Finite Group Databasebeta

← C59×#24485 #28436594

Subgroups — C59×#24485 #28436594

Order 15104.

954 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#485C211yesmaximal, characteristic, complemented
2C2×C59×#416C211yesmaximal, characteristic
3C59×#2432C211yesmaximal, characteristic
4C59×#2347C211yesmaximal, characteristic, complemented
5C59×#2068C211yesmaximal, characteristic, complemented
6C59×#2067C211yesmaximal, characteristic, complemented
7C59×#2043C211yesmaximal, characteristic, complemented
8C59×#2042C211yesmaximal, characteristic, complemented
9C59×#1983C211yesmaximal, characteristic, complemented
10C59×#1981C211yesmaximal, characteristic, complemented
11C59×#1927C211yesmaximal, characteristic, complemented
12C59×#1926C211yesmaximal, characteristic, complemented
13C59×#1892C211yesmaximal, characteristic, complemented
14C59×#1850C211yesmaximal, characteristic, complemented
15C59×#1788C211yesmaximal, characteristic
16C22×#41×C59C2211yescharacteristic
17C23×C8×C59C2211yescharacteristic
18C2×C4⋊Q8×C59C2211yescharacteristic
19C2×#124×C59C2211yescharacteristic
20C2×C22⋊Q8×C59C2211yescharacteristic
21C2×#117×C59C2211yescharacteristic
22C59×#485—24no—
23C2×#107×C59C2211yescharacteristic
24C2×#106×C59C2211yescharacteristic
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×C4⋊C8×C59C2211yescharacteristic
27C59×#416—24no—
28C2×#103×C59C2211yescharacteristic
29C2×#103×C59C2211yescharacteristic
30C2×#103×C59C2211yescharacteristic
31C2×#103×C59C2211yescharacteristic
32C2×#103×C59C2211yescharacteristic
33C2×#103×C59C2211yescharacteristic
34C2×#103×C59C2211yescharacteristic
35C2×#103×C59C2211yescharacteristic
36C2×#102×C59C2211yescharacteristic
37C2×#102×C59C2211yescharacteristic
38C2×#102×C59C2211yescharacteristic
39C2×#102×C59C2211yescharacteristic
40C2×C22⋊C8×C59C2211yescharacteristic
41C59×#394—21no—
42C59×#394—21no—
43C59×#391C2211yescharacteristic
44C59×#390C2211yescharacteristic
45C59×#389C2211yescharacteristic
46C59×#389C2211yescharacteristic
47C59×#388—21no—
48C59×#388—21no—
49C59×#385—21no—
50C59×#385—21no—
51C59×#383—21no—
52C59×#380C2211yescharacteristic
53C4×C4⋊C4×C59—21no—
54C4×C4⋊C4×C59C2211yescharacteristic
55C4×C4⋊C4×C59C2211yescharacteristic
56C4×C22⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C2×#41×C59—22no—
62C2×#41×C59—22no—
63C2×#41×C59—22no—
64C2×#41×C59—22no—
65C2×#41×C59—41no—
66C2×#41×C59—41no—
67C22×Q8×C59C2311yescharacteristic
68C22×Q8×C59C2311yescharacteristic
69C22×D4×C59—21no—
70C22×D4×C59C2311yescharacteristic
71C23×C4×C59—21no—
72C23×C4×C59C2311yescharacteristic
73C22×C8×C59—22no—
74C22×C8×C59—41no—
75C22×C8×C59—41no—
76C22×C8×C59C2311yescharacteristic
77C22×C8×C59C2311yescharacteristic
78C22×C8×C59C2311yescharacteristic
79C22×C8×C59C2311yescharacteristic
80C4⋊Q8×C59—22no—
81C4⋊Q8×C59—41no—
82#124×C59—22no—
83#124×C59—41no—
84C22⋊Q8×C59—22no—
85C22⋊Q8×C59—22no—
86#117×C59—22no—
87#117×C59D414yes—
88C2×C4⋊C4×C59—21no—
89C2×C4⋊C4×C59—21no—
90C2×C4⋊C4×C59—21no—
91C2×C4⋊C4×C59—21no—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59C2311yescharacteristic
94C2×C4⋊C4×C59C2311yescharacteristic
95C2×C4⋊C4×C59C2311yescharacteristic
96C2×C4⋊C4×C59C2311yescharacteristic
97C2×C4⋊C4×C59C2311yescharacteristic
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—21no—
100C2×C22⋊C4×C59—21no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—21no—
103C2×C22⋊C4×C59—21no—
104C2×C22⋊C4×C59—21no—
105C2×C22⋊C4×C59D411yescharacteristic
