Finite Group Databasebeta

← C59×#16265 #28428374

Subgroups — C59×#16265 #28428374

Order 15104.

2102 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C59C211yesmaximal, characteristic, complemented
2C2×C59×#396C212yesmaximal, complemented
3C2×C59×#393C211yesmaximal, characteristic, complemented
4C2×C59×#386C211yesmaximal, characteristic
5C2×C59×#380C211yesmaximal, characteristic, complemented
6C59×#1446C211yesmaximal, characteristic, complemented
7C59×#1444C211yesmaximal, characteristic, complemented
8C59×#1441C212yesmaximal, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C212yesmaximal, complemented
11C59×#1438C212yesmaximal
12C23×Q8×C59C2211yescharacteristic
13C23×D4×C59C2211yescharacteristic
14C24×C4×C59C2211yescharacteristic
15C2×C22⋊Q8×C59—24no—
16C2×C22⋊Q8×C59—28no—
17C22×C4⋊C4×C59C2211yescharacteristic
18C22×C4⋊C4×C59C2212yes—
19C22×C4⋊C4×C59C2212yes—
20C22×C4⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2211yescharacteristic
23C22×C22⋊C4×C59C2212yes—
24C22×C22⋊C4×C59C2212yes—
25C22×C22⋊C4×C59C2212yes—
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C22⋊C4×C59C2212yes—
28C59×#396—28no—
29C59×#393—24no—
30C59×#386—24no—
31C59×#380—24no—
32C2×#95×C59C2211yescharacteristic
33C2×#95×C59C2211yescharacteristic
34C2×#95×C59C2211yescharacteristic
35C2×#95×C59C2212yes—
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2211yescharacteristic
41C25×C59C2311yescharacteristic
42C25×C59C2311yescharacteristic
43C22×Q8×C59—24no—
44C22×Q8×C59—22no—
45C22×Q8×C59—22no—
46C22×Q8×C59—22no—
47C22×Q8×C59—42no—
48C22×D4×C59—22no—
49C22×D4×C59—22no—
50C22×D4×C59—42no—
51C22×D4×C59—42no—
52C22×D4×C59Q814yescomplemented
53C23×C4×C59—22no—
54C23×C4×C59—24no—
55C23×C4×C59—22no—
56C23×C4×C59—42no—
57C23×C4×C59D414yes—
58C23×C4×C59C2311yescharacteristic
59C23×C4×C59C2312yes—
60C23×C4×C59C2311yescharacteristic
61C23×C4×C59C2312yes—
62C23×C4×C59C2312yes—
63C23×C4×C59C2312yes—
64C23×C4×C59C2311yescharacteristic
65C23×C4×C59C2311yescharacteristic
66C23×C4×C59C2311yescharacteristic
67C22⋊Q8×C59—232no—
68C2×C4⋊C4×C59—24no—
69C2×C4⋊C4×C59—22no—
70C2×C4⋊C4×C59—24no—
71C2×C4⋊C4×C59—24no—
72C2×C4⋊C4×C59—24no—
73C2×C4⋊C4×C59—24no—
74C2×C4⋊C4×C59—24no—
75C2×C4⋊C4×C59—42no—
76C2×C4⋊C4×C59—42no—
77C2×C4⋊C4×C59—42no—
78C2×C4⋊C4×C59D418yescomplemented
79C2×C22⋊C4×C59—24no—
80C2×C22⋊C4×C59—24no—
81C2×C22⋊C4×C59—24no—
82C2×C22⋊C4×C59—22no—
83C2×C22⋊C4×C59—24no—
84C2×C22⋊C4×C59—24no—
85C2×C22⋊C4×C59—22no—
86C2×C22⋊C4×C59—22no—
87C2×C22⋊C4×C59—24no—
88C2×C22⋊C4×C59—22no—
89C2×C22⋊C4×C59—24no—
90C2×C22⋊C4×C59—24no—
91C2×C22⋊C4×C59—24no—
92C2×C22⋊C4×C59—22no—
93C2×C22⋊C4×C59—42no—
94C2×C22⋊C4×C59—42no—
95C2×C22⋊C4×C59—42no—
96C2×C22⋊C4×C59—42no—
97C2×C22⋊C4×C59—42no—
98#95×C59—22no—
99#95×C59—22no—
100#95×C59—22no—
101#95×C59—24no—
102#95×C59—24no—
103#95×C59—42no—
104#95×C59—42no—
105#95×C59—42no—
106#95×C59D414yescomplemented
107C24×C59—22no—
108C24×C59—21no—
109C24×C59—21no—
110C24×C59—21no—
111C24×C59—22no—
112C24×C59—22no—
113C24×C59—22no—
114C24×C59—21no—
115C24×C59—22no—
116C24×C59—21no—
117C24×C59—21no—
118C24×C59—21no—
119C24×C59—21no—
120C24×C59—21no—
121C24×C59—22no—
122C24×C59—22no—
123C24×C59—22no—
124C24×C59—21no—
125C24×C59C2×D412yes—
126C24×C59C2×Q812yes—
127C24×C59C2×Q812yes—
128C24×C59#4112yes—
129C24×C59C2411yescharacteristic
130C2×Q8×C59—28no—
131C2×Q8×C59—48no—
