Finite Group Databasebeta

← #12020549

Subgroups — #12020549

Order 1280.

2102 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C211yesmaximal, characteristic
2C2×C4×#683C211yesmaximal, characteristic, complemented
3C2×#64956C212yesmaximal
4C2×#64938C211yesmaximal, characteristic, complemented
5C5×#1436C211yesmaximal, characteristic, complemented
6#10602357C211yesmaximal, characteristic, complemented
7#10602330C211yesmaximal, characteristic
8#10600201C211yesmaximal, characteristic
9#10600201C212yesmaximal
10#10600200C212yesmaximal, complemented
11#10600197C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C22×#685C2211yescharacteristic
16C22×#685C2211yescharacteristic
17C22×#685C2212yes—
18C22×#685C2212yes—
19C22×C4⋊Dic5C2211yescharacteristic
20C22×#683C2212yes—
21C22×#683C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C22×C4×Dic5C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C2×#4038—24no—
27C2×#4038—24no—
28C2×#4038C418yescomplemented
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C4×#683—24no—
39#64956C4116yescomplemented
40#64938—24no—
41#13777—51nomaximal, Sylow
42C24×D5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—24no—
56C22×C4×D5C2×C414yes—
57C22×C4×D5C2×C418yes—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4C2×C414yes—
61C2×C42×C5—22no—
62C2×C42×C5—42no—
63C2×#685—22no—
64C2×#685—22no—
65C2×#685—22no—
66C2×#685—22no—
67C2×#685—42no—
68C2×#685—42no—
69C2×#685—42no—
70C2×#685—42no—
71C2×#685C2×C414yes—
72C2×#685C2×C414yes—
73C2×#685C2×C418yes—
74C2×#685C2×C418yes—
75C2×C4⋊Dic5—22no—
76C2×C4⋊Dic5—22no—
77C2×C4⋊Dic5C2×C414yes—
78C2×#683—24no—
79C2×#683—24no—
80C2×#683—24no—
81C2×#683—24no—
82C2×#683C2×C418yes—
83C2×#683C2×C418yes—
84C2×C4×Dic5—22no—
85C2×C4×Dic5—22no—
86C2×C4×Dic5—22no—
87C2×C4×Dic5—24no—
88C2×C4×Dic5—42no—
89C2×C4×Dic5—42no—
90C2×C4×Dic5—42no—
91C2×C4×Dic5C2×C414yes—
92C2×C4×Dic5C2×C414yes—
93C2×C4×Dic5D414yes—
94C2×C4×Dic5D414yes—
95#4038—232no—
96C5×#95—22no—
97C5×#95—42no—
98C5×#95C2×C418yes—
99#3963—22no—
100#3963—24no—
101#3963—42no—
102#3963—42no—
103#3963—42no—
104#3963C2×C418yes—
105C22×#117—51no—
106C2×#380—52no—
107C2×C4×C4⋊C4—51no—
108C2×C4×C4⋊C4—51no—
109#1437—51no—
110#1437—52no—
111#1437—51no—
112#1436—52no—
113#1436—51no—
114#1436D511yescharacteristic, complemented
115C4⋊#95—52no—
116C24×C5C2411yescharacteristic
117C23×D5—21no—
118C23×D5—21no—
119C23×D5—22no—
120C23×D5—22no—
121C23×D5—22no—
122C23×D5—22no—
123C23×D5—22no—
124C23×D5C22×C412yes—
125C23×D5C22×C414yes—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
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×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5C22×C412yes—
148C22×C4×C5C22×C414yes—
149C22×C4×C5C22×C414yes—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C22×C414yes—
152C22×C4×C5C22×C412yes—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D412yes—
