Finite Group Databasebeta

← #13033671

Subgroups — #13033671

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65697C211yesmaximal, characteristic
2C2×#65691C211yesmaximal, characteristic
3#10607182C211yesmaximal, characteristic
4#10604316C211yesmaximal, characteristic, complemented
5#10604315C211yesmaximal, characteristic, complemented
6#10604227C211yesmaximal, characteristic
7#10604227C211yesmaximal, characteristic
8#10604226C211yesmaximal, characteristic
9#10604226C211yesmaximal, characteristic
10#10604175C211yesmaximal, characteristic, complemented
11C4×#4002C211yesmaximal, characteristic, complemented
12#10603781C211yesmaximal, characteristic, complemented
13#10603780C211yesmaximal, characteristic, complemented
14#10603774C211yesmaximal, characteristic, complemented
15#10603773C211yesmaximal, characteristic, complemented
16C22×#704C2211yescharacteristic
17C23×#170C2211yescharacteristic
18C2×#4023C2211yescharacteristic
19C2×C22⋊#170C2211yescharacteristic
20C2×C22⋊#170C2211yescharacteristic
21C2×#4004C2211yescharacteristic
22C2×#4002C2211yescharacteristic
23C2×#4002C2211yescharacteristic
24C2×#4002C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
27C2×#4002C2211yescharacteristic
28C2×#4002C2211yescharacteristic
29C2×#4002C2211yescharacteristic
30C2×#4002C2211yescharacteristic
31C2×C4⋊#170C2211yescharacteristic
32C2×C4×#170C2211yescharacteristic
33C2×C4×#170C2211yescharacteristic
34C2×C4×#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37#65697C418yescomplemented
38#65691C418yescomplemented
39C5×#388C411yescharacteristic
40#65267C411yescharacteristic
41C4⋊C4×Dic5C2211yescharacteristic
42#65240C411yescharacteristic
43#65234C411yescharacteristic
44#65233C411yescharacteristic
45C22⋊C4×Dic5C2211yescharacteristic
46C22⋊C4×Dic5C2211yescharacteristic
47#65222C411yescharacteristic
48C42×Dic5C2211yescharacteristic
49#64944C411yescharacteristic
50#64941C411yescharacteristic
51#64938C2211yescharacteristic
52#64937C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#20475—51nomaximal, Sylow
62C23×Dic5C2311yescharacteristic
63C2×#704—22no—
64C2×#704—22no—
65C2×#704C2×C414yes—
66C22×#170—22no—
67C22×#170—22no—
68C22×#170C2×C414yes—
69C22×#170C2311yescharacteristic
70C22×#170C2311yescharacteristic
71C22×#170C2311yescharacteristic
72C22×#170C2311yescharacteristic
73C22×#170C2311yescharacteristic
74C22×#170C2311yescharacteristic
75C22×#170C2311yescharacteristic
76C22×#170C2311yescharacteristic
77C2×C5×C4⋊C4C2×C411yescharacteristic
78C2×C5×C22⋊C4C2×C411yescharacteristic
79C2×C5×C22⋊C4C2×C411yescharacteristic
80C2×C5×C22⋊C4C2×C411yescharacteristic
81C2×C42×C5C2×C411yescharacteristic
82C2×C22⋊Dic5C2×C411yescharacteristic
83C2×C22⋊Dic5C2×C411yescharacteristic
84C2×C22⋊Dic5C2×C411yescharacteristic
85C2×C4⋊Dic5C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×#683C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2×C411yescharacteristic
92C2×C4×Dic5C2×C411yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95C2×C4×Dic5C2311yescharacteristic
96C2×C4×Dic5C2311yescharacteristic
97C2×C4×Dic5C2311yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99#4023C2×C414yes—
100#4023C2×C414yes—
101C22⋊#170C2×C414yes—
102C22⋊#170C2×C414yes—
103#4004C2×C414yes—
104#4002—22no—
105#4002—22no—
106#4002—22no—
107#4002—22no—
108#4002—22no—
109#4002—22no—
110#4002C2×C414yes—
111#4002C2×C414yes—
112#4002C2×C414yes—
113C4⋊#170C2×C414yes—
114C4×#170—22no—
115C4×#170—22no—
116C4×#170C2×C414yes—
117C4×#170C2×C414yes—
118C4×#170C2×C414yes—
119C5×#95C2×C411yescharacteristic
120C5×#95C2×C411yescharacteristic
121#3963C2×C411yescharacteristic
122#3963C2×C411yescharacteristic
123#3963C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131C2×#433—51no—
132C2×#405—51no—
133#2298—51no—
134#1771—51no—
135#1771—51no—
136#1770—51no—
137#1770—51no—
138#1753—51no—
139#1753—51no—
140#1752—51no—
141#1752—51no—
142#1746—51no—
143#1745—51no—
