Finite Group Databasebeta

← C59×#16526 #28428635

Subgroups — C59×#16526 #28428635

Order 15104.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#397C211yesmaximal, characteristic, complemented
2C2×C59×#394C211yesmaximal, characteristic, complemented
3C2×C59×#394C211yesmaximal, characteristic, complemented
4C2×C59×#394C211yesmaximal, characteristic, complemented
5C2×C59×#392C211yesmaximal, characteristic
6C2×C59×#390C211yesmaximal, characteristic, complemented
7C59×#1444C211yesmaximal, characteristic, complemented
8C59×#1440C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1439C211yesmaximal, characteristic, complemented
12C59×#1438C211yesmaximal, characteristic, complemented
13C59×#1438C211yesmaximal, characteristic, complemented
14C59×#1437C211yesmaximal, characteristic, complemented
15C59×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C22×C22⋊C4×C59C2211yescharacteristic
24C22×C22⋊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×C22⋊C4×C59C2211yescharacteristic
38C22×C42×C59C2211yescharacteristic
39C59×#397—24no—
40C59×#394—24no—
41C59×#394—24no—
42C59×#394—24no—
43C59×#392—24no—
44C59×#390—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
57C25×C59C2311yescharacteristic
58C25×C59C2311yescharacteristic
59C25×C59C2311yescharacteristic
60C22×D4×C59—22no—
61C22×D4×C59—22no—
62C22×D4×C59—22no—
63C22×D4×C59—22no—
64C22×D4×C59—22no—
65C22×D4×C59—22no—
66C22×D4×C59—22no—
67C22×D4×C59—22no—
68C22×D4×C59—41no—
69C22×D4×C59—41no—
70C22×D4×C59—41no—
71C22×D4×C59—41no—
72C22×D4×C59—41no—
73C22×D4×C59—41no—
74C22×D4×C59—41no—
75C22×D4×C59—41no—
76C22×D4×C59—41no—
77C22×D4×C59—41no—
78C22×D4×C59—41no—
79C22×D4×C59—41no—
80C22×D4×C59D414yes—
81C23×C4×C59C2311yescharacteristic
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2311yescharacteristic
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2311yescharacteristic
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—41no—
100C2×C4⋊C4×C59—41no—
101C2×C4⋊C4×C59—41no—
102C2×C4⋊C4×C59—41no—
103C2×C4⋊C4×C59—41no—
104C2×C4⋊C4×C59—41no—
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—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—41no—
132C2×C22⋊C4×C59—41no—
133C2×C22⋊C4×C59—41no—
134C2×C22⋊C4×C59—41no—
135C2×C22⋊C4×C59—41no—
136C2×C22⋊C4×C59—41no—
137C2×C22⋊C4×C59—41no—
138C2×C22⋊C4×C59—41no—
139C2×C22⋊C4×C59—41no—
140C2×C22⋊C4×C59—41no—
141C2×C22⋊C4×C59—41no—
142C2×C22⋊C4×C59—41no—
143C2×C22⋊C4×C59—41no—
144C2×C22⋊C4×C59—41no—
145C2×C22⋊C4×C59—41no—
146C2×C22⋊C4×C59—41no—
147C2×C22⋊C4×C59—41no—
148C2×C22⋊C4×C59—41no—
149C2×C22⋊C4×C59D414yescomplemented
150C2×C42×C59—22no—
151C2×C42×C59—41no—
152C2×C42×C59—41no—
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—22no—
160#95×C59—41no—
161#95×C59—41no—
162#95×C59—41no—
163#95×C59—41no—
164#95×C59D414yescomplemented
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×C59—21no—
187C24×C59—21no—
188C24×C59—21no—
189C24×C59—21no—
190C24×C59—21no—
191C24×C59—21no—
192C24×C59—21no—
193C24×C59—21no—
194C24×C59—21no—
195C24×C59—21no—
196C24×C59—21no—
