Finite Group Databasebeta

← #12022055

Subgroups — #12022055

Order 1280.

2150 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65278C212yesmaximal
2C2×C4×#685C211yesmaximal, characteristic
3C2×#64957C212yesmaximal
4C2×#64956C211yesmaximal, characteristic
5C2×D5×#95C211yesmaximal, characteristic
6C5×C4⋊#95C211yesmaximal, characteristic, complemented
7#10602361C212yesmaximal, complemented
8#10602328C211yesmaximal, characteristic, complemented
9#10600213C212yesmaximal, complemented
10#10600197C211yesmaximal, characteristic, complemented
11#10600197C211yesmaximal, characteristic, complemented
12C23×C4×D5C2212yes—
13C23×C4×D5C2211yescharacteristic
14C22×C5×C4⋊C4C2212yes—
15C22×C42×C5C2211yescharacteristic
16C22×#685C2212yes—
17C22×#685C2211yescharacteristic
18C22×#685C2211yescharacteristic
19C22×C4⋊Dic5C2212yes—
20C22×#683C2212yes—
21C22×#683C2212yes—
22C22×#683C2212yes—
23C22×C4×Dic5C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2211yescharacteristic
29C2×#3963C2211yescharacteristic
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35#65278—28no—
36C4×#685C418yescomplemented
37#64957—28no—
38#64956—24no—
39D5×#95—24no—
40#13965—51nomaximal, Sylow
41C24×D5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C22×C4×D5—24no—
53C22×C4×D5—24no—
54C22×C4×D5—24no—
55C22×C4×D5—24no—
56C22×C4×D5—24no—
57C22×C4×D5—42no—
58C22×C4×D5—42no—
59C22×C4×D5—42no—
60C22×C4×D5—42no—
61C22×C4×D5C2×C414yes—
62C22×C4×D5D414yes—
63C22×C4×D5Q814yes—
64C2×C5×C4⋊C4—24no—
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—42no—
67C2×C42×C5—42no—
68C2×C42×C5C2×C414yescomplemented
69C2×#685—24no—
70C2×#685—24no—
71C2×#685—24no—
72C2×#685C2×C414yes—
73C2×#685C2×C414yes—
74C2×#685D414yes—
75C2×#685D414yes—
76C2×#685Q814yes—
77C2×#685Q814yes—
78C2×C4⋊Dic5—24no—
79C2×C4⋊Dic5—24no—
80C2×C4⋊Dic5—42no—
81C2×#683—24no—
82C2×#683—24no—
83C2×#683—24no—
84C2×#683—24no—
85C2×#683—24no—
86C2×#683—42no—
87C2×#683—42no—
88C2×#683—42no—
89C2×#683—42no—
90C2×C4×Dic5—42no—
91C2×C4×Dic5C2×C414yescomplemented
92C5×#95—22no—
93C5×#95—22no—
94C5×#95—24no—
95#3963—22no—
96#3963—22no—
97#3963—24no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101#3963C2×C414yescomplemented
102#3963C2×C414yescomplemented
103C2×#385—52no—
104C2×#385—52no—
105C2×#380—51no—
106C2×C4×C22⋊C4—51no—
107C22×#95—51no—
108#1444—52no—
109#1444—52no—
110C4⋊#95—51no—
111C4⋊#95—51no—
112C4⋊#95—51no—
113C4⋊#95D511yescharacteristic, complemented
114C24×C5C2411yescharacteristic
115C23×D5—22no—
116C23×D5—22no—
117C23×D5—22no—
118C23×D5—22no—
119C23×D5C22×C412yes—
120C23×D5C2×D412yes—
121C23×D5C2×D412yes—
122C23×D5C2×D412yes—
123C23×D5C2×Q812yes—
124C23×D5C2×Q812yes—
125C23×D5C2×Q812yes—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
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×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5C22×C412yes—
146C22×C4×C5C22×C412yes—
147C22×C4×C5C22×C412yes—
148C22×C4×C5C2×D412yes—
149C22×C4×C5C2×D412yes—
150C22×C4×C5C2×D412yes—
151C22×C4×C5C2×Q812yes—
152C22×C4×C5C2×Q812yes—
153C22×C4×C5C2×Q812yes—
154C22×C4×C5#4114yes—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
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×C412yes—
