Finite Group Databasebeta

← #12016693

Subgroups — #12016693

Order 1280.

510 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3050C211yesmaximal, characteristic
2C22×#3944C211yesmaximal, characteristic, complemented
3C2×#64786C212yesmaximal, complemented
4#10602763C211yesmaximal, characteristic, complemented
5#10598217C212yesmaximal, complemented
6C2×C5×#135C2211yescharacteristic
7C23×C5×C8C2211yescharacteristic
8C5×#525—21no—
9C5×#467C411yescharacteristic, complemented
10C5×#467C411yescharacteristic, complemented
11C5×#466C411yescharacteristic, complemented
12C5×#466C411yescharacteristic, complemented
13C5×#465—21no—
14C5×#465—21no—
15C5×#427C2211yescharacteristic
16C5×#416—21no—
17#65501—21no—
18C2×#3949C2212yes—
19C2×#3944—24no—
20C2×#3944—21no—
21C2×#3944C2212yes—
22C22×#672—21no—
23#64786—24no—
24#64771—21no—
25#13065—51nomaximal, Sylow
26C2×C5×#41—21no—
27C23×C4×C5D411yescharacteristic
28C5×#135—22no—
29C5×#135—22no—
30C2×C5×Q16C2×C411yescharacteristic
31C2×C5×SD16—21no—
32C2×C5×D8C2×C411yescharacteristic
33C22×C5×C8—22no—
34C22×C5×C8—22no—
35C22×C5×C8C2×C411yescharacteristic
36C22×C5×C8C2×C411yescharacteristic
37C22×C5×C8D411yescharacteristic
38C22×C5×C8D411yescharacteristic
39C22×C5×C8D411yescharacteristic
40C22×C5×C8C2311yescharacteristic
41C5×#123—41no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×#121—21no—
45C5×#121—21no—
46C5×#120—41no—
47C4×C5×D4—41no—
48C4×C5×D4—41no—
49C5×#117—21no—
50C2×C22⋊Dic5—41no—
51C2×C4⋊Dic5—22no—
52C5×#107C2×C411yescharacteristic
53C5×#107C2×C411yescharacteristic
54C5×#106—21no—
55C5×#103—21no—
56C5×#103—21no—
57C5×#102—21no—
58C5×#102—21no—
59#3963—41no—
60#3949—22no—
61#3949—22no—
62#3944—24no—
63#3944—22no—
64#3944D414yescomplemented
65C2×#672—24no—
66C2×#672—22no—
67C22×M32—51no—
68#3050D511yescharacteristic
69C2×#360—52no—
70#1807—51no—
71#1386—52no—
72C24×C5D811yescharacteristic
73C5×#41—42no—
74C5×#41—42no—
75C2×C5×Q8—21no—
76C2×C5×D4—21no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—41no—
83C22×C4×C5C22⋊C411yescharacteristic
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5D811yescharacteristic
86C22×C4×C5SD1611yescharacteristic
87C22×C4×C5SD1611yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×Dic5—42no—
90C5×Q16—22no—
91C5×SD16—41no—
92C5×SD16—41no—
93C5×D8—22no—
94C2×C5×C8—22no—
95C2×C5×C8—22no—
96C2×C5×C8—22no—
97C2×C5×C8—21no—
98C2×C5×C8—21no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8C22⋊C411yescharacteristic
102C2×C5×C8C22⋊C411yescharacteristic
103C2×C5×C8C22×C411yescharacteristic
104C2×C5×C8C2×D412yes—
105C2×C5×C8C2×D411yescharacteristic
106C2×C5×C8#4112yes—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C22⋊C4—41no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—41no—
116C42×C5—41no—
117C22⋊Dic5—82no—
118C4⋊Dic5—42no—
119C4⋊Dic5—42no—
120#672—24no—
121C2×#135C2×D511yescharacteristic
122C23×C8C2×D511yescharacteristic
123#525—21no—
124C2×M32—52no—
125C2×M32—104no—
126C2×M32—101no—
127C22×C16—101no—
128#467Dic511yescharacteristic, complemented
129#467Dic511yescharacteristic, complemented
130#466Dic511yescharacteristic, complemented
131#466Dic511yescharacteristic, complemented
132#465—21no—
133#465—21no—
134#427C2×D511yescharacteristic
135C2×#106—52no—
136#416—21no—
137#380—101no—
138#360—104no—
139#340—101no—
140C23×C5—22no—
141C23×C5—22no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5#10211yescharacteristic
145C23×C5#10211yescharacteristic
146C23×C5C2×D811yescharacteristic
147C5×Q8—41no—
148C5×Q8—41no—
149C5×D4—41no—
150C5×D4—41no—
151C5×D4—82no—
152C5×D4—82no—
153C5×D4—82no—
154C2×C4×C5—22no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—22no—
160C2×C4×C5—22no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—82no—
165C2×C4×C5#10211yescharacteristic
166C2×C4×C5#10211yescharacteristic
167C2×C4×C5C2×C22⋊C411yescharacteristic
168C2×C4×C5#12112yes—
169C2×C4×C5C2×SD1611yescharacteristic
170C2×C4×C5#13512yes—
171C2×Dic5—82no—
172C2×Dic5—82no—
173C2×Dic5—82no—
174C5×C8—21no—
175C5×C8—21no—
176C5×C8C4×D412yes—
177C5×C8#12011yescharacteristic
178C5×C8#12311yescharacteristic
