Finite Group Databasebeta

← #12099183

Subgroups — #12099183

Order 1280.

1974 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D5C211yesmaximal, characteristic
2C2×#65124C212yesmaximal, complemented
3C5×#1797C211yesmaximal, characteristic, complemented
4#10602323C211yesmaximal, characteristic, complemented
5#10601268C212yesmaximal, complemented
6#10600748C212yesmaximal
7#10600699C212yesmaximal, complemented
8#10599457C212yesmaximal, complemented
9#10599393C212yesmaximal, complemented
10C23×C4×D5C411yescharacteristic
11C23×C4×D5C411yescharacteristic
12C23×C4×D5C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×C4×Dic5C411yescharacteristic
15C22×C4×Dic5C411yescharacteristic
16C22×C4×Dic5C2211yescharacteristic
17C2×C42×D5—28no—
18C2×C42×D5C411yescharacteristic
19C2×C42×D5C411yescharacteristic
20C2×C42×D5C411yescharacteristic
21C2×C42×D5C411yescharacteristic
22C2×C42×D5C2211yescharacteristic
23C2×C42×D5C2211yescharacteristic
24C2×C42×D5C2211yescharacteristic
25C2×C42×D5C2211yescharacteristic
26C2×C5×C4⋊C8C2212yescomplemented
27C2×C5×C22⋊C8C2212yes—
28C2×C22⋊#168C2212yes—
29C2×#3952C2214yes—
30C2×#3952C2214yes—
31C2×#3947C2214yescomplemented
32C2×C4⋊#168C2212yescomplemented
33#65124—28no—
34C5×#336C2212yescomplemented
35#64770C2214yescomplemented
36#64744C2212yescomplemented
37#20715—51nomaximal, Sylow
38C24×D5C2×C411yescharacteristic
39C23×C4×C5C2×C411yescharacteristic
40C23×C4×C5C2×C411yescharacteristic
41C23×C4×C5C2311yescharacteristic
42C23×Dic5C2×C411yescharacteristic
43C23×Dic5C2×C411yescharacteristic
44C23×Dic5C2×C411yescharacteristic
45C22×C4×D5—24no—
46C22×C4×D5—24no—
47C22×C4×D5—22no—
48C22×C4×D5—22no—
49C22×C4×D5—24no—
50C22×C4×D5—24no—
51C22×C4×D5—24no—
52C22×C4×D5—24no—
53C22×C4×D5—24no—
54C22×C4×D5—24no—
55C22×C4×D5C2×C411yescharacteristic
56C22×C4×D5C2×C411yescharacteristic
57C22×C4×D5C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2×C411yescharacteristic
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2×C411yescharacteristic
62C22×C4×D5C2×C411yescharacteristic
63C22×C4×D5C2×C411yescharacteristic
64C22×C4×D5C2×C411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×C4×D5C2311yescharacteristic
67C22×C5×C8C2314yes—
68C2×C42×C5—24no—
69C2×C42×C5C2×C411yescharacteristic
70C2×C42×C5C2×C411yescharacteristic
71C2×C42×C5C2311yescharacteristic
72C2×C42×C5C2311yescharacteristic
73C2×C4×Dic5—24no—
74C2×C4×Dic5—24no—
75C2×C4×Dic5—24no—
76C2×C4×Dic5C2×C411yescharacteristic
77C2×C4×Dic5C2×C411yescharacteristic
78C2×C4×Dic5C2×C411yescharacteristic
79C2×C4×Dic5C2×C411yescharacteristic
80C2×C4×Dic5C2×C411yescharacteristic
81C2×C4×Dic5C2×C411yescharacteristic
82C2×C4×Dic5C2×C411yescharacteristic
83C2×C4×Dic5C2×C411yescharacteristic
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5C2×C411yescharacteristic
86C2×C4×Dic5C2311yescharacteristic
87C2×C4×Dic5C2311yescharacteristic
88C22×#168C2314yes—
89C42×D5—24no—
90C42×D5—24no—
91C42×D5—24no—
92C42×D5—24no—
93C42×D5—24no—
94C42×D5—24no—
95C42×D5—24no—
96C42×D5D418yes—
97C5×C4⋊C8—24no—
98C5×C22⋊C8—24no—
99C22⋊#168—24no—
100#3952—28no—
101#3952—28no—
102#3947—28no—
103C4⋊#168—24no—
104C23×C42—51no—
105C2×#432—52no—
106#1817—52no—
107#1797—51no—
108#1797—52no—
109#1797D511yescharacteristic, complemented
110#1779—52no—
111#1749—52no—
112#1749—52no—
113C24×C5C22×C411yescharacteristic
114C23×D5—22no—
115C23×D5—22no—
116C23×D5—22no—
117C23×D5—22no—
118C23×D5—22no—
119C23×D5—22no—
120C23×D5M1614yes—
