Finite Group Databasebeta

← C59×#14761 #28426870

Subgroups — C59×#14761 #28426870

Order 15104.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C59C211yesmaximal, characteristic
2C2×C59×#394C211yesmaximal, characteristic
3C2×C59×#389C211yesmaximal, characteristic, complemented
4C2×C59×#388C211yesmaximal, characteristic, complemented
5C2×C59×#385C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
7C59×#1444C211yesmaximal, characteristic, complemented
8C59×#1442C211yesmaximal, characteristic, complemented
9C59×#1440C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1439C211yesmaximal, characteristic, complemented
12C59×#1439C211yesmaximal, characteristic, complemented
13C59×#1438C211yesmaximal, characteristic
14C59×#1437C211yesmaximal, characteristic, complemented
15C59×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C24×C4×C59C2211yescharacteristic
18C2×#123×C59—24no—
19C2×#123×C59—24no—
20C2×#123×C59—24no—
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C4⋊C4×C59C2211yescharacteristic
26C22×C4⋊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×C22⋊C4×C59C2211yescharacteristic
38C22×C42×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C59×#394—24no—
41C59×#389—24no—
42C59×#388—24no—
43C59×#385—24no—
44C4×C22⋊C4×C59—24no—
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
57C2×#95×C59C2211yescharacteristic
58C2×#95×C59C2211yescharacteristic
59C25×C59C2311yescharacteristic
60C25×C59C2311yescharacteristic
61C22×D4×C59—22no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—22no—
65C22×D4×C59—22no—
66C22×D4×C59—41no—
67C22×D4×C59—41no—
68C23×C4×C59—22no—
69C23×C4×C59—22no—
70C23×C4×C59—22no—
71C23×C4×C59—22no—
72C23×C4×C59—41no—
73C23×C4×C59—41no—
74C23×C4×C59D414yes—
75C23×C4×C59C2311yescharacteristic
76C23×C4×C59C2311yescharacteristic
77C23×C4×C59C2311yescharacteristic
78C23×C4×C59C2311yescharacteristic
79C23×C4×C59C2311yescharacteristic
80C23×C4×C59C2311yescharacteristic
81C23×C4×C59C2311yescharacteristic
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2311yescharacteristic
88#123×C59—232no—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—22no—
91C2×C4⋊C4×C59—22no—
92C2×C4⋊C4×C59—22no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59—22no—
95C2×C4⋊C4×C59—22no—
96C2×C4⋊C4×C59—22no—
97C2×C4⋊C4×C59—22no—
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—22no—
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—22no—
102C2×C4⋊C4×C59—22no—
103C2×C4⋊C4×C59—41no—
104C2×C4⋊C4×C59—41no—
105C2×C4⋊C4×C59—41no—
106C2×C4⋊C4×C59D414yes—
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—22no—
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59—22no—
125C2×C22⋊C4×C59—22no—
126C2×C22⋊C4×C59—22no—
127C2×C22⋊C4×C59—22no—
128C2×C22⋊C4×C59—22no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59—22no—
131C2×C22⋊C4×C59—22no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—41no—
137C2×C22⋊C4×C59—41no—
138C2×C22⋊C4×C59D414yes—
139C2×C22⋊C4×C59D414yes—
140C2×C42×C59—22no—
141C2×C42×C59—22no—
142C2×C42×C59—22no—
143C2×C42×C59—22no—
144C2×C42×C59—41no—
145C2×C42×C59—41no—
146#95×C59—22no—
147#95×C59—22no—
148#95×C59—22no—
149#95×C59—22no—
150#95×C59—22no—
151#95×C59—22no—
152#95×C59—22no—
153#95×C59—22no—
154#95×C59—22no—
155#95×C59—22no—
156#95×C59—22no—
157#95×C59—22no—
158#95×C59—22no—
159#95×C59—41no—