132C2×Q8×C59—48no—
133C2×Q8×C59—44no—
134C2×Q8×C59—44no—
135C2×D4×C59—28no—
136C2×D4×C59—48no—
137C2×D4×C59—44no—
138C2×D4×C59—44no—
139C2×D4×C59—48no—
140C22×C4×C59—21no—
141C22×C4×C59—22no—
142C22×C4×C59—21no—
143C22×C4×C59—22no—
144C22×C4×C59—22no—
145C22×C4×C59—21no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—21no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—28no—
168C22×C4×C59—28no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—21no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—21no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—22no—
186C22×C4×C59—44no—
187C22×C4×C59—48no—
188C22×C4×C59—48no—
189C22×C4×C59C2×D414yes—
190C22×C4×C59C2×D414yes—
191C22×C4×C59C2×D414yes—
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2×D414yes—
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2×Q812yes—
197C22×C4×C59#4112yes—
198C4⋊C4×C59—28no—
199C4⋊C4×C59—216no—
200C4⋊C4×C59—48no—
201C4⋊C4×C59—48no—
202C22⋊C4×C59—216no—
203C22⋊C4×C59—48no—
204C22⋊C4×C59—48no—
205C22⋊C4×C59—48no—
206C22⋊C4×C59—44no—
207C22⋊C4×C59—44no—
208C22⋊C4×C59—44no—
209C23×C59—22no—
210C23×C59—22no—
211C23×C59—22no—
212C23×C59—22no—
213C23×C59—22no—
214C23×C59—22no—
215C23×C59—24no—
216C23×C59—24no—
217C23×C59—22no—
218C23×C59—24no—
219C23×C59—24no—
220C23×C59—22no—
221C23×C59—22no—
222C23×C59—22no—
223C23×C59—22no—
224C23×C59—24no—
225C23×C59—24no—
226C23×C59—22no—
227C23×C59—22no—
228C23×C59—42no—
229C23×C59—42no—
230C23×C59—42no—
231C23×C59—42no—
232C23×C59—42no—
233C23×C59—42no—
234C23×C59—42no—
235C23×C59—42no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—42no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—42no—
244C23×C59—42no—
245C23×C59—42no—
246C23×C59—42no—
247C23×C59—42no—
248C23×C59—41no—
249C23×C59—42no—
250C23×C59—42no—
251C23×C59—41no—
252C23×C59—42no—
253C23×C59—42no—
254C23×C59C22⋊Q814yes—
255C23×C59C22×D411yescharacteristic
256C23×C59C22×D412yes—
257C23×C59C22×D411yescharacteristic
258C23×C59C22×Q811yescharacteristic
259C23×C59C2×#4111yescharacteristic
260C23×C59C2×#4111yescharacteristic
261C23×C59H(5,𝔽2)12yes—
262C23×C59H(5,𝔽2)12yes—
263C23×C59H(5,𝔽2)11yescharacteristic
264C23×C592−1+412yes—
265C23×C592−1+411yescharacteristic
266Q8×C59—416no—
267D4×C59—416no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—24no—
273C2×C4×C59—24no—
274C2×C4×C59—24no—
275C2×C4×C59—24no—
276C2×C4×C59—24no—
277C2×C4×C59—24no—
278C2×C4×C59—22no—
279C2×C4×C59—24no—
280C2×C4×C59—24no—
281C2×C4×C59—24no—
282C2×C4×C59—24no—
283C2×C4×C59—24no—
284C2×C4×C59—24no—
285C2×C4×C59—24no—
286C2×C4×C59—24no—
287C2×C4×C59—416no—
288C2×C4×C59—42no—
289C2×C4×C59—41no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—41no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—42no—
312C2×C4×C59—42no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59#12014yes—
321C2×C4×C59#12114yes—
322#16265C5911yesmaximal, characteristic, direct product factor, Sylow
323C22×C59—24no—
324C22×C59—24no—
325C22×C59—24no—
326C22×C59—42no—
327C22×C59—42no—
328C22×C59—42no—
329C22×C59—44no—
330C22×C59—44no—
331C22×C59—44no—
332C22×C59—44no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—44no—
338C22×C59—44no—
339C22×C59—81no—
340C22×C59—81no—
341C22×C59—81no—
342C22×C59—82no—
343C22×C59—82no—
344C22×C59—81no—
345C22×C59C2×#12011yescharacteristic
346C22×C59C2×#12111yescharacteristic
