Finite Group Databasebeta

← #13085746

Subgroups — #13085746

Order 1440.

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

normal subgroups only

This group has 288 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#10624220C211yesmaximal, characteristic, complemented
2#10624148C211yesmaximal, characteristic, complemented
3#10623808C211yesmaximal, characteristic, complemented
4#10623803C211yesmaximal, characteristic, complemented
5C5×#3710C211yesmaximal, characteristic, complemented
6C3×#6657C211yesmaximal, characteristic, complemented
7C3×#6653C211yesmaximal, characteristic, complemented
8#91273—31nomaximal
9#91272—31nomaximal
10#67180C2211yescharacteristic
11C4×C5×C3⋊D3C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×Dic30C2211yescharacteristic
14C32×D20C2211yescharacteristic
15#67156—21no—
16#67154—21no—
17#67138—21no—
18D5×C3⋊Dic3—21no—
19C3×C5×C3⋊C8C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63936—51nomaximal, Hall
22#6769—31no—
23#6765—31no—
24#6765—31no—
25#6765—31no—
26#6765—61no—
27Dic60—31no—
28#6706—31no—
29C5×D3×C8—31no—
30C5×D3×C8—31no—
31C3×D40—31no—
32C3×#677—31no—
33#6662—31no—
34#6657—31no—
35#6657D311yescharacteristic, complemented
36#6653D311yescharacteristic, complemented
37C2×C5×C3⋊D3D411yescharacteristic
38C2×C3×D15—21no—
39C2×C32×D5—21no—
40C32×C4×C5C2311yescharacteristic
41C3⋊Dic15—21no—
42C5×C3⋊Dic3D411yescharacteristic
43C3×Dic15—21no—
44#4050—91noHall
45#3830—51no—
46#3796—51no—
47C3×#214—51no—
48C3×#213—51no—
49#3719—51no—
50#3716—51no—
51#3710D511yescharacteristic, complemented
52D60C2×D311yescharacteristic
53Dic30—31no—
54Dic30—31no—
55Dic30—61no—
56Dic30C2×D311yescharacteristic
57C4×C5×D3—31no—
58C4×C5×D3—31no—
59C4×C5×D3—61no—
60C3×D20—21no—
61C3×D20—31no—
62C3×D20C2×D311yescharacteristic
63C3×D20C2×D311yescharacteristic
64C3×Dic10—31no—
65#1203—61no—
66#1201—61no—
67#1201—61no—
68#1201—61no—
69#1201—62no—
70#1200—61no—
71D5×Dic3—61no—
72D5×Dic3—61no—
73D5×Dic3—61no—
74D5×Dic3—62no—
75C3×C5×C8—31no—
76C3×C5×C8—31no—
77C5×C3⋊C8C2×D311yescharacteristic
78C5×C3⋊C8C2×D311yescharacteristic
79#916—151no—
80#912—151no—
81C2×C32×C5C2×D411yescharacteristic
82C5×C3⋊D3—21no—
83C3×D15—41no—
84C32×D5—41no—
85#709—91no—
86#709—91no—
87C2×C5×C8—91no—
88Dic20—91no—
89D40—31no—
90#677—31no—
91#677—91no—
92C32×D4—51no—
93#638—101no—
94C2×C3⋊Dic3—101no—
95C4×C3⋊D3C2×D511yescharacteristic
96#634—51no—
97C3×D12—51no—
98C3×Dic6—51no—
99#626—101no—
100D3×Dic3—101no—
101C3×C3⋊C8C2×D511yescharacteristic
102C3×C3⋊C8C2×D511yescharacteristic
103C2×D15—21no—
104C2×C5×D3—31no—
105C2×C5×D3—31no—
106C2×C5×D3—61no—
107C2×C3×D5—22no—
108C2×C3×D5—21no—
109C2×C3×D5—21no—
110C2×C3×D5—61no—
111C3×C4×C5—21no—
112C3×C4×C5C22×D311yescharacteristic
113C3×C4×C5C22×D311yescharacteristic
114Dic15—21no—
115Dic15—62no—
116Dic15—61no—
117Dic15—61no—
118C3×Dic5—61no—
119C5×Dic3—31no—
120C5×Dic3—31no—
121C5×Dic3—61no—
122#239—151no—
123#237—151no—
124#237—151no—
125#237—151no—
126#237—301no—
127C3×SD16—151no—
128C3×D8—151no—
129#216—151no—
130#214—51no—
131#214—151no—
132#213—51no—
133Dic12—151no—
134#204—151no—
135D3×C8—31no—
136D3×C8—31no—
137C32×C5#13511yescharacteristic, complemented, Hall
138C2×C4×C5—91no—
139C22⋊D5—181no—
140C22⋊D5—181no—
141D20—31no—
142D20D3211yescharacteristic
