Finite Group Databasebeta

← #13085752

Subgroups — #13085752

Order 1440.

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

normal subgroups only

This group has 268 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
2#10624200C211yesmaximal, characteristic, complemented
3#10623808C211yesmaximal, characteristic, complemented
4C5×#3714C211yesmaximal, characteristic, complemented
5#10623764C211yesmaximal, characteristic, complemented
6C3×#6659C211yesmaximal, characteristic, complemented
7C3×#6648C211yesmaximal, characteristic, complemented
8#91499—31nomaximal
9#91270—31nomaximal
10#67180C2211yescharacteristic
11C5×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×C4×D15C2211yescharacteristic
13C3×Dic30C2211yescharacteristic
14C3×C5×D12C2211yescharacteristic
15#67156—21no—
16#67155—21no—
17#67150—21no—
18D3×Dic15—21no—
19C3×C5×C3⋊C8C2211yescharacteristic
20C32×#168C2211yescharacteristic
21#63806—51nomaximal, Hall
22#6819—31no—
23#6772—31no—
24#6772—31no—
25#6768—31no—
26Dic60—31no—
27C5×#213—31no—
28C5×D24—31no—
29C3×#687—31no—
30C3×C8×D5—31no—
31#6662—31no—
32#6659—31no—
33#6659—31no—
34#6659—61no—
35#6659D311yescharacteristic, complemented
36#6648D311yescharacteristic, complemented
37C2×C5×C3⋊D3—21no—
38C2×C3×D15D411yescharacteristic
39C2×C3×C5×D3—21no—
40C32×C4×C5C2311yescharacteristic
41C3⋊Dic15—21no—
42C3×Dic15—21no—
43C3×Dic15D411yescharacteristic
44#4058—91noHall
45#3799—51no—
46#3795—51no—
47#3744—51no—
48C3×#204—51no—
49C3×D3×C8—51no—
50#3719—51no—
51#3714D511yescharacteristic, complemented
52C3×C5×D4—31no—
53#1220—61no—
54C2×Dic15—61no—
55C4×D15C2×D311yescharacteristic
56Dic30—31no—
57Dic30—31no—
58Dic30—61no—
59Dic30C2×D311yescharacteristic
60C5×D12—31no—
61C5×D12—31no—
62C5×D12—61no—
63C5×D12C2×D311yescharacteristic
64C3×C4×D5—31no—
65C3×Dic10—31no—
66#1203—61no—
67#1201—61no—
68#1201—61no—
69D3×Dic5—61no—
70D3×Dic5—61no—
71D3×Dic5—61no—
72C3×C5×C8—31no—
73C3×#168—21no—
74C3×#168C2×D311yescharacteristic
75C3×#168C2×D311yescharacteristic
76C5×C3⋊C8C2×D311yescharacteristic
77#916—151no—
78#904—151no—
79C2×C32×C5C2×D411yescharacteristic
80C5×C3⋊D3—41no—
81C3×D15—21no—
82C3×C5×D3—41no—
83#711—91no—
84#711—91no—
85C5×D8—91no—
86#687—31no—
87#687—91no—
88Dic20—91no—
89C8×D5—31no—
90C4⋊(C3⋊D3)C2×D511yescharacteristic
91#634—51no—
92C3×D12C2×D511yescharacteristic
93C3×C4×D3—51no—
94C3×Dic6—51no—
95#626—101no—
96#625—101no—
97#624—101no—
98D3×Dic3—101no—
99C32×C8—51no—
100C3×C3⋊C8C2×D511yescharacteristic
101C22×C3×C5—61no—
102C2×D15D1211yescharacteristic
103C2×C5×D3—21no—
104C2×C5×D3—61no—
105C2×C5×D3—61no—
106C2×C5×D3—121no—
107C2×C3×D5—31no—
108C3×C4×C5—21no—
109C3×C4×C5C22×D311yescharacteristic
110C3×C4×C5C22×D311yescharacteristic
111Dic15—21no—
112Dic15—61no—
113Dic15—61no—
114Dic15—121no—
115Dic15D1211yescharacteristic
116C3×Dic5—31no—
117C3×Dic5—61no—
118#239—151no—
119#237—151no—
120#235—151no—
121#235—151no—
122C3×SD16—151no—
123C2×C3×C8—151no—
124#216—151no—
125#213—31no—
126Dic12—151no—
127D24—31no—
128#204—51no—
129#204—151no—
130#204—151no—
131#204—301no—
132D3×C8—51no—
133C32×C5#13511yescharacteristic, complemented, Hall
134C5×D4—31no—
