Finite Group Databasebeta

← #12030543

Subgroups — #12030543

Order 1280.

2574 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic5C211yesmaximal, characteristic
2C2×#65239C211yesmaximal, characteristic
3C2×#65235C211yesmaximal, characteristic
4C2×#65231C211yesmaximal, characteristic
5C2×#65231C211yesmaximal, characteristic
6C2×#64936C212yesmaximal, complemented
7C5×C22⋊#95C211yesmaximal, characteristic
8#10602920C211yesmaximal, characteristic
9#10600200C212yesmaximal, complemented
10#10600199C212yesmaximal, complemented
11#10600197C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C24×Dic5C2211yescharacteristic
14C24×Dic5C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic5C2211yescharacteristic
18C22×C22⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2212yes—
20C22×#683C2211yescharacteristic
21C22×#683C2211yescharacteristic
22C22×#683C2212yes—
23C22×#683C2212yes—
24C22×C4×Dic5—28no—
25C22×C4×Dic5—24no—
26C22×C4×Dic5C2212yes—
27C22×C4×Dic5C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C2×#3963C2212yes—
37#65239—24no—
38#65235—24no—
39#65231—24no—
40#65231C418yescomplemented
41#64936—28no—
42#14697—51nomaximal, Sylow
43C25×C5C2311yescharacteristic
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—24no—
47C23×C4×C5—24no—
48C23×C4×C5Q814yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×C4×C5C2312yes—
52C23×C4×C5C2312yes—
53C23×Dic5—22no—
54C23×Dic5—22no—
55C23×Dic5—24no—
56C23×Dic5—24no—
57C23×Dic5—24no—
58C23×Dic5—24no—
59C23×Dic5C2×C414yes—
60C23×Dic5D414yes—
61C23×Dic5D414yes—
62C23×Dic5Q814yes—
63C23×Dic5C2311yescharacteristic
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2312yes—
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2312yes—
68C23×Dic5C2311yescharacteristic
69C2×C5×C22⋊C4—22no—
70C2×C5×C22⋊C4—22no—
71C2×C5×C22⋊C4—22no—
72C2×C5×C22⋊C4—22no—
73C2×C5×C22⋊C4—22no—
74C2×C5×C22⋊C4C2×C414yes—
75C2×C22⋊Dic5—22no—
76C2×C22⋊Dic5—22no—
77C2×C22⋊Dic5—22no—
78C2×C22⋊Dic5—22no—
79C2×C22⋊Dic5—22no—
80C2×C22⋊Dic5C2×C414yes—
81C2×C4⋊Dic5—24no—
82C2×C4⋊Dic5—24no—
83C2×C4⋊Dic5—24no—
84C2×#683—24no—
85C2×#683—24no—
86C2×#683—24no—
87C2×#683—24no—
88C2×#683—22no—
89C2×#683—22no—
90C2×#683—24no—
91C2×#683—24no—
92C2×#683—24no—
93C2×#683C2×C418yescomplemented
94C2×C4×Dic5—232no—
95C2×C4×Dic5—24no—
96C2×C4×Dic5—24no—
97C2×C4×Dic5—24no—
98C2×C4×Dic5—24no—
99C2×C4×Dic5—24no—
100C2×C4×Dic5D418yes—
101C5×#95—24no—
102C5×#95—24no—
103#3963—24no—
104#3963—24no—
105#3963—22no—
106#3963—22no—
107#3963—24no—
108#3963—24no—
109#3963C2×C418yescomplemented
110C23×C42—51no—
111C2×#389—52no—
112C2×#385—51no—
113C2×#385—51no—
114C2×#380—51no—
115C2×#380—51no—
116#1436—52no—
117#1436—52no—
118C4⋊#95—52no—
119C22⋊#95—51no—
120C22⋊#95D511yescharacteristic
121C24×C5—22no—
122C24×C5—22no—
123C24×C5—22no—
124C24×C5—22no—
125C24×C5C22×C412yes—
126C24×C5C2×D412yes—
127C24×C5C2×D412yes—
128C24×C5C2×Q812yes—
129C24×C5C2×Q812yes—
130C24×C5#4112yes—
131C24×C5#4112yes—
132C24×C5C2411yescharacteristic
133C22×C4×C5—216no—
134C22×C4×C5—28no—
135C22×C4×C5—28no—
136C22×C4×C5—28no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—216no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5C22×C414yes—
159C22×C4×C5C2×D414yes—
160C22×C4×C5C2×Q814yes—
161C22×C4×C5#4114yes—
162C22×Dic5—216no—
163C22×Dic5—28no—
164C22×Dic5—28no—
