Finite Group Databasebeta

← C59×#18252 #28430361

Subgroups — C59×#18252 #28430361

Order 15104.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3534C211yesmaximal, characteristic, complemented
2C59×#3006C211yesmaximal, characteristic, complemented
3C59×#3002C211yesmaximal, characteristic, complemented
4C59×#2430C211yesmaximal, characteristic, complemented
5C59×#1606C211yesmaximal, characteristic, complemented
6C59×#1604C211yesmaximal, characteristic, complemented
7C59×#1603C211yesmaximal, characteristic, complemented
8C59×#1601C211yesmaximal, characteristic, complemented
9C59×#1600C211yesmaximal, characteristic, complemented
10C59×#1598C211yesmaximal, characteristic, complemented
11C59×#1597C211yesmaximal, characteristic, complemented
12C59×#1595C211yesmaximal, characteristic, complemented
13C59×#1504C211yesmaximal, characteristic, complemented
14C2×C59×#327C211yesmaximal, characteristic, complemented
15C59×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C59—21no—
18C2×#135×C59—21no—
19C59×#562—21no—
20C59×#560—21no—
21C59×#553—21no—
22C59×#551—21no—
23C59×#546—21no—
24C59×#546—21no—
25C59×#546—21no—
26D42×C59—21no—
27C59×#540—21no—
28C59×#539—21no—
29C59×#539C2211yescharacteristic
30C59×#538—21no—
31C59×#538C2211yescharacteristic
32C59×#537C2211yescharacteristic
33C59×#534—21no—
34C59×#534C2211yescharacteristic
35C59×#525C2211yescharacteristic
36C2×#123×C59C2211yescharacteristic
37C2×#121×C59—21no—
38C2×#121×C59C2211yescharacteristic
39C59×#452—21no—
40C59×#451C2211yescharacteristic, complemented
41C59×#450C2211yescharacteristic, complemented
42C59×#449—21no—
43C59×#449—21no—
44C59×#449—21no—
45C59×#448C2211yescharacteristic
46C59×#448C2211yescharacteristic, complemented
47C59×#448C2211yescharacteristic, complemented
48C59×#447C2211yescharacteristic
49C59×#447C2211yescharacteristic, complemented
50C59×#447C2211yescharacteristic, complemented
51C59×#417—21no—
52C59×#416—21no—
53C59×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C59C2211yescharacteristic, complemented
55C59×#395C2211yescharacteristic, complemented
56C59×#394C2211yescharacteristic, complemented
57C59×#393C2211yescharacteristic, complemented
58C59×#392C2211yescharacteristic, complemented
59C59×#386—21no—
60C59×#386—21no—
61C59×#385—21no—
62C2×#95×C59C2211yescharacteristic, complemented
63C59×#328C2211yescharacteristic, complemented
64C59×#328C2211yescharacteristic, complemented
65C59×#327C2211yescharacteristic
66C59×#327C2211yescharacteristic
67C59×#327C2211yescharacteristic, complemented
68C59×#327C2211yescharacteristic, complemented
69C59×#327C2211yescharacteristic, complemented
70C59×#327C2211yescharacteristic, complemented
71C59×#324C2211yescharacteristic, complemented
72C59×#324C2211yescharacteristic, complemented
73C59×#323C2211yescharacteristic, complemented
74C59×#323C2211yescharacteristic, complemented
75C2×#41×C59—21no—
76C2×#41×C59—21no—
77C2×#41×C59—21no—
78C2×#41×C59—21no—
79C2×#41×C59—21no—
80C2×#41×C59—44no—
81C2×#41×C59D411yescharacteristic, complemented
82C22×Q8×C59C2311yescharacteristic
83C22×D4×C59—21no—
84C22×D4×C59—21no—
85C22×D4×C59—21no—
86C22×D4×C59—21no—
87C22×D4×C59—21no—
88C22×D4×C59D411yescharacteristic
89C22×D4×C59D411yescharacteristic, complemented
90C22×D4×C59C2311yescharacteristic
91C23×C4×C59—21no—
92C23×C4×C59—21no—
93C23×C4×C59C2311yescharacteristic
