Finite Group Databasebeta

← C59×#33556 #28445665

Subgroups — C59×#33556 #28445665

Order 15104.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3540C211yesmaximal, characteristic, complemented
2C59×#3028C211yesmaximal, characteristic, complemented
3C59×#3025C211yesmaximal, characteristic, complemented
4C59×#3021C211yesmaximal, characteristic, complemented
5C59×#2200C214yesmaximal, complemented
6C59×#2198C214yesmaximal, complemented
7C59×#2128C211yesmaximal, characteristic, complemented
8C59×#2123C211yesmaximal, characteristic, complemented
9C59×#2120C211yesmaximal, characteristic, complemented
10C59×#585C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C59—21no—
12C59×H(3,𝔽4)—21no—
13C59×#560C2212yescomplemented
14C59×#559C2212yescomplemented
15C59×#556—21no—
16C59×#555—21no—
17C59×#551—21no—
18C59×#548—21no—
19C59×#546—21no—
20C59×#542—22no—
21C59×#542—21no—
22C59×#538—22no—
23C59×#536—21no—
24C59×#536C2211yescharacteristic
25C59×#535C2211yescharacteristic
26C59×#525—21no—
27C59×#525—21no—
28C59×#525C2211yescharacteristic
29C59×#458—21no—
30C59×#458—22no—
31C59×#458C2212yescomplemented
32C59×#458C2214yescomplemented
33C59×B(4,𝔽2)—21no—
34C59×B(4,𝔽2)C2212yescomplemented
35C59×#454—22no—
36C59×#453C2214yes—
37C59×#421—21no—
38C59×#413C2211yescharacteristic
39C59×#410—21no—
40C59×#410—21no—
41C59×#410C2211yescharacteristic
42C59×#410C2211yescharacteristic
43C59×#353C2214yescomplemented
44C59×#352C2212yescomplemented
45C59×#352C2214yescomplemented
46C59×AΣL(1,𝔽16)C2212yescomplemented
472−1+4×C59—21no—
482−1+4×C59—41no—
49H(5,𝔽2)×C59—21no—
50H(5,𝔽2)×C59—21no—
51H(5,𝔽2)×C59—41no—
52H(5,𝔽2)×C59C2312yes—
53C2×#41×C59—21no—
54C2×#41×C59—21no—
55C2×#41×C59—21no—
56C2×#41×C59—21no—
57C2×#41×C59—42no—
58C2×#41×C59C2311yescharacteristic
59C22×Q8×C59D411yescharacteristic, complemented
60C22×D4×C59D411yescharacteristic, complemented
61C23×C4×C59D411yescharacteristic
62AGL(1,ℤ/8)×C59—24no—
63AGL(1,ℤ/8)×C59—42no—
64C2×SD16×C59—41no—
65C2×D8×C59—41no—
66C2×M16×C59—21no—
67C4⋊Q8×C59—21no—
68C4⋊Q8×C59—21no—
69C4⋊Q8×C59—41no—
70#127×C59C2312yes—
71#126×C59—22no—
72#126×C59—22no—
73#126×C59—22no—
74#124×C59—22no—
75#124×C59—21no—
76#124×C59—22no—
77#124×C59—22no—
78#124×C59—21no—
79#124×C59—22no—
80#124×C59—22no—
81#124×C59—41no—
82#124×C59D412yescomplemented
83#123×C59—22no—
84#123×C59—22no—
85#123×C59—22no—
86#123×C59—22no—
87#123×C59—24no—
88#123×C59D411yescharacteristic
89#123×C59D412yescomplemented
90#123×C59C2311yescharacteristic
91#123×C59C2312yes—
92C22⋊Q8×C59—21no—
93C22⋊Q8×C59—22no—
94C22⋊Q8×C59—22no—
95C22⋊Q8×C59—21no—
96C22⋊Q8×C59—21no—
97C22⋊Q8×C59—21no—
98C22⋊Q8×C59—42no—
99C22⋊Q8×C59—41no—
100#121×C59—21no—
101#121×C59—21no—
102#121×C59—22no—
103#121×C59—21no—
104#121×C59—21no—
105#121×C59—22no—
106#121×C59—22no—
107#121×C59—41no—
108#120×C59—22no—
109#120×C59—22no—
110#120×C59—21no—
111#120×C59—21no—
112#120×C59—22no—
113#120×C59D411yescharacteristic
114#120×C59C2311yescharacteristic
115C4×Q8×C59—21no—
116C4×Q8×C59—22no—
117C4×D4×C59—22no—
118C4×D4×C59—21no—
119C4×D4×C59—22no—
120C4×D4×C59—21no—
121C4×D4×C59—21no—
122C4×D4×C59—22no—
123C4×D4×C59—42no—
124#117×C59—21no—
125#117×C59—22no—
126#117×C59—21no—
127#117×C59—21no—
128#117×C59D411yescharacteristic
