Finite Group Databasebeta

← #12099189

Subgroups — #12099189

Order 1280.

1418 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4018C211yesmaximal, characteristic
2C2×#65129C212yesmaximal, complemented
3C5×#1797C211yesmaximal, characteristic, complemented
4#10602323C211yesmaximal, characteristic, complemented
5#10601269C212yesmaximal, complemented
6#10600748C211yesmaximal, characteristic
7#10600748C211yesmaximal, characteristic
8#10600699C211yesmaximal, characteristic, complemented
9Dic5×C22⋊C8C211yesmaximal, characteristic, complemented
10#10599458C212yesmaximal, complemented
11#10599394C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×#685C411yescharacteristic
15C22×#685C411yescharacteristic
16C22×#683C411yescharacteristic
17C22×#683C411yescharacteristic
18C22×C4×Dic5C2211yescharacteristic
19C2×#4018—28no—
20C2×#4018C411yescharacteristic
21C2×#4018C411yescharacteristic
22C2×#4018C411yescharacteristic
23C2×#4018C411yescharacteristic
24C2×#4018C2211yescharacteristic
25C2×#4018C2211yescharacteristic
26C2×#4018C2211yescharacteristic
27C2×#4018C2211yescharacteristic
28C2×C5×C4⋊C8C2212yescomplemented
29C2×C5×C22⋊C8C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C22⋊#168C2211yescharacteristic
32C2×C22⋊#168C2211yescharacteristic
33C2×#3952C2212yes—
34C2×#3952C2212yes—
35C2×#3952C2212yes—
36C2×#3952C2212yes—
37C2×#3947C2212yescomplemented
38C2×C8×Dic5C2212yescomplemented
39C2×C4⋊#168C2212yescomplemented
40#65129—28no—
41C5×#336C2212yescomplemented
42#64770C2212yescomplemented
43#64770C2212yescomplemented
44#64744C2212yescomplemented
45#20716—51nomaximal, Sylow
46C24×D5C2×C411yescharacteristic
47C23×C4×C5C2×C411yescharacteristic
48C23×C4×C5C2×C411yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2×C411yescharacteristic
51C23×Dic5C2×C411yescharacteristic
52C23×Dic5C2×C411yescharacteristic
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—24no—
56C22×C4×D5—24no—
57C22×C4×D5C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2311yescharacteristic
60C22×C4×D5C2311yescharacteristic
61C22×C5×C8C2312yes—
62C22×C5×C8C2312yes—
63C2×C42×C5—24no—
64C2×C42×C5C2×C411yescharacteristic
65C2×C42×C5C2×C411yescharacteristic
66C2×C42×C5C2311yescharacteristic
67C2×C42×C5C2311yescharacteristic
68C2×#685—24no—
69C2×#685—24no—
70C2×#685C2×C411yescharacteristic
71C2×#685C2×C411yescharacteristic
72C2×#685C2×C411yescharacteristic
73C2×#685C2×C411yescharacteristic
74C2×#685C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#683—24no—
79C2×#683—24no—
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×C4×Dic5—24no—
89C2×C4×Dic5C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C22×#168C2312yes—
94C22×#168C2312yes—
95#4018—24no—
96#4018—24no—
97#4018—24no—
98#4018—24no—
99#4018—24no—
100#4018—24no—
101#4018—24no—
102#4018D418yes—
103C5×C4⋊C8—24no—
104C5×C22⋊C8—22no—
105C5×C22⋊C8—22no—
106C22⋊#168—22no—
107C22⋊#168—22no—
108#3952—24no—
109#3952—24no—
110#3952—24no—
111#3952—24no—
112#3947—24no—
113C8×Dic5—24no—
114C4⋊#168—24no—
115C22×#117—51no—
116C2×#433—52no—
117#1818—52no—
118#1798—52no—
119#1797—51no—
120#1797D511yescharacteristic, complemented
121#1779—51no—
122#1779—51no—
123#1750—52no—
124#1749—51no—
125C4×C22⋊C8—51no—
126C24×C5C22×C411yescharacteristic
127C23×D5—22no—
