Finite Group Databasebeta

← #12030593

Subgroups — #12030593

Order 1280.

2734 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4043C211yesmaximal, characteristic
2C22×C42×D5C211yesmaximal, characteristic
3C2×#65276C211yesmaximal, characteristic
4C2×#65263C211yesmaximal, characteristic, complemented
5C2×#65218C211yesmaximal, characteristic, complemented
6C5×C4⋊#95C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10600218C214yesmaximal
9#10600200C214yesmaximal, complemented
10C23×C4×D5C2212yes—
11C23×C4×D5C2211yescharacteristic
12C23×Dic10C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×#685C2212yes—
17C22×#685C2212yes—
18C22×C4⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2212yes—
20C22×C4×Dic5C2212yes—
21C22×C4×Dic5C2211yescharacteristic
22C2×#4043—24no—
23C2×#4043—24no—
24C2×#4043C418yescomplemented
25C2×C42×D5—24no—
26C2×C42×D5—24no—
27C2×C42×D5—24no—
28C2×C5×#95C2214yes—
29C2×#3963C2212yes—
30C2×#3963C2214yes—
31C2×#3963C2214yes—
32C2×#3963C2214yes—
33#65276—24no—
34#65263—24no—
35#65218—24no—
36#14702—51nomaximal, Sylow
37C24×D5C2311yescharacteristic
38C23×C4×C5C2312yes—
39C23×C4×C5C2312yes—
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×Dic5C2312yes—
43C23×Dic5C2312yes—
44C23×Dic5C2311yescharacteristic
45C23×Dic5C2312yes—
46C22×C4×D5—24no—
47C22×C4×D5—24no—
48C22×C4×D5—24no—
49C22×C4×D5—22no—
50C22×C4×D5—22no—
51C22×C4×D5—22no—
52C22×C4×D5—24no—
53C22×C4×D5—22no—
54C22×C4×D5—24no—
55C22×C4×D5—24no—
56C22×C4×D5C2×C414yes—
57C22×C4×D5D414yes—
58C22×C4×D5D414yes—
59C22×C4×D5Q818yescomplemented
60C22×Dic10—22no—
61C22×Dic10—22no—
62C22×Dic10—22no—
63C22×Dic10—22no—
64C22×Dic10—22no—
65C22×Dic10—22no—
66C22×Dic10C2×C414yescomplemented
67C2×C5×C4⋊C4—22no—
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4C2×C414yescomplemented
73C2×C42×C5—22no—
74C2×C42×C5—22no—
75C2×C42×C5D414yes—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—24no—
79C2×#685—28no—
80C2×#685C2×C418yes—
81C2×C4⋊Dic5—24no—
82C2×C4⋊Dic5—24no—
83C2×C4⋊Dic5—22no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5C2×C418yescomplemented
87C2×C4×Dic5—24no—
88C2×C4×Dic5—22no—
89C2×C4×Dic5—22no—
90C2×C4×Dic5—24no—
91C2×C4×Dic5—24no—
92C2×C4×Dic5D414yes—
93#4043—232no—
94C42×D5—232no—
95C5×#95—28no—
96#3963—28no—
97#3963—28no—
98#3963—24no—
99#3963—28no—
100C22×C22⋊Q8—51no—
101C23×C42—51no—
102C2×#391—51no—
103C2×#391—51no—
104C2×#380—51no—
105#1436—54no—
106C4⋊#95—51no—
107C4⋊#95D511yescharacteristic, complemented
108C22⋊#95—54no—
109C24×C5C2411yescharacteristic
110C23×D5—21no—
111C23×D5—21no—
112C23×D5—21no—
113C23×D5—22no—
114C23×D5—21no—
115C23×D5—22no—
116C23×D5C22×C412yes—
117C23×D5C2×D412yes—
