Finite Group Databasebeta

← C59×#14722 #28426831

Subgroups — C59×#14722 #28426831

Order 15104.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C59C211yesmaximal, characteristic, complemented
2C22×C4×D4×C59C211yesmaximal, characteristic, complemented
3C2×C59×#394C211yesmaximal, characteristic, complemented
4C2×C59×#392C211yesmaximal, characteristic, complemented
5C2×C59×#392C212yesmaximal, complemented
6C2×C59×#386C212yesmaximal, complemented
7C59×#1441C211yesmaximal, characteristic, complemented
8C59×#1439C211yesmaximal, characteristic, complemented
9C59×#1438C212yesmaximal, complemented
10C59×#1437C212yesmaximal, complemented
11C59×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C59C2211yescharacteristic
13C23×D4×C59C2212yes—
14C23×D4×C59C2211yescharacteristic
15C23×D4×C59C2212yes—
16C24×C4×C59C2211yescharacteristic
17C24×C4×C59C2211yescharacteristic
18C2×#121×C59—24no—
19C2×#121×C59—28no—
20C2×C4×D4×C59—24no—
21C2×C4×D4×C59—24no—
22C2×C4×D4×C59—24no—
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2212yes—
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C22⋊C4×C59C2212yes—
28C22×C22⋊C4×C59C2212yes—
29C22×C22⋊C4×C59C2212yes—
30C22×C22⋊C4×C59C2212yes—
31C22×C22⋊C4×C59C2212yes—
32C22×C22⋊C4×C59C2211yescharacteristic
33C22×C42×C59C2211yescharacteristic
34C59×#394—24no—
35C59×#392—28no—
36C59×#392—24no—
37C59×#386—28no—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2211yescharacteristic
41C2×#95×C59C2212yes—
42C2×#95×C59C2211yescharacteristic
43C2×#95×C59C2212yes—
44C25×C59C2312yes—
45C25×C59C2311yescharacteristic
46C25×C59C2311yescharacteristic
47C22×D4×C59—22no—
48C22×D4×C59—22no—
49C22×D4×C59—22no—
50C22×D4×C59—22no—
51C22×D4×C59—24no—
52C22×D4×C59—24no—
53C22×D4×C59—24no—
54C22×D4×C59—24no—
55C22×D4×C59—24no—
56C22×D4×C59—24no—
57C22×D4×C59—24no—
58C22×D4×C59—24no—
59C22×D4×C59—24no—
60C22×D4×C59—22no—
61C22×D4×C59—24no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—22no—
65C22×D4×C59—22no—
66C22×D4×C59—24no—
67C22×D4×C59—42no—
68C22×D4×C59—42no—
69C22×D4×C59—42no—
70C22×D4×C59—42no—
71C22×D4×C59—42no—
72C22×D4×C59D414yescomplemented
73C23×C4×C59—22no—
74C23×C4×C59—22no—
75C23×C4×C59—22no—
76C23×C4×C59—22no—
77C23×C4×C59—22no—
78C23×C4×C59—24no—
79C23×C4×C59—24no—
80C23×C4×C59—42no—
81C23×C4×C59—42no—
82C23×C4×C59D414yescomplemented
83C23×C4×C59C2312yes—
84C23×C4×C59C2312yes—
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2312yes—
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91#121×C59—232no—
92C4×D4×C59—232no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59—22no—
95C2×C4⋊C4×C59—24no—
96C2×C4⋊C4×C59—22no—
97C2×C4⋊C4×C59D414yescomplemented
98C2×C22⋊C4×C59—22no—
99C2×C22⋊C4×C59—22no—
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—22no—
102C2×C22⋊C4×C59—22no—
103C2×C22⋊C4×C59—24no—
104C2×C22⋊C4×C59—24no—
105C2×C22⋊C4×C59—24no—
106C2×C22⋊C4×C59—24no—
107C2×C22⋊C4×C59—24no—
108C2×C22⋊C4×C59—24no—
109C2×C22⋊C4×C59—24no—
110C2×C22⋊C4×C59—24no—
111C2×C22⋊C4×C59—24no—
112C2×C22⋊C4×C59—24no—
