Finite Group Databasebeta

← C59×#17094 #28429203

Subgroups — C59×#17094 #28429203

Order 15104.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1292 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×#392C211yesmaximal, characteristic
5C59×#1442C211yesmaximal, characteristic, complemented
6C59×#1442C211yesmaximal, characteristic, complemented
7C59×#1440C211yesmaximal, characteristic, complemented
8C59×#1439C211yesmaximal, characteristic, complemented
9C59×#1439C211yesmaximal, characteristic, complemented
10C59×#1439C211yesmaximal, characteristic, complemented
11C59×#1439C211yesmaximal, characteristic, complemented
12C59×#1438C211yesmaximal, characteristic, complemented
13C59×#1438C211yesmaximal, characteristic, complemented
14C59×#1438C211yesmaximal, characteristic, complemented
15C59×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C23×D4×C59C2211yescharacteristic
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊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
35C22×C22⋊C4×C59C2211yescharacteristic
36C22×C22⋊C4×C59C2211yescharacteristic
37C59×#397—24no—
38C59×#394—24no—
39C59×#394—24no—
40C59×#392—24no—
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—41no—
65C22×D4×C59—41no—
66C22×D4×C59—41no—
67C22×D4×C59—41no—
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×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
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59—22no—
92C2×C4⋊C4×C59—22no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59—41no—
95C2×C4⋊C4×C59—41no—
96C2×C4⋊C4×C59—41no—
97C2×C4⋊C4×C59—41no—
98C2×C4⋊C4×C59—41no—
99C2×C4⋊C4×C59—41no—
100C2×C22⋊C4×C59—22no—
101C2×C22⋊C4×C59—22no—
102C2×C22⋊C4×C59—22no—
103C2×C22⋊C4×C59—22no—
104C2×C22⋊C4×C59—22no—
105C2×C22⋊C4×C59—22no—
106C2×C22⋊C4×C59—22no—
107C2×C22⋊C4×C59—22no—
108C2×C22⋊C4×C59—22no—
109C2×C22⋊C4×C59—22no—
110C2×C22⋊C4×C59—22no—
111C2×C22⋊C4×C59—22no—
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—22no—
114C2×C22⋊C4×C59—22no—
115C2×C22⋊C4×C59—22no—
116C2×C22⋊C4×C59—22no—
117C2×C22⋊C4×C59—22no—
118C2×C22⋊C4×C59—22no—
119C2×C22⋊C4×C59—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—
143C2×C22⋊C4×C59—41no—
144C2×C22⋊C4×C59—41no—
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×C59—21no—
200C24×C59—21no—
201C24×C59C2×D412yes—
202C24×C59C2×D412yes—
203C24×C59#4112yes—
204C24×C59C2411yescharacteristic
205C2×D4×C59—44no—
206C2×D4×C59—44no—
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×C59C2×D412yes—
305C22×C4×C59C2×D412yes—
306C22×C4×C59C2×D412yes—
307C22×C4×C59C2×D412yes—
308C22×C4×C59#4112yes—
309C22×C4×C59#4112yes—
310C4⋊C4×C59—44no—
311C4⋊C4×C59—44no—
312C4⋊C4×C59—44no—
313C22⋊C4×C59—44no—
314C22⋊C4×C59—44no—
315C22⋊C4×C59—44no—
316C22⋊C4×C59—44no—
317C22⋊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—
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—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—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—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×C59C22×D411yescharacteristic
434C23×C59C22×D411yescharacteristic
435C23×C59C2×#4111yescharacteristic
436C23×C59C2×#4111yescharacteristic
437C23×C59C2×#4111yescharacteristic
438C23×C59H(5,𝔽2)11yescharacteristic
439C23×C59H(5,𝔽2)11yescharacteristic
440C23×C59H(5,𝔽2)11yescharacteristic
441C23×C59H(5,𝔽2)11yescharacteristic
442C23×C59H(5,𝔽2)11yescharacteristic
443C23×C59H(5,𝔽2)11yescharacteristic
444C23×C59H(5,𝔽2)11yescharacteristic
445C23×C59H(5,𝔽2)11yescharacteristic
446C23×C59H(5,𝔽2)11yescharacteristic
447C23×C592−1+411yescharacteristic
448D4×C59—416no—
449D4×C59—416no—
450D4×C59—416no—
451C2×C4×C59—22no—
452C2×C4×C59—22no—
453C2×C4×C59—22no—
454C2×C4×C59—22no—
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—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—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—
535#17094C5911yesmaximal, characteristic, direct product factor, Sylow
536C22×C59—42no—
537C22×C59—42no—
538C22×C59—42no—
539C22×C59—42no—
540C22×C59—42no—
541C22×C59—42no—
542C22×C59—42no—
543C22×C59—42no—
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—81no—
558C22×C59—81no—