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×C59—21no—
183C24×C59—21no—
184C24×C59—21no—
185C24×C59—21no—
186C24×C59C2×D412yes—
187C24×C59C2×D412yes—
188C24×C59C2×D412yes—
189C24×C59#4112yes—
190C24×C59C2411yescharacteristic
191C2×D4×C59—28no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—44no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C2×D4×C59—44no—
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—28no—
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—28no—
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×C59—21no—
269C22×C4×C59—21no—
270C22×C4×C59—21no—
271C22×C4×C59—21no—
272C22×C4×C59—21no—
273C22×C4×C59—21no—
274C22×C4×C59—21no—
275C22×C4×C59—21no—
276C22×C4×C59—44no—
277C22×C4×C59—44no—
278C22×C4×C59—44no—
279C22×C4×C59—44no—
280C22×C4×C59—44no—
281C22×C4×C59C2×D412yes—
282C22×C4×C59C2×D412yes—
283C22×C4×C59C2×D412yes—
284C22×C4×C59C2×D412yes—
285C22×C4×C59C2×D412yes—
286C22×C4×C59C2×D412yes—
287C22×C4×C59C2×D412yes—
288C22×C4×C59C2×D412yes—
289C22×C4×C59C2×D412yes—
290C22×C4×C59#4112yes—
291C22×C4×C59#4112yes—
292C22×C4×C59#4112yes—
293C22×C4×C59#4112yes—
294C22×C4×C59#4112yes—
295C22×C4×C59#4112yes—
296C4⋊C4×C59—28no—
297C4⋊C4×C59—28no—
298C4⋊C4×C59—28no—
299C4⋊C4×C59—44no—
300C4⋊C4×C59—44no—
301C4⋊C4×C59—44no—
302C22⋊C4×C59—28no—
303C22⋊C4×C59—28no—
304C22⋊C4×C59—28no—
305C22⋊C4×C59—28no—
306C22⋊C4×C59—28no—
307C22⋊C4×C59—28no—
308C22⋊C4×C59—28no—
309C22⋊C4×C59—44no—
310C22⋊C4×C59—44no—
311C22⋊C4×C59—44no—
312C22⋊C4×C59—44no—
313C42×C59—44no—
314C42×C59—44no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
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×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—41no—
379C23×C59—41no—
380C23×C59—41no—
381C23×C59—41no—
382C23×C59—41no—
383C23×C59—41no—
384C23×C59#12114yes—
385C23×C59C22×D411yescharacteristic
386C23×C59C22×D411yescharacteristic
387C23×C59C22×D411yescharacteristic
388C23×C59C22×D411yescharacteristic
389C23×C59C2×#4111yescharacteristic
390C23×C59C2×#4111yescharacteristic
391C23×C59C2×#4111yescharacteristic
392C23×C59C2×#4111yescharacteristic
393C23×C59C2×#4111yescharacteristic
394C23×C59C2×#4111yescharacteristic
395C23×C59C2×#4111yescharacteristic
396C23×C59H(5,𝔽2)11yescharacteristic
397C23×C59H(5,𝔽2)11yescharacteristic
398C23×C592−1+411yescharacteristic
399C23×C592−1+411yescharacteristic
400D4×C59—416no—
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—22no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—22no—
432C2×C4×C59—22no—
433C2×C4×C59—22no—
434C2×C4×C59—22no—
435C2×C4×C59—22no—
436C2×C4×C59—22no—
437C2×C4×C59—22no—
438C2×C4×C59—22no—
439C2×C4×C59—22no—
440C2×C4×C59—416no—
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—41no—
479C2×C4×C59—41no—
480C2×C4×C59—41no—
481C2×C4×C59—41no—
482C2×C4×C59—41no—
483C2×C4×C59—41no—
484C2×C4×C59—41no—
485C2×C4×C59—41no—
486C2×C4×C59—41no—
487C2×C4×C59—41no—
488C2×C4×C59—41no—
489C2×C4×C59—41no—
490C2×C4×C59—41no—
491C2×C4×C59#12014yes—
492C2×C4×C59#12314yescomplemented
493#14761C5911yesmaximal, characteristic, direct product factor, Sylow
494C22×C59—24no—
495C22×C59—24no—
496C22×C59—24no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59—42no—
501C22×C59—42no—
502C22×C59—42no—
503C22×C59—42no—
504C22×C59—42no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—42no—