129#117×C59D411yescharacteristic, complemented
130#117×C59D411yescharacteristic, complemented
131C2×C22⋊C4×C59—22no—
132#104×C59—24no—
133#101×C59—21no—
134#100×C59C2312yes—
135#99×C59—21no—
136#99×C59—21no—
137#99×C59—22no—
138#99×C59—22no—
139#99×C59—24no—
140#99×C59C2312yes—
141#99×C59C2312yes—
142C24×C59—21no—
143C24×C59C2×D411yescharacteristic
144#41×C59—22no—
145#41×C59—22no—
146#41×C59—41no—
147#41×C59—41no—
148#41×C59—42no—
149#41×C59—41no—
150#41×C59—41no—
151#41×C59—41no—
152#41×C59—41no—
153#41×C59—41no—
154#41×C59—42no—
155#41×C59—42no—
156#41×C59—42no—
157#41×C59—41no—
158#41×C59—41no—
159#41×C59—41no—
160#41×C59—81no—
161#41×C59—81no—
162C2×Q8×C59—21no—
163C2×Q8×C59—21no—
164C2×Q8×C59—22no—
165C2×Q8×C59—21no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—41no—
169C2×Q8×C59—41no—
170C2×Q8×C59—42no—
171C2×Q8×C59C2×D411yescharacteristic
172C2×D4×C59—21no—
173C2×D4×C59—21no—
174C2×D4×C59—21no—
175C2×D4×C59—22no—
176C2×D4×C59—22no—
177C2×D4×C59—22no—
178C2×D4×C59—22no—
179C2×D4×C59—21no—
180C2×D4×C59—22no—
181C2×D4×C59—22no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—41no—
185C2×D4×C59—41no—
186C2×D4×C59—42no—
187C2×D4×C59—42no—
188C2×D4×C59—42no—
189C2×D4×C59—41no—
190C2×D4×C59—42no—
191C2×D4×C59C2×D411yescharacteristic
192C2×D4×C59C2×D411yescharacteristic
193C2×D4×C59C2×D412yes—
194C2×D4×C59C2411yescharacteristic
195C22×C4×C59—22no—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—41no—
202C22×C4×C59—41no—
203C22×C4×C59—41no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D412yes—
209SD16×C59—44no—
210D8×C59—44no—
211M16×C59—22no—
212M16×C59—41no—
213C2×C8×C59—41no—
214C4⋊C4×C59—22no—
215C4⋊C4×C59—22no—
216C4⋊C4×C59—22no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—22no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59—21no—
222C4⋊C4×C59—21no—
223C4⋊C4×C59—22no—
224C4⋊C4×C59—41no—
225C4⋊C4×C59—41no—
226C4⋊C4×C59—42no—
227C4⋊C4×C59—44no—
228C22⋊C4×C59—22no—
229C22⋊C4×C59—22no—
230C22⋊C4×C59—22no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—22no—
233C22⋊C4×C59—22no—
234C22⋊C4×C59—21no—
235C22⋊C4×C59—22no—
236C22⋊C4×C59—21no—
237C22⋊C4×C59—21no—
238C22⋊C4×C59—22no—
239C22⋊C4×C59—22no—
240C22⋊C4×C59—22no—
241C22⋊C4×C59—21no—
242C22⋊C4×C59—21no—
243C22⋊C4×C59—22no—
244C22⋊C4×C59—22no—
245C22⋊C4×C59—42no—
246C22⋊C4×C59—42no—
247C22⋊C4×C59—44no—
248C22⋊C4×C59C2×D411yescharacteristic
249C22⋊C4×C59C2×D411yescharacteristic
250C22⋊C4×C59C2×D412yes—
251C42×C59—22no—
252C42×C59—22no—
253C42×C59—21no—
254C42×C59—21no—
255C42×C59—41no—
256C42×C59—41no—
257C42×C59C2×D412yes—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—21no—
261C23×C59—22no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—81no—
265C23×C59—81no—
266C23×C59—82no—
267C23×C59#12011yescharacteristic
268C23×C59C22×D411yescharacteristic
269C23×C59C22×D411yescharacteristic
270Q8×C59—22no—
271Q8×C59—41no—
272Q8×C59—41no—
273Q8×C59—41no—
274Q8×C59—41no—
275Q8×C59—41no—
276Q8×C59—41no—
277Q8×C59—81no—
278Q8×C59—82no—
279D4×C59—22no—
280D4×C59—41no—
281D4×C59—41no—
282D4×C59—41no—
283D4×C59—42no—
284D4×C59—41no—
285D4×C59—41no—
286D4×C59—42no—
287D4×C59—42no—
288D4×C59—42no—
289D4×C59—42no—
290D4×C59—41no—
291D4×C59—41no—
292D4×C59—41no—
293D4×C59—81no—
294D4×C59—82no—
