Finite Group Databasebeta

← C2×C59×#2197 #28445653

Subgroups — C2×C59×#2197 #28445653

Order 15104.

1320 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#551C211yesmaximal, characteristic, complemented
2C2×C59×#458C211yesmaximal, characteristic, complemented
3C2×C59×B(4,𝔽2)C211yesmaximal, characteristic
4C2×C59×#455C211yesmaximal, characteristic, complemented
5C59×#2197C218yesmaximal, direct product factor
6C2×C59×#354C211yesmaximal, characteristic, complemented
7C2×C59×#352C211yesmaximal, characteristic, complemented
8C2×C59×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C59C2211yescharacteristic
10C2×#137×C59—21no—
11C59×#551—22no—
12C59×#551—22no—
13C59×#551—22no—
14C59×#551C2214yescomplemented
15C2×#126×C59—21no—
16C2×#124×C59C2211yescharacteristic
17C2×#123×C59—21no—
18C2×#123×C59—21no—
19C2×#123×C59C2211yescharacteristic
20C2×C22⋊Q8×C59—21no—
21C2×#120×C59—21no—
22C2×#120×C59C2211yescharacteristic
23C2×C4×D4×C59—21no—
24C2×#117×C59—21no—
25C22×C22⋊C4×C59—21no—
26C59×#458—22no—
27C59×#458C2214yescomplemented
28C59×B(4,𝔽2)—22no—
29C59×B(4,𝔽2)C2214yes—
30C59×#455—22no—
31C59×#455C2214yescomplemented
32C2×#104×C59—21no—
33C2×#100×C59C2211yescharacteristic
34C2×#99×C59—21no—
35C2×#99×C59—21no—
36C2×#99×C59C2211yescharacteristic
37C2×#99×C59C2211yescharacteristic
38C59×#354C2214yescomplemented
39C59×#352C2214yescomplemented
40C59×AΣL(1,𝔽16)C2214yescomplemented
41C25×C59D411yescharacteristic
42H(5,𝔽2)×C59—21no—
43H(5,𝔽2)×C59—21no—
44H(5,𝔽2)×C59—21no—
45H(5,𝔽2)×C59—42no—
46H(5,𝔽2)×C59C2312yes—
47C2×#41×C59—21no—
48C2×#41×C59—41no—
49C22×Q8×C59D411yescharacteristic, complemented
50C22×D4×C59—21no—
51C22×D4×C59—21no—
52C22×D4×C59—21no—
53C22×D4×C59—41no—
54C22×D4×C59—41no—
55C22×D4×C59C2311yescharacteristic
56C23×C4×C59—21no—
57C23×C4×C59—21no—
58C23×C4×C59D411yescharacteristic, complemented
59#137×C59—24no—
60#137×C59—42no—
61C2×Q16×C59—41no—
62C2×SD16×C59—41no—
63C2×M16×C59—21no—
64#126×C59—24no—
65#126×C59—24no—
66#124×C59—21no—
67#124×C59—21no—
68#124×C59D412yescomplemented
69#124×C59C2312yes—
70#123×C59—24no—
71#123×C59—21no—
72#123×C59—21no—
73#123×C59—24no—
74#123×C59—24no—
75#123×C59—42no—
76#123×C59D412yescomplemented
77#123×C59C2312yes—
78C22⋊Q8×C59—24no—
79C22⋊Q8×C59—24no—
80#120×C59—21no—
81#120×C59—21no—
82#120×C59—24no—
83#120×C59—42no—
84#120×C59D412yes—
85#120×C59C2312yes—
86C4×D4×C59—24no—
87C4×D4×C59—24no—
88#117×C59—24no—
89#117×C59—24no—
90C2×C4⋊C4×C59—21no—
91C2×C4⋊C4×C59—21no—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59—41no—
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—24no—
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—21no—
100C2×C22⋊C4×C59—24no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—21no—
103C2×C22⋊C4×C59—21no—
104C2×C22⋊C4×C59—21no—
105C2×C22⋊C4×C59—41no—
106C2×C22⋊C4×C59—41no—
107C2×C22⋊C4×C59D411yescharacteristic
108C2×C22⋊C4×C59D411yescharacteristic, complemented
109C2×C42×C59—21no—
110C2×C42×C59D411yescharacteristic, complemented
111#104×C59—24no—
112#100×C59—21no—
113#100×C59C2312yes—
114#99×C59—21no—
115#99×C59—21no—
116#99×C59—24no—
117#99×C59—24no—
118#99×C59C2312yes—
119#99×C59C2312yes—
120C24×C59—21no—
121C24×C59—21no—
122C24×C59—21no—
123C24×C59—21no—
124C24×C59—41no—
125C24×C59—44no—
126C24×C59—41no—
127C24×C59C2×D411yescharacteristic
128C24×C59C2×D411yescharacteristic
129C24×C59C2×D412yes—
130#41×C59—22no—
131#41×C59—22no—
132#41×C59—42no—
133#41×C59—41no—
134#41×C59—42no—
135#41×C59—42no—
136#41×C59—42no—
137#41×C59—41no—
138C2×Q8×C59—21no—
139C2×Q8×C59—21no—
140C2×Q8×C59—41no—
141C2×Q8×C59—41no—
142C2×Q8×C59C2×D412yescomplemented
