Finite Group Databasebeta

← C59×#18434 #28430543

Subgroups — C59×#18434 #28430543

Order 15104.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3560C211yesmaximal, characteristic, complemented
2C59×#3213C211yesmaximal, characteristic, complemented
3C59×#3211C211yesmaximal, characteristic, complemented
4C59×#2662C211yesmaximal, 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×#1509C211yesmaximal, characteristic, complemented
14C59×#1502C211yesmaximal, characteristic, complemented
15C59×#1473C211yesmaximal, characteristic, complemented
16C59×#563—21no—
17C59×#560—21no—
18C59×#553—21no—
19C59×#553—21no—
20C59×#551—21no—
21C59×#547—21no—
22C59×#546—21no—
23C59×#546—21no—
24C59×#542—21no—
25C59×#539—21no—
26C59×#539C2211yescharacteristic
27C59×#538—21no—
28C59×#538—21no—
29C59×#538C2211yescharacteristic
30C59×#537C2211yescharacteristic
31C59×#534C2211yescharacteristic
32C59×#532C2211yescharacteristic
33C59×#529C2211yescharacteristic
34C2×#126×C59C2211yescharacteristic
35C2×#124×C59C2211yescharacteristic, complemented
36C59×#496—21no—
37C59×#495—21no—
38C59×#489—21no—
39C59×#488—21no—
40C59×#464—21no—
41C59×#463—21no—
42C59×#463—21no—
43C59×#463—21no—
44C59×#451C2211yescharacteristic, complemented
45C59×#450C2211yescharacteristic, complemented
46C59×#448C2211yescharacteristic
47C59×#448C2211yescharacteristic
48C59×#448C2211yescharacteristic, complemented
49C59×#447C2211yescharacteristic
50C59×#447C2211yescharacteristic
51C59×#447C2211yescharacteristic, complemented
52C59×#432C2211yescharacteristic, complemented
53C59×#431C2211yescharacteristic, complemented
54C59×#396—21no—
55C59×#395C2211yescharacteristic, complemented
56C59×#394—21no—
57C59×#394C2211yescharacteristic, complemented
58C59×#393C2211yescharacteristic
59C59×#392C2211yescharacteristic
60C59×#390—21no—
61C59×#388—21no—
62C4×C4⋊C4×C59C2211yescharacteristic, complemented
63C59×#328C2211yescharacteristic, complemented
64C59×#328C2211yescharacteristic, complemented
65C59×#327C2211yescharacteristic
66C59×#327C2211yescharacteristic
67C59×#327C2211yescharacteristic
68C59×#327C2211yescharacteristic
69C59×#327C2211yescharacteristic, complemented
70C59×#327C2211yescharacteristic, complemented
71C59×#324C2211yescharacteristic, complemented
72C59×#324C2211yescharacteristic, complemented
73C59×#323C2211yescharacteristic
74C59×#323C2211yescharacteristic
75C2×#41×C59—21no—
76C2×#41×C59—21no—
77C22×Q8×C59C2311yescharacteristic
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59C2311yescharacteristic
81C2×Q16×C59—21no—
82C2×SD16×C59—21no—
83C2×SD16×C59—21no—
84C2×SD16×C59—21no—
85C2×SD16×C59—21no—
86C2×D8×C59—21no—
87C2×D8×C59—21no—
88C2×D8×C59—21no—
89C4⋊Q8×C59—21no—
90C4⋊Q8×C59D411yescharacteristic, complemented
91#127×C59D411yescharacteristic, complemented
92#126×C59—21no—
93#126×C59—21no—
94#126×C59—21no—
95#126×C59—21no—
96#126×C59—21no—
97#126×C59—21no—
98#126×C59—21no—
99#126×C59—21no—
100#126×C59—21no—
101#125×C59—21no—
102#125×C59—21no—
103#125×C59D411yescharacteristic, complemented
104#124×C59—21no—
105#124×C59—21no—
106#124×C59—21no—
107#124×C59—21no—
108#124×C59—21no—
109#124×C59—21no—
110#124×C59—21no—
111#124×C59—21no—
112#124×C59D411yescharacteristic, complemented
113#123×C59—21no—
114#123×C59—21no—
115#123×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—
125C22⋊Q8×C59—21no—
126C22⋊Q8×C59—21no—
127C22⋊Q8×C59—21no—
128C22⋊Q8×C59—21no—
129C22⋊Q8×C59—21no—
130C22⋊Q8×C59—21no—
131C22⋊Q8×C59—21no—
132C22⋊Q8×C59C2311yescharacteristic
