Finite Group Databasebeta

← #12108393

Subgroups — #12108393

Order 1280.

1518 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66164C211yesmaximal, characteristic
2C5×#2311C211yesmaximal, characteristic, complemented
3C2×#65523C211yesmaximal, characteristic, complemented
4#10602379C212yesmaximal, complemented
5#10602353C212yesmaximal, complemented
6#10600314C212yesmaximal, complemented
7#10600310C212yesmaximal, complemented
8#10600308C212yesmaximal, complemented
9#10600296C212yesmaximal, complemented
10C22×C5×#41C2211yescharacteristic
11C23×D20C2211yescharacteristic
12C2×C5×#117C2211yescharacteristic, complemented
13C22×C5×C4⋊C4C2211yescharacteristic, complemented
14#66164—24no—
15#66164C418yescomplemented
16C2×#4093—21no—
17C2×#4086—21no—
18C2×#4083—21no—
19C2×#4083—21no—
20C2×#4076C2212yes—
21C2×#4076C2212yes—
22C2×#4072C2211yescharacteristic
23C22×#681C2211yescharacteristic, complemented
24C23×#168C2211yescharacteristic, complemented
25C5×#391—21no—
26C5×#390—21no—
27C5×#386—21no—
28C5×#386—21no—
29C5×#380C2212yes—
30C5×#380C2212yescomplemented
31#65523—24no—
32C2×C22⋊#168C2212yes—
33C2×C22⋊#168C2212yescomplemented
34C2×#3941C2212yes—
35C2×#3941C2212yes—
36C2×#3941C2212yes—
37C2×#3941C2212yes—
38#64749C2212yescomplemented
39#64749C2212yescomplemented
40#64749C2212yescomplemented
41#64749C2212yescomplemented
42#21770—51nomaximal, Sylow
43C24×D5—21no—
44C2×C5×#41—41no—
45C2×C5×#41—41no—
46C2×C5×#41—41no—
47C2×C5×#41—41no—
48C2×C5×#41C2×C414yes—
49C2×C5×#41D414yes—
50C22×C5×Q8D411yescharacteristic
51C22×C5×D4D411yescharacteristic
52C22×C5×D4D411yescharacteristic
53C22×C5×D4D411yescharacteristic
54C23×C4×C5—21no—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C22×C22⋊D5—22no—
59C22×C22⋊D5—22no—
60C22×D20—21no—
61C22×D20—22no—
62C22×D20—41no—
63C22×D20—41no—
64C22×D20—41no—
65C22×D20—41no—
66C22×D20C2×C414yescomplemented
67C22×D20C2312yes—
68C5×#117—41no—
69C5×#117—41no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—41no—
72C2×C5×C4⋊C4—41no—
73C2×C5×C4⋊C4C2312yes—
74C2×C5×C4⋊C4C2312yes—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—22no—
77C2×C5×C22⋊C4—22no—
78C2×C42×C5—21no—
79C2×C22⋊Dic5—21no—
80#4093—28no—
81#4086—28no—
82#4083—28no—
83#4083—28no—
84#4076—24no—
85#4076—24no—
86#4076C2×C418yes—
87#4076C2×C418yescomplemented
88C2×#685—22no—
89C2×#685—22no—
90#4072—22no—
91#4072C2×C414yescomplemented
92C2×C4⋊Dic5C2312yes—
93C2×C4×Dic5—21no—
94C2×#681—22no—
95C2×#681—41no—
96C2×#681—41no—
97C22×#168—22no—
98C22×#168—41no—
99C22×#168—41no—
100C22×#168C2312yes—
101C22×#168C2312yes—
102C5×#95—22no—
103C5×#95—22no—
104C22⋊#168—24no—
105C22⋊#168—24no—
106#3941—42no—
107#3941—42no—
108#3941—42no—
109#3941—42no—
110C2×#535—51no—
111C2×#408—51no—
112#2311D511yescharacteristic, complemented
113#1895—52no—
114#1893—52no—
115#1875—52no—
116#1874—52no—
117#1825—52no—
118#1786—52no—
119C24×C5C2×D411yescharacteristic
120C24×C5C2×D411yescharacteristic
121C24×C5C2×D411yescharacteristic
122C23×D5—22no—
123C23×D5—24no—
124C23×D5—42no—
125C23×D5—42no—
126C23×D5—82no—
127C23×D5—82no—
128C5×#41—44no—
129C5×#41—44no—
130C5×#41—44no—
131C5×#41—44no—
132C2×C5×Q8—41no—