347C22×C59C2×C22⋊Q811yescharacteristic
348C22×C59#53411yescharacteristic
349C22×C59#53511yescharacteristic
350C22×C59#53512yes—
351C22×C59#53611yescharacteristic
352C22×C59#53711yescharacteristic
353C22×C59#53712yes—
354C22×C59#53712yes—
355C22×C59#53812yes—
356C22×C59#54212yes—
357C22×C59#54312yes—
358C22×C59D4212yes—
359C22×C59#54612yes—
360C22×C59#54611yescharacteristic
361C22×C59#54812yes—
362C22×C59D4×Q812yes—
363C22×C59D4×Q811yescharacteristic
364C22×C59#55211yescharacteristic
365C22×C59#55411yescharacteristic
366C22×C59#56212yes—
367C22×C59#56312yes—
368C4×C59—24no—
369C4×C59—24no—
370C4×C59—44no—
371C4×C59—42no—
372C4×C59—44no—
373C4×C59—44no—
374C4×C59—81no—
375C4×C59—81no—
376C4×C59—82no—
377C22×C22⋊Q8C2×C5911yescharacteristic, complemented
378C2×#396C2×C5912yescomplemented
379C2×#393C2×C5911yescharacteristic, complemented
380C2×#386C2×C5911yescharacteristic
381C2×#380C2×C5911yescharacteristic, complemented
382#1446C2×C5911yescharacteristic, complemented
383#1444C2×C5911yescharacteristic, complemented
384#1441C2×C5912yescomplemented
385#1439C2×C5911yescharacteristic, complemented
386#1439C2×C5912yescomplemented
387#1438C2×C5912yes—
388C2×C59—44no—
389C2×C59—82no—
390C2×C59#240911yescharacteristic
391C2×C59#241011yescharacteristic
392C2×C59#241711yescharacteristic
393C2×C59#261511yescharacteristic
394C2×C59#262011yescharacteristic
395C2×C59#262611yescharacteristic
396C2×C59#267612yes—
397C2×C59#268312yes—
398C2×C59#269212yes—
399C2×C59#270212yes—
400C2×C59#281411yescharacteristic
401C23×Q8C22×C5911yescharacteristic
402C23×D4C22×C5911yescharacteristic
403C24×C4C22×C5911yescharacteristic
404C2×C22⋊Q8—24no—
405C2×C22⋊Q8—28no—
406C22×C4⋊C4C22×C5911yescharacteristic
407C22×C4⋊C4C22×C5912yes—
408C22×C4⋊C4C22×C5912yes—
409C22×C4⋊C4C22×C5912yes—
410C22×C22⋊C4C22×C5911yescharacteristic
411C22×C22⋊C4C22×C5911yescharacteristic
412C22×C22⋊C4C22×C5912yes—
413C22×C22⋊C4C22×C5912yes—
414C22×C22⋊C4C22×C5912yes—
415C22×C22⋊C4C22×C5912yes—
416C22×C22⋊C4C22×C5911yescharacteristic
417#396—28no—
418#393—24no—
419#386—24no—
420#380—24no—
421C2×#95C22×C5912yes—
422C2×#95C22×C5912yes—
423C2×#95C22×C5911yescharacteristic
424C2×#95C22×C5911yescharacteristic
425C2×#95C22×C5911yescharacteristic
426C2×#95C22×C5912yes—
427C2×#95C22×C5912yes—
428C2×#95C22×C5912yes—
429C2×#95C22×C5911yescharacteristic
430C59#1626511yescharacteristic, direct product factor, Sylow
431C25C23×C5911yescharacteristic
432C25C23×C5911yescharacteristic
433C22×Q8—24no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—22no—
437C22×Q8—42no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—42no—
441C22×D4—42no—
442C22×D4Q8×C5914yescomplemented
443C23×C4—24no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—42no—
447C23×C4D4×C5914yes—
448C23×C4C23×C5911yescharacteristic
449C23×C4C23×C5912yes—
450C23×C4C23×C5911yescharacteristic
451C23×C4C23×C5912yes—
452C23×C4C23×C5912yes—
453C23×C4C23×C5912yes—
454C23×C4C23×C5911yescharacteristic
455C23×C4C23×C5911yescharacteristic
456C23×C4C23×C5911yescharacteristic
457C22⋊Q8—232no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4D4×C5918yescomplemented
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—24no—
492#95—24no—
493#95—42no—
494#95—42no—
495#95—42no—
496#95D4×C5914yescomplemented
497C24—22no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24C2×D4×C5912yes—