516C22×C59—81no—
517C22×C59—81no—
518C22×C59—81no—
519C22×C59—81no—
520C22×C59—81no—
521C22×C59—81no—
522C22×C59—81no—
523C22×C59—81no—
524C22×C59C2×#12011yescharacteristic
525C22×C59C2×#12111yescharacteristic
526C22×C59C2×#12311yescharacteristic
527C22×C59#52511yescharacteristic
528C22×C59#52511yescharacteristic
529C22×C59#52511yescharacteristic
530C22×C59#52511yescharacteristic
531C22×C59#52911yescharacteristic
532C22×C59#52911yescharacteristic
533C22×C59#53211yescharacteristic
534C22×C59#53211yescharacteristic
535C22×C59#53211yescharacteristic
536C22×C59#53211yescharacteristic
537C22×C59#53411yescharacteristic
538C22×C59#53611yescharacteristic
539C22×C59#53911yescharacteristic
540C22×C59#53911yescharacteristic
541C22×C59#54211yescharacteristic
542C22×C59#54211yescharacteristic
543C22×C59D4211yescharacteristic
544C22×C59D4211yescharacteristic
545C22×C59#54611yescharacteristic
546C22×C59#54611yescharacteristic
547C22×C59#54711yescharacteristic
548C22×C59#54711yescharacteristic
549C22×C59#54711yescharacteristic
550C22×C59#54711yescharacteristic
551C22×C59#54811yescharacteristic
552C22×C59#54811yescharacteristic
553C22×C59#55111yescharacteristic
554C22×C59#55211yescharacteristic
555C22×C59#55211yescharacteristic
556C22×C59#55311yescharacteristic
557C22×C59#55311yescharacteristic
558C22×C59#55911yescharacteristic
559C4×C59—24no—
560C4×C59—24no—
561C4×C59—42no—
562C4×C59—42no—
563C4×C59—42no—
564C4×C59—42no—
565C4×C59—42no—
566C4×C59—42no—
567C4×C59—42no—
568C4×C59—42no—
569C4×C59—42no—
570C4×C59—81no—
571C4×C59—81no—
572C22×#123C2×C5911yescharacteristic
573C2×#394C2×C5911yescharacteristic
574C2×#389C2×C5911yescharacteristic, complemented
575C2×#388C2×C5911yescharacteristic, complemented
576C2×#385C2×C5911yescharacteristic, complemented
577C2×C4×C22⋊C4C2×C5911yescharacteristic, complemented
578#1444C2×C5911yescharacteristic, complemented
579#1442C2×C5911yescharacteristic, complemented
580#1440C2×C5911yescharacteristic, complemented
581#1439C2×C5911yescharacteristic, complemented
582#1439C2×C5911yescharacteristic, complemented
583#1439C2×C5911yescharacteristic, complemented
584#1438C2×C5911yescharacteristic
585#1437C2×C5911yescharacteristic, complemented
586#1436C2×C5911yescharacteristic, complemented
587C2×C59—44no—
588C2×C59—82no—
589C2×C59#238811yescharacteristic
590C2×C59#241011yescharacteristic
591C2×C59#241311yescharacteristic
592C2×C59#242211yescharacteristic
593C2×C59#243211yescharacteristic
594C2×C59#244311yescharacteristic
595C2×C59#245511yescharacteristic
596C2×C59#245811yescharacteristic
597C2×C59#246111yescharacteristic
598C2×C59#247011yescharacteristic
599C2×C59#255311yescharacteristic
600C2×C59#255811yescharacteristic
601C2×C59#260211yescharacteristic
602C2×C59#266311yescharacteristic
603C2×C59#285411yescharacteristic
604C23×D4C22×C5911yescharacteristic
605C24×C4C22×C5911yescharacteristic
606C2×#123—24no—
607C2×#123—24no—
608C2×#123—24no—
609C22×C4⋊C4C22×C5911yescharacteristic
610C22×C4⋊C4C22×C5911yescharacteristic
611C22×C4⋊C4C22×C5911yescharacteristic
612C22×C4⋊C4C22×C5911yescharacteristic
613C22×C4⋊C4C22×C5911yescharacteristic
614C22×C4⋊C4C22×C5911yescharacteristic
615C22×C22⋊C4C22×C5911yescharacteristic
616C22×C22⋊C4C22×C5911yescharacteristic
617C22×C22⋊C4C22×C5911yescharacteristic
618C22×C22⋊C4C22×C5911yescharacteristic