295D4×C59—82no—
296D4×C59—82no—
297D4×C59—81no—
298D4×C59—82no—
299D4×C59—84no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—21no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—21no—
312C2×C4×C59—22no—
313C2×C4×C59—21no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—41no—
318C2×C4×C59—42no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59—81no—
326C2×C4×C59—82no—
327C2×C4×C59—82no—
328C2×C4×C59#12011yescharacteristic
329C2×C4×C59#12011yescharacteristic
330C2×C4×C59#12011yescharacteristic
331C2×C4×C59C22×D411yescharacteristic
332C8×C59—42no—
333#33556C5911yesmaximal, characteristic, direct product factor, Sylow
334C22×C59—21no—
335C22×C59—21no—
336C22×C59—21no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59—42no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—41no—
347C22×C59—42no—
348C22×C59—82no—
349C22×C59—82no—
350C22×C59—81no—
351C22×C59—161no—
352C22×C59—162no—
353C22×C59C2×#12011yescharacteristic
354C4×C59—21no—
355C4×C59—21no—
356C4×C59—21no—
357C4×C59—41no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59—41no—
361C4×C59—42no—
362C4×C59—41no—
363C4×C59—42no—
364C4×C59—82no—
365C4×C59—82no—
366C4×C59B(4,𝔽2)11yescharacteristic
367C4×C59B(4,𝔽2)11yescharacteristic
368#3540C2×C5911yescharacteristic, complemented
369#3028C2×C5911yescharacteristic, complemented
370#3025C2×C5911yescharacteristic, complemented
371#3021C2×C5911yescharacteristic, complemented
372#2200C2×C5914yescomplemented
373#2198C2×C5914yescomplemented
374#2128C2×C5911yescharacteristic, complemented
375#2123C2×C5911yescharacteristic, complemented
376#2120C2×C5911yescharacteristic, complemented
377C2×C59—21no—
378C2×C59—41no—
379C2×C59—41no—
380C2×C59—41no—
381C2×C59—81no—
382C2×C59—82no—
383C2×C59—82no—
384C2×C59C2×B(4,𝔽2)11yescharacteristic
385#585C22×C5911yescharacteristic
386C2×AGL(1,ℤ/8)—21no—
387H(3,𝔽4)—21no—
388#560C22×C5912yescomplemented
389#559C22×C5912yescomplemented
390#556—21no—
391#555—21no—
392#551—21no—
393#548—21no—
394#546—21no—
395#542—22no—
396#542—21no—
397#538—22no—
398#536—21no—
399#536C22×C5911yescharacteristic
400#535C22×C5911yescharacteristic
401#525—21no—
402#525—21no—
403#525C22×C5911yescharacteristic
404#458—21no—
405#458—22no—
406#458C22×C5912yescomplemented
407#458C22×C5914yescomplemented
408B(4,𝔽2)—21no—
409B(4,𝔽2)C22×C5912yescomplemented
410#454—22no—
411#453C22×C5914yes—
412#421—21no—
413#413C22×C5911yescharacteristic
414#410—21no—
415#410—21no—
416#410C22×C5911yescharacteristic
417#410C22×C5911yescharacteristic
418#353C22×C5914yescomplemented
419#352C22×C5912yescomplemented
420#352C22×C5914yescomplemented
421AΣL(1,𝔽16)C22×C5912yescomplemented
422C59#3355611yescharacteristic, direct product factor, Sylow
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C5912yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C5911yescharacteristic
435C22×Q8D4×C5911yescharacteristic, complemented
436C22×D4D4×C5911yescharacteristic, complemented
437C23×C4D4×C5911yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C5912yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C5912yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C5911yescharacteristic
465#123D4×C5912yescomplemented
466#123C23×C5911yescharacteristic
