Finite Group Databasebeta

← #12024595

Subgroups — #12024595

Order 1280.

2062 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×Q8C211yesmaximal, characteristic, complemented
2C2×#65520C211yesmaximal, characteristic
3C2×#65278C212yesmaximal
4C2×C4×#685C211yesmaximal, characteristic
5#10602927C211yesmaximal, characteristic, complemented
6#10602363C211yesmaximal, characteristic
7#10602361C211yesmaximal, characteristic, complemented
8#10602357C212yesmaximal, complemented
9#10602330C212yesmaximal
10#10602329C212yesmaximal, complemented
11#10602327C211yesmaximal, characteristic, complemented
12C23×C5×Q8C2211yescharacteristic
13C23×C4×D5C2211yescharacteristic
14C2×C4×C5×Q8—28no—
15C2×C4×C5×Q8—24no—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2212yes—
18C22×C42×C5C2212yes—
19C22×C42×C5C2211yescharacteristic
20C22×#685C2212yes—
21C22×#685C2211yescharacteristic
22C22×#685C2212yes—
23C22×#685C2211yescharacteristic
24C22×#683C2212yes—
25C22×C4×Dic5C2211yescharacteristic
26#65520C418yescomplemented
27C2×#3963C2211yescharacteristic
28C2×#3963C2211yescharacteristic
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C2×#3963C2212yes—
38#65278—28no—
39C4×#685—24no—
40#14172—51nomaximal, Sylow
41C24×D5C2311yescharacteristic
42C22×C5×Q8—24no—
43C22×C5×Q8—22no—
44C22×C5×Q8—22no—
45C22×C5×Q8—24no—
46C22×C5×Q8C2×C414yescomplemented
47C23×C4×C5C2312yes—
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×C4×C5C2311yescharacteristic
52C23×Dic5C2312yes—
53C23×Dic5C2311yescharacteristic
54C23×Dic5C2312yes—
55C23×Dic5C2311yescharacteristic
56C23×Dic5C2311yescharacteristic
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—22no—
60C22×C4×D5—24no—
61C22×C4×D5—42no—
62C4×C5×Q8—232no—
63C2×C5×C4⋊C4—24no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—24no—
67C2×C5×C4⋊C4D418yes—
68C2×C42×C5—24no—
69C2×C42×C5—24no—
70C2×C42×C5—24no—
71C2×C42×C5—24no—
72C2×C42×C5D414yes—
73C2×#685—22no—
74C2×#685—22no—
75C2×#685—24no—
76C2×#685—22no—
77C2×#685—24no—
78C2×#685—22no—
79C2×#685—24no—
80C2×#685—24no—
81C2×#685—42no—
82C2×#685C2×C414yes—
83C2×#685C2×C418yes—
84C2×#685Q814yescomplemented
85C2×#683—24no—
86C2×#683—24no—
87C2×#683—42no—
88C2×C4×Dic5—22no—
89C2×C4×Dic5—42no—
90#3963—22no—
91#3963—22no—
92#3963—24no—
93#3963—24no—
94#3963—24no—
95#3963—22no—
96#3963—24no—
97#3963—42no—
98#3963—42no—
99#3963C2×C414yescomplemented
100#3963C2×C418yescomplemented
101C22×C4×Q8D511yescharacteristic, complemented
102C2×#393—51no—
103C2×#385—52no—
104C2×C4×C22⋊C4—51no—
105#1446—51no—
106#1444—51no—
107#1439—51no—
108#1437—52no—
109#1436—52no—
110#1436—52no—
111#1434—51no—
112C24×C5C2411yescharacteristic
113C23×D5—21no—
114C23×D5—22no—
115C23×D5—21no—
116C23×D5—21no—
117C23×D5—22no—
118C23×D5—21no—
119C23×D5—22no—
120C23×D5—22no—
121C23×D5C22×C412yes—
122C23×D5C2×Q812yes—
123C23×D5#4112yes—
124C2×C5×Q8—28no—
125C2×C5×Q8—28no—
126C2×C5×Q8—216no—
127C2×C5×Q8—28no—
128C2×C5×Q8—216no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
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×C5—22no—
146C22×C4×C5C22×C414yes—
147C22×C4×C5C22×C412yes—
148C22×C4×C5C2×D414yes—
149C22×C4×C5C2×D414yes—