94AGL(1,ℤ/8)×C59—44no—
95#135×C59—44no—
96C2×Q16×C59—21no—
97C2×SD16×C59—21no—
98C2×SD16×C59—21no—
99C2×SD16×C59—21no—
100C2×SD16×C59—21no—
101C2×D8×C59—21no—
102C2×D8×C59—21no—
103C2×D8×C59—21no—
104C2×M16×C59—21no—
105C22×C8×C59—21no—
106#127×C59—21no—
107#126×C59—21no—
108#126×C59—21no—
109#126×C59—21no—
110#126×C59—21no—
111#125×C59—21no—
112#125×C59—21no—
113#124×C59—21no—
114#124×C59—21no—
115#124×C59—21no—
116#123×C59—21no—
117#123×C59—21no—
118#123×C59—21no—
119#123×C59—21no—
120#123×C59—21no—
121#123×C59—21no—
122#123×C59—21no—
123#123×C59—21no—
124#123×C59—21no—
125#123×C59—21no—
126#123×C59—21no—
127#123×C59—21no—
128#123×C59—21no—
129#123×C59—21no—
130C22⋊Q8×C59—21no—
131C22⋊Q8×C59—21no—
132C22⋊Q8×C59—21no—
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59D411yescharacteristic, complemented
136C22⋊Q8×C59C2311yescharacteristic
137#121×C59—21no—
138#121×C59—21no—
139#121×C59—21no—
140#121×C59—21no—
141#121×C59—21no—
142#121×C59—21no—
143#121×C59—21no—
144#121×C59—21no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—21no—
149#121×C59—21no—
150#121×C59—21no—
151#121×C59—21no—
152#121×C59—44no—
153#121×C59D411yescharacteristic, complemented
154#121×C59D411yescharacteristic, complemented
155#121×C59D411yescharacteristic, complemented
156#121×C59C2311yescharacteristic
157#121×C59C2311yescharacteristic
158#121×C59C2311yescharacteristic
159#120×C59—21no—
160#120×C59—21no—
161#120×C59—21no—
162#120×C59—21no—
163#120×C59—21no—
164#120×C59—21no—
165#120×C59—21no—
166#120×C59—21no—
167C4×D4×C59—21no—
168C4×D4×C59—21no—
169C4×D4×C59—21no—
170C4×D4×C59—21no—
171C4×D4×C59—21no—
172C4×D4×C59—21no—
173C4×D4×C59—21no—
174C4×D4×C59—21no—
175#117×C59—21no—
176#117×C59D411yescharacteristic, complemented
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59D411yescharacteristic
179C2×C4⋊C4×C59D411yescharacteristic, complemented
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182C2×C22⋊C4×C59—21no—
183C2×C22⋊C4×C59—21no—
184C2×C22⋊C4×C59—21no—
185C2×C22⋊C4×C59—21no—
186C2×C22⋊C4×C59—21no—
187C2×C22⋊C4×C59—21no—
188C2×C22⋊C4×C59D411yescharacteristic
189C2×C22⋊C4×C59D411yescharacteristic
190C2×C22⋊C4×C59C2311yescharacteristic
191#103×C59—21no—
192#103×C59—21no—
193#103×C59—21no—
194#103×C59—21no—
195#102×C59—21no—
196#102×C59—21no—
197#102×C59—21no—
198#102×C59—21no—
199C22⋊C8×C59—21no—
200C22⋊C8×C59—21no—
201C22⋊C8×C59C2311yescharacteristic
202C22⋊C8×C59C2311yescharacteristic
203C22⋊C8×C59C2311yescharacteristic
204C22⋊C8×C59C2311yescharacteristic
205#95×C59—21no—
206#95×C59—21no—
207#95×C59—21no—
208#95×C59C2311yescharacteristic
209#95×C59C2311yescharacteristic
210C24×C59—21no—
211C24×C59—21no—
212C24×C59—21no—
213C24×C59C2×D411yescharacteristic
214C24×C59C2×D411yescharacteristic
215#41×C59—24no—
216#41×C59—24no—
217#41×C59—42no—
218#41×C59—42no—
219#41×C59—42no—
220#41×C59—42no—
221#41×C59—42no—
222#41×C59—42no—
223#41×C59—42no—
224#41×C59—81no—
225#41×C59—81no—
226C2×Q8×C59—21no—
227C2×Q8×C59—21no—
228C2×Q8×C59—21no—
229C2×Q8×C59—42no—
230C2×Q8×C59C2×D411yescharacteristic
231C2×D4×C59—24no—
232C2×D4×C59—21no—
233C2×D4×C59—21no—
234C2×D4×C59—21no—
235C2×D4×C59—21no—
236C2×D4×C59—21no—
237C2×D4×C59—21no—
238C2×D4×C59—21no—
239C2×D4×C59—21no—
240C2×D4×C59—21no—
241C2×D4×C59—21no—
242C2×D4×C59—21no—
243C2×D4×C59—21no—
244C2×D4×C59—21no—
245C2×D4×C59—21no—
246C2×D4×C59—21no—
