Finite Group Databasebeta

← #13087285

Subgroups — #13087285

Order 1440.

268 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 66 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#10624197C211yesmaximal, characteristic, complemented
2#10624193C211yesmaximal, characteristic, complemented
3#10623900C211yesmaximal, characteristic, complemented
4C3×#6706C211yesmaximal, characteristic, complemented
5C3×C5×D3×C8C211yesmaximal, characteristic, complemented
6#10623808C211yesmaximal, characteristic, complemented
7#10623799C211yesmaximal, characteristic, complemented
8#91793—31nomaximal
9#91272—31nomaximal
10C4⋊(C3⋊D15)C2211yescharacteristic
11#67180C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×Dic30C2211yescharacteristic
14C3×C4×C5×D3C2211yescharacteristic
15#67152—21no—
16#67150—21no—
17#67149—21no—
18Dic3×D15—21no—
19C32×C5×C8C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63806—51nomaximal, Hall
22#6817—31no—
23#6817—31no—
24#6769—31no—
25#6765—31no—
26C2×C3×C5×C8—31no—
27Dic60—31no—
28D120—31no—
29#6706—31no—
30#6706—31no—
31#6706—61no—
32#6706D311yescharacteristic, complemented
33C5×D3×C8D311yescharacteristic, complemented
34C3×#677—31no—
35#6662—31no—
36#6653—31no—
37C2×C3⋊D15—21no—
38C2×C3×D15—21no—
39C2×C3×C5×D3D411yescharacteristic
40C32×C4×C5C2311yescharacteristic
41C3⋊Dic15—21no—
42C3×Dic15—21no—
43C3×C5×Dic3D411yescharacteristic
44#4050—91noHall
45#3799—51no—
46#3795—51no—
47#3744—51no—
48C3×#204—51no—
49C3×D3×C8D511yescharacteristic, complemented
50#3719—51no—
51#3714—51no—
52C2×C3×C4×C5—31no—
53#1220—61no—
54#1220—61no—
55D60—31no—
56D60—31no—
57D60—61no—
58D60C2×D311yescharacteristic
59C4×D15—61no—
60C4×D15—61no—
61Dic30—31no—
62Dic30—31no—
63Dic30—61no—
64Dic30C2×D311yescharacteristic
65C4×C5×D3C2×D311yescharacteristic
66C3×D20—31no—
67C3×Dic10—31no—
68#1203—61no—
69#1201—61no—
70#1200—61no—
71D5×Dic3—61no—
72C3×C5×C8—21no—
73C3×C5×C8—31no—
74C3×C5×C8C2×D311yescharacteristic
75C3×C5×C8C2×D311yescharacteristic
76C5×C3⋊C8C2×D311yescharacteristic
77#916—151no—
78#904—151no—
79C2×C32×C5C2×D411yescharacteristic
80C3⋊D15—41no—
81C3×D15—41no—
82C3×C5×D3—21no—
83#709—91no—
84#709—91no—
85C2×C5×C8—31no—
86Dic20—91no—
87D40—91no—
88#677—31no—
89#677—91no—
90C4⋊(C3⋊D3)—51no—
91#634—51no—
92C3×D12—51no—
93C3×C4×D3C2×D511yescharacteristic
94C3×Dic6—51no—
95#626—101no—
96#625—101no—
97#624—101no—
98D3×Dic3—101no—
99C32×C8C2×D511yescharacteristic
100C3×C3⋊C8C2×D511yescharacteristic
101C22×C3×C5—31no—
102C2×D15—21no—
103C2×D15—61no—
104C2×D15—61no—
105C2×D15—121no—
106C2×C5×D3D1211yescharacteristic
107C2×C3×D5—61no—
108C3×C4×C5—21no—
109C3×C4×C5—31no—
110C3×C4×C5C22×D311yescharacteristic
111C3×C4×C5C22×D311yescharacteristic
112Dic15—21no—
113Dic15—61no—
114Dic15—61no—
115Dic15—121no—
116C3×Dic5—61no—
117C5×Dic3D1211yescharacteristic
118#239—151no—
119#237—151no—
120#235—151no—
121#235—151no—
122C3×SD16—151no—
123C2×C3×C8—31no—
124#216—151no—
125#213—151no—
126Dic12—151no—
127D24—151no—
128#204—51no—
129#204—151no—
130#204—151no—
131#204—301no—
132D3×C8D1511yescharacteristic, complemented
133C32×C5#13511yescharacteristic, complemented, Hall
134C2×C4×C5—31no—
135C22⋊D5—181no—
136C22⋊D5—181no—
137D20—31no—
138D20—91no—
139C4×D5—181no—
140C4×D5—181no—
141Dic10—31no—
142Dic10—91no—