143C2×D4×C59—21no—
144C2×D4×C59—22no—
145C2×D4×C59—22no—
146C2×D4×C59—22no—
147C2×D4×C59—22no—
148C2×D4×C59—22no—
149C2×D4×C59—22no—
150C2×D4×C59—41no—
151C2×D4×C59—41no—
152C2×D4×C59—42no—
153C2×D4×C59—42no—
154C2×D4×C59—44no—
155C2×D4×C59—41no—
156C2×D4×C59—41no—
157C2×D4×C59—41no—
158C2×D4×C59—41no—
159C2×D4×C59—42no—
160C2×D4×C59—42no—
161C2×D4×C59—41no—
162C2×D4×C59—41no—
163C2×D4×C59—41no—
164C2×D4×C59—44no—
165C2×D4×C59—84no—
166C2×D4×C59C2×D411yescharacteristic
167C2×D4×C59C2×D411yescharacteristic
168C2×D4×C59C2×D411yescharacteristic
169C2×D4×C59C2411yescharacteristic
170C22×C4×C59—24no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—24no—
179C22×C4×C59—21no—
180C22×C4×C59—41no—
181C22×C4×C59—44no—
182C22×C4×C59—41no—
183C22×C4×C59—41no—
184C22×C4×C59—41no—
185C22×C4×C59—41no—
186C22×C4×C59—81no—
187C22×C4×C59—81no—
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D412yescomplemented
190Q16×C59—44no—
191SD16×C59—44no—
192M16×C59—22no—
193M16×C59—41no—
194C2×C8×C59—41no—
195C4⋊C4×C59—24no—
196C4⋊C4×C59—24no—
197C4⋊C4×C59—24no—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—22no—
200C4⋊C4×C59—44no—
201C22⋊C4×C59—24no—
202C22⋊C4×C59—24no—
203C22⋊C4×C59—22no—
204C22⋊C4×C59—22no—
205C22⋊C4×C59—22no—
206C22⋊C4×C59—21no—
207C22⋊C4×C59—21no—
208C22⋊C4×C59—22no—
209C22⋊C4×C59—22no—
210C22⋊C4×C59—22no—
211C22⋊C4×C59—22no—
212C22⋊C4×C59—22no—
213C22⋊C4×C59—22no—
214C22⋊C4×C59—22no—
215C22⋊C4×C59—44no—
216C22⋊C4×C59—41no—
217C22⋊C4×C59—41no—
218C22⋊C4×C59—44no—
219C22⋊C4×C59C2×D412yes—
220C22⋊C4×C59C2×D412yescomplemented
221C42×C59—24no—
222C42×C59—21no—
223C42×C59C2×D412yescomplemented
224C23×C59—24no—
225C23×C59—22no—
226C23×C59—21no—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—22no—
231C23×C59—22no—
232C23×C59—42no—
233C23×C59—42no—
234C23×C59—42no—
235C23×C59—42no—
236C23×C59—44no—
237C23×C59—44no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—44no—
243C23×C59—41no—
244C23×C59—81no—
245C23×C59—84no—
246C23×C59—82no—
247C23×C59—82no—
248C23×C59—82no—
249C23×C59#12011yescharacteristic
250C23×C59#12011yescharacteristic
251C23×C59#12011yescharacteristic
252C23×C59C22×D411yescharacteristic
253C23×C59C22×D411yescharacteristic
254Q8×C59—22no—
255Q8×C59—42no—
256Q8×C59—41no—
257Q8×C59—81no—
258D4×C59—22no—
259D4×C59—41no—
260D4×C59—41no—
261D4×C59—41no—
262D4×C59—41no—
263D4×C59—41no—
264D4×C59—44no—
265D4×C59—44no—
266D4×C59—42no—
267D4×C59—42no—
268D4×C59—42no—
269D4×C59—42no—
270D4×C59—42no—
271D4×C59—42no—
272D4×C59—88no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—48no—
287C2×C4×C59—42no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—81no—
299C2×C4×C59—84no—
300C2×C4×C59—82no—
301C2×C4×C59—82no—
302C2×C4×C59#12011yescharacteristic
303C2×C4×C59C22×D411yescharacteristic
304C8×C59—42no—
305C2×#2197C5911yesmaximal, characteristic, direct product factor, Sylow
306C22×C59—22no—
307C22×C59—24no—
308C22×C59—21no—
309C22×C59—21no—
310C22×C59—21no—
311C22×C59—21no—
312C22×C59—41no—
313C22×C59—41no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59—42no—
317C22×C59—44no—
318C22×C59—44no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—44no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—82no—
327C22×C59—84no—
328C22×C59—82no—
329C22×C59—82no—
330C22×C59—82no—
331C22×C59—161no—
332C22×C59—161no—
333C22×C59B(4,𝔽2)11yescharacteristic
334C22×C59B(4,𝔽2)11yescharacteristic
335C22×C59C2×#12011yescharacteristic
336C4×C59—21no—
337C4×C59—21no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—82no—
345C4×C59—82no—
346C2×#551C2×C5911yescharacteristic, complemented