113C2×C22⋊C4×C59—24no—
114C2×C22⋊C4×C59—24no—
115C2×C22⋊C4×C59—24no—
116C2×C22⋊C4×C59—42no—
117C2×C22⋊C4×C59—42no—
118C2×C22⋊C4×C59—42no—
119C2×C22⋊C4×C59—42no—
120C2×C22⋊C4×C59D418yescomplemented
121C2×C22⋊C4×C59D414yescomplemented
122C2×C42×C59—22no—
123C2×C42×C59—22no—
124C2×C42×C59—22no—
125#95×C59—24no—
126#95×C59—24no—
127#95×C59—22no—
128#95×C59—24no—
129#95×C59—22no—
130#95×C59—42no—
131C24×C59—21no—
132C24×C59—21no—
133C24×C59—21no—
134C24×C59—21no—
135C24×C59—22no—
136C24×C59—22no—
137C24×C59—22no—
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—21no—
141C24×C59—21no—
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—22no—
155C24×C59—22no—
156C24×C59—22no—
157C24×C59—22no—
158C24×C59—22no—
159C24×C59—22no—
160C24×C59—22no—
161C24×C59C2×D414yes—
162C24×C59C2×D412yes—
163C24×C59C2×D412yes—
164C24×C59C2×D412yes—
165C24×C59C2×D412yes—
166C24×C59#4112yes—
167C24×C59#4112yes—
168C24×C59C2411yescharacteristic
169C2×D4×C59—28no—
170C2×D4×C59—28no—
171C2×D4×C59—28no—
172C2×D4×C59—28no—
173C2×D4×C59—28no—
174C2×D4×C59—28no—
175C2×D4×C59—28no—
176C2×D4×C59—216no—
177C2×D4×C59—216no—
178C2×D4×C59—28no—
179C2×D4×C59—48no—
180C2×D4×C59—48no—
181C2×D4×C59—48no—
182C2×D4×C59—48no—
183C2×D4×C59—48no—
184C2×D4×C59—48no—
185C2×D4×C59—44no—
186C2×D4×C59—48no—
187C2×D4×C59—48no—
188C2×D4×C59—48no—
189C2×D4×C59—48no—
190C2×D4×C59—48no—
191C2×D4×C59—48no—
192C2×D4×C59—48no—
193C2×D4×C59—48no—
194C2×D4×C59—44no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—22no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—28no—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—22no—
208C22×C4×C59—22no—
209C22×C4×C59—22no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—22no—
215C22×C4×C59—22no—
216C22×C4×C59—22no—
217C22×C4×C59—22no—
218C22×C4×C59—22no—
219C22×C4×C59—22no—
220C22×C4×C59—22no—
221C22×C4×C59—22no—
222C22×C4×C59—22no—
223C22×C4×C59—22no—
224C22×C4×C59—22no—
225C22×C4×C59—28no—
226C22×C4×C59—28no—
227C22×C4×C59—22no—
228C22×C4×C59—22no—
229C22×C4×C59—22no—
230C22×C4×C59—22no—
231C22×C4×C59—22no—
232C22×C4×C59—22no—
233C22×C4×C59—22no—
234C22×C4×C59—44no—
235C22×C4×C59—48no—
236C22×C4×C59—48no—
237C22×C4×C59—48no—
238C22×C4×C59—48no—
239C22×C4×C59—44no—
240C22×C4×C59—44no—
241C22×C4×C59C2×D414yes—
242C22×C4×C59C2×D412yes—
243C22×C4×C59C2×D412yes—
244C22×C4×C59C2×D414yes—
245C22×C4×C59C2×D412yes—
246C22×C4×C59C2×D412yes—
247C22×C4×C59C2×D412yes—
248C22×C4×C59C2×D412yes—
249C22×C4×C59C2×D412yes—
250C22×C4×C59C2×D412yes—
251C22×C4×C59#4114yes—
252C22×C4×C59#4112yes—
253C4⋊C4×C59—28no—
254C4⋊C4×C59—28no—
255C22⋊C4×C59—28no—
256C22⋊C4×C59—28no—
257C22⋊C4×C59—216no—
258C22⋊C4×C59—48no—
259C22⋊C4×C59—48no—
260C22⋊C4×C59—48no—
261C22⋊C4×C59—48no—
262C22⋊C4×C59—48no—
263C42×C59—28no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—24no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—24no—
282C23×C59—24no—
283C23×C59—24no—
284C23×C59—24no—
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—24no—
295C23×C59—24no—
296C23×C59—24no—
