Finite Group Databasebeta

← #12172011

Subgroups — #12172011

Order 1280.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2360C211yesmaximal, characteristic
2#10605243C211yesmaximal, characteristic
3#10602487C211yesmaximal, characteristic
4#10602487C211yesmaximal, characteristic
5C4×#3967C211yesmaximal, characteristic, complemented
6#10602422C211yesmaximal, characteristic, complemented
7#10602349C211yesmaximal, characteristic
8#10602347C211yesmaximal, characteristic
9#10600475C211yesmaximal, characteristic, complemented
10#10600463C211yesmaximal, characteristic, complemented
11#10600411C211yesmaximal, characteristic, complemented
12#10600395C211yesmaximal, characteristic, complemented
13#10600260C211yesmaximal, characteristic, complemented
14#10600252C211yesmaximal, characteristic, complemented
15#10600244C211yesmaximal, characteristic
16C2×C5×C22⋊Q8C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C2×#4025—21no—
20C5×#391C2211yescharacteristic
21C5×#389—21no—
22C5×#389C2211yescharacteristic
23C5×#387—21no—
24C5×#385—21no—
25C4×C5×C4⋊C4C2211yescharacteristic
26C4×C5×C22⋊C4—21no—
27C4×C5×C22⋊C4C2211yescharacteristic
28C2×#3967C2211yescharacteristic
29C2×#3967C2211yescharacteristic
30C2×#3967C2211yescharacteristic
31C2×#3967C2211yescharacteristic
32#65501C2211yescharacteristic
33#65501C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35C2×C22⋊#168C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40#65242—21no—
41#65224C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65217C2211yescharacteristic
44#65217C2211yescharacteristic
45C2×C4⋊#168C2211yescharacteristic
46C2×C4×#168C2211yescharacteristic
47#64948—21no—
48#64942—21no—
49#64749C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#27034—51nomaximal, Sylow
60C22×C5×Q8C2311yescharacteristic
61C23×C4×C5—21no—
62C23×C4×C5C2311yescharacteristic
63C5×C22⋊Q8—22no—
64C5×C22⋊Q8—22no—
65C4×C5×Q8—22no—
66C4×C5×Q8—41no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—41no—
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4D411yescharacteristic
78C2×C5×C22⋊C4D411yescharacteristic
79C2×C42×C5—21no—
80C2×C42×C5—21no—
81C2×C42×C5C2311yescharacteristic
82C2×C42×C5C2311yescharacteristic
83C2×C22⋊Dic5—21no—
84C2×C22⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×#683—21no—
92C2×#683—21no—
93C2×C4×Dic5—21no—
94C22×#168C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98#4025—44no—
99C5×#95—21no—
100C5×#95—21no—
101C5×#95—21no—
102C5×#95—21no—
103C5×#95D411yescharacteristic
104C5×#95D411yescharacteristic
105#3967—22no—
106#3967—22no—
107#3967—22no—
108#3967—41no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114C22⋊#168—22no—
115C22⋊#168—41no—
116#3940—22no—
117#3940—22no—
118#3940—22no—
119#3940—41no—
120C4⋊#168—22no—
121C4×#168—41no—
122#2496—51no—
123#2360D511yescharacteristic
124#2072—51no—
125#2066—51no—
126#2035—51no—
127#2035—51no—
128#1948—51no—
129#1941—51no—
130#1923—51no—
131#1920—51no—
132#1919—51no—
133#1865—51no—
134#1853—51no—
135#1824—51no—
136C4×#103—51no—
137C24×C5C2×D411yescharacteristic
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8#4112yes—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—42no—
155C22×C4×C5—42no—
156C22×C4×C5—81no—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2411yescharacteristic
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C5×C4⋊C4—24no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—42no—
173C5×C4⋊C4—42no—
174C5×C4⋊C4—81no—
175C5×C4⋊C4#4112yes—
176C5×C4⋊C4#4112yes—
177C5×C22⋊C4—24no—
178C5×C22⋊C4—41no—
179C5×C22⋊C4SD1614yes—
180C42×C5—21no—
181C42×C5—21no—
182C42×C5—21no—
183C42×C5—21no—
184C42×C5—42no—
185C42×C5—81no—
186C22⋊Dic5—42no—
187C22⋊Dic5—42no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—42no—
197C4⋊Dic5—42no—
198#683—42no—
199#683—42no—
200C4×Dic5—42no—
201C2×#168—21no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168#4112yes—
213C2×#126—101no—
214C2×C22⋊Q8C2×D511yescharacteristic
215C2×C4×Q8C2×D511yescharacteristic
216C22×C4⋊C4C2×D511yescharacteristic
217C2×#106—51no—
218C2×#106—51no—
219C2×#106—51no—
220C2×#106—51no—
221C2×C4⋊C8—51no—
222C2×#103—51no—
223C2×#103—51no—
224C2×#103—51no—
225C2×#103—51no—
226C2×C22⋊C8—51no—
227C2×C22⋊C8—51no—
228C2×C4×C8—51no—
229#400—101no—
230#397—101no—
231#391C2×D511yescharacteristic
232#389—21no—
233#389—51no—
234#389—51no—
235#389C2×D511yescharacteristic
236#387—21no—
237#387—101no—
238#385—21no—
239#384—51no—
240#380—51no—
241#380—51no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4C2×D511yescharacteristic
244C4×C22⋊C4—21no—
245C4×C22⋊C4C2×D511yescharacteristic
246#340—51no—
247#340—51no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#336—51no—
255#336—51no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5—21no—
262C23×C5C2×SD1612yes—
263C23×C5C22×D411yescharacteristic
264C5×Q8—22no—
265C5×Q8—22no—
266C5×Q8—41no—
267C5×Q8—41no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—84no—
298C2×C4×C5C2×SD1612yes—