619C22×C22⋊C4C22×C5911yescharacteristic
620C22×C22⋊C4C22×C5911yescharacteristic
621C22×C22⋊C4C22×C5911yescharacteristic
622C22×C22⋊C4C22×C5911yescharacteristic
623C22×C22⋊C4C22×C5911yescharacteristic
624C22×C22⋊C4C22×C5911yescharacteristic
625C22×C22⋊C4C22×C5911yescharacteristic
626C22×C42C22×C5911yescharacteristic
627C22×C42C22×C5911yescharacteristic
628#394—24no—
629#389—24no—
630#388—24no—
631#385—24no—
632C4×C22⋊C4—24no—
633C2×#95C22×C5911yescharacteristic
634C2×#95C22×C5911yescharacteristic
635C2×#95C22×C5911yescharacteristic
636C2×#95C22×C5911yescharacteristic
637C2×#95C22×C5911yescharacteristic
638C2×#95C22×C5911yescharacteristic
639C2×#95C22×C5911yescharacteristic
640C2×#95C22×C5911yescharacteristic
641C2×#95C22×C5911yescharacteristic
642C2×#95C22×C5911yescharacteristic
643C2×#95C22×C5911yescharacteristic
644C2×#95C22×C5911yescharacteristic
645C2×#95C22×C5911yescharacteristic
646C2×#95C22×C5911yescharacteristic
647C59#1476111yescharacteristic, direct product factor, Sylow
648C25C23×C5911yescharacteristic
649C25C23×C5911yescharacteristic
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—41no—
656C22×D4—41no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4D4×C5914yes—
664C23×C4C23×C5911yescharacteristic
665C23×C4C23×C5911yescharacteristic
666C23×C4C23×C5911yescharacteristic
667C23×C4C23×C5911yescharacteristic
668C23×C4C23×C5911yescharacteristic
669C23×C4C23×C5911yescharacteristic
670C23×C4C23×C5911yescharacteristic
671C23×C4C23×C5911yescharacteristic
672C23×C4C23×C5911yescharacteristic
673C23×C4C23×C5911yescharacteristic
674C23×C4C23×C5911yescharacteristic
675C23×C4C23×C5911yescharacteristic
676C23×C4C23×C5911yescharacteristic
677#123—232no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4D4×C5914yes—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4D4×C5914yes—
728C2×C22⋊C4D4×C5914yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—41no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×D4×C5912yes—
776C24C2×D4×C5912yes—
777C24C2×D4×C5912yes—
778C24#41×C5912yes—
779C24C24×C5911yescharacteristic
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
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—28no—
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×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—28no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4C2×D4×C5912yes—
871C22×C4C2×D4×C5912yes—
872C22×C4C2×D4×C5912yes—
873C22×C4C2×D4×C5912yes—
874C22×C4C2×D4×C5912yes—
875C22×C4C2×D4×C5912yes—
876C22×C4C2×D4×C5912yes—
877C22×C4C2×D4×C5912yes—
878C22×C4C2×D4×C5912yes—
879C22×C4#41×C5912yes—
880C22×C4#41×C5912yes—
881C22×C4#41×C5912yes—
882C22×C4#41×C5912yes—
883C22×C4#41×C5912yes—
884C22×C4#41×C5912yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C42—44no—
903C42—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
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—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23#121×C5914yes—
974C23C22×D4×C5911yescharacteristic
975C23C22×D4×C5911yescharacteristic
976C23C22×D4×C5911yescharacteristic
977C23C22×D4×C5911yescharacteristic
978C23C2×#41×C5911yescharacteristic
979C23C2×#41×C5911yescharacteristic
980C23C2×#41×C5911yescharacteristic
981C23C2×#41×C5911yescharacteristic
982C23C2×#41×C5911yescharacteristic
983C23C2×#41×C5911yescharacteristic