150C22×C4×C5C2×D412yes—
151C22×C4×C5C2×D414yes—
152C22×C4×C5C2×D412yes—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×Q812yes—
155C22×C4×C5#4112yes—
156C22×C4×C5#4114yes—
157C22×C4×C5#4112yes—
158C22×Dic5—21no—
159C22×Dic5—22no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5—22no—
163C22×Dic5—21no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—21no—
168C22×Dic5—22no—
169C22×Dic5—21no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5C22×C414yes—
184C22×Dic5C22×C412yes—
185C22×Dic5C2×Q812yes—
186C22×Dic5#4112yes—
187C2×C4×D5—28no—
188C2×C4×D5—48no—
189C2×C4×D5—48no—
190C2×C4×D5—44no—
191C2×C4×D5—44no—
192C5×C4⋊C4—28no—
193C5×C4⋊C4—216no—
194C42×C5—216no—
195C42×C5—28no—
196#685—28no—
197#685—216no—
198#685—28no—
199#685—48no—
200#683—48no—
201C4×Dic5—44no—
202C23×Q8C2×D511yescharacteristic
203C24×C4—51no—
204C2×C4×Q8—28no—
205C2×C4×Q8—24no—
206C22×C4⋊C4—52no—
207C22×C4⋊C4C2×D511yescharacteristic
208C22×C4⋊C4C2×D512yes—
209C22×C22⋊C4—52no—
210C22×C22⋊C4—51no—
211C22×C22⋊C4—51no—
212C22×C22⋊C4—52no—
213C22×C42—51no—
214C22×C42C2×D512yes—
215C22×C42C2×D511yescharacteristic
216#393—58no—
217#385—108no—
218C4×C22⋊C4—104no—
219C2×#95—51no—
220C2×#95—52no—
221C2×#95—52no—
222C2×#95—52no—
223C2×#95—51no—
224C2×#95—51no—
225C2×#95—52no—
226C2×#95—52no—
227C2×#95—51no—
228C2×#95—52no—
229C2×#95—52no—
230C23×C5C23×C411yescharacteristic
231C23×C5C22×D411yescharacteristic
232C23×C5C22×D412yes—
233C23×C5C22×Q811yescharacteristic
234C23×C5C2×#4111yescharacteristic
235C23×C5C2×#4112yes—
236C23×C5C2×#4111yescharacteristic
237C23×C5C2×#4111yescharacteristic
238C23×C5C2×#4111yescharacteristic
239C23×C5H(5,𝔽2)12yes—
240C23×C52−1+412yes—
241C22×D5—24no—
242C22×D5—22no—
243C22×D5—22no—
244C22×D5—24no—
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—41no—
254C22×D5—41no—
255C22×D5—42no—
256C22×D5—41no—
257C22×D5—41no—
258C22×D5—42no—
259C22×D5—42no—
260C22×D5—42no—
261C22×D5—42no—
262C22×D5—42no—
263C22×D5C4×Q814yescomplemented
264C5×Q8—232no—
265C2×C4×C5—24no—
266C2×C4×C5—24no—
267C2×C4×C5—24no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—42no—
289C2×C4×C5—42no—
290C2×C4×C5C4×D414yes—
291C2×C4×C5C4×D418yes—
292C2×C4×C5#12014yes—
293C2×C4×C5C22⋊Q814yes—
294C2×Dic5—22no—
295C2×Dic5—24no—
296C2×Dic5—24no—
297C2×Dic5—24no—
298C2×Dic5—24no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—24no—
302C2×Dic5—24no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
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×Dic5—42no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C4×D5—416no—
324C25—51no—
325C22×Q8—24no—
326C22×Q8—22no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8C4×D514yescomplemented
330C23×C4—52no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—51no—
334C23×C4—52no—
335C23×C4—102no—
336C23×C4—102no—
337C23×C4—102no—
338C23×C4—104no—
339C23×C4—202no—
340C23×C4C22×D512yes—
341C23×C4C22×D512yes—
342C23×C4C22×D511yescharacteristic
343C23×C4C22×D511yescharacteristic
344C23×C4C22×D511yescharacteristic
345C4×Q8—232no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—104no—
351C2×C4⋊C4—104no—
352C2×C4⋊C4—202no—
353C2×C4⋊C4C22⋊D518yes—
