Finite Group Databasebeta

← #12254175

Subgroups — #12254175

Order 1280.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2913C211yesmaximal, characteristic, complemented
2#10615532C211yesmaximal, characteristic
3#10602797C211yesmaximal, characteristic, complemented
4#10601448C212yesmaximal, complemented
5#10601446C212yesmaximal, complemented
6#10601444C211yesmaximal, characteristic, complemented
7#10601442C211yesmaximal, characteristic, complemented
8#10601395C212yesmaximal, complemented
9#10601393C212yesmaximal, complemented
10#10601391C211yesmaximal, characteristic, complemented
11C2×#64710C211yesmaximal, characteristic, complemented
12C2×C5×#131C2211yescharacteristic
13C5×#520—21no—
14#66167—21no—
15C2×#4050C2211yescharacteristic
16C5×#428—21no—
17C5×#428—22no—
18C5×#427C2211yescharacteristic
19C5×#427C2212yes—
20C2×C5×#107C2211yescharacteristic
21C2×C5×#107C2212yes—
22#65423—22no—
23#65422—21no—
24#65405C2212yes—
25#65404C2212yes—
26C2×#3950C2211yescharacteristic
27C2×#3944C2211yescharacteristic
28C22×#672C2211yescharacteristic
29C22⋊#672C2212yes—
30C22⋊#672C2212yes—
31#64712C2212yes—
32#64712C2211yescharacteristic
33#64712C2211yescharacteristic
34#64711C2212yes—
35#64711C2211yescharacteristic
36#64711C2211yescharacteristic
37#64710C2212yes—
38#64710C2212yes—
39#64710C2212yes—
40#64709C2212yes—
41#33653—51nomaximal, Sylow
42C2×C5×#41D411yescharacteristic
43C2×#709—21no—
44C5×#131—22no—
45C5×#131—22no—
46C2×C5×M16D411yescharacteristic
47C2×C5×M16D412yes—
48C22×C5×C8C2312yes—
49C22×C5×C8C2311yescharacteristic
50C4×C5×Q8—41no—
51C4×C5×D4—41no—
52C4×C5×D4—42no—
53C5×#117—22no—
54C5×#117—21no—
55C2×C5×C4⋊C4—22no—
56C2×C5×C4⋊C4—21no—
57#4092—41no—
58#4085—42no—
59#4084—41no—
60#4076—22no—
61C2×C4⋊Dic5—21no—
62#4070—22no—
63C2×Dic20C2311yescharacteristic
64#4050—22no—
65#4050—22no—
66C2×D40C2311yescharacteristic
67C2×#677—21no—
68C5×#107—22no—
69C5×#107—21no—
70C5×#107C2312yes—
71C5×#107C2311yescharacteristic
72C5×#107C2311yescharacteristic
73C5×#106—22no—
74C5×#106—21no—
75#3953—22no—
76#3950—21no—
77#3950C2312yes—
78#3948—22no—
79#3944—22no—
80C2×#672—22no—
81C2×#672C2311yescharacteristic
82C2×#672C2311yescharacteristic
83C2×#672C2312yes—
84#3061—51no—
85#2913D511yescharacteristic, complemented
86#2237—52no—
87#2235—52no—
88#2234—52no—
89#2233—52no—
90#2159—51no—
91C2×#367—51no—
92#2139—51no—
93#2138—51no—
94#2113—51no—
95C5×#41—22no—
96C5×#41—22no—
97C2×C5×Q8D811yescharacteristic
98C2×C5×D4D811yescharacteristic
99C2×C5×D4D812yes—
100C22×C4×C5—42no—
101C22×C4×C5—41no—
102C22×C4×C5C2×D412yes—
103C22×C4×C5C2×D411yescharacteristic
104C2×C22⋊D5—41no—
105C2×C22⋊D5—42no—
106C22×Dic5—41no—
107#709—42no—
108#709—42no—
109C2×D20—21no—
110C2×C4×D5—41no—
111C2×Dic10—21no—
112C5×M16—22no—
113C5×M16—24no—
114C2×C5×C8—22no—
115C2×C5×C8—22no—
