Finite Group Databasebeta

← #12021457

Subgroups — #12021457

Order 1280.

1962 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65225C211yesmaximal, characteristic, complemented
2C2×C4×#685C211yesmaximal, characteristic
3C2×#64957C212yesmaximal
4C2×D5×#95C211yesmaximal, characteristic
5C5×#1434C211yesmaximal, characteristic, complemented
6#10600218C211yesmaximal, characteristic
7#10600218C212yesmaximal
8#10600208C212yesmaximal, complemented
9#10600207C212yesmaximal, complemented
10#10600197C211yesmaximal, characteristic, complemented
11#10600194C211yesmaximal, characteristic, complemented
12C23×C4×D5C2212yes—
13C23×C4×D5C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C22×#685C2212yes—
16C22×#685C2211yescharacteristic
17C22×#685C2211yescharacteristic
18C22×C4⋊Dic5C2212yes—
19C22×#683C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C2×C5×#95C2211yescharacteristic
22C2×C5×#95C2211yescharacteristic
23C2×C5×#95C2212yes—
24C2×C5×#95C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2211yescharacteristic
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2211yescharacteristic
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C4×#685C418yescomplemented
36#65225—24no—
37#64957—28no—
38D5×#95—24no—
39#13896—51nomaximal, Sylow
40C24×D5C2311yescharacteristic
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C22×C4×D5—24no—
52C22×C4×D5—24no—
53C22×C4×D5—22no—
54C22×C4×D5—24no—
55C22×C4×D5—22no—
56C22×C4×D5—24no—
57C22×C4×D5—24no—
58C22×C4×D5—24no—
59C22×C4×D5—42no—
60C22×C4×D5—42no—
61C22×C4×D5—42no—
62C22×C4×D5C2×C414yes—
63C2×C42×C5—22no—
64C2×C42×C5—22no—
65C2×C42×C5C2×C414yescomplemented
66C2×#685—24no—
67C2×#685—24no—
68C2×#685—24no—
69C2×#685—24no—
70C2×#685C2×C414yes—
71C2×#685C2×C414yes—
72C2×#685D414yes—
73C2×#685Q814yes—
74C2×C4⋊Dic5—24no—
75C2×C4⋊Dic5—24no—
76C2×C4⋊Dic5—42no—
77C2×#683—24no—
78C2×#683—24no—
79C2×#683—42no—
80C2×C4×Dic5—42no—
81C2×C4×Dic5C2×C414yescomplemented
82C5×#95—22no—
83C5×#95—24no—
84C5×#95—24no—
85C5×#95—22no—
86#3963—22no—
87#3963—24no—
88#3963—24no—
89#3963—24no—
90#3963—42no—
91#3963—42no—
92#3963—42no—
93#3963C2×C414yescomplemented
94#3963C2×C414yescomplemented
95#3963D414yes—
96C2×#385—52no—
97C2×#382—51no—
98C2×C4×C22⋊C4—51no—
99C22×#95—51no—
100#1442—52no—
101#1442—52no—
102C4⋊#95—51no—
103#1434—51no—
104#1434D511yescharacteristic, complemented
105C22⋊#95—52no—
106C22⋊#95—51no—
107C24×C5C2411yescharacteristic
108C23×D5—21no—
109C23×D5—22no—
110C23×D5—21no—
111C23×D5—22no—
112C23×D5—21no—
113C23×D5—21no—
114C23×D5C22×C412yes—
115C23×D5C2×D412yes—
116C23×D5C2×Q812yes—
117C23×D5#4114yes—
118C23×D5#4114yes—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—21no—
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×C5C22×C412yes—
143C22×C4×C5C22×C412yes—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C2×D412yes—
146C22×C4×C5C2×D412yes—
147C22×C4×C5C2×Q812yes—
148C22×C4×C5#4114yes—
149C22×C4×C5#4112yes—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—21no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—21no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—21no—
