Finite Group Databasebeta

← #13087509

Subgroups — #13087509

Order 1440.

294 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 66 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×C5×D3×D4C211yesmaximal, characteristic, complemented
2#10624197C211yesmaximal, characteristic, complemented
3#10623909C211yesmaximal, characteristic, complemented
4C3×#6716C211yesmaximal, characteristic, complemented
5#10623802C211yesmaximal, characteristic, complemented
6#10623800C211yesmaximal, characteristic, complemented
7#10623796C211yesmaximal, characteristic, complemented
8#91821—31nomaximal
9#91496—31nomaximal
10C22×C3×C5×D3—21no—
11C32×C5×D4C2211yescharacteristic
12C4⋊(C3⋊D15)C2211yescharacteristic, complemented
13C3×Dic30C2211yescharacteristic, complemented
14C3×C5×#67—21no—
15C3×C5×D12C2211yescharacteristic
16C3×C4×C5×D3C2211yescharacteristic
17#67152—21no—
18#67149—21no—
19C3⋊(C3⋊#168)C2211yescharacteristic, complemented
20C3×C3⋊#168C2211yescharacteristic, complemented
21#63934—51nomaximal, Hall
22C2×C3×C5×D4—31no—
23#6817—31no—
24C5×D3×D4D311yescharacteristic, complemented
25#6769—31no—
26#6716—31no—
27#6716D311yescharacteristic, complemented
28#6715—31no—
29#6715—31no—
30#6715—31no—
31#6715—61no—
32#6710—31no—
33C3×#687—31no—
34#6656—31no—
35#6654—31no—
36#6650—31no—
37C22×C32×C5—21no—
38C2×C3⋊D15—21no—
39C2×C3×C5×D3—21no—
40C2×C3×C5×D3—42no—
41C2×C3×C5×D3D411yescharacteristic
42C32×C4×C5C2311yescharacteristic
43C3×Dic15—21no—
44C3×C5×Dic3D411yescharacteristic
45#4078—91noHall
46C3×D3×D4D511yescharacteristic, complemented
47#3799—51no—
48#3753—51no—
49C3×#214—51no—
50#3715—51no—
51#3714—51no—
52#3711—51no—
53C23×C3×C5—61no—
54C22×C5×D3—21no—
55C3×C5×D4—21no—
56C3×C5×D4—31no—
57C3×C5×D4—61no—
58C3×C5×D4C2×D311yescharacteristic
59C3×C5×D4C2×D311yescharacteristic
60C2×C3×C4×C5—31no—
61#1220—61no—
62D60—31no—
63D60—31no—
64D60—61no—
65C4×D15—61no—
66Dic30C2×D311yescharacteristic, complemented
67C5×#67—21no—
68C5×D12C2×D311yescharacteristic
69C4×C5×D3C2×D311yescharacteristic
70C3×Dic10—31no—
71#1203—61no—
72#1200—61no—
73C3⋊#168—31no—
74C3⋊#168—31no—
75C3⋊#168—61no—
76C3⋊#168C2×D311yescharacteristic, complemented
77C3×#168—31no—
78#932—151no—
79#914—151no—
80C2×C32×C5—41no—
81C2×C32×C5C2×D411yescharacteristic
82C3⋊D15—41no—
83C3×C5×D3—21no—
84C3×C5×D3—41no—
85C2×C5×D4—31no—
86#709—91no—
87#687—31no—
88#687—91no—
89#686—91no—
90#686—91no—
91#681—91no—
92C22×C3×D3—21no—
93C32×D4C2×D511yescharacteristic
94C4⋊(C3⋊D3)—51no—
95C3×#67—21no—
96C3×D12C2×D511yescharacteristic
97C3×C4×D3C2×D511yescharacteristic
98C3×Dic6—51no—
99#626—101no—
100#624—101no—
101C3⋊(C3⋊C8)—51no—
102C3×C3⋊C8—51no—
103C22×C3×C5—21no—
104C22×C3×C5—21no—
105C22×C3×C5—31no—
106C22×C3×C5—41no—
107C22×C3×C5—61no—
108C22×C3×C5—122no—
109C2×D15—61no—
110C2×D15—61no—
111C2×D15—121no—
112C2×C5×D3—21no—
113C2×C5×D3—42no—
114C2×C5×D3#6711yescharacteristic
115C3×C4×C5—21no—
116C3×C4×C5—31no—
117C3×C4×C5C22×D311yescharacteristic
118C3×C4×C5C22×D311yescharacteristic
119Dic15—21no—
120C3×Dic5—61no—
121C5×Dic3#6711yescharacteristic
122C2×C3×D4—31no—
123#239—151no—
124D3×D4D1511yescharacteristic, complemented
125#235—151no—
126C3×SD16—151no—
127#215—151no—
128#214—51no—
129#214—151no—
130#213—151no—
131#213—151no—
132#213—151no—
133#213—301no—
134#208—151no—
135D24—151no—
136ΓL(1,𝔽25)—151no—
137C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
138C23×C5—61no—
139C5×D4—31no—
140C5×D4—61no—
141C5×D4D3211yescharacteristic
142C2×C4×C5—31no—
143C22⋊D5—181no—
144D20—91no—
145C4×D5—181no—
146Dic10—31no—
147#168—31no—
148#168—91no—
149C22×C32—21no—
