Finite Group Databasebeta

← C59×#33552 #28445661

Subgroups — C59×#33552 #28445661

Order 15104.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3533C211yesmaximal, characteristic, complemented
2C59×#3026C211yesmaximal, characteristic, complemented
3C2×C59×#458C211yesmaximal, characteristic, complemented
4C59×#3019C211yesmaximal, characteristic, complemented
5C59×#2201C212yesmaximal, complemented
6C59×#2200C212yesmaximal, complemented
7C59×#2198C212yesmaximal, complemented
8C59×#2197C212yesmaximal, complemented
9C59×#2127C211yesmaximal, characteristic, complemented
10C59×#2121C211yesmaximal, characteristic, complemented
11C2×C59×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C59C2211yescharacteristic
13C59×#575—21no—
14C59×#563C2211yescharacteristic, complemented
15C59×#562—21no—
16C59×#560C2211yescharacteristic, complemented
17C59×#559C2211yescharacteristic, complemented
18C59×#553—21no—
19C59×#552—21no—
20C59×#551—21no—
21C59×#551C2211yescharacteristic, complemented
22C59×#547—21no—
23C59×#546—21no—
24C59×#542—21no—
25C59×#540—21no—
26C59×#539—21no—
27C59×#538—21no—
28C59×#538—21no—
29C59×#535C2211yescharacteristic
30C59×#534—21no—
31C59×#534C2211yescharacteristic
32C59×#525—21no—
33C2×#123×C59—21no—
34C2×#123×C59C2211yescharacteristic
35C59×#458—21no—
36C59×#458—21no—
37C59×#458—21no—
38C59×#458C2212yes—
39C59×#458C2212yes—
40C59×#458C2212yes—
41C59×B(4,𝔽2)—21no—
42C59×B(4,𝔽2)C2212yes—
43C59×#455—21no—
44C59×#455C2212yes—
45C59×#453—21no—
46C59×#453C2212yes—
47C59×#421—21no—
48C2×#100×C59C2211yescharacteristic
49C2×#99×C59—21no—
50C2×#99×C59—21no—
51C2×#99×C59C2211yescharacteristic
52C2×#99×C59C2211yescharacteristic
53C59×#354C2212yescomplemented
54C59×#353C2212yescomplemented
55C59×#352C2212yescomplemented
56C59×#352C2212yescomplemented
57C59×#352C2212yescomplemented
58C59×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C59—21no—
60H(5,𝔽2)×C59—21no—
61H(5,𝔽2)×C59—21no—
62H(5,𝔽2)×C59—42no—
63H(5,𝔽2)×C59C2312yes—
64C2×#41×C59—21no—
65C2×#41×C59—21no—
66C2×#41×C59—41no—
67C2×#41×C59D411yescharacteristic, complemented
68C22×D4×C59—21no—
69C22×D4×C59—21no—
70C22×D4×C59—41no—
71C22×D4×C59D411yescharacteristic
72C22×D4×C59C2311yescharacteristic
73C23×C4×C59D411yescharacteristic, complemented
74#137×C59—22no—
75#137×C59—41no—
76AGL(1,ℤ/8)×C59—22no—
77AGL(1,ℤ/8)×C59—41no—
78#135×C59—42no—
79C2×M16×C59—21no—
80C4⋊Q8×C59—21no—
81#127×C59D411yescharacteristic, complemented
82#127×C59C2311yescharacteristic
83#126×C59—21no—
84#126×C59—21no—
85#126×C59—21no—
86#126×C59—21no—
87#126×C59—21no—
88#126×C59—21no—
89#125×C59—21no—
90#125×C59—21no—
91#125×C59—21no—
92#124×C59—21no—
93#124×C59—21no—
94#124×C59—21no—
95#124×C59—21no—
96#124×C59D411yescharacteristic, complemented
97#124×C59C2311yescharacteristic
98#123×C59—21no—
99#123×C59—21no—
100#123×C59—21no—
101#123×C59—21no—
102#123×C59—21no—
103#123×C59—21no—
104#123×C59—21no—
105#123×C59—21no—
106#123×C59—21no—
107#123×C59—21no—
108#123×C59—21no—
109#123×C59—21no—
110#123×C59—22no—
111#123×C59—22no—
112#123×C59—22no—
113#123×C59—41no—
114#123×C59—42no—
115#123×C59D411yescharacteristic
116#123×C59D411yescharacteristic, complemented
