Finite Group Databasebeta

← #12117463

Subgroups — #12117463

Order 1280.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2352C211yesmaximal, characteristic
2#10614068C211yesmaximal, characteristic
3C2×#65300C211yesmaximal, characteristic
4C2×#65287C211yesmaximal, characteristic, complemented
5C2×#65253C211yesmaximal, characteristic, complemented
6#10602369C211yesmaximal, characteristic, complemented
7#10602348C211yesmaximal, characteristic, complemented
8#10600343C211yesmaximal, characteristic, complemented
9#10600333C211yesmaximal, characteristic, complemented
10#10600306C211yesmaximal, characteristic, complemented
11#10600305C211yesmaximal, characteristic, complemented
12#10600299C211yesmaximal, characteristic, complemented
13#10600299C211yesmaximal, characteristic, complemented
14#10600274C211yesmaximal, characteristic, complemented
15#10600259C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×C5×#117C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C2×#4072C2211yescharacteristic
20C2×#4072C2211yescharacteristic
21C22×#681C2211yescharacteristic
22C23×#168C2211yescharacteristic
23C5×#388—21no—
24C5×#387—21no—
25C5×#386—21no—
26C5×#382C2211yescharacteristic
27C5×#380C2211yescharacteristic
28C5×#380C2211yescharacteristic
29C4×C5×C4⋊C4C2211yescharacteristic
30C4×C5×C22⋊C4—21no—
31#65510—21no—
32#65501C2211yescharacteristic
33#65501C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35C2×C22⋊#168C2211yescharacteristic
36#65300C418yescomplemented
37#65287—24no—
38C4⋊C4×Dic5—21no—
39#65253—24no—
40C2×#3940C2211yescharacteristic
41C2×#3940C2211yescharacteristic
42C2×#3940C2211yescharacteristic
43C2×#3940C2211yescharacteristic
44C2×#3939C2211yescharacteristic
45C2×#3939C2211yescharacteristic
46C2×#3939C2211yescharacteristic
47C2×#3939C2211yescharacteristic
48C2×#3939C2211yescharacteristic
49C2×#3939C2211yescharacteristic
50#65240—21no—
51#65240—21no—
52#65224C2211yescharacteristic
53C4×C4⋊Dic5C2211yescharacteristic
54C2×C4⋊#168C2211yescharacteristic
55C2×#3935C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#64749C2211yescharacteristic
61#64749C2211yescharacteristic
62#22660—51nomaximal, Sylow
63C22×C5×D4D411yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C4×C5×D4C2×C414yes—
68C4×C5×D4Q814yes—
69C5×#117—22no—
70C5×#117—41no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—41no—
74C2×C5×C4⋊C4D411yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4D411yescharacteristic
83C2×C5×C22⋊C4D411yescharacteristic
84C2×C42×C5—21no—
85C2×C42×C5—21no—
86C2×C42×C5C2311yescharacteristic
87C2×C22⋊Dic5—21no—
88C2×C22⋊Dic5—21no—
89C2×C22⋊Dic5—21no—
90C2×C22⋊Dic5—21no—
91#4072—22no—
92#4072—22no—
93#4072—41no—
94#4072—41no—
95C2×C4⋊Dic5—21no—
96C2×C4⋊Dic5—21no—
97C2×C4⋊Dic5C2311yescharacteristic
98C2×C4⋊Dic5C2311yescharacteristic
99C2×C4⋊Dic5C2311yescharacteristic
100C2×C4⋊Dic5C2311yescharacteristic
101C2×C4×Dic5—21no—
102C2×C4×Dic5—21no—
103C2×C4×Dic5—21no—
104C2×#681—22no—
105C2×#681—22no—
106C2×#681C2×C414yes—
107C22×#168—22no—
108C22×#168—22no—
109C22×#168C2×C414yescomplemented
110C22×#168C2311yescharacteristic
111C22×#168C2311yescharacteristic
112C22×#168C2311yescharacteristic
