Finite Group Databasebeta

← C59×#16512 #28428621

Subgroups — C59×#16512 #28428621

Order 15104.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#394C211yesmaximal, characteristic, complemented
2C2×C59×#394C211yesmaximal, characteristic, complemented
3C2×C59×#392C211yesmaximal, characteristic
4C2×C59×#386C211yesmaximal, characteristic, complemented
5C2×C59×#386C211yesmaximal, characteristic, complemented
6C2×C59×#380C211yesmaximal, characteristic, complemented
7C59×#1443C211yesmaximal, characteristic, complemented
8C59×#1441C211yesmaximal, characteristic, complemented
9C59×#1440C211yesmaximal, characteristic, complemented
10C59×#1440C211yesmaximal, characteristic, complemented
11C59×#1439C211yesmaximal, characteristic, complemented
12C59×#1439C211yesmaximal, characteristic, complemented
13C59×#1439C211yesmaximal, characteristic, complemented
14C59×#1438C211yesmaximal, characteristic, complemented
15C59×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C24×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
37C59×#394—24no—
38C59×#394—24no—
39C59×#392—24no—
40C59×#386—24no—
41C59×#386—24no—
42C59×#380—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
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—22no—
69C22×D4×C59—22no—
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×C59—22no—
82C23×C4×C59—22no—
83C23×C4×C59—41no—
84C23×C4×C59—41no—
85C23×C4×C59—41no—
86C23×C4×C59—41no—
87C23×C4×C59D414yescomplemented
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2311yescharacteristic
93C23×C4×C59C2311yescharacteristic
94C23×C4×C59C2311yescharacteristic
95C23×C4×C59C2311yescharacteristic
96C23×C4×C59C2311yescharacteristic
97C23×C4×C59C2311yescharacteristic
98C23×C4×C59C2311yescharacteristic
99C23×C4×C59C2311yescharacteristic
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—22no—
102C2×C4⋊C4×C59—41no—
103C2×C4⋊C4×C59—41no—
104C2×C4⋊C4×C59—41no—
105C2×C4⋊C4×C59—41no—
106C2×C4⋊C4×C59—41no—
107C2×C4⋊C4×C59—41no—
108C2×C4⋊C4×C59D414yescomplemented
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—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×C59—41no—
150C2×C22⋊C4×C59—41no—
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—22no—
160#95×C59—22no—
161#95×C59—41no—
162#95×C59—41no—
163#95×C59—41no—
164#95×C59—41no—
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×C59C2×D412yes—
206C24×C59C2×D412yes—
207C24×C59C2×D412yes—
208C24×C59#4112yes—
209C24×C59#4112yes—
210C24×C59C2411yescharacteristic
211C2×D4×C59—28no—
212C2×D4×C59—28no—
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—28no—
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×C59—21no—
307C22×C4×C59—21no—
308C22×C4×C59—21no—
309C22×C4×C59—44no—
310C22×C4×C59—44no—
311C22×C4×C59—44no—
312C22×C4×C59—44no—
313C22×C4×C59—44no—
314C22×C4×C59—44no—
315C22×C4×C59C2×D412yes—
316C22×C4×C59C2×D412yes—
317C22×C4×C59C2×D412yes—
318C22×C4×C59C2×D412yes—
319C22×C4×C59C2×D412yes—
320C22×C4×C59C2×D412yes—
321C22×C4×C59#4112yes—
322C22×C4×C59#4112yes—
323C4⋊C4×C59—44no—
324C4⋊C4×C59—44no—
325C4⋊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—
335C22⋊C4×C59—44no—
336C22⋊C4×C59—44no—
337C22⋊C4×C59—44no—
338C22⋊C4×C59—44no—
339C22⋊C4×C59—44no—
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—22no—
358C23×C59—22no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—22no—
369C23×C59—22no—
370C23×C59—22no—
371C23×C59—22no—
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×C59—41no—
442C23×C59—41no—
443C23×C59—41no—
444C23×C59#12114yes—
445C23×C59C22×D411yescharacteristic
