Finite Group Databasebeta

← #12099182

Subgroups — #12099182

Order 1280.

1974 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D5C211yesmaximal, characteristic
2C2×#64994C212yesmaximal, complemented
3C5×#1749C211yesmaximal, characteristic, complemented
4#10602322C211yesmaximal, characteristic, complemented
5#10600748C212yesmaximal
6#10600701C212yesmaximal, complemented
7#10600600C212yesmaximal, complemented
8#10599457C212yesmaximal, complemented
9#10599455C212yesmaximal, 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×C22⋊C8C2212yes—
27C2×C5×#97C2212yescomplemented
28C2×C22⋊#168C2212yes—
29C2×#3952C2214yes—
30C2×#3952C2214yes—
31C2×#3946C2214yescomplemented
32C2×#3935C2212yescomplemented
33#64994—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—24no—
48C22×C4×D5—24no—
49C22×C4×D5—24no—
50C22×C4×D5—24no—
51C22×C4×D5—24no—
52C22×C4×D5—24no—
53C22×C4×D5—24no—
54C22×C4×D5C2×C411yescharacteristic
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×D5C2311yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×C5×C8C2314yes—
67C2×C42×C5—24no—
68C2×C42×C5C2×C411yescharacteristic
69C2×C42×C5C2×C411yescharacteristic
70C2×C42×C5C2311yescharacteristic
71C2×C42×C5C2311yescharacteristic
72C2×C4×Dic5—24no—
73C2×C4×Dic5—24no—
74C2×C4×Dic5—24no—
75C2×C4×Dic5C2×C411yescharacteristic
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×Dic5C2311yescharacteristic
86C2×C4×Dic5C2311yescharacteristic
87C22×#168C2314yes—
88C42×D5—24no—
89C42×D5—24no—
90C42×D5—24no—
91C42×D5—24no—
92C42×D5—24no—
93C42×D5—24no—
94C42×D5—24no—
95C42×D5D418yes—
96C5×C22⋊C8—24no—
97C5×#97—24no—
98C22⋊#168—24no—
99#3952—28no—
100#3952—28no—
101#3946—28no—
102#3935—24no—
103C23×C42—51no—
104C2×#432—52no—
105#1817—52no—
106#1797—52no—
107#1797—52no—
108#1779—52no—
109#1749—51no—
110#1749—52no—
111#1749D511yescharacteristic, complemented
112C24×C5C22×C411yescharacteristic
113C23×D5—22no—
114C23×D5—22no—
115C23×D5—22no—
116C23×D5—22no—
117C23×D5—22no—
118C23×D5—22no—
119C23×D5M1614yes—
120C23×D5C22×C411yescharacteristic
121C23×D5C22×C411yescharacteristic
122C22×C4×C5—22no—
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×C5C22×C411yescharacteristic
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C22×C411yescharacteristic
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C22×C411yescharacteristic
135C22×C4×C5#4114yes—
136C22×C4×C5C2411yescharacteristic
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5M1614yes—
146C22×Dic5C22×C411yescharacteristic
147C22×Dic5C22×C411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C2×C4×D5—232no—
153C2×C4×D5—232no—
154C2×C4×D5—232no—
155C2×C4×D5—22no—
156C2×C4×D5—22no—
157C2×C4×D5—22no—
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—22no—
180C2×C4×D5—22no—
181C2×C4×D5—22no—
182C2×C4×D5—22no—
183C2×C4×D5—22no—
184C2×C4×D5—22no—
185C2×C4×D5C22⋊C414yes—
186C2×C4×D5C22⋊C414yes—
187C2×C4×D5M1614yes—