197C24×C59—21no—
198C24×C59—21no—
199C24×C59—21no—
200C24×C59—21no—
201C24×C59—21no—
202C24×C59—21no—
203C24×C59—21no—
204C24×C59—21no—
205C24×C59—21no—
206C24×C59—21no—
207C24×C59C2×D412yes—
208C24×C59C2×D412yes—
209C24×C59C2×D412yes—
210C24×C59C2411yescharacteristic
211C2×D4×C59—28no—
212C2×D4×C59—44no—
213C2×D4×C59—44no—
214C2×D4×C59—44no—
215C2×D4×C59—44no—
216C2×D4×C59—44no—
217C2×D4×C59—44no—
218C2×D4×C59—44no—
219C2×D4×C59—44no—
220C2×D4×C59—44no—
221C2×D4×C59—44no—
222C2×D4×C59—44no—
223C2×D4×C59—44no—
224C2×D4×C59—44no—
225C2×D4×C59—44no—
226C2×D4×C59—44no—
227C2×D4×C59—44no—
228C2×D4×C59—44no—
229C2×D4×C59—44no—
230C2×D4×C59—44no—
231C2×D4×C59—44no—
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×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—21no—
277C22×C4×C59—21no—
278C22×C4×C59—21no—
279C22×C4×C59—21no—
280C22×C4×C59—21no—
281C22×C4×C59—21no—
282C22×C4×C59—21no—
283C22×C4×C59—21no—
284C22×C4×C59—21no—
285C22×C4×C59—21no—
286C22×C4×C59—21no—
287C22×C4×C59—21no—
288C22×C4×C59—21no—
289C22×C4×C59—21no—
290C22×C4×C59—21no—
291C22×C4×C59—21no—
292C22×C4×C59—21no—
293C22×C4×C59—21no—
294C22×C4×C59—21no—
295C22×C4×C59—21no—
296C22×C4×C59—21no—
297C22×C4×C59—21no—
298C22×C4×C59—21no—
299C22×C4×C59—21no—
300C22×C4×C59—21no—
301C22×C4×C59—21no—
302C22×C4×C59—21no—
303C22×C4×C59—21no—
304C22×C4×C59—21no—
305C22×C4×C59—21no—
306C22×C4×C59C2×D412yes—
307C22×C4×C59C2×D412yes—
308C22×C4×C59C2×D412yes—
309C22×C4×C59C2×D412yes—
310C22×C4×C59C2×D412yes—
311C22×C4×C59C2×D412yes—
312C22×C4×C59#4112yes—
313C22×C4×C59#4112yes—
314C22×C4×C59#4112yes—
315C22×C4×C59#4112yes—
316C4⋊C4×C59—44no—
317C4⋊C4×C59—44no—
318C4⋊C4×C59—44no—
319C4⋊C4×C59—44no—
320C22⋊C4×C59—44no—
321C22⋊C4×C59—44no—
322C22⋊C4×C59—44no—
323C22⋊C4×C59—44no—
324C22⋊C4×C59—44no—
325C22⋊C4×C59—44no—
326C22⋊C4×C59—44no—
327C22⋊C4×C59—44no—
328C22⋊C4×C59—44no—
329C22⋊C4×C59—44no—
330C22⋊C4×C59—44no—
331C22⋊C4×C59—44no—
332C22⋊C4×C59—44no—
333C22⋊C4×C59—44no—
334C22⋊C4×C59—44no—
335C42×C59—44no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—22no—
345C23×C59—22no—
346C23×C59—22no—
347C23×C59—22no—
348C23×C59—22no—
349C23×C59—22no—
350C23×C59—22no—
351C23×C59—22no—
352C23×C59—22no—
353C23×C59—22no—
354C23×C59—22no—
355C23×C59—22no—
356C23×C59—22no—
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—41no—
385C23×C59—41no—
386C23×C59—41no—
387C23×C59—41no—
388C23×C59—41no—
389C23×C59—41no—
390C23×C59—41no—
391C23×C59—41no—
392C23×C59—41no—
393C23×C59—41no—
394C23×C59—41no—
395C23×C59—41no—
396C23×C59—41no—
397C23×C59—41no—
398C23×C59—41no—
399C23×C59—41no—
400C23×C59—41no—
401C23×C59—41no—
402C23×C59—41no—
403C23×C59—41no—
404C23×C59—41no—
405C23×C59—41no—
406C23×C59—41no—
407C23×C59—41no—
408C23×C59—41no—
409C23×C59—41no—
410C23×C59—41no—
411C23×C59—41no—
412C23×C59—41no—
413C23×C59—41no—
414C23×C59—41no—
415C23×C59—41no—
416C23×C59—41no—
417C23×C59—41no—
418C23×C59—41no—
419C23×C59—41no—
420C23×C59—41no—
421C23×C59—41no—
422C23×C59—41no—
423C23×C59—41no—
424C23×C59—41no—
425C23×C59—41no—
426C23×C59—41no—