106C2×C22⋊C4×C59D411yescharacteristic
107C2×C42×C59—21no—
108C2×C42×C59—21no—
109C2×C42×C59—21no—
110C2×C42×C59C2311yescharacteristic
111C2×C42×C59C2311yescharacteristic
112#107×C59—22no—
113#106×C59—22no—
114C4⋊C8×C59—41no—
115C4⋊C8×C59—41no—
116#103×C59—22no—
117#103×C59—22no—
118#103×C59—22no—
119#103×C59—22no—
120#103×C59—22no—
121#103×C59—41no—
122#103×C59—41no—
123#103×C59—41no—
124#102×C59—22no—
125#102×C59—22no—
126#102×C59—22no—
127#102×C59—41no—
128C22⋊C8×C59—22no—
129#95×C59—21no—
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59—21no—
139C24×C59C2×D411yescharacteristic
140#41×C59—28no—
141#41×C59—44no—
142#41×C59—44no—
143#41×C59—44no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59#4112yes—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59#4112yes—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—42no—
177C22×C4×C59—42no—
178C22×C4×C59—42no—
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D412yes—
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59#4112yes—
186C22×C4×C59C2411yescharacteristic
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—44no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—42no—
209C4⋊C4×C59—42no—
210C4⋊C4×C59—42no—
211C4⋊C4×C59—42no—
212C4⋊C4×C59—42no—
213C4⋊C4×C59C2×D412yes—
214C4⋊C4×C59C2×D412yes—
215C22⋊C4×C59—24no—
216C22⋊C4×C59—22no—
217C22⋊C4×C59—41no—
218C22⋊C4×C59—42no—
219C22⋊C4×C59—42no—
220C22⋊C4×C59—42no—
221C22⋊C4×C59—42no—
222C22⋊C4×C59—42no—
223C22⋊C4×C59—81no—
224C42×C59—24no—
225C42×C59—21no—
226C42×C59—21no—
227C42×C59—21no—
228C42×C59—21no—
229C42×C59—81no—
230C42×C59—81no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—22no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59#12112yes—
245C23×C59C22×D411yescharacteristic
246Q8×C59—22no—
247Q8×C59—22no—
248Q8×C59—41no—
249Q8×C59—41no—
250Q8×C59—41no—
251Q8×C59—41no—
252Q8×C59—41no—
253Q8×C59—41no—
254D4×C59—22no—
255D4×C59—22no—
256D4×C59—48no—
257D4×C59—41no—
258D4×C59—41no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—22no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—48no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
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—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59#12112yes—
299C2×C4×C59#13512yes—
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C2×#4111yescharacteristic
302C2×C4×C59C2×#4111yescharacteristic
303C2×C4×C59C2×#4111yescharacteristic
304C2×C4×C59H(5,𝔽2)11yescharacteristic
305C2×C4×C59H(5,𝔽2)11yescharacteristic
306C8×C59—41no—
307C8×C59—41no—
308C8×C59—41no—
309C8×C59—41no—
310#24485C5911yesmaximal, characteristic, direct product factor, Sylow
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—42no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—81no—
322C22×C59—81no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59C2×#12111yescharacteristic
326C22×C59#54611yescharacteristic
327C22×C59#54611yescharacteristic
328C22×C59C2×#13511yescharacteristic
329C22×C59#57511yescharacteristic
330C22×C59#57711yescharacteristic
331C22×C59#57811yescharacteristic
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—42no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—41no—
338C4×C59—41no—
339C4×C59—41no—
340C4×C59—81no—
341C4×C59—81no—
342C4×C59—81no—
343C4×C59—81no—
344C4×C59#52511yescharacteristic
345C4×C59#53511yescharacteristic
346C4×C59#55111yescharacteristic
347C4×C59#55111yescharacteristic