446C23×C59C22×D411yescharacteristic
447C23×C59C22×D411yescharacteristic
448C23×C59C2×#4111yescharacteristic
449C23×C59C2×#4111yescharacteristic
450C23×C59C2×#4111yescharacteristic
451C23×C59C2×#4111yescharacteristic
452C23×C59H(5,𝔽2)11yescharacteristic
453C23×C59H(5,𝔽2)11yescharacteristic
454C23×C59H(5,𝔽2)11yescharacteristic
455C23×C59H(5,𝔽2)11yescharacteristic
456C23×C59H(5,𝔽2)11yescharacteristic
457C23×C59H(5,𝔽2)11yescharacteristic
458C23×C59H(5,𝔽2)11yescharacteristic
459C23×C592−1+411yescharacteristic
460D4×C59—416no—
461D4×C59—416no—
462D4×C59—416no—
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—416no—
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—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—41no—
543C2×C4×C59—41no—
544C2×C4×C59—41no—
545C2×C4×C59—41no—
546C2×C4×C59—41no—
547C2×C4×C59#12114yes—
548#16512C5911yesmaximal, characteristic, direct product factor, Sylow
549C22×C59—24no—
550C22×C59—24no—
551C22×C59—24no—
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—42no—
566C22×C59—42no—
567C22×C59—42no—
568C22×C59—42no—
569C22×C59—42no—
570C22×C59—42no—
571C22×C59—42no—
572C22×C59—42no—
573C22×C59—42no—
574C22×C59—42no—
575C22×C59—42no—
576C22×C59—42no—
577C22×C59—42no—
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×C59—81no—
590C22×C59—81no—
591C22×C59—81no—
592C22×C59—81no—
593C22×C59—81no—
594C22×C59C2×#12111yescharacteristic
595C22×C59C2×#12111yescharacteristic
596C22×C59#52511yescharacteristic
597C22×C59#53411yescharacteristic
598C22×C59#53411yescharacteristic
599C22×C59#53411yescharacteristic
600C22×C59#53411yescharacteristic
601C22×C59#53411yescharacteristic
602C22×C59#53511yescharacteristic
603C22×C59#53511yescharacteristic
604C22×C59#53711yescharacteristic
605C22×C59#53811yescharacteristic
606C22×C59#53811yescharacteristic
607C22×C59#53811yescharacteristic
608C22×C59#53811yescharacteristic
609C22×C59#53811yescharacteristic
610C22×C59#53911yescharacteristic
611C22×C59#54011yescharacteristic
612C22×C59#54211yescharacteristic
613C22×C59D4211yescharacteristic
614C22×C59#54611yescharacteristic
615C22×C59#54611yescharacteristic
616C22×C59#54611yescharacteristic
617C22×C59#54711yescharacteristic
618C22×C59#54811yescharacteristic
619C22×C59#55011yescharacteristic
620C22×C59#55111yescharacteristic
621C22×C59#55111yescharacteristic
622C22×C59#55311yescharacteristic
623C22×C59#55311yescharacteristic
624C22×C59#55511yescharacteristic
625C22×C59#56011yescharacteristic
626C22×C59#56011yescharacteristic
627C22×C59#56211yescharacteristic
628C22×C59#56211yescharacteristic
629C4×C59—24no—
630C4×C59—42no—
631C4×C59—42no—
632C4×C59—42no—
633C4×C59—42no—
634C4×C59—42no—
635C4×C59—81no—
636C4×C59—81no—
637C4×C59—81no—
638C4×C59—81no—
639C4×C59—81no—
640C4×C59—81no—
641C2×#394C2×C5911yescharacteristic, complemented
642C2×#394C2×C5911yescharacteristic, complemented
643C2×#392C2×C5911yescharacteristic
644C2×#386C2×C5911yescharacteristic, complemented
645C2×#386C2×C5911yescharacteristic, complemented
646C2×#380C2×C5911yescharacteristic, complemented
647#1443C2×C5911yescharacteristic, complemented
648#1441C2×C5911yescharacteristic, complemented
649#1440C2×C5911yescharacteristic, complemented
650#1440C2×C5911yescharacteristic, complemented
651#1439C2×C5911yescharacteristic, complemented
652#1439C2×C5911yescharacteristic, complemented
653#1439C2×C5911yescharacteristic, complemented
654#1438C2×C5911yescharacteristic, complemented
655#1438C2×C5911yescharacteristic, complemented
656C2×C59—44no—
657C2×C59—82no—
658C2×C59—82no—
659C2×C59#241411yescharacteristic
