Finite Group Databasebeta

← #13087739

Subgroups — #13087739

Order 1440.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2#10624220C211yesmaximal, characteristic, complemented
3C3×#6716C211yesmaximal, characteristic, complemented
4C3×#6715C211yesmaximal, characteristic, complemented
5#10623824C211yesmaximal, characteristic, complemented
6#10623821C211yesmaximal, characteristic, complemented
7#10623820C211yesmaximal, characteristic, complemented
8#91496—31nomaximal
9#91494—31nomaximal
10C22×C5×C3⋊D3—21no—
11C32×C5×D4C2211yescharacteristic
12C5×#638—21no—
13C5×C4⋊(C3⋊D3)C2211yescharacteristic
14C4×C5×C3⋊D3C2211yescharacteristic
15C3×D60C2211yescharacteristic, complemented
16C3×Dic30C2211yescharacteristic, complemented
17#67156—21no—
18#67154—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C3⋊#168C2211yescharacteristic, complemented
21#63937—51nomaximal, Hall
22C5×D3×D4—31no—
23C5×D3×D4—31no—
24C5×D3×D4—61no—
25#6769—31no—
26#6765—31no—
27#6716D311yescharacteristic, complemented
28#6715D311yescharacteristic, complemented
29C3×#687—31no—
30C3×#686—31no—
31#6659—31no—
32#6656—31no—
33#6654—31no—
34#6652—31no—
35#6650—31no—
36#6650—31no—
37C22×C32×C5—21no—
38C2×C5×C3⋊D3—21no—
39C2×C5×C3⋊D3—42no—
40C2×C5×C3⋊D3D411yescharacteristic
41C2×C3×D15—21no—
42C32×C4×C5C2311yescharacteristic
43C5×C3⋊Dic3D411yescharacteristic
44C3×Dic15—21no—
45#4078—91noHall
46D4×C3⋊D3D511yescharacteristic, complemented
47#3796—51no—
48C3×#214—51no—
49C3×#213—51no—
50#3717—51no—
51#3714—51no—
52#3712—51no—
53C22×C5×D3—61no—
54C22×C5×D3—61no—
55C22×C5×D3—62no—
56C3×C5×D4—21no—
57C3×C5×D4C2×D311yescharacteristic
58C3×C5×D4C2×D311yescharacteristic
59D60C2×D311yescharacteristic, complemented
60Dic30C2×D311yescharacteristic, complemented
61C5×#67—61no—
62C5×#67—61no—
63C5×#67—62no—
64C5×D12—31no—
65C5×D12—31no—
66C5×D12—61no—
67C4×C5×D3—31no—
68C4×C5×D3—31no—
69C4×C5×D3—61no—
70C3×D20—31no—
71C3×Dic10—31no—
72#1203—61no—
73#1201—61no—
74#1200—61no—
75D5×Dic3—61no—
76C3⋊#168C2×D311yescharacteristic, complemented
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C3×#168—31no—
80#914—151no—
81#911—151no—
82C2×C32×C5—41no—
83C2×C32×C5C2×D411yescharacteristic
84C5×C3⋊D3—21no—
85C5×C3⋊D3—41no—
86C3×D15—41no—
87C2×C5×D4—91no—
88#709—91no—
89#687—31no—
90#687—91no—
91#686—31no—
92#686—91no—
93#681—91no—
94C22×C3⋊D3—21no—
95C32×D4C2×D511yescharacteristic
96#638—21no—
97C4⋊(C3⋊D3)C2×D511yescharacteristic
98C4×C3⋊D3C2×D511yescharacteristic
99C3×D12—51no—
100C3×Dic6—51no—
101#626—101no—
102D3×Dic3—101no—
103C3×C3⋊C8—51no—
104C3×C3⋊C8—51no—
105C22×C3×C5—22no—
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C2×D15—21no—
109C2×C5×D3—31no—
110C2×C5×D3—31no—
111C2×C5×D3—61no—
112C2×C5×D3—62no—
113C2×C5×D3—61no—
114C2×C5×D3—61no—
115C2×C5×D3—124no—
116C2×C5×D3—122no—
117C2×C5×D3—122no—
118C2×C3×D5—61no—
119C3×C4×C5—21no—
120C3×C4×C5C22×D311yescharacteristic
121C3×C4×C5C22×D311yescharacteristic
122Dic15—21no—
123C3×Dic5—61no—
124C5×Dic3—31no—
125C5×Dic3—31no—
126C5×Dic3—61no—
127#239—151no—
128#237—151no—
129D3×D4—31no—
130D3×D4—31no—
131D3×D4—61no—
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
143C23×C5—181no—
144C5×D4—91no—
145C5×D4—181no—
146C5×D4D3211yescharacteristic
147C2×C4×C5—91no—
148C22⋊D5—181no—
149D20—31no—
150C4×D5—181no—
151Dic10—31no—
152#168—31no—
153#168—31no—
154C22×C32—21no—
155C2×C3⋊D3—21no—
156C2×C3⋊D3—42no—
157C2×C3⋊D3C22⋊D511yescharacteristic
158C2×C3×D3—101no—
159C32×C4C22×D511yescharacteristic
160C3⋊Dic3C22⋊D511yescharacteristic
161C3×Dic3—101no—
162AGL(1,ℤ/8)—451noSylow
