Finite Group Databasebeta

← #13087497

Subgroups — #13087497

Order 1440.

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

normal subgroups only

This group has 260 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
1C3×#6819C211yesmaximal, characteristic
2Dic6×D15C211yesmaximal, characteristic, complemented
3#10623910C211yesmaximal, characteristic, complemented
4C3×C5×#214C211yesmaximal, characteristic, complemented
5#10623808C211yesmaximal, characteristic, complemented
6#10623807C211yesmaximal, characteristic, complemented
7#10623795C211yesmaximal, characteristic, complemented
8#91804—31nomaximal
9#91484—31nomaximal
10C32×C5×D4C2211yescharacteristic
11#67180C2211yescharacteristic
12C3×#1220—21no—
13C2×C3×Dic15—21no—
14C3×C4×D15C2211yescharacteristic
15C3×Dic30C2211yescharacteristic
16C3×C5×Dic6C2211yescharacteristic
17#67153—21no—
18Dic3×D15—21no—
19C3⋊(C3⋊#168)C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63929—51nomaximal, Hall
22Q8×D15—31no—
23#6819D311yescharacteristic
24C3×#711—31no—
25D5×Dic6—31no—
26C3×C5×SD16—31no—
27#6718—31no—
28#6716—31no—
29#6716—31no—
30#6716—61no—
31Dic60—31no—
32#6705—31no—
33C5×#214D311yescharacteristic, complemented
34#6662—31no—
35#6661—31no—
36#6649—31no—
37C22×C32×C5—21no—
38C2×C3×D15D411yescharacteristic
39C32×C4×C5C2311yescharacteristic
40C3⋊Dic15—21no—
41C3×Dic15—21no—
42C3×Dic15D411yescharacteristic
43C3×C5×Dic3—21no—
44#4061—91noHall
45C3×#237—51no—
46D3×Dic6—51no—
47#3754—51no—
48C3×#214D511yescharacteristic, complemented
49#3719—51no—
50#3718—51no—
51#3711—51no—
52C3×C5×Q8—31no—
53C3×C5×D4—21no—
54C3×C5×D4C2×D311yescharacteristic
55C3×C5×D4C2×D311yescharacteristic
56#1220—21no—
57C2×Dic15—21no—
58C4×D15—61no—
59C4×D15C2×D311yescharacteristic
60Dic30—31no—
61Dic30—31no—
62Dic30—61no—
63Dic30—61no—
64Dic30C2×D311yescharacteristic
65C5×Dic6C2×D311yescharacteristic
66C3×C22⋊D5—61no—
67C2×C3×Dic5—61no—
68C3×C4×D5—31no—
69C3×Dic10—31no—
70#1204—61no—
71D5×Dic3—61no—
72C3×C5×C8—31no—
73C3⋊#168—31no—
74C3⋊#168—31no—
75C3⋊#168—61no—
76C5×C3⋊C8C2×D311yescharacteristic
77#951—151no—
78#915—151no—
79C2×C32×C5—41no—
80C2×C32×C5C2×D411yescharacteristic
81C3×D15—21no—
82Q8×D5—91no—
83#711—31no—
84C5×SD16—31no—
85#689—91no—
86#687—91no—
87Dic20—91no—
88#676—91no—
89C32×D4C2×D511yescharacteristic
90#634—51no—
91C3×#67—101no—
92C2×C3×Dic3—101no—
93C3×C4×D3—51no—
94C3×Dic6—51no—
95C3×Dic6C2×D511yescharacteristic
96#627—101no—
97D3×Dic3—101no—
98C3⋊(C3⋊C8)—51no—
99C3×C3⋊C8C2×D511yescharacteristic
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5—41no—
103C2×D15#6711yescharacteristic
104C2×C3×D5—31no—
105C3×C4×C5—21no—
106C3×C4×C5—61no—
107C3×C4×C5C22×D311yescharacteristic
108C3×C4×C5C22×D311yescharacteristic
109Dic15—21no—
110Dic15—61no—
111Dic15—61no—
112Dic15—121no—
113Dic15#6711yescharacteristic
114C3×Dic5—31no—
115C3×Dic5—61no—
116C5×Dic3—21no—
117C3×#41—151no—
118D3×Q8—151no—
119#237—51no—
120C2×Dic6—151no—
121C3×SD16—31no—
122#216—151no—
123#216—151no—
124#216—151no—
125#214—151no—
126#214—151no—
127#214—301no—
128#214D1511yescharacteristic, complemented
129#208—151no—
130Dic12—151no—
131ΓL(1,𝔽25)—151no—
132C32×C5#13711yescharacteristic, complemented, Hall
133C5×Q8—31no—
134C5×D4D3211yescharacteristic
