Finite Group Databasebeta

← #13085784

Subgroups — #13085784

Order 1440.

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

normal subgroups only

This group has 326 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
1C5×#3796C211yesmaximal, characteristic, complemented
2C3⋊D3×D20C211yesmaximal, characteristic, complemented
3#10623820C211yesmaximal, characteristic, complemented
4#10623806C211yesmaximal, characteristic, complemented
5#10623800C211yesmaximal, characteristic, complemented
6C3×#6655C211yesmaximal, characteristic, complemented
7C3×#6652C211yesmaximal, characteristic, complemented
8#91504—31nomaximal
9#91480—31nomaximal
10C2×D5×C3⋊D3—21no—
11C4⋊(C3⋊D15)C2211yescharacteristic
12C4×C5×C3⋊D3C2211yescharacteristic
13C3×C5×D12C2211yescharacteristic, complemented
14C3×C5×Dic6C2211yescharacteristic, complemented
15C32×D20C2211yescharacteristic
16C5×#626—21no—
17C5×D3×Dic3—21no—
18#67139—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C3⋊#168C2211yescharacteristic, complemented
21#63937—51nomaximal, Hall
22C5×#239—31no—
23C5×#237—31no—
24D3×D20—31no—
25D3×D20—31no—
26D3×D20—61no—
27#6717—31no—
28#6715—31no—
29C3×#688—31no—
30C3×#686—31no—
31#6660—31no—
32#6655D311yescharacteristic, complemented
33#6654—31no—
34#6652D311yescharacteristic, complemented
35#6650—31no—
36#6650—31no—
37C2×C3⋊D15—21no—
38C2×C5×C3⋊D3D411yescharacteristic
39C2×C3×C5×D3—21no—
40C2×C32×D5—21no—
41D5×C3⋊D3—42no—
42C32×C4×C5C2311yescharacteristic
43C5×C3⋊Dic3D411yescharacteristic
44C3×C5×Dic3—21no—
45#4095—91noHall
46D4×C3⋊D3—51no—
47#3796D511yescharacteristic, complemented
48C3×#214—51no—
49C3×#213—51no—
50#3717—51no—
51#3714—51no—
52#3712—51no—
53C2×D3×D5—61no—
54C2×D3×D5—61no—
55C2×D3×D5—62no—
56C3×C5×Q8—31no—
57C3×C5×D4—31no—
58D60—31no—
59D60—31no—
60D60—61no—
61C5×#67—61no—
62C2×C5×Dic3—61no—
63C5×D12—61no—
64C5×D12C2×D311yescharacteristic, complemented
65C4×C5×D3—31no—
66C4×C5×D3—31no—
67C4×C5×D3—61no—
68C4×C5×D3—61no—
69C5×Dic6C2×D311yescharacteristic, complemented
70C3×D20—21no—
71C3×D20C2×D311yescharacteristic
72C3×D20C2×D311yescharacteristic
73#1202—61no—
74#1202—61no—
75#1202—62no—
76C3⋊#168C2×D311yescharacteristic, complemented
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C3×#168—31no—
80#914—151no—
81#911—151no—
82C2×C32×C5C2×D411yescharacteristic
83C3⋊D15—41no—
84C5×C3⋊D3—21no—
85C3×C5×D3—41no—
86C32×D5—41no—
87C5×#41—91no—
88C2×D20—91no—
89#688—31no—
90#688—91no—
91#686—31no—
92#686—91no—
93#681—91no—
94C22×C3⋊D3—101no—
95C32×D4—51no—
96#638—101no—
97C4⋊(C3⋊D3)—51no—
98C4×C3⋊D3C2×D511yescharacteristic
99C3×D12C2×D511yescharacteristic, complemented
100C3×Dic6C2×D511yescharacteristic, complemented
101#626—21no—
102D3×Dic3—21no—
103C3×C3⋊C8—51no—
104C3×C3⋊C8—51no—
105C22×C3×C5—61no—
106C2×D15—62no—
107C2×D15—61no—
108C2×D15—61no—
109C2×C5×D3—21no—
110C2×C5×D3—31no—
111C2×C5×D3—31no—
112C2×C5×D3—61no—
113C2×C3×D5—22no—
114C2×C3×D5—21no—
115C2×C3×D5—21no—
116D3×D5—124no—
117D3×D5—122no—
118D3×D5—122no—
119C3×C4×C5—21no—
120C3×C4×C5—61no—
121C3×C4×C5C22×D311yescharacteristic
122C3×C4×C5C22×D311yescharacteristic
123C5×Dic3—21no—
124C5×Dic3—31no—
125C5×Dic3—31no—
126C5×Dic3—61no—
127#239—31no—
128#237—31no—
129D3×D4—151no—
130D3×D4—151no—
131D3×D4—301no—
132C3×SD16—151no—
133C3×D8—151no—
134#215—151no—
135#214—51no—
136#213—51no—
137#213—151no—
138D24—151no—
139#204—151no—
140ΓL(1,𝔽25)—151no—
141ΓL(1,𝔽25)—151no—
142C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
143C22×D5—181no—
144C5×Q8—31no—
145C5×D4—31no—
146C5×D4—181no—
147C2×C4×C5—91no—
148C2×C4×C5—181no—
149D20—91no—
150D20—181no—
151D20D3211yescharacteristic
152#168—31no—
153#168—31no—
154C22×C32—101no—
155C2×C3⋊D3—101no—
156C2×C3⋊D3—202no—