143C4×D5—181no—
144C4×D5—181no—
145Dic10—31no—
146Dic10—91no—
147C5×C8—31no—
148C5×C8—31no—
149C22×C32—101no—
150C2×C3⋊D3D2011yescharacteristic
151C2×C3×D3—101no—
152C32×C4C22×D511yescharacteristic
153C3⋊Dic3—101no—
154C3⋊Dic3D2011yescharacteristic
155C3×Dic3—101no—
156#135—451noSylow
157C2×C3×C5—21no—
158C2×C3×C5D3×D411yescharacteristic
159C2×C3×C5D3×D411yescharacteristic
160D15—41no—
161C3×D5—42no—
162C3×D5—41no—
163C3×D5—41no—
164C3×D5—121no—
165C5×D3—61no—
166C5×D3—61no—
167C5×D3—121no—
168C3×Q8—151no—
169C3×D4—51no—
170C3×D4—51no—
171C3×D4—101no—
172C3×D4—151no—
173#67—301no—
174#67—301no—
175#67—301no—
176#67—302no—
177C2×Dic3—301no—
178C2×Dic3—301no—
179C2×Dic3—301no—
180C2×Dic3—302no—
181D12—51no—
182D12—301no—
183C4×D3—31no—
184C4×D3—31no—
185C4×D3—61no—
186C4×D3—301no—
187Dic6—51no—
188Dic6—151no—
189Dic6—151no—
190Dic6—301no—
191C3×C8—31no—
192C3×C8—31no—
193C3⋊C8D3×D511yescharacteristic
194C3⋊C8D3×D511yescharacteristic
195C22×C5—91no—
196C2×D5—21no—
197C2×D5—61no—
198C4×C5—91no—
199C4×C5C2×D3211yescharacteristic
200Dic5—61no—
201Dic5—181no—
202C2×C32—201no—
203C2×C32C2×D2011yescharacteristic
204C3⋊D3—21no—
205C3×D3—201no—
206#41—451no—
207#41—451no—
208Q16—451no—
209SD16—151no—
210SD16—451no—
211D8—151no—
212C2×C8—91no—
213C3×C5—21no—
214C3×C5#91211yescharacteristic, complemented
215C3×C5#91611yescharacteristic, complemented
216C22×C3—102no—
217C22×C3—101no—
218C22×C3—101no—
219C22×C3—301no—
220C2×D3—31no—
221C2×D3—31no—
222C2×D3—61no—
223C2×D3—101no—
224C3×C4—21no—
225C3×C4—301no—
226C3×C4C2×D3×D511yescharacteristic
227C3×C4C2×D3×D511yescharacteristic
228Dic3—31no—
229Dic3—31no—
230Dic3—61no—
231Dic3—101no—
232Dic3—302no—
233Dic3—301no—
234Dic3—301no—
235C2×C5—181no—
236C2×C5#381111yescharacteristic
237D5—41no—
238D5—121no—
239C32#405011yescharacteristic, complemented, Sylow
240Q8—151no—
241Q8—451no—
242D4—51no—
243D4—151no—
244D4—901no—
245D4—901no—
246C2×C4—91no—
247C2×C4—901no—
248C2×C4—901no—
249C8—31no—
250C8—31no—
251C2×C3—21no—
252C2×C3—202no—
253C2×C3—201no—
254C2×C3—201no—
255C2×C3—601no—
256C2×C3D3×D2011yescharacteristic
257C2×C3D3×D2011yescharacteristic
258D3—61no—
259D3—61no—
260D3—121no—
261D3—201no—
262C5#6393611yescharacteristic, complemented, Sylow
263C22—91no—
264C22—101no—
265C22—301no—
266C4—91no—
267C4—301no—
268C4—901no—
269C4D32×D511yescharacteristic
270C3—21no—
271C3#9127211yescharacteristic, complemented
272C3#9127311yescharacteristic, complemented
273C2—181no—
274C2—201no—
275C2—601no—
276C2#1062403111yescharacteristic
subgroupG/H
centerC2#10624031
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5#135
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. #10624220C2semidirect
2. #10624148C2semidirect
3. #10623808C2semidirect
4. #10623803C2semidirect
5. C5×#3710C2semidirect
6. C3×#6657C2semidirect
7. C3×#6653C2semidirect
35. #6657D3semidirect
36. #6653D3semidirect
51. #3710D5semidirect
137. C32×C5#135semidirect
214. C3×C5#912semidirect
215. C3×C5#916semidirect
239. C32#4050semidirect
262. C5#63936semidirect
271. C3#91272semidirect
272. C3#91273semidirect

Maximal subgroups

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

subgroupindex
#106242202
#106241482
#106238082
#106238032
C5×#37102
C3×#66572
C3×#66532
#912733
#912723
#639365