247C2×D4×C59—21no—
248C2×D4×C59—21no—
249C2×D4×C59—21no—
250C2×D4×C59—21no—
251C2×D4×C59—42no—
252C2×D4×C59—42no—
253C2×D4×C59—42no—
254C2×D4×C59—42no—
255C2×D4×C59—41no—
256C2×D4×C59—41no—
257C2×D4×C59—42no—
258C2×D4×C59—42no—
259C2×D4×C59—81no—
260C2×D4×C59—81no—
261C2×D4×C59—81no—
262C2×D4×C59—81no—
263C2×D4×C59—81no—
264C2×D4×C59—82no—
265C2×D4×C59C2×D411yescharacteristic
266C2×D4×C59C2×D411yescharacteristic
267C2×D4×C59C2×D411yescharacteristic
268C22×C4×C59—21no—
269C22×C4×C59—21no—
270C22×C4×C59—21no—
271C22×C4×C59—21no—
272C22×C4×C59—21no—
273C22×C4×C59—21no—
274C22×C4×C59—21no—
275C22×C4×C59—21no—
276C22×C4×C59—21no—
277C22×C4×C59—21no—
278C22×C4×C59—42no—
279C22×C4×C59—42no—
280C22×C4×C59—42no—
281C22×C4×C59—42no—
282C22×C4×C59—41no—
283C22×C4×C59—41no—
284C22×C4×C59—42no—
285C22×C4×C59—81no—
286C22×C4×C59C2×D411yescharacteristic
287C22×C4×C59C2×D411yescharacteristic
288C22×C4×C59C2×D411yescharacteristic
289C22×C4×C59C2×D411yescharacteristic
290C22×C4×C59C2×D411yescharacteristic
291C22×C4×C59C2×D411yescharacteristic
292C22×C4×C59C2×D411yescharacteristic
293C22×C4×C59C2×D411yescharacteristic
294C22×C4×C59C2411yescharacteristic
295Q16×C59—42no—
296SD16×C59—42no—
297SD16×C59—42no—
298SD16×C59—42no—
299SD16×C59—42no—
300D8×C59—42no—
301D8×C59—42no—
302D8×C59—42no—
303M16×C59—42no—
304C2×C8×C59—21no—
305C2×C8×C59—21no—
306C2×C8×C59—21no—
307C2×C8×C59—21no—
308C2×C8×C59—42no—
309C4⋊C4×C59—21no—
310C4⋊C4×C59—21no—
311C4⋊C4×C59—21no—
312C4⋊C4×C59—21no—
313C4⋊C4×C59—21no—
314C4⋊C4×C59—21no—
315C4⋊C4×C59—21no—
316C4⋊C4×C59—21no—
317C4⋊C4×C59—21no—
318C4⋊C4×C59—21no—
319C4⋊C4×C59—21no—
320C4⋊C4×C59—21no—
321C4⋊C4×C59—21no—
322C4⋊C4×C59—42no—
323C4⋊C4×C59C2×D411yescharacteristic
324C4⋊C4×C59C2×D411yescharacteristic
325C4⋊C4×C59C2×D411yescharacteristic
326C4⋊C4×C59C2×D411yescharacteristic
327C22⋊C4×C59—21no—
328C22⋊C4×C59—21no—
329C22⋊C4×C59—21no—
330C22⋊C4×C59—21no—
331C22⋊C4×C59—21no—
332C22⋊C4×C59—21no—
333C22⋊C4×C59—21no—
334C22⋊C4×C59—21no—
335C22⋊C4×C59—21no—
336C22⋊C4×C59—21no—
337C22⋊C4×C59—21no—
338C22⋊C4×C59—21no—
339C22⋊C4×C59—21no—
340C22⋊C4×C59—21no—
341C22⋊C4×C59—21no—
342C22⋊C4×C59—21no—
343C22⋊C4×C59—21no—
344C22⋊C4×C59—21no—
345C22⋊C4×C59—21no—
346C22⋊C4×C59—21no—
347C22⋊C4×C59—21no—
348C22⋊C4×C59—21no—
349C22⋊C4×C59—21no—
350C22⋊C4×C59—21no—
351C22⋊C4×C59—21no—
352C22⋊C4×C59—42no—
353C22⋊C4×C59—42no—
354C22⋊C4×C59—42no—
355C22⋊C4×C59—81no—
356C42×C59—21no—
357C42×C59—21no—
358C42×C59—21no—
359C23×C59—21no—
360C23×C59—21no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—21no—
364C23×C59—21no—
365C23×C59—21no—
366C23×C59—21no—
367C23×C59—21no—
368C23×C59—21no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—42no—
379C23×C59—81no—
380C23×C59—81no—
381C23×C59—81no—
382C23×C59—81no—
383C23×C59—81no—
384C23×C59#12011yescharacteristic
385C23×C59#12011yescharacteristic
386C23×C59C22×D411yescharacteristic
387Q8×C59—22no—
388Q8×C59—22no—
389Q8×C59—41no—
390Q8×C59—41no—
391Q8×C59—41no—
392Q8×C59—81no—
393D4×C59—22no—
394D4×C59—22no—
395D4×C59—41no—
396D4×C59—41no—
397D4×C59—41no—
398D4×C59—41no—
399D4×C59—41no—
400D4×C59—44no—
401D4×C59—41no—
402D4×C59—41no—
403D4×C59—41no—
404D4×C59—41no—
405D4×C59—41no—
406D4×C59—41no—
407D4×C59—44no—
408D4×C59—42no—
409D4×C59—42no—
410D4×C59—81no—
411D4×C59—81no—
412D4×C59—81no—
413D4×C59—81no—
414D4×C59—81no—
415D4×C59—81no—
