Finite Group Databasebeta

← #12099185

Subgroups — #12099185

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×#4072C211yesmaximal, characteristic
2C2×#65009C212yesmaximal, complemented
3C5×#1779C211yesmaximal, characteristic
4#10602919C211yesmaximal, characteristic
5#10600704C212yesmaximal, complemented
6#10600702C212yesmaximal, complemented
7#10600701C211yesmaximal, characteristic, complemented
8#10600701C211yesmaximal, characteristic, complemented
9#10600700C212yesmaximal, complemented
10#10600699C211yesmaximal, characteristic, complemented
11Dic5×C22⋊C8C211yesmaximal, characteristic, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C22⋊Dic5C411yescharacteristic
14C22×C22⋊Dic5C411yescharacteristic
15C2×#4072—28no—
16C2×#4072C411yescharacteristic
17C2×#4072C411yescharacteristic
18C2×#4072C411yescharacteristic
19C2×#4072C411yescharacteristic
20C2×#4072C2211yescharacteristic
21C2×#4072C2211yescharacteristic
22C2×#4072C2211yescharacteristic
23C2×#4072C2211yescharacteristic
24C22×C4⋊Dic5C411yescharacteristic
25C22×C4⋊Dic5C411yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C2×C5×C22⋊C8C2212yes—
29C2×C5×C22⋊C8C2211yescharacteristic
30C2×C5×C22⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2212yes—
32C2×C22⋊#168C2212yes—
33C2×C22⋊#168C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35C2×C22⋊#168C2212yes—
36C2×#3947C2212yescomplemented
37C2×#3946C2212yescomplemented
38C2×#3946C2212yescomplemented
39C2×C8×Dic5C2212yescomplemented
40#65009—28no—
41#64770C2212yescomplemented
42#64770C2212yescomplemented
43#64770C2212yescomplemented
44#64770C2212yescomplemented
45#20716—51nomaximal, Sylow
46C25×C5C2×C411yescharacteristic
47C23×C4×C5—24no—
48C23×C4×C5—24no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5C2×C411yescharacteristic
52C23×C4×C5C2×C411yescharacteristic
53C23×C4×C5C2×C411yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×Dic5C2×C411yescharacteristic
58C23×Dic5C2×C411yescharacteristic
59C23×Dic5C2×C411yescharacteristic
60C23×Dic5C2×C411yescharacteristic
61C22×C5×C8C2312yes—
62C22×C5×C8C2312yes—
63C2×C22⋊Dic5—24no—
64C2×C22⋊Dic5—24no—
65C2×C22⋊Dic5C2×C411yescharacteristic
66C2×C22⋊Dic5C2×C411yescharacteristic
67C2×C22⋊Dic5C2×C411yescharacteristic
68C2×C22⋊Dic5C2×C411yescharacteristic
69C2×C22⋊Dic5C2×C411yescharacteristic
70C2×C22⋊Dic5C2×C411yescharacteristic
71C2×C22⋊Dic5C2×C411yescharacteristic
72C2×C22⋊Dic5C2×C411yescharacteristic
73#4072—24no—
74#4072—24no—
75#4072—24no—
76#4072—24no—
77#4072—24no—
78#4072—24no—
79#4072—24no—
80#4072D418yes—
81C2×C4⋊Dic5—24no—
82C2×C4⋊Dic5—24no—
83C2×C4⋊Dic5C2×C411yescharacteristic
84C2×C4⋊Dic5C2×C411yescharacteristic
85C2×C4⋊Dic5C2×C411yescharacteristic
86C2×C4⋊Dic5C2×C411yescharacteristic
87C2×C4⋊Dic5C2×C411yescharacteristic
88C2×C4⋊Dic5C2×C411yescharacteristic
89C2×C4⋊Dic5C2×C411yescharacteristic
90C2×C4⋊Dic5C2×C411yescharacteristic
91C2×C4×Dic5—24no—
92C2×C4×Dic5—24no—
93C2×C4×Dic5C2×C411yescharacteristic
94C2×C4×Dic5C2×C411yescharacteristic
95C2×C4×Dic5C2×C411yescharacteristic
96C2×C4×Dic5C2×C411yescharacteristic
97C2×C4×Dic5C2311yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99C2×C4×Dic5C2311yescharacteristic
100C2×C4×Dic5C2311yescharacteristic
101C22×#168C2312yes—
102C22×#168C2312yes—
103C5×C22⋊C8—24no—
104C5×C22⋊C8—22no—
105C5×C22⋊C8—22no—
106C5×C22⋊C8—24no—
107C22⋊#168—24no—
108C22⋊#168—22no—
109C22⋊#168—22no—
110C22⋊#168—24no—
111#3947—24no—
112#3946—24no—
113#3946—24no—
114C8×Dic5—24no—
115C22×#117—51no—
116C2×#433—52no—
117#1818—52no—
118#1798—52no—
119#1797—51no—
120#1797—51no—
121#1779—51no—
122#1779D511yescharacteristic
123#1750—52no—
124#1749—51no—
125C4×C22⋊C8—51no—
126C24×C5—22no—
127C24×C5—22no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5—22no—
131C24×C5—41no—
132C24×C5—41no—
133C24×C5C22×C411yescharacteristic
134C24×C5C22×C411yescharacteristic
135C24×C5C22×C411yescharacteristic
136C22×C4×C5—216no—