516C24C2×Q8×C5912yes—
517C24C2×Q8×C5912yes—
518C24#41×C5912yes—
519C24C24×C5911yescharacteristic
520C2×Q8—28no—
521C2×Q8—48no—
522C2×Q8—48no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—48no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4C2×D4×C5914yes—
580C22×C4C2×D4×C5914yes—
581C22×C4C2×D4×C5914yes—
582C22×C4C2×D4×C5912yes—
583C22×C4C2×D4×C5914yes—
584C22×C4C2×D4×C5912yes—
585C22×C4C2×D4×C5912yes—
586C22×C4C2×Q8×C5912yes—
587C22×C4#41×C5912yes—
588C4⋊C4—28no—
589C4⋊C4—216no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C22⋊C4—216no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23C22⋊Q8×C5914yes—
645C23C22×D4×C5911yescharacteristic
646C23C22×D4×C5912yes—
647C23C22×D4×C5911yescharacteristic
648C23C22×Q8×C5911yescharacteristic
649C23C2×#41×C5911yescharacteristic
650C23C2×#41×C5911yescharacteristic
651C23H(5,𝔽2)×C5912yes—
652C23H(5,𝔽2)×C5912yes—
653C23H(5,𝔽2)×C5911yescharacteristic
654C232−1+4×C5912yes—
655C232−1+4×C5911yescharacteristic
656Q8—416no—
657D4—416no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—416no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4#120×C5914yes—
711C2×C4#121×C5914yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—44no—
727C22—44no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—82no—
733C22—82no—
734C22C2×#120×C5911yescharacteristic
735C22C2×#121×C5911yescharacteristic
736C22C2×C22⋊Q8×C5911yescharacteristic
737C22C59×#53411yescharacteristic
738C22C59×#53511yescharacteristic
739C22C59×#53512yes—
740C22C59×#53611yescharacteristic
741C22C59×#53711yescharacteristic
742C22C59×#53712yes—
743C22C59×#53712yes—
744C22C59×#53812yes—
745C22C59×#54212yes—
746C22C59×#54312yes—
747C22D42×C5912yes—
748C22C59×#54612yes—
749C22C59×#54611yescharacteristic
750C22C59×#54812yes—
751C22D4×Q8×C5912yes—
752C22D4×Q8×C5911yescharacteristic
753C22C59×#55211yescharacteristic
754C22C59×#55411yescharacteristic
755C22C59×#56212yes—
756C22C59×#56312yes—
757C4—24no—
758C4—24no—
759C4—44no—
760C4—42no—
761C4—44no—
762C4—44no—
763C4—81no—
764C4—81no—
765C4—82no—
766C2—44no—
767C2—82no—
768C2C59×#240911yescharacteristic
769C2C59×#241011yescharacteristic
770C2C59×#241711yescharacteristic
771C2C59×#261511yescharacteristic
772C2C59×#262011yescharacteristic
773C2C59×#262611yescharacteristic
774C2C59×#267612yes—
775C2C59×#268312yes—
776C2C59×#269212yes—
777C2C59×#270212yes—
778C2C59×#281411yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC23×D4×C59C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C59C2semidirect
2. C2×C59×#396C2semidirect
3. C2×C59×#393C2semidirect
5. C2×C59×#380C2semidirect
6. C59×#1446C2semidirect
7. C59×#1444C2semidirect
8. C59×#1441C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
52. C22×D4×C59Q8semidirect
78. C2×C4⋊C4×C59D4semidirect
106. #95×C59D4semidirect
322. #16265C59direct (N × H)
377. C22×C22⋊Q8C2×C59semidirect
378. C2×#396C2×C59semidirect
379. C2×#393C2×C59semidirect
381. C2×#380C2×C59semidirect
382. #1446C2×C59semidirect
383. #1444C2×C59semidirect
384. #1441C2×C59semidirect
385. #1439C2×C59semidirect
386. #1439C2×C59semidirect
430. C59#16265direct (N × H)
442. C22×D4Q8×C59semidirect
468. C2×C4⋊C4D4×C59semidirect
496. #95D4×C59semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C592
C2×C59×#3962
C2×C59×#3932
C2×C59×#3862
C2×C59×#3802
C59×#14462
C59×#14442
C59×#14412
C59×#14392
C59×#14382
#1626559