113C22×#168C2311yescharacteristic
114C5×#95—21no—
115C5×#95—21no—
116C5×#95—21no—
117C5×#95—21no—
118C5×#95—21no—
119#3963—21no—
120#3963—21no—
121#3963—21no—
122C22⋊#168C2×C414yes—
123C22⋊#168C2×C414yescomplemented
124#3940—22no—
125#3940—22no—
126#3940—41no—
127#3940D414yescomplemented
128#3939—22no—
129#3939—22no—
130#3939—22no—
131#3939—22no—
132#3939—22no—
133#3939—41no—
134C4⋊#168C2×C414yescomplemented
135#3935C2×C414yescomplemented
136C2×#435—51no—
137C2×#428—51no—
138C2×#427—51no—
139#2354—51no—
140#2352D511yescharacteristic
141#1949—51no—
142#1947—51no—
143#1854—51no—
144#1854—51no—
145#1854—51no—
146#1852—51no—
147#1847—51no—
148#1809—51no—
149#1808—51no—
150#1776—51no—
151C24×C5C2×D411yescharacteristic
152C24×C5C2×D411yescharacteristic
153C2×C5×D4—41no—
154C2×C5×D4—41no—
155C2×C5×D4C4⋊C414yes—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—42no—
169C22×C4×C5—42no—
170C22×C4×C5—81no—
171C22×C4×C5C22×C412yes—
172C22×C4×C5C22×C412yes—
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5C2×D411yescharacteristic
177C22×C4×C5C2×Q812yes—
178C22×C4×C5C2×Q812yes—
179C22×C4×C5C2411yescharacteristic
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—42no—
192C5×C4⋊C4C4⋊C414yes—
193C5×C4⋊C4C2×D412yes—
194C5×C22⋊C4—42no—
195C5×C22⋊C4—42no—
196C5×C22⋊C4—81no—
197C5×C22⋊C4C4⋊C414yes—
198C5×C22⋊C4C4⋊C414yes—
199C42×C5—42no—
200C42×C5—81no—
201C42×C5C22×C412yes—
202C42×C5C2×Q812yes—
203C22⋊Dic5—42no—
204C22⋊Dic5—42no—
205C22⋊Dic5—81no—
206C22⋊Dic5—81no—
207C4⋊Dic5—21no—
208C4⋊Dic5—21no—
209C4⋊Dic5—21no—
210C4⋊Dic5—21no—
211C4⋊Dic5—21no—
212C4⋊Dic5—21no—
213C4⋊Dic5—21no—
214C4⋊Dic5—42no—
215C4⋊Dic5—81no—
216C4⋊Dic5C2×D412yes—
217C4×Dic5—42no—
218C4×Dic5—42no—
219C4×Dic5—42no—
220#681—28no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—21no—
225C2×#168—21no—
226C2×#168—21no—
227C2×#168—28no—
228C2×#168C22×C412yes—
229C2×#168C22×C412yes—
230C2×#168C22×C412yes—
231C2×#168C22×C412yes—
232C2×#168C2×D412yes—
233C2×#168#4112yes—
234C22×M16—51no—
235C23×C8—51no—
236C2×C4×D4C2×D511yescharacteristic
237C2×#117—51no—
238C2×#117—51no—
239C2×#117C2×D511yescharacteristic
240C22×C4⋊C4C2×D511yescharacteristic
241#435—58no—
242#428—104no—
243#427—104no—
244C2×#107—51no—
245C2×#107—51no—
246C2×#107—51no—
247C2×#107—51no—
248C2×#107—51no—
249C2×#107—51no—
250C2×#106—51no—
251C2×#106—51no—
252C2×#106—51no—
253C2×#106—51no—
254C2×C4⋊C8—51no—
255C2×C22⋊C8—51no—
256C2×C22⋊C8—51no—
257C2×#97—51no—
258#390—101no—
259#388—21no—
260#388—101no—
261#388—101no—
262#387—21no—
263#386—21no—
264#384—51no—
265#382C2×D511yescharacteristic
266#380—51no—
267#380—51no—
268#380C2×D511yescharacteristic
269#380C2×D511yescharacteristic
270C4×C4⋊C4—51no—
271C4×C4⋊C4—101no—
272C4×C4⋊C4C2×D511yescharacteristic
273C4×C22⋊C4—21no—
274#340—51no—
275#340—51no—
276#340—51no—
277#340—51no—
278#340—51no—
279#340—51no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5C2×C4⋊C412yes—
293C23×C5C2×C4⋊C412yes—
294C23×C5C22×D411yescharacteristic
295C5×D4—44no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—84no—
325C2×C4×C5C2×C4⋊C412yes—
326C2×C4×C5C2×C4⋊C412yes—
327C2×C4×C5C2×C4⋊C412yes—
328C2×C4×C5C2×C4⋊C412yes—
