Finite Group Databasebeta

← C59×#16270 #28428379

Subgroups — C59×#16270 #28428379

Order 15104.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#397C211yesmaximal, characteristic, complemented
2C2×C59×#392C211yesmaximal, characteristic
3C2×C59×#386C211yesmaximal, characteristic, complemented
4C2×C59×#386C211yesmaximal, characteristic, complemented
5C59×#1443C211yesmaximal, characteristic, complemented
6C59×#1443C211yesmaximal, characteristic, complemented
7C59×#1440C211yesmaximal, characteristic, complemented
8C59×#1440C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1438C211yesmaximal, characteristic, complemented
12C59×#1438C211yesmaximal, characteristic, complemented
13C59×#1438C211yesmaximal, characteristic, complemented
14C59×#1438C211yesmaximal, characteristic, complemented
15C59×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C24×C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊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
35C59×#397—24no—
36C59×#392—24no—
37C59×#386—24no—
38C59×#386—24no—
39C2×#95×C59C2211yescharacteristic
40C2×#95×C59C2211yescharacteristic
41C2×#95×C59C2211yescharacteristic
42C2×#95×C59C2211yescharacteristic
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
55C25×C59C2311yescharacteristic
56C25×C59C2311yescharacteristic
57C25×C59C2311yescharacteristic
58C22×D4×C59—22no—
59C22×D4×C59—22no—
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×C59D414yes—
79C23×C4×C59—22no—
80C23×C4×C59—22no—
81C23×C4×C59—22no—
82C23×C4×C59—41no—
83C23×C4×C59—41no—
84C23×C4×C59—41no—
85C23×C4×C59—41no—
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2311yescharacteristic
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
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—41no—
100C2×C4⋊C4×C59—41no—
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—41no—
120C2×C22⋊C4×C59—41no—
121C2×C22⋊C4×C59—41no—
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×C59—41no—
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—
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—41no—
151#95×C59—41no—
152#95×C59—41no—
153#95×C59—41no—
154#95×C59—41no—
155#95×C59—41no—
156#95×C59—41no—
157#95×C59—41no—
158#95×C59D414yescomplemented
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×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×C59C2×D412yes—
200C24×C59C2×D412yes—
201C24×C59#4112yes—
202C24×C59#4112yes—
203C24×C59#4112yes—
204C24×C59C2411yescharacteristic
205C2×D4×C59—28no—
206C2×D4×C59—28no—
207C2×D4×C59—44no—
208C2×D4×C59—44no—
209C2×D4×C59—44no—
210C2×D4×C59—44no—
211C2×D4×C59—44no—
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—
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×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—44no—
305C22×C4×C59—44no—
306C22×C4×C59—44no—
307C22×C4×C59—44no—
308C22×C4×C59—44no—
309C22×C4×C59—44no—
310C22×C4×C59—44no—
311C22×C4×C59C2×D412yes—
312C22×C4×C59C2×D412yes—
313C22×C4×C59C2×D412yes—
314C22×C4×C59C2×D412yes—
315C22×C4×C59#4112yes—
316C22×C4×C59#4112yes—
317C4⋊C4×C59—44no—
318C22⋊C4×C59—44no—
319C22⋊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—
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—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—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#12314yes—
437C23×C59C22×D411yescharacteristic
438C23×C59C22×D411yescharacteristic
439C23×C59C2×#4111yescharacteristic
440C23×C59C2×#4111yescharacteristic
441C23×C59C2×#4111yescharacteristic
442C23×C59C2×#4111yescharacteristic
443C23×C59C2×#4111yescharacteristic
444C23×C59H(5,𝔽2)11yescharacteristic
445C23×C59H(5,𝔽2)11yescharacteristic
446C23×C59H(5,𝔽2)11yescharacteristic
447C23×C59H(5,𝔽2)11yescharacteristic
448C23×C59H(5,𝔽2)11yescharacteristic
449C23×C59H(5,𝔽2)11yescharacteristic
450C23×C59H(5,𝔽2)11yescharacteristic
451C23×C59H(5,𝔽2)11yescharacteristic
452D4×C59—416no—
453D4×C59—416no—
454D4×C59—416no—
455C2×C4×C59—22no—
456C2×C4×C59—22no—
457C2×C4×C59—22no—
458C2×C4×C59—22no—
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—416no—
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—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—
540#16270C5911yesmaximal, characteristic, direct product factor, Sylow
541C22×C59—24no—
542C22×C59—24no—
543C22×C59—24no—
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—42no—
566C22×C59—42no—
567C22×C59—42no—
568C22×C59—42no—
569C22×C59—42no—
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×C59C2×#12311yescharacteristic
587C22×C59#52511yescharacteristic
