Finite Group Databasebeta

← C59×#14725 #28426834

Subgroups — C59×#14725 #28426834

Order 15104.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C59C211yesmaximal, characteristic
2C23×C22⋊C4×C59C211yesmaximal, characteristic, complemented
3C2×C59×#394C212yesmaximal, complemented
4C2×C59×#386C211yesmaximal, characteristic, complemented
5C2×C59×#386C211yesmaximal, characteristic, complemented
6C2×C59×#380C211yesmaximal, characteristic, complemented
7C2×C59×#379C211yesmaximal, characteristic, complemented
8C59×#1440C212yesmaximal, complemented
9C59×#1439C212yesmaximal, complemented
10C59×#1438C212yesmaximal, complemented
11C59×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C59C2211yescharacteristic
13C23×D4×C59C2211yescharacteristic
14C23×D4×C59C2212yes—
15C24×C4×C59C2211yescharacteristic
16C24×C4×C59C2211yescharacteristic
17C2×#120×C59—24no—
18C2×#120×C59—24no—
19C2×#120×C59—24no—
20C22×C4⋊C4×C59C2212yescomplemented
21C22×C22⋊C4×C59—24no—
22C22×C22⋊C4×C59—28no—
23C22×C22⋊C4×C59C2211yescharacteristic
24C22×C22⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2212yes—
26C22×C22⋊C4×C59C2212yes—
27C22×C22⋊C4×C59C2212yes—
28C22×C22⋊C4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2212yes—
30C22×C22⋊C4×C59C2212yes—
31C22×C22⋊C4×C59C2211yescharacteristic, complemented
32C22×C22⋊C4×C59C2212yescomplemented
33C22×C22⋊C4×C59C2211yescharacteristic, complemented
34C59×#394—28no—
35C59×#386—24no—
36C59×#386—24no—
37C59×#380—24no—
38C59×#379—24no—
39C2×#95×C59C2212yescomplemented
40C2×#95×C59C2211yescharacteristic, complemented
41C2×#95×C59C2212yescomplemented
42C2×#95×C59C2211yescharacteristic, complemented
43C2×#95×C59C2212yescomplemented
44C2×#95×C59C2212yescomplemented
45C25×C59—24no—
46C25×C59—22no—
47C25×C59—24no—
48C25×C59—22no—
49C25×C59—22no—
50C25×C59—22no—
51C25×C59—22no—
52C25×C59—22no—
53C25×C59—42no—
54C25×C59—42no—
55C25×C59D414yes—
56C25×C59C2311yescharacteristic
57C25×C59C2312yes—
58C25×C59C2311yescharacteristic
59C22×D4×C59—22no—
60C22×D4×C59—24no—
61C22×D4×C59—24no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—22no—
65C22×D4×C59—22no—
66C22×D4×C59—22no—
67C22×D4×C59—24no—
68C22×D4×C59—24no—
69C22×D4×C59—24no—
70C22×D4×C59—42no—
71C22×D4×C59—42no—
72C22×D4×C59D414yes—
73C23×C4×C59—22no—
74C23×C4×C59—22no—
75C23×C4×C59—22no—
76C23×C4×C59—24no—
77C23×C4×C59—24no—
78C23×C4×C59—22no—
79C23×C4×C59—22no—
80C23×C4×C59—42no—
81C23×C4×C59—42no—
82C23×C4×C59D414yescomplemented
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85C23×C4×C59C2312yes—
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2311yescharacteristic
88C23×C4×C59C2312yes—
89C23×C4×C59C2312yes—
90C23×C4×C59C2311yescharacteristic
91#120×C59—232no—
92C2×C4⋊C4×C59—24no—
93C2×C4⋊C4×C59—24no—
94C2×C4⋊C4×C59—42no—
95C2×C22⋊C4×C59—232no—
96C2×C22⋊C4×C59—24no—
97C2×C22⋊C4×C59—24no—
98C2×C22⋊C4×C59—22no—
99C2×C22⋊C4×C59—22no—