137C22×C4×C5—216no—
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×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5C22×C411yescharacteristic
156C22×C4×C5C22×C411yescharacteristic
157C22×C4×C5C22×C411yescharacteristic
158C22×C4×C5C2×D414yes—
159C22×C4×C5#4114yes—
160C22×C4×C5#4112yes—
161C22×C4×C5#4112yes—
162C22×C4×C5C2411yescharacteristic
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—41no—
172C22×Dic5—41no—
173C22×Dic5—41no—
174C22×Dic5—41no—
175C22×Dic5C22×C411yescharacteristic
176C22×Dic5C22×C411yescharacteristic
177C22×Dic5C22×C411yescharacteristic
178C22×Dic5C22×C411yescharacteristic
179C22×Dic5C22×C411yescharacteristic
180C22×Dic5C22×C411yescharacteristic
181C22×Dic5C22×C411yescharacteristic
182C22×Dic5C22×C411yescharacteristic
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C22⋊Dic5—22no—
190C22⋊Dic5—22no—
191C22⋊Dic5—22no—
192C22⋊Dic5—22no—
193C22⋊Dic5—22no—
194C22⋊Dic5—22no—
195C22⋊Dic5C22⋊C414yes—
196C22⋊Dic5C22⋊C414yes—
197C4⋊Dic5—22no—
198C4⋊Dic5—22no—
199C4⋊Dic5—22no—
200C4⋊Dic5—22no—
201C4⋊Dic5—22no—
202C4⋊Dic5—22no—
203C4⋊Dic5C22⋊C414yes—
204C4⋊Dic5C22⋊C414yes—
205C4×Dic5—22no—
206C4×Dic5—22no—
207C4×Dic5—22no—
208C4×Dic5—22no—
209C4×Dic5—22no—
210C4×Dic5—22no—
211C4×Dic5C2×D414yes—
212C4×Dic5C2×D414yes—
213C2×#168—22no—
214C2×#168—22no—
215C2×#168—22no—
216C2×#168—22no—
217C2×#168—22no—
218C2×#168—22no—
219C24×C4C2×D511yescharacteristic
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×C42—51no—
235#433—108no—
236C2×C4⋊C8—52no—
237C2×C4⋊C8—52no—
238C2×C22⋊C8—51no—
239C2×C22⋊C8—51no—
240C2×C22⋊C8—52no—
241C2×C22⋊C8—52no—
242C2×C22⋊C8C2×D511yescharacteristic
243C2×C22⋊C8C2×D511yescharacteristic
244C2×C22⋊C8C2×D512yes—
245C2×C22⋊C8C2×D512yes—
246C2×#97—52no—
247C2×C4×C8—52no—
248#336—52no—
249#336—52no—
250#336—52no—
251#336—52no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—28no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5—21no—
262C23×C5—21no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5—44no—
270C23×C5—44no—
271C23×C5—44no—
272C23×C5—44no—
273C23×C5—44no—
274C23×C5—44no—
275C23×C5C2×C22⋊C412yes—
276C23×C5#11712yes—
277C23×C5#11712yes—
278C23×C5#13112yes—
279C23×C5#13112yes—
280C23×C5C23×C411yescharacteristic
281C2×C4×C5—28no—
282C2×C4×C5—28no—
283C2×C4×C5—28no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—24no—
291C2×C4×C5—24no—
292C2×C4×C5—24no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5C2×C22⋊C412yes—
297C2×C4×C5#11712yes—
298C2×C4×C5#11712yes—
299C2×C4×C5C22×D412yes—
300C2×C4×C5C2×#4111yescharacteristic
301C2×C4×C5C2×#4111yescharacteristic
302C2×C4×C5C2×#4112yes—
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×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—44no—
324C2×Dic5—44no—
325C2×Dic5—44no—
326C2×Dic5—44no—
327C2×Dic5C2×C22⋊C412yes—
328C2×Dic5C2×C22⋊C412yes—
329C2×Dic5C2×C22⋊C412yes—
330C2×Dic5C2×C22⋊C412yes—
331C5×C8—42no—
332C5×C8—42no—
333#168—42no—
334#168—42no—
335C25C4×D511yescharacteristic
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—51no—
344C23×C4C4×D511yescharacteristic
345C23×C4C4×D511yescharacteristic
346C23×C4C4×D511yescharacteristic
347C23×C4C22×D511yescharacteristic
348C23×C4C22×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—51no—
383C2×C42—51no—
384C2×C42—51no—
385C2×C42—51no—
386C2×C42—51no—
387C2×C42—51no—
388C2×C42—51no—
389C2×C42—51no—
390C2×C42—104no—
391C2×C42—104no—
392C4⋊C8—104no—
393C4⋊C8—104no—
394C22⋊C8—24no—
395C22⋊C8—22no—
396C22⋊C8—22no—
397C22⋊C8—24no—
398C22⋊C8—104no—
399C22⋊C8—102no—
400C22⋊C8—102no—
401C22⋊C8—104no—
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—22no—
411C22×C5—22no—
412C22×C5—22no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5—416no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5#43314yescomplemented
426C22×C5C22×C22⋊C411yescharacteristic
427C22×C5C2×#11711yescharacteristic
428C22×C5C2×#11711yescharacteristic