329C2×C4×C5C23×C411yescharacteristic
330C2×C4×C5C22×D411yescharacteristic
331C2×C4×C5C22×Q811yescharacteristic
332C2×C4×C5C2×#4111yescharacteristic
333C2×C4×C5H(5,𝔽2)11yescharacteristic
334C2×C4×C52−1+411yescharacteristic
335C2×Dic5—22no—
336C2×Dic5—41no—
337C2×Dic5—41no—
338C2×Dic5—41no—
339C2×Dic5—41no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342C2×Dic5—41no—
343C2×Dic5—41no—
344C2×Dic5—41no—
345C2×Dic5—41no—
346C2×Dic5—41no—
347#168—22no—
348#168—22no—
349#168—22no—
350#168C4×D414yes—
351C22×D4C22⋊D511yescharacteristic
352C23×C4—21no—
353C23×C4C22×D511yescharacteristic
354C23×C4C22×D511yescharacteristic
355C2×M16—54no—
356C2×M16—102no—
357C2×M16—102no—
358C22×C8—51no—
359C22×C8—54no—
360C22×C8—51no—
361C22×C8—51no—
362C22×C8—51no—
363C22×C8—102no—
364C22×C8—102no—
365C4×D4Dic1014yes—
366C4×D4C4×D514yes—
367#117—22no—
368#117—41no—
369#117—102no—
370#117—102no—
371#117—201no—
372#117—201no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—51no—
377C2×C4⋊C4—51no—
378C2×C4⋊C4—51no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4—101no—
382C2×C4⋊C4C22⋊D511yescharacteristic
383C2×C4⋊C4C22×D511yescharacteristic
384C2×C4⋊C4C22×D511yescharacteristic
385C2×C4⋊C4C22×D511yescharacteristic
386C2×C4⋊C4C22×D511yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—101no—
391C2×C22⋊C4—101no—
392C2×C22⋊C4—101no—
393C2×C22⋊C4—101no—
394C2×C22⋊C4C22⋊D511yescharacteristic
395C2×C22⋊C4C22⋊D511yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—101no—
399C2×C42—101no—
400C2×C42—101no—
401C2×C42C22×D511yescharacteristic
402#107—102no—
403#107—102no—
404#107—102no—
405#107—102no—
406#107—102no—
407#107—201no—
408#106—54no—
409#106—102no—
410#106—102no—
411#106—201no—
412C4⋊C8—54no—
413C22⋊C8—54no—
414C22⋊C8—54no—
415#97—54no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—101no—
422#95—101no—
423#95—101no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5C22×C4⋊C411yescharacteristic
439C22×C5D4211yescharacteristic
440C22×C5#54711yescharacteristic
441C22×C5#57511yescharacteristic
442C22×C5#57511yescharacteristic
443C22×C5#57611yescharacteristic
444C22×C5#57811yescharacteristic
445C4×C5—22no—
446C4×C5—22no—
447C4×C5—22no—
448C4×C5—22no—
449C4×C5—42no—
450C4×C5—81no—
451C4×C5—81no—
452C4×C5—81no—
453C4×C5C2×C4×D411yescharacteristic
454C4×C5#52011yescharacteristic
455C4×C5D4×Q811yescharacteristic
456C4×C5#55411yescharacteristic
457Dic5—42no—
458Dic5—81no—
459Dic5—81no—
460Dic5—81no—
461C24C2×C22⋊D511yescharacteristic
462C24C2×C22⋊D511yescharacteristic
463C2×D4—41no—
464C2×D4—41no—
465C2×D4#68314yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4C2×Dic1012yes—
486C22×C4C2×Dic1012yes—
487C22×C4C2×C4×D512yes—
488C22×C4C2×C4×D512yes—
489C22×C4C2×C22⋊D511yescharacteristic
490C22×C4C2×C22⋊D511yescharacteristic
491C22×C4C2×C22⋊D511yescharacteristic
492C22×C4C2×C22⋊D511yescharacteristic
493C22×C4C23×D511yescharacteristic
494M16—108no—
495C2×C8—52no—
496C2×C8—52no—
497C2×C8—52no—
498C2×C8—52no—
499C2×C8—52no—
500C2×C8—52no—
501C2×C8—108no—
502C2×C8—101no—
503C2×C8—101no—
504C2×C8—101no—
505C2×C8—101no—
506C2×C8—101no—
507C2×C8—101no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—52no—
517C4⋊C4—101no—