348C2×#485C2×C5911yescharacteristic, complemented
349C2×#416C2×C5911yescharacteristic
350#2432C2×C5911yescharacteristic
351#2347C2×C5911yescharacteristic, complemented
352#2068C2×C5911yescharacteristic, complemented
353#2067C2×C5911yescharacteristic, complemented
354#2043C2×C5911yescharacteristic, complemented
355#2042C2×C5911yescharacteristic, complemented
356#1983C2×C5911yescharacteristic, complemented
357#1981C2×C5911yescharacteristic, complemented
358#1927C2×C5911yescharacteristic, complemented
359#1926C2×C5911yescharacteristic, complemented
360#1892C2×C5911yescharacteristic, complemented
361#1850C2×C5911yescharacteristic, complemented
362#1788C2×C5911yescharacteristic
363C2×C59—42no—
364C2×C59—82no—
365C2×C59#241111yescharacteristic
366C2×C59#303511yescharacteristic
367C2×C59#304611yescharacteristic
368C2×C59#330111yescharacteristic
369C2×C59#330211yescharacteristic
370C2×C59#330711yescharacteristic
371C2×C59#331311yescharacteristic
372C22×#41C22×C5911yescharacteristic
373C23×C8C22×C5911yescharacteristic
374C2×C4⋊Q8C22×C5911yescharacteristic
375C2×#124C22×C5911yescharacteristic
376C2×C22⋊Q8C22×C5911yescharacteristic
377C2×#117C22×C5911yescharacteristic
378#485—24no—
379C2×#107C22×C5911yescharacteristic
380C2×#106C22×C5911yescharacteristic
381C2×C4⋊C8C22×C5911yescharacteristic
382C2×C4⋊C8C22×C5911yescharacteristic
383#416—24no—
384C2×#103C22×C5911yescharacteristic
385C2×#103C22×C5911yescharacteristic
386C2×#103C22×C5911yescharacteristic
387C2×#103C22×C5911yescharacteristic
388C2×#103C22×C5911yescharacteristic
389C2×#103C22×C5911yescharacteristic
390C2×#103C22×C5911yescharacteristic
391C2×#103C22×C5911yescharacteristic
392C2×#102C22×C5911yescharacteristic
393C2×#102C22×C5911yescharacteristic
394C2×#102C22×C5911yescharacteristic
395C2×#102C22×C5911yescharacteristic
396C2×C22⋊C8C22×C5911yescharacteristic
397#394—21no—
398#394—21no—
399#391C22×C5911yescharacteristic
400#390C22×C5911yescharacteristic
401#389C22×C5911yescharacteristic
402#389C22×C5911yescharacteristic
403#388—21no—
404#388—21no—
405#385—21no—
406#385—21no—
407#383—21no—
408#380C22×C5911yescharacteristic
409C4×C4⋊C4—21no—
410C4×C4⋊C4C22×C5911yescharacteristic
411C4×C4⋊C4C22×C5911yescharacteristic
412C4×C22⋊C4C22×C5911yescharacteristic
413#340C22×C5911yescharacteristic
414#340C22×C5911yescharacteristic
415#336C22×C5911yescharacteristic
416#336C22×C5911yescharacteristic
417C59#2448511yescharacteristic, direct product factor, Sylow
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—41no—
423C2×#41—41no—
424C22×Q8C23×C5911yescharacteristic
425C22×Q8C23×C5911yescharacteristic
426C22×D4—21no—
427C22×D4C23×C5911yescharacteristic
428C23×C4—21no—
429C23×C4C23×C5911yescharacteristic
430C22×C8—22no—
431C22×C8—41no—
432C22×C8—41no—
433C22×C8C23×C5911yescharacteristic
434C22×C8C23×C5911yescharacteristic
435C22×C8C23×C5911yescharacteristic
436C22×C8C23×C5911yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8—41no—
439#124—22no—
440#124—41no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443#117—22no—
444#117D4×C5914yes—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C5911yescharacteristic
451C2×C4⋊C4C23×C5911yescharacteristic
452C2×C4⋊C4C23×C5911yescharacteristic
453C2×C4⋊C4C23×C5911yescharacteristic
454C2×C4⋊C4C23×C5911yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C5911yescharacteristic
463C2×C22⋊C4D4×C5911yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C5911yescharacteristic
468C2×C42C23×C5911yescharacteristic