133C2×C5×Q8—41no—
134C2×C5×Q8C22⋊C414yes—
135C2×C5×D4—41no—
136C2×C5×D4—41no—
137C2×C5×D4—41no—
138C2×C5×D4—41no—
139C2×C5×D4—41no—
140C2×C5×D4—41no—
141C2×C5×D4C22⋊C414yes—
142C2×C5×D4C22⋊C414yes—
143C2×C5×D4C22⋊C414yes—
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—21no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—42no—
159C22×C4×C5—82no—
160C22×C4×C5C22×C412yes—
161C22×C4×C5C22×C412yes—
162C22×C4×C5C22×C412yes—
163C22×C4×C5C2×D412yes—
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×D412yes—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2411yescharacteristic
170C2×C22⋊D5—28no—
171C2×C22⋊D5—28no—
172C2×C22⋊D5—82no—
173C2×C22⋊D5—82no—
174C2×C22⋊D5—82no—
175C2×C22⋊D5—82no—
176C22×Dic5—22no—
177C2×D20—22no—
178C2×D20—22no—
179C2×D20—22no—
180C2×D20—22no—
181C2×D20—24no—
182C2×D20—22no—
183C2×D20—44no—
184C2×D20—44no—
185C2×D20—42no—
186C2×D20—42no—
187C2×D20—44no—
188C2×D20—44no—
189C2×D20C22×C414yes—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—42no—
195C5×C22⋊C4—42no—
196C5×C22⋊C4—82no—
197C5×C22⋊C4—82no—
198C42×C5—42no—
199C22⋊Dic5—24no—
200#685—28no—
201#685—28no—
202C4⋊Dic5—22no—
203C4⋊Dic5C22×C414yes—
204C4×Dic5—24no—
205#681—44no—
206C2×#168—22no—
207C2×#168—22no—
208C2×#168—22no—
209C2×#168—22no—
210C2×#168—22no—
211C2×#168—22no—
212C2×#168—44no—
213C22×#41C2×D511yescharacteristic
214C23×D4—51no—
215C22×M16—51no—
216C23×C8—51no—
217#535—58no—
218#535—104no—
219C2×#127—101no—
220C2×#124—101no—
221C2×#121—52no—
222C2×#121—52no—
223C2×#120—101no—
224C2×#120—101no—
225C2×#117—51no—
226C2×#117C2×D511yescharacteristic, complemented
227C22×C4⋊C4C2×D511yescharacteristic, complemented
228C2×#102—52no—
229C2×#102—52no—
230C2×#102—52no—
231C2×#102—52no—
232#408—104no—
233C2×C22⋊C8—52no—
234C2×C22⋊C8—52no—
235#391—21no—
236#390—21no—
237#386—21no—
238#386—21no—
239#380C2×D512yes—
240#380C2×D512yescomplemented
241#340—52no—
242#340—52no—
243#340—52no—
244#340—52no—
245C23×C5—21no—
246C23×C5—21no—
247C23×C5—21no—
248C23×C5—21no—
249C23×C5—21no—
250C23×C5—21no—
251C23×C5—22no—
252C23×C5—22no—
253C23×C5—22no—
254C23×C5—22no—
255C23×C5—22no—
256C23×C5—22no—
257C23×C5C2×C22⋊C412yes—
258C23×C5C2×C22⋊C412yes—
259C23×C5C2×C22⋊C412yes—
260C23×C5C22×D411yescharacteristic
261C22×D5—24no—
262C22×D5—48no—
263C22×D5—42no—
264C22×D5—42no—
265C22×D5—42no—
266C22×D5—42no—
267C22×D5—42no—
268C22×D5—42no—
269C22×D5—88no—
270C22×D5—88no—
271C22×D5—84no—
272C22×D5—84no—
273C5×Q8—44no—
274C5×D4—44no—
275C5×D4—44no—
276C5×D4—44no—
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—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—42no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—84no—
302C2×C4×C5C2×C22⋊C412yes—
303C2×C4×C5C2×C22⋊C412yes—
304C2×C4×C5C2×C22⋊C412yes—
305C2×C4×C5C23×C411yescharacteristic
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5H(5,𝔽2)11yescharacteristic
308C2×C4×C5H(5,𝔽2)11yescharacteristic
309C2×C4×C5H(5,𝔽2)11yescharacteristic
310C2×C4×C5H(5,𝔽2)11yescharacteristic
311C22⋊D5—88no—
312C22⋊D5—88no—
313C2×Dic5—24no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316D20—24no—
317D20—24no—
318D20—48no—
319D20—42no—
320D20—42no—
