Finite Group Databasebeta

← C59×#14930 #28427039

Subgroups — C59×#14930 #28427039

Order 15104.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C59C211yesmaximal, characteristic, complemented
2C2×C59×#390C211yesmaximal, characteristic
3C2×C59×#388C211yesmaximal, characteristic, complemented
4C2×C59×#388C211yesmaximal, characteristic, complemented
5C59×#1444C211yesmaximal, characteristic, complemented
6C59×#1441C211yesmaximal, characteristic, complemented
7C59×#1440C211yesmaximal, characteristic, complemented
8C59×#1439C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1438C211yesmaximal, characteristic
12C59×#1438C211yesmaximal, characteristic
13C59×#1437C211yesmaximal, characteristic, complemented
14C59×#1436C211yesmaximal, characteristic, complemented
15C4×#95×C59C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C2×#126×C59—24no—
18C2×#126×C59—24no—
19C2×#126×C59—24no—
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2211yescharacteristic
30C22×C22⋊C4×C59C2211yescharacteristic
31C22×C22⋊C4×C59C2211yescharacteristic
32C22×C22⋊C4×C59C2211yescharacteristic
33C22×C22⋊C4×C59C2211yescharacteristic
34C22×C22⋊C4×C59C2211yescharacteristic
35C22×C22⋊C4×C59C2211yescharacteristic
36C22×C22⋊C4×C59C2211yescharacteristic
37C22×C42×C59C2211yescharacteristic
38C22×C42×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C59×#390—24no—
41C59×#388—24no—
42C59×#388—24no—
43C2×#95×C59C2211yescharacteristic
44C2×#95×C59C2211yescharacteristic
45C2×#95×C59C2211yescharacteristic
46C2×#95×C59C2211yescharacteristic
47C2×#95×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C25×C59C2311yescharacteristic
58C25×C59C2311yescharacteristic
59C22×D4×C59—22no—
60C22×D4×C59—22no—
61C22×D4×C59—22no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—41no—
65C22×D4×C59—41no—
66C23×C4×C59C2311yescharacteristic
67C23×C4×C59C2311yescharacteristic
68C23×C4×C59C2311yescharacteristic
69C23×C4×C59C2311yescharacteristic
70C23×C4×C59C2311yescharacteristic
71C23×C4×C59C2311yescharacteristic
72C23×C4×C59C2311yescharacteristic
73C23×C4×C59C2311yescharacteristic
74C23×C4×C59C2311yescharacteristic
75C23×C4×C59C2311yescharacteristic
76C23×C4×C59C2311yescharacteristic
77C23×C4×C59C2311yescharacteristic
78C23×C4×C59C2311yescharacteristic
79#126×C59—232no—
80C2×C4⋊C4×C59—22no—
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—22no—
86C2×C4⋊C4×C59—22no—
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—22no—
91C2×C4⋊C4×C59—41no—
92C2×C4⋊C4×C59—41no—
93C2×C4⋊C4×C59—41no—
94C2×C4⋊C4×C59D414yescomplemented
95C2×C22⋊C4×C59—22no—
96C2×C22⋊C4×C59—22no—
97C2×C22⋊C4×C59—22no—
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—22no—
104C2×C22⋊C4×C59—22no—
105C2×C22⋊C4×C59—22no—
106C2×C22⋊C4×C59—22no—
107C2×C22⋊C4×C59—22no—
108C2×C22⋊C4×C59—22no—
109C2×C22⋊C4×C59—22no—
110C2×C22⋊C4×C59—22no—
111C2×C22⋊C4×C59—22no—
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—22no—
114C2×C22⋊C4×C59—22no—
115C2×C22⋊C4×C59—22no—
116C2×C22⋊C4×C59—22no—
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—22no—
119C2×C22⋊C4×C59—22no—
120C2×C22⋊C4×C59—22no—
121C2×C22⋊C4×C59—22no—
122C2×C22⋊C4×C59—41no—
123C2×C22⋊C4×C59—41no—
124C2×C22⋊C4×C59—41no—
125C2×C22⋊C4×C59—41no—
126C2×C22⋊C4×C59—41no—
127C2×C22⋊C4×C59—41no—
128C2×C22⋊C4×C59—41no—
129C2×C22⋊C4×C59—41no—
130C2×C22⋊C4×C59D414yes—
131C2×C42×C59—22no—
132C2×C42×C59—22no—
133C2×C42×C59—22no—