100C2×C22⋊C4×C59—24no—
101C2×C22⋊C4×C59—24no—
102C2×C22⋊C4×C59—24no—
103C2×C22⋊C4×C59—24no—
104C2×C22⋊C4×C59—24no—
105C2×C22⋊C4×C59—24no—
106C2×C22⋊C4×C59—24no—
107C2×C22⋊C4×C59—22no—
108C2×C22⋊C4×C59—24no—
109C2×C22⋊C4×C59—22no—
110C2×C22⋊C4×C59—22no—
111C2×C22⋊C4×C59—22no—
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—24no—
114C2×C22⋊C4×C59—24no—
115C2×C22⋊C4×C59—24no—
116C2×C22⋊C4×C59—22no—
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—22no—
119C2×C22⋊C4×C59—24no—
120C2×C22⋊C4×C59—24no—
121C2×C22⋊C4×C59—42no—
122C2×C22⋊C4×C59—42no—
123C2×C22⋊C4×C59—42no—
124C2×C22⋊C4×C59—42no—
125C2×C22⋊C4×C59D414yes—
126C2×C22⋊C4×C59D418yescomplemented
127#95×C59—24no—
128#95×C59—22no—
129#95×C59—22no—
130#95×C59—24no—
131#95×C59—24no—
132#95×C59—42no—
133C24×C59—22no—
134C24×C59—22no—
135C24×C59—22no—
136C24×C59—22no—
137C24×C59—28no—
138C24×C59—28no—
139C24×C59—216no—
140C24×C59—216no—
141C24×C59—28no—
142C24×C59—22no—
143C24×C59—22no—
144C24×C59—22no—
145C24×C59—22no—
146C24×C59—22no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—28no—
155C24×C59—28no—
156C24×C59—21no—
157C24×C59—22no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—22no—
164C24×C59—22no—
165C24×C59—22no—
166C24×C59—48no—
167C24×C59—48no—
168C24×C59—48no—
169C24×C59—48no—
170C24×C59—48no—
171C24×C59—48no—
172C24×C59—48no—
173C24×C59—48no—
174C24×C59—48no—
175C24×C59—44no—
176C24×C59—44no—
177C24×C59—48no—
178C24×C59—44no—
179C24×C59—44no—
180C24×C59—44no—
181C24×C59—44no—
182C24×C59C2×D412yes—
183C24×C59C2×D414yes—
184C24×C59C2×D414yes—
185C24×C59C2×D412yes—
186C24×C59C2×D412yes—
187C24×C59C2×D412yes—
188C24×C59C2×D412yes—
189C24×C59#4114yes—
190C24×C59#4112yes—
191C24×C59#4112yes—
192C24×C59#4112yes—
193C24×C59C2411yescharacteristic
194C2×D4×C59—216no—
195C2×D4×C59—28no—
196C2×D4×C59—28no—
197C2×D4×C59—28no—
198C2×D4×C59—48no—
199C2×D4×C59—48no—
200C2×D4×C59—48no—
201C2×D4×C59—48no—
202C2×D4×C59—48no—
203C2×D4×C59—48no—
204C2×D4×C59—44no—
205C2×D4×C59—44no—
206C2×D4×C59—44no—
207C2×D4×C59—44no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—22no—
211C22×C4×C59—28no—
212C22×C4×C59—28no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—22no—
216C22×C4×C59—22no—
217C22×C4×C59—22no—
218C22×C4×C59—22no—
219C22×C4×C59—22no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—22no—
223C22×C4×C59—22no—
224C22×C4×C59—21no—
225C22×C4×C59—22no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
229C22×C4×C59—22no—
230C22×C4×C59—22no—
231C22×C4×C59—22no—
232C22×C4×C59—22no—
233C22×C4×C59—22no—
234C22×C4×C59—22no—
235C22×C4×C59—28no—
236C22×C4×C59—21no—
237C22×C4×C59—22no—
238C22×C4×C59—22no—
239C22×C4×C59—21no—
240C22×C4×C59—22no—
241C22×C4×C59—22no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—22no—
245C22×C4×C59—21no—
246C22×C4×C59—22no—
247C22×C4×C59—21no—
248C22×C4×C59—22no—
249C22×C4×C59—22no—
250C22×C4×C59—22no—