121C23×D5C22×C411yescharacteristic
122C23×D5C22×C411yescharacteristic
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5M1614yes—
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C22×C411yescharacteristic
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C22×C411yescharacteristic
135C22×C4×C5C22×C411yescharacteristic
136C22×C4×C5#4112yes—
137C22×C4×C5#4112yes—
138C22×C4×C5C2411yescharacteristic
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C2×C4×D5—232no—
155C2×C4×D5—216no—
156C2×C4×D5—216no—
157C2×C4×D5—232no—
158C2×C4×D5—22no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—22no—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—22no—
175C2×C4×D5—22no—
176C2×C4×D5—22no—
177C2×C4×D5—22no—
178C2×C4×D5—22no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×C4×D5—21no—
182C2×C4×D5—21no—
183C2×C4×D5—22no—
184C2×C4×D5—22no—
185C2×C4×D5—22no—
186C2×C4×D5—22no—
187C2×C4×D5—22no—
188C2×C4×D5—22no—
189C2×C4×D5—22no—
190C2×C4×D5C22⋊C414yes—
191C2×C4×D5C22⋊C414yes—
192C2×C4×D5M1614yes—
193C2×C4×D5M1614yes—
194C2×C4×D5C2×D414yes—
195C2×C4×D5#4114yes—
196C2×C5×C8—24no—
197C2×C5×C8—24no—
198C2×C5×C8—24no—
199C42×C5—22no—
200C42×C5—22no—
201C42×C5—22no—
202C42×C5C2×D414yes—
203C4×Dic5—22no—
204C4×Dic5—22no—
205C4×Dic5—22no—
206C4×Dic5—22no—
207C4×Dic5—22no—
208C4×Dic5—22no—
209C4×Dic5—22no—
210C4×Dic5—22no—
211C4×Dic5—22no—
212C4×Dic5C22⋊C414yes—
213C4×Dic5C22⋊C414yes—
214C4×Dic5C2×D414yes—
215C2×#168—24no—
216C2×#168—24no—
217C2×#168—24no—
218C24×C4—51no—
219C24×C4—51no—
220C24×C4—51no—
221C22×C42—51no—
222C22×C42—51no—
223C22×C42—51no—
224C22×C42—51no—
225C22×C42—51no—
226C22×C42—51no—
227C22×C42—51no—
228C22×C42—51no—
229C22×C42—51no—
230C22×C42—51no—
231C22×C42—51no—
232C22×C42—108no—
233C22×C42C2×D511yescharacteristic
234#432—108no—
235C2×C4⋊C8—52no—
236C2×C4⋊C8C2×D512yescomplemented
237C2×C22⋊C8—52no—
238C2×C22⋊C8—54no—
239C2×C22⋊C8—54no—
240C2×C22⋊C8C2×D512yes—
241C2×#97—54no—
242#336—54no—
243#336—52no—
244#336C2×D512yescomplemented
245C23×C5—21no—
246C23×C5—21no—
247C23×C5—21no—
248C23×C5—21no—
249C23×C5#11712yes—
250C23×C5C2×M1612yes—
251C23×C5C2×M1612yes—
252C23×C5C23×C411yescharacteristic
253C22×D5—28no—
254C22×D5—28no—
255C22×D5—28no—
256C22×D5—28no—
257C22×D5—21no—
258C22×D5—21no—
259C22×D5—21no—
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—28no—
266C22×D5—28no—
267C22×D5—28no—
268C22×D5C2×C22⋊C412yes—
269C22×D5#11712yes—
270C22×D5C2×M1612yes—
271C22×D5C2×M1612yes—
272C22×D5C2×M1612yes—
273C22×D5C2×M1612yes—
274C2×C4×C5—28no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—28no—
286C2×C4×C5C2×C22⋊C412yes—
287C2×C4×C5C2×C22⋊C412yes—
288C2×C4×C5#11712yes—
289C2×C4×C5C2×M1612yes—
290C2×C4×C5C2×M1612yes—
291C2×C4×C5C2×M1612yes—
292C2×C4×C5C2×M1612yes—
293C2×C4×C5C22×D412yes—
294C2×C4×C5C2×#4111yescharacteristic
295C2×C4×C5C2×#4111yescharacteristic
296C2×C4×C5C2×#4112yes—
297C2×Dic5—28no—
298C2×Dic5—28no—
299C2×Dic5—28no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5C2×C22⋊C412yes—
313C2×Dic5C2×C22⋊C412yes—
314C2×Dic5C2×C22⋊C412yes—
315C2×Dic5#11712yes—
316C2×Dic5C2×M1612yes—
317C2×Dic5C2×M1612yes—
318C4×D5—28no—
319C4×D5—28no—
320C4×D5—28no—
321C4×D5—28no—
322C4×D5—28no—
323C4×D5—28no—
324C4×D5—28no—
325C4×D5—28no—
326C4×D5—24no—
327C4×D5—24no—
328C4×D5—24no—
329C4×D5—24no—
330C4×D5—28no—
331C4×D5—28no—
332C5×C8—44no—
333#168—44no—
334C25—51no—
335C23×C4—51no—
336C23×C4—51no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—51no—
