Finite Group Databasebeta

← #12021951

Subgroups — #12021951

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4018C211yesmaximal, characteristic
2C2×#65261C212yesmaximal, complemented
3C2×#64956C211yesmaximal, characteristic
4C2×#64955C211yesmaximal, characteristic
5C5×C4⋊#95C211yesmaximal, characteristic, complemented
6#10602363C212yesmaximal
7#10602327C211yesmaximal, characteristic, complemented
8#10600221C212yesmaximal
9#10600197C211yesmaximal, characteristic, complemented
10#10600197C212yesmaximal, complemented
11#10600196C211yesmaximal, characteristic, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C42×C5C2211yescharacteristic
15C22×#685C2212yes—
16C22×#685C2211yescharacteristic
17C22×#685C2211yescharacteristic
18C22×#685C2212yes—
19C22×#683C2212yes—
20C22×#683C2212yes—
21C22×#683C2211yescharacteristic
22C22×#683C2211yescharacteristic
23C22×C4×Dic5C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C2×#4018—28no—
26C2×#4018C418yescomplemented
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37#65261—28no—
38#64956—24no—
39#64955—24no—
40#13951—51nomaximal, Sylow
41C24×D5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C22×C4×D5—24no—
53C22×C4×D5—24no—
54C22×C4×D5C2×C414yes—
55C22×C4×D5D414yes—
56C22×C4×D5Q814yes—
57C2×C5×C4⋊C4—24no—
58C2×C5×C4⋊C4—24no—
59C2×C5×C4⋊C4—42no—
60C2×C42×C5—24no—
61C2×C42×C5C2×C414yes—
62C2×#685—24no—
63C2×#685—24no—
64C2×#685—24no—
65C2×#685—24no—
66C2×#685—24no—
67C2×#685—24no—
68C2×#685—42no—
69C2×#685—42no—
70C2×#685C2×C414yes—
71C2×#685C2×C414yes—
72C2×#683—24no—
73C2×#683—24no—
74C2×#683—24no—
75C2×#683—24no—
76C2×#683—24no—
77C2×#683—24no—
78C2×#683—42no—
79C2×#683C2×C414yes—
80C2×#683C2×C414yes—
81C2×#683D418yes—
82C2×C4×Dic5—24no—
83C2×C4×Dic5—24no—
84C2×C4×Dic5—24no—
85C2×C4×Dic5—24no—
86C2×C4×Dic5C2×C414yes—
87#4018—232no—
88C5×#95—22no—
89C5×#95—22no—
90C5×#95—42no—
91#3963—22no—
92#3963—22no—
93#3963—24no—
94#3963—24no—
95#3963—24no—
96#3963—24no—
97#3963—42no—
98C22×#117—51no—
99C2×#389—52no—
100C2×#380—51no—
101C2×C4×C22⋊C4—51no—
102#1439—52no—
103#1439—52no—
104C4⋊#95—52no—
105C4⋊#95—51no—
106C4⋊#95D511yescharacteristic, complemented
107#1434—51no—
108#1434—51no—
109C24×C5C2411yescharacteristic
110C23×D5—22no—
111C23×D5—22no—
112C23×D5—22no—
113C23×D5—22no—
114C23×D5—21no—
115C23×D5—21no—
116C23×D5—21no—
117C23×D5—21no—
118C23×D5C22×C412yes—
119C23×D5C2×D412yes—
120C23×D5C2×Q812yes—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
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—21no—
135C22×C4×C5—21no—
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×C412yes—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C22×C412yes—
146C22×C4×C5C2×D414yes—
147C22×C4×C5C2×D412yes—
148C22×C4×C5C2×Q812yes—
149C22×C4×C5#4114yes—
150C22×Dic5—22no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—21no—
160C22×Dic5—21no—
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×Dic5C22×C412yes—
171C22×Dic5C22×C412yes—
172C22×Dic5C22×C412yes—