321#168—42no—
322#168—42no—
323C25—101no—
324C2×#41—41no—
325C2×#41—41no—
326C2×#41—41no—
327C2×#41—41no—
328C2×#41C4×D514yes—
329C2×#41D2014yes—
330C22×Q8C22⋊D511yescharacteristic
331C22×D4—54no—
332C22×D4—52no—
333C22×D4—102no—
334C22×D4—102no—
335C22×D4—102no—
336C22×D4—101no—
337C22×D4—201no—
338C22×D4—201no—
339C22×D4—201no—
340C22×D4—201no—
341C22×D4C22⋊D511yescharacteristic
342C22×D4C22⋊D511yescharacteristic
343C22×D4C22⋊D511yescharacteristic
344C23×C4—21no—
345C23×C4C22×D511yescharacteristic
346C23×C4C22×D511yescharacteristic
347C23×C4C22×D511yescharacteristic
348C2×M16—102no—
349C2×M16—201no—
350C2×M16—201no—
351C22×C8—52no—
352C22×C8—52no—
353C22×C8—102no—
354C22×C8—201no—
355C22×C8—201no—
356#127—108no—
357#124—108no—
358#121—58no—
359#121—58no—
360#121—104no—
361#121—104no—
362#120—108no—
363#120—108no—
364#117—41no—
365#117—41no—
366#117—54no—
367#117—102no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—52no—
372C2×C4⋊C4C22×D512yes—
373C2×C4⋊C4C22×D512yes—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—101no—
378C2×C22⋊C4—102no—
379C2×C22⋊C4—102no—
380C2×C42—21no—
381C2×C42—101no—
382#102—202no—
383#102—202no—
384#102—202no—
385#102—202no—
386C22⋊C8—104no—
387C22⋊C8—104no—
388#95—22no—
389#95—22no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5—22no—
393C22×C5—24no—
394C22×C5—24no—
395C22×C5—24no—
396C22×C5—42no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5C22×C22⋊C411yescharacteristic
406C22×C5#53411yescharacteristic
407C22×C5#53411yescharacteristic
408C22×C5#57612yes—
409C22×C5#57712yes—
410C2×D5—44no—
411C2×D5—44no—
412C2×D5—44no—
413C2×D5—816no—
414C2×D5—82no—
415C2×D5—82no—
416C2×D5—82no—
417C2×D5—82no—
418C4×C5—22no—
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—82no—
422C4×C5—82no—
423C4×C5#51811yescharacteristic
424C4×C5#51811yescharacteristic
425C4×C5#53411yescharacteristic
426C4×C5#53411yescharacteristic
427Dic5—44no—
428C24—102no—
429C24—104no—
430C24—202no—
431C24—202no—
432C24—402no—
433C24—402no—
434C24C2×C22⋊D511yescharacteristic
435C24C2×C22⋊D511yescharacteristic
436C24C2×C22⋊D511yescharacteristic
437#41—44no—
438#41—44no—
439#41—44no—
440#41—44no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8#68514yes—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—54no—
451C2×D4—108no—
452C2×D4—108no—
453C2×D4—102no—
454C2×D4—102no—
455C2×D4—102no—
456C2×D4—102no—
457C2×D4—102no—
458C2×D4—104no—
459C2×D4—204no—
460C2×D4—204no—
461C2×D4—202no—
462C2×D4—202no—
463C2×D4—204no—
464C2×D4—204no—
465C2×D4—402no—
466C2×D4—402no—
467C2×D4—402no—
468C2×D4—402no—
469C2×D4#68514yes—
470C2×D4#68514yes—
471C2×D4#68514yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4—82no—
488C22×C4—102no—
489C22×C4C2×C4×D512yes—
490C22×C4C2×C4×D512yes—
491C22×C4C2×C4×D512yes—
492C22×C4C2×D2012yes—
493C22×C4C2×D2012yes—
494C22×C4C2×D2012yes—
495C22×C4C2×C22⋊D511yescharacteristic
496C22×C4C2×C22⋊D511yescharacteristic
497C22×C4C2×C22⋊D511yescharacteristic
498C22×C4C23×D511yescharacteristic
499M16—204no—
500C2×C8—102no—
501C2×C8—102no—
502C2×C8—102no—
503C2×C8—102no—
504C2×C8—102no—
505C2×C8—102no—