427C23×C59—41no—
428C23×C59—41no—
429C23×C59—41no—
430C23×C59—41no—
431C23×C59—41no—
432C23×C59—41no—
433C23×C59—41no—
434C23×C59—41no—
435C23×C59—41no—
436C23×C59—41no—
437C23×C59—41no—
438C23×C59—41no—
439C23×C59—41no—
440C23×C59—41no—
441C23×C59C22×D411yescharacteristic
442C23×C59C22×D411yescharacteristic
443C23×C59C22×D411yescharacteristic
444C23×C59C2×#4111yescharacteristic
445C23×C59C2×#4111yescharacteristic
446C23×C59C2×#4111yescharacteristic
447C23×C59C2×#4111yescharacteristic
448C23×C59H(5,𝔽2)11yescharacteristic
449C23×C59H(5,𝔽2)11yescharacteristic
450C23×C59H(5,𝔽2)11yescharacteristic
451C23×C59H(5,𝔽2)11yescharacteristic
452C23×C59H(5,𝔽2)11yescharacteristic
453C23×C59H(5,𝔽2)11yescharacteristic
454C23×C59H(5,𝔽2)11yescharacteristic
455C23×C592−1+411yescharacteristic
456D4×C59—416no—
457D4×C59—416no—
458D4×C59—416no—
459C2×C4×C59—22no—
460C2×C4×C59—22no—
461C2×C4×C59—22no—
462C2×C4×C59—22no—
463C2×C4×C59—22no—
464C2×C4×C59—22no—
465C2×C4×C59—22no—
466C2×C4×C59—22no—
467C2×C4×C59—22no—
468C2×C4×C59—22no—
469C2×C4×C59—22no—
470C2×C4×C59—22no—
471C2×C4×C59—22no—
472C2×C4×C59—22no—
473C2×C4×C59—22no—
474C2×C4×C59—22no—
475C2×C4×C59—22no—
476C2×C4×C59—22no—
477C2×C4×C59—22no—
478C2×C4×C59—22no—
479C2×C4×C59—22no—
480C2×C4×C59—22no—
481C2×C4×C59—22no—
482C2×C4×C59—22no—
483C2×C4×C59—22no—
484C2×C4×C59—22no—
485C2×C4×C59—22no—
486C2×C4×C59—41no—
487C2×C4×C59—41no—
488C2×C4×C59—41no—
489C2×C4×C59—41no—
490C2×C4×C59—41no—
491C2×C4×C59—41no—
492C2×C4×C59—41no—
493C2×C4×C59—41no—
494C2×C4×C59—41no—
495C2×C4×C59—41no—
496C2×C4×C59—41no—
497C2×C4×C59—41no—
498C2×C4×C59—41no—
499C2×C4×C59—41no—
500C2×C4×C59—41no—
501C2×C4×C59—41no—
502C2×C4×C59—41no—
503C2×C4×C59—41no—
504C2×C4×C59—41no—
505C2×C4×C59—41no—
506C2×C4×C59—41no—
507C2×C4×C59—41no—
508C2×C4×C59—41no—
509C2×C4×C59—41no—
510C2×C4×C59—41no—
511C2×C4×C59—41no—
512C2×C4×C59—41no—
513C2×C4×C59—41no—
514C2×C4×C59—41no—
515C2×C4×C59—41no—
516C2×C4×C59—41no—
517C2×C4×C59—41no—
518C2×C4×C59—41no—
519C2×C4×C59—41no—
520C2×C4×C59—41no—
521C2×C4×C59—41no—
522C2×C4×C59—41no—
523C2×C4×C59—41no—
524C2×C4×C59—41no—
525C2×C4×C59—41no—
526C2×C4×C59—41no—
527C2×C4×C59—41no—
528C2×C4×C59—41no—
529C2×C4×C59—41no—
530C2×C4×C59—41no—
531C2×C4×C59—41no—
532C2×C4×C59—41no—
533C2×C4×C59—41no—
534C2×C4×C59—41no—
535C2×C4×C59—41no—
536C2×C4×C59—41no—
537C2×C4×C59—41no—
538C2×C4×C59—41no—
539C2×C4×C59—41no—
540C2×C4×C59—41no—
541C2×C4×C59—41no—
542C2×C4×C59#12314yes—
543#16526C5911yesmaximal, characteristic, direct product factor, Sylow
544C22×C59—42no—
545C22×C59—42no—
546C22×C59—42no—
547C22×C59—42no—
548C22×C59—42no—
549C22×C59—42no—
550C22×C59—42no—
551C22×C59—42no—
552C22×C59—42no—
553C22×C59—42no—
554C22×C59—42no—
555C22×C59—42no—
556C22×C59—42no—
557C22×C59—42no—
558C22×C59—42no—
559C22×C59—42no—
560C22×C59—42no—
561C22×C59—42no—
562C22×C59—42no—
563C22×C59—42no—
564C22×C59—42no—
565C22×C59—81no—
566C22×C59—81no—
567C22×C59—81no—
568C22×C59—81no—
569C22×C59—81no—
570C22×C59—81no—
571C22×C59—81no—
572C22×C59—81no—
573C22×C59—81no—
574C22×C59—81no—