118C23×D5C2×D412yes—
119C23×D5C2×Q814yes—
120C23×D5#4114yes—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—24no—
128C22×C4×C5—24no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—24no—
133C22×C4×C5—24no—
134C22×C4×C5C22×C414yes—
135C22×C4×C5C22×C412yes—
136C22×C4×C5C2×D414yes—
137C22×C4×C5C2×D412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×D412yes—
140C22×C4×C5C2×D412yes—
141C22×C4×C5C2×Q814yes—
142C22×C4×C5#4112yes—
143C22×C4×C5#4114yes—
144C22×C4×C5#4112yes—
145C22×Dic5—21no—
146C22×Dic5—22no—
147C22×Dic5—21no—
148C22×Dic5—22no—
149C22×Dic5—21no—
150C22×Dic5—22no—
151C22×Dic5—21no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—24no—
162C22×Dic5—22no—
163C22×Dic5—24no—
164C22×Dic5C22×C414yes—
165C22×Dic5C22×C412yes—
166C22×Dic5C2×D412yes—
167C22×Dic5C2×D412yes—
168C22×Dic5C2×D414yes—
169C22×Dic5C2×Q814yes—
170C22×Dic5#4114yes—
171C2×C4×D5—216no—
172C2×C4×D5—216no—
173C2×C4×D5—216no—
174C2×C4×D5—216no—
175C2×C4×D5—216no—
176C2×C4×D5—28no—
177C2×C4×D5—28no—
178C2×C4×D5—28no—
179C2×C4×D5—28no—
180C2×C4×D5—28no—
181C2×C4×D5—216no—
182C2×C4×D5—28no—
183C2×C4×D5—216no—
184C2×C4×D5C22⋊C4116yes—
185C2×Dic10—28no—
186C2×Dic10—28no—
187C2×Dic10—28no—
188C2×Dic10—44no—
189C2×Dic10—44no—
190C2×Dic10—44no—
191C2×Dic10—44no—
192C5×C4⋊C4—28no—
193C5×C4⋊C4—44no—
194C42×C5—28no—
195#685—216no—
196#685—48no—
197C4⋊Dic5—216no—
198C4⋊Dic5—44no—
199C4×Dic5—216no—
200C4×Dic5—28no—
201C23×Q8—51no—
202C24×C4—51no—
203C24×C4—52no—
204C2×C22⋊Q8—58no—
205C2×C22⋊Q8—104no—
206C2×C22⋊Q8—104no—
207C22×C4⋊C4—52no—
208C22×C4⋊C4—51no—
209C22×C4⋊C4C2×D511yescharacteristic
210C22×C4⋊C4C2×D511yescharacteristic
211C22×C22⋊C4—52no—
212C22×C22⋊C4—52no—
213C22×C42—51no—
214C22×C42—52no—
215C22×C42—104no—
216C22×C42—104no—
217C22×C42—104no—
218C22×C42C2×D511yescharacteristic
219#391—104no—
220#391—104no—
221#380—104no—
222C2×#95—54no—
223C2×#95—54no—
224C2×#95—54no—
225C2×#95—52no—
226C2×#95C2×D514yes—
227C23×C5C23×C411yescharacteristic
228C23×C5C22×D411yescharacteristic
229C23×C5C22×D411yescharacteristic
230C23×C5C22×D411yescharacteristic
231C23×C5C22×D411yescharacteristic
232C23×C5C22×Q812yes—
233C23×C5C2×#4111yescharacteristic
234C23×C5C2×#4112yes—
235C23×C5C2×#4111yescharacteristic
236C23×C5C2×#4112yes—
237C23×C5C2×#4112yes—
238C22×D5—22no—
239C22×D5—22no—
240C22×D5—24no—
241C22×D5—22no—
242C22×D5—22no—
243C22×D5—22no—
244C22×D5—24no—
245C22×D5—24no—
246C22×D5—22no—
247C22×D5—24no—
248C22×D5—24no—
249C22×D5—24no—
250C22×D5—24no—
251C22×D5—24no—
252C22×D5—22no—
253C22×D5—22no—
254C22×D5—24no—
255C22×D5—24no—
256C22×D5C2×C22⋊C414yes—
257C22×D5C4×Q818yes—
258C22×D5C22⋊Q818yes—
259C22×D5#12414yes—
260C22×D5C4⋊Q814yes—