188C2×C4×D5M1614yes—
189C2×C4×D5C2×D414yes—
190C2×C4×D5#4114yes—
191C2×C5×C8—24no—
192C2×C5×C8—24no—
193C2×C5×C8—24no—
194C42×C5—22no—
195C42×C5—22no—
196C42×C5—22no—
197C42×C5C2×D414yes—
198C4×Dic5—22no—
199C4×Dic5—22no—
200C4×Dic5—22no—
201C4×Dic5—22no—
202C4×Dic5—22no—
203C4×Dic5—22no—
204C4×Dic5—22no—
205C4×Dic5—22no—
206C4×Dic5—22no—
207C4×Dic5C22⋊C414yes—
208C4×Dic5C22⋊C414yes—
209C4×Dic5C2×D414yes—
210C2×#168—24no—
211C2×#168—24no—
212C2×#168—24no—
213C24×C4—51no—
214C24×C4—51no—
215C24×C4—51no—
216C22×C42—51no—
217C22×C42—51no—
218C22×C42—51no—
219C22×C42—51no—
220C22×C42—51no—
221C22×C42—51no—
222C22×C42—51no—
223C22×C42—51no—
224C22×C42—51no—
225C22×C42—51no—
226C22×C42—51no—
227C22×C42—108no—
228C22×C42C2×D511yescharacteristic
229#432—108no—
230C2×C4⋊C8—54no—
231C2×C22⋊C8—52no—
232C2×C22⋊C8—54no—
233C2×C22⋊C8—54no—
234C2×C22⋊C8C2×D512yes—
235C2×#97—52no—
236C2×#97C2×D512yescomplemented
237#336—54no—
238#336—52no—
239#336C2×D512yescomplemented
240C23×C5—21no—
241C23×C5—21no—
242C23×C5—21no—
243C23×C5—21no—
244C23×C5#11712yes—
245C23×C5C2×M1612yes—
246C23×C5C2×M1612yes—
247C23×C5C23×C411yescharacteristic
248C22×D5—28no—
249C22×D5—28no—
250C22×D5—28no—
251C22×D5—28no—
252C22×D5—21no—
253C22×D5—21no—
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5—21no—
259C22×D5—21no—
260C22×D5—28no—
261C22×D5—28no—
262C22×D5—28no—
263C22×D5C2×C22⋊C412yes—
264C22×D5#11712yes—
265C22×D5C2×M1612yes—
266C22×D5C2×M1612yes—
267C22×D5C2×M1612yes—
268C22×D5C2×M1612yes—
269C2×C4×C5—28no—
270C2×C4×C5—28no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
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—28no—
282C2×C4×C5C2×C22⋊C412yes—
283C2×C4×C5C2×C22⋊C412yes—
284C2×C4×C5#11712yes—
285C2×C4×C5C2×M1612yes—
286C2×C4×C5C2×M1612yes—
287C2×C4×C5C22×D412yes—
288C2×C4×C5C2×#4112yes—
289C2×C4×C5C2×#4112yes—
290C2×Dic5—28no—
291C2×Dic5—28no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—28no—
303C2×Dic5C2×C22⋊C412yes—
304C2×Dic5C2×C22⋊C412yes—
305C2×Dic5C2×C22⋊C412yes—
306C2×Dic5#11712yes—
307C2×Dic5C2×M1612yes—
308C2×Dic5C2×M1612yes—
309C2×Dic5C2×M1612yes—
310C2×Dic5C2×M1612yes—
311C4×D5—28no—
312C4×D5—28no—
313C4×D5—28no—
314C4×D5—28no—
315C4×D5—28no—
316C4×D5—28no—
317C4×D5—28no—
318C4×D5—28no—
319C4×D5—28no—
320C4×D5—28no—
321C4×D5—28no—
322C4×D5—28no—
323C5×C8—44no—
324#168—44no—
325C25—51no—
326C23×C4—51no—
327C23×C4—51no—
328C23×C4—51no—
329C23×C4—51no—
330C23×C4—51no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—51no—
334C23×C4—51no—
335C23×C4—51no—
336C23×C4—51no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4—104no—
342C23×C4—104no—
343C23×C4—104no—
344C23×C4—104no—
345C23×C4—104no—
346C23×C4—104no—
347C23×C4—104no—
348C23×C4—104no—
349C23×C4—104no—
350C23×C4C4×D511yescharacteristic
351C23×C4C4×D511yescharacteristic
352C23×C4C22×D511yescharacteristic
353C22×C8—54no—
354C22×C8C22×D514yes—
355C2×C42—24no—
356C2×C42—51no—
