Finite Group Databasebeta

← #12083245

Subgroups — #12083245

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C8×#41C211yesmaximal, characteristic
2#10614266C212yesmaximal
3#10610173C211yesmaximal, characteristic, complemented
4#10601738C211yesmaximal, characteristic, complemented
5#10601737C211yesmaximal, characteristic, complemented
6#10601736C212yesmaximal, complemented
7#10601646C211yesmaximal, characteristic, complemented
8#10601645C211yesmaximal, characteristic, complemented
9#10601644C212yesmaximal, complemented
10#10601574C212yesmaximal, complemented
11#10600525C211yesmaximal, characteristic, complemented
12C4×C5×#41C2211yescharacteristic
13#65804C2212yes—
14C5×C8×Q8C2211yescharacteristic
15C5×C8×Q8C2211yescharacteristic
16C5×C8×D4—21no—
17C5×C8×D4—21no—
18C5×C8×D4C2211yescharacteristic
19C5×C8×D4C2211yescharacteristic
20C5×#431—21no—
21C5×#431C2211yescharacteristic
22C2×C4×C5×C8—21no—
23C2×C4×C5×C8C2211yescharacteristic
24#65528—22no—
25#65395—21no—
26#65395—21no—
27#65320C2212yes—
28#65319—22no—
29#65310C2212yes—
30#65308C2212yes—
31#65307—22no—
32#65297C2212yes—
33#65285—22no—
34#65215C2212yes—
35#64972—21no—
36#64972—21no—
37#64971C2211yescharacteristic
38#64971C2211yescharacteristic
39#64969C2212yes—
40#64706C2212yes—
41#64706C2212yes—
42#64701C2212yes—
43#64701C2212yes—
44#64678C2211yescharacteristic
45#64678C2211yescharacteristic
46#64677C2212yes—
47#19273—51nomaximal, Sylow
48C2×C5×#41D411yescharacteristic
49C22×C5×C8—21no—
50C22×C5×C8—21no—
51C22×C5×C8D411yescharacteristic
52C22×C5×C8D411yescharacteristic
53C4×C5×Q8D411yescharacteristic
54C4×C5×Q8C2311yescharacteristic
55C4×C5×D4—21no—
56C4×C5×D4—21no—
57C4×C5×D4D411yescharacteristic
58C4×C5×D4C2311yescharacteristic
59C5×#117—21no—
60C5×#117D411yescharacteristic
61C2×C42×C5—21no—
62C2×C42×C5C2311yescharacteristic
63C2×#689—22no—
64C2×#687—22no—
65#4072—22no—
66#4070—22no—
67#4070—22no—
68#4016—22no—
69#4015C2312yes—
70#4015C2312yes—
71C4×Dic10—22no—
72C4×Dic10—22no—
73C5×C4⋊C8—21no—
74C5×C4⋊C8—21no—
75C5×C4⋊C8C2311yescharacteristic
76C5×C4⋊C8C2311yescharacteristic
77C5×C22⋊C8—21no—
78C5×C22⋊C8—21no—
79C5×C22⋊C8—21no—
80C4×C5×C8—21no—
81C4×C5×C8—21no—
82C4×C5×C8—21no—
83C4×C5×C8D411yescharacteristic
84C4×C5×C8D411yescharacteristic
85C4×C5×C8C2311yescharacteristic
86C4×C5×C8C2311yescharacteristic
87#3967—22no—
88#3964—22no—
89C22⋊#168—22no—
90#3950—21no—
91#3950—21no—
92#3950—21no—
93#3950—21no—
94#3949—22no—
95#3949—22no—
96#3942—22no—
97#3942—22no—
98#3940—22no—
99#3939—22no—
100C4⋊#168C2312yes—
101C4⋊#168C2312yes—
102#3935—22no—
103#3160—51no—
104#3116—52no—
105C8×#41D511yescharacteristic
106#1676—51no—
107#1675—51no—
108#1674—51no—
109#1673—51no—
110#1672—52no—
111#1671—52no—
112#1568—51no—
113#1554—52no—
114C5×#41—22no—
115C5×#41—22no—
116C2×C5×Q8C2×D411yescharacteristic
117C2×C5×D4—21no—
118C2×C5×D4C2×D411yescharacteristic
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5C2×D411yescharacteristic
123C22×C4×C5C2×D411yescharacteristic
124C22×C4×C5#4111yescharacteristic
125C2×Dic10—22no—
126C2×Dic10—22no—
127C2×C5×C8—22no—
128C2×C5×C8—22no—
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C2×C5×C8—42no—
132C2×C5×C8—42no—
133C2×C5×C8C2×D411yescharacteristic
