Finite Group Databasebeta

← #12020813

Subgroups — #12020813

Order 1280.

2298 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65278C212yesmaximal
2C2×C4×#685C211yesmaximal, characteristic
3C2×D5×#95C211yesmaximal, characteristic
4C2×#64938C211yesmaximal, characteristic, complemented
5C2×#64955C212yesmaximal
6C5×C4⋊#95C211yesmaximal, characteristic, complemented
7#10602357C212yesmaximal, complemented
8C4×#3963C211yesmaximal, characteristic, complemented
9#10600218C211yesmaximal, characteristic
10#10600199C212yesmaximal, complemented
11#10600195C211yesmaximal, characteristic, complemented
12C23×C4×D5C2211yescharacteristic
13C23×C4×D5C2212yes—
14C22×C5×C4⋊C4C2212yes—
15C22×C42×C5C2211yescharacteristic
16C22×#685C2212yes—
17C22×#685C2211yescharacteristic
18C22×#685C2211yescharacteristic
19C22×#683C2212yes—
20C22×C4×Dic5C2212yes—
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2212yes—
25C2×C5×#95C2211yescharacteristic
26C2×#3963C2211yescharacteristic
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35#65278C4116yescomplemented
36C4×#685C418yescomplemented
37#64955—28no—
38D5×#95—24no—
39#64938—24no—
40#13814—51nomaximal, Sylow
41C24×D5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2312yes—
52C22×C4×D5—24no—
53C22×C4×D5—24no—
54C22×C4×D5—24no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—24no—
58C22×C4×D5—24no—
59C22×C4×D5—42no—
60C22×C4×D5—42no—
61C22×C4×D5—42no—
62C22×C4×D5C2×C414yes—
63C22×C4×D5C2×C418yes—
64C2×C5×C4⋊C4—42no—
65C2×C5×C4⋊C4—42no—
66C2×C5×C4⋊C4C2×C418yescomplemented
67C2×C42×C5—42no—
68C2×C42×C5C2×C414yescomplemented
69C2×#685—24no—
70C2×#685—24no—
71C2×#685C2×C418yes—
72C2×#685C2×C414yes—
73C2×#685C2×C418yes—
74C2×#685C2×C414yes—
75C2×#685D414yes—
76C2×#685Q814yes—
77C2×#683—24no—
78C2×#683—24no—
79C2×#683C2×C418yescomplemented
80C2×C4×Dic5—22no—
81C2×C4×Dic5—22no—
82C2×C4×Dic5—24no—
83C2×C4×Dic5—24no—
84C2×C4×Dic5—24no—
85C2×C4×Dic5—24no—
86C2×C4×Dic5—42no—
87C2×C4×Dic5—42no—
88C2×C4×Dic5C2×C414yescomplemented
89C5×#95—22no—
90C5×#95—22no—
91C5×#95—24no—
92#3963—22no—
93#3963—24no—
94#3963—24no—
95#3963—42no—
96#3963C2×C414yescomplemented
97#3963C2×C414yescomplemented
98#3963C2×C418yescomplemented
99#3963C2×C418yescomplemented
100#3963D414yes—
101C2×#385—52no—
102C2×C4×C4⋊C4—51no—
103C2×C4×C22⋊C4—51no—
104C2×C4×C22⋊C4—52no—
105C22×#95—51no—
106#1436—52no—
107#1436—52no—
108C4⋊#95D511yescharacteristic, complemented
109#1434—51no—
110C22⋊#95—51no—
111C4×#95—51no—
112C24×C5C2411yescharacteristic
113C23×D5—21no—
114C23×D5—21no—
115C23×D5—22no—
116C23×D5—21no—
117C23×D5—22no—
118C23×D5—21no—
119C23×D5C22×C412yes—
120C23×D5C22×C414yes—
121C23×D5C2×D412yes—
122C23×D5C2×Q812yes—
123C23×D5#4114yes—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5C22×C414yes—
144C22×C4×C5C22×C414yes—
145C22×C4×C5C22×C412yes—
146C22×C4×C5C22×C414yes—
147C22×C4×C5C22×C412yes—
148C22×C4×C5C22×C412yes—
149C22×C4×C5C2×D412yes—
150C22×C4×C5C2×D412yes—
151C22×C4×C5C2×Q812yes—
152C22×C4×C5#4112yes—
153C22×Dic5—22no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—22no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—22no—
166C22×Dic5—21no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5C22×C412yes—
175C22×Dic5C22×C414yes—
176C22×Dic5C22×C412yes—
177C22×Dic5C22×C414yes—
