Finite Group Databasebeta

← C59×#23582 #28435691

Subgroups — C59×#23582 #28435691

Order 15104.

1186 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#540C211yesmaximal, characteristic
2C2×C59×#440C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
4C59×#2323C211yesmaximal, characteristic, complemented
5C59×#2059C211yesmaximal, characteristic, complemented
6C59×#2041C211yesmaximal, characteristic, complemented
7C59×#2034C211yesmaximal, characteristic, complemented
8C59×#2033C211yesmaximal, characteristic, complemented
9C59×#2026C211yesmaximal, characteristic, complemented
10C59×#2014C211yesmaximal, characteristic, complemented
11C59×#2000C211yesmaximal, characteristic, complemented
12C59×#2000C211yesmaximal, characteristic, complemented
13C59×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C59C211yesmaximal, characteristic, complemented
15C59×#1750C211yesmaximal, characteristic, complemented
16C22×SD16×C59C2211yescharacteristic
17C22×SD16×C59C2211yescharacteristic
18C59×#540—24no—
19C59×#540—24no—
20C2×#127×C59C2211yescharacteristic
21C2×#125×C59C2211yescharacteristic
22C2×#123×C59—21no—
23C2×#123×C59—21no—
24C2×C22⋊Q8×C59C2211yescharacteristic
25C2×#121×C59—21no—
26C2×#121×C59—21no—
27C2×#121×C59C2211yescharacteristic
28C2×#121×C59C2211yescharacteristic
29C2×C4×Q8×C59C2211yescharacteristic
30C2×C4×D4×C59C2211yescharacteristic
31C2×C4×D4×C59C2211yescharacteristic
32C2×#117×C59C2211yescharacteristic
33C59×#440—24no—
34C4×SD16×C59—24no—
35C2×#107×C59C2211yescharacteristic
36C2×#106×C59C2211yescharacteristic
37C2×#103×C59C2211yescharacteristic
38C2×#103×C59C2211yescharacteristic
39C2×#102×C59C2211yescharacteristic
40C2×#102×C59C2211yescharacteristic
41C2×#102×C59C2211yescharacteristic
42C2×#102×C59C2211yescharacteristic
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×C22⋊C8×C59C2211yescharacteristic
46C2×C22⋊C8×C59C2211yescharacteristic
47C2×#97×C59C2211yescharacteristic
48C2×C4×C8×C59C2211yescharacteristic
49C59×#391C2211yescharacteristic
50C59×#389—21no—
51C59×#389C2211yescharacteristic
52C59×#388—21no—
53C59×#388—21no—
54C59×#387—21no—
55C59×#380C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×Q8×C59C2311yescharacteristic
64C22×D4×C59—21no—
65C22×D4×C59—21no—
66C22×D4×C59—21no—
67C22×D4×C59—21no—
68C22×D4×C59C2311yescharacteristic
69C22×D4×C59C2311yescharacteristic
70C23×C4×C59—21no—
71C23×C4×C59—21no—
72C23×C4×C59C2311yescharacteristic
73C2×SD16×C59—22no—
74C2×SD16×C59—22no—
75C2×SD16×C59—22no—
76C2×SD16×C59—22no—
77C2×SD16×C59—22no—
78C2×SD16×C59—22no—
79C22×C8×C59C2311yescharacteristic
80C22×C8×C59C2311yescharacteristic
81C22×C8×C59C2311yescharacteristic
82C22×C8×C59C2311yescharacteristic
83#127×C59—22no—
84#127×C59—22no—
85#125×C59—22no—
86#125×C59—22no—
87#123×C59—28no—
88#123×C59—28no—
89C22⋊Q8×C59—22no—
90C22⋊Q8×C59—22no—
91#121×C59—28no—
92#121×C59—28no—
93#121×C59—22no—
94#121×C59—22no—
95#121×C59—22no—
96#121×C59—22no—
97C4×Q8×C59—22no—
98C4×Q8×C59—22no—
99C4×D4×C59—22no—
100C4×D4×C59—22no—
101C4×D4×C59D414yes—
102C4×D4×C59D414yes—
103#117×C59—22no—
104#117×C59—22no—
105C2×C4⋊C4×C59—21no—
106C2×C4⋊C4×C59—21no—
107C2×C4⋊C4×C59—21no—
108C2×C4⋊C4×C59—21no—
109C2×C4⋊C4×C59—21no—
110C2×C4⋊C4×C59D411yescharacteristic
111C2×C4⋊C4×C59D411yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C4⋊C4×C59C2311yescharacteristic
116C2×C4⋊C4×C59C2311yescharacteristic
117C2×C22⋊C4×C59—21no—
118C2×C22⋊C4×C59—21no—
119C2×C22⋊C4×C59—21no—
120C2×C22⋊C4×C59—21no—
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59D411yescharacteristic
124C2×C22⋊C4×C59D411yescharacteristic
125C2×C42×C59—21no—
126C2×C42×C59—21no—
127C2×C42×C59C2311yescharacteristic