179C2×#41—21no—
180C23×C4C22⋊D511yescharacteristic
181#135—22no—
182#135—22no—
183C2×Q16C2×Dic511yescharacteristic
184C2×SD16—21no—
185C2×D8C2×Dic511yescharacteristic
186C22×C8—22no—
187C22×C8—22no—
188C22×C8C2×Dic511yescharacteristic
189C22×C8C2×Dic511yescharacteristic
190C22×C8C22⋊D511yescharacteristic
191C22×C8C22⋊D511yescharacteristic
192C22×C8C22⋊D511yescharacteristic
193C22×C8C22×D511yescharacteristic
194#123—41no—
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197#121—21no—
198#121—21no—
199#120—41no—
200C4×D4—41no—
201C4×D4—41no—
202#117—21no—
203C2×C4⋊C4—102no—
204C2×C22⋊C4—201no—
205M32—54no—
206M32—104no—
207M32—102no—
208C2×C16—104no—
209C2×C16—102no—
210#107C2×Dic511yescharacteristic
211#107C2×Dic511yescharacteristic
212#106—21no—
213#106—102no—
214#106—102no—
215#103—21no—
216#103—21no—
217#102—21no—
218#102—21no—
219#95—201no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—44no—
228C22×C5—81no—
229C22×C5—81no—
230C22×C5—81no—
231C22×C5#36012yescomplemented
232C22×C5C2×#10211yescharacteristic
233C22×C5#46612yes—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—81no—
237C4×C5—81no—
238C4×C5—81no—
239C4×C5#38611yescharacteristic
240C4×C5#41611yescharacteristic
241C4×C5#46512yes—
242Dic5—162no—
243C24#68611yescharacteristic
244#41—42no—
245#41—42no—
246C2×Q8—21no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—202no—
255C22×C4#68611yescharacteristic
256C22×C4#68711yescharacteristic
257C22×C4#68711yescharacteristic
258C22×C4C22⋊Dic511yescharacteristic
259C22×C4C22⋊Dic511yescharacteristic
260C22×C4C2×C22⋊D511yescharacteristic
261Q16—22no—
262SD16—41no—
263SD16—41no—
264D8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8C22⋊Dic511yescharacteristic
273C2×C8C22⋊Dic511yescharacteristic
274C2×C8D4×D512yes—
275C2×C8#71112yes—
276C2×C8C22×Dic511yescharacteristic
277C2×C8C2×C22⋊D511yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—202no—
283C4⋊C4—202no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—402no—
290C42—41no—
291C16—104no—
292C2×C5—22no—
293C2×C5—22no—
294C2×C5—41no—
295C2×C5—161no—
296C2×C5#189311yescharacteristic
297C2×C5C2×#36011yescharacteristic
298C2×C5#214511yescharacteristic
299C23—22no—
300C23—22no—
301C23—41no—
302C23—41no—
303C23#396411yescharacteristic
304C23#396411yescharacteristic
305C23C2×#68611yescharacteristic
306Q8—41no—
307Q8—41no—
308D4—41no—
309D4—41no—
310D4—82no—
311D4—82no—
312D4—82no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—82no—
324C2×C4—402no—
325C2×C4—402no—
326C2×C4—402no—
327C2×C4#396411yescharacteristic
328C2×C4#396411yescharacteristic
329C2×C4C2×#68711yescharacteristic
330C2×C4#408512yes—
331C2×C4#409612yes—
332C2×C4C2×C22⋊Dic511yescharacteristic
333C8—21no—
334C8—21no—
335C8D4×Dic512yes—
336C8#408111yescharacteristic
337C8#408311yescharacteristic
338C5#1306511yescharacteristic, complemented, Sylow
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#6478612yescomplemented
351C22#6532712yes—
352C22C2×#396411yescharacteristic
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—802no—
359C4#6533012yes—
360C4#6550911yescharacteristic
361C4#6552211yescharacteristic
362C2—22no—
363C2—22no—
364C2—41no—
365C2—161no—
366C2#1060247411yescharacteristic
367C2C2×#6478611yescharacteristic
368C2#1060286911yescharacteristic
subgroupG/H
centerC22C2×#3964
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
Fitting, prime radicalC5×#3050C2
socleC22×C5C2×#102
cosocleC22×C5×C8C23
hypercenter#3050D5
hypocenterC5#13065
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
2. C22×#3944C2semidirect
3. C2×#64786C2semidirect
4. #10602763C2semidirect
5. #10598217C2semidirect
9. C5×#467C4semidirect
10. C5×#467C4semidirect
11. C5×#466C4semidirect
12. C5×#466C4semidirect
64. #3944D4semidirect
128. #467Dic5semidirect
129. #467Dic5semidirect
130. #466Dic5semidirect
131. #466Dic5semidirect
231. C22×C5#360semidirect
338. C5#13065semidirect
350. C22#64786semidirect

Maximal subgroups

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

subgroupindex
C5×#30502
C22×#39442
C2×#647862
#106027632
#105982172
#130655