518C4⋊C4—101no—
519C4⋊C4—101no—
520C4⋊C4—101no—
521C4⋊C4—101no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4—202no—
525C4⋊C4—401no—
526C4⋊C4#68314yes—
527C4⋊C4D4×D512yes—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—202no—
532C22⋊C4—202no—
533C22⋊C4—401no—
534C22⋊C4—401no—
535C22⋊C4#68314yes—
536C22⋊C4#68314yes—
537C42—42no—
538C42—81no—
539C42—202no—
540C42—202no—
541C42—202no—
542C42C2×Dic1012yes—
543C42C2×C4×D512yes—
544C2×C5—42no—
545C2×C5—42no—
546C2×C5D4×C4⋊C411yescharacteristic
547C2×C5#291111yescharacteristic
548C2×C5#291311yescharacteristic
549C2×C5#326811yescharacteristic
550C2×C5#326911yescharacteristic
551C2×C5#334711yescharacteristic
552C2×C5#334911yescharacteristic
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23C2×#68312yes—
566C23C2×#68312yes—
567C23C22×C22⋊D511yescharacteristic
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—102no—
599C2×C4—201no—
600C2×C4—201no—
601C2×C4—201no—
602C2×C4—201no—
603C2×C4—201no—
604C2×C4—201no—
605C2×C4—201no—
606C2×C4—201no—
607C2×C4—201no—
608C2×C4—201no—
609C2×C4—201no—
610C2×C4C2×#68312yes—
611C2×C4C2×#68312yes—
612C2×C4C2×#68312yes—
613C2×C4C2×#68312yes—
614C2×C4C22×Dic1011yescharacteristic
615C2×C4C22×C4×D511yescharacteristic
616C2×C4C2×D4×D511yescharacteristic
617C2×C4#414411yescharacteristic
618C2×C4D5×#4111yescharacteristic
619C2×C4#415011yescharacteristic
620C8—54no—
621C8—102no—
622C8—102no—
623C8—102no—
624C5#2266011yescharacteristic, complemented, Sylow
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C22×#68311yescharacteristic
640C22D4×C22⋊D511yescharacteristic
641C22#6615611yescharacteristic
642C22#6615611yescharacteristic
643C22#6615811yescharacteristic
644C22#6616911yescharacteristic
645C22#6617211yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—202no—
655C4—401no—
656C4—401no—
657C4—401no—
658C4D4×Dic1011yescharacteristic
659C4#6587311yescharacteristic
660C4C4×D4×D511yescharacteristic
661C4#6588011yescharacteristic
662C2—42no—
663C2—42no—
664C2#1061393811yescharacteristic
665C2D4×#68311yescharacteristic
666C2#1061429311yescharacteristic
667C2#1061523811yescharacteristic
668C2#1061527411yescharacteristic
669C2#1061532611yescharacteristic
670C2#1061534111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2352C2
socleC23×C5C22×D4
prime radicalC22×C5×D4D4
cosocleC22×C4×C5C24
hypercenter#2352D5
hypocenterC5#22660
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
4. C2×#65287C2semidirect
5. C2×#65253C2semidirect
6. #10602369C2semidirect
7. #10602348C2semidirect
8. #10600343C2semidirect
9. #10600333C2semidirect
10. #10600306C2semidirect
11. #10600305C2semidirect
12. #10600299C2semidirect
13. #10600299C2semidirect
14. #10600274C2semidirect
15. #10600259C2semidirect
36. #65300C4semidirect
109. C22×#168C2×C4semidirect
123. C22⋊#168C2×C4semidirect
127. #3940D4semidirect
134. C4⋊#168C2×C4semidirect
135. #3935C2×C4semidirect
624. C5#22660semidirect

Maximal subgroups

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

subgroupindex
C5×#23522
#106140682
C2×#653002
C2×#652872
C2×#652532
#106023692
#106023482
#106003432
#106003332
#106003062
#106003052
#106002992
#106002742
#106002592
#226605