251C22×C4×C59—22no—
252C22×C4×C59—22no—
253C22×C4×C59—44no—
254C22×C4×C59—48no—
255C22×C4×C59—48no—
256C22×C4×C59—48no—
257C22×C4×C59—48no—
258C22×C4×C59—44no—
259C22×C4×C59—44no—
260C22×C4×C59C2×D412yes—
261C22×C4×C59C2×D412yes—
262C22×C4×C59C2×D414yes—
263C22×C4×C59C2×D414yes—
264C22×C4×C59C2×D412yes—
265C22×C4×C59C2×D414yes—
266C4⋊C4×C59—48no—
267C22⋊C4×C59—216no—
268C22⋊C4×C59—216no—
269C22⋊C4×C59—28no—
270C22⋊C4×C59—216no—
271C22⋊C4×C59—48no—
272C22⋊C4×C59—44no—
273C22⋊C4×C59—48no—
274C22⋊C4×C59—44no—
275C22⋊C4×C59—48no—
276C22⋊C4×C59—44no—
277C22⋊C4×C59—44no—
278C23×C59—22no—
279C23×C59—24no—
280C23×C59—22no—
281C23×C59—24no—
282C23×C59—22no—
283C23×C59—24no—
284C23×C59—22no—
285C23×C59—24no—
286C23×C59—24no—
287C23×C59—24no—
288C23×C59—24no—
289C23×C59—24no—
290C23×C59—24no—
291C23×C59—24no—
292C23×C59—24no—
293C23×C59—24no—
294C23×C59—232no—
295C23×C59—24no—
296C23×C59—24no—
297C23×C59—24no—
298C23×C59—24no—
299C23×C59—24no—
300C23×C59—24no—
301C23×C59—24no—
302C23×C59—24no—
303C23×C59—24no—
304C23×C59—24no—
305C23×C59—24no—
306C23×C59—24no—
307C23×C59—24no—
308C23×C59—24no—
309C23×C59—24no—
310C23×C59—24no—
311C23×C59—24no—
312C23×C59—24no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—24no—
317C23×C59—24no—
318C23×C59—432no—
319C23×C59—432no—
320C23×C59—416no—
321C23×C59—416no—
322C23×C59—416no—
323C23×C59—416no—
324C23×C59—432no—
325C23×C59—432no—
326C23×C59—416no—
327C23×C59—42no—
328C23×C59—42no—
329C23×C59—42no—
330C23×C59—42no—
331C23×C59—42no—
332C23×C59—42no—
333C23×C59—42no—
334C23×C59—42no—
335C23×C59—42no—
336C23×C59—42no—
337C23×C59—42no—
338C23×C59—42no—
339C23×C59—42no—
340C23×C59—42no—
341C23×C59—42no—
342C23×C59—42no—
343C23×C59—416no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—42no—
348C23×C59—41no—
349C23×C59—42no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—42no—
354C23×C59—41no—
355C23×C59—42no—
356C23×C59—42no—
357C23×C59—42no—
358C23×C59—42no—
359C23×C59—42no—
360C23×C59—42no—
361C23×C59—42no—
362C23×C59#12014yes—
363C23×C59#12118yes—
364C23×C59#12114yes—
365C23×C59#12114yes—
366C23×C59#12114yes—
367C23×C59#12314yes—
368C23×C59#12314yes—
369C23×C59#12414yes—
370C23×C59C22×D411yescharacteristic
371C23×C59C22×D411yescharacteristic
372C23×C59C22×D411yescharacteristic
373C23×C59C22×D412yes—
374C23×C59C22×D411yescharacteristic
375C23×C59C2×#4111yescharacteristic
376C23×C59C2×#4111yescharacteristic
377C23×C59C2×#4111yescharacteristic
378C23×C59C2×#4112yes—
379C23×C59H(5,𝔽2)12yes—
380C23×C59H(5,𝔽2)12yes—
381D4×C59—432no—
382D4×C59—416no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—24no—
386C2×C4×C59—24no—
387C2×C4×C59—24no—
388C2×C4×C59—22no—
389C2×C4×C59—22no—
390C2×C4×C59—24no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
393C2×C4×C59—22no—
394C2×C4×C59—22no—
395C2×C4×C59—24no—
396C2×C4×C59—24no—
397C2×C4×C59—24no—
398C2×C4×C59—24no—
399C2×C4×C59—416no—