133#121×C59—21no—
134#121×C59—21no—
135#121×C59—21no—
136#121×C59—21no—
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×C59C2311yescharacteristic
146#121×C59C2311yescharacteristic
147#121×C59C2311yescharacteristic
148#120×C59—21no—
149#120×C59—21no—
150#120×C59—21no—
151#120×C59—21no—
152#120×C59—21no—
153C4×Q8×C59D411yescharacteristic, complemented
154C4×D4×C59—21no—
155C4×D4×C59—21no—
156C4×D4×C59—21no—
157C4×D4×C59—21no—
158C4×D4×C59—21no—
159C4×D4×C59—21no—
160C4×D4×C59—21no—
161C4×D4×C59—21no—
162C4×D4×C59D411yescharacteristic, complemented
163C4×D4×C59D411yescharacteristic, complemented
164C4×D4×C59D411yescharacteristic, complemented
165#117×C59—21no—
166#117×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59D411yescharacteristic
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59D411yescharacteristic
183C2×C22⋊C4×C59C2311yescharacteristic
184C2×C42×C59—21no—
185C2×C42×C59C2311yescharacteristic
186C4⋊C8×C59—21no—
187C4⋊C8×C59—21no—
188#103×C59—21no—
189#103×C59—21no—
190#103×C59—21no—
191#103×C59—21no—
192#102×C59—21no—
193#102×C59—21no—
194#102×C59—21no—
195#102×C59—21no—
196C22⋊C8×C59C2311yescharacteristic
197C22⋊C8×C59C2311yescharacteristic
198C22⋊C8×C59C2311yescharacteristic
199C22⋊C8×C59C2311yescharacteristic
200#97×C59—21no—
201C4×C8×C59—21no—
202#95×C59—21no—
203#95×C59—21no—
204#95×C59C2311yescharacteristic
205#95×C59C2311yescharacteristic
206C24×C59—21no—
207C24×C59—21no—
208C24×C59C2×D411yescharacteristic
209#41×C59—81no—
210#41×C59—81no—
211#41×C59—81no—
212#41×C59—81no—
213C2×Q8×C59—21no—
214C2×Q8×C59—21no—
215C2×Q8×C59—21no—
216C2×Q8×C59—21no—
217C2×Q8×C59—81no—
218C2×Q8×C59C2×D411yescharacteristic
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59—21no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—21no—
228C2×D4×C59—21no—
229C2×D4×C59—21no—
230C2×D4×C59—21no—
231C2×D4×C59—21no—
232C2×D4×C59—21no—
233C2×D4×C59—42no—
234C2×D4×C59—81no—
235C2×D4×C59—81no—
236C2×D4×C59—81no—
237C2×D4×C59—81no—
238C2×D4×C59—81no—
239C2×D4×C59C2×D411yescharacteristic
240C2×D4×C59C2×D411yescharacteristic
241C2×D4×C59C2×D411yescharacteristic
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59C2×D411yescharacteristic
254C22×C4×C59C2×D411yescharacteristic
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D411yescharacteristic
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2411yescharacteristic
259Q16×C59—81no—
260SD16×C59—81no—
261SD16×C59—81no—
262SD16×C59—81no—
263SD16×C59—81no—
264D8×C59—81no—
265D8×C59—81no—
266D8×C59—81no—
267C2×C8×C59—21no—
268C2×C8×C59—21no—
269C2×C8×C59—21no—
270C2×C8×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59—21no—
273C4⋊C4×C59—21no—
274C4⋊C4×C59—21no—
275C4⋊C4×C59—21no—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—21no—
285C4⋊C4×C59—21no—
286C4⋊C4×C59—21no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59—42no—
289C4⋊C4×C59—81no—
290C4⋊C4×C59C2×D411yescharacteristic
291C4⋊C4×C59C2×D411yescharacteristic
292C4⋊C4×C59C2×D411yescharacteristic
293C4⋊C4×C59C2×D411yescharacteristic
294C22⋊C4×C59—21no—
295C22⋊C4×C59—21no—
296C22⋊C4×C59—21no—
297C22⋊C4×C59—21no—
298C22⋊C4×C59—21no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—21no—
302C22⋊C4×C59—21no—
303C22⋊C4×C59—21no—
304C22⋊C4×C59—21no—
305C22⋊C4×C59—21no—
306C22⋊C4×C59—21no—
307C22⋊C4×C59—21no—
308C22⋊C4×C59—21no—
309C22⋊C4×C59—21no—
310C22⋊C4×C59—21no—
311C22⋊C4×C59—21no—
312C22⋊C4×C59—21no—
313C22⋊C4×C59—21no—
314C22⋊C4×C59—21no—