354C2×C22⋊C4—58no—
355C2×C22⋊C4—54no—
356C2×C22⋊C4—54no—
357C2×C22⋊C4—104no—
358C2×C22⋊C4—102no—
359C2×C22⋊C4—102no—
360C2×C22⋊C4—102no—
361C2×C22⋊C4—102no—
362C2×C22⋊C4—104no—
363C2×C22⋊C4—104no—
364C2×C22⋊C4—104no—
365C2×C22⋊C4—202no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—102no—
371C2×C42—202no—
372C2×C42C22⋊D514yes—
373#95—54no—
374#95—58no—
375#95—104no—
376#95—102no—
377#95—104no—
378#95—102no—
379#95—102no—
380#95—104no—
381#95—104no—
382#95—202no—
383#95—202no—
384C22×C5C2×C4×D411yescharacteristic
385C22×C5C2×C4×D412yes—
386C22×C5C2×C4×Q811yescharacteristic
387C22×C5C4×#4111yescharacteristic
388C22×C5#52012yes—
389C22×C5C2×#12011yescharacteristic
390C22×C5C2×C22⋊Q811yescharacteristic
391C22×C5#52511yescharacteristic
392C22×C5#52512yes—
393C22×C5#52511yescharacteristic
394C22×C5#52911yescharacteristic
395C22×C5#53311yescharacteristic
396C22×C5#53511yescharacteristic
397C22×C5#53611yescharacteristic
398C22×C5#54212yes—
399C22×C5#54612yes—
400C22×C5#54612yes—
401C22×C5#54812yes—
402C22×C5D4×Q812yes—
403C22×C5#55212yes—
404C22×C5#55412yes—
405C22×C5#55612yes—
406C22×C5#55912yes—
407C2×D5—28no—
408C2×D5—24no—
409C2×D5—42no—
410C2×D5—42no—
411C2×D5—42no—
412C2×D5—44no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—44no—
416C2×D5—44no—
417C2×D5—42no—
418C4×C5—24no—
419C4×C5—24no—
420C4×C5—28no—
421C4×C5—24no—
422C4×C5—44no—
423Dic5—42no—
424Dic5—42no—
425Dic5—44no—
426Dic5—42no—
427Dic5—82no—
428C24—52no—
429C24—52no—
430C24—52no—
431C24—101no—
432C24—102no—
433C24—101no—
434C24—102no—
435C24—101no—
436C24—102no—
437C24—101no—
438C24—102no—
439C24C23×D511yescharacteristic
440C2×Q8—28no—
441C2×Q8—216no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—216no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
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—54no—
463C22×C4—52no—
464C22×C4—52no—
465C22×C4—52no—
466C22×C4—108no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—101no—
470C22×C4—102no—
471C22×C4—101no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—101no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
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—208no—
493C22×C4—208no—
494C22×C4—204no—
495C22×C4—204no—
496C22×C4C2×C4×D514yes—
497C22×C4C2×C4×D512yes—
498C22×C4#70914yes—
499C22×C4#70912yes—
500C22×C4Q8×D512yes—
501C22×C4#71312yes—
502C22×C4C2×C22⋊D514yes—
503C22×C4C2×C22⋊D514yes—
504C22×C4C2×C22⋊D512yes—
505C22×C4C2×C22⋊D514yes—
506C22×C4C2×C22⋊D512yes—
507C22×C4C2×C22⋊D512yes—
508C4⋊C4—28no—
509C4⋊C4—216no—
510C4⋊C4—208no—
511C22⋊C4—108no—
512C22⋊C4—1016no—
513C22⋊C4—108no—
514C22⋊C4—208no—
515C42—216no—
516C42—28no—
517C42—204no—
518C2×C5C4×#12011yescharacteristic
519C2×C5C4×C22⋊Q811yescharacteristic
520C2×C5#232611yescharacteristic
521C2×C5#236012yes—
522C2×C5#236712yes—
523C2×C5#240411yescharacteristic
524C2×C5#240911yescharacteristic
525C2×C5#245812yes—
526C2×C5#246512yes—
527C2×C5#258011yescharacteristic
528C2×C5#259911yescharacteristic
529D5—44no—
530C23—54no—
531C23—102no—
532C23—104no—
533C23—102no—
534C23—104no—
535C23—102no—
536C23—102no—
537C23—104no—
538C23—104no—
539C23—102no—