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×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5C22×C414yes—
174C22×Dic5C22×C414yes—
175C22×Dic5C22×C412yes—
176C22×Dic5C22×C412yes—
177C22×Dic5C22×C412yes—
178C22×Dic5C22×C414yes—
179C22×Dic5C2×D412yes—
180C22×Dic5C2×D412yes—
181C22×Dic5C2×D412yes—
182C22×Dic5C2×D412yes—
183C22×Dic5#4114yes—
184C2×C4×D5—28no—
185C2×C4×D5—28no—
186C2×C4×D5—216no—
187C2×C4×D5—216no—
188C2×C4×D5C42116yescomplemented
189C5×C4⋊C4—28no—
190C42×C5—44no—
191#685—28no—
192#685—28no—
193#685—48no—
194#685—48no—
195C4⋊Dic5—28no—
196#683—216no—
197#683—216no—
198C4×Dic5—28no—
199C4×Dic5—48no—
200C4×Dic5—44no—
201C4×Dic5C22⋊C4116yescomplemented
202C24×C4—51no—
203C2×#117—58no—
204C2×#117—104no—
205C2×#117—104no—
206C22×C4⋊C4—52no—
207C22×C4⋊C4—52no—
208C22×C4⋊C4—51no—
209C22×C4⋊C4C2×D511yescharacteristic
210C22×C22⋊C4—51no—
211C22×C22⋊C4—51no—
212C22×C22⋊C4—52no—
213C22×C22⋊C4—52no—
214C22×C42—51no—
215C22×C42—51no—
216C22×C42—52no—
217C22×C42—51no—
218C22×C42C2×D511yescharacteristic
219#380—516no—
220C4×C4⋊C4—104no—
221C4×C4⋊C4—104no—
222C2×#95—52no—
223C2×#95—52no—
224C2×#95—51no—
225C2×#95—52no—
226C2×#95—52no—
227C2×#95—52no—
228C2×#95C2×D511yescharacteristic
229C2×#95C2×D512yes—
230C2×#95C2×D512yes—
231C23×C5C23×C411yescharacteristic
232C23×C5C23×C412yes—
233C23×C5C22×D411yescharacteristic
234C23×C5C22×D411yescharacteristic
235C23×C5C2×#4112yes—
236C23×C5H(5,𝔽2)12yes—
237C23×C5H(5,𝔽2)12yes—
238C23×C52−1+412yes—
239C23×C52−1+412yes—
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—24no—
243C22×D5—24no—
244C22×D5—24no—
245C22×D5—24no—
246C22×D5—24no—
247C22×D5—24no—
248C22×D5—24no—
249C22×D5—24no—
250C22×D5—41no—
251C22×D5—41no—
252C22×D5—41no—
253C22×D5—41no—
254C22×D5—42no—
255C22×D5—42no—
256C22×D5—42no—
257C22×D5—42no—
258C22×D5—42no—
259C22×D5—42no—
260C22×D5C2×C4214yes—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—24no—
264C2×C4×C5—24no—
265C2×C4×C5—24no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—24no—
269C2×C4×C5—22no—
270C2×C4×C5—24no—
271C2×C4×C5—24no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
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×C4214yes—
289C2×C4×C5C2×C22⋊C414yes—
290C2×Dic5—24no—
291C2×Dic5—22no—
292C2×Dic5—22no—
293C2×Dic5—24no—
294C2×Dic5—22no—
295C2×Dic5—24no—
296C2×Dic5—24no—
297C2×Dic5—24no—
298C2×Dic5—24no—
299C2×Dic5—24no—
300C2×Dic5—24no—
301C2×Dic5—24no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C2×Dic5—42no—
309C2×Dic5—42no—
310C2×Dic5—42no—
311C2×Dic5—42no—
312C2×Dic5—42no—
313C2×Dic5C2×C4214yes—
314C2×Dic5C2×C22⋊C414yes—
315C2×Dic5C2×C22⋊C414yes—
316C2×Dic5#11714yes—
317C2×Dic5C4×D418yes—
318C2×Dic5C4×D418yes—
319C4×D5—232no—
320C25—51no—
321C23×C4—51no—
322C23×C4—51no—
323C23×C4—54no—
324C23×C4—58no—
325C23×C4—52no—
326C23×C4—52no—
327C23×C4—51no—
328C23×C4—102no—
329C23×C4—102no—
330C23×C4—104no—
331C23×C4C22×D512yes—
332C23×C4C22×D512yes—