660C2×C59#241611yescharacteristic
661C2×C59#253411yescharacteristic
662C2×C59#261711yescharacteristic
663C2×C59#261711yescharacteristic
664C2×C59#263011yescharacteristic
665C2×C59#266811yescharacteristic
666C2×C59#267311yescharacteristic
667C2×C59#268611yescharacteristic
668C2×C59#269611yescharacteristic
669C2×C59#270811yescharacteristic
670C2×C59#273011yescharacteristic
671C2×C59#275611yescharacteristic
672C2×C59#277811yescharacteristic
673C2×C59#281311yescharacteristic
674C23×D4C22×C5911yescharacteristic
675C23×D4C22×C5911yescharacteristic
676C23×D4C22×C5911yescharacteristic
677C24×C4C22×C5911yescharacteristic
678C22×C4⋊C4C22×C5911yescharacteristic
679C22×C4⋊C4C22×C5911yescharacteristic
680C22×C4⋊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×C22⋊C4C22×C5911yescharacteristic
692C22×C22⋊C4C22×C5911yescharacteristic
693C22×C22⋊C4C22×C5911yescharacteristic
694C22×C22⋊C4C22×C5911yescharacteristic
695#394—24no—
696#394—24no—
697#392—24no—
698#386—24no—
699#386—24no—
700#380—24no—
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
710C2×#95C22×C5911yescharacteristic
711C2×#95C22×C5911yescharacteristic
712C2×#95C22×C5911yescharacteristic
713C2×#95C22×C5911yescharacteristic
714C2×#95C22×C5911yescharacteristic
715C59#1651211yescharacteristic, direct product factor, Sylow
716C25C23×C5911yescharacteristic
717C25C23×C5911yescharacteristic
718C25C23×C5911yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C5914yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4D4×C5914yescomplemented
747C23×C4C23×C5911yescharacteristic
748C23×C4C23×C5911yescharacteristic
749C23×C4C23×C5911yescharacteristic
750C23×C4C23×C5911yescharacteristic
751C23×C4C23×C5911yescharacteristic
752C23×C4C23×C5911yescharacteristic
753C23×C4C23×C5911yescharacteristic
754C23×C4C23×C5911yescharacteristic
755C23×C4C23×C5911yescharacteristic
756C23×C4C23×C5911yescharacteristic
757C23×C4C23×C5911yescharacteristic
758C23×C4C23×C5911yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4—41no—
767C2×C4⋊C4D4×C5914yescomplemented
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—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
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⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—22no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95—41no—
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—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×D4×C5912yes—
865C24C2×D4×C5912yes—
866C24C2×D4×C5912yes—
867C24#41×C5912yes—
868C24#41×C5912yes—
869C24C24×C5911yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
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—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
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—28no—
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×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C5912yes—
975C22×C4C2×D4×C5912yes—
976C22×C4C2×D4×C5912yes—
977C22×C4C2×D4×C5912yes—
978C22×C4C2×D4×C5912yes—
979C22×C4C2×D4×C5912yes—
980C22×C4#41×C5912yes—
981C22×C4#41×C5912yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
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—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
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—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23#121×C5914yes—
1104C23C22×D4×C5911yescharacteristic
1105C23C22×D4×C5911yescharacteristic
1106C23C22×D4×C5911yescharacteristic
1107C23C2×#41×C5911yescharacteristic
1108C23C2×#41×C5911yescharacteristic
1109C23C2×#41×C5911yescharacteristic