347C2×#458C2×C5911yescharacteristic, complemented
348C2×B(4,𝔽2)C2×C5911yescharacteristic
349C2×#455C2×C5911yescharacteristic, complemented
350#2197C2×C5918yesdirect product factor
351C2×#354C2×C5911yescharacteristic, complemented
352C2×#352C2×C5911yescharacteristic, complemented
353C2×AΣL(1,𝔽16)C2×C5911yescharacteristic, complemented
354C2×C59—21no—
355C2×C59—21no—
356C2×C59—41no—
357C2×C59—41no—
358C2×C59—44no—
359C2×C59—41no—
360C2×C59—41no—
361C2×C59—82no—
362C2×C59#219712yesdirect product factor
363C2×C59C2×B(4,𝔽2)11yescharacteristic
364C2×H(5,𝔽2)C22×C5911yescharacteristic
365C2×#137—21no—
366#551—22no—
367#551—22no—
368#551—22no—
369#551C22×C5914yescomplemented
370C2×#126—21no—
371C2×#124C22×C5911yescharacteristic
372C2×#123—21no—
373C2×#123—21no—
374C2×#123C22×C5911yescharacteristic
375C2×C22⋊Q8—21no—
376C2×#120—21no—
377C2×#120C22×C5911yescharacteristic
378C2×C4×D4—21no—
379C2×#117—21no—
380C22×C22⋊C4—21no—
381#458—22no—
382#458C22×C5914yescomplemented
383B(4,𝔽2)—22no—
384B(4,𝔽2)C22×C5914yes—
385#455—22no—
386#455C22×C5914yescomplemented
387C2×#104—21no—
388C2×#100C22×C5911yescharacteristic
389C2×#99—21no—
390C2×#99—21no—
391C2×#99C22×C5911yescharacteristic
392C2×#99C22×C5911yescharacteristic
393#354C22×C5914yescomplemented
394#352C22×C5914yescomplemented
395AΣL(1,𝔽16)C22×C5914yescomplemented
396C59C2×#219711yescharacteristic, direct product factor, Sylow
397C25D4×C5911yescharacteristic
398H(5,𝔽2)—21no—
399H(5,𝔽2)—21no—
400H(5,𝔽2)—21no—
401H(5,𝔽2)—42no—
402H(5,𝔽2)C23×C5912yes—
403C2×#41—21no—
404C2×#41—41no—
405C22×Q8D4×C5911yescharacteristic, complemented
406C22×D4—21no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4—41no—
410C22×D4—41no—
411C22×D4C23×C5911yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4D4×C5911yescharacteristic, complemented
415#137—24no—
416#137—42no—
417C2×Q16—41no—
418C2×SD16—41no—
419C2×M16—21no—
420#126—24no—
421#126—24no—
422#124—21no—
423#124—21no—
424#124D4×C5912yescomplemented
425#124C23×C5912yes—
426#123—24no—
427#123—21no—
428#123—21no—
429#123—24no—
430#123—24no—
431#123—42no—
432#123D4×C5912yescomplemented
433#123C23×C5912yes—
434C22⋊Q8—24no—
435C22⋊Q8—24no—
436#120—21no—
437#120—21no—
438#120—24no—
439#120—42no—
440#120D4×C5912yes—
441#120C23×C5912yes—
442C4×D4—24no—
443C4×D4—24no—
444#117—24no—
445#117—24no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—41no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4D4×C5911yescharacteristic
464C2×C22⋊C4D4×C5911yescharacteristic, complemented
465C2×C42—21no—
466C2×C42D4×C5911yescharacteristic, complemented
467#104—24no—
468#100—21no—
469#100C23×C5912yes—
470#99—21no—
471#99—21no—
472#99—24no—
473#99—24no—
474#99C23×C5912yes—
475#99C23×C5912yes—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—41no—
481C24—44no—
482C24—41no—
483C24C2×D4×C5911yescharacteristic
484C24C2×D4×C5911yescharacteristic
485C24C2×D4×C5912yes—
486#41—22no—
487#41—22no—
488#41—42no—
489#41—41no—
490#41—42no—
491#41—42no—
492#41—42no—
493#41—41no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8C2×D4×C5912yescomplemented
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—44no—
521C2×D4—84no—
522C2×D4C2×D4×C5911yescharacteristic
523C2×D4C2×D4×C5911yescharacteristic
524C2×D4C2×D4×C5911yescharacteristic
525C2×D4C24×C5911yescharacteristic
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4—44no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4C2×D4×C5911yescharacteristic
545C22×C4C2×D4×C5912yescomplemented
546Q16—44no—
547SD16—44no—
548M16—22no—
549M16—41no—