575C22×C59—81no—
576C22×C59—81no—
577C22×C59—81no—
578C22×C59—81no—
579C22×C59—81no—
580C22×C59—81no—
581C22×C59—81no—
582C22×C59—81no—
583C22×C59—81no—
584C22×C59—81no—
585C22×C59—81no—
586C22×C59—81no—
587C22×C59—81no—
588C22×C59—81no—
589C22×C59C2×#12311yescharacteristic
590C22×C59#53211yescharacteristic
591C22×C59#53211yescharacteristic
592C22×C59#53411yescharacteristic
593C22×C59#53411yescharacteristic
594C22×C59#53411yescharacteristic
595C22×C59#53511yescharacteristic
596C22×C59#53511yescharacteristic
597C22×C59#53711yescharacteristic
598C22×C59#53811yescharacteristic
599C22×C59#53811yescharacteristic
600C22×C59#53811yescharacteristic
601C22×C59#53811yescharacteristic
602C22×C59#53811yescharacteristic
603C22×C59#53811yescharacteristic
604C22×C59#54011yescharacteristic
605C22×C59#54011yescharacteristic
606C22×C59#54211yescharacteristic
607C22×C59#54211yescharacteristic
608C22×C59D4211yescharacteristic
609C22×C59D4211yescharacteristic
610C22×C59D4211yescharacteristic
611C22×C59#54611yescharacteristic
612C22×C59#54611yescharacteristic
613C22×C59#54611yescharacteristic
614C22×C59#54711yescharacteristic
615C22×C59#54711yescharacteristic
616C22×C59#55011yescharacteristic
617C22×C59#55311yescharacteristic
618C22×C59#55511yescharacteristic
619C22×C59#55911yescharacteristic
620C22×C59#56011yescharacteristic
621C22×C59#56011yescharacteristic
622C22×C59#56211yescharacteristic
623C22×C59#56211yescharacteristic
624C4×C59—24no—
625C4×C59—42no—
626C4×C59—42no—
627C4×C59—42no—
628C4×C59—42no—
629C4×C59—42no—
630C4×C59—42no—
631C4×C59—42no—
632C4×C59—81no—
633C4×C59—81no—
634C4×C59—81no—
635C4×C59—81no—
636C2×#397C2×C5911yescharacteristic, complemented
637C2×#394C2×C5911yescharacteristic, complemented
638C2×#394C2×C5911yescharacteristic, complemented
639C2×#394C2×C5911yescharacteristic, complemented
640C2×#392C2×C5911yescharacteristic
641C2×#390C2×C5911yescharacteristic, complemented
642#1444C2×C5911yescharacteristic, complemented
643#1440C2×C5911yescharacteristic, complemented
644#1439C2×C5911yescharacteristic, complemented
645#1439C2×C5911yescharacteristic, complemented
646#1439C2×C5911yescharacteristic, complemented
647#1438C2×C5911yescharacteristic, complemented
648#1438C2×C5911yescharacteristic, complemented
649#1437C2×C5911yescharacteristic, complemented
650#1436C2×C5911yescharacteristic, complemented
651C2×C59—82no—
652C2×C59—82no—
653C2×C59—82no—
654C2×C59#242211yescharacteristic
655C2×C59#244511yescharacteristic
656C2×C59#255511yescharacteristic
657C2×C59#262211yescharacteristic
658C2×C59#266111yescharacteristic
659C2×C59#266211yescharacteristic
660C2×C59#266811yescharacteristic
661C2×C59#266911yescharacteristic
662C2×C59#267111yescharacteristic
663C2×C59#268211yescharacteristic
664C2×C59#268611yescharacteristic
665C2×C59#271011yescharacteristic
666C2×C59#271411yescharacteristic
667C2×C59#280311yescharacteristic
668C2×C59#282911yescharacteristic
669C23×D4C22×C5911yescharacteristic
670C23×D4C22×C5911yescharacteristic
671C23×D4C22×C5911yescharacteristic
672C22×C4⋊C4C22×C5911yescharacteristic
