Finite Group Databasebeta

← #12017095

Subgroups — #12017095

Order 1280.

390 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64729C211yesmaximal, characteristic
2#10601421C211yesmaximal, characteristic
3Dic5×#107C211yesmaximal, characteristic, complemented
4C2×#64711C211yesmaximal, characteristic
5C2×#64709C211yesmaximal, characteristic, complemented
6C5×#1380C211yesmaximal, characteristic, complemented
7#10598295C211yesmaximal, characteristic, complemented
8C22×D40C2211yescharacteristic
9C22×C5×C16C2211yescharacteristic
10C2×C5×#107C2211yescharacteristic
11C2×C5×#107C2211yescharacteristic
12C2×#3950C2211yescharacteristic
13C2×C8×Dic5C2211yescharacteristic
14C22×#672C2211yescharacteristic
15#65277—21no—
16C4⋊C4×Dic5—21no—
17C2×#3941—21no—
18#64749—21no—
19#64729—22no—
20#64711C414yescomplemented
21#64709—22no—
22#13130—51nomaximal, Sylow
23C22×D20—21no—
24C22×C5×C8C2311yescharacteristic
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—21no—
27C2×#685—41no—
28C2×#685—41no—
29C2×C4⋊Dic5—21no—
30C2×C4×Dic5—41no—
31C2×C4×Dic5D411yescharacteristic
32C22×#168D411yescharacteristic
33C2×D40—21no—
34C2×D40—21no—
35C2×D40—21no—
36C2×D40—21no—
37C2×D40—21no—
38C2×D40C2×C412yes—
39C2×C5×C16—21no—
40C2×C5×C16—21no—
41C2×C5×C16—21no—
42C5×#107—21no—
43C5×#107—21no—
44C5×#107—21no—
45C5×#107C2×C412yes—
46#3963—41no—
47#3950—21no—
48#3950D412yes—
49C8×Dic5—21no—
50C8×Dic5—21no—
51C2×#672—21no—
52C2×#672—21no—
53C2×#672C2×C412yes—
54#3941—42no—
55C2×#366—51no—
56C2×#357—51no—
57C2×#357—51no—
58#1970—51no—
59C4×#107—51no—
60#1380D511yescharacteristic, complemented
61#1374—51no—
62C23×D5—41no—
63C22×C4×C5—41no—
64C22×C4×C5—41no—
65C22×C4×C5C2×D411yescharacteristic
66C22×Dic5—41no—
67C22×Dic5D811yescharacteristic
68C22×Dic5D811yescharacteristic
69C2×D20—22no—
70C2×D20—41no—
71C2×D20—41no—
72C2×D20—41no—
73C2×D20—41no—
74C2×D20—41no—
75C2×C5×C8C22×C411yescharacteristic
76C2×C5×C8C2×D411yescharacteristic
77C2×C5×C8#4111yescharacteristic
78C2×C5×C8#4111yescharacteristic
79C2×C5×C8#4111yescharacteristic
80C2×C5×C8#4111yescharacteristic
81C5×C4⋊C4—22no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85#685—82no—
86#685—82no—
87C4⋊Dic5—22no—
88C4⋊Dic5—41no—
89C4×Dic5—21no—
90C4×Dic5—21no—
91C4×Dic5—82no—
92C2×#168—21no—
93C2×#168—21no—
94C2×#168—21no—
95D40—22no—
96D40—22no—
97D40—41no—
98D40—41no—
99C5×C16—41no—
100#672—22no—
101C22×D8—51no—
102C22×C16—51no—
103C22×C16C2×D511yescharacteristic
104C2×#107—51no—
105C2×#107C2×D511yescharacteristic
106C2×#107C2×D511yescharacteristic
107C2×#102—101no—
108C2×C4×C8—51no—
109#390—101no—
110C4×C4⋊C4—101no—
111#366—102no—
112#357—54no—
113#357—102no—
114#340—101no—
115C23×C5C2×D811yescharacteristic
116C22×D5—42no—
117C22×D5—81no—
118C22×D5—81no—
119C22×D5—81no—
120C22×D5—81no—
121C22×D5—81no—
122C22×D5—81no—
123C2×C4×C5—42no—
124C2×C4×C5—81no—
125C2×C4×C5—81no—
126C2×C4×C5—81no—
127C2×C4×C5—81no—
128C2×C4×C5—81no—
129C2×C4×C5C4×D411yescharacteristic
130C2×C4×C5#12111yescharacteristic
131C2×C4×C5#12311yescharacteristic
132C2×C4×C5#13511yescharacteristic
133C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C5#13711yescharacteristic
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—42no—
141C2×Dic5—81no—
142C2×Dic5—81no—
143C2×Dic5D1612yes—
144D20—42no—
145D20—42no—
146D20—81no—
147D20—81no—
148C5×C8#11711yescharacteristic
149C5×C8C4×D411yescharacteristic
150C5×C8#12411yescharacteristic
151C5×C8#12611yescharacteristic
152#168—41no—
153C22×D4—101no—
154C2×D8—52no—
155C2×D8—101no—
156C2×D8—101no—
157C2×D8—101no—
158C2×D8—101no—
159C2×D8—101no—
160C22×C8—51no—
161C22×C8C22×D511yescharacteristic
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—101no—
165C2×C22⋊C4—201no—
166C2×C22⋊C4—201no—
167C2×C42—51no—
168C2×C42—201no—
169C2×C16—21no—