164C22×Dic5—22no—
165C22×Dic5—21no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5C22×C412yes—
174C22×Dic5C22×C412yes—
175C22×Dic5C22×C412yes—
176C22×Dic5C2×D414yes—
177C22×Dic5C2×D412yes—
178C22×Dic5C2×Q812yes—
179C2×C4×D5—216no—
180C2×C4×D5—28no—
181C2×C4×D5—28no—
182C2×C4×D5—44no—
183C2×C4×D5—48no—
184C2×C4×D5—48no—
185C2×C4×D5—48no—
186C2×C4×D5—48no—
187C2×C4×D5—48no—
188C2×C4×D5—48no—
189C2×C4×D5—48no—
190C2×C4×D5—48no—
191C42×C5—28no—
192#685—28no—
193#685—48no—
194#685C4⋊C4116yes—
195C4⋊Dic5—48no—
196#683—48no—
197C4×Dic5—44no—
198C24×C4—51no—
199C24×C4—52no—
200C22×C4⋊C4—52no—
201C22×C4⋊C4—52no—
202C22×C22⋊C4—51no—
203C22×C22⋊C4—51no—
204C22×C22⋊C4—52no—
205C22×C42—51no—
206C22×C42C2×D511yescharacteristic
207#385—108no—
208#382—104no—
209C4×C22⋊C4—58no—
210C2×#95—51no—
211C2×#95—51no—
212C2×#95—51no—
213C2×#95—51no—
214C2×#95—52no—
215C2×#95—52no—
216C2×#95—52no—
217C2×#95—52no—
218C2×#95—52no—
219C2×#95—52no—
220C2×#95—104no—
221C2×#95C2×D511yescharacteristic
222C2×#95C2×D512yes—
223C2×#95C2×D511yescharacteristic
224C2×#95C2×D512yes—
225C23×C5C23×C411yescharacteristic
226C23×C5C22×D411yescharacteristic
227C23×C5C22×D411yescharacteristic
228C23×C5C22×Q811yescharacteristic
229C23×C5C2×#4112yes—
230C23×C5C2×#4111yescharacteristic
231C23×C5C2×#4112yes—
232C23×C5C2×#4112yes—
233C23×C5H(5,𝔽2)12yes—
234C23×C5H(5,𝔽2)11yescharacteristic
235C23×C52−1+411yescharacteristic
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—22no—
240C22×D5—24no—
241C22×D5—24no—
242C22×D5—24no—
243C22×D5—24no—
244C22×D5—22no—
245C22×D5—24no—
246C22×D5—24no—
247C22×D5—22no—
248C22×D5—22no—
249C22×D5—24no—
250C22×D5—24no—
251C22×D5—24no—
252C22×D5—24no—
253C22×D5—22no—
254C22×D5C2×C4⋊C414yes—
255C22×D5#11714yes—
256C22×D5#11714yes—
257C22×D5#12418yes—
258C22×D5#12518yes—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—24no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—24no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5C2×C4⋊C414yes—
289C2×C4×C5C4×D414yes—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—24no—
293C2×Dic5—24no—
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—24no—
301C2×Dic5—24no—
302C2×Dic5—24no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—42no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C2×Dic5—42no—
309C2×Dic5—42no—
310C2×Dic5—42no—
311C2×Dic5—42no—
312C2×Dic5—42no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316C2×Dic5—42no—
317C2×Dic5—42no—
318C2×Dic5C2×C4⋊C414yes—
319C4×D5—416no—
320C4×D5—432no—
321C25—51no—
322C23×C4—51no—
323C23×C4—51no—
324C23×C4—52no—
325C23×C4—51no—
326C23×C4—54no—
327C23×C4—52no—
328C23×C4—104no—
329C23×C4—104no—
330C23×C4—104no—
331C23×C4—104no—
332C23×C4—104no—
333C23×C4—104no—
334C23×C4—102no—
335C23×C4—102no—
336C23×C4—202no—
337C23×C4—202no—
338C23×C4—202no—
339C23×C4C22×D512yes—
340C23×C4C22×D511yescharacteristic
341C23×C4C22×D512yes—
342C23×C4C22×D511yescharacteristic
343C23×C4C22×D511yescharacteristic
344C2×C4⋊C4—104no—
345C2×C4⋊C4—104no—
346C2×C4⋊C4—104no—
347C2×C4⋊C4—104no—
348C2×C4⋊C4—202no—
349C2×C4⋊C4—202no—
