Finite Group Databasebeta

← #13085808

Subgroups — #13085808

Order 1440.

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

normal subgroups only

This group has 280 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#10624156C211yesmaximal, characteristic
2C3×D5×Dic6C211yesmaximal, characteristic, complemented
3#10623826C211yesmaximal, characteristic, complemented
4#10623806C211yesmaximal, characteristic, complemented
5#10623804C211yesmaximal, characteristic, complemented
6C5×#3719C211yesmaximal, characteristic, complemented
7C3×#6649C211yesmaximal, characteristic, complemented
8#91515—31nomaximal
9#91261—31nomaximal
10C4⋊(C3⋊D15)C2211yescharacteristic
11C5×#634C2211yescharacteristic
12C3×Dic30C2211yescharacteristic
13C3×C5×Dic6C2211yescharacteristic
14C32×C4×D5C2211yescharacteristic
15#67139—21no—
16#67137—21no—
17C3×#1204—21no—
18C3×D5×Dic3—21no—
19C3×C3⋊#168C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63833—51nomaximal, Hall
22C3×Q8×D5—31no—
23#6773—31no—
24#6773—31no—
25#6773—61no—
26D5×Dic6D311yescharacteristic, complemented
27#6717—31no—
28#6706—31no—
29C5×#216—31no—
30C5×Dic12—31no—
31C3×#676—31no—
32#6663—31no—
33#6661—31no—
34#6660—31no—
35#6658—31no—
36#6649D311yescharacteristic, complemented
37C2×C3⋊D15—21no—
38C2×C32×D5D411yescharacteristic
39C32×C4×C5C2311yescharacteristic
40C5×C3⋊Dic3—21no—
41C3×Dic15—21no—
42C3×C5×Dic3—21no—
43C32×Dic5D411yescharacteristic
44#4064—91noHall
45#3828—51no—
46C2×C3×Dic6—51no—
47C3×#208—51no—
48#3719—51no—
49#3719D511yescharacteristic, complemented
50#3717—51no—
51#3717—51no—
52C3×C5×Q8—31no—
53D60—31no—
54D60—31no—
55D60—61no—
56Dic30C2×D311yescharacteristic
57C5×Dic6—31no—
58C5×Dic6—31no—
59C5×Dic6—61no—
60C5×Dic6C2×D311yescharacteristic
61C3×C4×D5—21no—
62C3×C4×D5—61no—
63C3×C4×D5C2×D311yescharacteristic
64C3×C4×D5C2×D311yescharacteristic
65C3×Dic10—31no—
66C3×Dic10—61no—
67#1204—21no—
68#1202—62no—
69#1202—61no—
70#1202—61no—
71#1200—62no—
72#1200—61no—
73#1200—61no—
74D5×Dic3—21no—
75C3×C5×C8—31no—
76C3⋊#168C2×D311yescharacteristic
77C3×#168—31no—
78C5×C3⋊C8C2×D311yescharacteristic
79#942—151no—
80#909—151no—
81C2×C32×C5C2×D411yescharacteristic
82C3⋊D15—41no—
83C32×D5—21no—
84#713—91no—
85Q8×D5—31no—
86C5×Q16—91no—
87#689—91no—
88#688—91no—
89#677—91no—
90#676—31no—
91C2×C32×C4—51no—
92#638—101no—
93C4⋊(C3⋊D3)—51no—
94C4×C3⋊D3—101no—
95#634C2×D511yescharacteristic
96C2×C3×Dic3—101no—
97C3×Dic6—51no—
98C3×Dic6—101no—
99C3×Dic6C2×D511yescharacteristic
100C3×C3⋊C8—51no—
101C3×C3⋊C8C2×D511yescharacteristic
102C2×D15—62no—
103C2×D15—61no—
104C2×D15—61no—
105C2×C3×D5—21no—
106C2×C3×D5D1211yescharacteristic
107C2×C3×D5#6711yescharacteristic
108C3×C4×C5—21no—
109C3×C4×C5—61no—
110C3×C4×C5C22×D311yescharacteristic
111C3×C4×C5C22×D311yescharacteristic
112Dic15—21no—
113C3×Dic5—21no—
114C3×Dic5—61no—
115C3×Dic5D1211yescharacteristic
116C3×Dic5#6711yescharacteristic
117C5×Dic3—21no—
118C5×Dic3—62no—
119C5×Dic3—61no—
120C5×Dic3—61no—
121C2×C3×Q8—151no—
122#235—151no—
123#235—151no—
124#235—301no—
125C2×Dic6—51no—
126C3×M16—151no—
127#216—31no—
128#216—151no—
129#215—151no—
130#215—151no—
131#208—51no—
132Dic12—31no—
133Dic12—151no—
134#204—151no—
135#204—151no—
136C32×C5#13711yescharacteristic, complemented, Hall
137C5×Q8—31no—