673C22×C4⋊C4C22×C5911yescharacteristic
674C22×C4⋊C4C22×C5911yescharacteristic
675C22×C4⋊C4C22×C5911yescharacteristic
676C22×C22⋊C4C22×C5911yescharacteristic
677C22×C22⋊C4C22×C5911yescharacteristic
678C22×C22⋊C4C22×C5911yescharacteristic
679C22×C22⋊C4C22×C5911yescharacteristic
680C22×C22⋊C4C22×C5911yescharacteristic
681C22×C22⋊C4C22×C5911yescharacteristic
682C22×C22⋊C4C22×C5911yescharacteristic
683C22×C22⋊C4C22×C5911yescharacteristic
684C22×C22⋊C4C22×C5911yescharacteristic
685C22×C22⋊C4C22×C5911yescharacteristic
686C22×C22⋊C4C22×C5911yescharacteristic
687C22×C22⋊C4C22×C5911yescharacteristic
688C22×C22⋊C4C22×C5911yescharacteristic
689C22×C22⋊C4C22×C5911yescharacteristic
690C22×C22⋊C4C22×C5911yescharacteristic
691C22×C42C22×C5911yescharacteristic
692#397—24no—
693#394—24no—
694#394—24no—
695#394—24no—
696#392—24no—
697#390—24no—
698C2×#95C22×C5911yescharacteristic
699C2×#95C22×C5911yescharacteristic
700C2×#95C22×C5911yescharacteristic
701C2×#95C22×C5911yescharacteristic
702C2×#95C22×C5911yescharacteristic
703C2×#95C22×C5911yescharacteristic
704C2×#95C22×C5911yescharacteristic
705C2×#95C22×C5911yescharacteristic
706C2×#95C22×C5911yescharacteristic
707C2×#95C22×C5911yescharacteristic
708C2×#95C22×C5911yescharacteristic
709C2×#95C22×C5911yescharacteristic
710C59#1652611yescharacteristic, direct product factor, Sylow
711C25C23×C5911yescharacteristic
712C25C23×C5911yescharacteristic
713C25C23×C5911yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4D4×C5914yes—
735C23×C4C23×C5911yescharacteristic
736C23×C4C23×C5911yescharacteristic
737C23×C4C23×C5911yescharacteristic
738C23×C4C23×C5911yescharacteristic
739C23×C4C23×C5911yescharacteristic
740C23×C4C23×C5911yescharacteristic
741C23×C4C23×C5911yescharacteristic
742C23×C4C23×C5911yescharacteristic
743C23×C4C23×C5911yescharacteristic
744C23×C4C23×C5911yescharacteristic
745C23×C4C23×C5911yescharacteristic
746C23×C4C23×C5911yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4D4×C5914yescomplemented
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C5914yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C5912yes—
862C24C2×D4×C5912yes—
863C24C2×D4×C5912yes—
864C24C24×C5911yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4C2×D4×C5912yes—
961C22×C4C2×D4×C5912yes—
962C22×C4C2×D4×C5912yes—
963C22×C4C2×D4×C5912yes—
964C22×C4C2×D4×C5912yes—
965C22×C4C2×D4×C5912yes—
966C22×C4#41×C5912yes—
967C22×C4#41×C5912yes—
968C22×C4#41×C5912yes—
969C22×C4#41×C5912yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C5911yescharacteristic
1096C23C22×D4×C5911yescharacteristic
1097C23C22×D4×C5911yescharacteristic
1098C23C2×#41×C5911yescharacteristic
1099C23C2×#41×C5911yescharacteristic
1100C23C2×#41×C5911yescharacteristic
1101C23C2×#41×C5911yescharacteristic
1102C23H(5,𝔽2)×C5911yescharacteristic
1103C23H(5,𝔽2)×C5911yescharacteristic
1104C23H(5,𝔽2)×C5911yescharacteristic
1105C23H(5,𝔽2)×C5911yescharacteristic
1106C23H(5,𝔽2)×C5911yescharacteristic
1107C23H(5,𝔽2)×C5911yescharacteristic
1108C23H(5,𝔽2)×C5911yescharacteristic
