Finite Group Databasebeta

← #12107221

Subgroups — #12107221

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65417C211yesmaximal, characteristic
2C2×#64990C211yesmaximal, characteristic, complemented
3#10605212C211yesmaximal, characteristic
4C5×#1753C211yesmaximal, characteristic, complemented
5#10602776C211yesmaximal, characteristic, complemented
6#10600710C211yesmaximal, characteristic
7#10600707C211yesmaximal, characteristic, complemented
8#10600601C211yesmaximal, characteristic, complemented
9#10600574C211yesmaximal, characteristic, complemented
10#10600542C211yesmaximal, characteristic, complemented
11#10600245C211yesmaximal, characteristic, complemented
12#10599451C211yesmaximal, characteristic, complemented
13#10599413C211yesmaximal, characteristic, complemented
14#10599409C211yesmaximal, characteristic, complemented
15#10599399C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×C4×C22⋊D5C2211yescharacteristic
18C22×#676C2211yescharacteristic
19C2×C4×Dic10C2211yescharacteristic
20C2×C5×C22⋊C8C2211yescharacteristic
21C2×C5×#97C2211yescharacteristic
22C2×C4×C5×C8C2211yescharacteristic
23C4×C5×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊#168C2211yescharacteristic
26C2×C22⋊#168C2211yescharacteristic
27#65417—24no—
28C2×#3952C2211yescharacteristic
29C2×#3952C2211yescharacteristic
30C2×#3952C2211yescharacteristic
31C2×#3947C2211yescharacteristic
32C2×#3947C2211yescharacteristic
33C2×#3947C2211yescharacteristic
34C2×#3946C2211yescharacteristic
35C2×#3946C2211yescharacteristic
36C2×#3946C2211yescharacteristic
37C2×C8×Dic5C2211yescharacteristic
38C2×C8×Dic5C2211yescharacteristic
39#65250C411yescharacteristic
40#65248C411yescharacteristic
41#65241C411yescharacteristic
42#65236C411yescharacteristic
43C4×#685C2211yescharacteristic
44C4×#685C2211yescharacteristic
45#65221C2211yescharacteristic
46C2×C4⋊#168C2211yescharacteristic
47C2×#3935C2211yescharacteristic
48#64990—24no—
49#64964C411yescharacteristic
50#64962C411yescharacteristic
51#64949C411yescharacteristic
52#64947C411yescharacteristic
53C5×#336C2211yescharacteristic
54C5×#336C2211yescharacteristic
55#64770C2211yescharacteristic
56#64770C2211yescharacteristic
57#64770C2211yescharacteristic
58#64770C2211yescharacteristic
59#64744C2211yescharacteristic
60#64744C2211yescharacteristic
61#21636—51nomaximal, Sylow
62C23×C4×C5C2311yescharacteristic
63C22×C22⋊D5C2×C411yescharacteristic
64C22×C4×D5C2311yescharacteristic
65C22×Dic10C2×C411yescharacteristic
66C2×C5×M16—22no—
67C2×C5×M16—22no—
68C2×C5×M16—22no—
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C2×C5×C22⋊C4C2×C411yescharacteristic
74C2×C5×C22⋊C4C2×C411yescharacteristic
75C2×C42×C5C2311yescharacteristic
76C2×C42×C5C2311yescharacteristic
77C2×C22⋊Dic5C2×C411yescharacteristic
78C2×C22⋊Dic5C2×C411yescharacteristic
79C2×C22⋊Dic5C2×C411yescharacteristic
80C4×C22⋊D5—22no—
81C4×C22⋊D5—22no—
82C2×#685C2×C411yescharacteristic
83C2×#685C2×C411yescharacteristic
84C2×#685C2×C411yescharacteristic
85C2×#685C2×C411yescharacteristic
86C2×#685C2×C411yescharacteristic
87C2×C4⋊Dic5C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×#683C2×C411yescharacteristic
90C2×#683C2×C411yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C2×#676—22no—
99C2×#676—22no—
100C2×#676—22no—
101C4×Dic10—22no—
102C4×Dic10—22no—
103C5×C22⋊C8—22no—
104C5×#97—22no—
105C4×C5×C8—22no—
106C5×#95C2×C411yescharacteristic