135C5×D4—91no—
136C22⋊D5—181no—
137C22⋊D5—181no—
138C2×Dic5—181no—
139C2×Dic5—181no—
140C4×D5—31no—
141Dic10—31no—
142Dic10—91no—
143C5×C8—31no—
144#168D3211yescharacteristic
145C2×C3⋊D3—21no—
146C2×C3×D3—21no—
147C2×C3×D3—51no—
148C32×C4C22×D511yescharacteristic
149C3⋊Dic3—101no—
150C3×Dic3—51no—
151C3×Dic3—101no—
152#135—451noSylow
153C2×C3×C5—21no—
154C2×C3×C5—121no—
155C2×C3×C5C2×D1211yescharacteristic
156C2×C3×C5D3×D411yescharacteristic
157D15—21no—
158C3×D5—61no—
159C5×D3—41no—
160C5×D3—121no—
161C5×D3—121no—
162C5×D3—241no—
163C3×Q8—151no—
164C3×D4—31no—
165C2×C3×C4—151no—
166#67—301no—
167#67—301no—
168#67—301no—
169C2×Dic3—301no—
170D12—31no—
171D12—31no—
172D12—61no—
173D12—301no—
174D12D3×D511yescharacteristic
175C4×D3—51no—
176C4×D3—301no—
177C4×D3—301no—
178C4×D3—301no—
179Dic6—51no—
180Dic6—151no—
181Dic6—151no—
182Dic6—301no—
183C3×C8—31no—
184C3×C8—51no—
185C3×C8—51no—
186C3×C8—101no—
187C3⋊C8D3×D511yescharacteristic
188C22×C5—61no—
189C22×C5—181no—
190C2×D5—31no—
191C4×C5C2×D3211yescharacteristic
192Dic5—31no—
193Dic5—61no—
194Dic5—181no—
195C2×C32D4×D511yescharacteristic
196C3⋊D3—41no—
197C3×D3—41no—
198C3×D3—101no—
199#41—451no—
200#41—451no—
201Q16—451no—
202SD16—151no—
203SD16—451no—
204D8—91no—
205C2×C8—151no—
206C3×C5—21no—
207C3×C5#90411yescharacteristic, complemented
208C3×C5#91611yescharacteristic, complemented
209C22×C3—61no—
210C22×C3—151no—
211C2×D3—21no—
212C2×D3—51no—
213C2×D3—61no—
214C2×D3—61no—
215C2×D3—121no—
216C3×C4—21no—
217C3×C4—151no—
218C3×C4—301no—
219C3×C4C2×D3×D511yescharacteristic
220C3×C4C2×D3×D511yescharacteristic
221Dic3—51no—
222Dic3—101no—
223Dic3—301no—
224Dic3—301no—
225Dic3—601no—
226C2×C5—121no—
227C2×C5—361no—
228C2×C5D3×D1211yescharacteristic
229D5—61no—
230C32#405811yescharacteristic, complemented, Sylow
231Q8—151no—
232Q8—451no—
233D4—31no—
234D4—91no—
235D4—901no—
236D4—901no—
237C2×C4—151no—
238C2×C4—901no—
239C2×C4—901no—
240C8—31no—
241C8—51no—
242C2×C3—21no—
243C2×C3—121no—
244C2×C3—301no—
245C2×C3D5×D1211yescharacteristic
246C2×C3#679011yescharacteristic
247D3—41no—
248D3—101no—
249D3—121no—
250D3—121no—
251D3—241no—
252C5#6380611yescharacteristic, complemented, Sylow
253C22—61no—
254C22—151no—
255C22—181no—
256C4—151no—
257C4—301no—
258C4—901no—
259C4D32×D511yescharacteristic
260C3—21no—
261C3#9127011yescharacteristic, complemented
262C3#9149911yescharacteristic, complemented
263C2—121no—
264C2—301no—
265C2—361no—
266C2#1062403311yescharacteristic
subgroupG/H
centerC2#10624033
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. #10624224C2semidirect
2. #10624200C2semidirect
3. #10623808C2semidirect
4. C5×#3714C2semidirect
5. #10623764C2semidirect
6. C3×#6659C2semidirect
7. C3×#6648C2semidirect
35. #6659D3semidirect
36. #6648D3semidirect
51. #3714D5semidirect
133. C32×C5#135semidirect
207. C3×C5#904semidirect
208. C3×C5#916semidirect
230. C32#4058semidirect
252. C5#63806semidirect
261. C3#91270semidirect
262. C3#91499semidirect

Maximal subgroups

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

subgroupindex
#106242242
#106242002
#106238082
C5×#37142
#106237642
C3×#66592
C3×#66482
#914993
#912703
#638065