170C2×C16—21no—
171C2×C16—21no—
172C2×C16—52no—
173C2×C16—101no—
174C2×C16—101no—
175#107—21no—
176#107—21no—
177#107—21no—
178#107—52no—
179#107—101no—
180#107C4×D512yes—
181#102—202no—
182C4×C8—101no—
183C4×C8—101no—
184#95—201no—
185C22×C5C4×D811yescharacteristic
186C22×C5#45911yescharacteristic
187C22×C5#48011yescharacteristic
188C22×C5C2×D1611yescharacteristic
189C22×C5#50811yescharacteristic
190C22×C5#50911yescharacteristic
191C22×C5#51011yescharacteristic
192C2×D5—82no—
193C2×D5—82no—
194C2×D5—82no—
195C2×D5—161no—
196C2×D5—161no—
197C2×D5—161no—
198C2×D5—161no—
199C4×C5—82no—
200C4×C5—161no—
201C4×C5#38811yescharacteristic
202C4×C5#44011yescharacteristic
203C4×C5#46411yescharacteristic
204C4×C5#48211yescharacteristic
205Dic5—22no—
206Dic5—41no—
207Dic5—82no—
208C24—201no—
209C2×D4—102no—
210C2×D4—201no—
211C2×D4—201no—
212C2×D4—201no—
213C2×D4—201no—
214C2×D4—201no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—51no—
218C22×C4—51no—
219C22×C4—201no—
220C22×C4D4×D511yescharacteristic
221D8—102no—
222D8—102no—
223D8—201no—
224D8—201no—
225C2×C8—101no—
226C2×C8—101no—
227C2×C8—101no—
228C2×C8C2×C4×D511yescharacteristic
229C2×C8#70911yescharacteristic
230C2×C8#70911yescharacteristic
231C2×C8D4×D511yescharacteristic
232C2×C8#71111yescharacteristic
233C2×C8#71311yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—102no—
239C4⋊C4—201no—
240C22⋊C4—402no—
241C22⋊C4—402no—
242C42—101no—
243C42—101no—
244C42—402no—
245C16—41no—
246C16—102no—
247C2×C5#192511yescharacteristic
248C2×C5C4×D1611yescharacteristic
249C2×C5#217511yescharacteristic
250C2×C5#220611yescharacteristic
251C2×C5#221111yescharacteristic
252C2×C5#223211yescharacteristic
253C2×C5#223411yescharacteristic
254D5—162no—
255C23—202no—
256C23—401no—
257C23—401no—
258C23—401no—
259C23—401no—
260C23—401no—
261C23—401no—
262C23D5×D811yescharacteristic
263D4—202no—
264D4—202no—
265D4—401no—
266D4—401no—
267C2×C4—42no—
268C2×C4—52no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—202no—
280C2×C4—401no—
281C2×C4—401no—
282C2×C4#402711yescharacteristic
283C2×C4#403011yescharacteristic
284C2×C4#404011yescharacteristic
285C2×C4#406011yescharacteristic
286C2×C4#406211yescharacteristic
287C2×C4#406411yescharacteristic
288C8—201no—
289C8#401811yescharacteristic
290C8#403111yescharacteristic
291C8#403911yescharacteristic
292C8#404411yescharacteristic
293C5#1313011yescharacteristic, complemented, Sylow
294C22—402no—
295C22—402no—
296C22—402no—
297C22—801no—
298C22—801no—
299C22—801no—
300C22—801no—
301C22#6504511yescharacteristic
302C22#6507511yescharacteristic
303C22#6517111yescharacteristic
304C22D5×D1611yescharacteristic
305C22#6520311yescharacteristic
306C22#6520511yescharacteristic
307C22#6520711yescharacteristic
308C4—82no—
309C4—102no—
310C4—161no—
311C4—201no—
312C4—402no—
313C4#6495811yescharacteristic
314C4#6508711yescharacteristic
315C4#6510611yescharacteristic
316C4#6515511yescharacteristic
317C2—802no—
318C2#1059958411yescharacteristic
319C2#1059996711yescharacteristic
320C2#1059999511yescharacteristic
321C2#1060000111yescharacteristic
322C2#1060003011yescharacteristic
323C2#1060012311yescharacteristic
324C2#1060014411yescharacteristic
subgroupG/H
centerC23D5×D8
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#1380C2
socleC23×C5C2×D8
prime radicalC22×D40C22
cosocleC22×C5×C8C23
hypercenter#1380D5
hypocenterC5#13130
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. Dic5×#107C2semidirect
5. C2×#64709C2semidirect
6. C5×#1380C2semidirect
7. #10598295C2semidirect
20. #64711C4semidirect
60. #1380D5semidirect
293. C5#13130semidirect

Maximal subgroups

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

subgroupindex
C2×#647292
#106014212
Dic5×#1072
C2×#647112
C2×#647092
C5×#13802
#105982952
#131305