350C2×C22⋊C4—54no—
351C2×C22⋊C4—54no—
352C2×C22⋊C4—54no—
353C2×C22⋊C4—54no—
354C2×C22⋊C4—104no—
355C2×C22⋊C4—104no—
356C2×C22⋊C4—104no—
357C2×C22⋊C4—104no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—54no—
361C2×C42—202no—
362C2×C42C4×D514yescomplemented
363#95—24no—
364#95—22no—
365#95—24no—
366#95—22no—
367#95—54no—
368#95—54no—
369#95—54no—
370#95—104no—
371#95—104no—
372#95—104no—
373#95—102no—
374#95—202no—
375#95—202no—
376#95—202no—
377C22×C5C22×C4⋊C411yescharacteristic
378C22×C5C2×#11711yescharacteristic
379C22×C5C2×#11711yescharacteristic
380C22×C5C2×C4×D411yescharacteristic
381C22×C5C4×#4111yescharacteristic
382C22×C5#51811yescharacteristic
383C22×C5#52011yescharacteristic
384C22×C5#52512yes—
385C22×C5C2×#12412yes—
386C22×C5C2×#12512yes—
387C22×C5#52912yes—
388C22×C5#53812yes—
389C22×C5#53912yes—
390C22×C5D4211yescharacteristic
391C22×C5#54612yes—
392C22×C5#54612yes—
393C22×C5#54711yescharacteristic
394C22×C5D4×Q811yescharacteristic
395C22×C5#55112yes—
396C22×C5#55112yes—
397C22×C5#55212yes—
398C22×C5#55412yes—
399C22×C5#55411yescharacteristic
400C2×D5—24no—
401C2×D5—24no—
402C2×D5—24no—
403C2×D5—24no—
404C2×D5—24no—
405C2×D5—28no—
406C2×D5—28no—
407C2×D5—28no—
408C2×D5—28no—
409C2×D5—24no—
410C2×D5#38218yescomplemented
411C4×C5—24no—
412C4×C5—24no—
413C4×C5—44no—
414C4×C5—42no—
415C4×C5—82no—
416Dic5—24no—
417Dic5—42no—
418Dic5—42no—
419Dic5—44no—
420Dic5—82no—
421C24—52no—
422C24—52no—
423C24—52no—
424C24—54no—
425C24—54no—
426C24—102no—
427C24—101no—
428C24—101no—
429C24—102no—
430C24—101no—
431C24—101no—
432C24C23×D511yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
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—52no—
457C22×C4—52no—
458C22×C4—52no—
459C22×C4—52no—
460C22×C4—52no—
461C22×C4—54no—
462C22×C4—108no—
463C22×C4—1016no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—101no—
468C22×C4—102no—
469C22×C4—101no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—101no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4—102no—
479C22×C4—101no—
480C22×C4—108no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—102no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—204no—
489C22×C4—208no—
490C22×C4—208no—
491C22×C4—208no—
492C22×C4—208no—
493C22×C4—208no—
494C22×C4—208no—
495C22×C4—208no—
496C22×C4—208no—
497C22×C4C2×C4×D512yes—
498C22×C4C2×C4×D512yes—
499C22×C4C2×C4×D512yes—
500C22×C4#70914yes—
501C22×C4D4×D512yes—
502C22×C4D4×D512yes—
503C22×C4#71112yes—
504C22×C4Q8×D512yes—
505C4⋊C4—208no—
506C4⋊C4—208no—
507C22⋊C4—516no—
508C22⋊C4—108no—
509C22⋊C4—208no—
510C42—28no—
511C42—204no—
512C2×C5C2×#38211yescharacteristic
513C2×C5#229011yescharacteristic
514C2×C5#231811yescharacteristic
515C2×C5#234211yescharacteristic
516C2×C5#234311yescharacteristic
517C2×C5D4×C4⋊C411yescharacteristic
518C2×C5#234911yescharacteristic
519C2×C5#247212yes—
520C2×C5#247312yes—
521C2×C5#248812yes—
522C2×C5#250512yes—
523D5—28no—
524C23—54no—
525C23—54no—
526C23—54no—
527C23—58no—
528C23—58no—
529C23—102no—
530C23—102no—
531C23—102no—
532C23—102no—
533C23—104no—
534C23—104no—
535C23—104no—
536C23—104no—