297C23×C59—41no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59—42no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—42no—
305C23×C59—42no—
306C23×C59—42no—
307C23×C59—42no—
308C23×C59—42no—
309C23×C59—42no—
310C23×C59—42no—
311C23×C59—42no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59—42no—
318C23×C59—42no—
319C23×C59—42no—
320C23×C59—42no—
321C23×C59—42no—
322C23×C59—42no—
323C23×C59—42no—
324C23×C59—42no—
325C23×C59—42no—
326C23×C59—42no—
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#12114yes—
344C23×C59#12114yescomplemented
345C23×C59C22×D411yescharacteristic
346C23×C59C22×D411yescharacteristic
347C23×C59C22×D411yescharacteristic
348C23×C59C22×D412yes—
349C23×C59C22×D411yescharacteristic
350C23×C59C2×#4111yescharacteristic
351C23×C59C2×#4111yescharacteristic
352C23×C59C2×#4111yescharacteristic
353C23×C59C2×#4112yes—
354C23×C59H(5,𝔽2)12yes—
355C23×C59H(5,𝔽2)12yes—
356D4×C59—232no—
357D4×C59—416no—
358D4×C59—432no—
359D4×C59—432no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—24no—
371C2×C4×C59—24no—
372C2×C4×C59—24no—
373C2×C4×C59—24no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—24no—
377C2×C4×C59—24no—
378C2×C4×C59—24no—
379C2×C4×C59—24no—
380C2×C4×C59—24no—
381C2×C4×C59—24no—
382C2×C4×C59—24no—
383C2×C4×C59—24no—
384C2×C4×C59—416no—
385C2×C4×C59—416no—
386C2×C4×C59—41no—
387C2×C4×C59—42no—
388C2×C4×C59—42no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—42no—
393C2×C4×C59—42no—
394C2×C4×C59—42no—
395C2×C4×C59—42no—
396C2×C4×C59—42no—
397C2×C4×C59—42no—
398C2×C4×C59—42no—
399C2×C4×C59—42no—
400C2×C4×C59—42no—
401C2×C4×C59—42no—
402C2×C4×C59—42no—
403C2×C4×C59—42no—
404C2×C4×C59—42no—
405C2×C4×C59—42no—
406C2×C4×C59—42no—
407C2×C4×C59#12014yes—
408C2×C4×C59#12014yes—
409C2×C4×C59#12114yescomplemented
410#14722C5911yesmaximal, characteristic, direct product factor, Sylow
411C22×C59—24no—
412C22×C59—24no—
413C22×C59—24no—
414C22×C59—28no—
415C22×C59—24no—
416C22×C59—42no—
417C22×C59—42no—
418C22×C59—42no—
419C22×C59—42no—
420C22×C59—42no—
421C22×C59—42no—
422C22×C59—42no—
423C22×C59—44no—
424C22×C59—44no—
425C22×C59—44no—
426C22×C59—42no—
427C22×C59—42no—
428C22×C59—44no—
429C22×C59—44no—
430C22×C59—44no—
431C22×C59—44no—
432C22×C59—42no—
433C22×C59—44no—
434C22×C59—44no—
435C22×C59—44no—
436C22×C59—44no—
437C22×C59—44no—
438C22×C59—44no—
439C22×C59—44no—
440C22×C59—82no—
441C22×C59—82no—
442C22×C59—82no—
443C22×C59—82no—
444C22×C59—82no—
445C22×C59—82no—
446C22×C59—82no—
447C22×C59—82no—
448C22×C59C2×#12011yescharacteristic
449C22×C59C2×#12011yescharacteristic
450C22×C59C2×#12111yescharacteristic
451C22×C59C2×#12111yescharacteristic
452C22×C59C2×#12111yescharacteristic
453C22×C59#52511yescharacteristic
454C22×C59#52511yescharacteristic
455C22×C59#52511yescharacteristic
456C22×C59#52512yes—
457C22×C59#53212yes—
458C22×C59#53211yescharacteristic
459C22×C59#53411yescharacteristic
460C22×C59#53511yescharacteristic
461C22×C59#53812yes—
462C22×C59#54012yes—
463C22×C59D4212yes—
464C22×C59D4212yes—