400C2×C4×C59—416no—
401C2×C4×C59—42no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—42no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—42no—
408C2×C4×C59—42no—
409C2×C4×C59—42no—
410C2×C4×C59—42no—
411C2×C4×C59—42no—
412C2×C4×C59—42no—
413C2×C4×C59—42no—
414C2×C4×C59—42no—
415C2×C4×C59—41no—
416C2×C4×C59—42no—
417C2×C4×C59—41no—
418C2×C4×C59—42no—
419C2×C4×C59—41no—
420C2×C4×C59—42no—
421C2×C4×C59—41no—
422C2×C4×C59—42no—
423C2×C4×C59—42no—
424C2×C4×C59—41no—
425C2×C4×C59—42no—
426C2×C4×C59—41no—
427C2×C4×C59—42no—
428C2×C4×C59—42no—
429C2×C4×C59—42no—
430C2×C4×C59—42no—
431C2×C4×C59—42no—
432C2×C4×C59#12014yescomplemented
433#14725C5911yesmaximal, characteristic, direct product factor, Sylow
434C22×C59—24no—
435C22×C59—24no—
436C22×C59—24no—
437C22×C59—24no—
438C22×C59—28no—
439C22×C59—24no—
440C22×C59—28no—
441C22×C59—28no—
442C22×C59—28no—
443C22×C59—24no—
444C22×C59—28no—
445C22×C59—28no—
446C22×C59—28no—
447C22×C59—464no—
448C22×C59—44no—
449C22×C59—44no—
450C22×C59—44no—
451C22×C59—44no—
452C22×C59—44no—
453C22×C59—44no—
454C22×C59—44no—
455C22×C59—44no—
456C22×C59—44no—
457C22×C59—44no—
458C22×C59—44no—
459C22×C59—44no—
460C22×C59—42no—
461C22×C59—42no—
462C22×C59—44no—
463C22×C59—44no—
464C22×C59—42no—
465C22×C59—81no—
466C22×C59—81no—
467C22×C59—81no—
468C22×C59—81no—
469C22×C59—82no—
470C22×C59—82no—
471C22×C59#39418yescomplemented
472C22×C59C2×#12011yescharacteristic
473C22×C59C2×#12011yescharacteristic
474C22×C59C2×#12111yescharacteristic
475C22×C59C2×#12112yes—
476C22×C59C2×#12111yescharacteristic
477C22×C59C2×#12111yescharacteristic
478C22×C59C2×#12311yescharacteristic
479C22×C59C2×#12311yescharacteristic
480C22×C59#52511yescharacteristic
481C22×C59#52512yes—
482C22×C59C2×#12411yescharacteristic
483C22×C59#53412yes—
484C22×C59#53411yescharacteristic
485C22×C59#53511yescharacteristic
486C22×C59#53812yes—
487C22×C59D4212yes—
488C22×C59D4212yes—
489C22×C59#54612yes—
490C22×C59#54612yes—
491C22×C59#54612yes—
492C22×C59#54612yes—
493C22×C59#55112yes—
494C22×C59#55112yes—
495C4×C59—24no—
496C4×C59—42no—
497C4×C59—44no—
498C4×C59—42no—
499C4×C59—44no—
500C4×C59—81no—
501C4×C59—81no—
502C4×C59—82no—
503C22×#120C2×C5911yescharacteristic
504C23×C22⋊C4C2×C5911yescharacteristic, complemented
505C2×#394C2×C5912yescomplemented
506C2×#386C2×C5911yescharacteristic, complemented
507C2×#386C2×C5911yescharacteristic, complemented
508C2×#380C2×C5911yescharacteristic, complemented
509C2×#379C2×C5911yescharacteristic, complemented
510#1440C2×C5912yescomplemented
511#1439C2×C5912yescomplemented
512#1438C2×C5912yescomplemented
513C22⋊#95C2×C5911yescharacteristic, complemented
514C2×C59—28no—
515C2×C59—48no—
516C2×C59—82no—
517C2×C59C2×#39411yescharacteristic
518C2×C59#240811yescharacteristic
519C2×C59#241011yescharacteristic
520C2×C59#241012yes—
521C2×C59#241111yescharacteristic
522C2×C59#241212yes—
523C2×C59#241812yes—