116C2×C5×C8C2×D412yes—
117C2×C5×C8C2×D411yescharacteristic
118C2×C5×C8#4112yes—
119C2×C5×C8#4112yes—
120C2×C5×C8C2411yescharacteristic
121C5×C4⋊C4—21no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—42no—
125C5×C4⋊C4—41no—
126C5×C22⋊C4—42no—
127C5×C22⋊C4—41no—
128C42×C5—42no—
129C42×C5—41no—
130C22⋊Dic5—42no—
131#685—42no—
132C4⋊Dic5—22no—
133C4⋊Dic5—41no—
134#683—42no—
135Dic20—21no—
136Dic20—21no—
137D40—21no—
138D40—21no—
139#677—42no—
140#672—21no—
141#672—21no—
142#672—22no—
143C2×#135—51no—
144C2×#131C2×D511yescharacteristic
145#537—101no—
146#520—21no—
147C2×M32—51no—
148C22×C16—51no—
149#468—102no—
150#467—52no—
151#466—52no—
152#428—21no—
153#428—22no—
154#427C2×D511yescharacteristic
155#427C2×D512yes—
156C2×#107—51no—
157C2×#107C2×D511yescharacteristic
158C2×#107C2×D512yes—
159#417—101no—
160#367—52no—
161#367—52no—
162#367—52no—
163#366—52no—
164#358—51no—
165#358—51no—
166#358—52no—
167#357—51no—
168#357—51no—
169#357—52no—
170C22⋊C16—52no—
171C22⋊C16—52no—
172C23×C5C2×D812yes—
173C23×C5C2×D811yescharacteristic
174C22×D5—41no—
175C5×Q8—22no—
176C5×D4—24no—
177C5×D4—22no—
178C2×C4×C5—22no—
179C2×C4×C5—22no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—41no—
183C2×C4×C5—161no—
184C2×C4×C5—162no—
185C2×C4×C5#12312yes—
186C2×C4×C5C2×D812yes—
187C2×C4×C5C2×D811yescharacteristic
188C2×C4×C5#13712yes—
189C2×C4×C5C22×D411yescharacteristic
190C22⋊D5—82no—
191C22⋊D5—162no—
192C2×Dic5—41no—
193C2×Dic5—42no—
194C2×Dic5—161no—
195D20—41no—
196D20—41no—
197C4×D5—82no—
198Dic10—41no—
199Dic10—41no—
200C5×C8—22no—
201C5×C8#12312yes—
202C5×C8C2×#4111yescharacteristic
203C5×C8C2×#4111yescharacteristic
204C2×#41—101no—
205C2×#41C22⋊D511yescharacteristic
206#135—102no—
207#135—102no—
208C2×Q16—51no—
209C2×SD16—101no—
210C2×D8—51no—
211#131—22no—
212#131—22no—
213C2×M16C22⋊D511yescharacteristic
214C2×M16C22⋊D512yes—
215C22×C8C22×D512yes—
216C22×C8C22×D511yescharacteristic
217C22⋊Q8—102no—
218C22⋊Q8—201no—
219#121—102no—
220#121—201no—
221#121—202no—
222C4×Q8—41no—
223C4×D4—42no—
224C4×D4—41no—
225#117—22no—
226#117—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—101no—
230M32—102no—
231C2×C16—52no—
232C2×C16—51no—
233C2×C16—51no—
234C2×C16—102no—
235#107—22no—
236#107—21no—
237#107—52no—
238#107—101no—
239#107C22×D511yescharacteristic
240#107C22×D511yescharacteristic
241#107C22×D512yes—
242#106—22no—
243#106—21no—
244#103—102no—
245#102—102no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—22no—
249C22×C5—22no—
250C22×C5—22no—
251C22×C5#48012yes—
252C22×C5C22×D811yescharacteristic
253C2×D5—81no—
254C2×D5—81no—
255C2×D5—81no—
256C4×C5—22no—
257C4×C5—81no—
258C4×C5—82no—
259C4×C5—81no—
260C4×C5#48012yes—
261C4×C5C2×#12311yescharacteristic
262C4×C5C2×#13711yescharacteristic
263Dic5—81no—
264Dic5—82no—
265#41—22no—
266#41—22no—