107C5×#95C2×C411yescharacteristic
108#3963C2×C411yescharacteristic
109#3963C2×C411yescharacteristic
110#3963C2×C411yescharacteristic
111#3963C2×C411yescharacteristic
112#3963C2×C411yescharacteristic
113#3963C2×C411yescharacteristic
114#3963C2×C411yescharacteristic
115#3963C2×C411yescharacteristic
116#3963C2×C411yescharacteristic
117#3963C2×C411yescharacteristic
118C22⋊#168—22no—
119C22⋊#168—22no—
120#3952—22no—
121#3952—22no—
122#3952—22no—
123#3947—22no—
124#3947—22no—
125#3947—22no—
126#3946—22no—
127#3946—22no—
128#3946—22no—
129C8×Dic5—22no—
130C8×Dic5D414yes—
131C4⋊#168—22no—
132#3935—22no—
133C2×#446—51no—
134C2×#436—51no—
135#2398—51no—
136#1985—51no—
137#1955—51no—
138#1924—51no—
139#1924—51no—
140#1924—51no—
141#1924—51no—
142#1832—51no—
143#1753—51no—
144#1753—51no—
145#1753—51no—
146#1753D511yescharacteristic, complemented
147#1726—51no—
148C24×C5C22×C411yescharacteristic
149C23×D5C22×C411yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5C22×C411yescharacteristic
157C22×C4×C5C22×C411yescharacteristic
158C22×C4×C5C22×C411yescharacteristic
159C22×C4×C5C22×C411yescharacteristic
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C2411yescharacteristic
162C2×C22⋊D5—22no—
163C2×C22⋊D5—41no—
164C2×C22⋊D5—41no—
165C22×Dic5C22×C411yescharacteristic
166C22×Dic5C22×C411yescharacteristic
167C22×Dic5C22×C411yescharacteristic
168C22×Dic5C22×C411yescharacteristic
169C22×Dic5C22×C411yescharacteristic
170C22×Dic5C22×C411yescharacteristic
171C22×Dic5C22×C411yescharacteristic
172C2×C4×D5—21no—
173C2×C4×D5—21no—
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×Dic10—22no—
179C2×Dic10—41no—
180C2×Dic10—41no—
181C5×M16—44no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8C2×D412yes—
191C2×C5×C8#4112yes—
192C2×C5×C8#4112yes—
193C2×C5×C8#4112yes—
194C5×C22⋊C4—41no—
195C5×C22⋊C4—41no—
196C42×C5—21no—
197C42×C5—21no—
198C42×C5—21no—
199C42×C5—21no—
200C22⋊Dic5—22no—
201C22⋊Dic5—41no—
202C22⋊Dic5—41no—
203#685—22no—
204#685—41no—
205#685—41no—
206#685—41no—
207#685—41no—
208C4⋊Dic5—22no—
209#683—22no—
210#683—22no—
211#683—22no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5C2×D412yes—
217C4×Dic5#4112yes—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—21no—
225C2×#168—21no—
226C2×#168—21no—
227C2×#168—21no—
228C2×#168C2×D412yes—
229C2×#168#4112yes—
230#676—44no—
231C22×M16—51no—
232C22×M16C2×D511yescharacteristic
233C2×C4×Q8—51no—
234C2×C4×D4—51no—
235#446—104no—
236#436—104no—
237C2×C4⋊C8—51no—
238C2×C4⋊C8—51no—
239C2×C4⋊C8—51no—
240C2×C4⋊C8—51no—
241C2×C22⋊C8—51no—
242C2×C22⋊C8—51no—
243C2×C22⋊C8—51no—
244C2×C22⋊C8—51no—
245C2×C22⋊C8—51no—
246C2×C22⋊C8C2×D511yescharacteristic
247C2×#97—51no—
248C2×#97—51no—
249C2×#97—51no—
250C2×#97—51no—
251C2×#97C2×D511yescharacteristic
252C2×C4×C8—51no—
253C2×C4×C8—51no—
254C2×C4×C8C2×D511yescharacteristic
255#400—51no—
256#400—51no—
257#397—51no—
258#397—51no—
259#394—51no—
260#394—51no—
261#393—51no—
262#393—51no—
263C4×C22⋊C4—51no—
264C4×C22⋊C4—51no—
265C4×C22⋊C4—51no—
266C4×C22⋊C4C2×D511yescharacteristic
267#376—51no—
268#336—51no—
269#336—51no—
270#336—51no—
271#336—51no—
272#336—51no—
273#336—51no—
274#336C2×D511yescharacteristic
275#336C2×D511yescharacteristic
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5C23×C411yescharacteristic
284C22×D5—21no—
285C22×D5—21no—
286C22×D5—21no—
287C22×D5—21no—