524C2×C59#247212yes—
525C2×C59#253411yescharacteristic
526C2×C59#261711yescharacteristic
527C2×C59#284711yescharacteristic
528C26C22×C5911yescharacteristic
529C23×D4C22×C5911yescharacteristic
530C23×D4C22×C5912yes—
531C24×C4C22×C5911yescharacteristic
532C24×C4C22×C5911yescharacteristic
533C2×#120—24no—
534C2×#120—24no—
535C2×#120—24no—
536C22×C4⋊C4C22×C5912yescomplemented
537C22×C22⋊C4—24no—
538C22×C22⋊C4—28no—
539C22×C22⋊C4C22×C5912yes—
540C22×C22⋊C4C22×C5912yes—
541C22×C22⋊C4C22×C5912yes—
542C22×C22⋊C4C22×C5911yescharacteristic
543C22×C22⋊C4C22×C5911yescharacteristic
544C22×C22⋊C4C22×C5911yescharacteristic
545C22×C22⋊C4C22×C5912yes—
546C22×C22⋊C4C22×C5912yes—
547C22×C22⋊C4C22×C5911yescharacteristic, complemented
548C22×C22⋊C4C22×C5912yescomplemented
549C22×C22⋊C4C22×C5911yescharacteristic, complemented
550#394—28no—
551#386—24no—
552#386—24no—
553#380—24no—
554#379—24no—
555C2×#95C22×C5912yescomplemented
556C2×#95C22×C5912yescomplemented
557C2×#95C22×C5911yescharacteristic, complemented
558C2×#95C22×C5912yescomplemented
559C2×#95C22×C5911yescharacteristic, complemented
560C2×#95C22×C5912yescomplemented
561C59#1472511yescharacteristic, direct product factor, Sylow
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C5914yes—
573C25C23×C5911yescharacteristic
574C25C23×C5912yes—
575C25C23×C5911yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C5914yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C5914yescomplemented
600C23×C4C23×C5912yes—
601C23×C4C23×C5911yescharacteristic
602C23×C4C23×C5911yescharacteristic
603C23×C4C23×C5911yescharacteristic
604C23×C4C23×C5912yes—
605C23×C4C23×C5912yes—
606C23×C4C23×C5911yescharacteristic
607C23×C4C23×C5911yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C5914yes—
643C2×C22⋊C4D4×C5918yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C5912yes—
700C24C2×D4×C5914yes—
701C24C2×D4×C5914yes—
702C24C2×D4×C5912yes—
703C24C2×D4×C5912yes—
704C24C2×D4×C5912yes—
705C24C2×D4×C5912yes—
706C24#41×C5914yes—
707C24#41×C5912yes—
708C24#41×C5912yes—
709C24#41×C5912yes—
710C24C24×C5911yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C5912yes—
778C22×C4C2×D4×C5912yes—
779C22×C4C2×D4×C5914yes—
780C22×C4C2×D4×C5914yes—
781C22×C4C2×D4×C5912yes—
782C22×C4C2×D4×C5914yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—416no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C5914yes—
880C23#121×C5918yes—
881C23#121×C5914yes—
882C23#121×C5914yes—
883C23#121×C5914yes—
884C23#123×C5914yes—
885C23#123×C5914yes—
886C23#124×C5914yes—
887C23C22×D4×C5911yescharacteristic
888C23C22×D4×C5911yescharacteristic
889C23C22×D4×C5911yescharacteristic
890C23C22×D4×C5912yes—
891C23C22×D4×C5911yescharacteristic
892C23C2×#41×C5911yescharacteristic
893C23C2×#41×C5911yescharacteristic
894C23C2×#41×C5911yescharacteristic
895C23C2×#41×C5912yes—
896C23H(5,𝔽2)×C5912yes—