261C2×C4×C5—24no—
262C2×C4×C5—24no—
263C2×C4×C5—24no—
264C2×C4×C5—24no—
265C2×C4×C5—24no—
266C2×C4×C5—24no—
267C2×C4×C5—24no—
268C2×C4×C5—28no—
269C2×C4×C5—44no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—44no—
274C2×C4×C5—42no—
275C2×C4×C5—44no—
276C2×C4×C5—42no—
277C2×C4×C5C2×C22⋊C414yes—
278C2×C4×C5C4×D414yes—
279C2×C4×C5C4×D414yes—
280C2×C4×C5#12014yes—
281C2×C4×C5#12114yes—
282C2×C4×C5#12114yes—
283C2×C4×C5C22⋊Q818yescomplemented
284C2×C4×C5#12314yes—
285C2×Dic5—22no—
286C2×Dic5—22no—
287C2×Dic5—24no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—24no—
292C2×Dic5—24no—
293C2×Dic5—22no—
294C2×Dic5—24no—
295C2×Dic5—24no—
296C2×Dic5—24no—
297C2×Dic5—24no—
298C2×Dic5—24no—
299C2×Dic5—24no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—44no—
306C2×Dic5—42no—
307C2×Dic5—44no—
308C2×Dic5—42no—
309C2×Dic5C2×C22⋊C414yes—
310C2×Dic5C22⋊Q818yescomplemented
311C4×D5—264no—
312C4×D5—232no—
313Dic10—416no—
314C25—51no—
315C22×Q8—54no—
316C22×Q8—102no—
317C22×Q8—102no—
318C22×Q8—102no—
319C22×Q8—102no—
320C22×Q8—102no—
321C22×Q8—102no—
322C23×C4—51no—
323C23×C4—52no—
324C23×C4—54no—
325C23×C4—54no—
326C23×C4—54no—
327C23×C4—52no—
328C23×C4—58no—
329C23×C4—52no—
330C23×C4—104no—
331C23×C4—104no—
332C23×C4—104no—
333C23×C4—104no—
334C23×C4—104no—
335C23×C4—102no—
336C23×C4—102no—
337C23×C4—102no—
338C23×C4—104no—
339C23×C4—102no—
340C23×C4C22×D512yes—
341C23×C4C22×D512yes—
342C23×C4C22×D512yes—
343C23×C4C22×D511yescharacteristic
344C22⋊Q8—1032no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—58no—
351C2×C4⋊C4—104no—
352C2×C4⋊C4—104no—
353C2×C4⋊C4—102no—
354C2×C4⋊C4—102no—
355C2×C4⋊C4—102no—
356C2×C4⋊C4C4×D514yescomplemented
357C2×C22⋊C4—58no—
358C2×C22⋊C4—104no—
359C2×C22⋊C4—104no—
360C2×C22⋊C4—104no—
361C2×C22⋊C4—108no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—54no—
365C2×C42—1032no—
366C2×C42—104no—
367C2×C42—104no—
368C2×C42—104no—
369C2×C42—102no—
370C2×C42—102no—
371C2×C42D2014yes—
372#95—28no—
373#95—108no—
374#95—104no—
375#95—108no—
376#95—108no—
377C22×C5C22×C22⋊C411yescharacteristic
378C22×C5C2×C4×D411yescharacteristic
379C22×C5C2×C4×D411yescharacteristic
380C22×C5C2×C4×Q812yes—
381C22×C5C4×#4112yes—
382C22×C5C2×#12011yescharacteristic
383C22×C5C2×#12111yescharacteristic
384C22×C5C2×#12111yescharacteristic
385C22×C5C2×C22⋊Q812yes—
386C22×C5C2×C22⋊Q812yes—
387C22×C5C2×C22⋊Q812yes—
388C22×C5C2×#12311yescharacteristic
389C22×C5#52512yes—
390C22×C5#52512yes—
391C22×C5#52512yes—
392C22×C5C2×#12411yescharacteristic
393C22×C5#52912yes—
394C22×C5#52912yes—
395C22×C5C2×C4⋊Q811yescharacteristic
396C22×C5#53211yescharacteristic
397C22×C5#53211yescharacteristic
398C22×C5#53312yes—
