Finite Group Databasebeta

← #13087268

Subgroups — #13087268

Order 1440.

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

normal subgroups only

This group has 294 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#10624205C211yesmaximal, characteristic
2#10624198C211yesmaximal, characteristic, complemented
3C8×C3⋊D15C211yesmaximal, characteristic, complemented
4C3×#6706C211yesmaximal, characteristic, complemented
5C3×C5×#204C211yesmaximal, characteristic, complemented
6#10623802C211yesmaximal, characteristic, complemented
7#10623801C211yesmaximal, characteristic, complemented
8SD16×D15—31nomaximal
9#91255—31nomaximal
10C2×D3×D15—21no—
11C4×C3⋊D15C2211yescharacteristic
12C3×D60C2211yescharacteristic
13C3×Dic30C2211yescharacteristic, complemented
14C3×C5×D12C2211yescharacteristic
15C3×C5×Dic6C2211yescharacteristic, complemented
16#67153—21no—
17#67150—21no—
18#67149—21no—
19C32×C5×C8C2211yescharacteristic, complemented
20C3⋊(C3⋊#168)C2211yescharacteristic, complemented
21#63796—51nomaximal, Hall
22Q8×D15—31no—
23D4×D15—31no—
24#6777—31no—
25D15⋊Q8—31no—
26C3×C5×SD16—31no—
27#6717—31no—
28#6716—31no—
29#6706D311yescharacteristic, complemented
30C8×D15—31no—
31C8×D15—31no—
32C8×D15—61no—
33C5×#204D311yescharacteristic, complemented
34C3×#677—31no—
35#6656—31no—
36#6655—31no—
37C2×C3⋊D15D411yescharacteristic
38C2×C3×D15—21no—
39C2×C3×C5×D3—21no—
40D3×D15—42no—
41C32×C4×C5C2311yescharacteristic
42C3⋊Dic15D411yescharacteristic
43C3×Dic15—21no—
44C3×C5×Dic3—21no—
45D5×SD16—91noHall
46#3802—51no—
47#3797—51no—
48C8×C3⋊D3—51no—
49C3×#204—51no—
50C3×#204D511yescharacteristic, complemented
51#3715—51no—
52#3715—51no—
53C22×D15—61no—
54C2×D3×D5—61no—
55C3×C5×Q8—31no—
56C3×C5×D4—31no—
57#1220—61no—
58D60C2×D311yescharacteristic
59C4×D15—31no—
60C4×D15—31no—
61C4×D15—61no—
62C4×D15—61no—
63Dic30—61no—
64Dic30C2×D311yescharacteristic, complemented
65C5×D12C2×D311yescharacteristic
66C5×Dic6C2×D311yescharacteristic, complemented
67C3×D20—31no—
68C3×Dic10—31no—
69#1204—61no—
70#1201—61no—
71#1200—61no—
72C3×C5×C8—21no—
73C3×C5×C8C2×D311yescharacteristic, complemented
74C3×C5×C8C2×D311yescharacteristic, complemented
75C3⋊#168—31no—
76C3⋊#168—31no—
77C3⋊#168—61no—
78D3×SD16—151no—
79D3×SD16—151no—
80C2×C32×C5C2×D411yescharacteristic
81C3⋊D15SD1612yescomplemented
82C3×D15—41no—
83C3×C5×D3—41no—
84Q8×D5—91no—
85D4×D5—91no—
86C5×SD16—31no—
87#688—91no—
88#687—91no—
89#677—31no—
90C8×D5—91no—
91C2×D32—101no—
92C4×C3⋊D3—51no—
93C3×D12—51no—
94C3×D12C2×D511yescharacteristic
95C3×Dic6—51no—
96C3×Dic6C2×D511yescharacteristic, complemented
97#627—101no—
98#625—101no—
99#624—101no—
100C32×C8C2×D511yescharacteristic, complemented
101C3⋊(C3⋊C8)—51no—
102C22×C3×C5—61no—
103C2×D15—21no—
104C2×D15—31no—
105C2×D15—31no—
106C2×D15—61no—
107C2×D15—122no—
108C2×C5×D3—21no—
109C2×C3×D5—61no—
110D3×D5—122no—
111C3×C4×C5—21no—
112C3×C4×C5—61no—
113C3×C4×C5C22×D311yescharacteristic
114C3×C4×C5C22×D311yescharacteristic
115Dic15—21no—
116Dic15—31no—
117Dic15—31no—
118Dic15—61no—
119C3×Dic5—61no—
120C5×Dic3—21no—
121D3×Q8—151no—
122D3×Q8—151no—
123D3×D4—151no—
124D3×D4—151no—
125C3×SD16—31no—
126C3×SD16—151no—
127#215—151no—
128#215—151no—
129#214—151no—
130#214—151no—
131#204—51no—
132#204D1511yescharacteristic, complemented
133D3×C8—151no—
134D3×C8—151no—
135D3×C8—301no—
136C32×C5C2×SD1611yescharacteristic, complemented, Hall
137C22×D5—181no—
138C5×Q8—31no—
139C5×D4—31no—
140C22⋊D5—181no—
141D20—31no—
142C4×D5—91no—
143C4×D5—181no—
144Dic10—31no—
145Dic10—181no—
146C5×C8D3211yescharacteristic, complemented
147#168—91no—
148C2×C3⋊D3—51no—
149C2×C3×D3—21no—
150C2×C3×D3—101no—
151D32—202no—
152C32×C4C22×D511yescharacteristic