128C23×D5—22no—
129C23×D5—22no—
130C23×D5—22no—
131C23×D5—22no—
132C23×D5—41no—
133C23×D5—41no—
134C23×D5C22×C411yescharacteristic
135C23×D5C22×C411yescharacteristic
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—41no—
143C22×C4×C5—41no—
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5C22×C411yescharacteristic
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5#4112yes—
150C22×C4×C5#4112yes—
151C22×C4×C5C2411yescharacteristic
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—41no—
160C22×Dic5—41no—
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C22×C411yescharacteristic
165C22×Dic5C22×C411yescharacteristic
166C22×Dic5C22×C411yescharacteristic
167C2×C4×D5—216no—
168C2×C4×D5—216no—
169C2×C4×D5—22no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—22no—
179C2×C4×D5—22no—
180C2×C4×D5—22no—
181C2×C4×D5C2×D414yes—
182C2×C4×D5#4114yes—
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C42×C5—22no—
190C42×C5—22no—
191C42×C5—22no—
192C42×C5C2×D414yes—
193#685—22no—
194#685—22no—
195#685—22no—
196#685—22no—
197#685—22no—
198#685—22no—
199#685C22⋊C414yes—
200#685C22⋊C414yes—
201#683—22no—
202#683—22no—
203#683—22no—
204#683—22no—
205#683—22no—
206#683—22no—
207#683C22⋊C414yes—
208#683C22⋊C414yes—
209C4×Dic5—22no—
210C4×Dic5—22no—
211C4×Dic5—22no—
212C4×Dic5C2×D414yes—
213C2×#168—22no—
214C2×#168—22no—
215C2×#168—22no—
216C2×#168—22no—
217C2×#168—22no—
218C2×#168—22no—
219C24×C4—51no—
220C2×#117—51no—
221C2×#117—51no—
222C2×#117—51no—
223C2×#117—51no—
224C2×#117—51no—
225C2×#117—51no—
226C2×#117—51no—
227C2×#117—51no—
228C2×#117—108no—
229C22×C4⋊C4—51no—
230C22×C4⋊C4—51no—
231C22×C22⋊C4—51no—
232C22×C22⋊C4—51no—
233C22×C42—51no—
234C22×C42C2×D511yescharacteristic
235#433—108no—
236C2×C4⋊C8—52no—
237C2×C4⋊C8C2×D512yescomplemented
238C2×C22⋊C8—51no—
239C2×C22⋊C8—51no—
240C2×C22⋊C8—52no—
241C2×C22⋊C8—52no—
242C2×C22⋊C8—52no—
243C2×C22⋊C8—52no—
244C2×C22⋊C8C2×D511yescharacteristic
245C2×C22⋊C8C2×D511yescharacteristic
246C2×#97—52no—
247C2×C4×C8—52no—
248#336—52no—
249#336—52no—
250#336—52no—
251#336C2×D512yescomplemented
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5#11712yes—
257C23×C5#13112yes—
258C23×C5#13112yes—
259C23×C5C23×C411yescharacteristic
260C22×D5—28no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—21no—
269C22×D5—21no—
270C22×D5—21no—
271C22×D5—21no—
272C22×D5—21no—
273C22×D5—44no—
274C22×D5—44no—
275C22×D5—44no—
276C22×D5—44no—
277C22×D5—44no—
278C22×D5—44no—
279C22×D5C2×C22⋊C412yes—
280C22×D5#11712yes—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—44no—
296C2×C4×C5—44no—
297C2×C4×C5C2×C22⋊C412yes—
298C2×C4×C5C2×C22⋊C412yes—
299C2×C4×C5#11712yes—
300C2×C4×C5C22×D412yes—
301C2×C4×C5C2×#4111yescharacteristic
302C2×C4×C5C2×#4111yescharacteristic
303C2×C4×C5C2×#4112yes—
304C2×Dic5—28no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—44no—
320C2×Dic5—44no—
321C2×Dic5C2×C22⋊C412yes—
322C2×Dic5C2×C22⋊C412yes—
323C2×Dic5C2×C22⋊C412yes—
324C2×Dic5#11712yes—
325C4×D5—28no—
326C4×D5—28no—
327C4×D5—24no—
328C4×D5—24no—
329C4×D5—24no—
330C4×D5—24no—
331C5×C8—42no—
332C5×C8—42no—
333#168—42no—
334#168—42no—
335C25—51no—
336C23×C4—51no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—104no—
344C23×C4—104no—
345C23×C4—102no—
346C23×C4—102no—
