Finite Group Databasebeta

← #11995406

Subgroups — #11995406

Order 1280.

510 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3035C211yesmaximal, characteristic
2#10614248C211yesmaximal, characteristic, complemented
3#10602604C211yesmaximal, characteristic, complemented
4#10602595C211yesmaximal, characteristic, complemented
5#10602439C211yesmaximal, characteristic, complemented
6#10598198C211yesmaximal, characteristic, complemented
7#10598195C211yesmaximal, characteristic, complemented
8C2×C5×#135—21no—
9C5×#532C2211yescharacteristic
10C4×C5×#41C2211yescharacteristic
11C5×#464—21no—
12C5×#463—21no—
13C5×#462C411yescharacteristic, complemented
14C5×#461C411yescharacteristic, complemented
15C5×#460C411yescharacteristic, complemented
16C5×#459C411yescharacteristic, complemented
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#416—21no—
19C2×#3969—21no—
20#65313—21no—
21#65301—21no—
22#65300—22no—
23C4×C4⋊Dic5C2211yescharacteristic
24#65214—21no—
25#65214C2211yescharacteristic
26#65213C2211yescharacteristic
27C4×#681—21no—
28C2×C4×#168C2211yescharacteristic
29#64757—22no—
30D4⋊#168—21no—
31D4⋊#168—21no—
32#64752—21no—
33#9210—51nomaximal, Sylow
34C2×C5×#41—21no—
35C2×C5×#41D411yescharacteristic
36C5×#135—42no—
37C5×#135—42no—
38C2×C5×Q16—21no—
39C2×C5×SD16—21no—
40C2×C5×SD16—21no—
41C2×C5×D8—21no—
42C22×C5×C8—21no—
43C5×C4⋊Q8C2×C411yescharacteristic
44C5×#127C2×C411yescharacteristic
45C5×#124—21no—
46C5×#121—21no—
47C5×#121—21no—
48C4×C5×Q8C2×C411yescharacteristic
49C4×C5×Q8D411yescharacteristic
50C4×C5×D4—21no—
51C4×C5×D4—21no—
52C4×C5×D4—21no—
53C4×C5×D4—21no—
54C4×C5×D4C2×C411yescharacteristic
55C4×C5×D4D411yescharacteristic
56C5×#117—21no—
57C5×#117D411yescharacteristic
58C2×C42×C5—21no—
59C2×C42×C5C2311yescharacteristic
60C2×C4⋊Dic5—21no—
61C2×C4×Dic5—21no—
62C2×#681—22no—
63C2×#681—21no—
64C22×#168—21no—
65C5×C4⋊C8—21no—
66C5×C4⋊C8C2×C411yescharacteristic
67C5×C4⋊C8C2×C411yescharacteristic
68C5×#103—21no—
69C5×#103—21no—
70C5×#102—21no—
71C5×#102—21no—
72#3969—42no—
73#3963—21no—
74C22⋊#168—22no—
75C22⋊#168D412yes—
76C4⋊#168—22no—
77C4⋊#168—21no—
78C4⋊#168—21no—
79C4⋊#168—21no—
80#3935—22no—
81C4×#168—21no—
82C4×#168—21no—
83C4×#168D411yescharacteristic
84C4×#168D411yescharacteristic
85#3035D511yescharacteristic
86#2965—51no—
87#1806—51no—
88#1502—51no—
89#1492—51no—
90#1301—51no—
91#1279—51no—
92C5×#41—21no—
93C5×#41—21no—
94C5×#41—21no—
95C5×#41—21no—
96C5×#41—41no—
97C5×#41—41no—
98C5×#41—41no—
99C5×#41—41no—
100C2×C5×Q8—21no—
101C2×C5×Q8C22⋊C411yescharacteristic
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×C5×D4—21no—
106C2×C5×D4—41no—
107C2×C5×D4C22⋊C411yescharacteristic
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—41no—
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5#4111yescharacteristic
115C22×Dic5—41no—
116C5×Q16—42no—
117C5×SD16—42no—
118C5×SD16—42no—
119C5×D8—42no—
120C2×C5×C8—21no—
121C2×C5×C8—21no—
122C2×C5×C8—41no—
123C2×C5×C8—41no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C22⋊C411yescharacteristic
129C5×C4⋊C4C22⋊C411yescharacteristic
130C5×C22⋊C4—21no—
131C5×C22⋊C4—21no—
132C5×C22⋊C4—21no—
133C5×C22⋊C4—41no—
134C5×C22⋊C4—41no—
135C42×C5—21no—
136C42×C5—21no—
137C42×C5—21no—
138C42×C5C22×C411yescharacteristic
139C42×C5C2×D411yescharacteristic
140C42×C5C2×D411yescharacteristic