465C22×C59D4212yes—
466C22×C59#54612yes—
467C22×C59#54612yes—
468C22×C59#54612yes—
469C22×C59#55012yes—
470C22×C59#55312yes—
471C4×C59—24no—
472C4×C59—24no—
473C4×C59—24no—
474C4×C59—42no—
475C4×C59—44no—
476C4×C59—44no—
477C4×C59—42no—
478C4×C59—82no—
479C22×#121C2×C5911yescharacteristic, complemented
480C22×C4×D4C2×C5911yescharacteristic, complemented
481C2×#394C2×C5911yescharacteristic, complemented
482C2×#392C2×C5912yescomplemented
483C2×#392C2×C5911yescharacteristic, complemented
484C2×#386C2×C5912yescomplemented
485#1441C2×C5911yescharacteristic, complemented
486#1439C2×C5911yescharacteristic, complemented
487#1438C2×C5912yescomplemented
488#1437C2×C5912yescomplemented
489C22⋊#95C2×C5911yescharacteristic, complemented
490C2×C59—44no—
491C2×C59—44no—
492C2×C59—84no—
493C2×C59#238811yescharacteristic
494C2×C59#240311yescharacteristic
495C2×C59#240811yescharacteristic
496C2×C59#242412yes—
497C2×C59#242812yes—
498C2×C59#243111yescharacteristic
499C2×C59#245612yes—
500C2×C59#246412yes—
501C2×C59#254311yescharacteristic
502C2×C59#263511yescharacteristic
503C2×C59#284711yescharacteristic
504C23×D4C22×C5911yescharacteristic
505C23×D4C22×C5912yes—
506C23×D4C22×C5911yescharacteristic
507C23×D4C22×C5912yes—
508C24×C4C22×C5911yescharacteristic
509C24×C4C22×C5911yescharacteristic
510C2×#121—24no—
511C2×#121—28no—
512C2×C4×D4—24no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C22×C4⋊C4C22×C5911yescharacteristic
516C22×C4⋊C4C22×C5911yescharacteristic
517C22×C22⋊C4C22×C5912yes—
518C22×C22⋊C4C22×C5911yescharacteristic
519C22×C22⋊C4C22×C5912yes—
520C22×C22⋊C4C22×C5912yes—
521C22×C22⋊C4C22×C5912yes—
522C22×C22⋊C4C22×C5912yes—
523C22×C22⋊C4C22×C5911yescharacteristic
524C22×C22⋊C4C22×C5912yes—
525C22×C42C22×C5911yescharacteristic
526#394—24no—
527#392—28no—
528#392—24no—
529#386—28no—
530C2×#95C22×C5911yescharacteristic
531C2×#95C22×C5912yes—
532C2×#95C22×C5911yescharacteristic
533C2×#95C22×C5912yes—
534C2×#95C22×C5912yes—
535C2×#95C22×C5912yes—
536C59#1472211yescharacteristic, direct product factor, Sylow
537C25C23×C5912yes—
538C25C23×C5911yescharacteristic
539C25C23×C5911yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C5914yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C5914yescomplemented
576C23×C4C23×C5912yes—
577C23×C4C23×C5911yescharacteristic
578C23×C4C23×C5911yescharacteristic
579C23×C4C23×C5912yes—
580C23×C4C23×C5912yes—
581C23×C4C23×C5911yescharacteristic
582C23×C4C23×C5911yescharacteristic
583C23×C4C23×C5911yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C5914yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C5914yescomplemented
614C2×C22⋊C4D4×C5918yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C5914yes—
655C24C2×D4×C5912yes—
656C24C2×D4×C5912yes—
657C24C2×D4×C5912yes—
658C24C2×D4×C5912yes—
659C24#41×C5912yes—
660C24#41×C5912yes—
661C24C24×C5911yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C5914yes—
735C22×C4C2×D4×C5912yes—
736C22×C4C2×D4×C5912yes—
737C22×C4C2×D4×C5914yes—
738C22×C4C2×D4×C5912yes—