117#123×C59D411yescharacteristic, complemented
118#123×C59C2311yescharacteristic
119#123×C59C2311yescharacteristic
120#123×C59C2311yescharacteristic
121C22⋊Q8×C59—21no—
122C22⋊Q8×C59—21no—
123C22⋊Q8×C59—21no—
124C22⋊Q8×C59—21no—
125C22⋊Q8×C59—21no—
126C22⋊Q8×C59—21no—
127C22⋊Q8×C59—21no—
128C22⋊Q8×C59—21no—
129#121×C59—21no—
130#121×C59—21no—
131#121×C59—21no—
132#121×C59—21no—
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—42no—
142#120×C59—21no—
143#120×C59—21no—
144#120×C59—21no—
145#120×C59—21no—
146#120×C59—22no—
147#120×C59—41no—
148#120×C59D411yescharacteristic
149#120×C59C2311yescharacteristic
150C4×Q8×C59—21no—
151C4×D4×C59—21no—
152C4×D4×C59—21no—
153C4×D4×C59—21no—
154C4×D4×C59—21no—
155C4×D4×C59—21no—
156C4×D4×C59—21no—
157C4×D4×C59—21no—
158C4×D4×C59—21no—
159C4×D4×C59—21no—
160#117×C59—21no—
161#117×C59—21no—
162#117×C59—21no—
163#117×C59D411yescharacteristic, complemented
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—41no—
167C2×C22⋊C4×C59—21no—
168C2×C22⋊C4×C59—21no—
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59—41no—
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59D411yescharacteristic, complemented
174#104×C59—22no—
175#104×C59—22no—
176#100×C59—21no—
177#100×C59C2312yes—
178#99×C59—21no—
179#99×C59—21no—
180#99×C59—22no—
181#99×C59—22no—
182#99×C59—22no—
183#99×C59—22no—
184#99×C59C2312yes—
185#99×C59C2312yes—
186C24×C59—21no—
187C24×C59—21no—
188C24×C59C2×D411yescharacteristic
189C24×C59C2×D411yescharacteristic
190C24×C59C2×D411yescharacteristic
191#41×C59—22no—
192#41×C59—22no—
193#41×C59—42no—
194#41×C59—41no—
195#41×C59—42no—
196#41×C59—42no—
197#41×C59—41no—
198#41×C59—41no—
199#41×C59—42no—
200#41×C59—41no—
201#41×C59—81no—
202#41×C59—81no—
203C2×Q8×C59—21no—
204C2×Q8×C59—21no—
205C2×Q8×C59—21no—
206C2×Q8×C59C2×D411yescharacteristic
207C2×D4×C59—21no—
208C2×D4×C59—22no—
209C2×D4×C59—22no—
210C2×D4×C59—21no—
211C2×D4×C59—21no—
212C2×D4×C59—22no—
213C2×D4×C59—22no—
214C2×D4×C59—21no—
215C2×D4×C59—21no—
216C2×D4×C59—21no—
217C2×D4×C59—21no—
218C2×D4×C59—21no—
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—41no—
224C2×D4×C59—41no—
225C2×D4×C59—42no—
226C2×D4×C59—42no—
227C2×D4×C59—41no—
228C2×D4×C59—41no—
229C2×D4×C59—41no—
230C2×D4×C59—41no—
231C2×D4×C59—42no—
232C2×D4×C59—42no—
233C2×D4×C59—41no—
234C2×D4×C59—41no—
235C2×D4×C59—41no—
236C2×D4×C59—41no—
237C2×D4×C59—41no—
238C2×D4×C59—42no—
239C2×D4×C59C2×D411yescharacteristic
240C2×D4×C59C2×D411yescharacteristic
241C2×D4×C59C2×D411yescharacteristic
242C2×D4×C59C2×D411yescharacteristic
243C2×D4×C59C2411yescharacteristic
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×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—41no—
256C22×C4×C59—41no—
257C22×C4×C59—41no—
258C22×C4×C59—41no—
259C22×C4×C59—41no—
260C22×C4×C59C2×D411yescharacteristic
261C22×C4×C59C2×D411yescharacteristic
262C22×C4×C59C2×D411yescharacteristic
263C22×C4×C59C2×D411yescharacteristic
264Q16×C59—42no—
265SD16×C59—42no—
266SD16×C59—42no—
267D8×C59—42no—
268M16×C59—22no—
269M16×C59—41no—
270C2×C8×C59—41no—
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—21no—
289C4⋊C4×C59—21no—
290C4⋊C4×C59—42no—
291C4⋊C4×C59—42no—
292C4⋊C4×C59—42no—