416D4×C59—81no—
417D4×C59—81no—
418D4×C59—81no—
419D4×C59—81no—
420D4×C59—81no—
421D4×C59—81no—
422D4×C59—84no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—21no—
428C2×C4×C59—21no—
429C2×C4×C59—21no—
430C2×C4×C59—21no—
431C2×C4×C59—21no—
432C2×C4×C59—21no—
433C2×C4×C59—21no—
434C2×C4×C59—21no—
435C2×C4×C59—21no—
436C2×C4×C59—21no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—44no—
442C2×C4×C59—44no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—41no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—81no—
453C2×C4×C59—81no—
454C2×C4×C59—81no—
455C2×C4×C59—81no—
456C2×C4×C59—81no—
457C2×C4×C59—81no—
458C2×C4×C59—81no—
459C2×C4×C59—84no—
460C2×C4×C59#12011yescharacteristic
461C2×C4×C59#12011yescharacteristic
462C2×C4×C59C22×D411yescharacteristic
463C2×C4×C59C22×D411yescharacteristic
464C8×C59—41no—
465C8×C59—41no—
466C8×C59—41no—
467C8×C59—41no—
468#18252C5911yesmaximal, characteristic, direct product factor, Sylow
469C22×C59—21no—
470C22×C59—21no—
471C22×C59—21no—
472C22×C59—21no—
473C22×C59—21no—
474C22×C59—21no—
475C22×C59—21no—
476C22×C59—42no—
477C22×C59—42no—
478C22×C59—42no—
479C22×C59—42no—
480C22×C59—41no—
481C22×C59—41no—
482C22×C59—41no—
483C22×C59—41no—
484C22×C59—41no—
485C22×C59—41no—
486C22×C59—41no—
487C22×C59—41no—
488C22×C59—42no—
489C22×C59—41no—
490C22×C59—41no—
491C22×C59—41no—
492C22×C59—41no—
493C22×C59—81no—
494C22×C59—81no—
495C22×C59—81no—
496C22×C59—81no—
497C22×C59—81no—
498C22×C59—81no—
499C22×C59—162no—
500C22×C59—162no—
501C22×C59B(4,𝔽2)12yes—
502C22×C59C2×#12011yescharacteristic
503C22×C59#57611yescharacteristic
504C22×C59#57711yescharacteristic
505C4×C59—21no—
506C4×C59—21no—
507C4×C59—21no—
508C4×C59—21no—
509C4×C59—42no—
510C4×C59—41no—
511C4×C59—41no—
512C4×C59—41no—
513C4×C59—41no—
514C4×C59—41no—
515C4×C59—41no—
516C4×C59—42no—
517C4×C59—41no—
518C4×C59—41no—
519C4×C59—81no—
520#3534C2×C5911yescharacteristic, complemented
521#3006C2×C5911yescharacteristic, complemented
522#3002C2×C5911yescharacteristic, complemented
523#2430C2×C5911yescharacteristic, complemented
524#1606C2×C5911yescharacteristic, complemented
525#1604C2×C5911yescharacteristic, complemented
526#1603C2×C5911yescharacteristic, complemented
527#1601C2×C5911yescharacteristic, complemented
528#1600C2×C5911yescharacteristic, complemented
529#1598C2×C5911yescharacteristic, complemented
530#1597C2×C5911yescharacteristic, complemented
531#1595C2×C5911yescharacteristic, complemented
532#1504C2×C5911yescharacteristic, complemented
533C2×#327C2×C5911yescharacteristic, complemented
534#1468C2×C5911yescharacteristic, complemented
535C2×C59—21no—
536C2×C59—21no—
537C2×C59—22no—
538C2×C59—41no—
539C2×C59—82no—
540C2×C59—81no—
541C2×C59—81no—
542C2×C59—81no—
543C2×C59—81no—
544C2×C59#301211yescharacteristic
545C2×C59#301811yescharacteristic
546C2×C59C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C5911yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C5911yescharacteristic
561#538—21no—
562#538C22×C5911yescharacteristic
563#537C22×C5911yescharacteristic
564#534—21no—
565#534C22×C5911yescharacteristic
566#525C22×C5911yescharacteristic
567C2×#123C22×C5911yescharacteristic
568C2×#121—21no—
569C2×#121C22×C5911yescharacteristic
570#452—21no—
571#451C22×C5911yescharacteristic, complemented
572#450C22×C5911yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C5911yescharacteristic