588C22×C59#52911yescharacteristic
589C22×C59#53411yescharacteristic
590C22×C59#53411yescharacteristic
591C22×C59#53511yescharacteristic
592C22×C59#53511yescharacteristic
593C22×C59#53811yescharacteristic
594C22×C59#53811yescharacteristic
595C22×C59#53811yescharacteristic
596C22×C59#53811yescharacteristic
597C22×C59#53811yescharacteristic
598C22×C59#53811yescharacteristic
599C22×C59#53811yescharacteristic
600C22×C59#53811yescharacteristic
601C22×C59#53811yescharacteristic
602C22×C59#53811yescharacteristic
603C22×C59#54011yescharacteristic
604C22×C59#54011yescharacteristic
605C22×C59D4211yescharacteristic
606C22×C59#54611yescharacteristic
607C22×C59#54611yescharacteristic
608C22×C59#54611yescharacteristic
609C22×C59#54611yescharacteristic
610C22×C59#54611yescharacteristic
611C22×C59#55011yescharacteristic
612C22×C59#55111yescharacteristic
613C22×C59#55111yescharacteristic
614C22×C59#55311yescharacteristic
615C22×C59#55311yescharacteristic
616C22×C59#55311yescharacteristic
617C22×C59#56011yescharacteristic
618C22×C59#56011yescharacteristic
619C22×C59#56011yescharacteristic
620C22×C59#56011yescharacteristic
621C4×C59—42no—
622C4×C59—42no—
623C4×C59—42no—
624C4×C59—42no—
625C4×C59—42no—
626C4×C59—42no—
627C4×C59—81no—
628C4×C59—81no—
629C4×C59—81no—
630C4×C59—81no—
631C4×C59—81no—
632C4×C59—81no—
633C2×#397C2×C5911yescharacteristic, complemented
634C2×#392C2×C5911yescharacteristic
635C2×#386C2×C5911yescharacteristic, complemented
636C2×#386C2×C5911yescharacteristic, complemented
637#1443C2×C5911yescharacteristic, complemented
638#1443C2×C5911yescharacteristic, complemented
639#1440C2×C5911yescharacteristic, complemented
640#1440C2×C5911yescharacteristic, complemented
641#1439C2×C5911yescharacteristic, complemented
642#1439C2×C5911yescharacteristic, complemented
643#1438C2×C5911yescharacteristic, complemented
644#1438C2×C5911yescharacteristic, complemented
645#1438C2×C5911yescharacteristic, complemented
646#1438C2×C5911yescharacteristic, complemented
647C22⋊#95C2×C5911yescharacteristic, complemented
648C2×C59—44no—
649C2×C59—82no—
650C2×C59—82no—
651C2×C59#241811yescharacteristic
652C2×C59#244411yescharacteristic
653C2×C59#246711yescharacteristic
654C2×C59#262211yescharacteristic
655C2×C59#263111yescharacteristic
656C2×C59#264811yescharacteristic
657C2×C59#267311yescharacteristic
658C2×C59#267811yescharacteristic
659C2×C59#268811yescharacteristic
660C2×C59#269711yescharacteristic
661C2×C59#270311yescharacteristic
662C2×C59#271411yescharacteristic
663C2×C59#274911yescharacteristic
664C2×C59#277811yescharacteristic
665C2×C59#282511yescharacteristic
666C23×D4C22×C5911yescharacteristic
667C23×D4C22×C5911yescharacteristic
668C23×D4C22×C5911yescharacteristic
669C24×C4C22×C5911yescharacteristic
670C22×C4⋊C4C22×C5911yescharacteristic
671C22×C22⋊C4C22×C5911yescharacteristic
672C22×C22⋊C4C22×C5911yescharacteristic
673C22×C22⋊C4C22×C5911yescharacteristic
674C22×C22⋊C4C22×C5911yescharacteristic
675C22×C22⋊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
685#397—24no—
686#392—24no—
687#386—24no—
688#386—24no—
689C2×#95C22×C5911yescharacteristic
690C2×#95C22×C5911yescharacteristic
691C2×#95C22×C5911yescharacteristic
692C2×#95C22×C5911yescharacteristic
693C2×#95C22×C5911yescharacteristic
694C2×#95C22×C5911yescharacteristic
695C2×#95C22×C5911yescharacteristic
696C2×#95C22×C5911yescharacteristic
697C2×#95C22×C5911yescharacteristic
698C2×#95C22×C5911yescharacteristic
699C2×#95C22×C5911yescharacteristic
700C2×#95C22×C5911yescharacteristic
701C2×#95C22×C5911yescharacteristic
702C2×#95C22×C5911yescharacteristic
703C2×#95C22×C5911yescharacteristic
704C2×#95C22×C5911yescharacteristic
705C59#1627011yescharacteristic, direct product factor, Sylow
706C25C23×C5911yescharacteristic
707C25C23×C5911yescharacteristic
708C25C23×C5911yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4D4×C5914yes—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
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
747C23×C4C23×C5911yescharacteristic
748C23×C4C23×C5911yescharacteristic
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
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—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
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—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95D4×C5914yescomplemented
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
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—
850C24C2×D4×C5912yes—
851C24C2×D4×C5912yes—
852C24#41×C5912yes—
853C24#41×C5912yes—