469#107—22no—
470#106—22no—
471C4⋊C8—41no—
472C4⋊C8—41no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—41no—
479#103—41no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—41no—
485C22⋊C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95D4×C5911yescharacteristic
494#95D4×C5911yescharacteristic
495C24—21no—
496C24C2×D4×C5911yescharacteristic
497#41—28no—
498#41—44no—
499#41—44no—
500#41—44no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8#41×C5912yes—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4#41×C5912yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4C2×D4×C5911yescharacteristic
537C22×C4C2×D4×C5911yescharacteristic
538C22×C4C2×D4×C5911yescharacteristic
539C22×C4C2×D4×C5911yescharacteristic
540C22×C4C2×D4×C5912yes—
541C22×C4C2×D4×C5911yescharacteristic
542C22×C4#41×C5912yes—
543C22×C4C24×C5911yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—44no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4C2×D4×C5912yes—
571C4⋊C4C2×D4×C5912yes—
572C22⋊C4—24no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C42—24no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—81no—
587C42—81no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#121×C5912yes—
602C23C22×D4×C5911yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—48no—
614D4—41no—
615D4—41no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4#121×C5912yes—
656C2×C4#135×C5912yes—
657C2×C4C22×D4×C5911yescharacteristic
658C2×C4C2×#41×C5911yescharacteristic
659C2×C4C2×#41×C5911yescharacteristic
660C2×C4C2×#41×C5911yescharacteristic
661C2×C4H(5,𝔽2)×C5911yescharacteristic
662C2×C4H(5,𝔽2)×C5911yescharacteristic
663C8—41no—
664C8—41no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#121×C5911yescharacteristic
682C22C59×#54611yescharacteristic
683C22C59×#54611yescharacteristic
684C22C2×#135×C5911yescharacteristic
685C22C59×#57511yescharacteristic
686C22C59×#57711yescharacteristic
687C22C59×#57811yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C59×#52511yescharacteristic
701C4C59×#53511yescharacteristic
702C4C59×#55111yescharacteristic
703C4C59×#55111yescharacteristic
704C2—42no—
705C2—82no—
706C2C59×#241111yescharacteristic
707C2C59×#303511yescharacteristic
708C2C59×#304611yescharacteristic
709C2C59×#330111yescharacteristic
710C2C59×#330211yescharacteristic
711C2C59×#330711yescharacteristic
712C2C59×#331311yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC22×#41×C59C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C4×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#485C2semidirect
4. C59×#2347C2semidirect
5. C59×#2068C2semidirect
6. C59×#2067C2semidirect
7. C59×#2043C2semidirect
8. C59×#2042C2semidirect
9. C59×#1983C2semidirect
10. C59×#1981C2semidirect
11. C59×#1927C2semidirect
12. C59×#1926C2semidirect
13. C59×#1892C2semidirect
14. C59×#1850C2semidirect
310. #24485C59direct (N × H)
348. C2×#485C2×C59semidirect
351. #2347C2×C59semidirect
352. #2068C2×C59semidirect
353. #2067C2×C59semidirect
354. #2043C2×C59semidirect
355. #2042C2×C59semidirect
356. #1983C2×C59semidirect
357. #1981C2×C59semidirect
358. #1927C2×C59semidirect
359. #1926C2×C59semidirect
360. #1892C2×C59semidirect
361. #1850C2×C59semidirect
417. C59#24485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4852
C2×C59×#4162
C59×#24322
C59×#23472
C59×#20682
C59×#20672
C59×#20432
C59×#20422
C59×#19832
C59×#19812
C59×#19272
C59×#19262
C59×#18922
C59×#18502
C59×#17882
#2448559