165C22×Dic5—28no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—216no—
173C22×Dic5—28no—
174C22×Dic5—216no—
175C22×Dic5—216no—
176C22×Dic5—28no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—22no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5C4⋊C4116yescomplemented
194C22×Dic5C22×C414yes—
195C22×Dic5C22×C412yes—
196C22×Dic5C22×C412yes—
197C22×Dic5C2×D412yes—
198C22×Dic5C2×D414yes—
199C22×Dic5C2×D414yes—
200C22×Dic5C2×D412yes—
201C22×Dic5C2×D414yes—
202C22×Dic5C2×Q812yes—
203C22×Dic5C2×Q812yes—
204C22×Dic5#4114yes—
205C22×Dic5#4114yes—
206C5×C22⋊C4—28no—
207C5×C22⋊C4—44no—
208C22⋊Dic5—28no—
209C22⋊Dic5—44no—
210C4⋊Dic5—48no—
211#683—216no—
212#683—44no—
213#683—48no—
214#683—44no—
215C4×Dic5—216no—
216C4×Dic5—216no—
217C24×C4—51no—
218C24×C4—51no—
219C24×C4C2×D511yescharacteristic
220C22×C4⋊C4—52no—
221C22×C4⋊C4—51no—
222C22×C4⋊C4—52no—
223C22×C4⋊C4—51no—
224C22×C4⋊C4—52no—
225C22×C22⋊C4—51no—
226C22×C22⋊C4—51no—
227C22×C22⋊C4C2×D511yescharacteristic
228C22×C22⋊C4C2×D511yescharacteristic
229C22×C42—52no—
230C22×C42—52no—
231C22×C42—108no—
232C22×C42—104no—
233#389—108no—
234#385—104no—
235#385—104no—
236#380—58no—
237#380—104no—
238C2×#95—52no—
239C2×#95—52no—
240C2×#95—52no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—51no—
244C2×#95—51no—
245C2×#95C2×D512yes—
246C2×#95C2×D512yes—
247C23×C5—24no—
248C23×C5—24no—
249C23×C5—22no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5—24no—
253C23×C5—22no—
254C23×C5—22no—
255C23×C5—24no—
256C23×C5—22no—
257C23×C5—24no—
258C23×C5—24no—
259C23×C5—24no—
260C23×C5—24no—
261C23×C5—24no—
262C23×C5—24no—
263C23×C5C2×C4⋊C414yes—
264C23×C5C4×D414yes—
265C23×C5C4×Q814yes—
266C23×C5#12114yes—
267C23×C5C22⋊Q814yes—
268C23×C5#12514yes—
269C23×C5C4⋊Q814yes—
270C23×C5C23×C411yescharacteristic
271C23×C5C22×D411yescharacteristic
272C23×C5C22×D412yes—
273C23×C5C22×D411yescharacteristic
274C23×C5C22×Q811yescharacteristic
275C23×C5C22×Q811yescharacteristic
276C23×C5C2×#4111yescharacteristic
277C23×C5C2×#4111yescharacteristic
278C23×C5C2×#4112yes—
279C23×C5C2×#4112yes—
280C23×C5C2×#4112yes—
281C2×C4×C5—232no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—24no—
290C2×C4×C5—24no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—41no—
296C2×C4×C5—42no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—42no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5C22⋊Q818yes—
306C2×Dic5—232no—
307C2×Dic5—24no—
308C2×Dic5—24no—
309C2×Dic5—22no—
310C2×Dic5—24no—
311C2×Dic5—24no—
312C2×Dic5—24no—
313C2×Dic5—22no—
314C2×Dic5—24no—
315C2×Dic5—24no—
316C2×Dic5—24no—
317C2×Dic5—232no—
318C2×Dic5—24no—
319C2×Dic5—24no—
320C2×Dic5—24no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5—42no—
324C2×Dic5—42no—
325C2×Dic5—41no—
326C2×Dic5—42no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—42no—
331C2×Dic5—41no—
332C2×Dic5—41no—
333C2×Dic5—42no—
334C2×Dic5—42no—
335C2×Dic5C2×C4⋊C414yes—
336C2×Dic5C2×C4⋊C414yes—
337C2×Dic5C4×D418yes—
338C2×Dic5#12014yes—
339C2×Dic5#12118yes—
340C2×Dic5C22⋊Q818yes—
341C2×Dic5#12314yes—
342C25C22×D511yescharacteristic
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—51no—
348C23×C4—54no—
349C23×C4—54no—
350C23×C4—54no—
351C23×C4—52no—
352C23×C4—51no—
353C23×C4—54no—
354C23×C4—52no—
355C23×C4—51no—
356C23×C4—51no—
357C23×C4—104no—
358C23×C4—104no—
359C23×C4—104no—
360C23×C4—104no—