178C22×Dic5C22×C412yes—
179C22×Dic5C22×C414yes—
180C22×Dic5C2×D412yes—
181C22×Dic5C2×D414yes—
182C22×Dic5C2×Q812yes—
183C22×Dic5#4114yes—
184C2×C4×D5—28no—
185C2×C4×D5—216no—
186C2×C4×D5—28no—
187C2×C4×D5—216no—
188C2×C4×D5—48no—
189C2×C4×D5—44no—
190C2×C4×D5—48no—
191C2×C4×D5—48no—
192C2×C4×D5—48no—
193C2×C4×D5—48no—
194C2×C4×D5—48no—
195C2×C4×D5—48no—
196C5×C4⋊C4—48no—
197C42×C5—44no—
198#685—216no—
199#685C42116yescomplemented
200#685C4⋊C4116yescomplemented
201#683—216no—
202C4×Dic5—28no—
203C4×Dic5—48no—
204C4×Dic5—48no—
205C24×C4—51no—
206C24×C4—52no—
207C22×C4⋊C4—52no—
208C22×C4⋊C4C2×D512yes—
209C22×C22⋊C4—51no—
210C22×C22⋊C4—51no—
211C22×C22⋊C4—52no—
212C22×C42—51no—
213C22×C42—52no—
214C22×C42—52no—
215C22×C42C2×D511yescharacteristic
216#385—516no—
217C4×C4⋊C4—104no—
218C4×C22⋊C4—58no—
219C4×C22⋊C4—108no—
220C2×#95—52no—
221C2×#95—51no—
222C2×#95—52no—
223C2×#95—51no—
224C2×#95—51no—
225C2×#95—51no—
226C2×#95—52no—
227C2×#95—52no—
228C2×#95—52no—
229C2×#95—104no—
230C2×#95C2×D511yescharacteristic
231C2×#95C2×D511yescharacteristic
232C2×#95C2×D512yes—
233C23×C5C23×C411yescharacteristic
234C23×C5C23×C412yes—
235C23×C5C22×D411yescharacteristic
236C23×C5C22×D411yescharacteristic
237C23×C5C22×Q811yescharacteristic
238C23×C5C2×#4111yescharacteristic
239C23×C5C2×#4112yes—
240C23×C5C2×#4112yes—
241C23×C5H(5,𝔽2)11yescharacteristic
242C23×C5H(5,𝔽2)12yes—
243C23×C52−1+411yescharacteristic
244C22×D5—22no—
245C22×D5—24no—
246C22×D5—22no—
247C22×D5—24no—
248C22×D5—22no—
249C22×D5—24no—
250C22×D5—22no—
251C22×D5—24no—
252C22×D5—22no—
253C22×D5—24no—
254C22×D5—24no—
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—24no—
258C22×D5—24no—
259C22×D5—24no—
260C22×D5—22no—
261C22×D5—24no—
262C22×D5C2×C4214yes—
263C22×D5C2×C4⋊C414yes—
264C22×D5#11714yes—
265C22×D5C4×D418yes—
266C22×D5C4×Q818yes—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—24no—
273C2×C4×C5—22no—
274C2×C4×C5—24no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—24no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—42no—
289C2×C4×C5—42no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5C2×C4214yes—
294C2×C4×C5C2×C4⋊C414yes—
295C2×C4×C5C4×D414yes—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—24no—
299C2×Dic5—24no—
300C2×Dic5—22no—
301C2×Dic5—24no—
302C2×Dic5—24no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—24no—
306C2×Dic5—24no—
307C2×Dic5—24no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—24no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—24no—
314C2×Dic5—22no—
315C2×Dic5—24no—
316C2×Dic5—22no—
317C2×Dic5—24no—
318C2×Dic5—42no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5—42no—
324C2×Dic5C2×C4214yes—
325C2×Dic5C2×C4⋊C414yes—
326C2×Dic5C4×D418yes—
327C4×D5—432no—
328C4×D5—416no—
329C25—51no—
330C23×C4—51no—
331C23×C4—51no—
332C23×C4—52no—
333C23×C4—52no—
334C23×C4—51no—
335C23×C4—54no—
336C23×C4—58no—
337C23×C4—104no—
338C23×C4—104no—
339C23×C4—104no—
340C23×C4—104no—
341C23×C4—104no—
342C23×C4—102no—
343C23×C4—102no—
344C23×C4—202no—
345C23×C4—202no—
346C23×C4—202no—
347C23×C4C22×D512yes—
348C23×C4C22×D512yes—
349C23×C4C22×D511yescharacteristic
350C23×C4C22×D511yescharacteristic
351C23×C4C22×D511yescharacteristic
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—58no—