163C2×C3×C5—21no—
164C2×C3×C5—42no—
165C2×C3×C5—41no—
166C2×C3×C5—41no—
167C2×C3×C5D3×D411yescharacteristic
168C2×C3×C5D3×D411yescharacteristic
169D15—41no—
170C3×D5—121no—
171C5×D3—62no—
172C5×D3—61no—
173C5×D3—61no—
174C5×D3—122no—
175C5×D3—121no—
176C5×D3—121no—
177C22×D3—61no—
178C22×D3—61no—
179C22×D3—62no—
180C3×Q8—151no—
181C3×D4—21no—
182C3×D4—151no—
183C3×D4D3×D511yescharacteristic
184C3×D4D3×D511yescharacteristic
185#67—61no—
186#67—61no—
187#67—62no—
188#67—301no—
189C2×Dic3—301no—
190D12—31no—
191D12—31no—
192D12—51no—
193D12—61no—
194D12—301no—
195C4×D3—31no—
196C4×D3—31no—
197C4×D3—61no—
198C4×D3—301no—
199Dic6—51no—
200C3×C8—151no—
201C3×C8—151no—
202C3⋊C8—51no—
203C3⋊C8—51no—
204C22×C5—21no—
205C22×C5—91no—
206C22×C5—181no—
207C22×C5—362no—
208C2×D5—61no—
209C4×C5—91no—
210C4×C5C2×D3211yescharacteristic
211Dic5—61no—
212C2×C32—41no—
213C2×C32C2×C22⋊D511yescharacteristic
214C3⋊D3—21no—
215C3⋊D3—41no—
216C3×D3—201no—
217#41—451no—
218C2×D4—91no—
219SD16—151no—
220SD16—451no—
221D8—151no—
222D8—451no—
223M16—451no—
224C3×C5—21no—
225C3×C5#91111yescharacteristic, complemented
226C3×C5#91411yescharacteristic, complemented
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—301no—
231C2×D3—31no—
232C2×D3—31no—
233C2×D3—61no—
234C2×D3—62no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—101no—
238C2×D3—124no—
239C2×D3—122no—
240C2×D3—122no—
241C3×C4—21no—
242C3×C4—301no—
243C3×C4C2×D3×D511yescharacteristic
244C3×C4C2×D3×D511yescharacteristic
245Dic3—31no—
246Dic3—31no—
247Dic3—61no—
248Dic3—101no—
249C2×C5—41no—
250C2×C5—181no—
251C2×C5—361no—
252C2×C5#381111yescharacteristic
253D5—121no—
254C32#407811yescharacteristic, complemented, Sylow
255C23—181no—
256Q8—151no—
257D4—91no—
258D4—151no—
259D4—181no—
260D4—901no—
261D4(C3⋊D3)⋊D511yescharacteristic
262C2×C4—91no—
263C2×C4—901no—
264C8—151no—
265C8—151no—
266C2×C3—21no—
267C2×C3—42no—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3—601no—
271C2×C3D3×C22⋊D511yescharacteristic
272C2×C3D3×C22⋊D511yescharacteristic
273D3—62no—
274D3—61no—
275D3—61no—
276D3—122no—
277D3—121no—
278D3—121no—
279D3—201no—
280C5#6393711yescharacteristic, complemented, Sylow
281C22—21no—
282C22—91no—
283C22—181no—
284C22—301no—
285C22—362no—
286C4—91no—
287C4—301no—
288C4C2×(C3⋊D3)⋊D511yescharacteristic
289C3—21no—
290C3#9149411yescharacteristic, complemented
291C3#9149611yescharacteristic, complemented
292C2—41no—
293C2—181no—
294C2—361no—
295C2—601no—
296C2#1062423611yescharacteristic
subgroupG/H
centerC2#10624236
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×(C3⋊D3)⋊D5
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4(C3⋊D3)⋊D5
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. C5×D4×C3⋊D3C2semidirect
2. #10624220C2semidirect
3. C3×#6716C2semidirect
4. C3×#6715C2semidirect
5. #10623824C2semidirect
6. #10623821C2semidirect
7. #10623820C2semidirect
15. C3×D60C22semidirect
16. C3×Dic30C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C3⋊#168C22semidirect
27. #6716D3semidirect
28. #6715D3semidirect
46. D4×C3⋊D3D5semidirect
59. D60C2×D3semidirect
60. Dic30C2×D3semidirect
76. C3⋊#168C2×D3semidirect
77. C3⋊#168C2×D3semidirect
142. C32×C5AGL(1,ℤ/8)semidirect
225. C3×C5#911semidirect
226. C3×C5#914semidirect
254. C32#4078semidirect
280. C5#63937semidirect
290. C3#91494semidirect
291. C3#91496semidirect

Maximal subgroups

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

subgroupindex
C5×D4×C3⋊D32
#106242202
C3×#67162
C3×#67152
#106238242
#106238212
#106238202
#914963
#914943
#639375