Finite Group Databasebeta

← #13085738

Subgroups — #13085738

Order 1440.

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

normal subgroups only

This group has 266 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#10624221C211yesmaximal, characteristic, complemented
2C3×#6768C211yesmaximal, characteristic, complemented
3#10623798C211yesmaximal, characteristic, complemented
4C3⋊C8×D15C211yesmaximal, characteristic, complemented
5C5×#3716C211yesmaximal, characteristic, complemented
6#10623766C211yesmaximal, characteristic, complemented
7C3×#6658C211yesmaximal, characteristic, complemented
8#91492—31nomaximal
9#91276—31nomaximal
10C5×#634C2211yescharacteristic
11C3×D60C2211yescharacteristic
12C3×C4×D15C2211yescharacteristic
13C3×C5×D12C2211yescharacteristic
14C32×Dic10C2211yescharacteristic
15#67157—21no—
16#67154—21no—
17C3×#1203—21no—
18C3×D3×Dic5—21no—
19C3⋊(C3⋊#168)C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63947—51nomaximal, Hall
22C3×#711—31no—
23#6773—31no—
24#6768D311yescharacteristic, complemented
25#6766—31no—
26#6715—31no—
27C8×D15—31no—
28C5×#214—31no—
29C5×#204—31no—
30C3×#677—31no—
31#6661—31no—
32#6661—31no—
33#6661—61no—
34#6658D311yescharacteristic, complemented
35#6652—31no—
36D5×C3⋊C8—31no—
37C2×C3×D15—21no—
38C2×C3×D15D411yescharacteristic
39C2×C3×C5×D3—21no—
40C32×C4×C5C2311yescharacteristic
41C5×C3⋊Dic3—21no—
42C3×Dic15D411yescharacteristic
43C32×Dic5—21no—
44#4062—91noHall
45C3×#239—51no—
46#3795—51no—
47#3756—51no—
48C3×#215—51no—
49#3716D511yescharacteristic, complemented
50#3713—51no—
51D3×C3⋊C8—51no—
52C3×C5×D4—31no—
53D60C2×D311yescharacteristic
54C4×D15C2×D311yescharacteristic
55C5×D12C2×D311yescharacteristic
56C5×Dic6—31no—
57C5×Dic6—31no—
58C5×Dic6—61no—
59C3×C22⋊D5—61no—
60C2×C3×Dic5—61no—
61C3×D20—31no—
62C3×C4×D5—31no—
63C3×Dic10—21no—
64C3×Dic10C2×D311yescharacteristic
65C3×Dic10C2×D311yescharacteristic
66#1203—21no—
67#1202—61no—
68#1202—61no—
69#1200—61no—
70D3×Dic5—21no—
71D5×Dic3—61no—
72C3×C5×C8—31no—
73C3⋊#168—31no—
74C3⋊#168—31no—
75C3⋊#168—61no—
76C5×C3⋊C8C2×D311yescharacteristic
77#950—151no—
78#916—151no—
79C2×C32×C5C2×D411yescharacteristic
80C3×D15—21no—
81C3×D15—41no—
82C3×C5×D3—41no—
83#713—91no—
84#711—31no—
85C5×SD16—91no—
86#689—91no—
87#686—91no—
88#677—31no—
89C8×D5—91no—
90C32×Q8—51no—
91#634C2×D511yescharacteristic
92C3×D12—51no—
93C3×D12—101no—
94C3×D12C2×D511yescharacteristic
95C3×C4×D3—51no—
96C3×C4×D3—101no—
97#625—101no—
98D3×Dic3—101no—
99C3⋊(C3⋊C8)—51no—
100C3×C3⋊C8C2×D511yescharacteristic
101C22×C3×C5—61no—
102C2×D15—21no—
103C2×D15#6711yescharacteristic
104C2×C5×D3—21no—
105C2×C3×D5—31no—
106C2×C3×D5—61no—
107C3×C4×C5—21no—
108C3×C4×C5C22×D311yescharacteristic
109C3×C4×C5C22×D311yescharacteristic
110Dic15#6711yescharacteristic
111C3×Dic5—21no—
112C3×Dic5—21no—
113C3×Dic5—31no—
114C3×Dic5—41no—
115C5×Dic3—61no—
116C5×Dic3—61no—
117C5×Dic3—121no—
118C3×#41—151no—
119#239—51no—
120#237—151no—
121#235—151no—
122C3×SD16—151no—
123#216—151no—
124#216—151no—
125#216—301no—
126#215—51no—
127#214—31no—
128#213—151no—
129#213—151no—
130C2×C3⋊C8—151no—
131#204—31no—
132D3×C8—151no—
133C32×C5#13511yescharacteristic, complemented, Hall
