Finite Group Databasebeta

← #11995943

Subgroups — #11995943

Order 1280.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2932C211yesmaximal, characteristic
2#10615002C211yesmaximal, characteristic
3#10602607C211yesmaximal, characteristic
4#10601300C211yesmaximal, characteristic, complemented
5#10600621C211yesmaximal, characteristic, complemented
6#10598204C211yesmaximal, characteristic, complemented
7#10598151C211yesmaximal, characteristic, complemented
8C2×C5×#131—21no—
9C5×#532C2211yescharacteristic
10C2×#4015C2211yescharacteristic
11C5×#435—22no—
12C5×#435—22no—
13C5×#423C2211yescharacteristic
14C5×#408—21no—
15C2×C5×#97C2211yescharacteristic
16#65368C412yescomplemented
17#65359C412yescomplemented
18#65323—22no—
19#65297—22no—
20#65225C2211yescharacteristic
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23#64771—21no—
24#64771—21no—
25#64757—22no—
26#64701—22no—
27#9287—51nomaximal, Sylow
28C2×C5×#41—21no—
29C22×Dic10—21no—
30C5×#131—42no—
31C5×#131—42no—
32C2×C5×M16—22no—
33C2×C5×M16—21no—
34C22×C5×C8—22no—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8D411yescharacteristic
37C5×C4⋊Q8C2×C411yescharacteristic
38C5×#127C2×C411yescharacteristic
39C5×#124—21no—
40C5×#121—21no—
41C5×#121D412yes—
42C4×C5×D4—21no—
43C4×C5×D4D412yes—
44C2×C42×C5C2311yescharacteristic
45C2×C4⋊Dic5—21no—
46C2×C4⋊Dic5—21no—
47C2×C4⋊Dic5—21no—
48#4015—21no—
49#4015—21no—
50#4015—21no—
51#4015C2×C412yes—
52C5×C4⋊C8—21no—
53C5×C4⋊C8D412yes—
54C5×C22⋊C8—24no—
55C5×#97—21no—
56C5×#97—21no—
57#3964—24no—
58#3963—21no—
59#3963—21no—
60C22⋊#168—21no—
61C22⋊#168—21no—
62#3940—24no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4×#168—21no—
66C4×#168C2×C412yes—
67#3227—51no—
68#2932D511yescharacteristic
69#1993—51no—
70#1548—51no—
71#1517—51no—
72#1286—51no—
73#1275—51no—
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C2×C5×Q8—21no—
79C2×C5×D4—22no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4C22⋊C412yes—
83C22×C4×C5—22no—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—41no—
88C22×Dic5—41no—
89C2×Dic10—22no—
90C2×Dic10—41no—
91C2×Dic10—82no—
92C5×M16—44no—
93C5×M16—41no—
94C5×M16—41no—
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—22no—
98C2×C5×C8—21no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—44no—
102C2×C5×C8SD1612yes—
103C5×C4⋊C4—21no—
104C5×C4⋊C4C22⋊C412yes—
105C5×C22⋊C4—22no—
106C5×C22⋊C4—22no—
107C42×C5C22×C411yescharacteristic
108C42×C5C2×D411yescharacteristic
109C42×C5C2×D411yescharacteristic
110C42×C5#4111yescharacteristic
111C4⋊Dic5—22no—
112C4⋊Dic5—22no—
113C4⋊Dic5—41no—
114C4⋊Dic5—41no—
115C4⋊Dic5—41no—
116C4⋊Dic5—41no—
117C2×#168—22no—
118C2×#168—41no—
119C2×#131—21no—
120#532C2×D511yescharacteristic
121C2×C4⋊Q8—51no—
122#498—52no—
123#486—52no—
124#481—102no—
125#476—102no—
126#435—22no—
127#435—22no—
128#431—51no—
129#431—51no—
130#423C2×D511yescharacteristic
131#408—21no—
132C2×#97C2×D511yescharacteristic
133#382—51no—
134#340—101no—
135#340—101no—
136#333—102no—
137#327—102no—
138C23×C5—22no—
139C23×C5#12111yescharacteristic
140C5×Q8—41no—
141C5×Q8—41no—
142C5×D4—42no—
143C5×D4—42no—
144C5×D4—42no—
145C5×D4—41no—
146C5×D4—41no—
147C5×D4—81no—
148C2×C4×C5—22no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5C2×C22⋊C411yescharacteristic
154C2×C4×C5C4×D411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5#12011yescharacteristic
157C2×C4×C5#12111yescharacteristic
158C2×C4×C5#12311yescharacteristic
159C2×C4×C5C2×SD1611yescharacteristic
160C2×C4×C5#13511yescharacteristic
161C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C5#13711yescharacteristic
163C2×Dic5—42no—
164C2×Dic5—82no—
165C2×Dic5—81no—
166C2×Dic5—81no—
167C2×Dic5—81no—
168Dic10—82no—
169Dic10—82no—
170C5×C8—22no—
171C5×C8—42no—
172C5×C8—41no—
173#168—42no—
174#168—81no—
175C2×#41—21no—