399C22×C5#53312yes—
400C2×D5—28no—
401C2×D5—24no—
402C2×D5—24no—
403C2×D5—28no—
404C2×D5—24no—
405C2×D5—24no—
406C2×D5—24no—
407C2×D5—24no—
408C2×D5—28no—
409C2×D5—28no—
410C2×D5#39118yescomplemented
411C4×C5—28no—
412C4×C5—44no—
413C4×C5—82no—
414C4×C5#38618yes—
415Dic5—28no—
416Dic5—24no—
417Dic5—44no—
418Dic5—82no—
419C24—52no—
420C24—52no—
421C24—52no—
422C24—54no—
423C24—54no—
424C24—101no—
425C24—101no—
426C24—101no—
427C24—102no—
428C24—101no—
429C24—102no—
430C24C23×D511yescharacteristic
431C2×Q8—108no—
432C2×Q8—108no—
433C2×Q8—108no—
434C2×Q8—204no—
435C2×Q8—204no—
436C2×Q8—204no—
437C2×Q8—204no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—52no—
452C22×C4—54no—
453C22×C4—52no—
454C22×C4—52no—
455C22×C4—54no—
456C22×C4—54no—
457C22×C4—516no—
458C22×C4—54no—
459C22×C4—1016no—
460C22×C4—1016no—
461C22×C4—1016no—
462C22×C4—1016no—
463C22×C4—1016no—
464C22×C4—1016no—
465C22×C4—101no—
466C22×C4—102no—
467C22×C4—101no—
468C22×C4—101no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—101no—
472C22×C4—102no—
473C22×C4—108no—
474C22×C4—108no—
475C22×C4—108no—
476C22×C4—108no—
477C22×C4—108no—
478C22×C4—108no—
479C22×C4—1016no—
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—104no—
490C22×C4—104no—
491C22×C4C2×C4×D514yes—
492C22×C4C2×C4×D512yes—
493C22×C4C2×D2014yes—
494C22×C4C2×D2012yes—
495C22×C4#70912yes—
496C22×C4D4×D512yes—
497C22×C4D4×D512yes—
498C22×C4D4×D512yes—
499C22×C4#71114yes—
500C22×C4Q8×D514yes—
501C22×C4#71312yes—
502C4⋊C4—28no—
503C4⋊C4—44no—
504C4⋊C4—1016no—
505C4⋊C4—204no—
506C22⋊C4—1016no—
507C22⋊C4—208no—
508C42—28no—
509C42—1016no—
510C42—108no—
511C2×C5C2×#38611yescharacteristic
512C2×C5C2×#39111yescharacteristic
513C2×C5#229711yescharacteristic
514C2×C5C4×C22⋊Q812yes—
515C2×C5C4×C22⋊Q812yes—
516C2×C5#284812yes—
517C2×C5#285011yescharacteristic
518C2×C5#285011yescharacteristic
519C2×C5#285512yes—
520C2×C5#285711yescharacteristic
521C2×C5#285711yescharacteristic
522D5—28no—
523C23—54no—
524C23—54no—
525C23—58no—
526C23—58no—
527C23—54no—
528C23—102no—
529C23—104no—
530C23—102no—
531C23—102no—
532C23—102no—
533C23—102no—
534C23—102no—
535C23—102no—
536C23—104no—
537C23—104no—
538C23—104no—
539C23—104no—
540C23—104no—
541C23—104no—
542C23—104no—
543C23—104no—
544C23—102no—
545C23—104no—
546C23C22×C4×D511yescharacteristic
547C23C22×D2011yescharacteristic
548C23C2×#70911yescharacteristic
549C23C2×D4×D511yescharacteristic
550C23C2×D4×D511yescharacteristic
551C23C2×D4×D511yescharacteristic
552C23C2×#71112yes—
553C23C2×Q8×D512yes—
554C23C2×#71311yescharacteristic
555C23D5×#4112yes—
556C23D5×#4112yes—
557Q8—2016no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—42no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—54no—
