no—
234C3×C4C2×D3×D511yescharacteristic
235C3×C4C2×D3×D511yescharacteristic
236Dic3—51no—
237Dic3—101no—
238C2×C5—121no—
239C2×C5—361no—
240C2×C5D3×D1211yescharacteristic
241D5—61no—
242D5—361no—
243C32#405711yescharacteristic, complemented, Sylow
244C23—901no—
245Q8—151no—
246D4—31no—
247D4—91no—
248D4—451no—
249D4—901no—
250D4—901no—
251C2×C4—151no—
252C2×C4—901no—
253C8—31no—
254C8—51no—
255C2×C3—21no—
256C2×C3—121no—
257C2×C3—301no—
258C2×C3D5×D1211yescharacteristic
259C2×C3#679011yescharacteristic
260D3—41no—
261D3—101no—
262D3—121no—
263D3—121no—
264D3—241no—
265D3—601no—
266D3—601no—
267D3—1201no—
268C5#6379411yescharacteristic, complemented, Sylow
269C22—61no—
270C22—151no—
271C22—181no—
272C22—901no—
273C22—1802no—
274C4—151no—
275C4—301no—
276C4D32×D511yescharacteristic
277C3—21no—
278C3#9125011yescharacteristic, complemented
279C3#9150011yescharacteristic, complemented
280C2—121no—
281C2—301no—
282C2—361no—
283C2—1801no—
284C2#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. #10624224C2semidirect
2. D12×D15C2semidirect
3. #10623804C2semidirect
4. C5×#3714C2semidirect
5. #10623759C2semidirect
6. C3×#6659C2semidirect
7. C3×#6651C2semidirect
12. C5×C4⋊(C3⋊D3)C22semidirect
14. C3×Dic30C22semidirect
19. C3×C5×C3⋊C8C22semidirect
20. C32×#168C22semidirect
31. #6659D3semidirect
36. #6651D3semidirect
52. #3714D5semidirect
61. Dic30C2×D3semidirect
75. C3×#168C2×D3semidirect
76. C3×#168C2×D3semidirect
77. C5×C3⋊C8C2×D3semidirect
94. C4⋊(C3⋊D3)C2×D5semidirect
102. C3×C3⋊C8C2×D5semidirect
137. C32×C5AGL(1,ℤ/8)semidirect
148. #168D32semidirect
195. C3⋊C8D3×D5semidirect
217. C3×C5#908semidirect
218. C3×C5#914semidirect
243. C32#4057semidirect
268. C5#63794semidirect
278. C3#91250semidirect
279. C3#91500semidirect

Maximal subgroups

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

subgroupindex
#106242242
D12×D152
#106238042
C5×#37142
#106237592
C3×#66592
C3×#66512
#915003
#912503
#637945