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
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—21no—
305C2×C4×C5—21no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5C22×D411yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C22⋊D5—44no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—21no—
331C2×Dic5—21no—
332C2×Dic5—21no—
333C2×Dic5—21no—
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5C4×D412yes—
337C2×Dic5C4×D412yes—
338C4×D5—41no—
339C4×D5—41no—
340C4×D5—41no—
341C4×D5—41no—
342Dic10—44no—
343C5×C8—22no—
344C5×C8—41no—
345C5×C8—41no—
346C5×C8#12414yes—
347#168—22no—
348#168—22no—
349#168—41no—
350#168—41no—
351C22×Q8—51no—
352C22×D4—51no—
353C23×C4—51no—
354C23×C4C22×D511yescharacteristic
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—102no—
359C2×M16—102no—
360C2×M16—102no—
361C22×C8—51no—
362C22×C8—51no—
363C22×C8—51no—
364C22×C8—51no—
365C22×C8C22×D511yescharacteristic
366C22×C8C22×D511yescharacteristic
367C22×C8C22×D511yescharacteristic
368C22×C8C22×D511yescharacteristic
369C4×Q8—102no—
370C4×Q8—102no—
371C4×D4—102no—
372C4×D4—102no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—51no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—51no—
377C2×C22⋊C4—51no—
378C2×C22⋊C4—51no—
379C2×C22⋊C4—51no—
380C2×C22⋊C4—51no—
381C2×C22⋊C4—51no—
382C2×C22⋊C4—51no—
383C2×C22⋊C4—51no—
384C2×C22⋊C4—51no—
385C2×C22⋊C4C4×D511yescharacteristic
386C2×C22⋊C4C4×D511yescharacteristic
387C2×C42—51no—
388C2×C42—51no—
389C2×C42—51no—
390C2×C42C22×D511yescharacteristic
391C2×C42C22×D511yescharacteristic
392C4⋊C8—102no—
393C4⋊C8—102no—
394C4⋊C8—102no—
395C4⋊C8—102no—
396C22⋊C8—22no—
397C22⋊C8—102no—
398C22⋊C8—102no—
399C22⋊C8—102no—
400C22⋊C8—102no—
401C22⋊C8—102no—
402#97—22no—
403#97—102no—
404#97—102no—
405#97—102no—
406#97—102no—
407C4×C8—22no—
408C4×C8—54no—
409C4×C8—102no—
410#95—51no—
411#95—51no—
412#95—51no—
413#95—51no—
414#95—51no—
415#95—51no—
416#95—51no—
417#95—51no—
418#95—51no—
419#95—51no—
420#95C4×D511yescharacteristic
421#95C4×D511yescharacteristic
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5C2×C4×D411yescharacteristic
430C22×C5C4×#4111yescharacteristic
431C22×C5C4×#4111yescharacteristic
432C22×C5#56811yescharacteristic
433C22×C5#56811yescharacteristic
434C22×C5#56811yescharacteristic
435C22×C5#56811yescharacteristic
436C2×D5—41no—
437C2×D5—41no—
438C2×D5—41no—
439C2×D5—41no—
440C2×D5—41no—
441C2×D5—41no—
442C2×D5—41no—
443C4×C5—41no—
444C4×C5—41no—
445C4×C5—41no—
446C4×C5—41no—
447C4×C5—41no—
448C4×C5C2×#12411yescharacteristic
449C4×C5#52911yescharacteristic
450C4×C5#52911yescharacteristic
451C4×C5#53211yescharacteristic
452Dic5—22no—
453Dic5—22no—
454Dic5—41no—
455Dic5—41no—
456Dic5—41no—
457Dic5—41no—
458Dic5—41no—
459C24—51no—
460C24C2×C4×D511yescharacteristic
461C2×Q8—102no—
462C2×Q8—201no—
463C2×Q8—201no—
464C2×D4—102no—
465C2×D4—201no—
466C2×D4—201no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4C2×C4×D511yescharacteristic
487C22×C4C2×C4×D511yescharacteristic
488C22×C4C2×C4×D511yescharacteristic
489C22×C4C2×C4×D511yescharacteristic
490C22×C4C2×C4×D511yescharacteristic
491C22×C4C23×D511yescharacteristic
492M16—44no—
493M16—204no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—52no—
503C2×C8—52no—
504C2×C8—101no—
505C2×C8—101no—
506C2×C8—101no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—101no—
510C2×C8—101no—
511C2×C8—101no—