128C2×C42×C59C2311yescharacteristic
129#107×C59—22no—
130#106×C59—22no—
131#103×C59—22no—
132#103×C59—22no—
133#102×C59—22no—
134#102×C59—22no—
135#102×C59—22no—
136#102×C59—22no—
137#102×C59—22no—
138#102×C59—22no—
139C22⋊C8×C59—22no—
140C22⋊C8×C59—22no—
141#97×C59—22no—
142C4×C8×C59—22no—
143#95×C59—21no—
144#95×C59—21no—
145#95×C59—21no—
146#95×C59—21no—
147#95×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59C2×D411yescharacteristic
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59#4112yes—
157C2×D4×C59—24no—
158C2×D4×C59—24no—
159C2×D4×C59—24no—
160C2×D4×C59—24no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59—21no—
166C2×D4×C59—21no—
167C2×D4×C59—21no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—21no—
171C2×D4×C59—81no—
172C2×D4×C59—81no—
173C2×D4×C59—81no—
174C2×D4×C59—81no—
175C2×D4×C59—81no—
176C2×D4×C59—81no—
177C2×D4×C59—81no—
178C2×D4×C59—81no—
179C2×D4×C59C2×D412yes—
180C2×D4×C59C2×D412yes—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—24no—
192C22×C4×C59—24no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—81no—
196C22×C4×C59—81no—
197C22×C4×C59—81no—
198C22×C4×C59—81no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2411yescharacteristic
205SD16×C59—28no—
206SD16×C59—28no—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59—21no—
212C2×C8×C59—21no—
213C2×C8×C59—21no—
214C2×C8×C59—21no—
215C2×C8×C59—21no—
216C2×C8×C59—21no—
217C2×C8×C59#4112yes—
218C2×C8×C59#4112yes—
219C4⋊C4×C59—24no—
220C4⋊C4×C59—24no—
221C4⋊C4×C59—24no—
222C4⋊C4×C59—22no—
223C4⋊C4×C59—22no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—42no—
232C4⋊C4×C59—81no—
233C4⋊C4×C59C2×D412yes—
234C4⋊C4×C59C2×D412yes—
235C4⋊C4×C59#4112yes—
236C22⋊C4×C59—24no—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—22no—
242C22⋊C4×C59—22no—
243C22⋊C4×C59—81no—
244C42×C59—21no—
245C42×C59—21no—
246C42×C59—42no—
247C42×C59—81no—
248C42×C59C2×D412yes—
249C42×C59C2×D412yes—
250C23×C59—21no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59C22×D411yescharacteristic
272Q8×C59—22no—
273Q8×C59—22no—
274Q8×C59—41no—
275Q8×C59—41no—
276D4×C59—22no—
277D4×C59—22no—
278D4×C59—22no—
279D4×C59—22no—
280D4×C59—41no—
281D4×C59—41no—
282D4×C59—41no—
283D4×C59—41no—
284D4×C59—84no—
285D4×C59—84no—
286D4×C59—84no—
287D4×C59—84no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—41no—
315C2×C4×C59—41no—
316C2×C4×C59—41no—
317C2×C4×C59—41no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—84no—
324C2×C4×C59—84no—
325C2×C4×C59#12012yes—
326C2×C4×C59#12012yes—
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4111yescharacteristic
330C2×C4×C59C2×#4111yescharacteristic
331C2×C4×C59C2×#4111yescharacteristic
332C2×C4×C59C2×#4111yescharacteristic
333C8×C59—22no—
334C8×C59—22no—
335C8×C59—41no—
336C8×C59—41no—
337#23582C5911yesmaximal, characteristic, direct product factor, Sylow
338C22×C59—41no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—42no—
346C22×C59—41no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—41no—
350C22×C59—42no—
351C22×C59—81no—
352C22×C59—81no—
353C22×C59—81no—
354C22×C59—81no—
355C22×C59—81no—
356C22×C59—81no—
357C22×C59—81no—
358C22×C59—81no—
359C22×C59C2×#12011yescharacteristic
360C22×C59#52511yescharacteristic
361C22×C59#53211yescharacteristic
362C22×C59#57611yescharacteristic
363C22×C59#57711yescharacteristic
364C22×C59#57711yescharacteristic
365C22×C59#57711yescharacteristic
366C4×C59—22no—
367C4×C59—22no—
368C4×C59—42no—
369C4×C59—41no—
370C4×C59—42no—
371C4×C59—41no—
372C4×C59—42no—
373C4×C59—41no—
374C4×C59—42no—
375C4×C59—81no—
376C4×C59—81no—
377C4×C59#52511yescharacteristic
378C4×C59#52511yescharacteristic
