Finite Group Databasebeta

← #11997643

Subgroups — #11997643

Order 1280.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#332C211yesmaximal, characteristic
2#10602580C211yesmaximal, characteristic
3#10602571C211yesmaximal, characteristic
4#10601258C211yesmaximal, characteristic
5#10601247C211yesmaximal, characteristic
6#10598194C211yesmaximal, characteristic
7#10598193C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×#3967—21no—
12C2×#3967—21no—
13C2×#3949—21no—
14C2×C8×Dic5—21no—
15#65224C2211yescharacteristic
16C4×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C2×C4×#168C2211yescharacteristic
19C5×#332C414yescomplemented
20#64771—21no—
21#64770—21no—
22#64749—21no—
23#64749—21no—
24#9565—51nomaximal, Sylow
25C22×C5×Q8—21no—
26C22×C5×C8—21no—
27C22×C5×C8—21no—
28C5×C4⋊Q8—21no—
29C5×C4⋊Q8—21no—
30C5×C4⋊Q8—21no—
31C5×C4⋊Q8C2×C412yes—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C42×C5C2311yescharacteristic
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5D411yescharacteristic
39C2×C4⋊Dic5D411yescharacteristic
40C2×C4×Dic5—21no—
41C22×#168—21no—
42C22×#168D411yescharacteristic
43C22×#168D411yescharacteristic
44C5×C4⋊C8—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8C2×C412yes—
47C5×C4⋊C8C2×C412yes—
48#3967—42no—
49#3967—42no—
50#3963—21no—
51#3949—42no—
52C8×Dic5—42no—
53C4⋊#168—21no—
54C4⋊#168—21no—
55C4×#168—21no—
56C4×#168—21no—
57#1990—51no—
58#1981—51no—
59#1948—51no—
60C8×C4⋊C4—51no—
61C2×#332D511yescharacteristic
62#1296—51no—
63#1277—51no—
64C2×C5×Q8—22no—
65C2×C5×Q8—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8—41no—
68C2×C5×Q8—41no—
69C2×C5×Q8—41no—
70C22×C4×C5—41no—
71C22×C4×C5C2×D411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5#4111yescharacteristic
74C22×Dic5—21no—
75C22×Dic5—21no—
76C22×Dic5—41no—
77C2×C5×C8—22no—
78C2×C5×C8—22no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C2×C5×C8—41no—
82C2×C5×C8—41no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C42×C5C22×C411yescharacteristic
88C42×C5#4111yescharacteristic
89C42×C5#4111yescharacteristic
90C42×C5#4111yescharacteristic
91C4⋊Dic5—21no—
92C4⋊Dic5—21no—
93C4⋊Dic5—41no—
94C4⋊Dic5—41no—
95C4⋊Dic5—41no—
96C4⋊Dic5—41no—
97C4⋊Dic5—81no—
98C4⋊Dic5D812yes—
99C4⋊Dic5SD1612yes—
100C4×Dic5—41no—
101C4×Dic5—41no—
102C2×#168—21no—
103C2×#168—21no—
104C2×#168—21no—
105C2×#168—21no—
106C2×#168—21no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168SD1612yes—
111C2×C4⋊Q8C2×D511yescharacteristic
112C2×#106—101no—
113C2×C4⋊C8—51no—
114C2×C4⋊C8C2×D511yescharacteristic
115C2×C4⋊C8C2×D511yescharacteristic
116C2×#103—101no—
117C2×#103—101no—
118C2×C4×C8—51no—
119C2×C4×C8—101no—
120#384—51no—
121C4×C4⋊C4—51no—
122#340—101no—
123#340—101no—
124#340—101no—
125#336—101no—
126#332Dic514yescomplemented
127C23×C5#12111yescharacteristic
128C5×Q8—42no—
129C5×Q8—42no—
130C5×Q8—81no—
131C5×Q8—81no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—42no—
135C2×C4×C5—81no—
136C2×C4×C5—81no—
137C2×C4×C5#11711yescharacteristic
138C2×C4×C5C4×D411yescharacteristic
139C2×C4×C5C4×D411yescharacteristic
140C2×C4×C5#12311yescharacteristic
141C2×C4×C5#12411yescharacteristic
142C2×C4×C5#12611yescharacteristic
143C2×C4×C5C2×D811yescharacteristic
144C2×C4×C5C2×SD1611yescharacteristic
145C2×C4×C5C2×SD1611yescharacteristic
146C2×C4×C5#13511yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×C4×C5#13511yescharacteristic
149C2×C4×C5#13711yescharacteristic
150C2×C4×C5#13711yescharacteristic
151C2×Dic5—22no—
152C2×Dic5—22no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—81no—
158C2×Dic5—81no—
159C2×Dic5—81no—
160C5×C8—42no—
161C5×C8—42no—
162#168—22no—
163#168—41no—
164#168—81no—
165C22×Q8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—51no—
169C22×C8—51no—
170C22×C8—101no—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8C2×Dic512yes—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C42—101no—