512C2×C8—101no—
513C2×C8—101no—
514C2×C8#70912yes—
515C2×C8#70912yes—
516C2×C8D4×D512yes—
517C2×C8#71112yes—
518C4⋊C4—102no—
519C4⋊C4—102no—
520C4⋊C4—102no—
521C4⋊C4—102no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—102no—
525C22⋊C4—102no—
526C22⋊C4—201no—
527C22⋊C4—201no—
528C22⋊C4—201no—
529C22⋊C4—201no—
530C22⋊C4—201no—
531C22⋊C4—201no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—52no—
537C42—52no—
538C42—101no—
539C42—101no—
540C42—101no—
541C42—101no—
542C2×C5—81no—
543C2×C5C4×#12411yescharacteristic
544C2×C5#293011yescharacteristic
545C2×C5#293011yescharacteristic
546C2×C5#296711yescharacteristic
547C2×C5#296711yescharacteristic
548C2×C5#296711yescharacteristic
549C2×C5#296711yescharacteristic
550D5—81no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23—101no—
562C23—101no—
563C23—101no—
564C23—101no—
565C23C22×C4×D511yescharacteristic
566Q8—204no—
567D4—204no—
568C2×C4—21no—
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—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—52no—
588C2×C4—52no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—101no—
592C2×C4—101no—
593C2×C4—101no—
594C2×C4—101no—
595C2×C4—101no—
596C2×C4—101no—
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—201no—
609C2×C4—201no—
610C2×C4—201no—
611C2×C4—201no—
612C2×C4C2×#70911yescharacteristic
613C2×C4C2×#70911yescharacteristic
614C2×C4C2×D4×D511yescharacteristic
615C2×C4C2×#71111yescharacteristic
616C2×C4D5×#4111yescharacteristic
617C2×C4D5×#4111yescharacteristic
618C8—22no—
619C8—41no—
620C8—41no—
621C8—102no—
622C8—102no—
623C8—201no—
624C8—201no—
625C8#403114yes—
626C5#2163611yescharacteristic, complemented, Sylow
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—201no—
635C22—201no—
636C22—201no—
637C22—201no—
638C22—201no—
639C22—201no—
640C22—201no—
641C22C4×#70911yescharacteristic
642C22C4×#71111yescharacteristic
643C22C4×D4×D511yescharacteristic
644C22#6607911yescharacteristic
645C22#6607911yescharacteristic
646C22#6608411yescharacteristic
647C22#6608411yescharacteristic
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—102no—
654C4—102no—
655C4—201no—
656C4—201no—
657C4—201no—
658C4—201no—
659C4—201no—
660C4C2×#403111yescharacteristic
661C4#6586211yescharacteristic
662C4#6587211yescharacteristic
663C4#6588211yescharacteristic
664C2—81no—
665C2—401no—
666C2C4×#403111yescharacteristic
667C2#1061024111yescharacteristic
668C2#1061028811yescharacteristic
669C2#1061118611yescharacteristic
670C2#1061118711yescharacteristic
671C2#1061126811yescharacteristic
672C2#1061126811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1753C2
prime radicalC22×C22⋊D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1753D5
hypocenterC5#21636
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#64990C2semidirect
4. C5×#1753C2semidirect
5. #10602776C2semidirect
7. #10600707C2semidirect
8. #10600601C2semidirect
9. #10600574C2semidirect
10. #10600542C2semidirect
11. #10600245C2semidirect
12. #10599451C2semidirect
13. #10599413C2semidirect
14. #10599409C2semidirect
15. #10599399C2semidirect
146. #1753D5semidirect
626. C5#21636semidirect

Maximal subgroups

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

subgroupindex
C2×#654172
C2×#649902
#106052122
C5×#17532
#106027762
#106007102
#106007072
#106006012
#106005742
#106005422
#106002452
#105994512
#105994132
#105994092
#105993992
#216365