299C2×C4×C5C2×SD1612yes—
300C2×C4×C5C2×#4111yescharacteristic
301C2×C4×C5C2×#4111yescharacteristic
302C2×C4×C5C2×#4111yescharacteristic
303C2×C4×C5C2×#4111yescharacteristic
304C2×C4×C5H(5,𝔽2)11yescharacteristic
305C2×C4×C52−1+411yescharacteristic
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318#168—22no—
319#168—41no—
320#168—41no—
321#168—41no—
322C22×Q8C22×D511yescharacteristic
323C23×C4—21no—
324C23×C4C22×D511yescharacteristic
325C22×C8—51no—
326C22×C8—51no—
327C22×C8—51no—
328C22×C8—51no—
329#126—204no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C4×Q8—22no—
333C4×Q8—41no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—101no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4C22×D511yescharacteristic
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—101no—
353C2×C22⋊C4—101no—
354C2×C22⋊C4C22⋊D511yescharacteristic
355C2×C22⋊C4C22⋊D511yescharacteristic
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—101no—
359C2×C42C22×D511yescharacteristic
360C2×C42C22×D511yescharacteristic
361#106—102no—
362#106—102no—
363#106—102no—
364#106—201no—
365C4⋊C8—102no—
366#103—102no—
367#103—102no—
368#103—102no—
369#103—201no—
370C22⋊C8—102no—
371C22⋊C8—201no—
372C4×C8—201no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—101no—
378#95—101no—
379#95—101no—
380#95—101no—
381#95—101no—
382#95C22⋊D511yescharacteristic
383#95C22⋊D511yescharacteristic
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—22no—
387C22×C5—41no—
388C22×C5—41no—
389C22×C5—41no—
390C22×C5—41no—
391C22×C5#52511yescharacteristic
392C22×C5#54611yescharacteristic
393C22×C5#54711yescharacteristic
394C22×C5C22×SD1611yescharacteristic
395C22×C5#57511yescharacteristic
396C22×C5#57711yescharacteristic
397C22×C5#57811yescharacteristic
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—41no—
401C4×C5—42no—
402C4×C5—41no—
403C4×C5—42no—
404C4×C5—41no—
405C4×C5—42no—
406C4×C5—81no—
407C4×C5#52911yescharacteristic
408C4×C5#53911yescharacteristic
409C4×C5#55311yescharacteristic
410C4×C5#55611yescharacteristic
411Dic5—81no—
412Dic5—81no—
413Dic5—81no—
414Dic5—81no—
415C24C2×C22⋊D511yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8#70912yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4C2×C22⋊D511yescharacteristic
440C22×C4C2×C22⋊D511yescharacteristic
441C22×C4C2×C22⋊D511yescharacteristic
442C22×C4C2×C22⋊D511yescharacteristic
443C22×C4C2×C22⋊D511yescharacteristic
444C22×C4C23×D511yescharacteristic
445C2×C8—52no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—202no—
474C4⋊C4—202no—
475C4⋊C4—202no—
476C4⋊C4—202no—
477C4⋊C4#70912yes—
478C4⋊C4#71112yes—
479C22⋊C4—24no—
480C22⋊C4—41no—
481C22⋊C4—202no—
482C22⋊C4—202no—
483C22⋊C4#68814yes—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—42no—
489C42—81no—
490C42—202no—
491C2×C5—42no—
492C2×C5#246611yescharacteristic
493C2×C5#310311yescharacteristic
494C2×C5#312011yescharacteristic
495C2×C5#329811yescharacteristic
496C2×C5#331111yescharacteristic
497C2×C5#333511yescharacteristic
498C2×C5#335211yescharacteristic
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23C2×#68812yes—
506C23C22×C22⋊D511yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—84no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4C2×#68812yes—
554C2×C4C2×#68812yes—
555C2×C4C2×#70911yescharacteristic
556C2×C4C2×#70911yescharacteristic
557C2×C4C2×#71111yescharacteristic
558C2×C4#414411yescharacteristic
559C2×C4D5×#4111yescharacteristic
560C2×C4#415011yescharacteristic
561C8—102no—
562C8—201no—
563C8—201no—
564C8—201no—
565C5#2703411yescharacteristic, complemented, Sylow
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#6612511yescharacteristic
574C22#6614011yescharacteristic
575C22C22×#68811yescharacteristic
576C22#6615611yescharacteristic
577C22#6615811yescharacteristic
578C22#6617011yescharacteristic
579C22#6617211yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—401no—
590C4—401no—
591C4—401no—
592C4—401no—
593C4#6587211yescharacteristic
594C4#6587611yescharacteristic
595C4#6589211yescharacteristic
596C4#6589811yescharacteristic
597C2—42no—
598C2#1061410011yescharacteristic
599C2#1061417311yescharacteristic
600C2#1061430611yescharacteristic
601C2#1061522811yescharacteristic
602C2#1061528111yescharacteristic
603C2#1061532811yescharacteristic
604C2#1061535311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2360C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenter#2360D5
hypocenterC5#27034
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
5. C4×#3967C2semidirect
6. #10602422C2semidirect
9. #10600475C2semidirect
10. #10600463C2semidirect
11. #10600411C2semidirect
12. #10600395C2semidirect
13. #10600260C2semidirect
14. #10600252C2semidirect
565. C5#27034semidirect

Maximal subgroups

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

subgroupindex
C5×#23602
#106052432
#106024872
C4×#39672
#106024222
#106023492
#106023472
#106004752
#106004632
#106004112
#106003952
#106002602
#106002522
#106002442
#270345