153C3⋊Dic3—51no—
154C3×Dic3—21no—
155C3×Dic3—101no—
156C2×SD16—451noSylow
157C2×C3×C5—21no—
158C2×C3×C5—121no—
159C2×C3×C5D3×D411yescharacteristic
160C2×C3×C5D3×D411yescharacteristic
161D15—32no—
162D15—32no—
163D15—41no—
164D15—62no—
165C3×D5—121no—
166C5×D3—41no—
167C22×D3—301no—
168C22×D3—301no—
169C3×Q8—31no—
170C3×Q8—151no—
171C3×D4—31no—
172C3×D4—151no—
173#67—301no—
174#67—301no—
175D12—51no—
176D12C2×D1511yescharacteristic
177C4×D3—151no—
178C4×D3—151no—
179C4×D3—301no—
180C4×D3—301no—
181C4×D3—301no—
182Dic6—51no—
183Dic6—301no—
184Dic6—301no—
185Dic6C2×D1511yescharacteristic, complemented
186C3×C8—21no—
187C3×C8D3×D511yescharacteristic, complemented
188C3×C8C2×D1511yescharacteristic, complemented
189C3⋊C8—151no—
190C3⋊C8—151no—
191C3⋊C8—301no—
192C22×C5—61no—
193C2×D5—61no—
194C2×D5—91no—
195C2×D5—362no—
196C4×C5—61no—
197C4×C5C2×D3211yescharacteristic
198Dic5—61no—
199Dic5—91no—
200C2×C32D4×D511yescharacteristic
201C3⋊D3—52no—
202C3×D3—41no—
203C3×D3—201no—
204C2×Q8—451no—
205C2×D4—451no—
206SD16—31no—
207SD16—151no—
208SD16—451no—
209SD16—451no—
210C2×C8—451no—
211C3×C5—21no—
212C3×C5D3×SD1611yescharacteristic, complemented
213C3×C5D3×SD1611yescharacteristic, complemented
214C22×C3—61no—
215C22×C3—301no—
216C2×D3—21no—
217C2×D3—101no—
218C2×D3—151no—
219C2×D3—151no—
220C2×D3—301no—
221C2×D3—602no—
222C2×D3—602no—
223C3×C4—21no—
224C3×C4—61no—
225C3×C4—301no—
226C3×C4C2×D3×D511yescharacteristic
227C3×C4C22×D1511yescharacteristic
228Dic3—21no—
229Dic3—101no—
230Dic3—151no—
231Dic3—151no—
232Dic3—301no—
233C2×C5—121no—
234C2×C5#380211yescharacteristic
235D5—92no—
236D5—121no—
237C32D5×SD1611yescharacteristic, complemented, Sylow
238C23—901no—
239Q8—31no—
240Q8—151no—
241Q8—901no—
242D4—31no—
243D4—151no—
244D4—901no—
245C2×C4—451no—
246C2×C4—901no—
247C8—451no—
248C8D3×D1511yescharacteristic, complemented
249C2×C3—21no—
250C2×C3—121no—
251C2×C3—601no—
252C2×C3#677711yescharacteristic
253C2×C3D4×D1511yescharacteristic
254D3—41no—
255D3—152no—
256D3—152no—
257D3—201no—
258D3—302no—
259C5#6379611yescharacteristic, complemented, Sylow
260C22—61no—
261C22—301no—
262C22—451no—
263C22—1802no—
264C4—61no—
265C4—301no—
266C4—451no—
267C4C2×D3×D1511yescharacteristic
268C3—21no—
269C3#9125511yescharacteristic, complemented
270C3SD16×D1511yescharacteristic, complemented
271C2—121no—
272C2—452no—
273C2—601no—
274C2#1062420511yescharacteristic
subgroupG/H
centerC2#10624205
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
prime radical#10624205C2
hypercenterC8D3×D15
hypocenterC32×C5C2×SD16
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
2. #10624198C2semidirect
3. C8×C3⋊D15C2semidirect
4. C3×#6706C2semidirect
5. C3×C5×#204C2semidirect
6. #10623802C2semidirect
7. #10623801C2semidirect
13. C3×Dic30C22semidirect
15. C3×C5×Dic6C22semidirect
19. C32×C5×C8C22semidirect
20. C3⋊(C3⋊#168)C22semidirect
29. #6706D3semidirect
33. C5×#204D3semidirect
50. C3×#204D5semidirect
64. Dic30C2×D3semidirect
66. C5×Dic6C2×D3semidirect
73. C3×C5×C8C2×D3semidirect
74. C3×C5×C8C2×D3semidirect
81. C3⋊D15SD16semidirect
96. C3×Dic6C2×D5semidirect
100. C32×C8C2×D5semidirect
132. #204D15semidirect
136. C32×C5C2×SD16semidirect
146. C5×C8D32semidirect
185. Dic6C2×D15semidirect
187. C3×C8D3×D5semidirect
188. C3×C8C2×D15semidirect
212. C3×C5D3×SD16semidirect
213. C3×C5D3×SD16semidirect
237. C32D5×SD16semidirect
248. C8D3×D15semidirect
259. C5#63796semidirect
269. C3#91255semidirect
270. C3SD16×D15semidirect

Maximal subgroups

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

subgroupindex
#106242052
#106241982
C8×C3⋊D152
C3×#67062
C3×C5×#2042
#106238022
#106238012
SD16×D153
#912553
#637965