429C22×C5C2×#13111yescharacteristic
430C22×C5C2×#13111yescharacteristic
431C22×C5#56811yescharacteristic
432C22×C5#56811yescharacteristic
433C4×C5—22no—
434C4×C5—22no—
435C4×C5—22no—
436C4×C5#52512yes—
437C4×C5#52512yes—
438Dic5—22no—
439Dic5—22no—
440Dic5—22no—
441Dic5—22no—
442Dic5—41no—
443Dic5—41no—
444Dic5—41no—
445Dic5—41no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—41no—
452C24—41no—
453C24C2×C4×D511yescharacteristic
454C24C2×C4×D511yescharacteristic
455C24C2×C4×D511yescharacteristic
456C22×C4—216no—
457C22×C4—216no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—51no—
481C22×C4—51no—
482C22×C4—51no—
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—201no—
492C22×C4—201no—
493C22×C4—201no—
494C22×C4—201no—
495C22×C4C2×C4×D511yescharacteristic
496C22×C4C2×C4×D511yescharacteristic
497C22×C4C2×C4×D511yescharacteristic
498C22×C4D4×D514yes—
499C22×C4#71114yes—
500C22×C4#71112yes—
501C22×C4#71112yes—
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—54no—
532C42—54no—
533C42—102no—
534C42—102no—
535C42—102no—
536C42—102no—
537C42—102no—
538C42—102no—
539C2×C5—24no—
540C2×C5—42no—
541C2×C5—42no—
542C2×C5#228011yescharacteristic
543C2×C5#288011yescharacteristic
544C2×C5#288011yescharacteristic
545C2×C5C2×#43311yescharacteristic
546C2×C5#292111yescharacteristic
547C2×C5#292411yescharacteristic
548C2×C5#292411yescharacteristic
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—28no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23#402312yes—
573C23#402312yes—
574C23D5×C22⋊C412yes—
575C23#404712yes—
576C23#405312yes—
577C23C22×C4×D511yescharacteristic
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—52no—
594C2×C4—52no—
595C2×C4—52no—
596C2×C4—52no—
597C2×C4—101no—
598C2×C4—101no—
599C2×C4—101no—
600C2×C4—101no—
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—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—204no—
618C2×C4—204no—
619C2×C4—204no—
620C2×C4—204no—
621C2×C4#402312yes—
622C2×C4#402312yes—
623C2×C4D5×C22⋊C412yes—
624C2×C4C2×D4×D512yes—
625C2×C4C2×#71111yescharacteristic
626C2×C4C2×#71111yescharacteristic
627C2×C4C2×#71112yes—
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—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—416no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22#6500914yescomplemented
655C22C2×#402311yescharacteristic
656C22C2×#402311yescharacteristic
657C22C2×D5×C22⋊C411yescharacteristic
658C22C2×#404711yescharacteristic
659C22C2×#405311yescharacteristic
660C22#6607911yescharacteristic
661C22#6607911yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—102no—
666C4—102no—
667C4—102no—
668C4—102no—
669C4—201no—
670C4—201no—
671C4—201no—
672C4—201no—
673C4#6592012yes—
674C4#6592012yes—
675C2—24no—
676C2—42no—
677C2—42no—
678C2#1060554811yescharacteristic
679C2C2×#6500911yescharacteristic
680C2#1061031511yescharacteristic
681C2#1061033111yescharacteristic
682C2#1061035111yescharacteristic
683C2#1061035211yescharacteristic
684C2#1061036211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1779C2
prime radicalC25×C5C2×C4
cosocleC22×C4×C5C24
hypercenter#1779D5
hypocenterC5#20716
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#65009C2semidirect
5. #10600704C2semidirect
6. #10600702C2semidirect
7. #10600701C2semidirect
8. #10600701C2semidirect
9. #10600700C2semidirect
10. #10600699C2semidirect
11. Dic5×C22⋊C8C2semidirect
36. C2×#3947C22semidirect
37. C2×#3946C22semidirect
38. C2×#3946C22semidirect
39. C2×C8×Dic5C22semidirect
41. #64770C22semidirect
42. #64770C22semidirect
43. #64770C22semidirect
44. #64770C22semidirect
425. C22×C5#433semidirect
632. C5#20716semidirect
654. C22#65009semidirect

Maximal subgroups

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

subgroupindex
C22×#40722
C2×#650092
C5×#17792
#106029192
#106007042
#106007022
#106007012
#106007002
#106006992
Dic5×C22⋊C82
#207165