1109C232−1+4×C5911yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4#123×C5914yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C5911yescharacteristic
1243C22C59×#53211yescharacteristic
1244C22C59×#53211yescharacteristic
1245C22C59×#53411yescharacteristic
1246C22C59×#53411yescharacteristic
1247C22C59×#53411yescharacteristic
1248C22C59×#53511yescharacteristic
1249C22C59×#53511yescharacteristic
1250C22C59×#53711yescharacteristic
1251C22C59×#53811yescharacteristic
1252C22C59×#53811yescharacteristic
1253C22C59×#53811yescharacteristic
1254C22C59×#53811yescharacteristic
1255C22C59×#53811yescharacteristic
1256C22C59×#53811yescharacteristic
1257C22C59×#54011yescharacteristic
1258C22C59×#54011yescharacteristic
1259C22C59×#54211yescharacteristic
1260C22C59×#54211yescharacteristic
1261C22D42×C5911yescharacteristic
1262C22D42×C5911yescharacteristic
1263C22D42×C5911yescharacteristic
1264C22C59×#54611yescharacteristic
1265C22C59×#54611yescharacteristic
1266C22C59×#54611yescharacteristic
1267C22C59×#54711yescharacteristic
1268C22C59×#54711yescharacteristic
1269C22C59×#55011yescharacteristic
1270C22C59×#55311yescharacteristic
1271C22C59×#55511yescharacteristic
1272C22C59×#55911yescharacteristic
1273C22C59×#56011yescharacteristic
1274C22C59×#56011yescharacteristic
1275C22C59×#56211yescharacteristic
1276C22C59×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C59×#242211yescharacteristic
1293C2C59×#244511yescharacteristic
1294C2C59×#255511yescharacteristic
1295C2C59×#262211yescharacteristic
1296C2C59×#266111yescharacteristic
1297C2C59×#266211yescharacteristic
1298C2C59×#266811yescharacteristic
1299C2C59×#266911yescharacteristic
1300C2C59×#267111yescharacteristic
1301C2C59×#268211yescharacteristic
1302C2C59×#268611yescharacteristic
1303C2C59×#271011yescharacteristic
1304C2C59×#271411yescharacteristic
1305C2C59×#280311yescharacteristic
1306C2C59×#282911yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC2×C59×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#397C2semidirect
2. C2×C59×#394C2semidirect
3. C2×C59×#394C2semidirect
4. C2×C59×#394C2semidirect
6. C2×C59×#390C2semidirect
7. C59×#1444C2semidirect
8. C59×#1440C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
11. C59×#1439C2semidirect
12. C59×#1438C2semidirect
13. C59×#1438C2semidirect
14. C59×#1437C2semidirect
15. C59×#1436C2semidirect
149. C2×C22⋊C4×C59D4semidirect
164. #95×C59D4semidirect
543. #16526C59direct (N × H)
636. C2×#397C2×C59semidirect
637. C2×#394C2×C59semidirect
638. C2×#394C2×C59semidirect
639. C2×#394C2×C59semidirect
641. C2×#390C2×C59semidirect
642. #1444C2×C59semidirect
643. #1440C2×C59semidirect
644. #1439C2×C59semidirect
645. #1439C2×C59semidirect
646. #1439C2×C59semidirect
647. #1438C2×C59semidirect
648. #1438C2×C59semidirect
649. #1437C2×C59semidirect
650. #1436C2×C59semidirect
710. C59#16526direct (N × H)
803. C2×C22⋊C4D4×C59semidirect
818. #95D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3972
C2×C59×#3942
C2×C59×#3922
C2×C59×#3902
C59×#14442
C59×#14402
C59×#14392
C59×#14382
C59×#14372
C59×#14362
#1652659