540C23—104no—
541C23—102no—
542C23—104no—
543C23—202no—
544C23—201no—
545C23—201no—
546C23—202no—
547C23—202no—
548C23—202no—
549C23—201no—
550C23—202no—
551C23—201no—
552C23—202no—
553C23C22×C4×D511yescharacteristic
554C23C2×#70912yes—
555C23C2×#70911yescharacteristic
556C23C2×Q8×D511yescharacteristic
557C23C2×#71311yescharacteristic
558C23#414712yes—
559C23D5×#4111yescharacteristic
560C23D5×#4111yescharacteristic
561C23#414912yes—
562C23C22×C22⋊D511yescharacteristic
563C23C22×C22⋊D512yes—
564Q8—232no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—102no—
591C2×C4—104no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—104no—
595C2×C4—104no—
596C2×C4—104no—
597C2×C4—104no—
598C2×C4—104no—
599C2×C4—2016no—
600C2×C4—201no—
601C2×C4—201no—
602C2×C4—202no—
603C2×C4—202no—
604C2×C4—202no—
605C2×C4—202no—
606C2×C4—201no—
607C2×C4—201no—
608C2×C4—201no—
609C2×C4—202no—
610C2×C4—201no—
611C2×C4—202no—
612C2×C4—202no—
613C2×C4—202no—
614C2×C4—202no—
615C2×C4—202no—
616C2×C4—202no—
617C2×C4—202no—
618C2×C4—202no—
619C2×C4—202no—
620C2×C4C4×C22⋊D514yes—
621C2×C4C4×C22⋊D518yes—
622C2×C4#409214yes—
623C2×C4#409914yes—
624C5#1417211yescharacteristic, complemented, Sylow
625C22—104no—
626C22—108no—
627C22—202no—
628C22—202no—
629C22—204no—
630C22—202no—
631C22—204no—
632C22—204no—
633C22—202no—
634C22—202no—
635C22—202no—
636C22#6590212yes—
637C22C4×Q8×D511yescharacteristic
638C22C4×#71311yescharacteristic
639C22#6590812yes—
640C22#6591211yescharacteristic
641C22#6591312yes—
642C22#6591411yescharacteristic
643C22#6591512yes—
644C22#6591612yes—
645C22#6591912yes—
646C22C2×C4×C22⋊D511yescharacteristic
647C22C2×C4×C22⋊D512yes—
648C22#6612512yes—
649C22#6612511yescharacteristic
650C22C2×#409211yescharacteristic
651C22Q8×C22⋊D512yes—
652C22#6615011yescharacteristic
653C22#6615112yes—
654C22#6616211yescharacteristic
655C22#6616312yes—
656C22#6616312yes—
657C22#6616411yescharacteristic
658C22C2×#409911yescharacteristic
659C4—24no—
660C4—28no—
661C4—24no—
662C4—24no—
663C4—44no—
664C4—202no—
665C4—202no—
666C4—204no—
667C4—202no—
668C4—402no—
669C2—204no—
670C2#1061418611yescharacteristic
671C2#1061419712yes—
672C2C4×#409211yescharacteristic
673C2#1061422112yes—
674C2#1061422812yes—
675C2#1061422912yes—
676C2#1061423211yescharacteristic
677C2#1061423311yescharacteristic
678C2C4×#409911yescharacteristic
679C2#1061579911yescharacteristic
680C2#1061582711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC22×C4×C5×Q8C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC22×C4×Q8D5
hypocenterC5#14172
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×Q8C2semidirect
5. #10602927C2semidirect
7. #10602361C2semidirect
8. #10602357C2semidirect
10. #10602329C2semidirect
11. #10602327C2semidirect
26. #65520C4semidirect
46. C22×C5×Q8C2×C4semidirect
84. C2×#685Q8semidirect
99. #3963C2×C4semidirect
100. #3963C2×C4semidirect
101. C22×C4×Q8D5semidirect
263. C22×D5C4×Q8semidirect
329. C22×Q8C4×D5semidirect
624. C5#14172semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×Q82
C2×#655202
C2×#652782
C2×C4×#6852
#106029272
#106023632
#106023612
#106023572
#106023302
#106023292
#106023272
#141725