Finite Group Databasebeta

← #11994161

Subgroups — #11994161

Order 1280.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3100C211yesmaximal, characteristic
2D4×#681C211yesmaximal, characteristic, complemented
3#10602611C211yesmaximal, characteristic, complemented
4#10602595C211yesmaximal, characteristic, complemented
5C4×#3964C211yesmaximal, characteristic, complemented
6#10598237C211yesmaximal, characteristic, complemented
7#10598230C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C22×#681—21no—
11C5×#480—21no—
12C5×#474C411yescharacteristic, complemented
13C5×#474C411yescharacteristic, complemented
14C5×#459C411yescharacteristic, complemented
15C5×#459C411yescharacteristic, complemented
16C5×#447—21no—
17C4×C5×D8—21no—
18C4×C5×D8—21no—
19C5×#431C2211yescharacteristic
20C2×#3969—21no—
21C2×#3969—21no—
22C2×#3964—21no—
23#65496—21no—
24#65301—21no—
25#65300—22no—
26D4×#168—21no—
27C4×C4⋊Dic5C2211yescharacteristic
28#65213C2211yescharacteristic
29C4×#681C2211yescharacteristic
30C2×C4×#168C2211yescharacteristic
31D4⋊#168—22no—
32#64749—21no—
33#8991—51nomaximal, Sylow
34C2×C5×#41—21no—
35C22×C5×D4D411yescharacteristic
36C23×C4×C5—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C5×C4⋊Q8C2×C411yescharacteristic
40C5×#127C2×C411yescharacteristic
41C5×#124—21no—
42C5×#121—21no—
43C5×#121—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C4×C5×D4C2×C411yescharacteristic
49C4×C5×D4C2×C411yescharacteristic
50C4×C5×D4D411yescharacteristic
51C4×C5×D4D411yescharacteristic
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C22⋊C4—21no—
54C2×C42×C5C2311yescharacteristic
55C2×C4⋊Dic5—21no—
56C2×C4×Dic5—21no—
57C2×#681—22no—
58C2×#681—21no—
59C2×#681—42no—
60C2×#681—42no—
61C2×#681D411yescharacteristic
62C2×#681D411yescharacteristic
63C22×#168—22no—
64C22×#168—21no—
65C5×#107—21no—
66C5×#107—21no—
67C5×C4⋊C8C2×C411yescharacteristic
68C5×C4⋊C8C2×C411yescharacteristic
69C5×#102—21no—
70C5×#102—21no—
71C5×#102—21no—
72C5×#102—21no—
73C5×C22⋊C8—21no—
74C4×C5×C8—21no—
75#3969—42no—
76#3969—42no—
77#3964—24no—
78#3963—21no—
79C22⋊#168—22no—
80C22⋊#168—22no—
81C4⋊#168—21no—
82C4⋊#168D412yes—
83#3935—21no—
84C4×#168—21no—
85C4×#168—21no—
86C4×#168—21no—
87#3100D511yescharacteristic
88D4×M16—51no—
89#1980—51no—
90C4×#102—51no—
91#1492—51no—
92#1303—51no—
93#1278—51no—
94C24×C5—21no—
95C5×#41—41no—
96C5×#41—41no—
97C5×#41—41no—
98C5×#41—41no—
99C2×C5×Q8—21no—
100C2×C5×D4—22no—
101C2×C5×D4—21no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4C22⋊C411yescharacteristic
108C2×C5×D4C22⋊C411yescharacteristic
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—21no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—41no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5#4111yescharacteristic
122C22×Dic5—41no—
123C5×D8—42no—
124C5×D8—42no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4C22⋊C411yescharacteristic
131C5×C4⋊C4C22⋊C411yescharacteristic
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—41no—
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—21no—
147#681—21no—
148#681—21no—
149#681—44no—
150#681—41no—
151#681—41no—
152#681D812yescomplemented
153C2×#168—21no—
154C2×#168—22no—
155C2×#168—21no—
156C2×#168—22no—
157C2×#168—44no—
158C2×#168—41no—
159C2×#168—41no—
160C22×M16—101no—