347C23×C4C4×D511yescharacteristic
348C23×C4C4×D511yescharacteristic
349C23×C4C22×D511yescharacteristic
350C22×C8—52no—
351C22×C8—52no—
352C22×C8C22×D512yes—
353C22×C8C22×D512yes—
354#117—58no—
355#117—104no—
356#117—104no—
357#117—104no—
358#117—104no—
359#117—104no—
360#117—104no—
361#117—104no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—51no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—104no—
371C2×C4⋊C4—104no—
372C2×C22⋊C4—51no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—51no—
375C2×C22⋊C4—51no—
376C2×C22⋊C4—51no—
377C2×C22⋊C4—51no—
378C2×C22⋊C4—51no—
379C2×C22⋊C4—51no—
380C2×C22⋊C4—104no—
381C2×C22⋊C4—104no—
382C2×C42—24no—
383C2×C42—51no—
384C2×C42—51no—
385C2×C42—51no—
386C2×C42—51no—
387C2×C42—104no—
388C2×C42C4×D511yescharacteristic
389C2×C42C4×D511yescharacteristic
390C2×C42C22×D511yescharacteristic
391C2×C42C22×D511yescharacteristic
392C4⋊C8—24no—
393C4⋊C8—104no—
394C22⋊C8—22no—
395C22⋊C8—22no—
396C22⋊C8—104no—
397C22⋊C8—104no—
398C22⋊C8—104no—
399C22⋊C8—104no—
400C22⋊C8—102no—
401C22⋊C8—102no—
402#97—104no—
403C4×C8—104no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5#43314yescomplemented
411C22×C5C22×C22⋊C411yescharacteristic
412C22×C5C2×#11711yescharacteristic
413C22×C5C2×#11711yescharacteristic
414C22×C5C2×#13111yescharacteristic
415C22×C5C2×#13111yescharacteristic
416C22×C5#56811yescharacteristic
417C22×C5#56811yescharacteristic
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—22no—
424C2×D5—416no—
425C2×D5—41no—
426C2×D5—41no—
427C2×D5—41no—
428C2×D5—41no—
429C2×D5—41no—
430C2×D5—41no—
431C2×D5—41no—
432C2×D5—41no—
433C4×C5—22no—
434C4×C5—22no—
435C4×C5—22no—
436C4×C5—41no—
437C4×C5—41no—
438C4×C5#52512yes—
439C4×C5#52512yes—
440Dic5—22no—
441Dic5—22no—
442Dic5—22no—
443Dic5—22no—
444Dic5—41no—
445Dic5—41no—
446C24—51no—
447C24—51no—
448C24—102no—
449C24—102no—
450C24—102no—
451C24—102no—
452C24—102no—
453C24—201no—
454C24—201no—
455C24C2×C4×D511yescharacteristic
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—51no—
465C22×C4—51no—
466C22×C4—51no—
467C22×C4—51no—
468C22×C4—54no—
469C22×C4—54no—
470C22×C4—51no—
471C22×C4—51no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—1016no—
477C22×C4—1016no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—101no—
487C22×C4—101no—
488C22×C4—102no—
489C22×C4—102no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—201no—
494C22×C4—201no—
495C22×C4C2×C4×D511yescharacteristic
496C22×C4C2×C4×D511yescharacteristic
497C22×C4C2×C4×D511yescharacteristic
498C22×C4C2×C4×D511yescharacteristic
499C22×C4C2×C4×D511yescharacteristic
500C22×C4#71112yes—
501C22×C4#71312yes—
502C22×C4C23×D511yescharacteristic
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—102no—
510C2×C8—102no—
511C2×C8—102no—
512C2×C8—102no—
513C2×C8—102no—
514C2×C8—102no—
515C4⋊C4—54no—
516C4⋊C4—54no—
517C4⋊C4—102no—
518C4⋊C4—102no—
519C4⋊C4—102no—
520C4⋊C4—102no—
521C4⋊C4—102no—
522C4⋊C4—102no—
523C22⋊C4—54no—
524C22⋊C4—54no—
525C22⋊C4—102no—
526C22⋊C4—102no—
527C22⋊C4—102no—
528C22⋊C4—102no—
529C22⋊C4—102no—
530C22⋊C4—102no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—54no—
535C42—102no—
536C42—102no—
537C42—102no—
538C42D4×D514yes—
539C2×C5—24no—
540C2×C5#228011yescharacteristic
541C2×C5#288011yescharacteristic