361C23×C4—102no—
362C23×C4—102no—
363C23×C4Dic1014yes—
364C23×C4C22×D511yescharacteristic
365C23×C4C22×D511yescharacteristic
366C23×C4C22×D512yes—
367C23×C4C22×D512yes—
368C2×C4⋊C4—58no—
369C2×C4⋊C4—104no—
370C2×C4⋊C4—104no—
371C2×C4⋊C4—102no—
372C2×C4⋊C4—102no—
373C2×C4⋊C4—104no—
374C2×C4⋊C4—104no—
375C2×C4⋊C4—104no—
376C2×C4⋊C4—104no—
377C2×C4⋊C4—104no—
378C2×C4⋊C4—104no—
379C2×C4⋊C4—104no—
380C2×C4⋊C4—104no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—54no—
387C2×C22⋊C4—102no—
388C2×C22⋊C4—102no—
389C2×C22⋊C4—102no—
390C2×C22⋊C4—102no—
391C2×C22⋊C4—102no—
392C2×C22⋊C4C4×D514yes—
393C2×C42—58no—
394C2×C42—104no—
395C2×C42—104no—
396C2×C42—104no—
397C2×C42—104no—
398C2×C42—1032no—
399C2×C42—104no—
400#95—24no—
401#95—24no—
402#95—58no—
403#95—102no—
404#95—102no—
405#95—104no—
406#95—104no—
407#95—104no—
408#95—104no—
409C22×C5—24no—
410C22×C5—24no—
411C22×C5—28no—
412C22×C5—24no—
413C22×C5—24no—
414C22×C5—28no—
415C22×C5—24no—
416C22×C5—24no—
417C22×C5—28no—
418C22×C5—28no—
419C22×C5#38918yescomplemented
420C22×C5C22×C4⋊C411yescharacteristic
421C22×C5C2×C4×D411yescharacteristic
422C22×C5C2×C4×D412yes—
423C22×C5C2×C4×Q811yescharacteristic
424C22×C5C4×#4112yes—
425C22×C5C2×#12011yescharacteristic
426C22×C5C2×#12111yescharacteristic
427C22×C5C2×#12112yes—
428C22×C5C2×C22⋊Q811yescharacteristic
429C22×C5C2×C22⋊Q812yes—
430C22×C5C2×C22⋊Q812yes—
431C22×C5C2×#12311yescharacteristic
432C22×C5#52512yes—
433C22×C5#52512yes—
434C22×C5#52511yescharacteristic
435C22×C5#52511yescharacteristic
436C22×C5C2×#12511yescharacteristic
437C22×C5#52912yes—
438C22×C5#52912yes—
439C22×C5C2×C4⋊Q811yescharacteristic
440C22×C5#53212yes—
441C22×C5#53312yes—
442C22×C5#53312yes—
443C4×C5—28no—
444C4×C5—44no—
445C4×C5—81no—
446C4×C5—81no—
447Dic5—28no—
448Dic5—24no—
449Dic5—44no—
450Dic5—81no—
451Dic5—81no—
452Dic5#38518yescomplemented
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C2×Dic1012yes—
458C24C2×C4×D512yes—
459C24#70912yes—
460C24D4×D512yes—
461C24D4×D512yes—
462C24#71112yes—
463C24Q8×D512yes—
464C24C23×D511yescharacteristic
465C22×C4—28no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—216no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—52no—
491C22×C4—54no—
492C22×C4—52no—
493C22×C4—52no—
494C22×C4—54no—
495C22×C4—52no—
496C22×C4—52no—
497C22×C4—54no—
498C22×C4—54no—
499C22×C4—52no—
500C22×C4—54no—
501C22×C4—516no—
502C22×C4—54no—
503C22×C4—108no—
504C22×C4—1016no—
505C22×C4—1016no—
506C22×C4—108no—
507C22×C4—1016no—
508C22×C4—108no—
509C22×C4—1016no—
510C22×C4—108no—
511C22×C4—102no—
512C22×C4—102no—
513C22×C4—102no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—108no—
518C22×C4—102no—
519C22×C4—102no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4—102no—
523C22×C4—102no—
524C22×C4—101no—
525C22×C4—101no—
526C22×C4—101no—
527C22×C4—101no—
528C22×C4—101no—
529C22×C4—102no—
530C22×C4—101no—
531C22×C4—102no—
532C22×C4—102no—
533C22×C4—102no—
534C22×C4C2×Dic1014yes—
535C22×C4C2×C4×D514yes—
536C22×C4D4×D514yes—
537C22×C4#71114yes—
538C4⋊C4—1016no—
539C4⋊C4—204no—
540C4⋊C4—208no—
541C4⋊C4—204no—
542C4⋊C4—208no—
543C22⋊C4—28no—
544C22⋊C4—44no—
545C22⋊C4—108no—
546C22⋊C4—204no—
547C42—1016no—
548C42—1016no—
549C2×C5—28no—
550C2×C5C2×#38511yescharacteristic
551C2×C5C2×#38911yescharacteristic
552C2×C5#229611yescharacteristic