344C23×C4—51no—
345C23×C4—51no—
346C23×C4—51no—
347C23×C4—51no—
348C23×C4—51no—
349C23×C4—51no—
350C23×C4—104no—
351C23×C4—104no—
352C23×C4—104no—
353C23×C4—104no—
354C23×C4—104no—
355C23×C4—104no—
356C23×C4—104no—
357C23×C4—104no—
358C23×C4—102no—
359C23×C4—102no—
360C23×C4C4×D511yescharacteristic
361C23×C4C4×D511yescharacteristic
362C23×C4C22×D511yescharacteristic
363C22×C8—54no—
364C22×C8C22×D514yes—
365C2×C42—24no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42—58no—
370C2×C42—51no—
371C2×C42—51no—
372C2×C42—51no—
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—51no—
376C2×C42—51no—
377C2×C42—51no—
378C2×C42—51no—
379C2×C42—104no—
380C2×C42—104no—
381C2×C42—104no—
382C2×C42—104no—
383C2×C42—104no—
384C2×C42—104no—
385C2×C42—104no—
386C2×C42—104no—
387C2×C42—104no—
388C2×C42—104no—
389C2×C42C4×D511yescharacteristic
390C2×C42C4×D511yescharacteristic
391C2×C42C22×D511yescharacteristic
392C2×C42C22×D511yescharacteristic
393C4⋊C8—24no—
394C4⋊C8—104no—
395C22⋊C8—24no—
396C22⋊C8—108no—
397C22⋊C8—108no—
398C22⋊C8—104no—
399#97—108no—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5#43214yescomplemented
407C22×C5C22×C22⋊C411yescharacteristic
408C22×C5C2×#11711yescharacteristic
409C22×C5C2×#11711yescharacteristic
410C22×C5C22×M1611yescharacteristic
411C22×C5C22×M1611yescharacteristic
412C22×C5C22×M1611yescharacteristic
413C22×C5C22×M1611yescharacteristic
414C2×D5—232no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—22no—
424C2×D5—22no—
425C2×D5—22no—
426C2×D5—22no—
427C2×D5#40714yes—
428C2×D5#43214yescomplemented
429C4×C5—22no—
430C4×C5—22no—
431C4×C5—22no—
432C4×C5—22no—
433C4×C5#40714yes—
434C4×C5#52512yes—
435C4×C5#52512yes—
436Dic5—22no—
437Dic5—22no—
438Dic5—22no—
439Dic5—22no—
440Dic5—22no—
441Dic5—22no—
442C24—51no—
443C24—51no—
444C24—54no—
445C24—102no—
446C24—102no—
447C24—102no—
448C24—102no—
449C24—102no—
450C24—102no—
451C24C2×C4×D511yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—51no—
460C22×C4—51no—
461C22×C4—51no—
462C22×C4—51no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—54no—
466C22×C4—54no—
467C22×C4—54no—
468C22×C4—54no—
469C22×C4—54no—
470C22×C4—54no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
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—1032no—
488C22×C4—1016no—
489C22×C4—1016no—
490C22×C4—1032no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—102no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—102no—
498C22×C4—102no—
499C22×C4—102no—
500C22×C4—102no—
501C22×C4—101no—
502C22×C4—101no—
503C22×C4—101no—
504C22×C4—101no—
505C22×C4—102no—
506C22×C4—102no—
507C22×C4—102no—
508C22×C4—102no—
509C22×C4—102no—
510C22×C4—102no—
511C22×C4—102no—
512C22×C4—102no—
513C22×C4—102no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4#67614yes—
517C22×C4C2×C4×D511yescharacteristic
518C22×C4C2×C4×D511yescharacteristic
519C22×C4C2×C4×D511yescharacteristic
520C22×C4C2×C4×D511yescharacteristic
521C22×C4C2×C4×D511yescharacteristic
522C22×C4#71112yes—
523C22×C4#71312yes—
524C22×C4C23×D511yescharacteristic
525C2×C8—24no—
526C2×C8—24no—
527C2×C8—24no—
528C2×C8—104no—
529C2×C8—104no—
530C2×C8—104no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—54no—
535C42—54no—
536C42—54no—
537C42—102no—
538C42—102no—
539C42—102no—
540C42—102no—
541C42—102no—
542C42—102no—
543C42—102no—
544C42—102no—
545C42—102no—
546C42D4×D514yes—
547C2×C5—24no—
548C2×C5#228011yescharacteristic
549C2×C5C2×#40711yescharacteristic