144#1726—51no—
145C4×#97—51no—
146C24×C5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C22×C411yescharacteristic
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C22×C412yes—
165C22×Dic5C22×C412yes—
166C22×Dic5C2411yescharacteristic
167#704—28no—
168C2×#170—21no—
169C2×#170—21no—
170C2×#170—21no—
171C2×#170—21no—
172C2×#170—21no—
173C2×#170—21no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—28no—
181C2×#170C22×C412yes—
182C2×#170C22×C412yes—
183C2×#170C22×C412yes—
184C2×#170C22×C412yes—
185C2×#170C22×C412yes—
186C2×#170C22×C412yes—
187C2×#170C22×C412yes—
188C2×#170C22×C412yes—
189C2×#170#4112yes—
190C2×#170#4112yes—
191C2×#170#4112yes—
192C2×#170#4112yes—
193C5×C4⋊C4—41no—
194C5×C22⋊C4—41no—
195C5×C22⋊C4—41no—
196C5×C22⋊C4C4214yes—
197C42×C5—41no—
198C22⋊Dic5—41no—
199C22⋊Dic5—41no—
200C22⋊Dic5C4214yes—
201C4⋊Dic5—41no—
202#683—41no—
203#683—41no—
204#683C4214yes—
205#683C4214yes—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5—41no—
215C4×Dic5—41no—
216C4×Dic5—41no—
217C4×Dic5C22×C412yes—
218C4×Dic5C22×C412yes—
219C4×Dic5C22×C412yes—
220C4×Dic5C22×C412yes—
221C22×M16—51no—
222C23×C8—51no—
223C2×#117—51no—
224#433—58no—
225C2×C4⋊C8—51no—
226C2×C4⋊C8—51no—
227C2×C22⋊C8—51no—
228C2×C22⋊C8—51no—
229#405—58no—
230C2×#97—51no—
231C2×#97—51no—
232C2×#97—51no—
233C2×#97—51no—
234C2×#97—51no—
235C2×#97—51no—
236C2×#97—51no—
237C2×#97—51no—
238C2×#97—51no—
239C2×C4×C8—51no—
240C2×C4×C8—51no—
241C2×C4×C8—51no—
242C2×C4×C8—51no—
243C2×C4×C8—51no—
244#388—51no—
245#388—51no—
246#388—51no—
247#388AGL(1,𝔽5)11yescharacteristic
248#387—51no—
249#387—51no—
250#387—51no—
251#387—51no—
252C4×C4⋊C4—51no—
253C4×C4⋊C4—51no—
254C4×C22⋊C4—51no—
255C4×C22⋊C4—51no—
256#376—51no—
257C43—51no—
258#336—51no—
259#336—51no—
260#336—51no—
261#336—51no—
262#336—51no—
263#336—51no—
264#336—51no—
265#336—51no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5—21no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5C2×C4212yes—
273C23×C5C23×C411yescharacteristic
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
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—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5C2×C4212yes—
291C2×C4×C5C2×C4212yes—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5C2×C4212yes—
315C2×Dic5C2×C4212yes—
316C2×Dic5C2×C4212yes—
317C2×Dic5C23×C411yescharacteristic
318C2×Dic5C23×C411yescharacteristic
319C2×Dic5C2×#4111yescharacteristic
320C2×Dic5C2×#4111yescharacteristic
321C2×Dic5C2×#4111yescharacteristic
322C2×Dic5C2×#4111yescharacteristic
323#170—22no—
324#170—22no—
325#170—22no—
326#170—22no—
327#170—22no—
328#170—22no—
329#170#11714yes—
330#170#11714yes—
331C23×C4—51no—
332C2×M16—54no—
333C2×M16—102no—
334C2×M16—102no—
335C22×C8—51no—
336C22×C8—51no—
337C22×C8—54no—
338C22×C8—51no—
339C22×C8—51no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—102no—
345C22×C8—102no—
346#117—54no—
347#117—54no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
354C2×C22⋊C4—51no—
355C2×C22⋊C4—51no—
356C2×C22⋊C4—51no—
357C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
358C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
359C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42C2×AGL(1,𝔽5)11yescharacteristic
370C4⋊C8—54no—
371C4⋊C8—54no—
372C22⋊C8—54no—
373C22⋊C8—54no—
374#97—54no—
375#97—54no—
376#97—54no—
377#97—102no—
378#97—102no—
379#97—102no—
380#97—102no—
381#97—102no—
382#97—102no—
383C4×C8—54no—
384C4×C8—54no—
385C4×C8—54no—
386C4×C8—102no—
387C4×C8—102no—
388#95—51no—
389#95—51no—
390#95—51no—
391#95—51no—
392#95—51no—
393#95—51no—
394#95—51no—
395#95—51no—
396#95—51no—
397#95—51no—
398#95C2×AGL(1,𝔽5)11yescharacteristic
399#95C2×AGL(1,𝔽5)11yescharacteristic
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5C22×C4211yescharacteristic
408C22×C5C4×#4111yescharacteristic
409C22×C5C4×#4111yescharacteristic
410C22×C5#56811yescharacteristic