176C22×Q8—101no—
177#131—42no—
178#131—42no—
179C2×M16—22no—
180C2×M16—21no—
181C22×C8—22no—
182C22×C8C22⋊D511yescharacteristic
183C22×C8C22⋊D511yescharacteristic
184C4⋊Q8—52no—
185C4⋊Q8—101no—
186C4⋊Q8—101no—
187C4⋊Q8—101no—
188C4⋊Q8C4×D511yescharacteristic
189#127C4×D511yescharacteristic
190#124—21no—
191#121—21no—
192#121D2012yes—
193C4×D4—21no—
194C4×D4C22⋊D512yes—
195C2×C4⋊C4—101no—
196C2×C4⋊C4—101no—
197C2×C4⋊C4—101no—
198C2×C42C22×D511yescharacteristic
199#106—104no—
200C4⋊C8—21no—
201C4⋊C8—101no—
202C4⋊C8—101no—
203C4⋊C8C22⋊D512yes—
204#102—104no—
205C22⋊C8—24no—
206C22⋊C8—101no—
207C22⋊C8—101no—
208#97—21no—
209#97—21no—
210C4×C8—52no—
211C4×C8—101no—
212#95—101no—
213#95—101no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—42no—
217C22×C5—42no—
218C22×C5—42no—
219C22×C5#38611yescharacteristic
220C22×C5#46111yescharacteristic
221C22×C5#46311yescharacteristic
222C4×C5—21no—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—42no—
227C4×C5C4×SD1611yescharacteristic
228C4×C5#44011yescharacteristic
229C4×C5#45011yescharacteristic
230C4×C5#45211yescharacteristic
231Dic5—82no—
232Dic5—161no—
233#41—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×Q8—102no—
239C2×Q8—201no—
240C2×Q8—402no—
241C2×D4—22no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4#68512yes—
245C22×C4—22no—
246C22×C4—201no—
247C22×C4—201no—
248C22×C4C2×D2011yescharacteristic
249C22×C4#70911yescharacteristic
250C22×C4C2×C22⋊D511yescharacteristic
251M16—44no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—44no—
261C2×C8—102no—
262C2×C8—201no—
263C2×C8#68712yes—
264C4⋊C4—21no—
265C4⋊C4—102no—
266C4⋊C4—102no—
267C4⋊C4—201no—
268C4⋊C4—201no—
269C4⋊C4—201no—
270C4⋊C4—201no—
271C4⋊C4#68512yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42C2×C4×D511yescharacteristic
275C42#70911yescharacteristic
276C42C2×C22⋊D511yescharacteristic
277C42C2×C22⋊D511yescharacteristic
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—82no—
281C2×C5#187711yescharacteristic
282C2×C5#190311yescharacteristic
283C2×C5#190911yescharacteristic
284C23—22no—
285C23#407611yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—402no—
289Q8—402no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—81no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—202no—
302C2×C4—402no—
303C2×C4—401no—
304C2×C4—401no—
305C2×C4—401no—
306C2×C4C2×#68511yescharacteristic
307C2×C4C4×C22⋊D511yescharacteristic
308C2×C4C4×C22⋊D511yescharacteristic
309C2×C4#407511yescharacteristic
310C2×C4#407611yescharacteristic
311C2×C4#407811yescharacteristic
312C2×C4C2×#68711yescharacteristic
313C2×C4#409611yescharacteristic
314C2×C4#409711yescharacteristic
315C2×C4#409911yescharacteristic
316C8—22no—
317C8—42no—
318C8—41no—
319C8—202no—
320C8—401no—
321C5#928711yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#6530511yescharacteristic
328C22#6530811yescharacteristic
329C22#6550211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—402no—
336C4—801no—
337C4C4×#68711yescharacteristic
338C4#6530711yescharacteristic
339C4#6550711yescharacteristic
340C4#6552811yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1060240511yescharacteristic
345C2#1060281611yescharacteristic
346C2#1060281711yescharacteristic
subgroupG/H
centerC22#65502
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2932C2
socleC22×C5#386
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#2932D5
hypocenterC5#9287
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
4. #10601300C2semidirect
5. #10600621C2semidirect
6. #10598204C2semidirect
7. #10598151C2semidirect
16. #65368C4semidirect
17. #65359C4semidirect
321. C5#9287semidirect

Maximal subgroups

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

subgroupindex
C5×#29322
#106150022
#106026072
#106013002
#106006212
#105982042
#105981512
#92875