553C2×C5C4×#12112yes—
554C2×C5C4×C22⋊Q812yes—
555C2×C5#284711yescharacteristic
556C2×C5#284811yescharacteristic
557C2×C5#285112yes—
558C2×C5#285411yescharacteristic
559C2×C5#285511yescharacteristic
560C2×C5#285712yes—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—22no—
568C23—24no—
569C23—22no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—22no—
576C23—22no—
577C23C4×Dic1014yes—
578C23#402414yes—
579C23#402714yes—
580C23#403014yes—
581C23#403414yes—
582C23#403514yes—
583C23D5×C4⋊C414yes—
584C23C22×Dic1011yescharacteristic
585C23C22×C4×D511yescharacteristic
586C23C2×#70911yescharacteristic
587C23C2×D4×D511yescharacteristic
588C23C2×D4×D512yes—
589C23C2×D4×D511yescharacteristic
590C23C2×#71111yescharacteristic
591C23C2×#71112yes—
592C23C2×Q8×D511yescharacteristic
593C23D5×#4112yes—
594C23D5×#4112yes—
595C2×C4—232no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—54no—
620C2×C4—58no—
621C2×C4—54no—
622C2×C4—58no—
623C2×C4—54no—
624C2×C4—54no—
625C2×C4—58no—
626C2×C4—1032no—
627C2×C4—1032no—
628C2×C4—104no—
629C2×C4—104no—
630C2×C4—104no—
631C2×C4—104no—
632C2×C4—104no—
633C2×C4—102no—
634C2×C4—104no—
635C2×C4—104no—
636C2×C4—102no—
637C2×C4—104no—
638C2×C4—104no—
639C2×C4—104no—
640C2×C4—104no—
641C2×C4—202no—
642C2×C4—202no—
643C2×C4—202no—
644C2×C4—202no—
645C2×C4—201no—
646C2×C4—201no—
647C2×C4—202no—
648C2×C4—202no—
649C2×C4—201no—
650C2×C4—201no—
651C2×C4—202no—
652C2×C4—202no—
653C2×C4—201no—
654C2×C4—201no—
655C2×C4#402418yes—
656C5#1469711yescharacteristic, complemented, Sylow
657C22—24no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—28no—
662C22—24no—
663C22—28no—
664C22—28no—
665C22—28no—
666C22—24no—
667C22#6493618yescomplemented
668C22C2×C4×Dic1011yescharacteristic
669C22C2×#402411yescharacteristic
670C22C2×#402412yes—
671C22C2×#402711yescharacteristic
672C22C2×#403011yescharacteristic
673C22C2×#403411yescharacteristic
674C22C2×#403511yescharacteristic
675C22C2×D5×C4⋊C411yescharacteristic
676C22#6585112yes—
677C22C4×#71112yes—
678C22#6587212yes—
679C22C4×D4×D512yes—
680C22#6588112yes—
681C22#6592011yescharacteristic
682C22#6592012yes—
683C22D5×#12011yescharacteristic
684C22#6593012yes—
685C22D5×#12112yes—
686C22#6595612yes—
687C22D5×C22⋊Q812yes—
688C22#6598312yes—
689C22D5×#12311yescharacteristic
690C22#6599011yescharacteristic
691C4—28no—
692C4—44no—
693C4—58no—
694C4—81no—
695C4—81no—
696C4—108no—
697C4—104no—
698C4—204no—
699C4—401no—
700C4—401no—
701C2—28no—
702C2C2×#6493611yescharacteristic
703C2C4×#402412yes—
704C2#1060557711yescharacteristic
705C2#1060573212yes—
706C2#1060584811yescharacteristic
707C2#1060610911yescharacteristic
708C2#1060631712yes—
709C2D5×#38511yescharacteristic
710C2#1060639112yes—
711C2#1060660311yescharacteristic
712C2#1060666611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#14697
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
6. C2×#64936C2semidirect
9. #10600200C2semidirect
10. #10600199C2semidirect
11. #10600197C2semidirect
40. #65231C4semidirect
93. C2×#683C2×C4semidirect
109. #3963C2×C4semidirect
193. C22×Dic5C4⋊C4semidirect
419. C22×C5#389semidirect
452. Dic5#385semidirect
656. C5#14697semidirect
667. C22#64936semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic52
C2×#652392
C2×#652352
C2×#652312
C2×#649362
C5×C22⋊#952
#106029202
#106002002
#106001992
#106001972
#146975