1110C23C2×#41×C5911yescharacteristic
1111C23H(5,𝔽2)×C5911yescharacteristic
1112C23H(5,𝔽2)×C5911yescharacteristic
1113C23H(5,𝔽2)×C5911yescharacteristic
1114C23H(5,𝔽2)×C5911yescharacteristic
1115C23H(5,𝔽2)×C5911yescharacteristic
1116C23H(5,𝔽2)×C5911yescharacteristic
1117C23H(5,𝔽2)×C5911yescharacteristic
1118C232−1+4×C5911yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
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—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—416no—
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—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4#121×C5914yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×#121×C5911yescharacteristic
1253C22C2×#121×C5911yescharacteristic
1254C22C59×#52511yescharacteristic
1255C22C59×#53411yescharacteristic
1256C22C59×#53411yescharacteristic
1257C22C59×#53411yescharacteristic
1258C22C59×#53411yescharacteristic
1259C22C59×#53411yescharacteristic
1260C22C59×#53511yescharacteristic
1261C22C59×#53511yescharacteristic
1262C22C59×#53711yescharacteristic
1263C22C59×#53811yescharacteristic
1264C22C59×#53811yescharacteristic
1265C22C59×#53811yescharacteristic
1266C22C59×#53811yescharacteristic
1267C22C59×#53811yescharacteristic
1268C22C59×#53911yescharacteristic
1269C22C59×#54011yescharacteristic
1270C22C59×#54211yescharacteristic
1271C22D42×C5911yescharacteristic
1272C22C59×#54611yescharacteristic
1273C22C59×#54611yescharacteristic
1274C22C59×#54611yescharacteristic
1275C22C59×#54711yescharacteristic
1276C22C59×#54811yescharacteristic
1277C22C59×#55011yescharacteristic
1278C22C59×#55111yescharacteristic
1279C22C59×#55111yescharacteristic
1280C22C59×#55311yescharacteristic
1281C22C59×#55311yescharacteristic
1282C22C59×#55511yescharacteristic
1283C22C59×#56011yescharacteristic
1284C22C59×#56011yescharacteristic
1285C22C59×#56211yescharacteristic
1286C22C59×#56211yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C59×#241411yescharacteristic
1303C2C59×#241611yescharacteristic
1304C2C59×#253411yescharacteristic
1305C2C59×#261711yescharacteristic
1306C2C59×#261711yescharacteristic
1307C2C59×#263011yescharacteristic
1308C2C59×#266811yescharacteristic
1309C2C59×#267311yescharacteristic
1310C2C59×#268611yescharacteristic
1311C2C59×#269611yescharacteristic
1312C2C59×#270811yescharacteristic
1313C2C59×#273011yescharacteristic
1314C2C59×#275611yescharacteristic
1315C2C59×#277811yescharacteristic
1316C2C59×#281311yescharacteristic
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×#394C2semidirect
2. C2×C59×#394C2semidirect
4. C2×C59×#386C2semidirect
5. C2×C59×#386C2semidirect
6. C2×C59×#380C2semidirect
7. C59×#1443C2semidirect
8. C59×#1441C2semidirect
9. C59×#1440C2semidirect
10. C59×#1440C2semidirect
11. C59×#1439C2semidirect
12. C59×#1439C2semidirect
13. C59×#1439C2semidirect
14. C59×#1438C2semidirect
15. C59×#1438C2semidirect
87. C23×C4×C59D4semidirect
108. C2×C4⋊C4×C59D4semidirect
548. #16512C59direct (N × H)
641. C2×#394C2×C59semidirect
642. C2×#394C2×C59semidirect
644. C2×#386C2×C59semidirect
645. C2×#386C2×C59semidirect
646. C2×#380C2×C59semidirect
647. #1443C2×C59semidirect
648. #1441C2×C59semidirect
649. #1440C2×C59semidirect
650. #1440C2×C59semidirect
651. #1439C2×C59semidirect
652. #1439C2×C59semidirect
653. #1439C2×C59semidirect
654. #1438C2×C59semidirect
655. #1438C2×C59semidirect
715. C59#16512direct (N × H)
746. C23×C4D4×C59semidirect
767. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#3942
C2×C59×#3922
C2×C59×#3862
C2×C59×#3802
C59×#14432
C59×#14412
C59×#14402
C59×#14392
C59×#14382
#1651259