143C5×C8—31no—
144C5×C8D3211yescharacteristic
145C2×C3⋊D3—101no—
146C2×C3×D3—101no—
147C2×C3×D3D2011yescharacteristic
148C32×C4C22×D511yescharacteristic
149C3⋊Dic3—101no—
150C3×Dic3—101no—
151C3×Dic3D2011yescharacteristic
152#135—451noSylow
153C2×C3×C5—21no—
154C2×C3×C5—61no—
155C2×C3×C5C2×D1211yescharacteristic
156C2×C3×C5D3×D411yescharacteristic
157D15—41no—
158D15—121no—
159D15—121no—
160D15—241no—
161C3×D5—121no—
162C5×D3—21no—
163C3×Q8—151no—
164C3×D4—151no—
165C2×C3×C4—31no—
166#67—301no—
167#67—301no—
168#67—301no—
169C2×Dic3—301no—
170D12—51no—
171D12—151no—
172D12—151no—
173D12—301no—
174D12—301no—
175C4×D3—301no—
176C4×D3—301no—
177C4×D3—301no—
178C4×D3C2×D1511yescharacteristic
179Dic6—51no—
180Dic6—151no—
181Dic6—151no—
182Dic6—301no—
183C3×C8—21no—
184C3×C8—31no—
185C3×C8D3×D511yescharacteristic
186C3×C8C2×D1511yescharacteristic
187C3⋊C8C2×D1511yescharacteristic
188C22×C5—31no—
189C2×D5—61no—
190C2×D5—181no—
191C4×C5—31no—
192C4×C5C2×D3211yescharacteristic
193Dic5—61no—
194Dic5—181no—
195C2×C32C2×D2011yescharacteristic
196C3⋊D3—201no—
197C3×D3—21no—
198C3×D3—201no—
199#41—451no—
200#41—451no—
201Q16—451no—
202SD16—151no—
203SD16—451no—
204D8—451no—
205C2×C8—31no—
206C3×C5—21no—
207C3×C5#90411yescharacteristic, complemented
208C3×C5#91611yescharacteristic, complemented
209C22×C3—31no—
210C22×C3—301no—
211C2×D3—101no—
212C2×D3—301no—
213C2×D3—301no—
214C2×D3—601no—
215C2×D3D6011yescharacteristic
216C3×C4—21no—
217C3×C4—31no—
218C3×C4—301no—
219C3×C4C2×D3×D511yescharacteristic
220C3×C4C22×D1511yescharacteristic
221Dic3—101no—
222Dic3—301no—
223Dic3—301no—
224Dic3—601no—
225Dic3D6011yescharacteristic
226C2×C5—61no—
227C2×C5D3×D1211yescharacteristic
228D5—121no—
229D5—361no—
230C32#405011yescharacteristic, complemented, Sylow
231Q8—151no—
232Q8—451no—
233D4—151no—
234D4—451no—
235D4—901no—
236D4—901no—
237C2×C4—31no—
238C2×C4—901no—
239C2×C4—901no—
240C8—31no—
241C8D3×D1511yescharacteristic
242C2×C3—21no—
243C2×C3—61no—
244C2×C3—601no—
245C2×C3D3×D2011yescharacteristic
246C2×C3C2×D6011yescharacteristic
247D3—21no—
248D3—201no—
249D3—601no—
250D3—601no—
251D3—1201no—
252C5#6380611yescharacteristic, complemented, Sylow
253C22—31no—
254C22—301no—
255C22—901no—
256C4—31no—
257C4—301no—
258C4—901no—
259C4C2×D3×D1511yescharacteristic
260C3—21no—
261C3#9127211yescharacteristic, complemented
262C3#9179311yescharacteristic, complemented
263C2—61no—
264C2—601no—
265C2—1801no—
266C2D3×D6011yescharacteristic
subgroupG/H
centerC2D3×D60
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
hypercenterC8D3×D15
hypocenterC32×C5#135
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10624197C2semidirect
2. #10624193C2semidirect
3. #10623900C2semidirect
4. C3×#6706C2semidirect
5. C3×C5×D3×C8C2semidirect
6. #10623808C2semidirect
7. #10623799C2semidirect
32. #6706D3semidirect
33. C5×D3×C8D3semidirect
49. C3×D3×C8D5semidirect
132. D3×C8D15semidirect
133. C32×C5#135semidirect
207. C3×C5#904semidirect
208. C3×C5#916semidirect
230. C32#4050semidirect
252. C5#63806semidirect
261. C3#91272semidirect
262. C3#91793semidirect

Maximal subgroups

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

subgroupindex
#106241972
#106241932
#106239002
C3×#67062
C3×C5×D3×C82
#106238082
#106237992
#917933
#912723
#638065