161#532C2×D511yescharacteristic
162C2×C4×D4C2×D511yescharacteristic
163#480—21no—
164#474Dic511yescharacteristic, complemented
165#474Dic511yescharacteristic, complemented
166#459Dic511yescharacteristic, complemented
167#459Dic511yescharacteristic, complemented
168#447—21no—
169C4×D8—21no—
170C4×D8—21no—
171#436—101no—
172#435—102no—
173C8×D4—101no—
174#431C2×D511yescharacteristic
175#423—51no—
176C2×#104—101no—
177C2×#104—101no—
178C2×#102—101no—
179#407—101no—
180C4×M16—51no—
181C2×C4×C8—51no—
182C4×C4⋊C4—51no—
183#340—101no—
184D4⋊C8—102no—
185C23×C5—21no—
186C23×C5—21no—
187C23×C5—42no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5—81no—
192C23×C5#12111yescharacteristic
193C5×Q8—41no—
194C5×Q8—41no—
195C5×D4—21no—
196C5×D4—21no—
197C5×D4—21no—
198C5×D4—42no—
199C5×D4—42no—
200C5×D4—41no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—81no—
205C5×D4—81no—
206C5×D4#10412yescomplemented
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—81no—
224C2×C4×C5—81no—
225C2×C4×C5C2×C22⋊C411yescharacteristic
226C2×C4×C5C4×D411yescharacteristic
227C2×C4×C5C4×D411yescharacteristic
228C2×C4×C5#12011yescharacteristic
229C2×C4×C5#12111yescharacteristic
230C2×C4×C5#12311yescharacteristic
231C2×C4×C5C2×D811yescharacteristic
232C2×C4×C5#13511yescharacteristic
233C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
234C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
235C2×Dic5—42no—
236C2×Dic5—81no—
237C2×Dic5—81no—
238C5×C8—41no—
239C5×C8—41no—
240#168—22no—
241#168—42no—
242#168—42no—
243#168—41no—
244C2×#41—21no—
245C22×D4C22⋊D511yescharacteristic
246C23×C4—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×M16—51no—
250C2×M16—51no—
251C2×M16—102no—
252C2×M16—101no—
253C2×M16—202no—
254C2×M16—202no—
255C22×C8—102no—
256C22×C8—101no—
257C4⋊Q8C2×Dic511yescharacteristic
258#127C2×Dic511yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4C2×Dic511yescharacteristic
267C4×D4C2×Dic511yescharacteristic
268C4×D4C22⋊D511yescharacteristic
269C4×D4C22⋊D511yescharacteristic
270C2×C4⋊C4—101no—
271C2×C4⋊C4C22⋊D511yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42—101no—
274C2×C42C22×D511yescharacteristic
275#107—21no—
276#107—21no—
277C4⋊C8—52no—
278C4⋊C8—101no—
279C4⋊C8C2×Dic511yescharacteristic
280C4⋊C8C2×Dic511yescharacteristic
281#104—202no—
282#104—202no—
283#102—21no—
284#102—21no—
285#102—21no—
286#102—21no—
287#102—104no—
288C22⋊C8—21no—
289C22⋊C8—102no—
290C22⋊C8—102no—
291#97—101no—
292C4×C8—21no—
293C4×C8—101no—
294C4×C8—101no—
295C4×C8—101no—
296#95—101no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5—22no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—82no—
306C22×C5—82no—
307C22×C5—81no—
308C22×C5—81no—
309C22×C5—81no—
310C22×C5#38611yescharacteristic
311C22×C5#45911yescharacteristic
312C22×C5#46311yescharacteristic
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—41no—
317C4×C5—41no—
318C4×C5—81no—
319C4×C5C2×#10411yescharacteristic
320C4×C5#42111yescharacteristic
321C4×C5C4×D811yescharacteristic
322C4×C5#44211yescharacteristic
323C4×C5#44711yescharacteristic
324C4×C5#44911yescharacteristic
325Dic5—82no—
326C24—21no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—41no—
331C2×Q8—21no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4C22⋊Dic511yescharacteristic