550C2×C8—41no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—44no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—44no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—44no—
575C22⋊C4C2×D4×C5912yes—
576C22⋊C4C2×D4×C5912yescomplemented
577C42—24no—
578C42—21no—
579C42C2×D4×C5912yescomplemented
580C23—24no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—22no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—44no—
593C23—44no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—44no—
599C23—41no—
600C23—81no—
601C23—84no—
602C23—82no—
603C23—82no—
604C23—82no—
605C23#120×C5911yescharacteristic
606C23#120×C5911yescharacteristic
607C23#120×C5911yescharacteristic
608C23C22×D4×C5911yescharacteristic
609C23C22×D4×C5911yescharacteristic
610Q8—22no—
611Q8—42no—
612Q8—41no—
613Q8—81no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—44no—
621D4—44no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—42no—
626D4—42no—
627D4—42no—
628D4—88no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—48no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—81no—
655C2×C4—84no—
656C2×C4—82no—
657C2×C4—82no—
658C2×C4#120×C5911yescharacteristic
659C2×C4C22×D4×C5911yescharacteristic
660C8—42no—
661C22—22no—
662C22—24no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—44no—
673C22—44no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—44no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—82no—
682C22—84no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—161no—
687C22—161no—
688C22C59×B(4,𝔽2)11yescharacteristic
689C22C59×B(4,𝔽2)11yescharacteristic
690C22C2×#120×C5911yescharacteristic
691C4—21no—
692C4—21no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—82no—
700C4—82no—
701C2—21no—
702C2—21no—
703C2—41no—
704C2—41no—
705C2—44no—
706C2—41no—
707C2—41no—
708C2—82no—
709C2C59×#219712yesdirect product factor
710C2C2×C59×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C59B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C59
prime radicalC2×C59×B(4,𝔽2)C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#551C2semidirect
2. C2×C59×#458C2semidirect
4. C2×C59×#455C2semidirect
5. C59×#2197C2direct (N × H)
6. C2×C59×#354C2semidirect
7. C2×C59×#352C2semidirect
8. C2×C59×AΣL(1,𝔽16)C2semidirect
14. C59×#551C22semidirect
27. C59×#458C22semidirect
31. C59×#455C22semidirect
38. C59×#354C22semidirect
39. C59×#352C22semidirect
40. C59×AΣL(1,𝔽16)C22semidirect
49. C22×Q8×C59D4semidirect
58. C23×C4×C59D4semidirect
68. #124×C59D4semidirect
76. #123×C59D4semidirect
108. C2×C22⋊C4×C59D4semidirect
110. C2×C42×C59D4semidirect
142. C2×Q8×C59C2×D4semidirect
189. C22×C4×C59C2×D4semidirect
220. C22⋊C4×C59C2×D4semidirect
223. C42×C59C2×D4semidirect
305. C2×#2197C59direct (N × H)
346. C2×#551C2×C59semidirect
347. C2×#458C2×C59semidirect
349. C2×#455C2×C59semidirect
350. #2197C2×C59direct (N × H)
351. C2×#354C2×C59semidirect
352. C2×#352C2×C59semidirect
353. C2×AΣL(1,𝔽16)C2×C59semidirect
362. C2×C59#2197direct (N × H)
369. #551C22×C59semidirect
382. #458C22×C59semidirect
386. #455C22×C59semidirect
393. #354C22×C59semidirect
394. #352C22×C59semidirect
395. AΣL(1,𝔽16)C22×C59semidirect
396. C59C2×#2197direct (N × H)
405. C22×Q8D4×C59semidirect
414. C23×C4D4×C59semidirect
424. #124D4×C59semidirect
432. #123D4×C59semidirect
464. C2×C22⋊C4D4×C59semidirect
466. C2×C42D4×C59semidirect
498. C2×Q8C2×D4×C59semidirect
545. C22×C4C2×D4×C59semidirect
576. C22⋊C4C2×D4×C59semidirect
579. C42C2×D4×C59semidirect
709. C2C59×#2197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5512
C2×C59×#4582
C2×C59×B(4,𝔽2)2
C2×C59×#4552
C59×#21972
C2×C59×#3542
C2×C59×#3522
C2×C59×AΣL(1,𝔽16)2
C2×#219759