315C22⋊C4×C59—21no—
316C22⋊C4×C59—21no—
317C22⋊C4×C59—21no—
318C22⋊C4×C59—21no—
319C22⋊C4×C59—42no—
320C22⋊C4×C59—41no—
321C22⋊C4×C59—41no—
322C22⋊C4×C59—41no—
323C22⋊C4×C59—41no—
324C22⋊C4×C59—81no—
325C22⋊C4×C59—81no—
326C22⋊C4×C59—81no—
327C42×C59—21no—
328C42×C59—21no—
329C42×C59—21no—
330C42×C59—81no—
331C42×C59C2×D411yescharacteristic
332C42×C59C2×D411yescharacteristic
333C42×C59C2×D411yescharacteristic
334C42×C59C2×D411yescharacteristic
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—21no—
339C23×C59—21no—
340C23×C59—21no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—81no—
351C23×C59—81no—
352C23×C59—81no—
353C23×C59C22×D411yescharacteristic
354Q8×C59—41no—
355Q8×C59—41no—
356Q8×C59—41no—
357Q8×C59—41no—
358Q8×C59—41no—
359Q8×C59—81no—
360Q8×C59—81no—
361D4×C59—41no—
362D4×C59—41no—
363D4×C59—41no—
364D4×C59—41no—
365D4×C59—41no—
366D4×C59—41no—
367D4×C59—41no—
368D4×C59—41no—
369D4×C59—41no—
370D4×C59—41no—
371D4×C59—41no—
372D4×C59—41no—
373D4×C59—41no—
374D4×C59—81no—
375D4×C59—81no—
376D4×C59—81no—
377D4×C59—81no—
378D4×C59—81no—
379D4×C59—81no—
380D4×C59—81no—
381D4×C59—81no—
382D4×C59—81no—
383D4×C59—84no—
384C2×C4×C59—21no—
385C2×C4×C59—21no—
386C2×C4×C59—22no—
387C2×C4×C59—21no—
388C2×C4×C59—21no—
389C2×C4×C59—21no—
390C2×C4×C59—21no—
391C2×C4×C59—21no—
392C2×C4×C59—21no—
393C2×C4×C59—21no—
394C2×C4×C59—21no—
395C2×C4×C59—21no—
396C2×C4×C59—21no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—81no—
410C2×C4×C59—81no—
411C2×C4×C59—81no—
412C2×C4×C59—81no—
413C2×C4×C59—81no—
414C2×C4×C59—81no—
415C2×C4×C59—81no—
416C2×C4×C59—81no—
417C2×C4×C59#12011yescharacteristic
418C2×C4×C59#12011yescharacteristic
419C2×C4×C59#12011yescharacteristic
420C2×C4×C59#12011yescharacteristic
421C2×C4×C59C22×D411yescharacteristic
422C2×C4×C59C22×D411yescharacteristic
423C8×C59—41no—
424C8×C59—41no—
425C8×C59—41no—
426C8×C59—41no—
427#18434C5911yesmaximal, characteristic, direct product factor, Sylow
428C22×C59—21no—
429C22×C59—21no—
430C22×C59—41no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—41no—
435C22×C59—41no—
436C22×C59—41no—
437C22×C59—41no—
438C22×C59—41no—
439C22×C59—41no—
440C22×C59—41no—
441C22×C59—41no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59—81no—
448C22×C59—81no—
449C22×C59—81no—
450C22×C59—81no—
451C22×C59—162no—
452C22×C59C2×#12011yescharacteristic
453C22×C59#57611yescharacteristic
454C22×C59#57711yescharacteristic
455C4×C59—21no—
456C4×C59—21no—
457C4×C59—21no—
458C4×C59—21no—
459C4×C59—21no—
460C4×C59—21no—
461C4×C59—42no—
462C4×C59—41no—
463C4×C59—41no—
464C4×C59—41no—
465C4×C59—41no—
466C4×C59—41no—
467C4×C59—41no—
468C4×C59—41no—
469C4×C59—41no—
470C4×C59—81no—
471C4×C59—81no—
472#3560C2×C5911yescharacteristic, complemented
473#3213C2×C5911yescharacteristic, complemented
474#3211C2×C5911yescharacteristic, complemented
475#2662C2×C5911yescharacteristic, complemented
476#1606C2×C5911yescharacteristic, complemented
477#1604C2×C5911yescharacteristic, complemented
478#1603C2×C5911yescharacteristic, complemented
479#1601C2×C5911yescharacteristic, complemented
480#1600C2×C5911yescharacteristic, complemented
481#1598C2×C5911yescharacteristic, complemented
482#1597C2×C5911yescharacteristic, complemented
483#1595C2×C5911yescharacteristic, complemented
484#1509C2×C5911yescharacteristic, complemented
485#1502C2×C5911yescharacteristic, complemented
486#1473C2×C5911yescharacteristic, complemented
487C2×C59—21no—
488C2×C59—21no—
489C2×C59—81no—
490C2×C59—81no—