176C22×Dic5C22×C412yes—
177C22×Dic5C2×D412yes—
178C22×Dic5C2×D412yes—
179C22×Dic5C2×D412yes—
180C22×Dic5C2×Q812yes—
181C22×Dic5C2×Q812yes—
182C22×Dic5C2×Q812yes—
183C22×Dic5#4114yes—
184C2×C4×D5—216no—
185C2×C4×D5—44no—
186C2×C4×D5—44no—
187C2×C4×D5—48no—
188C2×C4×D5—48no—
189C2×C4×D5—48no—
190C2×C4×D5—48no—
191C2×C4×D5—48no—
192C2×C4×D5—48no—
193C2×C4×D5—48no—
194C2×C4×D5—48no—
195C2×C4×D5C4⋊C4116yescomplemented
196C5×C4⋊C4—48no—
197C42×C5—44no—
198#685—48no—
199#685C4⋊C4116yescomplemented
200#685C4⋊C4116yescomplemented
201C4⋊Dic5—48no—
202#683—48no—
203#683—48no—
204#683—48no—
205C4×Dic5—44no—
206C24×C4—51no—
207C24×C4—52no—
208C22×C4⋊C4—52no—
209C22×C4⋊C4—52no—
210C22×C4⋊C4—52no—
211C22×C4⋊C4—52no—
212C22×C4⋊C4C2×D512yes—
213C22×C22⋊C4—51no—
214C22×C22⋊C4—51no—
215C22×C22⋊C4—52no—
216C22×C42—51no—
217C22×C42C2×D511yescharacteristic
218#385—108no—
219#385—108no—
220#380—104no—
221C4×C22⋊C4—58no—
222C2×#95—51no—
223C2×#95—51no—
224C2×#95—51no—
225C2×#95—51no—
226C2×#95—52no—
227C2×#95—52no—
228C2×#95—52no—
229C2×#95—52no—
230C2×#95—104no—
231C2×#95C2×D511yescharacteristic
232C2×#95C2×D511yescharacteristic
233C2×#95C2×D512yes—
234C23×C5C23×C411yescharacteristic
235C23×C5C22×D411yescharacteristic
236C23×C5C22×D411yescharacteristic
237C23×C5C22×D411yescharacteristic
238C23×C5C22×Q811yescharacteristic
239C23×C5C22×Q811yescharacteristic
240C23×C5C22×Q811yescharacteristic
241C23×C5C2×#4112yes—
242C23×C5C2×#4112yes—
243C23×C5H(5,𝔽2)12yes—
244C23×C5H(5,𝔽2)12yes—
245C22×D5—22no—
246C22×D5—22no—
247C22×D5—22no—
248C22×D5—22no—
249C22×D5—24no—
250C22×D5—24no—
251C22×D5—24no—
252C22×D5—24no—
253C22×D5—24no—
254C22×D5—24no—
255C22×D5—24no—
256C22×D5—24no—
257C22×D5—24no—
258C22×D5—24no—
259C22×D5—24no—
260C22×D5—24no—
261C22×D5C2×C4⋊C414yes—
262C22×D5C2×C4⋊C414yes—
263C22×D5C2×C4⋊C414yes—
264C22×D5#12714yes—
265C22×D5C4⋊Q814yes—
266C22×D5C4⋊Q814yes—
267C22×D5C4⋊Q814yes—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
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—42no—
284C2×C4×C5—42no—
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×C5—42no—
294C2×C4×C5C2×C4⋊C414yes—
295C2×C4×C5C2×C4⋊C414yes—
296C2×C4×C5C2×C4⋊C414yes—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—24no—
304C2×Dic5—24no—
305C2×Dic5—24no—
306C2×Dic5—24no—
307C2×Dic5—24no—
308C2×Dic5—24no—
309C2×Dic5—24no—
310C2×Dic5—24no—
311C2×Dic5—24no—
312C2×Dic5—42no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316C2×Dic5—42no—
317C2×Dic5—42no—
318C2×Dic5—42no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5C2×C4⋊C414yes—
324C2×Dic5C2×C4⋊C414yes—
325C2×Dic5C2×C4⋊C414yes—
326C4×D5—416no—
327C4×D5—432no—
328C25—51no—
329C23×C4—51no—
330C23×C4—51no—
331C23×C4—51no—
332C23×C4—54no—
333C23×C4—54no—
334C23×C4—54no—
335C23×C4—52no—
336C23×C4—52no—
337C23×C4—104no—
338C23×C4—104no—
339C23×C4—104no—
340C23×C4—104no—
341C23×C4—104no—
342C23×C4—202no—
343C23×C4—202no—
344C23×C4—202no—
345C23×C4—202no—
346C23×C4C22×D512yes—
347C23×C4C22×D512yes—
348C23×C4C22×D511yescharacteristic
349C23×C4C22×D511yescharacteristic
350C23×C4C22×D511yescharacteristic
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—104no—
355C2×C4⋊C4—104no—
356C2×C4⋊C4—104no—
357C2×C4⋊C4—104no—