293C22⋊C4×C59—21no—
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—22no—
317C22⋊C4×C59—22no—
318C22⋊C4×C59—42no—
319C22⋊C4×C59—41no—
320C22⋊C4×C59—41no—
321C22⋊C4×C59—42no—
322C22⋊C4×C59—42no—
323C22⋊C4×C59—42no—
324C22⋊C4×C59C2×D411yescharacteristic
325C22⋊C4×C59C2×D411yescharacteristic
326C22⋊C4×C59C2×D411yescharacteristic
327C22⋊C4×C59C2×D411yescharacteristic
328C42×C59—21no—
329C42×C59—21no—
330C42×C59—21no—
331C42×C59—21no—
332C42×C59C2×D411yescharacteristic
333C42×C59C2×D411yescharacteristic
334C23×C59—21no—
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—21no—
341C23×C59—21no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—81no—
347C23×C59—81no—
348C23×C59—81no—
349C23×C59—82no—
350C23×C59—161no—
351C23×C59#12011yescharacteristic
352C23×C59#12011yescharacteristic
353C23×C59#12011yescharacteristic
354C23×C59C22×D411yescharacteristic
355C23×C59C22×D411yescharacteristic
356Q8×C59—22no—
357Q8×C59—41no—
358Q8×C59—41no—
359Q8×C59—81no—
360Q8×C59—81no—
361D4×C59—22no—
362D4×C59—41no—
363D4×C59—41no—
364D4×C59—41no—
365D4×C59—41no—
366D4×C59—41no—
367D4×C59—41no—
368D4×C59—42no—
369D4×C59—42no—
370D4×C59—42no—
371D4×C59—42no—
372D4×C59—42no—
373D4×C59—42no—
374D4×C59—41no—
375D4×C59—41no—
376D4×C59—41no—
377D4×C59—41no—
378D4×C59—81no—
379D4×C59—81no—
380D4×C59—81no—
381D4×C59—81no—
382D4×C59—81no—
383D4×C59—81no—
384D4×C59—81no—
385D4×C59—81no—
386D4×C59—81no—
387D4×C59—162no—
388C2×C4×C59—21no—
389C2×C4×C59—21no—
390C2×C4×C59—22no—
391C2×C4×C59—22no—
392C2×C4×C59—21no—
393C2×C4×C59—21no—
394C2×C4×C59—21no—
395C2×C4×C59—21no—
396C2×C4×C59—21no—
397C2×C4×C59—21no—
398C2×C4×C59—21no—
399C2×C4×C59—21no—
400C2×C4×C59—21no—
401C2×C4×C59—21no—
402C2×C4×C59—42no—
403C2×C4×C59—42no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—42no—
413C2×C4×C59—42no—
414C2×C4×C59—81no—
415C2×C4×C59—81no—
416C2×C4×C59—81no—
417C2×C4×C59—81no—
418C2×C4×C59—81no—
419C2×C4×C59—81no—
420C2×C4×C59—81no—
421C2×C4×C59—81no—
422C2×C4×C59—82no—
423C2×C4×C59—161no—
424C2×C4×C59#12011yescharacteristic
425C2×C4×C59C22×D411yescharacteristic
426C8×C59—42no—
427#33552C5911yesmaximal, characteristic, direct product factor, Sylow
428C22×C59—21no—
429C22×C59—21no—
430C22×C59—21no—
431C22×C59—21no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—41no—
435C22×C59—41no—
436C22×C59—41no—
437C22×C59—42no—
438C22×C59—41no—
439C22×C59—41no—
440C22×C59—41no—
441C22×C59—41no—
442C22×C59—42no—
443C22×C59—41no—
444C22×C59—41no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59—81no—
448C22×C59—82no—
449C22×C59—82no—
450C22×C59—82no—
451C22×C59—82no—
452C22×C59—161no—
453C22×C59—161no—
454C22×C59B(4,𝔽2)11yescharacteristic
455C22×C59B(4,𝔽2)11yescharacteristic
456C22×C59C2×#12011yescharacteristic
457C4×C59—21no—
458C4×C59—21no—
459C4×C59—41no—
460C4×C59—41no—
461C4×C59—41no—
462C4×C59—41no—
463C4×C59—41no—
464C4×C59—41no—
465C4×C59—42no—
466C4×C59—41no—
467C4×C59—41no—
468C4×C59—41no—
469C4×C59—41no—
470C4×C59—82no—
471C4×C59—82no—
472#3533C2×C5911yescharacteristic, complemented
473#3026C2×C5911yescharacteristic, complemented
474C2×#458C2×C5911yescharacteristic, complemented
475#3019C2×C5911yescharacteristic, complemented