854C24#41×C5912yes—
855C24C24×C5911yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
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—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
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—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C5912yes—
963C22×C4C2×D4×C5912yes—
964C22×C4C2×D4×C5912yes—
965C22×C4C2×D4×C5912yes—
966C22×C4#41×C5912yes—
967C22×C4#41×C5912yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊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—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
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—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
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#123×C5914yes—
1088C23C22×D4×C5911yescharacteristic
1089C23C22×D4×C5911yescharacteristic
1090C23C2×#41×C5911yescharacteristic
1091C23C2×#41×C5911yescharacteristic
1092C23C2×#41×C5911yescharacteristic
1093C23C2×#41×C5911yescharacteristic
1094C23C2×#41×C5911yescharacteristic
1095C23H(5,𝔽2)×C5911yescharacteristic
1096C23H(5,𝔽2)×C5911yescharacteristic
1097C23H(5,𝔽2)×C5911yescharacteristic
1098C23H(5,𝔽2)×C5911yescharacteristic
1099C23H(5,𝔽2)×C5911yescharacteristic
1100C23H(5,𝔽2)×C5911yescharacteristic
1101C23H(5,𝔽2)×C5911yescharacteristic
1102C23H(5,𝔽2)×C5911yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
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—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
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—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
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—42no—
1219C22—42no—
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—
1236C22C2×#123×C5911yescharacteristic
1237C22C59×#52511yescharacteristic
1238C22C59×#52911yescharacteristic
1239C22C59×#53411yescharacteristic
1240C22C59×#53411yescharacteristic
1241C22C59×#53511yescharacteristic
1242C22C59×#53511yescharacteristic
1243C22C59×#53811yescharacteristic
1244C22C59×#53811yescharacteristic
1245C22C59×#53811yescharacteristic
1246C22C59×#53811yescharacteristic
1247C22C59×#53811yescharacteristic
1248C22C59×#53811yescharacteristic
1249C22C59×#53811yescharacteristic
1250C22C59×#53811yescharacteristic
1251C22C59×#53811yescharacteristic
1252C22C59×#53811yescharacteristic
1253C22C59×#54011yescharacteristic
1254C22C59×#54011yescharacteristic
1255C22D42×C5911yescharacteristic
1256C22C59×#54611yescharacteristic
1257C22C59×#54611yescharacteristic
1258C22C59×#54611yescharacteristic
1259C22C59×#54611yescharacteristic
1260C22C59×#54611yescharacteristic
1261C22C59×#55011yescharacteristic
1262C22C59×#55111yescharacteristic
1263C22C59×#55111yescharacteristic
1264C22C59×#55311yescharacteristic
1265C22C59×#55311yescharacteristic
1266C22C59×#55311yescharacteristic
1267C22C59×#56011yescharacteristic
1268C22C59×#56011yescharacteristic
1269C22C59×#56011yescharacteristic
1270C22C59×#56011yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2C59×#241811yescharacteristic
1287C2C59×#244411yescharacteristic
1288C2C59×#246711yescharacteristic
1289C2C59×#262211yescharacteristic
1290C2C59×#263111yescharacteristic
1291C2C59×#264811yescharacteristic
1292C2C59×#267311yescharacteristic
1293C2C59×#267811yescharacteristic
1294C2C59×#268811yescharacteristic
1295C2C59×#269711yescharacteristic
1296C2C59×#270311yescharacteristic
1297C2C59×#271411yescharacteristic
1298C2C59×#274911yescharacteristic
1299C2C59×#277811yescharacteristic
1300C2C59×#282511yescharacteristic
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
3. C2×C59×#386C2semidirect
4. C2×C59×#386C2semidirect
5. C59×#1443C2semidirect
6. C59×#1443C2semidirect
7. C59×#1440C2semidirect
8. C59×#1440C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
11. C59×#1438C2semidirect
12. C59×#1438C2semidirect
13. C59×#1438C2semidirect
14. C59×#1438C2semidirect
15. C59×C22⋊#95C2semidirect
158. #95×C59D4semidirect
540. #16270C59direct (N × H)
633. C2×#397C2×C59semidirect
635. C2×#386C2×C59semidirect
636. C2×#386C2×C59semidirect
637. #1443C2×C59semidirect
638. #1443C2×C59semidirect
639. #1440C2×C59semidirect
640. #1440C2×C59semidirect
641. #1439C2×C59semidirect
642. #1439C2×C59semidirect
643. #1438C2×C59semidirect
644. #1438C2×C59semidirect
645. #1438C2×C59semidirect
646. #1438C2×C59semidirect
647. C22⋊#95C2×C59semidirect
705. C59#16270direct (N × H)
809. #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×#3922
C2×C59×#3862
C59×#14432
C59×#14402
C59×#14392
C59×#14382
C59×C22⋊#952
#1627059