141C42×C5#4111yescharacteristic
142C4⋊Dic5—22no—
143C4⋊Dic5—41no—
144C4×Dic5—41no—
145C4×Dic5—41no—
146#681—44no—
147#681—41no—
148#681—41no—
149C2×#168—21no—
150C2×#168—21no—
151C2×#168—22no—
152C2×#168—42no—
153C2×#168—41no—
154C2×#135—21no—
155#532C2×D511yescharacteristic
156C4×#41C2×D511yescharacteristic
157#464—21no—
158#463—21no—
159#462Dic511yescharacteristic, complemented
160#461Dic511yescharacteristic, complemented
161#460Dic511yescharacteristic, complemented
162#459Dic511yescharacteristic, complemented
163#446—101no—
164#436—101no—
165#435—102no—
166#431—51no—
167#431—101no—
168#423—51no—
169C2×C4⋊C8C2×D511yescharacteristic
170C2×#104—101no—
171#416—21no—
172C4×M16—101no—
173C2×C4×C8—51no—
174C4×C4⋊C4—51no—
175#339—101no—
176#327—102no—
177D4⋊C8—101no—
178D4⋊C8—101no—
179C23×C5—21no—
180C23×C5—41no—
181C23×C5#12111yescharacteristic
182C5×Q8—21no—
183C5×Q8—21no—
184C5×Q8—41no—
185C5×Q8—41no—
186C5×D4—21no—
187C5×D4—21no—
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—41no—
193C5×D4—41no—
194C5×D4—81no—
195C5×D4—81no—
196C5×D4—81no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—41no—
203C2×C4×C5—42no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—81no—
210C2×C4×C5—81no—
211C2×C4×C5C2×C22⋊C411yescharacteristic
212C2×C4×C5C4×D411yescharacteristic
213C2×C4×C5C4×D411yescharacteristic
214C2×C4×C5#12011yescharacteristic
215C2×C4×C5#12111yescharacteristic
216C2×C4×C5#12311yescharacteristic
217C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
218C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
219C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C5#13711yescharacteristic
221C2×Dic5—42no—
222C2×Dic5—81no—
223C2×Dic5—81no—
224C5×C8—41no—
225C5×C8—41no—
226#168—22no—
227#168—41no—
228#168—42no—
229#168—81no—
230C2×#41—21no—
231C2×#41C22⋊D511yescharacteristic
232#135—42no—
233#135—42no—
234C2×Q16—21no—
235C2×SD16—21no—
236C2×SD16—21no—
237C2×D8—21no—
238C2×M16—102no—
239C2×M16—101no—
240C22×C8—21no—
241C22×C8—101no—
242C4⋊Q8C2×Dic511yescharacteristic
243#127C2×Dic511yescharacteristic
244#124—21no—
245#121—21no—
246#121—21no—
247C4×Q8C2×Dic511yescharacteristic
248C4×Q8C22⋊D511yescharacteristic
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C2×Dic511yescharacteristic
254C4×D4C22⋊D511yescharacteristic
255#117—21no—
256#117C22⋊D511yescharacteristic
257C2×C4⋊C4—101no—
258C2×C42—21no—
259C2×C42—101no—
260C2×C42C22×D511yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—102no—
263C4⋊C8—101no—
264C4⋊C8—101no—
265C4⋊C8—101no—
266C4⋊C8C2×Dic511yescharacteristic
267C4⋊C8C2×Dic511yescharacteristic
268#104—202no—
269#103—21no—
270#103—21no—
271#102—21no—
272#102—21no—
273C22⋊C8—52no—
274C22⋊C8—102no—
275#97—102no—
276C4×C8—51no—
277C4×C8—51no—
278C4×C8—101no—
279C4×C8—101no—
280#95—101no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—41no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—81no—
287C22×C5—81no—
288C22×C5—81no—
289C22×C5#38611yescharacteristic
290C22×C5#46811yescharacteristic
291C22×C5#46911yescharacteristic
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—21no—
295C4×C5—41no—
296C4×C5—41no—
297C4×C5—41no—
298C4×C5—81no—
299C4×C5#41711yescharacteristic
300C4×C5#41811yescharacteristic
301C4×C5#44311yescharacteristic
302C4×C5#44411yescharacteristic
303C4×C5#46811yescharacteristic