134C2×C42×C59—22no—
135C2×C42×C59—22no—
136C2×C42×C59—22no—
137C2×C42×C59—41no—
138C2×C42×C59—41no—
139C2×C42×C59D414yescomplemented
140#95×C59—22no—
141#95×C59—22no—
142#95×C59—22no—
143#95×C59—22no—
144#95×C59—22no—
145#95×C59—22no—
146#95×C59—22no—
147#95×C59—22no—
148#95×C59—22no—
149#95×C59—22no—
150#95×C59—22no—
151#95×C59—41no—
152#95×C59—41no—
153#95×C59—41no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59—21no—
178C24×C59—21no—
179C24×C59—21no—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59C2×D412yes—
183C24×C59#4112yes—
184C24×C59C2411yescharacteristic
185C2×D4×C59—28no—
186C2×D4×C59—44no—
187C2×D4×C59—44no—
188C2×D4×C59—44no—
189C2×D4×C59—44no—
190C2×D4×C59—44no—
191C2×D4×C59—44no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
229C22×C4×C59—21no—
230C22×C4×C59—21no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—21no—
256C22×C4×C59—21no—
257C22×C4×C59—21no—
258C22×C4×C59—21no—
259C22×C4×C59—21no—
260C22×C4×C59—21no—
261C22×C4×C59—21no—
262C22×C4×C59—21no—
263C22×C4×C59—21no—
264C22×C4×C59—21no—
265C22×C4×C59—21no—
266C22×C4×C59—21no—
267C22×C4×C59—21no—
268C22×C4×C59C2×D412yes—
269C22×C4×C59C2×D412yes—
270C22×C4×C59C2×D412yes—
271C22×C4×C59C2×D412yes—
272C22×C4×C59C2×D412yes—
273C22×C4×C59C2×D412yes—
274C22×C4×C59C2×D412yes—
275C22×C4×C59C2×D412yes—
276C22×C4×C59#4112yes—
277C22×C4×C59#4112yes—
278C22×C4×C59#4112yes—
279C22×C4×C59#4112yes—
280C22×C4×C59#4112yes—
281C22×C4×C59#4112yes—
282C22×C4×C59#4112yes—
283C4⋊C4×C59—28no—
284C4⋊C4×C59—28no—
285C4⋊C4×C59—28no—
286C4⋊C4×C59—44no—
287C4⋊C4×C59—44no—
288C22⋊C4×C59—28no—
289C22⋊C4×C59—28no—
290C22⋊C4×C59—28no—
291C22⋊C4×C59—28no—
292C22⋊C4×C59—28no—
293C22⋊C4×C59—44no—
294C22⋊C4×C59—44no—
295C22⋊C4×C59—44no—
296C22⋊C4×C59—44no—
297C22⋊C4×C59—44no—
298C22⋊C4×C59—44no—
299C22⋊C4×C59—44no—
300C42×C59—28no—
301C42×C59—44no—
302C42×C59—44no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59—41no—
361C23×C59—41no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59C22×D411yescharacteristic
374C23×C59C22×D411yescharacteristic
375C23×C59C22×D411yescharacteristic
376C23×C59C2×#4111yescharacteristic
377C23×C59C2×#4111yescharacteristic
378C23×C59C2×#4111yescharacteristic
379C23×C59C2×#4111yescharacteristic
380C23×C59C2×#4111yescharacteristic
381C23×C59C2×#4111yescharacteristic
382C23×C59C2×#4111yescharacteristic
383C23×C59C2×#4111yescharacteristic
384C23×C59H(5,𝔽2)11yescharacteristic
385C23×C59H(5,𝔽2)11yescharacteristic
386C23×C59H(5,𝔽2)11yescharacteristic
387C23×C592−1+411yescharacteristic
388D4×C59—416no—
389C2×C4×C59—22no—
390C2×C4×C59—22no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
393C2×C4×C59—22no—
394C2×C4×C59—22no—
395C2×C4×C59—22no—
396C2×C4×C59—22no—
397C2×C4×C59—22no—
398C2×C4×C59—22no—
399C2×C4×C59—22no—
400C2×C4×C59—22no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—22no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59—41no—
446C2×C4×C59—41no—
447C2×C4×C59—41no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—41no—
453C2×C4×C59—41no—
454C2×C4×C59—41no—
455C2×C4×C59—41no—
456C2×C4×C59—41no—
457C2×C4×C59—41no—
458C2×C4×C59—41no—
459C2×C4×C59—41no—
460C2×C4×C59—41no—
461C2×C4×C59—41no—
462C2×C4×C59—41no—
463C2×C4×C59—41no—
464C2×C4×C59—41no—
465C2×C4×C59—41no—
466C2×C4×C59—41no—
467C2×C4×C59—41no—
468C2×C4×C59—41no—
469C2×C4×C59—41no—
470C2×C4×C59—41no—
471C2×C4×C59—41no—