134C5×Q8—91no—
135C5×D4—31no—
136C22⋊D5—61no—
137C2×Dic5—61no—
138D20—31no—
139D20—181no—
140C4×D5—31no—
141C4×D5—181no—
142Dic10D3211yescharacteristic
143C5×C8—31no—
144#168—91no—
145C2×C3×D3—21no—
146C2×C3×D3—51no—
147C2×C3×D3—101no—
148C32×C4—101no—
149C32×C4C22×D511yescharacteristic
150C3⋊Dic3—21no—
151C3×Dic3—51no—
152#135—451noSylow
153C2×C3×C5—21no—
154C2×C3×C5—121no—
155C2×C3×C5D3×D411yescharacteristic
156C2×C3×C5C2×#6711yescharacteristic
157D15—21no—
158D15—41no—
159C3×D5—61no—
160C3×D5—121no—
161C5×D3—41no—
162C3×Q8—51no—
163C3×Q8—51no—
164C3×Q8—101no—
165C3×D4—31no—
166C3×D4—151no—
167C3×D4—301no—
168C2×C3×C4—151no—
169C2×C3×C4—301no—
170#67—301no—
171#67—301no—
172C2×Dic3—301no—
173D12—51no—
174D12—101no—
175D12D3×D511yescharacteristic
176C4×D3—51no—
177C4×D3—101no—
178C4×D3—301no—
179Dic6—31no—
180Dic6—31no—
181Dic6—61no—
182C3×C8—31no—
183C3⋊C8—151no—
184C3⋊C8—151no—
185C3⋊C8—301no—
186C3⋊C8D3×D511yescharacteristic
187C22×C5—61no—
188C2×D5—31no—
189C2×D5—61no—
190C4×C5—181no—
191C4×C5C2×D3211yescharacteristic
192Dic5—21no—
193Dic5—31no—
194C2×C32D4×D511yescharacteristic
195C3×D3—41no—
196C3×D3—101no—
197C3×D3—201no—
198#41—151no—
199#41—451no—
200Q16—451no—
201SD16—91no—
202SD16—151no—
203D8—451no—
204C2×C8—451no—
205C3×C5—21no—
206C3×C5#91611yescharacteristic, complemented
207C3×C5#95011yescharacteristic, complemented
208C22×C3—61no—
209C22×C3—151no—
210C22×C3—301no—
211C2×D3—21no—
212C2×D3—51no—
213C2×D3—101no—
214C3×C4—21no—
215C3×C4—101no—
216C3×C4—101no—
217C3×C4—151no—
218C3×C4—201no—
219C3×C4C2×D3×D511yescharacteristic
220C3×C4C2×D3×D511yescharacteristic
221Dic3—51no—
222Dic3—61no—
223Dic3—61no—
224Dic3—121no—
225C2×C5—121no—
226C2×C5D3×#6711yescharacteristic
227D5—61no—
228D5—121no—
229C32#406211yescharacteristic, complemented, Sylow
230Q8—51no—
231Q8—91no—
232D4—31no—
233D4—151no—
234D4—301no—
235D4—901no—
236C2×C4—151no—
237C2×C4—301no—
238C2×C4—901no—
239C8—31no—
240C8—451no—
241C2×C3—21no—
242C2×C3—121no—
243C2×C3—301no—
244C2×C3—601no—
245C2×C3#677711yescharacteristic
246C2×C3D5×#6711yescharacteristic
247D3—41no—
248D3—101no—
249D3—201no—
250C5#6394711yescharacteristic, complemented, Sylow
251C22—61no—
252C22—151no—
253C22—301no—
254C4—101no—
255C4—151no—
256C4—181no—
257C4D32×D511yescharacteristic
258C3—21no—
259C3#9127611yescharacteristic, complemented
260C3#9149211yescharacteristic, complemented
261C2—121no—
262C2—301no—
263C2—601no—
264C2#1062402811yescharacteristic
subgroupG/H
centerC2#10624028
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. #10624221C2semidirect
2. C3×#6768C2semidirect
3. #10623798C2semidirect
4. C3⋊C8×D15C2semidirect
5. C5×#3716C2semidirect
6. #10623766C2semidirect
7. C3×#6658C2semidirect
24. #6768D3semidirect
34. #6658D3semidirect
49. #3716D5semidirect
133. C32×C5#135semidirect
206. C3×C5#916semidirect
207. C3×C5#950semidirect
229. C32#4062semidirect
250. C5#63947semidirect
259. C3#91276semidirect
260. C3#91492semidirect

Maximal subgroups

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

subgroupindex
#106242212
C3×#67682
#106237982
C3⋊C8×D152
C5×#37162
#106237662
C3×#66582
#914923
#912763
#639475