358C2×C4⋊C4—104no—
359C2×C4⋊C4—104no—
360C2×C4⋊C4—104no—
361C2×C4⋊C4—202no—
362C2×C4⋊C4—202no—
363C2×C4⋊C4—202no—
364C2×C4⋊C4—202no—
365C2×C4⋊C4—202no—
366C2×C22⋊C4—54no—
367C2×C22⋊C4—54no—
368C2×C22⋊C4—54no—
369C2×C22⋊C4—54no—
370C2×C22⋊C4—54no—
371C2×C22⋊C4—54no—
372C2×C22⋊C4—104no—
373C2×C22⋊C4—104no—
374C2×C22⋊C4—104no—
375C2×C42—42no—
376C2×C42—54no—
377C2×C42—202no—
378C2×C42C4×D514yescomplemented
379#95—22no—
380#95—22no—
381#95—24no—
382#95—54no—
383#95—54no—
384#95—104no—
385#95—104no—
386#95—104no—
387#95—102no—
388#95—102no—
389#95—104no—
390C22×C5C22×C4⋊C411yescharacteristic
391C22×C5C22×C4⋊C411yescharacteristic
392C22×C5C22×C4⋊C411yescharacteristic
393C22×C5C4×#4111yescharacteristic
394C22×C5C4×#4111yescharacteristic
395C22×C5#51811yescharacteristic
396C22×C5#51811yescharacteristic
397C22×C5#52512yes—
398C22×C5C2×#12711yescharacteristic
399C22×C5C2×C4⋊Q811yescharacteristic
400C22×C5C2×C4⋊Q811yescharacteristic
401C22×C5C2×C4⋊Q811yescharacteristic
402C22×C5#53312yes—
403C22×C5#53412yes—
404C22×C5#54312yes—
405C22×C5#54612yes—
406C22×C5#54612yes—
407C22×C5#54612yes—
408C22×C5#54612yes—
409C22×C5#55412yes—
410C22×C5#55412yes—
411C22×C5#55412yes—
412C22×C5#55412yes—
413C2×D5—24no—
414C2×D5—28no—
415C2×D5—24no—
416C2×D5—24no—
417C2×D5—24no—
418C2×D5—24no—
419C2×D5—28no—
420C2×D5—28no—
421C2×D5—28no—
422C2×D5—24no—
423C2×D5#38418yes—
424C4×C5—24no—
425C4×C5—24no—
426C4×C5—24no—
427C4×C5—44no—
428C4×C5—82no—
429Dic5—24no—
430Dic5—24no—
431Dic5—24no—
432Dic5—44no—
433Dic5—82no—
434C24—52no—
435C24—52no—
436C24—52no—
437C24—52no—
438C24—52no—
439C24—52no—
440C24—52no—
441C24—102no—
442C24—102no—
443C24—102no—
444C24—102no—
445C24C23×D511yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
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—22no—
465C22×C4—52no—
466C22×C4—52no—
467C22×C4—52no—
468C22×C4—52no—
469C22×C4—52no—
470C22×C4—52no—
471C22×C4—52no—
472C22×C4—52no—
473C22×C4—52no—
474C22×C4—516no—
475C22×C4—54no—
476C22×C4—1016no—
477C22×C4—102no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—102no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—102no—
489C22×C4—102no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—102no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—204no—
497C22×C4—204no—
498C22×C4—208no—
499C22×C4—208no—
500C22×C4—208no—
501C22×C4—208no—
502C22×C4—208no—
503C22×C4—208no—
504C22×C4—208no—
505C22×C4—208no—
506C22×C4C2×C4×D512yes—
507C22×C4C2×C4×D512yes—
508C22×C4C2×C4×D512yes—
509C22×C4#70914yes—
510C22×C4D4×D512yes—
511C22×C4D4×D512yes—
512C22×C4D4×D512yes—
513C22×C4Q8×D512yes—
514C22×C4Q8×D512yes—
515C22×C4Q8×D512yes—
516C4⋊C4—48no—
517C4⋊C4—208no—
518C4⋊C4—208no—
519C4⋊C4—208no—
520C4⋊C4—208no—
521C22⋊C4—516no—
522C22⋊C4—516no—
523C22⋊C4—208no—
524C42—44no—
525C42—204no—
526C2×C5C2×#38411yescharacteristic
527C2×C5#229611yescharacteristic
528C2×C5#231511yescharacteristic
529C2×C5#234911yescharacteristic
530C2×C5#234911yescharacteristic
531C2×C5#234911yescharacteristic
532C2×C5#234911yescharacteristic
533C2×C5#253912yes—
534C2×C5#254912yes—
535C2×C5#254912yes—
536C2×C5#258312yes—
537D5—28no—
538C23—54no—
539C23—54no—
540C23—54no—
541C23—54no—
542C23—54no—
543C23—54no—