183C2×C42C22×D511yescharacteristic
184#106—202no—
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—101no—
188C4⋊C8—101no—
189C4⋊C8C2×Dic512yes—
190C4⋊C8C2×Dic512yes—
191#103—202no—
192#103—202no—
193C4×C8—101no—
194C4×C8—101no—
195C4×C8—202no—
196#95—101no—
197C22×C5#38811yescharacteristic
198C22×C5#46111yescharacteristic
199C22×C5#46411yescharacteristic
200C22×C5#46511yescharacteristic
201C22×C5#46611yescharacteristic
202C22×C5#47111yescharacteristic
203C22×C5#47311yescharacteristic
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—82no—
207C4×C5C4×D811yescharacteristic
208C4×C5C4×SD1611yescharacteristic
209C4×C5C4×SD1611yescharacteristic
210C4×C5#44111yescharacteristic
211C4×C5#48311yescharacteristic
212C4×C5#48511yescharacteristic
213C4×C5#48611yescharacteristic
214C4×C5#48811yescharacteristic
215Dic5—42no—
216Dic5—42no—
217Dic5—161no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C22×C4—41no—
225C22×C4—101no—
226C22×C4—101no—
227C22×C4—201no—
228C22×C4#70911yescharacteristic
229C22×C4D4×D511yescharacteristic
230C22×C4D4×D511yescharacteristic
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—52no—
238C2×C8—101no—
239C2×C8—101no—
240C2×C8—101no—
241C2×C8—101no—
242C2×C8—101no—
243C2×C8—201no—
244C2×C8—201no—
245C2×C8—201no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—52no—
251C4⋊C4—52no—
252C4⋊C4—101no—
253C4⋊C4—101no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—401no—
259C42—201no—
260C42—201no—
261C42#70911yescharacteristic
262C42#71111yescharacteristic
263C42#71111yescharacteristic
264C42C22×Dic511yescharacteristic
265C2×C5#167111yescharacteristic
266C2×C5#167311yescharacteristic
267C2×C5#168011yescharacteristic
268C2×C5#168211yescharacteristic
269C2×C5#192711yescharacteristic
270C2×C5#193011yescharacteristic
271C2×C5#193411yescharacteristic
272C23#403011yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—81no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—102no—
283C2×C4—102no—
284C2×C4—201no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4—201no—
288C2×C4—401no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4#402511yescharacteristic
292C2×C4#402911yescharacteristic
293C2×C4#403111yescharacteristic
294C2×C4D5×D811yescharacteristic
295C2×C4#405811yescharacteristic
296C2×C4D5×SD1611yescharacteristic
297C2×C4D5×SD1611yescharacteristic
298C2×C4#406211yescharacteristic
299C2×C4#406211yescharacteristic
300C2×C4#406411yescharacteristic
301C2×C4#406411yescharacteristic
302C2×C4#407211yescharacteristic
303C2×C4D4×Dic511yescharacteristic
304C2×C4D4×Dic511yescharacteristic
305C8—42no—
306C8—42no—
307C8—102no—
308C8—201no—
309C8—401no—
310C5#956511yescharacteristic, complemented, Sylow
311C22#6504311yescharacteristic
312C22#6504411yescharacteristic
313C22#6506411yescharacteristic
314C22#6506711yescharacteristic
315C22#6508711yescharacteristic
316C22#6510711yescharacteristic
317C22#6524011yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—202no—
322C4—202no—
323C4—801no—
324C4#6504911yescharacteristic
325C4#6505711yescharacteristic
326C4#6509411yescharacteristic
327C4#6510411yescharacteristic
328C4D8×Dic511yescharacteristic
329C4SD16×Dic511yescharacteristic
330C4SD16×Dic511yescharacteristic
331C4#6547311yescharacteristic
332C2#1059923511yescharacteristic
333C2#1059923611yescharacteristic
334C2#1059926211yescharacteristic
335C2#1059926311yescharacteristic
336C2#1060089911yescharacteristic
337C2#1060097811yescharacteristic
338C2#1060101611yescharacteristic
subgroupG/H
centerC23#4030
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#332C2
socle, prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenterC2×#332D5
hypocenterC5#9565
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
19. C5×#332C4semidirect
126. #332Dic5semidirect
310. C5#9565semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3322
#106025802
#106025712
#106012582
#106012472
#105981942
#105981932
#95655