472C2×C4×C59—41no—
473C2×C4×C59—41no—
474C2×C4×C59—41no—
475C2×C4×C59—41no—
476C2×C4×C59—41no—
477C2×C4×C59—41no—
478C2×C4×C59#12014yes—
479C2×C4×C59#12614yescomplemented
480#14930C5911yesmaximal, characteristic, direct product factor, Sylow
481C22×C59—42no—
482C22×C59—42no—
483C22×C59—42no—
484C22×C59—42no—
485C22×C59—42no—
486C22×C59—42no—
487C22×C59—42no—
488C22×C59—42no—
489C22×C59—42no—
490C22×C59—42no—
491C22×C59—42no—
492C22×C59—42no—
493C22×C59—42no—
494C22×C59—42no—
495C22×C59—81no—
496C22×C59—81no—
497C22×C59—81no—
498C22×C59—81no—
499C22×C59—81no—
500C22×C59—81no—
501C22×C59—81no—
502C22×C59—81no—
503C22×C59—81no—
504C22×C59—81no—
505C22×C59—81no—
506C22×C59—81no—
507C22×C59—81no—
508C22×C59—81no—
509C22×C59—81no—
510C22×C59—81no—
511C22×C59C2×#12011yescharacteristic
512C22×C59#52511yescharacteristic
513C22×C59#52511yescharacteristic
514C22×C59#52511yescharacteristic
515C22×C59C2×#12611yescharacteristic
516C22×C59#52911yescharacteristic
517C22×C59#52911yescharacteristic
518C22×C59#52911yescharacteristic
519C22×C59#53211yescharacteristic
520C22×C59#53211yescharacteristic
521C22×C59#53211yescharacteristic
522C22×C59#53211yescharacteristic
523C22×C59#53211yescharacteristic
524C22×C59#53511yescharacteristic
525C22×C59#53711yescharacteristic
526C22×C59#53811yescharacteristic
527C22×C59#53811yescharacteristic
528C22×C59#54211yescharacteristic
529C22×C59#54211yescharacteristic
530C22×C59#54611yescharacteristic
531C22×C59#54611yescharacteristic
532C22×C59#54611yescharacteristic
533C22×C59#54611yescharacteristic
534C22×C59#54711yescharacteristic
535C22×C59#54711yescharacteristic
536C22×C59#55011yescharacteristic
537C22×C59#55011yescharacteristic
538C22×C59#55111yescharacteristic
539C22×C59#55111yescharacteristic
540C22×C59#55111yescharacteristic
541C22×C59#55211yescharacteristic
542C22×C59#55311yescharacteristic
543C22×C59#55311yescharacteristic
544C22×C59#55311yescharacteristic
545C22×C59#55611yescharacteristic
546C4×C59—24no—
547C4×C59—24no—
548C4×C59—42no—
549C4×C59—42no—
550C4×C59—42no—
551C4×C59—42no—
552C4×C59—42no—
553C4×C59—42no—
554C4×C59—42no—
555C4×C59—42no—
556C4×C59—42no—
557C4×C59—81no—
558C4×C59—81no—
559C22×#126C2×C5911yescharacteristic, complemented
560C2×#390C2×C5911yescharacteristic
561C2×#388C2×C5911yescharacteristic, complemented
562C2×#388C2×C5911yescharacteristic, complemented
563#1444C2×C5911yescharacteristic, complemented
564#1441C2×C5911yescharacteristic, complemented
565#1440C2×C5911yescharacteristic, complemented
566#1439C2×C5911yescharacteristic, complemented
567#1439C2×C5911yescharacteristic, complemented
568#1439C2×C5911yescharacteristic, complemented
569#1438C2×C5911yescharacteristic
570#1438C2×C5911yescharacteristic
571#1437C2×C5911yescharacteristic, complemented
572#1436C2×C5911yescharacteristic, complemented
573C4×#95C2×C5911yescharacteristic, complemented
574C2×C59—82no—
575C2×C59—82no—
576C2×C59#238811yescharacteristic
577C2×C59#243011yescharacteristic
578C2×C59#243111yescharacteristic
579C2×C59#246711yescharacteristic
580C2×C59#246811yescharacteristic
581C2×C59#247911yescharacteristic
582C2×C59#248011yescharacteristic
583C2×C59#251211yescharacteristic
584C2×C59#252111yescharacteristic
585C2×C59#255411yescharacteristic
586C2×C59#255911yescharacteristic
587C2×C59#260111yescharacteristic
588C2×C59#260311yescharacteristic
589C2×C59#266211yescharacteristic