550C2×C5C2×#40711yescharacteristic
551C2×C5C2×#43211yescharacteristic
552C2×C5C2×#43211yescharacteristic
553C2×C5#292011yescharacteristic
554C2×C5#292011yescharacteristic
555D5—24no—
556D5—24no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—52no—
562C23—52no—
563C23—52no—
564C23—52no—
565C23—52no—
566C23—52no—
567C23—108no—
568C23—108no—
569C23—108no—
570C23—108no—
571C23—108no—
572C23—108no—
573C23—101no—
574C23—101no—
575C23—101no—
576C23—101no—
577C23—101no—
578C23—101no—
579C23—101no—
580C23—101no—
581C23—108no—
582C23#403812yes—
583C23C2×#67612yes—
584C23D5×M1612yes—
585C23C22×C4×D511yescharacteristic
586C2×C4—28no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—28no—
598C2×C4—52no—
599C2×C4—52no—
600C2×C4—52no—
601C2×C4—52no—
602C2×C4—52no—
603C2×C4—52no—
604C2×C4—108no—
605C2×C4—108no—
606C2×C4—108no—
607C2×C4—108no—
608C2×C4—108no—
609C2×C4—108no—
610C2×C4—108no—
611C2×C4—108no—
612C2×C4—108no—
613C2×C4—108no—
614C2×C4—108no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—101no—
619C2×C4—101no—
620C2×C4—101no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—101no—
624C2×C4—101no—
625C2×C4—101no—
626C2×C4—101no—
627C2×C4—104no—
628C2×C4—104no—
629C2×C4—104no—
630C2×C4—104no—
631C2×C4—108no—
632C2×C4—108no—
633C2×C4D5×C22⋊C412yes—
634C2×C4D5×C22⋊C412yes—
635C2×C4#403812yes—
636C2×C4C2×#67612yes—
637C2×C4C2×#67612yes—
638C2×C4D5×M1612yes—
639C2×C4D5×M1612yes—
640C2×C4C2×D4×D512yes—
641C2×C4C2×#71111yescharacteristic
642C2×C4C2×#71311yescharacteristic
643C2×C4D5×#4112yes—
644C8—44no—
645C8—204no—
646C5#2071511yescharacteristic, complemented, Sylow
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—54no—
654C22—54no—
655C22—1032no—
656C22—102no—
657C22—102no—
658C22—102no—
659C22—102no—
660C22—102no—
661C22—102no—
662C22—102no—
663C22—102no—
664C22—102no—
665C22—102no—
666C22—102no—
667C22—102no—
668C22#6512414yescomplemented
669C22C2×D5×C22⋊C411yescharacteristic
670C22C2×#403811yescharacteristic
671C22D5×#11711yescharacteristic
672C22C22×#67611yescharacteristic
673C22C2×D5×M1611yescharacteristic
674C22C2×D5×M1611yescharacteristic
675C22C2×D5×M1611yescharacteristic
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—102no—
681C4—102no—
682C4—102no—
683C4—102no—
684C4—102no—
685C4—102no—
686C4#6501514yes—
687C4#6594012yes—
688C4#6596112yes—
689C2—24no—
690C2—104no—
691C2—104no—
692C2#1060559311yescharacteristic
693C2C2×#6501511yescharacteristic
694C2D5×#40711yescharacteristic
695C2C2×#6512411yescharacteristic
696C2#1061076911yescharacteristic
697C2#1061101311yescharacteristic
698C2D5×#43211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1797C2
prime radicalC24×D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1797D5
hypocenterC5#20715
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#65124C2semidirect
3. C5×#1797C2semidirect
4. #10602323C2semidirect
5. #10601268C2semidirect
7. #10600699C2semidirect
8. #10599457C2semidirect
9. #10599393C2semidirect
26. C2×C5×C4⋊C8C22semidirect
31. C2×#3947C22semidirect
32. C2×C4⋊#168C22semidirect
34. C5×#336C22semidirect
35. #64770C22semidirect
36. #64744C22semidirect
109. #1797D5semidirect
236. C2×C4⋊C8C2×D5semidirect
244. #336C2×D5semidirect
406. C22×C5#432semidirect
428. C2×D5#432semidirect
646. C5#20715semidirect
668. C22#65124semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D52
C2×#651242
C5×#17972
#106023232
#106012682
#106007482
#106006992
#105994572
#105993932
#207155