355C2×C4⋊C4—104no—
356C2×C4⋊C4—104no—
357C2×C4⋊C4C4×D518yescomplemented
358C2×C22⋊C4—54no—
359C2×C22⋊C4—54no—
360C2×C22⋊C4—58no—
361C2×C22⋊C4—54no—
362C2×C22⋊C4—54no—
363C2×C22⋊C4—58no—
364C2×C22⋊C4—104no—
365C2×C22⋊C4—104no—
366C2×C42—42no—
367C2×C42—54no—
368C2×C42—102no—
369C2×C42—102no—
370C2×C42—104no—
371C2×C42—104no—
372C2×C42—104no—
373C2×C42—104no—
374C2×C42—202no—
375C2×C42—202no—
376C2×C42C4×D514yescomplemented
377#95—22no—
378#95—24no—
379#95—22no—
380#95—54no—
381#95—54no—
382#95—58no—
383#95—58no—
384#95—54no—
385#95—104no—
386#95—104no—
387#95—102no—
388#95—202no—
389C22×C5C22×C4211yescharacteristic
390C22×C5C22×C4⋊C411yescharacteristic
391C22×C5C2×#11711yescharacteristic
392C22×C5C2×C4×D411yescharacteristic
393C22×C5C2×C4×D412yes—
394C22×C5C2×C4×D412yes—
395C22×C5C2×C4×Q812yes—
396C22×C5C4×#4111yescharacteristic
397C22×C5C4×#4112yes—
398C22×C5#51811yescharacteristic
399C22×C5#51812yes—
400C22×C5#52011yescharacteristic
401C22×C5#52012yes—
402C22×C5D4211yescharacteristic
403C22×C5#54612yes—
404C22×C5#54612yes—
405C22×C5#54711yescharacteristic
406C22×C5D4×Q811yescharacteristic
407C22×C5#55112yes—
408C22×C5#55112yes—
409C22×C5#55212yes—
410C22×C5#55411yescharacteristic
411C22×C5#55412yes—
412C2×D5—24no—
413C2×D5—24no—
414C2×D5—24no—
415C2×D5—24no—
416C2×D5—28no—
417C2×D5—28no—
418C2×D5—28no—
419C2×D5—28no—
420C2×D5—24no—
421C2×D5—24no—
422C2×D5C4×C4⋊C418yescomplemented
423C4×C5—24no—
424C4×C5—24no—
425C4×C5—24no—
426C4×C5—44no—
427C4×C5—44no—
428Dic5—24no—
429Dic5—28no—
430Dic5—24no—
431Dic5—42no—
432Dic5—44no—
433C24—52no—
434C24—54no—
435C24—52no—
436C24—52no—
437C24—54no—
438C24—101no—
439C24—101no—
440C24—102no—
441C24—101no—
442C24—101no—
443C24—102no—
444C24C23×D511yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—52no—
465C22×C4—52no—
466C22×C4—54no—
467C22×C4—54no—
468C22×C4—54no—
469C22×C4—52no—
470C22×C4—52no—
471C22×C4—54no—
472C22×C4—54no—
473C22×C4—52no—
474C22×C4—1016no—
475C22×C4—108no—
476C22×C4—1016no—
477C22×C4—101no—
478C22×C4—102no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—101no—
489C22×C4—102no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—101no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—102no—
498C22×C4—108no—
499C22×C4—204no—
500C22×C4—208no—
501C22×C4—208no—
502C22×C4—208no—
503C22×C4—208no—
504C22×C4—208no—
505C22×C4—208no—
506C22×C4—208no—
507C22×C4C2×C4×D514yes—
508C22×C4C2×C4×D514yes—
509C22×C4C2×C4×D512yes—
510C22×C4C2×C4×D514yes—
511C22×C4C2×C4×D512yes—
512C22×C4C2×C4×D512yes—
513C22×C4D4×D512yes—
514C22×C4D4×D512yes—
515C22×C4Q8×D512yes—
516C22×C4#71312yes—
517C4⋊C4—48no—
518C4⋊C4—1016no—
519C22⋊C4—516no—
520C22⋊C4—516no—
521C22⋊C4—1016no—
522C42—44no—
523C42—108no—
524C42—208no—
525C42—208no—
526C2×C5C2×C4×C4⋊C411yescharacteristic
527C2×C5C42×D411yescharacteristic
528C2×C5#227511yescharacteristic
529C2×C5#234211yescharacteristic
530C2×C5#234311yescharacteristic
531C2×C5D4×C4⋊C411yescharacteristic
532C2×C5#234911yescharacteristic
533C2×C5#235812yes—
534C2×C5#235912yes—
535C2×C5#236012yes—
536C2×C5#236812yes—
537D5—28no—
538C23—54no—
539C23—54no—
540C23—54no—
541C23—58no—
542C23—58no—
543C23—102no—
544C23—102no—
545C23—102no—
546C23—102no—
547C23—104no—
548C23—102no—
549C23—102no—
550C23—102no—
551C23—104no—