575C2×C4—58no—
576C2×C4—1064no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—104no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—104no—
585C2×C4—104no—
586C2×C4—104no—
587C2×C4—104no—
588C2×C4—104no—
589C2×C4—1032no—
590C2×C4—104no—
591C2×C4—104no—
592C2×C4—104no—
593C2×C4—202no—
594C2×C4—202no—
595C2×C4—202no—
596C2×C4—202no—
597C2×C4—202no—
598C2×C4—204no—
599C2×C4—202no—
600C2×C4—202no—
601C2×C4—204no—
602C2×C4C4×D2014yes—
603C2×C4D5×C22⋊C414yes—
604C2×C4#402814yes—
605C2×C4#403014yes—
606C2×C4#403914yes—
607C2×C4#404014yes—
608C2×C4#404114yes—
609C2×C4#404318yescomplemented
610C5#1470211yescharacteristic, complemented, Sylow
611C22—58no—
612C22—104no—
613C22—104no—
614C22—104no—
615C22—104no—
616C22—108no—
617C22—108no—
618C22—104no—
619C22—104no—
620C22—108no—
621C22—108no—
622C22C2×C4×D2011yescharacteristic
623C22C2×D5×C22⋊C411yescharacteristic
624C22C2×#402811yescharacteristic
625C22C2×#403011yescharacteristic
626C22C2×#403911yescharacteristic
627C22C2×#404011yescharacteristic
628C22C2×#404111yescharacteristic
629C22C2×#404312yes—
630C22#6585812yes—
631C22C4×#71112yes—
632C22#6589112yes—
633C22C4×Q8×D512yes—
634C22#6591212yes—
635C22#6594012yes—
636C22#6594012yes—
637C22D5×C22⋊Q812yes—
638C22D5×C22⋊Q812yes—
639C22#6600211yescharacteristic
640C22D5×#12411yescharacteristic
641C22#6602512yes—
642C22#6605011yescharacteristic
643C22D5×C4⋊Q811yescharacteristic
644C22#6606212yes—
645C4—28no—
646C4—44no—
647C4—82no—
648C4—104no—
649C4—108no—
650C4—204no—
651C4—402no—
652C4#6495418yes—
653C2—108no—
654C2C2×#6495411yescharacteristic
655C2C4×#404312yes—
656C2#1060578012yes—
657C2#1060598711yescharacteristic
658C2#1060610711yescharacteristic
659C2#1060769612yes—
660C2#1060801812yes—
661C2#1060802111yescharacteristic
662C2#1060820511yescharacteristic
663C2D5×#39111yescharacteristic
664C2#1060839511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#14702
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#65263C2semidirect
5. C2×#65218C2semidirect
6. C5×C4⋊#95C2semidirect
7. #10602356C2semidirect
9. #10600200C2semidirect
24. C2×#4043C4semidirect
59. C22×C4×D5Q8semidirect
66. C22×Dic10C2×C4semidirect
72. C2×C5×C4⋊C4C2×C4semidirect
86. C2×C4⋊Dic5C2×C4semidirect
107. C4⋊#95D5semidirect
283. C2×C4×C5C22⋊Q8semidirect
310. C2×Dic5C22⋊Q8semidirect
356. C2×C4⋊C4C4×D5semidirect
410. C2×D5#391semidirect
609. C2×C4#4043semidirect
610. C5#14702semidirect

Maximal subgroups

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

subgroupindex
C22×#40432
C22×C42×D52
C2×#652762
C2×#652632
C2×#652182
C5×C4⋊#952
#106023562
#106002182
#106002002
#147025