506C2×C8—204no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—42no—
512C4⋊C4—54no—
513C4⋊C4—102no—
514C22⋊C4—42no—
515C22⋊C4—82no—
516C22⋊C4—82no—
517C22⋊C4—104no—
518C22⋊C4—108no—
519C22⋊C4—108no—
520C42—42no—
521C42—104no—
522C2×C5—42no—
523C2×C5—42no—
524C2×C5—42no—
525C2×C5#230811yescharacteristic
526C2×C5#289712yes—
527C2×C5#319812yes—
528C2×C5#319911yescharacteristic
529C2×C5#320011yescharacteristic
530D5—84no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—104no—
544C23—208no—
545C23—202no—
546C23—202no—
547C23—202no—
548C23—202no—
549C23—202no—
550C23—202no—
551C23—408no—
552C23—404no—
553C23—404no—
554C23—408no—
555C23C2×#68512yes—
556C23C2×#68512yes—
557C23C2×#68512yes—
558C23C22×C22⋊D511yescharacteristic
559Q8—44no—
560D4—44no—
561D4—44no—
562D4—44no—
563D4—104no—
564D4—104no—
565D4—208no—
566D4—202no—
567D4—202no—
568D4—408no—
569D4—408no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—84no—
595C2×C4—104no—
596C2×C4—202no—
597C2×C4—202no—
598C2×C4C2×#68512yes—
599C2×C4C2×#68512yes—
600C2×C4C2×#68512yes—
601C2×C4C22×C4×D511yescharacteristic
602C2×C4C22×D2011yescharacteristic
603C2×C4#414411yescharacteristic
604C2×C4#414411yescharacteristic
605C2×C4#414411yescharacteristic
606C2×C4#414411yescharacteristic
607C8—202no—
608C8—202no—
609C5#2177011yescharacteristic, complemented, Sylow
610C22—24no—
611C22—24no—
612C22—24no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—204no—
626C22—204no—
627C22—204no—
628C22—4016no—
629C22—402no—
630C22—402no—
631C22—402no—
632C22—402no—
633C22C22×#68511yescharacteristic
634C22#6613811yescharacteristic
635C22#6613811yescharacteristic
636C22#6616912yes—
637C22#6617112yes—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—82no—
642C4—82no—
643C4—204no—
644C4#6582011yescharacteristic
645C4#6582011yescharacteristic
646C4#6582711yescharacteristic
647C4#6582711yescharacteristic
648C2—42no—
649C2—42no—
650C2—42no—
651C2—404no—
652C2#1061385211yescharacteristic
653C2#1061429412yes—
654C2#1061511811yescharacteristic
655C2#1061513811yescharacteristic
656C2#1061515612yes—
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2311C2
socleC23×C5C22×D4
prime radicalC2×#66164C2
cosocleC22×C4×C5C24
hypercenter#2311D5
hypocenterC5#21770
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C5×#2311C2semidirect
3. C2×#65523C2semidirect
4. #10602379C2semidirect
5. #10602353C2semidirect
6. #10600314C2semidirect
7. #10600310C2semidirect
8. #10600308C2semidirect
9. #10600296C2semidirect
12. C2×C5×#117C22semidirect
13. C22×C5×C4⋊C4C22semidirect
15. #66164C4semidirect
23. C22×#681C22semidirect
24. C23×#168C22semidirect
30. C5×#380C22semidirect
33. C2×C22⋊#168C22semidirect
38. #64749C22semidirect
39. #64749C22semidirect
40. #64749C22semidirect
41. #64749C22semidirect
66. C22×D20C2×C4semidirect
87. #4076C2×C4semidirect
91. #4072C2×C4semidirect
112. #2311D5semidirect
226. C2×#117C2×D5semidirect
227. C22×C4⋊C4C2×D5semidirect
240. #380C2×D5semidirect
609. C5#21770semidirect

Maximal subgroups

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

subgroupindex
C2×#661642
C5×#23112
C2×#655232
#106023792
#106023532
#106003142
#106003102
#106003082
#106002962
#217705