491C2×C59—81no—
492C2×C59—81no—
493C2×C59—161no—
494C2×C59#301211yescharacteristic
495C2×C59#301811yescharacteristic
496C2×C59#302711yescharacteristic
497#563—21no—
498#560—21no—
499#553—21no—
500#553—21no—
501#551—21no—
502#547—21no—
503#546—21no—
504#546—21no—
505#542—21no—
506#539—21no—
507#539C22×C5911yescharacteristic
508#538—21no—
509#538—21no—
510#538C22×C5911yescharacteristic
511#537C22×C5911yescharacteristic
512#534C22×C5911yescharacteristic
513#532C22×C5911yescharacteristic
514#529C22×C5911yescharacteristic
515C2×#126C22×C5911yescharacteristic
516C2×#124C22×C5911yescharacteristic, complemented
517#496—21no—
518#495—21no—
519#489—21no—
520#488—21no—
521#464—21no—
522#463—21no—
523#463—21no—
524#463—21no—
525#451C22×C5911yescharacteristic, complemented
526#450C22×C5911yescharacteristic, complemented
527#448C22×C5911yescharacteristic
528#448C22×C5911yescharacteristic
529#448C22×C5911yescharacteristic, complemented
530#447C22×C5911yescharacteristic
531#447C22×C5911yescharacteristic
532#447C22×C5911yescharacteristic, complemented
533#432C22×C5911yescharacteristic, complemented
534#431C22×C5911yescharacteristic, complemented
535#396—21no—
536#395C22×C5911yescharacteristic, complemented
537#394—21no—
538#394C22×C5911yescharacteristic, complemented
539#393C22×C5911yescharacteristic
540#392C22×C5911yescharacteristic
541#390—21no—
542#388—21no—
543C4×C4⋊C4C22×C5911yescharacteristic, complemented
544#328C22×C5911yescharacteristic, complemented
545#328C22×C5911yescharacteristic, complemented
546#327C22×C5911yescharacteristic
547#327C22×C5911yescharacteristic
548#327C22×C5911yescharacteristic
549#327C22×C5911yescharacteristic
550#327C22×C5911yescharacteristic, complemented
551#327C22×C5911yescharacteristic, complemented
552#324C22×C5911yescharacteristic, complemented
553#324C22×C5911yescharacteristic, complemented
554#323C22×C5911yescharacteristic
555#323C22×C5911yescharacteristic
556C59#1843411yescharacteristic, direct product factor, Sylow
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C5911yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C5911yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C5911yescharacteristic, complemented
573#127D4×C5911yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C5911yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C5911yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C5911yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C5911yescharacteristic
628#121C23×C5911yescharacteristic
629#121C23×C5911yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C5911yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C5911yescharacteristic, complemented
645C4×D4D4×C5911yescharacteristic, complemented
646C4×D4D4×C5911yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C5911yescharacteristic
653C2×C4⋊C4D4×C5911yescharacteristic
654C2×C4⋊C4C23×C5911yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C5911yescharacteristic
664C2×C22⋊C4D4×C5911yescharacteristic
665C2×C22⋊C4C23×C5911yescharacteristic
666C2×C42—21no—
667C2×C42C23×C5911yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C5911yescharacteristic
679C22⋊C8C23×C5911yescharacteristic
680C22⋊C8C23×C5911yescharacteristic
681C22⋊C8C23×C5911yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C5911yescharacteristic
687#95C23×C5911yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C5911yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C5911yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C5911yescharacteristic