157C2×C3⋊D3C22⋊D511yescharacteristic
158C2×C3×D3—21no—
159C32×C4C22×D511yescharacteristic
160C3⋊Dic3C22⋊D511yescharacteristic
161C3×Dic3—21no—
162AGL(1,ℤ/8)—451noSylow
163C2×C3×C5—21no—
164C2×C3×C5—121no—
165C2×C3×C5D3×D411yescharacteristic
166C2×C3×C5D3×D411yescharacteristic
167D15—122no—
168D15—121no—
169D15—121no—
170C3×D5—42no—
171C3×D5—41no—
172C3×D5—41no—
173C5×D3—41no—
174C5×D3—62no—
175C5×D3—61no—
176C5×D3—61no—
177C22×D3—301no—
178C22×D3—301no—
179C22×D3—302no—
180C3×Q8—31no—
181C3×D4—31no—
182C3×D4—51no—
183C3×D4—51no—
184C3×D4—101no—
185#67—61no—
186#67—301no—
187#67—301no—
188#67—302no—
189C2×Dic3—61no—
190D12—61no—
191D12—151no—
192D12—151no—
193D12—301no—
194D12D3×D511yescharacteristic, complemented
195C4×D3—31no—
196C4×D3—31no—
197C4×D3—61no—
198C4×D3—61no—
199Dic6D3×D511yescharacteristic, complemented
200C3×C8—151no—
201C3×C8—151no—
202C3⋊C8—51no—
203C3⋊C8—51no—
204C22×C5—61no—
205C22×C5—91no—
206C2×D5—21no—
207C2×D5—181no—
208C2×D5—362no—
209C4×C5—61no—
210C4×C5—91no—
211C4×C5C2×D3211yescharacteristic
212C2×C32—201no—
213C2×C32C2×C22⋊D511yescharacteristic
214C3⋊D3—21no—
215C3⋊D3—201no—
216C3×D3—41no—
217#41—91no—
218C2×D4—451no—
219SD16—151no—
220SD16—451no—
221D8—151no—
222D8—451no—
223M16—451no—
224C3×C5—21no—
225C3×C5#91111yescharacteristic, complemented
226C3×C5#91411yescharacteristic, complemented
227C22×C3—61no—
228C22×C3—102no—
229C22×C3—101no—
230C22×C3—101no—
231C2×D3—21no—
232C2×D3—31no—
233C2×D3—31no—
234C2×D3—61no—
235C2×D3—302no—
236C2×D3—301no—
237C2×D3—301no—
238C2×D3—604no—
239C2×D3—602no—
240C2×D3—602no—
241C3×C4—21no—
242C3×C4—61no—
243C3×C4C2×D3×D511yescharacteristic
244C3×C4C2×D3×D511yescharacteristic
245Dic3—21no—
246Dic3—31no—
247Dic3—31no—
248Dic3—61no—
249C2×C5—121no—
250C2×C5—181no—
251C2×C5#381111yescharacteristic
252D5—41no—
253D5—361no—
254C32#409511yescharacteristic, complemented, Sylow
255C23—901no—
256Q8—31no—
257D4—31no—
258D4—51no—
259D4—181no—
260D4—451no—
261D4—901no—
262C2×C4—91no—
263C2×C4—181no—
264C8—151no—
265C8—151no—
266C2×C3—21no—
267C2×C3—121no—
268C2×C3—202no—
269C2×C3—201no—
270C2×C3—201no—
271C2×C3D3×C22⋊D511yescharacteristic
272C2×C3D3×C22⋊D511yescharacteristic
273D3—41no—
274D3—62no—
275D3—61no—
276D3—61no—
277D3—602no—
278D3—601no—
279D3—601no—
280C5#6393711yescharacteristic, complemented, Sylow
281C22—61no—
282C22—91no—
283C22—101no—
284C22—901no—
285C22—1802no—
286C4—61no—
287C4—91no—
288C4D32×D511yescharacteristic
289C3—21no—
290C3#9148011yescharacteristic, complemented
291C3#9150411yescharacteristic, complemented
292C2—121no—
293C2—181no—
294C2—201no—
295C2—1801no—
296C2#1062402911yescharacteristic
subgroupG/H
centerC2#10624029
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5AGL(1,ℤ/8)
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. C5×#3796C2semidirect
2. C3⋊D3×D20C2semidirect
3. #10623820C2semidirect
4. #10623806C2semidirect
5. #10623800C2semidirect
6. C3×#6655C2semidirect
7. C3×#6652C2semidirect
13. C3×C5×D12C22semidirect
14. C3×C5×Dic6C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C3⋊#168C22semidirect
32. #6655D3semidirect
34. #6652D3semidirect
47. #3796D5semidirect
64. C5×D12C2×D3semidirect
69. C5×Dic6C2×D3semidirect
76. C3⋊#168C2×D3semidirect
77. C3⋊#168C2×D3semidirect
99. C3×D12C2×D5semidirect
100. C3×Dic6C2×D5semidirect
142. C32×C5AGL(1,ℤ/8)semidirect
194. D12D3×D5semidirect
199. Dic6D3×D5semidirect
225. C3×C5#911semidirect
226. C3×C5#914semidirect
254. C32#4095semidirect
280. C5#63937semidirect
290. C3#91480semidirect
291. C3#91504semidirect

Maximal subgroups

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

subgroupindex
C5×#37962
C3⋊D3×D202
#106238202
#106238062
#106238002
C3×#66552
C3×#66522
#915043
#914803
#639375