411C22×C5#56811yescharacteristic
412C22×C5#56811yescharacteristic
413C22×C5#56811yescharacteristic
414C4×C5—22no—
415C4×C5—22no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5—41no—
420Dic5—22no—
421Dic5—22no—
422Dic5—22no—
423Dic5—41no—
424Dic5—41no—
425Dic5—41no—
426Dic5—41no—
427Dic5C2×#11711yescharacteristic
428Dic5C2×#11711yescharacteristic
429Dic5C4×#4111yescharacteristic
430Dic5C4×#4111yescharacteristic
431C24C22×AGL(1,𝔽5)11yescharacteristic
432C22×C4—51no—
433C22×C4—52no—
434C22×C4—52no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—51no—
438C22×C4—51no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4C22×AGL(1,𝔽5)11yescharacteristic
447C22×C4C22×AGL(1,𝔽5)11yescharacteristic
448C22×C4C22×AGL(1,𝔽5)11yescharacteristic
449C22×C4C22×AGL(1,𝔽5)11yescharacteristic
450C22×C4C22×AGL(1,𝔽5)11yescharacteristic
451C22×C4C22×AGL(1,𝔽5)11yescharacteristic
452M16—108no—
453C2×C8—52no—
454C2×C8—52no—
455C2×C8—52no—
456C2×C8—52no—
457C2×C8—52no—
458C2×C8—52no—
459C2×C8—52no—
460C2×C8—52no—
461C2×C8—52no—
462C2×C8—52no—
463C2×C8—52no—
464C2×C8—52no—
465C2×C8—108no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C4⋊C4—41no—
479C4⋊C4—54no—
480C4⋊C4—54no—
481C4⋊C4—201no—
482C4⋊C4—201no—
483C4⋊C4—201no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—54no—
487C22⋊C4—201no—
488C22⋊C4—201no—
489C22⋊C4C4×AGL(1,𝔽5)14yes—
490C42—41no—
491C42—52no—
492C42—52no—
493C42—52no—
494C42—52no—
495C42—101no—
496C42—101no—
497C42—101no—
498C42—101no—
499C42—101no—
500C42—101no—
501C42—101no—
502C42—101no—
503C42—201no—
504C42—201no—
505C42—201no—
506C2×C5—42no—
507C2×C5C4×#11711yescharacteristic
508C2×C5#287511yescharacteristic
509C2×C5#287511yescharacteristic
510C2×C5#296711yescharacteristic
511C2×C5#296711yescharacteristic
512C2×C5#296711yescharacteristic
513C2×C5#296711yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23C2×C4×AGL(1,𝔽5)12yes—
521C23C23×AGL(1,𝔽5)11yescharacteristic
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—51no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—51no—
542C2×C4—51no—
543C2×C4—51no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—101no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—101no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—101no—
569C2×C4C2×C4×AGL(1,𝔽5)12yes—
570C2×C4C2×C4×AGL(1,𝔽5)12yes—
571C8—54no—
572C8—54no—
573C8—102no—
574C8—102no—
575C8—102no—
576C8—102no—
577C8—102no—
578C8—102no—
579C5#2047511yescharacteristic, complemented, Sylow
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C22×C4×AGL(1,𝔽5)11yescharacteristic
588C22#6625611yescharacteristic
589C22#6625611yescharacteristic
590C22#6626411yescharacteristic
591C22#6626411yescharacteristic
592C22#41×AGL(1,𝔽5)11yescharacteristic
593C22#41×AGL(1,𝔽5)11yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—51no—
601C4—51no—
602C4—51no—
603C4—51no—
604C4—102no—
605C4—102no—
606C4—102no—
607C4—201no—
608C4—201no—
609C4—201no—
610C4—201no—
611C2—42no—
612C2AGL(1,𝔽5)×#11711yescharacteristic
613C2#1061713611yescharacteristic
614C2#1061713611yescharacteristic
615C2#1061723411yescharacteristic
616C2#1061729311yescharacteristic
617C2#1061731311yescharacteristic
618C2#1061735011yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#388C4
socleC23×C5C23×C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenter#388AGL(1,𝔽5)
hypocenterC5#20475
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #10604316C2semidirect
5. #10604315C2semidirect
10. #10604175C2semidirect
11. C4×#4002C2semidirect
12. #10603781C2semidirect
13. #10603780C2semidirect
14. #10603774C2semidirect
15. #10603773C2semidirect
37. #65697C4semidirect
38. #65691C4semidirect
579. C5#20475semidirect

Maximal subgroups

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

subgroupindex
C2×#656972
C2×#656912
#106071822
#106043162
#106043152
#106042272
#106042262
#106041752
C4×#40022
#106037812
#106037802
#106037742
#106037732
#204755