577#448C22×C5911yescharacteristic, complemented
578#448C22×C5911yescharacteristic, complemented
579#447C22×C5911yescharacteristic
580#447C22×C5911yescharacteristic, complemented
581#447C22×C5911yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C5911yescharacteristic, complemented
585C2×C22⋊C8C22×C5911yescharacteristic, complemented
586#395C22×C5911yescharacteristic, complemented
587#394C22×C5911yescharacteristic, complemented
588#393C22×C5911yescharacteristic, complemented
589#392C22×C5911yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C5911yescharacteristic, complemented
594#328C22×C5911yescharacteristic, complemented
595#328C22×C5911yescharacteristic, complemented
596#327C22×C5911yescharacteristic
597#327C22×C5911yescharacteristic
598#327C22×C5911yescharacteristic, complemented
599#327C22×C5911yescharacteristic, complemented
600#327C22×C5911yescharacteristic, complemented
601#327C22×C5911yescharacteristic, complemented
602#324C22×C5911yescharacteristic, complemented
603#324C22×C5911yescharacteristic, complemented
604#323C22×C5911yescharacteristic, complemented
605#323C22×C5911yescharacteristic, complemented
606C59#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C5911yescharacteristic, complemented
614C22×Q8C23×C5911yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C5911yescharacteristic
621C22×D4D4×C5911yescharacteristic, complemented
622C22×D4C23×C5911yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C5911yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C5911yescharacteristic, complemented
668C22⋊Q8C23×C5911yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C5911yescharacteristic, complemented
686#121D4×C5911yescharacteristic, complemented
687#121D4×C5911yescharacteristic, complemented
688#121C23×C5911yescharacteristic
689#121C23×C5911yescharacteristic
690#121C23×C5911yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C5911yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C5911yescharacteristic
711C2×C4⋊C4D4×C5911yescharacteristic, complemented
712C2×C4⋊C4C23×C5911yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C5911yescharacteristic
721C2×C22⋊C4D4×C5911yescharacteristic
722C2×C22⋊C4C23×C5911yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C5911yescharacteristic
734C22⋊C8C23×C5911yescharacteristic
735C22⋊C8C23×C5911yescharacteristic
736C22⋊C8C23×C5911yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C5911yescharacteristic
741#95C23×C5911yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C5911yescharacteristic
746C24C2×D4×C5911yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C5911yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C5911yescharacteristic
798C2×D4C2×D4×C5911yescharacteristic
799C2×D4C2×D4×C5911yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C5911yescharacteristic
819C22×C4C2×D4×C5911yescharacteristic
820C22×C4C2×D4×C5911yescharacteristic
821C22×C4C2×D4×C5911yescharacteristic
822C22×C4C2×D4×C5911yescharacteristic
823C22×C4C2×D4×C5911yescharacteristic
824C22×C4C2×D4×C5911yescharacteristic
825C22×C4C2×D4×C5911yescharacteristic
826C22×C4C24×C5911yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C5911yescharacteristic
856C4⋊C4C2×D4×C5911yescharacteristic
857C4⋊C4C2×D4×C5911yescharacteristic
858C4⋊C4C2×D4×C5911yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C5911yescharacteristic