357C2×C42—51no—
358C2×C42—51no—
359C2×C42—58no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42—104no—
370C2×C42—104no—
371C2×C42—104no—
372C2×C42—104no—
373C2×C42—104no—
374C2×C42—104no—
375C2×C42—104no—
376C2×C42—104no—
377C2×C42—104no—
378C2×C42—104no—
379C2×C42C4×D511yescharacteristic
380C2×C42C4×D511yescharacteristic
381C2×C42C22×D511yescharacteristic
382C2×C42C22×D511yescharacteristic
383C4⋊C8—108no—
384C22⋊C8—24no—
385C22⋊C8—108no—
386C22⋊C8—108no—
387C22⋊C8—104no—
388#97—24no—
389#97—104no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5—22no—
393C22×C5—22no—
394C22×C5—22no—
395C22×C5—22no—
396C22×C5#43214yescomplemented
397C22×C5C22×C22⋊C411yescharacteristic
398C22×C5C2×#11711yescharacteristic
399C22×C5C2×#11711yescharacteristic
400C22×C5C22×M1611yescharacteristic
401C22×C5C22×M1611yescharacteristic
402C22×C5C22×M1611yescharacteristic
403C22×C5C22×M1611yescharacteristic
404C2×D5—232no—
405C2×D5—22no—
406C2×D5—22no—
407C2×D5—22no—
408C2×D5—22no—
409C2×D5—22no—
410C2×D5—22no—
411C2×D5—22no—
412C2×D5—22no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5#40714yes—
418C2×D5#43214yescomplemented
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—22no—
422C4×C5—22no—
423C4×C5—22no—
424C4×C5#52514yes—
425Dic5—22no—
426Dic5—22no—
427Dic5—22no—
428Dic5—22no—
429Dic5—22no—
430Dic5#40714yes—
431C24—51no—
432C24—51no—
433C24—54no—
434C24—102no—
435C24—102no—
436C24—102no—
437C24—102no—
438C24—102no—
439C24—102no—
440C24C2×C4×D511yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—54no—
456C22×C4—54no—
457C22×C4—54no—
458C22×C4—54no—
459C22×C4—54no—
460C22×C4—54no—
461C22×C4—54no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
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—1032no—
483C22×C4—1032no—
484C22×C4—1032no—
485C22×C4—102no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—102no—
489C22×C4—102no—
490C22×C4—102no—
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—102no—
502C22×C4—102no—
503C22×C4C2×C4×D511yescharacteristic
504C22×C4C2×C4×D511yescharacteristic
505C22×C4C2×C4×D511yescharacteristic
506C22×C4C2×C4×D511yescharacteristic
507C22×C4C2×C4×D511yescharacteristic
508C22×C4#70914yes—
509C22×C4C23×D511yescharacteristic
510C2×C8—24no—
511C2×C8—24no—
512C2×C8—24no—
513C2×C8—104no—
514C2×C8—104no—
515C2×C8—104no—
516C42—22no—
517C42—22no—
518C42—22no—
519C42—54no—
520C42—54no—
521C42—54no—
522C42—102no—
523C42—102no—
524C42—102no—
525C42—102no—
526C42—102no—
527C42—102no—
528C42—102no—
529C42—102no—
530C42—102no—
531C42D4×D514yes—
532C2×C5—24no—
533C2×C5#228011yescharacteristic
534C2×C5C2×#40711yescharacteristic
535C2×C5C2×#40711yescharacteristic
536C2×C5C2×#43211yescharacteristic
537C2×C5C2×#43211yescharacteristic
538C2×C5#292011yescharacteristic
539C2×C5#292011yescharacteristic
540D5—24no—
541D5—24no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—52no—
547C23—52no—
548C23—52no—