476#2201C2×C5912yescomplemented
477#2200C2×C5912yescomplemented
478#2198C2×C5912yescomplemented
479#2197C2×C5912yescomplemented
480#2127C2×C5911yescharacteristic, complemented
481#2121C2×C5911yescharacteristic, complemented
482C2×#352C2×C5911yescharacteristic, complemented
483C2×C59—21no—
484C2×C59—21no—
485C2×C59—21no—
486C2×C59—41no—
487C2×C59—41no—
488C2×C59—41no—
489C2×C59—41no—
490C2×C59—81no—
491C2×C59—81no—
492C2×C59—82no—
493C2×C59C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C5911yescharacteristic
495#575—21no—
496#563C22×C5911yescharacteristic, complemented
497#562—21no—
498#560C22×C5911yescharacteristic, complemented
499#559C22×C5911yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C5911yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C5911yescharacteristic
512#534—21no—
513#534C22×C5911yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C5911yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C5912yes—
521#458C22×C5912yes—
522#458C22×C5912yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C5912yes—
525#455—21no—
526#455C22×C5912yes—
527#453—21no—
528#453C22×C5912yes—
529#421—21no—
530C2×#100C22×C5911yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C5911yescharacteristic
534C2×#99C22×C5911yescharacteristic
535#354C22×C5912yescomplemented
536#353C22×C5912yescomplemented
537#352C22×C5912yescomplemented
538#352C22×C5912yescomplemented
539#352C22×C5912yescomplemented
540AΣL(1,𝔽16)C22×C5912yescomplemented
541C59#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C5912yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C5911yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C5911yescharacteristic
555C22×D4C23×C5911yescharacteristic
556C23×C4D4×C5911yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C5911yescharacteristic, complemented
565#127C23×C5911yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C5911yescharacteristic, complemented
580#124C23×C5911yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C5911yescharacteristic
599#123D4×C5911yescharacteristic, complemented
600#123D4×C5911yescharacteristic, complemented
601#123C23×C5911yescharacteristic
602#123C23×C5911yescharacteristic
603#123C23×C5911yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
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—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C5911yescharacteristic
632#120C23×C5911yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C5911yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C5911yescharacteristic
656C2×C22⋊C4D4×C5911yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C5912yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C5912yes—
668#99C23×C5912yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C5911yescharacteristic
672C24C2×D4×C5911yescharacteristic
673C24C2×D4×C5911yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C5911yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C5911yescharacteristic
723C2×D4C2×D4×C5911yescharacteristic
724C2×D4C2×D4×C5911yescharacteristic
725C2×D4C2×D4×C5911yescharacteristic
726C2×D4C24×C5911yescharacteristic
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×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C5911yescharacteristic