173C22×Dic5C2×D414yes—
174C22×Dic5C2×D414yes—
175C22×Dic5C2×D412yes—
176C22×Dic5C2×Q812yes—
177C22×Dic5#4114yes—
178C22×Dic5#4114yes—
179C2×C4×D5—28no—
180C2×C4×D5—28no—
181C2×C4×D5—216no—
182C2×C4×D5—216no—
183C2×C4×D5C4⋊C4116yescomplemented
184C5×C4⋊C4—48no—
185C42×C5—28no—
186#685—216no—
187#685—28no—
188#685—28no—
189#685—48no—
190#683—28no—
191#683—48no—
192#683—48no—
193#683C22⋊C4116yescomplemented
194C4×Dic5—28no—
195C4×Dic5—48no—
196C24×C4—51no—
197C2×#117—58no—
198C2×#117—108no—
199C22×C4⋊C4—51no—
200C22×C4⋊C4—51no—
201C22×C4⋊C4—52no—
202C22×C4⋊C4—52no—
203C22×C4⋊C4C2×D512yes—
204C22×C22⋊C4—51no—
205C22×C22⋊C4—51no—
206C22×C22⋊C4—52no—
207C22×C22⋊C4—52no—
208C22×C42—51no—
209C22×C42—52no—
210C22×C42C2×D511yescharacteristic
211#389—108no—
212#380—104no—
213C4×C22⋊C4—104no—
214C2×#95—51no—
215C2×#95—52no—
216C2×#95—52no—
217C2×#95—51no—
218C2×#95—52no—
219C2×#95—52no—
220C2×#95—52no—
221C2×#95C2×D511yescharacteristic
222C2×#95C2×D511yescharacteristic
223C2×#95C2×D512yes—
224C23×C5C23×C411yescharacteristic
225C23×C5C22×D412yes—
226C23×C5C22×D411yescharacteristic
227C23×C5C22×Q811yescharacteristic
228C23×C5C2×#4112yes—
229C23×C5C2×#4112yes—
230C23×C5C2×#4112yes—
231C23×C5H(5,𝔽2)11yescharacteristic
232C23×C5H(5,𝔽2)11yescharacteristic
233C23×C52−1+411yescharacteristic
234C23×C52−1+411yescharacteristic
235C22×D5—22no—
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—24no—
242C22×D5—24no—
243C22×D5—24no—
244C22×D5—24no—
245C22×D5—22no—
246C22×D5—22no—
247C22×D5—22no—
248C22×D5—22no—
249C22×D5—42no—
250C22×D5—42no—
251C22×D5—42no—
252C22×D5—42no—
253C22×D5—42no—
254C22×D5—42no—
255C22×D5—42no—
256C22×D5—42no—
257C22×D5C2×C4⋊C414yes—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—24no—
263C2×C4×C5—24no—
264C2×C4×C5—24no—
265C2×C4×C5—24no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—24no—
271C2×C4×C5—24no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
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×C5C2×C22⋊C414yes—
286C2×C4×C5C2×C4⋊C414yes—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—24no—
290C2×Dic5—24no—
291C2×Dic5—22no—
292C2×Dic5—22no—
293C2×Dic5—22no—
294C2×Dic5—24no—
295C2×Dic5—24no—
296C2×Dic5—24no—
297C2×Dic5—42no—
298C2×Dic5—42no—
299C2×Dic5—42no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—42no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C2×Dic5—42no—
309C2×Dic5—42no—
310C2×Dic5C2×C22⋊C414yes—
311C2×Dic5C2×C22⋊C414yes—
312C2×Dic5C2×C4⋊C414yes—
313C2×Dic5#11714yes—
314C2×Dic5#12118yes—
315C2×Dic5C22⋊Q818yes—
316C4×D5—232no—
317C25—51no—
318C23×C4—51no—
319C23×C4—51no—
320C23×C4—54no—
321C23×C4—54no—
322C23×C4—54no—
323C23×C4—51no—
324C23×C4—52no—
325C23×C4—52no—
326C23×C4—104no—
327C23×C4—104no—
328C23×C4C22×D512yes—
329C23×C4C22×D511yescharacteristic
330C23×C4C22×D512yes—
331C23×C4C22×D511yescharacteristic
332C23×C4C22×D511yescharacteristic
333#117—1032no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—54no—
338C2×C4⋊C4—58no—