549C23—52no—
550C23—52no—
551C23—52no—
552C23—108no—
553C23—108no—
554C23—108no—
555C23—108no—
556C23—108no—
557C23—108no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23—101no—
562C23—101no—
563C23—101no—
564C23—101no—
565C23—101no—
566C23—108no—
567C23#401812yes—
568C23D5×M1612yes—
569C23D5×M1612yes—
570C23C22×C4×D511yescharacteristic
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—28no—
584C2×C4—52no—
585C2×C4—52no—
586C2×C4—52no—
587C2×C4—52no—
588C2×C4—52no—
589C2×C4—52no—
590C2×C4—52no—
591C2×C4—52no—
592C2×C4—108no—
593C2×C4—108no—
594C2×C4—108no—
595C2×C4—108no—
596C2×C4—108no—
597C2×C4—108no—
598C2×C4—108no—
599C2×C4—108no—
600C2×C4—108no—
601C2×C4—108no—
602C2×C4—108no—
603C2×C4—108no—
604C2×C4—108no—
605C2×C4—101no—
606C2×C4—101no—
607C2×C4—101no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—108no—
616C2×C4—108no—
617C2×C4#401812yes—
618C2×C4D5×C22⋊C412yes—
619C2×C4D5×C22⋊C412yes—
620C2×C4D5×M1612yes—
621C2×C4D5×M1612yes—
622C2×C4C2×#70912yes—
623C2×C4C2×D4×D512yes—
624C2×C4D5×#4112yes—
625C8—44no—
626C8—204no—
627C5#2071511yescharacteristic, complemented, Sylow
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—54no—
635C22—54no—
636C22—1032no—
637C22—102no—
638C22—102no—
639C22—102no—
640C22—102no—
641C22—102no—
642C22—102no—
643C22—102no—
644C22—102no—
645C22—102no—
646C22—102no—
647C22—102no—
648C22—102no—
649C22#6499414yescomplemented
650C22C2×#401811yescharacteristic
651C22C2×D5×C22⋊C411yescharacteristic
652C22D5×#11711yescharacteristic
653C22C2×D5×M1611yescharacteristic
654C22C2×D5×M1611yescharacteristic
655C22C2×D5×M1611yescharacteristic
656C22C2×D5×M1611yescharacteristic
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—54no—
663C4—102no—
664C4—102no—
665C4—102no—
666C4—102no—
667C4—102no—
668C4#6588114yes—
669C2—24no—
670C2—104no—
671C2—104no—
672C2#1060529211yescharacteristic
673C2C2×#6499411yescharacteristic
674C2#1061024811yescharacteristic
675C2D5×#40711yescharacteristic
676C2D5×#40711yescharacteristic
677C2D5×#43211yescharacteristic
678C2#1061106211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1749C2
prime radicalC24×D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1749D5
hypocenterC5#20715
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#64994C2semidirect
3. C5×#1749C2semidirect
4. #10602322C2semidirect
6. #10600701C2semidirect
7. #10600600C2semidirect
8. #10599457C2semidirect
9. #10599455C2semidirect
27. C2×C5×#97C22semidirect
31. C2×#3946C22semidirect
32. C2×#3935C22semidirect
34. C5×#336C22semidirect
35. #64770C22semidirect
36. #64744C22semidirect
111. #1749D5semidirect
236. C2×#97C2×D5semidirect
239. #336C2×D5semidirect
396. C22×C5#432semidirect
418. C2×D5#432semidirect
627. C5#20715semidirect
649. C22#64994semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D52
C2×#649942
C5×#17492
#106023222
#106007482
#106007012
#106006002
#105994572
#105994552
#207155