544C23—54no—
545C23—102no—
546C23—102no—
547C23—104no—
548C23—104no—
549C23—102no—
550C23—102no—
551C23—104no—
552C23—104no—
553C23—104no—
554C23—104no—
555C23—104no—
556C23—104no—
557C23—104no—
558C23—104no—
559C23—104no—
560C23—104no—
561C23C22×C4×D511yescharacteristic
562C23C2×#70912yes—
563C23C2×D4×D511yescharacteristic
564C23C2×D4×D511yescharacteristic
565C23C2×D4×D511yescharacteristic
566C23#414412yes—
567C23C2×Q8×D511yescharacteristic
568C23C2×Q8×D511yescharacteristic
569C23C2×Q8×D511yescharacteristic
570C23D5×#4112yes—
571C23#414912yes—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
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—42no—
588C2×C4—42no—
589C2×C4—42no—
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—54no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—102no—
607C2×C4—104no—
608C2×C4—104no—
609C2×C4—104no—
610C2×C4—104no—
611C2×C4—104no—
612C2×C4—104no—
613C2×C4—104no—
614C2×C4—104no—
615C2×C4—104no—
616C2×C4—2016no—
617C2×C4—2032no—
618C2×C4—202no—
619C2×C4—202no—
620C2×C4—202no—
621C2×C4—202no—
622C2×C4—202no—
623C2×C4—202no—
624C2×C4—202no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4D5×C4⋊C414yes—
630C2×C4D5×C4⋊C414yes—
631C2×C4D5×C4⋊C414yes—
632C5#1396511yescharacteristic, complemented, Sylow
633C22—58no—
634C22—104no—
635C22—108no—
636C22—108no—
637C22—108no—
638C22—104no—
639C22—104no—
640C22—104no—
641C22—104no—
642C22—104no—
643C22—108no—
644C22C4×#70911yescharacteristic
645C22#6582011yescharacteristic
646C22#6582412yes—
647C22C2×D5×C4⋊C411yescharacteristic
648C22C2×D5×C4⋊C411yescharacteristic
649C22C2×D5×C4⋊C411yescharacteristic
650C22#6584512yes—
651C22#6585511yescharacteristic
652C22#6585611yescharacteristic
653C22#6588112yes—
654C22#6588412yes—
655C22#6591212yes—
656C22#6591312yes—
657C22#6593912yes—
658C22#6594412yes—
659C22#6596812yes—
660C22#6597012yes—
661C22#6601012yes—
662C22#6602412yes—
663C22D5×#12711yescharacteristic
664C22D5×C4⋊Q811yescharacteristic
665C22D5×C4⋊Q811yescharacteristic
666C22D5×C4⋊Q811yescharacteristic
667C4—24no—
668C4—24no—
669C4—24no—
670C4—44no—
671C4—82no—
672C4—104no—
673C4—104no—
674C4—104no—
675C4—204no—
676C4—402no—
677C2—108no—
678C2#1060510011yescharacteristic
679C2#1060548611yescharacteristic
680C2#1060550111yescharacteristic
681C2#1060573611yescharacteristic
682C2#1060574211yescharacteristic
683C2#1060595911yescharacteristic
684C2D5×#38411yescharacteristic
685C2#1060797512yes—
686C2#1060797812yes—
687C2#1060818512yes—
688C2#1060836812yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13965
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
6. C5×C4⋊#95C2semidirect
7. #10602361C2semidirect
8. #10602328C2semidirect
9. #10600213C2semidirect
10. #10600197C2semidirect
11. #10600197C2semidirect
36. C4×#685C4semidirect
68. C2×C42×C5C2×C4semidirect
91. C2×C4×Dic5C2×C4semidirect
101. #3963C2×C4semidirect
102. #3963C2×C4semidirect
113. C4⋊#95D5semidirect
195. C2×C4×D5C4⋊C4semidirect
199. #685C4⋊C4semidirect
200. #685C4⋊C4semidirect
378. C2×C42C4×D5semidirect
632. C5#13965semidirect

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×#649572
C2×#649562
C2×D5×#952
C5×C4⋊#952
#106023612
#106023282
#106002132
#106001972
#139655