267#41—202no—
268#41—202no—
269C2×Q8—101no—
270C2×Q8#68611yescharacteristic
271C2×D4—101no—
272C2×D4—201no—
273C2×D4—202no—
274C2×D4#68612yes—
275C2×D4#68611yescharacteristic
276C22×C4—42no—
277C22×C4—41no—
278C22×C4—201no—
279C22×C4—201no—
280C22×C4C2×C22⋊D512yes—
281C22×C4C2×C22⋊D511yescharacteristic
282Q16—101no—
283Q16—101no—
284SD16—202no—
285D8—101no—
286D8—101no—
287M16—22no—
288M16—24no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8#70912yes—
292C2×C8#70912yes—
293C2×C8C2×C22⋊D512yes—
294C2×C8C2×C22⋊D511yescharacteristic
295C2×C8C23×D511yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—102no—
302C4⋊C4—201no—
303C4⋊C4—202no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—202no—
307C22⋊C4—202no—
308C42—42no—
309C42—41no—
310C16—101no—
311C16—101no—
312C16—102no—
313C2×C5—22no—
314C2×C5—42no—
315C2×C5C2×#48011yescharacteristic
316C2×C5#341611yescharacteristic
317C2×C5#341611yescharacteristic
318D5—161no—
319C23—201no—
320C23C2×#68612yes—
321C23C2×#68611yescharacteristic
322Q8—22no—
323Q8—201no—
324Q8—201no—
325D4—24no—
326D4—22no—
327D4—201no—
328D4—201no—
329D4—402no—
330D4—802no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—161no—
337C2×C4—162no—
338C2×C4—202no—
339C2×C4—201no—
340C2×C4—402no—
341C2×C4—801no—
342C2×C4#407512yes—
343C2×C4C2×#68612yes—
344C2×C4C2×#68611yescharacteristic
345C2×C4#408812yes—
346C2×C4C22×C22⋊D511yescharacteristic
347C8—22no—
348C8#407512yes—
349C8C2×#70911yescharacteristic
350C8C2×#70911yescharacteristic
351C5#3365311yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—401no—
358C22—401no—
359C22—401no—
360C22#6525612yes—
361C22C22×#68611yescharacteristic
362C4—22no—
363C4—82no—
364C4—81no—
365C4—81no—
366C4—401no—
367C4—402no—
368C4#6525612yes—
369C4C2×#407511yescharacteristic
370C4C2×#408811yescharacteristic
371C2—22no—
372C2—42no—
373C2—801no—
374C2C2×#6525611yescharacteristic
375C2#1061573911yescharacteristic
376C2#1061574711yescharacteristic
subgroupG/H
centerC22C22×#686
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
FittingC5×#2913C2
socleC22×C5C22×D8
prime radical#10615532C2
hypercenter#2913D5
hypocenterC5#33653
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2913

Complements

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

NH ≅ G/Ntype
1. C5×#2913C2semidirect
3. #10602797C2semidirect
4. #10601448C2semidirect
5. #10601446C2semidirect
6. #10601444C2semidirect
7. #10601442C2semidirect
8. #10601395C2semidirect
9. #10601393C2semidirect
10. #10601391C2semidirect
11. C2×#64710C2semidirect
85. #2913D5semidirect
351. C5#33653semidirect

Maximal subgroups

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

subgroupindex
C5×#29132
#106155322
#106027972
#106014482
#106014462
#106014442
#106014422
#106013952
#106013932
#106013912
C2×#647102
#336535