590C2×C59#286011yescharacteristic
591C23×D4C22×C5911yescharacteristic
592C2×#126—24no—
593C2×#126—24no—
594C2×#126—24no—
595C22×C4⋊C4C22×C5911yescharacteristic
596C22×C4⋊C4C22×C5911yescharacteristic
597C22×C4⋊C4C22×C5911yescharacteristic
598C22×C4⋊C4C22×C5911yescharacteristic
599C22×C4⋊C4C22×C5911yescharacteristic
600C22×C22⋊C4C22×C5911yescharacteristic
601C22×C22⋊C4C22×C5911yescharacteristic
602C22×C22⋊C4C22×C5911yescharacteristic
603C22×C22⋊C4C22×C5911yescharacteristic
604C22×C22⋊C4C22×C5911yescharacteristic
605C22×C22⋊C4C22×C5911yescharacteristic
606C22×C22⋊C4C22×C5911yescharacteristic
607C22×C22⋊C4C22×C5911yescharacteristic
608C22×C22⋊C4C22×C5911yescharacteristic
609C22×C22⋊C4C22×C5911yescharacteristic
610C22×C22⋊C4C22×C5911yescharacteristic
611C22×C22⋊C4C22×C5911yescharacteristic
612C22×C42C22×C5911yescharacteristic
613C22×C42C22×C5911yescharacteristic
614C22×C42C22×C5911yescharacteristic
615#390—24no—
616#388—24no—
617#388—24no—
618C2×#95C22×C5911yescharacteristic
619C2×#95C22×C5911yescharacteristic
620C2×#95C22×C5911yescharacteristic
621C2×#95C22×C5911yescharacteristic
622C2×#95C22×C5911yescharacteristic
623C2×#95C22×C5911yescharacteristic
624C2×#95C22×C5911yescharacteristic
625C2×#95C22×C5911yescharacteristic
626C2×#95C22×C5911yescharacteristic
627C2×#95C22×C5911yescharacteristic
628C2×#95C22×C5911yescharacteristic
629C2×#95C22×C5911yescharacteristic
630C2×#95C22×C5911yescharacteristic
631C2×#95C22×C5911yescharacteristic
632C59#1493011yescharacteristic, direct product factor, Sylow
633C25C23×C5911yescharacteristic
634C25C23×C5911yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C23×C4C23×C5911yescharacteristic
643C23×C4C23×C5911yescharacteristic
644C23×C4C23×C5911yescharacteristic
645C23×C4C23×C5911yescharacteristic
646C23×C4C23×C5911yescharacteristic
647C23×C4C23×C5911yescharacteristic
648C23×C4C23×C5911yescharacteristic
649C23×C4C23×C5911yescharacteristic
650C23×C4C23×C5911yescharacteristic
651C23×C4C23×C5911yescharacteristic
652C23×C4C23×C5911yescharacteristic
653C23×C4C23×C5911yescharacteristic
654C23×C4C23×C5911yescharacteristic
655#126—232no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4D4×C5914yescomplemented
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4D4×C5914yes—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42D4×C5914yescomplemented
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—41no—
728#95—41no—
729#95—41no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24C2×D4×C5912yes—
759C24#41×C5912yes—
760C24C24×C5911yescharacteristic
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4C2×D4×C5912yes—
845C22×C4C2×D4×C5912yes—
846C22×C4C2×D4×C5912yes—
847C22×C4C2×D4×C5912yes—
848C22×C4C2×D4×C5912yes—
849C22×C4C2×D4×C5912yes—
850C22×C4C2×D4×C5912yes—
851C22×C4C2×D4×C5912yes—
852C22×C4#41×C5912yes—
853C22×C4#41×C5912yes—
854C22×C4#41×C5912yes—
855C22×C4#41×C5912yes—
856C22×C4#41×C5912yes—
857C22×C4#41×C5912yes—
858C22×C4#41×C5912yes—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C42—28no—
877C42—44no—
878C42—44no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C22×D4×C5911yescharacteristic
950C23C22×D4×C5911yescharacteristic
951C23C22×D4×C5911yescharacteristic
952C23C2×#41×C5911yescharacteristic
953C23C2×#41×C5911yescharacteristic
954C23C2×#41×C5911yescharacteristic
955C23C2×#41×C5911yescharacteristic
956C23C2×#41×C5911yescharacteristic