722C2×D4C2×D4×C5911yescharacteristic
723C2×D4C2×D4×C5911yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C5911yescharacteristic
736C22×C4C2×D4×C5911yescharacteristic
737C22×C4C2×D4×C5911yescharacteristic
738C22×C4C2×D4×C5911yescharacteristic
739C22×C4C2×D4×C5911yescharacteristic
740C22×C4C24×C5911yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C5911yescharacteristic
773C4⋊C4C2×D4×C5911yescharacteristic
774C4⋊C4C2×D4×C5911yescharacteristic
775C4⋊C4C2×D4×C5911yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C5911yescharacteristic
814C42C2×D4×C5911yescharacteristic
815C42C2×D4×C5911yescharacteristic
816C42C2×D4×C5911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C5911yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C5911yescharacteristic
900C2×C4#120×C5911yescharacteristic
901C2×C4#120×C5911yescharacteristic
902C2×C4#120×C5911yescharacteristic
903C2×C4C22×D4×C5911yescharacteristic
904C2×C4C22×D4×C5911yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C5911yescharacteristic
934C22C59×#57611yescharacteristic
935C22C59×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C59×#301211yescharacteristic
961C2C59×#301811yescharacteristic
962C2C59×#302711yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3560C2semidirect
2. C59×#3213C2semidirect
3. C59×#3211C2semidirect
4. C59×#2662C2semidirect
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×#1509C2semidirect
14. C59×#1502C2semidirect
15. C59×#1473C2semidirect
35. C2×#124×C59C22semidirect
44. C59×#451C22semidirect
45. C59×#450C22semidirect
48. C59×#448C22semidirect
51. C59×#447C22semidirect
52. C59×#432C22semidirect
53. C59×#431C22semidirect
55. C59×#395C22semidirect
57. C59×#394C22semidirect
62. C4×C4⋊C4×C59C22semidirect
63. C59×#328C22semidirect
64. C59×#328C22semidirect
69. C59×#327C22semidirect
70. C59×#327C22semidirect
71. C59×#324C22semidirect
72. C59×#324C22semidirect
90. C4⋊Q8×C59D4semidirect
91. #127×C59D4semidirect
103. #125×C59D4semidirect
112. #124×C59D4semidirect
153. C4×Q8×C59D4semidirect
162. C4×D4×C59D4semidirect
163. C4×D4×C59D4semidirect
164. C4×D4×C59D4semidirect
427. #18434C59direct (N × H)
472. #3560C2×C59semidirect
473. #3213C2×C59semidirect
474. #3211C2×C59semidirect
475. #2662C2×C59semidirect
476. #1606C2×C59semidirect
477. #1604C2×C59semidirect
478. #1603C2×C59semidirect
479. #1601C2×C59semidirect
480. #1600C2×C59semidirect
481. #1598C2×C59semidirect
482. #1597C2×C59semidirect
483. #1595C2×C59semidirect
484. #1509C2×C59semidirect
485. #1502C2×C59semidirect
486. #1473C2×C59semidirect
516. C2×#124C22×C59semidirect
525. #451C22×C59semidirect
526. #450C22×C59semidirect
529. #448C22×C59semidirect
532. #447C22×C59semidirect
533. #432C22×C59semidirect
534. #431C22×C59semidirect
536. #395C22×C59semidirect
538. #394C22×C59semidirect
543. C4×C4⋊C4C22×C59semidirect
544. #328C22×C59semidirect
545. #328C22×C59semidirect
550. #327C22×C59semidirect
551. #327C22×C59semidirect
552. #324C22×C59semidirect
553. #324C22×C59semidirect
556. C59#18434direct (N × H)
572. C4⋊Q8D4×C59semidirect
573. #127D4×C59semidirect
585. #125D4×C59semidirect
594. #124D4×C59semidirect
635. C4×Q8D4×C59semidirect
644. C4×D4D4×C59semidirect
645. C4×D4D4×C59semidirect
646. C4×D4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35602
C59×#32132
C59×#32112
C59×#26622
C59×#16062
C59×#16042
C59×#16032
C59×#16012
C59×#16002
C59×#15982
C59×#15972
C59×#15952
C59×#15092
C59×#15022
C59×#14732
#1843459