467#123C23×C5912yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C5911yescharacteristic
490#120C23×C5911yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C5911yescharacteristic
505#117D4×C5911yescharacteristic, complemented
506#117D4×C5911yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C5912yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C5912yes—
517#99C23×C5912yes—
518C24—21no—
519C24C2×D4×C5911yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C5911yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C5911yescharacteristic
568C2×D4C2×D4×C5911yescharacteristic
569C2×D4C2×D4×C5912yes—
570C2×D4C24×C5911yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C5911yescharacteristic
581C22×C4C2×D4×C5911yescharacteristic
582C22×C4C2×D4×C5911yescharacteristic
583C22×C4C2×D4×C5911yescharacteristic
584C22×C4C2×D4×C5912yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C5911yescharacteristic
625C22⋊C4C2×D4×C5911yescharacteristic
626C22⋊C4C2×D4×C5912yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C5912yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C5911yescharacteristic
644C23C22×D4×C5911yescharacteristic
645C23C22×D4×C5911yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—82no—
672D4—82no—
673D4—81no—
674D4—82no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C5911yescharacteristic
705C2×C4#120×C5911yescharacteristic
706C2×C4#120×C5911yescharacteristic
707C2×C4C22×D4×C5911yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C5911yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C59×B(4,𝔽2)11yescharacteristic
742C4C59×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×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 ◁ C2×C4×C59 ◁ C2×#41×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3540C2semidirect
2. C59×#3028C2semidirect
3. C59×#3025C2semidirect
4. C59×#3021C2semidirect
5. C59×#2200C2semidirect
6. C59×#2198C2semidirect
7. C59×#2128C2semidirect
8. C59×#2123C2semidirect
9. C59×#2120C2semidirect
13. C59×#560C22semidirect
14. C59×#559C22semidirect
31. C59×#458C22semidirect
32. C59×#458C22semidirect
34. C59×B(4,𝔽2)C22semidirect
43. C59×#353C22semidirect
44. C59×#352C22semidirect
45. C59×#352C22semidirect
46. C59×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C59D4semidirect
60. C22×D4×C59D4semidirect
82. #124×C59D4semidirect
89. #123×C59D4semidirect
129. #117×C59D4semidirect
130. #117×C59D4semidirect
333. #33556C59direct (N × H)
368. #3540C2×C59semidirect
369. #3028C2×C59semidirect
370. #3025C2×C59semidirect
371. #3021C2×C59semidirect
372. #2200C2×C59semidirect
373. #2198C2×C59semidirect
374. #2128C2×C59semidirect
375. #2123C2×C59semidirect
376. #2120C2×C59semidirect
388. #560C22×C59semidirect
389. #559C22×C59semidirect
406. #458C22×C59semidirect
407. #458C22×C59semidirect
409. B(4,𝔽2)C22×C59semidirect
418. #353C22×C59semidirect
419. #352C22×C59semidirect
420. #352C22×C59semidirect
421. AΣL(1,𝔽16)C22×C59semidirect
422. C59#33556direct (N × H)
435. C22×Q8D4×C59semidirect
436. C22×D4D4×C59semidirect
458. #124D4×C59semidirect
465. #123D4×C59semidirect
505. #117D4×C59semidirect
506. #117D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35402
C59×#30282
C59×#30252
C59×#30212
C59×#22002
C59×#21982
C59×#21282
C59×#21232
C59×#21202
#3355659