917C23#120×C5911yescharacteristic
918C23C22×D4×C5911yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C5911yescharacteristic
993C2×C4#120×C5911yescharacteristic
994C2×C4C22×D4×C5911yescharacteristic
995C2×C4C22×D4×C5911yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C59×B(4,𝔽2)12yes—
1033C22C2×#120×C5911yescharacteristic
1034C22C59×#57611yescharacteristic
1035C22C59×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C59×#301211yescharacteristic
1061C2C59×#301811yescharacteristic
1062C2C2×C59×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3534C2semidirect
2. C59×#3006C2semidirect
3. C59×#3002C2semidirect
4. C59×#2430C2semidirect
5. C59×#1606C2semidirect
6. C59×#1604C2semidirect
7. C59×#1603C2semidirect
8. C59×#1601C2semidirect
9. C59×#1600C2semidirect
10. C59×#1598C2semidirect
11. C59×#1597C2semidirect
12. C59×#1595C2semidirect
13. C59×#1504C2semidirect
14. C2×C59×#327C2semidirect
15. C59×#1468C2semidirect
16. C22×#41×C59C22semidirect
40. C59×#451C22semidirect
41. C59×#450C22semidirect
46. C59×#448C22semidirect
47. C59×#448C22semidirect
49. C59×#447C22semidirect
50. C59×#447C22semidirect
53. C59×#407C22semidirect
54. C2×C22⋊C8×C59C22semidirect
55. C59×#395C22semidirect
56. C59×#394C22semidirect
57. C59×#393C22semidirect
58. C59×#392C22semidirect
62. C2×#95×C59C22semidirect
63. C59×#328C22semidirect
64. C59×#328C22semidirect
67. C59×#327C22semidirect
68. C59×#327C22semidirect
69. C59×#327C22semidirect
70. C59×#327C22semidirect
71. C59×#324C22semidirect
72. C59×#324C22semidirect
73. C59×#323C22semidirect
74. C59×#323C22semidirect
81. C2×#41×C59D4semidirect
89. C22×D4×C59D4semidirect
135. C22⋊Q8×C59D4semidirect
153. #121×C59D4semidirect
154. #121×C59D4semidirect
155. #121×C59D4semidirect
176. #117×C59D4semidirect
179. C2×C4⋊C4×C59D4semidirect
468. #18252C59direct (N × H)
520. #3534C2×C59semidirect
521. #3006C2×C59semidirect
522. #3002C2×C59semidirect
523. #2430C2×C59semidirect
524. #1606C2×C59semidirect
525. #1604C2×C59semidirect
526. #1603C2×C59semidirect
527. #1601C2×C59semidirect
528. #1600C2×C59semidirect
529. #1598C2×C59semidirect
530. #1597C2×C59semidirect
531. #1595C2×C59semidirect
532. #1504C2×C59semidirect
533. C2×#327C2×C59semidirect
534. #1468C2×C59semidirect
547. C22×#41C22×C59semidirect
571. #451C22×C59semidirect
572. #450C22×C59semidirect
577. #448C22×C59semidirect
578. #448C22×C59semidirect
580. #447C22×C59semidirect
581. #447C22×C59semidirect
584. #407C22×C59semidirect
585. C2×C22⋊C8C22×C59semidirect
586. #395C22×C59semidirect
587. #394C22×C59semidirect
588. #393C22×C59semidirect
589. #392C22×C59semidirect
593. C2×#95C22×C59semidirect
594. #328C22×C59semidirect
595. #328C22×C59semidirect
598. #327C22×C59semidirect
599. #327C22×C59semidirect
600. #327C22×C59semidirect
601. #327C22×C59semidirect
602. #324C22×C59semidirect
603. #324C22×C59semidirect
604. #323C22×C59semidirect
605. #323C22×C59semidirect
606. C59#18252direct (N × H)
613. C2×#41D4×C59semidirect
621. C22×D4D4×C59semidirect
667. C22⋊Q8D4×C59semidirect
685. #121D4×C59semidirect
686. #121D4×C59semidirect
687. #121D4×C59semidirect
708. #117D4×C59semidirect
711. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35342
C59×#30062
C59×#30022
C59×#24302
C59×#16062
C59×#16042
C59×#16032
C59×#16012
C59×#16002
C59×#15982
C59×#15972
C59×#15952
C59×#15042
C2×C59×#3272
C59×#14682
#1825259