542C2×C5#288011yescharacteristic
543C2×C5C2×#43311yescharacteristic
544C2×C5#292111yescharacteristic
545C2×C5#292411yescharacteristic
546C2×C5#292411yescharacteristic
547D5—42no—
548D5—42no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—52no—
554C23—52no—
555C23—108no—
556C23—101no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23—101no—
562C23—101no—
563C23—101no—
564C23—101no—
565C23—101no—
566C23—101no—
567C23—101no—
568C23—204no—
569C23—204no—
570C23—204no—
571C23—204no—
572C23—204no—
573C23—204no—
574C23#403812yes—
575C23#404712yes—
576C23#405312yes—
577C23C22×C4×D511yescharacteristic
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—52no—
595C2×C4—52no—
596C2×C4—52no—
597C2×C4—52no—
598C2×C4—108no—
599C2×C4—108no—
600C2×C4—108no—
601C2×C4—101no—
602C2×C4—101no—
603C2×C4—101no—
604C2×C4—101no—
605C2×C4—101no—
606C2×C4—101no—
607C2×C4—101no—
608C2×C4—101no—
609C2×C4—104no—
610C2×C4—104no—
611C2×C4—104no—
612C2×C4—104no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—101no—
619C2×C4—204no—
620C2×C4—204no—
621C2×C4D5×C22⋊C412yes—
622C2×C4D5×C22⋊C412yes—
623C2×C4#403812yes—
624C2×C4C2×D4×D512yes—
625C2×C4C2×#71111yescharacteristic
626C2×C4C2×#71311yescharacteristic
627C2×C4D5×#4112yes—
628C8—42no—
629C8—42no—
630C8—202no—
631C8—202no—
632C5#2071611yescharacteristic, complemented, Sylow
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—102no—
640C22—102no—
641C22—102no—
642C22—102no—
643C22—102no—
644C22—102no—
645C22—2016no—
646C22—201no—
647C22—201no—
648C22—201no—
649C22—201no—
650C22—201no—
651C22—201no—
652C22—201no—
653C22—201no—
654C22#6512914yescomplemented
655C22C2×D5×C22⋊C411yescharacteristic
656C22C2×#403811yescharacteristic
657C22D5×#11711yescharacteristic
658C22C2×#404711yescharacteristic
659C22C2×#405311yescharacteristic
660C22#6607911yescharacteristic
661C22#6607911yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—102no—
668C4—102no—
669C4—102no—
670C4—102no—
671C4—201no—
672C4—201no—
673C4#6594012yes—
674C4#6596112yes—
675C2—24no—
676C2—202no—
677C2—202no—
678C2#1060559311yescharacteristic
679C2#1061033111yescharacteristic
680C2#1061036211yescharacteristic
681C2C2×#6512911yescharacteristic
682C2#1061077011yescharacteristic
683C2#1061101511yescharacteristic
684C2#1061106411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1797C2
prime radicalC24×D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1797D5
hypocenterC5#20716
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#65129C2semidirect
3. C5×#1797C2semidirect
4. #10602323C2semidirect
5. #10601269C2semidirect
8. #10600699C2semidirect
9. Dic5×C22⋊C8C2semidirect
10. #10599458C2semidirect
11. #10599394C2semidirect
28. C2×C5×C4⋊C8C22semidirect
37. C2×#3947C22semidirect
38. C2×C8×Dic5C22semidirect
39. C2×C4⋊#168C22semidirect
41. C5×#336C22semidirect
42. #64770C22semidirect
43. #64770C22semidirect
44. #64744C22semidirect
120. #1797D5semidirect
237. C2×C4⋊C8C2×D5semidirect
251. #336C2×D5semidirect
410. C22×C5#433semidirect
632. C5#20716semidirect
654. C22#65129semidirect

Maximal subgroups

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

subgroupindex
C22×#40182
C2×#651292
C5×#17972
#106023232
#106012692
#106007482
#106006992
Dic5×C22⋊C82
#105994582
#105993942
#207165