333C23×C4C22×D511yescharacteristic
334C23×C4C22×D511yescharacteristic
335C23×C4C22×D511yescharacteristic
336#117—1032no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—54no—
340C2×C4⋊C4—58no—
341C2×C4⋊C4—58no—
342C2×C4⋊C4—102no—
343C2×C4⋊C4—102no—
344C2×C4⋊C4—104no—
345C2×C4⋊C4—104no—
346C2×C4⋊C4—104no—
347C2×C4⋊C4—104no—
348C2×C4⋊C4C4×D514yes—
349C2×C22⋊C4—54no—
350C2×C22⋊C4—54no—
351C2×C22⋊C4—58no—
352C2×C22⋊C4—58no—
353C2×C22⋊C4—102no—
354C2×C22⋊C4—102no—
355C2×C22⋊C4—102no—
356C2×C22⋊C4—102no—
357C2×C22⋊C4—202no—
358C2×C22⋊C4—202no—
359C2×C22⋊C4—202no—
360C2×C22⋊C4—202no—
361C2×C42—22no—
362C2×C42—42no—
363C2×C42—54no—
364C2×C42—54no—
365C2×C42—54no—
366C2×C42—54no—
367C2×C42—102no—
368C2×C42—102no—
369C2×C42—104no—
370C2×C42—102no—
371C2×C42—202no—
372C2×C42—202no—
373C2×C42—202no—
374#95—22no—
375#95—42no—
376#95—58no—
377#95—104no—
378#95—102no—
379#95—202no—
380#95—202no—
381#95—202no—
382#95C4×D518yes—
383C22×C5C22×C4211yescharacteristic
384C22×C5C22×C22⋊C411yescharacteristic
385C22×C5C2×#11711yescharacteristic
386C22×C5C2×C4×D412yes—
387C22×C5C2×C4×D412yes—
388C22×C5#51812yes—
389C22×C5#51912yes—
390C22×C5#52012yes—
391C22×C5#52012yes—
392C22×C5#52012yes—
393C22×C5#52012yes—
394C22×C5#53511yescharacteristic
395C22×C5#53511yescharacteristic
396C22×C5#53611yescharacteristic
397C22×C5#53611yescharacteristic
398C22×C5#53712yes—
399C22×C5#53712yes—
400C22×C5#54012yes—
401C22×C5#54112yes—
402C22×C5#54212yes—
403C22×C5#54212yes—
404C2×D5—24no—
405C2×D5—28no—
406C2×D5—42no—
407C2×D5—42no—
408C2×D5—44no—
409C2×D5—44no—
410C2×D5—44no—
411C2×D5—44no—
412C2×D5—44no—
413C4×C5—24no—
414C4×C5—24no—
415C4×C5—42no—
416C4×C5—44no—
417C4×C5—44no—
418Dic5—24no—
419Dic5—42no—
420Dic5—44no—
421Dic5—44no—
422Dic5C4×C22⋊C418yes—
423C24—52no—
424C24—54no—
425C24—101no—
426C24—101no—
427C24—102no—
428C24—102no—
429C24—102no—
430C24—102no—
431C24—102no—
432C24C23×D511yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
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—22no—
453C22×C4—22no—
454C22×C4—52no—
455C22×C4—54no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—54no—
459C22×C4—52no—
460C22×C4—52no—
461C22×C4—52no—
462C22×C4—516no—
463C22×C4—54no—
464C22×C4—54no—
465C22×C4—52no—
466C22×C4—108no—
467C22×C4—108no—
468C22×C4—1016no—
469C22×C4—1016no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—101no—
475C22×C4—101no—
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×C4—102no—
487C22×C4—102no—
488C22×C4C2×C4×D514yes—
489C22×C4C2×C4×D514yes—
490C22×C4C2×C4×D512yes—
491C22×C4C2×C4×D514yes—
492C22×C4C2×C4×D512yes—
493C22×C4C2×C4×D512yes—
494C22×C4D4×D512yes—
495C22×C4D4×D512yes—
496C4⋊C4—28no—
497C4⋊C4—108no—
498C4⋊C4—1016no—
499C4⋊C4—1016no—
500C22⋊C4—108no—
501C22⋊C4—108no—
502C22⋊C4—208no—
503C22⋊C4—208no—
504C42—44no—
505C42—516no—
506C42—108no—
507C42—204no—
508C42—208no—
509C2×C5C2×C4×C22⋊C411yescharacteristic
510C2×C5#227412yes—