134C2×C5×C8C2×D411yescharacteristic
135C2×C5×C8C2×D411yescharacteristic
136C2×C5×C8C2×D411yescharacteristic
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4C2×D411yescharacteristic
140C5×C4⋊C4C2×D411yescharacteristic
141C5×C22⋊C4—21no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5—21no—
145C42×C5—21no—
146C42×C5—21no—
147C42×C5C2×D411yescharacteristic
148C42×C5C2×D411yescharacteristic
149C42×C5#4111yescharacteristic
150C42×C5C2411yescharacteristic
151C22⋊Dic5—42no—
152#689—44no—
153#687—44no—
154C4⋊Dic5—22no—
155C4⋊Dic5—22no—
156C4⋊Dic5—22no—
157C4⋊Dic5—22no—
158#683—42no—
159#683—42no—
160C4×Dic5—42no—
161C2×#168—22no—
162C2×#168—22no—
163#533—52no—
164C4×#41C2×D511yescharacteristic
165#500—51no—
166#500—51no—
167#499—101no—
168#499—101no—
169#498—52no—
170#485—102no—
171#477—52no—
172#476—52no—
173#462—52no—
174#461—52no—
175#452—102no—
176C8×Q8C2×D511yescharacteristic
177C8×Q8C2×D511yescharacteristic
178#441—102no—
179#440—102no—
180C8×D4—21no—
181C8×D4—21no—
182C8×D4C2×D511yescharacteristic
183C8×D4C2×D511yescharacteristic
184#432—52no—
185#431—21no—
186#431C2×D511yescharacteristic
187#427—101no—
188#427—101no—
189C2×C4×C8—21no—
190C2×C4×C8C2×D511yescharacteristic
191#335—51no—
192#335—51no—
193#334—52no—
194#333—52no—
195#333—52no—
196#332—52no—
197#332—52no—
198C23×C5—21no—
199C23×C5#12111yescharacteristic
200C5×Q8—21no—
201C5×Q8#13512yes—
202C5×D4—24no—
203C5×D4—21no—
204C5×D4#13512yes—
205C2×C4×C5—24no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—41no—
214C2×C4×C5—42no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5#12111yescharacteristic
218C2×C4×C5#12111yescharacteristic
219C2×C4×C5#12111yescharacteristic
220C2×C4×C5C22×D411yescharacteristic
221C2×C4×C5C22×D411yescharacteristic
222C2×C4×C5C2×#4111yescharacteristic
223C2×Dic5—42no—
224C2×Dic5—42no—
225Dic10—42no—
226Dic10—42no—
227Dic10—82no—
228C5×C8—21no—
229C5×C8—21no—
230C5×C8—41no—
231C5×C8—41no—
232C5×C8#13712yes—
233C5×C8#13712yes—
234#168—42no—
235#168—42no—
236C2×#41D2011yescharacteristic
237C2×Q16—102no—
238C2×SD16—102no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8C22⋊D511yescharacteristic
242C22×C8C22⋊D511yescharacteristic
243C4⋊Q8—52no—
244C4⋊Q8—52no—
245#125—102no—
246C22⋊Q8—102no—
247C22⋊Q8—102no—
248C4×Q8—102no—
249C4×Q8—102no—
250C4×Q8D2011yescharacteristic
251C4×Q8C22×D511yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C4×D4D2011yescharacteristic
255C4×D4C22×D511yescharacteristic
256#117—21no—
257#117—102no—
258#117D2011yescharacteristic
259C2×C42—21no—
260C2×C42C22×D511yescharacteristic
261#107—101no—
262#107—101no—
263#107—101no—
264#107—101no—
265#107—102no—
266#106—102no—
267#106—102no—
268#106—102no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—52no—
272C4⋊C8—52no—
273C4⋊C8C22×D511yescharacteristic
274C4⋊C8C22×D511yescharacteristic
275#103—102no—
276#103—102no—
277#103—102no—
278#102—102no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—102no—
283#97—102no—
284C4×C8—21no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8C22⋊D511yescharacteristic
288C4×C8C22⋊D511yescharacteristic
289C4×C8C22×D511yescharacteristic
290C4×C8C22×D511yescharacteristic
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—22no—
294C22×C5—21no—