339C2×C4⋊C4—54no—
340C2×C4⋊C4—104no—
341C2×C4⋊C4—104no—
342C2×C4⋊C4—104no—
343C2×C4⋊C4—104no—
344C2×C4⋊C4—104no—
345C2×C4⋊C4—104no—
346C2×C4⋊C4—202no—
347C2×C22⋊C4—54no—
348C2×C22⋊C4—54no—
349C2×C22⋊C4—104no—
350C2×C22⋊C4—104no—
351C2×C22⋊C4—104no—
352C2×C22⋊C4—104no—
353C2×C22⋊C4—104no—
354C2×C22⋊C4—104no—
355C2×C22⋊C4—202no—
356C2×C22⋊C4—202no—
357C2×C42—24no—
358C2×C42—54no—
359C2×C42—104no—
360C2×C42—104no—
361C2×C42—104no—
362C2×C42—104no—
363C2×C42C4×D514yes—
364#95—22no—
365#95—22no—
366#95—42no—
367#95—104no—
368#95—104no—
369#95—104no—
370#95—102no—
371#95—102no—
372#95—104no—
373#95—202no—
374C22×C5C22×C22⋊C411yescharacteristic
375C22×C5C22×C4⋊C411yescharacteristic
376C22×C5C2×#11711yescharacteristic
377C22×C5C4×#4111yescharacteristic
378C22×C5C4×#4111yescharacteristic
379C22×C5#52011yescharacteristic
380C22×C5#52011yescharacteristic
381C22×C5C2×#12112yes—
382C22×C5C2×C22⋊Q812yes—
383C22×C5#52512yes—
384C22×C5#53312yes—
385C22×C5#53511yescharacteristic
386C22×C5#53611yescharacteristic
387C22×C5#54411yescharacteristic
388C22×C5#54411yescharacteristic
389C22×C5#54612yes—
390C22×C5#54712yes—
391C22×C5#54812yes—
392C22×C5#55012yes—
393C22×C5#55212yes—
394C22×C5#55312yes—
395C22×C5#55512yes—
396C22×C5#55612yes—
397C2×D5—24no—
398C2×D5—24no—
399C2×D5—24no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C2×D5—44no—
405C2×D5—44no—
406C2×D5—44no—
407C2×D5—44no—
408C4×C5—24no—
409C4×C5—24no—
410C4×C5—42no—
411C4×C5—44no—
412C4×C5—82no—
413Dic5—24no—
414Dic5—42no—
415Dic5—44no—
416Dic5—82no—
417Dic5#38018yes—
418C24—52no—
419C24—52no—
420C24—52no—
421C24—102no—
422C24—102no—
423C24—101no—
424C24—101no—
425C24—101no—
426C24—101no—
427C24—102no—
428C24—102no—
429C24C23×D511yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
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—52no—
453C22×C4—52no—
454C22×C4—54no—
455C22×C4—52no—
456C22×C4—54no—
457C22×C4—52no—
458C22×C4—54no—
459C22×C4—516no—
460C22×C4—52no—
461C22×C4—54no—
462C22×C4—108no—
463C22×C4—108no—
464C22×C4—1016no—
465C22×C4—1016no—
466C22×C4—102no—
467C22×C4—101no—
468C22×C4—101no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—101no—
474C22×C4—101no—
475C22×C4—102no—
476C22×C4—102no—
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×C4C2×C4×D512yes—
487C22×C4C2×C4×D512yes—
488C22×C4C2×C4×D512yes—
489C22×C4#70914yes—
490C22×C4D4×D514yes—
491C22×C4D4×D512yes—
492C22×C4Q8×D512yes—
493C4⋊C4—48no—
494C4⋊C4—516no—
495C4⋊C4—108no—
496C4⋊C4—208no—
497C4⋊C4—208no—
498C22⋊C4—108no—
499C22⋊C4—1016no—
500C22⋊C4—108no—
501C22⋊C4—208no—
502C42—28no—
503C42—108no—
504C42—208no—
505C2×C5C2×#38011yescharacteristic
506C2×C5#229611yescharacteristic
507C2×C5#231711yescharacteristic
508C2×C5#233911yescharacteristic
509C2×C5#234111yescharacteristic
510C2×C5#234611yescharacteristic
511C2×C5#234711yescharacteristic
512C2×C5#241412yes—
513C2×C5#241512yes—
514C2×C5#243912yes—
515C2×C5#244112yes—
516D5—44no—
517C23—54no—
518C23—102no—
519C23—102no—