379C4×C59#53211yescharacteristic
380C4×C59#53211yescharacteristic
381C2×#540C2×C5911yescharacteristic
382C2×#440C2×C5911yescharacteristic, complemented
383C2×C4×SD16C2×C5911yescharacteristic, complemented
384#2323C2×C5911yescharacteristic, complemented
385#2059C2×C5911yescharacteristic, complemented
386#2041C2×C5911yescharacteristic, complemented
387#2034C2×C5911yescharacteristic, complemented
388#2033C2×C5911yescharacteristic, complemented
389#2026C2×C5911yescharacteristic, complemented
390#2014C2×C5911yescharacteristic, complemented
391#2000C2×C5911yescharacteristic, complemented
392#2000C2×C5911yescharacteristic, complemented
393#1762C2×C5911yescharacteristic, complemented
394C4×#102C2×C5911yescharacteristic, complemented
395#1750C2×C5911yescharacteristic, complemented
396C2×C59—81no—
397C2×C59—82no—
398C2×C59—82no—
399C2×C59#238811yescharacteristic
400C2×C59#300911yescharacteristic
401C2×C59#301211yescharacteristic
402C2×C59#311911yescharacteristic
403C2×C59#312611yescharacteristic
404C2×C59#317411yescharacteristic
405C2×C59#317911yescharacteristic
406C22×SD16C22×C5911yescharacteristic
407C22×SD16C22×C5911yescharacteristic
408#540—24no—
409#540—24no—
410C2×#127C22×C5911yescharacteristic
411C2×#125C22×C5911yescharacteristic
412C2×#123—21no—
413C2×#123—21no—
414C2×C22⋊Q8C22×C5911yescharacteristic
415C2×#121—21no—
416C2×#121—21no—
417C2×#121C22×C5911yescharacteristic
418C2×#121C22×C5911yescharacteristic
419C2×C4×Q8C22×C5911yescharacteristic
420C2×C4×D4C22×C5911yescharacteristic
421C2×C4×D4C22×C5911yescharacteristic
422C2×#117C22×C5911yescharacteristic
423#440—24no—
424C4×SD16—24no—
425C2×#107C22×C5911yescharacteristic
426C2×#106C22×C5911yescharacteristic
427C2×#103C22×C5911yescharacteristic
428C2×#103C22×C5911yescharacteristic
429C2×#102C22×C5911yescharacteristic
430C2×#102C22×C5911yescharacteristic
431C2×#102C22×C5911yescharacteristic
432C2×#102C22×C5911yescharacteristic
433C2×#102C22×C5911yescharacteristic
434C2×#102C22×C5911yescharacteristic
435C2×C22⋊C8C22×C5911yescharacteristic
436C2×C22⋊C8C22×C5911yescharacteristic
437C2×#97C22×C5911yescharacteristic
438C2×C4×C8C22×C5911yescharacteristic
439#391C22×C5911yescharacteristic
440#389—21no—
441#389C22×C5911yescharacteristic
442#388—21no—
443#388—21no—
444#387—21no—
445#380C22×C5911yescharacteristic
446C4×C4⋊C4C22×C5911yescharacteristic
447#340C22×C5911yescharacteristic
448#340C22×C5911yescharacteristic
449#340C22×C5911yescharacteristic
450#340C22×C5911yescharacteristic
451#336C22×C5911yescharacteristic
452#336C22×C5911yescharacteristic
453C59#2358211yescharacteristic, direct product factor, Sylow
454C22×Q8C23×C5911yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C5911yescharacteristic
460C22×D4C23×C5911yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C5911yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—22no—
470C22×C8C23×C5911yescharacteristic
471C22×C8C23×C5911yescharacteristic
472C22×C8C23×C5911yescharacteristic
473C22×C8C23×C5911yescharacteristic
474#127—22no—
475#127—22no—
476#125—22no—
477#125—22no—
478#123—28no—
479#123—28no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482#121—28no—
483#121—28no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4D4×C5914yes—
493C4×D4D4×C5914yes—
494#117—22no—
495#117—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C5911yescharacteristic
502C2×C4⋊C4D4×C5911yescharacteristic
503C2×C4⋊C4C23×C5911yescharacteristic
504C2×C4⋊C4C23×C5911yescharacteristic
505C2×C4⋊C4C23×C5911yescharacteristic
506C2×C4⋊C4C23×C5911yescharacteristic
507C2×C4⋊C4C23×C5911yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4D4×C5911yescharacteristic