744C22×C4C2×D4×C5911yescharacteristic
745C22×C4C2×D4×C5911yescharacteristic
746C22×C4C2×D4×C5911yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
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—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
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—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C5911yescharacteristic
808C22⋊C4C2×D4×C5911yescharacteristic
809C22⋊C4C2×D4×C5911yescharacteristic
810C22⋊C4C2×D4×C5911yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C5911yescharacteristic
816C42C2×D4×C5911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C5911yescharacteristic
835C23#120×C5911yescharacteristic
836C23#120×C5911yescharacteristic
837C23C22×D4×C5911yescharacteristic
838C23C22×D4×C5911yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C5911yescharacteristic
908C2×C4C22×D4×C5911yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C59×B(4,𝔽2)11yescharacteristic
937C22C59×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C5911yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×C59×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C59C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C59
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C23×C59 ◁ C22×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3533C2semidirect
2. C59×#3026C2semidirect
3. C2×C59×#458C2semidirect
4. C59×#3019C2semidirect
5. C59×#2201C2semidirect
6. C59×#2200C2semidirect
7. C59×#2198C2semidirect
8. C59×#2197C2semidirect
9. C59×#2127C2semidirect
10. C59×#2121C2semidirect
11. C2×C59×#352C2semidirect
14. C59×#563C22semidirect
16. C59×#560C22semidirect
17. C59×#559C22semidirect
21. C59×#551C22semidirect
53. C59×#354C22semidirect
54. C59×#353C22semidirect
55. C59×#352C22semidirect
56. C59×#352C22semidirect
57. C59×#352C22semidirect
58. C59×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C59D4semidirect
73. C23×C4×C59D4semidirect
81. #127×C59D4semidirect
96. #124×C59D4semidirect
116. #123×C59D4semidirect
117. #123×C59D4semidirect
163. #117×C59D4semidirect
173. C2×C22⋊C4×C59D4semidirect
427. #33552C59direct (N × H)
472. #3533C2×C59semidirect
473. #3026C2×C59semidirect
474. C2×#458C2×C59semidirect
475. #3019C2×C59semidirect
476. #2201C2×C59semidirect
477. #2200C2×C59semidirect
478. #2198C2×C59semidirect
479. #2197C2×C59semidirect
480. #2127C2×C59semidirect
481. #2121C2×C59semidirect
482. C2×#352C2×C59semidirect
496. #563C22×C59semidirect
498. #560C22×C59semidirect
499. #559C22×C59semidirect
503. #551C22×C59semidirect
535. #354C22×C59semidirect
536. #353C22×C59semidirect
537. #352C22×C59semidirect
538. #352C22×C59semidirect
539. #352C22×C59semidirect
540. AΣL(1,𝔽16)C22×C59semidirect
541. C59#33552direct (N × H)
550. C2×#41D4×C59semidirect
556. C23×C4D4×C59semidirect
564. #127D4×C59semidirect
579. #124D4×C59semidirect
599. #123D4×C59semidirect
600. #123D4×C59semidirect
646. #117D4×C59semidirect
656. C2×C22⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35332
C59×#30262
C2×C59×#4582
C59×#30192
C59×#22012
C59×#22002
C59×#21982
C59×#21972
C59×#21272
C59×#21212
C2×C59×#3522
#3355259