295C22×C5—41no—
296C22×C5—41no—
297C22×C5C2×#12111yescharacteristic
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—22no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—41no—
304C4×C5—41no—
305C4×C5C2×#13511yescharacteristic
306C4×C5C2×#13511yescharacteristic
307C4×C5C2×#13711yescharacteristic
308C4×C5C2×#13711yescharacteristic
309Dic5—82no—
310Dic5—82no—
311#41—22no—
312#41—22no—
313C2×Q8—102no—
314C2×Q8—102no—
315C2×Q8C2×D2011yescharacteristic
316C2×D4—21no—
317C2×D4C2×D2011yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4C2×D2011yescharacteristic
322C22×C4#70911yescharacteristic
323C22×C4C2×C22⋊D511yescharacteristic
324Q16—204no—
325SD16—204no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—102no—
333C2×C8—102no—
334C2×C8C2×C22⋊D511yescharacteristic
335C2×C8C2×C22⋊D511yescharacteristic
336C2×C8C2×C22⋊D511yescharacteristic
337C2×C8C2×C22⋊D511yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—102no—
341C4⋊C4—102no—
342C4⋊C4—102no—
343C4⋊C4—102no—
344C4⋊C4—202no—
345C4⋊C4—202no—
346C4⋊C4C2×D2011yescharacteristic
347C4⋊C4C2×D2011yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—202no—
352C42—21no—
353C42—21no—
354C42—21no—
355C42—202no—
356C42C2×D2011yescharacteristic
357C42#70911yescharacteristic
358C42C2×C22⋊D511yescharacteristic
359C42C23×D511yescharacteristic
360C2×C5—41no—
361C2×C5—42no—
362C2×C5#303911yescharacteristic
363C2×C5#305011yescharacteristic
364C2×C5#306711yescharacteristic
365C23—21no—
366C23#407611yescharacteristic
367Q8—21no—
368Q8—202no—
369Q8—202no—
370Q8—402no—
371Q8#405012yes—
372D4—24no—
373D4—21no—
374D4#405012yes—
375C2×C4—24no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—202no—
388C2×C4—202no—
389C2×C4#407611yescharacteristic
390C2×C4#407611yescharacteristic
391C2×C4#407611yescharacteristic
392C2×C4C22×D2011yescharacteristic
393C2×C4C2×#70911yescharacteristic
394C2×C4C22×C22⋊D511yescharacteristic
395C8—21no—
396C8—21no—
397C8—41no—
398C8—41no—
399C8—202no—
400C8—202no—
401C8#409712yes—
402C8#409712yes—
403C5#1927311yescharacteristic, complemented, Sylow
404C22—21no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22C2×#407611yescharacteristic
411C4—21no—
412C4—22no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—402no—
419C4—402no—
420C4C2×#405011yescharacteristic
421C4C2×#405011yescharacteristic
422C4C2×#409711yescharacteristic
423C4C2×#409711yescharacteristic
424C2—41no—
425C2—42no—
426C2#1061426411yescharacteristic
427C2#1061547311yescharacteristic
428C2#1061553611yescharacteristic
subgroupG/H
centerC22C2×#4076
commutator, cosocleC42×C5C24
FrattiniC42C23×D5
FittingC5×C8×#41C2
socleC22×C5C2×#121
prime radicalC2×C5×#41D4
hypercenterC8×#41D5
hypocenterC5#19273
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
3. #10610173C2semidirect
4. #10601738C2semidirect
5. #10601737C2semidirect
6. #10601736C2semidirect
7. #10601646C2semidirect
8. #10601645C2semidirect
9. #10601644C2semidirect
10. #10601574C2semidirect
11. #10600525C2semidirect
403. C5#19273semidirect

Maximal subgroups

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

subgroupindex
C5×C8×#412
#106142662
#106101732
#106017382
#106017372
#106017362
#106016462
#106016452
#106016442
#106015742
#106005252
#192735