520C23—102no—
521C23—102no—
522C23—102no—
523C23—102no—
524C23—102no—
525C23—102no—
526C23—102no—
527C23—102no—
528C23—104no—
529C23—104no—
530C23—104no—
531C23—104no—
532C23—202no—
533C23—202no—
534C23—202no—
535C23—202no—
536C23—202no—
537C23—202no—
538C23—202no—
539C23—202no—
540C23C22×C4×D511yescharacteristic
541C23C2×#70912yes—
542C23C2×D4×D511yescharacteristic
543C23C2×D4×D512yes—
544C23#414411yescharacteristic
545C23#414411yescharacteristic
546C23C2×Q8×D511yescharacteristic
547C23#414711yescharacteristic
548C23#414711yescharacteristic
549C23D5×#4112yes—
550C23D5×#4112yes—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—54no—
579C2×C4—54no—
580C2×C4—54no—
581C2×C4—58no—
582C2×C4—58no—
583C2×C4—54no—
584C2×C4—1032no—
585C2×C4—102no—
586C2×C4—104no—
587C2×C4—102no—
588C2×C4—104no—
589C2×C4—102no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4—104no—
593C2×C4—104no—
594C2×C4—104no—
595C2×C4—202no—
596C2×C4—202no—
597C2×C4—202no—
598C2×C4—202no—
599C2×C4—202no—
600C2×C4—202no—
601C2×C4—202no—
602C2×C4—202no—
603C2×C4—202no—
604C2×C4—202no—
605C2×C4—202no—
606C2×C4—202no—
607C2×C4—202no—
608C2×C4D5×C22⋊C414yes—
609C2×C4D5×C4⋊C414yes—
610C5#1395111yescharacteristic, complemented, Sylow
611C22—104no—
612C22—104no—
613C22—104no—
614C22—202no—
615C22—202no—
616C22—202no—
617C22—202no—
618C22—204no—
619C22—204no—
620C22—204no—
621C22—204no—
622C22C4×#70911yescharacteristic
623C22C2×D5×C22⋊C411yescharacteristic
624C22#6582412yes—
625C22C2×D5×C4⋊C411yescharacteristic
626C22#6583811yescharacteristic
627C22#6583811yescharacteristic
628C22#6584112yes—
629C22D5×#11711yescharacteristic
630C22#6585611yescharacteristic
631C22#6587412yes—
632C22#6588112yes—
633C22#6590212yes—
634C22#6591212yes—
635C22#6593312yes—
636C22D5×#12112yes—
637C22D5×C22⋊Q812yes—
638C22#6596712yes—
639C22#6600412yes—
640C22#6602712yes—
641C22#6604911yescharacteristic
642C22#6605811yescharacteristic
643C22#6606311yescharacteristic
644C22#6606311yescharacteristic
645C4—24no—
646C4—24no—
647C4—42no—
648C4—44no—
649C4—58no—
650C4—82no—
651C4—104no—
652C4—202no—
653C4—204no—
654C4—402no—
655C2—204no—
656C2#1060509911yescharacteristic
657C2#1060536611yescharacteristic
658C2#1060548611yescharacteristic
659C2#1060560811yescharacteristic
660C2D5×#38011yescharacteristic
661C2#1060588711yescharacteristic
662C2#1060609011yescharacteristic
663C2#1060772612yes—
664C2#1060773212yes—
665C2#1060804212yes—
666C2#1060823212yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13951
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#65261C2semidirect
5. C5×C4⋊#95C2semidirect
7. #10602327C2semidirect
9. #10600197C2semidirect
10. #10600197C2semidirect
11. #10600196C2semidirect
26. C2×#4018C4semidirect
106. C4⋊#95D5semidirect
183. C2×C4×D5C4⋊C4semidirect
193. #683C22⋊C4semidirect
610. C5#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#40182
C2×#652612
C2×#649562
C2×#649552
C5×C4⋊#952
#106023632
#106023272
#106002212
#106001972
#106001962
#139515