138C5×Q8—91no—
139D20—91no—
140D20—181no—
141C4×D5—61no—
142C4×D5—181no—
143C4×D5D3211yescharacteristic
144Dic10—31no—
145Dic10—61no—
146C5×C8—31no—
147#168—31no—
148C22×C32—51no—
149C2×C3⋊D3—101no—
150C32×C4—51no—
151C32×C4C22×D511yescharacteristic
152C3⋊Dic3—21no—
153C3×Dic3—21no—
154C3×Dic3—101no—
155#137—451noSylow
156C2×C3×C5—21no—
157C2×C3×C5C2×D1211yescharacteristic
158C2×C3×C5C2×#6711yescharacteristic
159D15—122no—
160D15—121no—
161D15—121no—
162C3×D5—21no—
163C3×D5—21no—
164C3×D5—41no—
165C3×Q8—31no—
166C3×Q8—151no—
167C3×Q8—301no—
168C2×C3×C4—51no—
169C2×C3×C4—51no—
170C2×C3×C4—101no—
171C2×C3×C4—301no—
172#67—301no—
173#67—301no—
174#67—302no—
175C2×Dic3—101no—
176D12—151no—
177D12—151no—
178D12—301no—
179C4×D3—301no—
180C4×D3—301no—
181C4×D3—302no—
182Dic6—31no—
183Dic6—31no—
184Dic6—51no—
185Dic6—61no—
186Dic6—101no—
187Dic6D3×D511yescharacteristic
188C3×C8—31no—
189C3×C8—151no—
190C3⋊C8—51no—
191C3⋊C8D3×D511yescharacteristic
192C2×D5—181no—
193C2×D5#62611yescharacteristic
194C4×C5—61no—
195C4×C5—181no—
196C4×C5C2×D3211yescharacteristic
197Dic5—61no—
198Dic5#62611yescharacteristic
199C2×C32—101no—
200C2×C32D4×D511yescharacteristic
201C3⋊D3—201no—
202#41—451no—
203C2×Q8—151no—
204Q16—91no—
205Q16—451no—
206SD16—451no—
207SD16—451no—
208M16—151no—
209C3×C5—21no—
210C3×C5#90911yescharacteristic, complemented
211C3×C5#94211yescharacteristic, complemented
212C22×C3—51no—
213C22×C3—51no—
214C22×C3—101no—
215C2×D3—302no—
216C2×D3—301no—
217C2×D3—301no—
218C3×C4—21no—
219C3×C4—51no—
220C3×C4—51no—
221C3×C4—61no—
222C3×C4—101no—
223C3×C4—301no—
224C3×C4C2×D3×D511yescharacteristic
225C3×C4C2×D3×D511yescharacteristic
226Dic3—21no—
227Dic3—62no—
228Dic3—61no—
229Dic3—61no—
230Dic3—101no—
231C2×C5C2×#62611yescharacteristic
232D5—21no—
233D5—361no—
234C32#406411yescharacteristic, complemented, Sylow
235Q8—31no—
236Q8—91no—
237Q8—151no—
238Q8—301no—
239D4—451no—
240D4—901no—
241C2×C4—51no—
242C2×C4—301no—
243C2×C4—901no—
244C8—31no—
245C8—151no—
246C2×C3—21no—
247C2×C3—101no—
248C2×C3—101no—
249C2×C3—201no—
250C2×C3D5×D1211yescharacteristic
251C2×C3D5×#6711yescharacteristic
252D3—602no—
253D3—601no—
254D3—601no—
255C5#6383311yescharacteristic, complemented, Sylow
256C22—51no—
257C22—901no—
258C4—51no—
259C4—61no—
260C4—181no—
261C4—301no—
262C4D32×D511yescharacteristic
263C3—21no—
264C3#9126111yescharacteristic, complemented
265C3#9151511yescharacteristic, complemented
266C2—101no—
267C2—1801no—
268C2D5×#62611yescharacteristic
subgroupG/H
centerC2D5×#626
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
prime radical#10624156C2
hypocenterC32×C5#137
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
2. C3×D5×Dic6C2semidirect
3. #10623826C2semidirect
4. #10623806C2semidirect
5. #10623804C2semidirect
6. C5×#3719C2semidirect
7. C3×#6649C2semidirect
26. D5×Dic6D3semidirect
36. #6649D3semidirect
49. #3719D5semidirect
136. C32×C5#137semidirect
210. C3×C5#909semidirect
211. C3×C5#942semidirect
234. C32#4064semidirect
255. C5#63833semidirect
264. C3#91261semidirect
265. C3#91515semidirect

Maximal subgroups

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

subgroupindex
#106241562
C3×D5×Dic62
#106238262
#106238062
#106238042
C5×#37192
C3×#66492
#915153
#912613
#638335