515C2×C22⋊C4D4×C5911yescharacteristic
516C2×C42—21no—
517C2×C42—21no—
518C2×C42C23×C5911yescharacteristic
519C2×C42C23×C5911yescharacteristic
520#107—22no—
521#106—22no—
522#103—22no—
523#103—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532#97—22no—
533C4×C8—22no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C5911yescharacteristic
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8#41×C5912yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×D4×C5912yes—
571C2×D4C2×D4×C5912yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C2×D4×C5911yescharacteristic
591C22×C4C2×D4×C5911yescharacteristic
592C22×C4C2×D4×C5911yescharacteristic
593C22×C4C2×D4×C5911yescharacteristic
594C22×C4C2×D4×C5911yescharacteristic
595C22×C4C24×C5911yescharacteristic
596SD16—28no—
597SD16—28no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8#41×C5912yes—
609C2×C8#41×C5912yes—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—81no—
624C4⋊C4C2×D4×C5912yes—
625C4⋊C4C2×D4×C5912yes—
626C4⋊C4#41×C5912yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—81no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C42C2×D4×C5912yes—
640C42C2×D4×C5912yes—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23C22×D4×C5911yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677D4—84no—
678D4—84no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4#120×C5912yes—
717C2×C4#120×C5912yes—
718C2×C4C22×D4×C5911yescharacteristic
719C2×C4C22×D4×C5911yescharacteristic
720C2×C4C2×#41×C5911yescharacteristic
721C2×C4C2×#41×C5911yescharacteristic
722C2×C4C2×#41×C5911yescharacteristic
723C2×C4C2×#41×C5911yescharacteristic
724C8—22no—
725C8—22no—
726C8—41no—
727C8—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C2×#120×C5911yescharacteristic
750C22C59×#52511yescharacteristic
751C22C59×#53211yescharacteristic
752C22C59×#57611yescharacteristic
753C22C59×#57711yescharacteristic
754C22C59×#57711yescharacteristic
755C22C59×#57711yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—42no—
762C4—42no—
763C4—41no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4C59×#52511yescharacteristic
768C4C59×#52511yescharacteristic
769C4C59×#53211yescharacteristic
770C4C59×#53211yescharacteristic
771C2—81no—
772C2—82no—
773C2—82no—
774C2C59×#238811yescharacteristic
775C2C59×#300911yescharacteristic
776C2C59×#301211yescharacteristic
777C2C59×#311911yescharacteristic
778C2C59×#312611yescharacteristic
779C2C59×#317411yescharacteristic
780C2C59×#317911yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×C59×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×#117×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#440C2semidirect
3. C2×C4×SD16×C59C2semidirect
4. C59×#2323C2semidirect
5. C59×#2059C2semidirect
6. C59×#2041C2semidirect
7. C59×#2034C2semidirect
8. C59×#2033C2semidirect
9. C59×#2026C2semidirect
10. C59×#2014C2semidirect
11. C59×#2000C2semidirect
12. C59×#2000C2semidirect
13. C59×#1762C2semidirect
14. C4×#102×C59C2semidirect
15. C59×#1750C2semidirect
337. #23582C59direct (N × H)
382. C2×#440C2×C59semidirect
383. C2×C4×SD16C2×C59semidirect
384. #2323C2×C59semidirect
385. #2059C2×C59semidirect
386. #2041C2×C59semidirect
387. #2034C2×C59semidirect
388. #2033C2×C59semidirect
389. #2026C2×C59semidirect
390. #2014C2×C59semidirect
391. #2000C2×C59semidirect
392. #2000C2×C59semidirect
393. #1762C2×C59semidirect
394. C4×#102C2×C59semidirect
395. #1750C2×C59semidirect
453. C59#23582direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#5402
C2×C59×#4402
C2×C4×SD16×C592
C59×#23232
C59×#20592
C59×#20412
C59×#20342
C59×#20332
C59×#20262
C59×#20142
C59×#20002
C59×#17622
C4×#102×C592
C59×#17502
#2358259