739C22×C4C2×D4×C5912yes—
740C22×C4C2×D4×C5912yes—
741C22×C4C2×D4×C5912yes—
742C22×C4C2×D4×C5912yes—
743C22×C4C2×D4×C5912yes—
744C22×C4#41×C5914yes—
745C22×C4#41×C5912yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C5914yes—
837C23#121×C5914yescomplemented
838C23C22×D4×C5911yescharacteristic
839C23C22×D4×C5911yescharacteristic
840C23C22×D4×C5911yescharacteristic
841C23C22×D4×C5912yes—
842C23C22×D4×C5911yescharacteristic
843C23C2×#41×C5911yescharacteristic
844C23C2×#41×C5911yescharacteristic
845C23C2×#41×C5911yescharacteristic
846C23C2×#41×C5912yes—
847C23H(5,𝔽2)×C5912yes—
848C23H(5,𝔽2)×C5912yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C5914yes—
901C2×C4#120×C5914yes—
902C2×C4#121×C5914yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C5911yescharacteristic
941C22C2×#120×C5911yescharacteristic
942C22C2×#121×C5911yescharacteristic
943C22C2×#121×C5911yescharacteristic
944C22C2×#121×C5911yescharacteristic
945C22C59×#52511yescharacteristic
946C22C59×#52511yescharacteristic
947C22C59×#52511yescharacteristic
948C22C59×#52512yes—
949C22C59×#53211yescharacteristic
950C22C59×#53212yes—
951C22C59×#53411yescharacteristic
952C22C59×#53511yescharacteristic
953C22C59×#53812yes—
954C22C59×#54012yes—
955C22D42×C5912yes—
956C22D42×C5912yes—
957C22D42×C5912yes—
958C22C59×#54612yes—
959C22C59×#54612yes—
960C22C59×#54612yes—
961C22C59×#55012yes—
962C22C59×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C59×#238811yescharacteristic
975C2C59×#240311yescharacteristic
976C2C59×#240811yescharacteristic
977C2C59×#242412yes—
978C2C59×#242812yes—
979C2C59×#243111yescharacteristic
980C2C59×#245612yes—
981C2C59×#246412yes—
982C2C59×#254311yescharacteristic
983C2C59×#263511yescharacteristic
984C2C59×#284711yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C59C2semidirect
2. C22×C4×D4×C59C2semidirect
3. C2×C59×#394C2semidirect
4. C2×C59×#392C2semidirect
5. C2×C59×#392C2semidirect
6. C2×C59×#386C2semidirect
7. C59×#1441C2semidirect
8. C59×#1439C2semidirect
9. C59×#1438C2semidirect
10. C59×#1437C2semidirect
11. C59×C22⋊#95C2semidirect
72. C22×D4×C59D4semidirect
82. C23×C4×C59D4semidirect
97. C2×C4⋊C4×C59D4semidirect
120. C2×C22⋊C4×C59D4semidirect
121. C2×C22⋊C4×C59D4semidirect
344. C23×C59#121semidirect
409. C2×C4×C59#121semidirect
410. #14722C59direct (N × H)
479. C22×#121C2×C59semidirect
480. C22×C4×D4C2×C59semidirect
481. C2×#394C2×C59semidirect
482. C2×#392C2×C59semidirect
483. C2×#392C2×C59semidirect
484. C2×#386C2×C59semidirect
485. #1441C2×C59semidirect
486. #1439C2×C59semidirect
487. #1438C2×C59semidirect
488. #1437C2×C59semidirect
489. C22⋊#95C2×C59semidirect
536. C59#14722direct (N × H)
565. C22×D4D4×C59semidirect
575. C23×C4D4×C59semidirect
590. C2×C4⋊C4D4×C59semidirect
613. C2×C22⋊C4D4×C59semidirect
614. C2×C22⋊C4D4×C59semidirect
837. C23#121×C59semidirect
902. C2×C4#121×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C592
C22×C4×D4×C592
C2×C59×#3942
C2×C59×#3922
C2×C59×#3862
C59×#14412
C59×#14392
C59×#14382
C59×#14372
C59×C22⋊#952
#1472259