Finite Group Databasebeta

← #13085764

Subgroups — #13085764

Order 1440.

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

normal subgroups only

This group has 312 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
1#10624155C211yesmaximal, characteristic, complemented
2C3×D5×D12C211yesmaximal, characteristic, complemented
3#10623821C211yesmaximal, characteristic, complemented
4#10623805C211yesmaximal, characteristic, complemented
5#10623803C211yesmaximal, characteristic, complemented
6C5×#3714C211yesmaximal, characteristic, complemented
7C3×#6649C211yesmaximal, characteristic, complemented
8#91489—31nomaximal
9#91250—31nomaximal
10C2×C3×D3×D5—21no—
11#67180C2211yescharacteristic, complemented
12C5×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
13C3×D60C2211yescharacteristic
14C3×C5×D12C2211yescharacteristic
15C32×C4×D5C2211yescharacteristic
16#67138—21no—
17C3⋊D3×Dic5—21no—
18C3×#1203—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63830—51nomaximal, Hall
22C3×D4×D5—31no—
23D5×D12D311yescharacteristic, complemented
24#6772—31no—
25#6772—31no—
26#6772—61no—
27#6716—31no—
28#6706—31no—
29C5×#213—31no—
30C5×D24—31no—
31C3×#676—31no—
32#6659—31no—
33#6657—31no—
34#6654—31no—
35#6652—31no—
36#6649D311yescharacteristic, complemented
37C2×C5×C3⋊D3—21no—
38C2×C3×D15—21no—
39C2×C3×C5×D3—21no—
40C2×C32×D5D411yescharacteristic
41C3×D3×D5—42no—
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15—21no—
44C32×Dic5D411yescharacteristic
45#4057—91noHall
46#3828—51no—
47C2×C3×D12—51no—
48C3×#208—51no—
49#3716—51no—
50#3716—51no—
51#3714—51no—
52#3714D511yescharacteristic, complemented
53C22×C3×D5—61no—
54C2×D3×D5—21no—
55C3×C5×D4—31no—
56D60C2×D311yescharacteristic
57Dic30—31no—
58Dic30—31no—
59Dic30—61no—
60C5×D12—31no—
61C5×D12—31no—
62C5×D12—61no—
63C5×D12C2×D311yescharacteristic
64C3×C22⋊D5—61no—
65C3×D20—31no—
66C3×C4×D5—21no—
67C3×C4×D5C2×D311yescharacteristic
68C3×C4×D5C2×D311yescharacteristic
69#1203—21no—
70#1201—62no—
71#1201—61no—
72#1201—61no—
73D3×Dic5—62no—
74D3×Dic5—61no—
75D3×Dic5—61no—
76C3×C5×C8—31no—
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C5×C3⋊C8C2×D311yescharacteristic, complemented
80#932—151no—
81#908—151no—
82C2×C32×C5C2×D411yescharacteristic
83C5×C3⋊D3—41no—
84C3×D15—41no—
85C3×C5×D3—41no—
86C32×D5—21no—
87#711—91no—
88D4×D5—31no—
89C5×D8—91no—
90#687—91no—
91#686—91no—
92#677—91no—
93#676—31no—
94C22×C3×D3—101no—
95C2×C32×C4—51no—
96#638—101no—
97C4⋊(C3⋊D3)C2×D511yescharacteristic, complemented
98C4×C3⋊D3—101no—
99#634—51no—
100C3×D12—51no—
101C3×D12—101no—
102C3×D12C2×D511yescharacteristic
103C3×C3⋊C8—51no—
104C3×C3⋊C8C2×D511yescharacteristic, complemented
105C22×C3×C5—61no—
106C2×D15—21no—
107C2×C5×D3—21no—
108C2×C5×D3—62no—
109C2×C5×D3—61no—
110C2×C5×D3—61no—
111C2×C3×D5—21no—
112C2×C3×D5—61no—
113C2×C3×D5—122no—
114C2×C3×D5D1211yescharacteristic
115C2×C3×D5#6711yescharacteristic
116D3×D5—42no—
117C3×C4×C5—21no—
118C3×C4×C5C22×D311yescharacteristic
119C3×C4×C5C22×D311yescharacteristic
120Dic15—62no—
121Dic15—61no—
122Dic15—61no—
123C3×Dic5—21no—
124C3×Dic5D1211yescharacteristic
125C3×Dic5#6711yescharacteristic
126C2×C3×D4—151no—
127#235—151no—
128#235—151no—
129#235—301no—
130C2×D12—51no—
131C3×M16—151no—
132#214—151no—
133#214—151no—
134#213—31no—
135#213—151no—
136#208—51no—
137D24—31no—
138D24—151no—
139#204—151no—
140#204—151no—
141C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
142C22×D5—61no—
143C5×D4—31no—
144C5×D4—91no—
145C22⋊D5—61no—
146C22⋊D5—181no—
147C2×Dic5—181no—
148D20—31no—
149C4×D5D3211yescharacteristic
150Dic10—91no—
151C5×C8—31no—