984C23C2×#41×C5911yescharacteristic
985C23H(5,𝔽2)×C5911yescharacteristic
986C23H(5,𝔽2)×C5911yescharacteristic
987C232−1+4×C5911yescharacteristic
988C232−1+4×C5911yescharacteristic
989D4—416no—
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—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—416no—
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—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4#120×C5914yes—
1081C2×C4#123×C5914yescomplemented
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×#120×C5911yescharacteristic
1113C22C2×#121×C5911yescharacteristic
1114C22C2×#123×C5911yescharacteristic
1115C22C59×#52511yescharacteristic
1116C22C59×#52511yescharacteristic
1117C22C59×#52511yescharacteristic
1118C22C59×#52511yescharacteristic
1119C22C59×#52911yescharacteristic
1120C22C59×#52911yescharacteristic
1121C22C59×#53211yescharacteristic
1122C22C59×#53211yescharacteristic
1123C22C59×#53211yescharacteristic
1124C22C59×#53211yescharacteristic
1125C22C59×#53411yescharacteristic
1126C22C59×#53611yescharacteristic
1127C22C59×#53911yescharacteristic
1128C22C59×#53911yescharacteristic
1129C22C59×#54211yescharacteristic
1130C22C59×#54211yescharacteristic
1131C22D42×C5911yescharacteristic
1132C22D42×C5911yescharacteristic
1133C22C59×#54611yescharacteristic
1134C22C59×#54611yescharacteristic
1135C22C59×#54711yescharacteristic
1136C22C59×#54711yescharacteristic
1137C22C59×#54711yescharacteristic
1138C22C59×#54711yescharacteristic
1139C22C59×#54811yescharacteristic
1140C22C59×#54811yescharacteristic
1141C22C59×#55111yescharacteristic
1142C22C59×#55211yescharacteristic
1143C22C59×#55211yescharacteristic
1144C22C59×#55311yescharacteristic
1145C22C59×#55311yescharacteristic
1146C22C59×#55911yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2C59×#238811yescharacteristic
1163C2C59×#241011yescharacteristic
1164C2C59×#241311yescharacteristic
1165C2C59×#242211yescharacteristic
1166C2C59×#243211yescharacteristic
1167C2C59×#244311yescharacteristic
1168C2C59×#245511yescharacteristic
1169C2C59×#245811yescharacteristic
1170C2C59×#246111yescharacteristic
1171C2C59×#247011yescharacteristic
1172C2C59×#255311yescharacteristic
1173C2C59×#255811yescharacteristic
1174C2C59×#260211yescharacteristic
1175C2C59×#266311yescharacteristic
1176C2C59×#285411yescharacteristic
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
3. C2×C59×#389C2semidirect
4. C2×C59×#388C2semidirect
5. C2×C59×#385C2semidirect
6. C2×C4×C22⋊C4×C59C2semidirect
7. C59×#1444C2semidirect
8. C59×#1442C2semidirect
9. C59×#1440C2semidirect
10. C59×#1439C2semidirect
11. C59×#1439C2semidirect
12. C59×#1439C2semidirect
14. C59×#1437C2semidirect
15. C59×#1436C2semidirect
492. C2×C4×C59#123semidirect
493. #14761C59direct (N × H)
574. C2×#389C2×C59semidirect
575. C2×#388C2×C59semidirect
576. C2×#385C2×C59semidirect
577. C2×C4×C22⋊C4C2×C59semidirect
578. #1444C2×C59semidirect
579. #1442C2×C59semidirect
580. #1440C2×C59semidirect
581. #1439C2×C59semidirect
582. #1439C2×C59semidirect
583. #1439C2×C59semidirect
585. #1437C2×C59semidirect
586. #1436C2×C59semidirect
647. C59#14761direct (N × H)
1081. C2×C4#123×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C592
C2×C59×#3942
C2×C59×#3892
C2×C59×#3882
C2×C59×#3852
C2×C4×C22⋊C4×C592
C59×#14442
C59×#14422
C59×#14402
C59×#14392
C59×#14382
C59×#14372
C59×#14362
#1476159