150C2×C3⋊D3—101no—
151C2×C3×D3—21no—
152C2×C3×D3—42no—
153C2×C3×D3C22⋊D511yescharacteristic
154C32×C4C22×D511yescharacteristic
155C3×Dic3—101no—
156C3×Dic3C22⋊D511yescharacteristic
157AGL(1,ℤ/8)—451noSylow
158C2×C3×C5—21no—
159C2×C3×C5—41no—
160C2×C3×C5—41no—
161C2×C3×C5—61no—
162C2×C3×C5—81no—
163C2×C3×C5—121no—
164C2×C3×C5D3×D411yescharacteristic
165C2×C3×C5C2×#6711yescharacteristic
166D15—121no—
167D15—121no—
168D15—241no—
169C5×D3—21no—
170C5×D3—41no—
171C23×C3—61no—
172C22×D3—21no—
173C3×Q8—151no—
174C3×D4—21no—
175C3×D4—31no—
176C3×D4—61no—
177C3×D4D3×D511yescharacteristic
178C3×D4C2×D1511yescharacteristic
179C2×C3×C4—31no—
180#67—21no—
181#67—301no—
182D12—151no—
183D12—151no—
184D12—301no—
185D12—301no—
186D12C2×D1511yescharacteristic
187C4×D3—301no—
188C4×D3—301no—
189C4×D3C2×D1511yescharacteristic
190Dic6—51no—
191C3×C8—151no—
192C3⋊C8—51no—
193C3⋊C8—151no—
194C3⋊C8—151no—
195C3⋊C8—301no—
196C22×C5—21no—
197C22×C5—31no—
198C22×C5—61no—
199C22×C5—122no—
200C2×D5—181no—
201C4×C5—31no—
202C4×C5C2×D3211yescharacteristic
203Dic5—61no—
204C2×C32—41no—
205C2×C32C2×C22⋊D511yescharacteristic
206C3⋊D3—201no—
207C3×D3—21no—
208C3×D3—41no—
209#41—451no—
210C2×D4—31no—
211SD16—151no—
212SD16—451no—
213D8—451no—
214D8—451no—
215M16—451no—
216C3×C5—21no—
217C3×C5#91411yescharacteristic, complemented
218C3×C5#93211yescharacteristic, complemented
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—31no—
222C22×C3—41no—
223C22×C3—61no—
224C22×C3—122no—
225C2×D3—21no—
226C2×D3—42no—
227C2×D3—301no—
228C2×D3—301no—
229C2×D3—601no—
230C2×D3#122011yescharacteristic
231C3×C4—21no—
232C3×C4—31no—
233C3×C4—301no—
234C3×C4C2×D3×D511yescharacteristic
235C3×C4C22×D1511yescharacteristic
236Dic3—101no—
237Dic3#122011yescharacteristic
238C2×C5—41no—
239C2×C5—61no—
240C2×C5—121no—
241C2×C5D3×#6711yescharacteristic
242D5—361no—
243C32#407811yescharacteristic, complemented, Sylow
244C23—61no—
245Q8—151no—
246D4—31no—
247D4—61no—
248D4—451no—
249D4—901no—
250D4D3×D1511yescharacteristic
251C2×C4—31no—
252C2×C4—901no—
253C8—151no—
254C8—451no—
255C2×C3—21no—
256C2×C3—41no—
257C2×C3—41no—
258C2×C3—61no—
259C2×C3—81no—
260C2×C3—121no—
261C2×C3D3×C22⋊D511yescharacteristic
262C2×C3C2×#122011yescharacteristic
263D3—21no—
264D3—41no—
265D3—601no—
266D3—601no—
267D3—1201no—
268C5#6393411yescharacteristic, complemented, Sylow
269C22—21no—
270C22—31no—
271C22—61no—
272C22—122no—
273C22—901no—
274C4—31no—
275C4—301no—
276C4C2×D3×D1511yescharacteristic
277C3—21no—
278C3#9149611yescharacteristic, complemented
279C3#9182111yescharacteristic, complemented
280C2—41no—
281C2—61no—
282C2—121no—
283C2—1801no—
284C2D3×#122011yescharacteristic
subgroupG/H
centerC2D3×#1220
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4D3×D15
hypocenterC32×C5AGL(1,ℤ/8)
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
1. C3×C5×D3×D4C2semidirect
2. #10624197C2semidirect
3. #10623909C2semidirect
4. C3×#6716C2semidirect
5. #10623802C2semidirect
6. #10623800C2semidirect
7. #10623796C2semidirect
12. C4⋊(C3⋊D15)C22semidirect
13. C3×Dic30C22semidirect
19. C3⋊(C3⋊#168)C22semidirect
20. C3×C3⋊#168C22semidirect
24. C5×D3×D4D3semidirect
27. #6716D3semidirect
46. C3×D3×D4D5semidirect
66. Dic30C2×D3semidirect
76. C3⋊#168C2×D3semidirect
124. D3×D4D15semidirect
137. C32×C5AGL(1,ℤ/8)semidirect
217. C3×C5#914semidirect
218. C3×C5#932semidirect
243. C32#4078semidirect
268. C5#63934semidirect
278. C3#91496semidirect
279. C3#91821semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×D42
#106241972
#106239092
C3×#67162
#106238022
#106238002
#106237962
#918213
#914963
#639345