304C4×C5#46911yescharacteristic
305Dic5—82no—
306#41—21no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—41no—
311#41—41no—
312#41—41no—
313#41—41no—
314C2×Q8—21no—
315C2×Q8C22⋊Dic511yescharacteristic
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4C22⋊Dic511yescharacteristic
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—201no—
327C22×C4D4×D511yescharacteristic
328C22×C4#71111yescharacteristic
329C22×C4C2×C22⋊D511yescharacteristic
330Q16—42no—
331SD16—42no—
332SD16—42no—
333D8—42no—
334M16—204no—
335M16—201no—
336M16—201no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—101no—
342C2×C8—101no—
343C2×C8—102no—
344C2×C8—202no—
345C2×C8—201no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—102no—
351C4⋊C4—201no—
352C4⋊C4C22⋊Dic511yescharacteristic
353C4⋊C4C22⋊Dic511yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C42—21no—
360C42—21no—
361C42—21no—
362C42—201no—
363C42—201no—
364C42D4×D511yescharacteristic
365C42#71111yescharacteristic
366C42C22×Dic511yescharacteristic
367C42C2×C22⋊D511yescharacteristic
368C2×C5—21no—
369C2×C5—21no—
370C2×C5—81no—
371C2×C5—161no—
372C2×C5#187611yescharacteristic
373C2×C5#189511yescharacteristic
374C2×C5#190611yescharacteristic
375C23—21no—
376C23—41no—
377C23#408511yescharacteristic
378Q8—21no—
379Q8—21no—
380Q8—41no—
381Q8—41no—
382D4—21no—
383D4—21no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—81no—
392D4—81no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—202no—
408C2×C4—401no—
409C2×C4—401no—
410C2×C4#407811yescharacteristic
411C2×C4#407811yescharacteristic
412C2×C4D4×Dic511yescharacteristic
413C2×C4D4×Dic511yescharacteristic
414C2×C4#408111yescharacteristic
415C2×C4#408311yescharacteristic
416C2×C4#408511yescharacteristic
417C2×C4#409511yescharacteristic
418C2×C4#409711yescharacteristic
419C2×C4C2×C22⋊Dic511yescharacteristic
420C8—41no—
421C8—41no—
422C8—102no—
423C8—201no—
424C8—202no—
425C8—401no—
426C5#921011yescharacteristic, complemented, Sylow
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22#6532811yescharacteristic
436C22#6533111yescharacteristic
437C22#6550911yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—402no—
446C4#6532811yescharacteristic
447C4#6533111yescharacteristic
448C4#6548511yescharacteristic
449C4#6548611yescharacteristic
450C4#6550411yescharacteristic
451C4#6552111yescharacteristic
452C2—21no—
453C2—21no—
454C2—81no—
455C2—161no—
456C2#1060247511yescharacteristic
457C2#1060288011yescharacteristic
458C2#1060290711yescharacteristic
subgroupG/H
centerC2×C4#4085
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
Fitting, prime radicalC5×#3035C2
socleC22×C5#386
cosocleC2×C42×C5C23
hypercenter#3035D5
hypocenterC5#9210
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
2. #10614248C2semidirect
3. #10602604C2semidirect
4. #10602595C2semidirect
5. #10602439C2semidirect
6. #10598198C2semidirect
7. #10598195C2semidirect
13. C5×#462C4semidirect
14. C5×#461C4semidirect
15. C5×#460C4semidirect
16. C5×#459C4semidirect
159. #462Dic5semidirect
160. #461Dic5semidirect
161. #460Dic5semidirect
162. #459Dic5semidirect
426. C5#9210semidirect

Maximal subgroups

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

subgroupindex
C5×#30352
#106142482
#106026042
#106025952
#106024392
#105981982
#105981952
#92105