340C2×D4C22⋊Dic511yescharacteristic
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—201no—
352C22×C4D4×D511yescharacteristic
353C22×C4#71111yescharacteristic
354C22×C4C2×C22⋊D511yescharacteristic
355D8—42no—
356D8—42no—
357M16—52no—
358M16—101no—
359M16—101no—
360M16—101no—
361M16—204no—
362M16—201no—
363M16—201no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—101no—
367C2×C8—102no—
368C2×C8—101no—
369C2×C8—102no—
370C2×C8—204no—
371C2×C8—201no—
372C2×C8—201no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—102no—
377C4⋊C4—201no—
378C4⋊C4C22⋊Dic511yescharacteristic
379C4⋊C4C22⋊Dic511yescharacteristic
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C42—201no—
387C42—201no—
388C42D4×D511yescharacteristic
389C42#71111yescharacteristic
390C42C22×Dic511yescharacteristic
391C42C2×C22⋊D511yescharacteristic
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—42no—
395C2×C5—81no—
396C2×C5—161no—
397C2×C5#187111yescharacteristic
398C2×C5#187911yescharacteristic
399C2×C5#188111yescharacteristic
400C23—21no—
401C23—21no—
402C23—42no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—81no—
407C23#408511yescharacteristic
408Q8—41no—
409Q8—41no—
410D4—21no—
411D4—21no—
412D4—21no—
413D4—42no—
414D4—42no—
415D4—41no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—81no—
420D4—81no—
421D4#396912yescomplemented
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—202no—
441C2×C4—401no—
442C2×C4—401no—
443C2×C4D5×D811yescharacteristic
444C2×C4#405711yescharacteristic
445C2×C4#405711yescharacteristic
446C2×C4#405811yescharacteristic
447C2×C4D4×Dic511yescharacteristic
448C2×C4D4×Dic511yescharacteristic
449C2×C4#408111yescharacteristic
450C2×C4#408311yescharacteristic
451C2×C4#408511yescharacteristic
452C2×C4C2×C22⋊Dic511yescharacteristic
453C8—41no—
454C8—41no—
455C8—102no—
456C8—202no—
457C8—202no—
458C8—201no—
459C5#899111yescharacteristic, complemented, Sylow
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22#6543911yescharacteristic
474C22#6544211yescharacteristic
475C22#6550911yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—81no—
482C4—402no—
483C4D8×Dic511yescharacteristic
484C4#6544111yescharacteristic
485C4#6544511yescharacteristic
486C4#6544711yescharacteristic
487C4C2×#396911yescharacteristic
488C4#6552511yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—161no—
494C2#1060250611yescharacteristic
495C2#1060283011yescharacteristic
496C2#1060290911yescharacteristic
subgroupG/H
centerC2×C4#4083
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
Fitting, prime radicalC5×#3100C2
socleC22×C5#386
cosocleC2×C42×C5C23
hypercenter#3100D5
hypocenterC5#8991
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
2. D4×#681C2semidirect
3. #10602611C2semidirect
4. #10602595C2semidirect
5. C4×#3964C2semidirect
6. #10598237C2semidirect
7. #10598230C2semidirect
12. C5×#474C4semidirect
13. C5×#474C4semidirect
14. C5×#459C4semidirect
15. C5×#459C4semidirect
152. #681D8semidirect
164. #474Dic5semidirect
165. #474Dic5semidirect
166. #459Dic5semidirect
167. #459Dic5semidirect
206. C5×D4#104semidirect
421. D4#3969semidirect
459. C5#8991semidirect

Maximal subgroups

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

subgroupindex
C5×#31002
D4×#6812
#106026112
#106025952
C4×#39642
#105982372
#105982302
#89915