957C23C2×#41×C5911yescharacteristic
958C23C2×#41×C5911yescharacteristic
959C23C2×#41×C5911yescharacteristic
960C23H(5,𝔽2)×C5911yescharacteristic
961C23H(5,𝔽2)×C5911yescharacteristic
962C23H(5,𝔽2)×C5911yescharacteristic
963C232−1+4×C5911yescharacteristic
964D4—416no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4#120×C5914yes—
1055C2×C4#126×C5914yescomplemented
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22C2×#120×C5911yescharacteristic
1087C22C59×#52511yescharacteristic
1088C22C59×#52511yescharacteristic
1089C22C59×#52511yescharacteristic
1090C22C2×#126×C5911yescharacteristic
1091C22C59×#52911yescharacteristic
1092C22C59×#52911yescharacteristic
1093C22C59×#52911yescharacteristic
1094C22C59×#53211yescharacteristic
1095C22C59×#53211yescharacteristic
1096C22C59×#53211yescharacteristic
1097C22C59×#53211yescharacteristic
1098C22C59×#53211yescharacteristic
1099C22C59×#53511yescharacteristic
1100C22C59×#53711yescharacteristic
1101C22C59×#53811yescharacteristic
1102C22C59×#53811yescharacteristic
1103C22C59×#54211yescharacteristic
1104C22C59×#54211yescharacteristic
1105C22C59×#54611yescharacteristic
1106C22C59×#54611yescharacteristic
1107C22C59×#54611yescharacteristic
1108C22C59×#54611yescharacteristic
1109C22C59×#54711yescharacteristic
1110C22C59×#54711yescharacteristic
1111C22C59×#55011yescharacteristic
1112C22C59×#55011yescharacteristic
1113C22C59×#55111yescharacteristic
1114C22C59×#55111yescharacteristic
1115C22C59×#55111yescharacteristic
1116C22C59×#55211yescharacteristic
1117C22C59×#55311yescharacteristic
1118C22C59×#55311yescharacteristic
1119C22C59×#55311yescharacteristic
1120C22C59×#55611yescharacteristic
1121C4—24no—
1122C4—24no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C2—82no—
1135C2—82no—
1136C2C59×#238811yescharacteristic
1137C2C59×#243011yescharacteristic
1138C2C59×#243111yescharacteristic
1139C2C59×#246711yescharacteristic
1140C2C59×#246811yescharacteristic
1141C2C59×#247911yescharacteristic
1142C2C59×#248011yescharacteristic
1143C2C59×#251211yescharacteristic
1144C2C59×#252111yescharacteristic
1145C2C59×#255411yescharacteristic
1146C2C59×#255911yescharacteristic
1147C2C59×#260111yescharacteristic
1148C2C59×#260311yescharacteristic
1149C2C59×#266211yescharacteristic
1150C2C59×#286011yescharacteristic
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×#126×C59C2semidirect
3. C2×C59×#388C2semidirect
4. C2×C59×#388C2semidirect
5. C59×#1444C2semidirect
6. C59×#1441C2semidirect
7. C59×#1440C2semidirect
8. C59×#1439C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
13. C59×#1437C2semidirect
14. C59×#1436C2semidirect
15. C4×#95×C59C2semidirect
94. C2×C4⋊C4×C59D4semidirect
139. C2×C42×C59D4semidirect
479. C2×C4×C59#126semidirect
480. #14930C59direct (N × H)
559. C22×#126C2×C59semidirect
561. C2×#388C2×C59semidirect
562. C2×#388C2×C59semidirect
563. #1444C2×C59semidirect
564. #1441C2×C59semidirect
565. #1440C2×C59semidirect
566. #1439C2×C59semidirect
567. #1439C2×C59semidirect
568. #1439C2×C59semidirect
571. #1437C2×C59semidirect
572. #1436C2×C59semidirect
573. C4×#95C2×C59semidirect
632. C59#14930direct (N × H)
670. C2×C4⋊C4D4×C59semidirect
715. C2×C42D4×C59semidirect
1055. C2×C4#126×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C592
C2×C59×#3902
C2×C59×#3882
C59×#14442
C59×#14412
C59×#14402
C59×#14392
C59×#14382
C59×#14372
C59×#14362
C4×#95×C592
#1493059