537C23—104no—
538C23—104no—
539C23—102no—
540C23—102no—
541C23—102no—
542C23—102no—
543C23—104no—
544C23—104no—
545C23—104no—
546C23—104no—
547C23C22×C4×D511yescharacteristic
548C23C2×#70912yes—
549C23C2×D4×D511yescharacteristic
550C23C2×D4×D511yescharacteristic
551C23C2×#71111yescharacteristic
552C23C2×Q8×D511yescharacteristic
553C23D5×#4112yes—
554C23D5×#4112yes—
555C23#414912yes—
556C23#414911yescharacteristic
557C23#415011yescharacteristic
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—54no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—104no—
591C2×C4—104no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—102no—
596C2×C4—102no—
597C2×C4—102no—
598C2×C4—104no—
599C2×C4—104no—
600C2×C4—104no—
601C2×C4—2016no—
602C2×C4—2032no—
603C2×C4—202no—
604C2×C4—202no—
605C2×C4—202no—
606C2×C4—202no—
607C2×C4—202no—
608C2×C4—202no—
609C2×C4—202no—
610C2×C4—202no—
611C2×C4—202no—
612C2×C4—202no—
613C2×C4—202no—
614C2×C4—202no—
615C2×C4—202no—
616C2×C4—202no—
617C2×C4—202no—
618C2×C4#402714yes—
619C2×C4D5×C4⋊C414yes—
620C5#1389611yescharacteristic, complemented, Sylow
621C22—58no—
622C22—104no—
623C22—104no—
624C22—108no—
625C22—108no—
626C22—104no—
627C22—104no—
628C22—104no—
629C22—108no—
630C22—104no—
631C22—108no—
632C22C4×#70911yescharacteristic
633C22C2×#402711yescharacteristic
634C22C2×D5×C4⋊C411yescharacteristic
635C22D5×#11711yescharacteristic
636C22D5×#11711yescharacteristic
637C22#6585511yescharacteristic
638C22#6585711yescharacteristic
639C22#6586112yes—
640C22#6586312yes—
641C22#6588112yes—
642C22#6588412yes—
643C22#6589112yes—
644C22#6591312yes—
645C22#6594311yescharacteristic
646C22#6594511yescharacteristic
647C22#6596611yescharacteristic
648C22#6596911yescharacteristic
649C22#6598812yes—
650C22#6599212yes—
651C22D5×#12412yes—
652C22D5×#12512yes—
653C22#6603812yes—
654C22#6604112yes—
655C4—24no—
656C4—24no—
657C4—44no—
658C4—42no—
659C4—82no—
660C4—104no—
661C4—202no—
662C4—204no—
663C4—202no—
664C4—402no—
665C2—108no—
666C2#1060514711yescharacteristic
667C2#1060529311yescharacteristic
668C2#1060550111yescharacteristic
669C2#1060574111yescharacteristic
670C2#1060585311yescharacteristic
671C2D5×#38211yescharacteristic
672C2#1060602611yescharacteristic
673C2#1060673912yes—
674C2#1060707112yes—
675C2#1060725712yes—
676C2#1060759912yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1434C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenter#1434D5
hypocenterC5#13896
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#65225C2semidirect
5. C5×#1434C2semidirect
8. #10600208C2semidirect
9. #10600207C2semidirect
10. #10600197C2semidirect
11. #10600194C2semidirect
35. C4×#685C4semidirect
65. C2×C42×C5C2×C4semidirect
81. C2×C4×Dic5C2×C4semidirect
93. #3963C2×C4semidirect
94. #3963C2×C4semidirect
104. #1434D5semidirect
362. C2×C42C4×D5semidirect
410. C2×D5#382semidirect
620. C5#13896semidirect

Maximal subgroups

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

subgroupindex
C2×#652252
C2×C4×#6852
C2×#649572
C2×D5×#952
C5×#14342
#106002182
#106002082
#106002072
#106001972
#106001942
#138965