552C23—102no—
553C23—104no—
554C23—104no—
555C23—104no—
556C23—104no—
557C23—104no—
558C23—104no—
559C23—104no—
560C23—104no—
561C23C22×C4×D511yescharacteristic
562C23C22×C4×D512yes—
563C23C2×D4×D511yescharacteristic
564C23C2×D4×D511yescharacteristic
565C23#414411yescharacteristic
566C23#414412yes—
567C23C2×Q8×D511yescharacteristic
568C23C2×#71311yescharacteristic
569C23#414711yescharacteristic
570C23D5×#4112yes—
571C23D5×#4112yes—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—54no—
599C2×C4—54no—
600C2×C4—58no—
601C2×C4—102no—
602C2×C4—104no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—104no—
607C2×C4—102no—
608C2×C4—102no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—104no—
612C2×C4—104no—
613C2×C4—104no—
614C2×C4—104no—
615C2×C4—104no—
616C2×C4—104no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—104no—
620C2×C4—102no—
621C2×C4—104no—
622C2×C4—104no—
623C2×C4—2016no—
624C2×C4—2032no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4—202no—
630C2×C4—202no—
631C2×C4C42×D514yes—
632C2×C4D5×C4⋊C414yes—
633C2×C4#403914yes—
634C5#1381411yescharacteristic, complemented, Sylow
635C22—58no—
636C22—104no—
637C22—104no—
638C22—108no—
639C22—108no—
640C22—108no—
641C22—104no—
642C22—104no—
643C22—104no—
644C22—108no—
645C22—104no—
646C22C2×C42×D511yescharacteristic
647C22#6582012yes—
648C22#6582011yescharacteristic
649C22C2×D5×C4⋊C411yescharacteristic
650C22C2×#403911yescharacteristic
651C22#6583811yescharacteristic
652C22#6583812yes—
653C22D5×#11711yescharacteristic
654C22#6585611yescharacteristic
655C22C4×D4×D512yes—
656C22C4×D4×D512yes—
657C22C4×Q8×D512yes—
658C22C4×#71312yes—
659C22#6594412yes—
660C22#6594412yes—
661C22#6597012yes—
662C22#6597112yes—
663C22#6601312yes—
664C22#6602712yes—
665C22#6605111yescharacteristic
666C22#6606011yescharacteristic
667C22#6606111yescharacteristic
668C22#6606411yescharacteristic
669C4—24no—
670C4—24no—
671C4—24no—
672C4—44no—
673C4—44no—
674C4—104no—
675C4—104no—
676C4—108no—
677C4—204no—
678C4—202no—
679C2—108no—
680C2#1060505311yescharacteristic
681C2C4×#403911yescharacteristic
682C2C4×D5×C4⋊C411yescharacteristic
683C2#1060574011yescharacteristic
684C2#1060574211yescharacteristic
685C2#1060595811yescharacteristic
686C2#1060609111yescharacteristic
687C2#1060771412yes—
688C2#1060793512yes—
689C2#1060816312yes—
690C2#1060834712yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13814
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#64938C2semidirect
6. C5×C4⋊#95C2semidirect
7. #10602357C2semidirect
8. C4×#3963C2semidirect
10. #10600199C2semidirect
11. #10600195C2semidirect
35. #65278C4semidirect
36. C4×#685C4semidirect
66. C2×C5×C4⋊C4C2×C4semidirect
68. C2×C42×C5C2×C4semidirect
79. C2×#683C2×C4semidirect
88. C2×C4×Dic5C2×C4semidirect
96. #3963C2×C4semidirect
97. #3963C2×C4semidirect
98. #3963C2×C4semidirect
99. #3963C2×C4semidirect
108. C4⋊#95D5semidirect
199. #685C42semidirect
200. #685C4⋊C4semidirect
357. C2×C4⋊C4C4×D5semidirect
376. C2×C42C4×D5semidirect
422. C2×D5C4×C4⋊C4semidirect
634. C5#13814semidirect

Maximal subgroups

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

subgroupindex
C2×#652782
C2×C4×#6852
C2×D5×#952
C2×#649382
C2×#649552
C5×C4⋊#952
#106023572
C4×#39632
#106002182
#106001992
#106001952
#138145