511C2×C5#231111yescharacteristic
512C2×C5#231111yescharacteristic
513C2×C5#231412yes—
514C2×C5#232312yes—
515C2×C5#232312yes—
516C2×C5#232412yes—
517C2×C5#232412yes—
518D5—44no—
519C23—54no—
520C23—102no—
521C23—104no—
522C23—102no—
523C23—104no—
524C23—104no—
525C23—104no—
526C23—104no—
527C23—104no—
528C23—104no—
529C23—104no—
530C23—201no—
531C23—201no—
532C23—202no—
533C23—202no—
534C23—202no—
535C23—201no—
536C23—202no—
537C23—201no—
538C23—202no—
539C23—202no—
540C23C22×C4×D511yescharacteristic
541C23C22×C4×D512yes—
542C23C2×D4×D511yescharacteristic
543C23C2×D4×D511yescharacteristic
544C23#414412yes—
545C23#414712yes—
546C23D5×#4112yes—
547C23#414912yes—
548C23#415012yes—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—54no—
577C2×C4—54no—
578C2×C4—54no—
579C2×C4—58no—
580C2×C4—58no—
581C2×C4—54no—
582C2×C4—1032no—
583C2×C4—102no—
584C2×C4—104no—
585C2×C4—104no—
586C2×C4—102no—
587C2×C4—102no—
588C2×C4—104no—
589C2×C4—104no—
590C2×C4—104no—
591C2×C4—104no—
592C2×C4—104no—
593C2×C4—104no—
594C2×C4—104no—
595C2×C4—201no—
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—201no—
605C2×C4—202no—
606C2×C4C42×D514yes—
607C2×C4D5×C22⋊C414yes—
608C5#1377711yescharacteristic, complemented, Sylow
609C22—108no—
610C22—104no—
611C22—204no—
612C22—202no—
613C22—204no—
614C22—202no—
615C22—204no—
616C22—204no—
617C22—204no—
618C22C2×C42×D511yescharacteristic
619C22C2×D5×C22⋊C411yescharacteristic
620C22#6583812yes—
621C22D5×#11711yescharacteristic
622C22#6585712yes—
623C22C4×D4×D512yes—
624C22C4×D4×D512yes—
625C22#6587912yes—
626C22#6588012yes—
627C22#6590612yes—
628C22#6590812yes—
629C22#6592611yescharacteristic
630C22#6593112yes—
631C22#6596312yes—
632C22#6597412yes—
633C22#6598211yescharacteristic
634C22#6599712yes—
635C22#6600811yescharacteristic
636C22#6603012yes—
637C22#6604412yes—
638C22#6605811yescharacteristic
639C4—24no—
640C4—24no—
641C4—44no—
642C4—42no—
643C4—44no—
644C4—58no—
645C4—104no—
646C4—204no—
647C4—202no—
648C4—204no—
649C2—204no—
650C2C4×D5×C22⋊C411yescharacteristic
651C2#1060548112yes—
652C2#1060611612yes—
653C2#1060639311yescharacteristic
654C2#1060667512yes—
655C2#1060667812yes—
656C2#1060719212yes—
657C2#1060770212yes—
658C2#1060821311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC5×#1436C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenter#1436D5
hypocenterC5#13777
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×C4×#683C2semidirect
4. C2×#64938C2semidirect
5. C5×#1436C2semidirect
6. #10602357C2semidirect
10. #10600200C2semidirect
11. #10600197C2semidirect
28. C2×#4038C4semidirect
39. #64956C4semidirect
114. #1436D5semidirect
188. C2×C4×D5C42semidirect
201. C4×Dic5C22⋊C4semidirect
608. C5#13777semidirect

Maximal subgroups

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

subgroupindex
C22×#40382
C2×C4×#6832
C2×#649562
C2×#649382
C5×#14362
#106023572
#106023302
#106002012
#106002002
#106001972
#137775