897C23H(5,𝔽2)×C5912yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C5914yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22C59×#39418yescomplemented
988C22C2×#120×C5911yescharacteristic
989C22C2×#120×C5911yescharacteristic
990C22C2×#121×C5911yescharacteristic
991C22C2×#121×C5911yescharacteristic
992C22C2×#121×C5912yes—
993C22C2×#121×C5911yescharacteristic
994C22C2×#123×C5911yescharacteristic
995C22C2×#123×C5911yescharacteristic
996C22C59×#52511yescharacteristic
997C22C59×#52512yes—
998C22C2×#124×C5911yescharacteristic
999C22C59×#53411yescharacteristic
1000C22C59×#53412yes—
1001C22C59×#53511yescharacteristic
1002C22C59×#53812yes—
1003C22D42×C5912yes—
1004C22D42×C5912yes—
1005C22C59×#54612yes—
1006C22C59×#54612yes—
1007C22C59×#54612yes—
1008C22C59×#54612yes—
1009C22C59×#55112yes—
1010C22C59×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C59×#39411yescharacteristic
1023C2C59×#240811yescharacteristic
1024C2C59×#241011yescharacteristic
1025C2C59×#241012yes—
1026C2C59×#241111yescharacteristic
1027C2C59×#241212yes—
1028C2C59×#241812yes—
1029C2C59×#247212yes—
1030C2C59×#253411yescharacteristic
1031C2C59×#261711yescharacteristic
1032C2C59×#284711yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC22×#120×C59C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C59C2semidirect
3. C2×C59×#394C2semidirect
4. C2×C59×#386C2semidirect
5. C2×C59×#386C2semidirect
6. C2×C59×#380C2semidirect
7. C2×C59×#379C2semidirect
8. C59×#1440C2semidirect
9. C59×#1439C2semidirect
10. C59×#1438C2semidirect
11. C59×C22⋊#95C2semidirect
20. C22×C4⋊C4×C59C22semidirect
31. C22×C22⋊C4×C59C22semidirect
32. C22×C22⋊C4×C59C22semidirect
33. C22×C22⋊C4×C59C22semidirect
39. C2×#95×C59C22semidirect
40. C2×#95×C59C22semidirect
41. C2×#95×C59C22semidirect
42. C2×#95×C59C22semidirect
43. C2×#95×C59C22semidirect
44. C2×#95×C59C22semidirect
82. C23×C4×C59D4semidirect
126. C2×C22⋊C4×C59D4semidirect
432. C2×C4×C59#120semidirect
433. #14725C59direct (N × H)
471. C22×C59#394semidirect
504. C23×C22⋊C4C2×C59semidirect
505. C2×#394C2×C59semidirect
506. C2×#386C2×C59semidirect
507. C2×#386C2×C59semidirect
508. C2×#380C2×C59semidirect
509. C2×#379C2×C59semidirect
510. #1440C2×C59semidirect
511. #1439C2×C59semidirect
512. #1438C2×C59semidirect
513. C22⋊#95C2×C59semidirect
536. C22×C4⋊C4C22×C59semidirect
547. C22×C22⋊C4C22×C59semidirect
548. C22×C22⋊C4C22×C59semidirect
549. C22×C22⋊C4C22×C59semidirect
555. C2×#95C22×C59semidirect
556. C2×#95C22×C59semidirect
557. C2×#95C22×C59semidirect
558. C2×#95C22×C59semidirect
559. C2×#95C22×C59semidirect
560. C2×#95C22×C59semidirect
561. C59#14725direct (N × H)
599. C23×C4D4×C59semidirect
643. C2×C22⋊C4D4×C59semidirect
949. C2×C4#120×C59semidirect
987. C22C59×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C592
C23×C22⋊C4×C592
C2×C59×#3942
C2×C59×#3862
C2×C59×#3802
C2×C59×#3792
C59×#14402
C59×#14392
C59×#14382
C59×C22⋊#952
#1472559