152#168—31no—
153C22×C32—51no—
154C2×C3⋊D3—21no—
155C2×C3×D3—21no—
156C2×C3×D3—101no—
157C2×C3×D3—202no—
158C32×C4—51no—
159C32×C4C22×D511yescharacteristic
160C3⋊Dic3—101no—
161AGL(1,ℤ/8)—451noSylow
162C2×C3×C5—21no—
163C2×C3×C5—121no—
164C2×C3×C5C2×D1211yescharacteristic
165C2×C3×C5C2×#6711yescharacteristic
166D15—41no—
167C3×D5—21no—
168C3×D5—21no—
169C3×D5—41no—
170C3×D5—121no—
171C5×D3—41no—
172C5×D3—122no—
173C5×D3—121no—
174C5×D3—121no—
175C23×C3—301no—
176C22×D3—101no—
177C3×D4—31no—
178C3×D4—151no—
179C3×D4—301no—
180C2×C3×C4—51no—
181C2×C3×C4—51no—
182C2×C3×C4—101no—
183#67—301no—
184#67—301no—
185#67—302no—
186D12—31no—
187D12—31no—
188D12—51no—
189D12—61no—
190D12—101no—
191D12D3×D511yescharacteristic
192C4×D3—301no—
193C4×D3—301no—
194C4×D3—302no—
195Dic6—151no—
196Dic6—151no—
197Dic6—301no—
198C3×C8—31no—
199C3×C8—151no—
200C3⋊C8—51no—
201C3⋊C8D3×D511yescharacteristic, complemented
202C22×C5—61no—
203C22×C5—181no—
204C2×D5—61no—
205C2×D5—122no—
206C2×D5#62611yescharacteristic
207C4×C5C2×D3211yescharacteristic
208Dic5—181no—
209Dic5#62611yescharacteristic
210C2×C32—101no—
211C2×C32D4×D511yescharacteristic
212C3⋊D3—41no—
213C3×D3—41no—
214C3×D3—201no—
215#41—451no—
216C2×D4—151no—
217SD16—451no—
218SD16—451no—
219D8—91no—
220D8—451no—
221M16—151no—
222C3×C5—21no—
223C3×C5#90811yescharacteristic, complemented
224C3×C5#93211yescharacteristic, complemented
225C22×C3—51no—
226C22×C3—51no—
227C22×C3—61no—
228C22×C3—101no—
229C22×C3—301no—
230C22×C3—602no—
231C2×D3—21no—
232C2×D3—62no—
233C2×D3—61no—
234C2×D3—61no—
235C2×D3—101no—
236C2×D3—202no—
237C3×C4—21no—
238C3×C4—51no—
239C3×C4—51no—
240C3×C4—101no—
241C3×C4C2×D3×D511yescharacteristic
242C3×C4C2×D3×D511yescharacteristic
243Dic3—302no—
244Dic3—301no—
245Dic3—301no—
246C2×C5—121no—
247C2×C5—361no—
248C2×C5C2×#62611yescharacteristic
249D5—21no—
250D5—121no—
251C32#405711yescharacteristic, complemented, Sylow
252C23—301no—
253Q8—451no—
254D4—31no—
255D4—91no—
256D4—151no—
257D4—301no—
258D4—901no—
259C2×C4—51no—
260C2×C4—901no—
261C8—31no—
262C8—151no—
263C2×C3—21no—
264C2×C3—101no—
265C2×C3—101no—
266C2×C3—121no—
267C2×C3—201no—
268C2×C3—601no—
269C2×C3D5×D1211yescharacteristic
270C2×C3D5×#6711yescharacteristic
271D3—41no—
272D3—122no—
273D3—121no—
274D3—121no—
275D3—201no—
276C5#6383011yescharacteristic, complemented, Sylow
277C22—51no—
278C22—61no—
279C22—181no—
280C22—301no—
281C22—602no—
282C4—51no—
283C4—901no—
284C4D32×D511yescharacteristic
285C3—21no—
286C3#9125011yescharacteristic, complemented
287C3#9148911yescharacteristic, complemented
288C2—101no—
289C2—121no—
290C2—361no—
291C2—601no—
292C2D5×#62611yescharacteristic
subgroupG/H
centerC2D5×#626
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. #10624155C2semidirect
2. C3×D5×D12C2semidirect
3. #10623821C2semidirect
4. #10623805C2semidirect
5. #10623803C2semidirect
6. C5×#3714C2semidirect
7. C3×#6649C2semidirect
11. #67180C22semidirect
12. C5×C4⋊(C3⋊D3)C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C5×C3⋊C8C22semidirect
23. D5×D12D3semidirect
36. #6649D3semidirect
52. #3714D5semidirect
77. C3⋊#168C2×D3semidirect
79. C5×C3⋊C8C2×D3semidirect
97. C4⋊(C3⋊D3)C2×D5semidirect
104. C3×C3⋊C8C2×D5semidirect
141. C32×C5AGL(1,ℤ/8)semidirect
201. C3⋊C8D3×D5semidirect
223. C3×C5#908semidirect
224. C3×C5#932semidirect
251. C32#4057semidirect
276. C5#63830semidirect
286. C3#91250semidirect
287. C3#91489semidirect

Maximal subgroups

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

subgroupindex
#106241552
C3×D5×D122
#106238212
#106238052
#106238032
C5×#37142
C3×#66492
#914893
#912503
#638305