135C22⋊D5—61no—
136C2×Dic5—61no—
137C4×D5—31no—
138C4×D5—181no—
139Dic10—31no—
140Dic10—91no—
141Dic10—181no—
142C5×C8—31no—
143#168—91no—
144C22×C32—21no—
145C2×C3×D3—51no—
146C32×C4C22×D511yescharacteristic
147C3⋊Dic3—101no—
148C3×Dic3—21no—
149C3×Dic3—51no—
150C3×Dic3—101no—
151#137—451noSylow
152C2×C3×C5—21no—
153C2×C3×C5—41no—
154C2×C3×C5—41no—
155C2×C3×C5—81no—
156C2×C3×C5D3×D411yescharacteristic
157C2×C3×C5C2×#6711yescharacteristic
158D15—21no—
159C3×D5—61no—
160C3×Q8—31no—
161C3×Q8—151no—
162C3×D4—21no—
163C3×D4—301no—
164C3×D4D3×D511yescharacteristic
165C3×D4C2×D1511yescharacteristic
166C2×C3×C4—151no—
167C2×C3×C4—301no—
168#67—101no—
169C2×Dic3—101no—
170C2×Dic3—301no—
171C4×D3—51no—
172C4×D3—301no—
173Dic6—51no—
174Dic6—151no—
175Dic6—151no—
176Dic6—301no—
177Dic6—301no—
178Dic6—301no—
179Dic6C2×D1511yescharacteristic
180C3×C8—31no—
181C3⋊C8—151no—
182C3⋊C8—151no—
183C3⋊C8—301no—
184C3⋊C8C2×D1511yescharacteristic
185C22×C5—21no—
186C2×D5—31no—
187C4×C5—61no—
188C4×C5C2×D3211yescharacteristic
189Dic5—31no—
190Dic5—61no—
191Dic5—181no—
192C2×C32—41no—
193C2×C32D4×D511yescharacteristic
194C3×D3—101no—
195#41—151no—
196C2×Q8—451no—
197Q16—451no—
198Q16—451no—
199SD16—31no—
200SD16—451no—
201M16—451no—
202C3×C5—21no—
203C3×C5#91511yescharacteristic, complemented
204C3×C5#95111yescharacteristic, complemented
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—41no—
208C22×C3—151no—
209C2×D3—51no—
210C3×C4—21no—
211C3×C4—61no—
212C3×C4—151no—
213C3×C4—301no—
214C3×C4C2×D3×D511yescharacteristic
215C3×C4C22×D1511yescharacteristic
216Dic3—21no—
217Dic3—51no—
218Dic3—101no—
219Dic3—301no—
220Dic3—301no—
221Dic3—601no—
222C2×C5—41no—
223C2×C5D3×#6711yescharacteristic
224D5—61no—
225C32#406111yescharacteristic, complemented, Sylow
226Q8—31no—
227Q8—151no—
228Q8—451no—
229Q8—901no—
230D4—301no—
231D4D3×D1511yescharacteristic
232C2×C4—151no—
233C2×C4—301no—
234C2×C4—901no—
235C8—31no—
236C8—451no—
237C2×C3—21no—
238C2×C3—41no—
239C2×C3—41no—
240C2×C3—81no—
241C2×C3—301no—
242C2×C3D5×#6711yescharacteristic
243C2×C3D4×D1511yescharacteristic
244D3—101no—
245C5#6392911yescharacteristic, complemented, Sylow
246C22—21no—
247C22—151no—
248C4—61no—
249C4—151no—
250C4—301no—
251C4—901no—
252C4C2×D3×D1511yescharacteristic
253C3—21no—
254C3#9148411yescharacteristic, complemented
255C3#9180411yescharacteristic, complemented
256C2—41no—
257C2—301no—
258C2#67×D1511yescharacteristic
subgroupG/H
centerC2#67×D15
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
prime radicalC3×#6819C2
hypercenterD4D3×D15
hypocenterC32×C5#137
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
2. Dic6×D15C2semidirect
3. #10623910C2semidirect
4. C3×C5×#214C2semidirect
5. #10623808C2semidirect
6. #10623807C2semidirect
7. #10623795C2semidirect
33. C5×#214D3semidirect
48. C3×#214D5semidirect
128. #214D15semidirect
132. C32×C5#137semidirect
203. C3×C5#915semidirect
204. C3×C5#951semidirect
225. C32#4061semidirect
245. C5#63929semidirect
254. C3#91484semidirect
255. C3#91804semidirect

Maximal subgroups

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

subgroupindex
C3×#68192
Dic6×D152
#106239102
C3×C5×#2142
#106238082
#106238072
#106237952
#918043
#914843
#639295