559C22×C59—81no—
560C22×C59—81no—
561C22×C59—81no—
562C22×C59—81no—
563C22×C59—81no—
564C22×C59—81no—
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#53411yescharacteristic
582C22×C59#53411yescharacteristic
583C22×C59#53411yescharacteristic
584C22×C59#53511yescharacteristic
585C22×C59#53511yescharacteristic
586C22×C59#53711yescharacteristic
587C22×C59#53811yescharacteristic
588C22×C59#53811yescharacteristic
589C22×C59#53811yescharacteristic
590C22×C59#53811yescharacteristic
591C22×C59#53911yescharacteristic
592C22×C59#54011yescharacteristic
593C22×C59#54011yescharacteristic
594C22×C59#54011yescharacteristic
595C22×C59#54211yescharacteristic
596C22×C59D4211yescharacteristic
597C22×C59#54611yescharacteristic
598C22×C59#54611yescharacteristic
599C22×C59#54611yescharacteristic
600C22×C59#54611yescharacteristic
601C22×C59#54711yescharacteristic
602C22×C59#55011yescharacteristic
603C22×C59#55111yescharacteristic
604C22×C59#55311yescharacteristic
605C22×C59#55311yescharacteristic
606C22×C59#56011yescharacteristic
607C22×C59#56011yescharacteristic
608C22×C59#56011yescharacteristic
609C22×C59#56011yescharacteristic
610C22×C59#56011yescharacteristic
611C22×C59H(3,𝔽4)11yescharacteristic
612C22×C59H(3,𝔽4)11yescharacteristic
613C22×C59#56211yescharacteristic
614C22×C59#56211yescharacteristic
615C22×C59#56211yescharacteristic
616C4×C59—42no—
617C4×C59—42no—
618C4×C59—42no—
619C4×C59—42no—
620C4×C59—42no—
621C4×C59—42no—
622C4×C59—81no—
623C4×C59—81no—
624C4×C59—81no—
625C4×C59—81no—
626C4×C59—81no—
627C4×C59—81no—
628C2×#397C2×C5911yescharacteristic, complemented
629C2×#394C2×C5911yescharacteristic, complemented
630C2×#394C2×C5911yescharacteristic, complemented
631C2×#392C2×C5911yescharacteristic
632#1442C2×C5911yescharacteristic, complemented
633#1442C2×C5911yescharacteristic, complemented
634#1440C2×C5911yescharacteristic, complemented
635#1439C2×C5911yescharacteristic, complemented
636#1439C2×C5911yescharacteristic, complemented
637#1439C2×C5911yescharacteristic, complemented
638#1439C2×C5911yescharacteristic, complemented
639#1438C2×C5911yescharacteristic, complemented
640#1438C2×C5911yescharacteristic, complemented
641#1438C2×C5911yescharacteristic, complemented
642#1438C2×C5911yescharacteristic, complemented
643C2×C59—82no—
644C2×C59—82no—
645C2×C59—82no—
646C2×C59#267111yescharacteristic
647C2×C59#267311yescharacteristic
648C2×C59#267811yescharacteristic
649C2×C59#268411yescharacteristic
650C2×C59#270111yescharacteristic
651C2×C59#270311yescharacteristic
652C2×C59#270511yescharacteristic
653C2×C59#270811yescharacteristic
654C2×C59#271411yescharacteristic
655C2×C59#275311yescharacteristic
656C2×C59#281211yescharacteristic
657C2×C59#281911yescharacteristic
658C2×C59#282611yescharacteristic
659C2×C59#282811yescharacteristic
660C2×C59#282911yescharacteristic
661C23×D4C22×C5911yescharacteristic
662C23×D4C22×C5911yescharacteristic
663C23×D4C22×C5911yescharacteristic
664C22×C4⋊C4C22×C5911yescharacteristic
665C22×C4⋊C4C22×C5911yescharacteristic
666C22×C4⋊C4C22×C5911yescharacteristic
667C22×C22⋊C4C22×C5911yescharacteristic
668C22×C22⋊C4C22×C5911yescharacteristic
669C22×C22⋊C4C22×C5911yescharacteristic
670C22×C22⋊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
682#397—24no—
683#394—24no—
684#394—24no—
685#392—24no—
686C2×#95C22×C5911yescharacteristic
687C2×#95C22×C5911yescharacteristic
688C2×#95C22×C5911yescharacteristic
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
700C59#1709411yescharacteristic, direct product factor, Sylow
701C25C23×C5911yescharacteristic
702C25C23×C5911yescharacteristic
703C25C23×C5911yescharacteristic
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—41no—
711C22×D4—41no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4D4×C5914yes—
725C23×C4C23×C5911yescharacteristic
726C23×C4C23×C5911yescharacteristic
727C23×C4C23×C5911yescharacteristic
728C23×C4C23×C5911yescharacteristic
729C23×C4C23×C5911yescharacteristic
730C23×C4C23×C5911yescharacteristic
731C23×C4C23×C5911yescharacteristic
732C23×C4C23×C5911yescharacteristic
733C23×C4C23×C5911yescharacteristic
734C23×C4C23×C5911yescharacteristic
735C23×C4C23×C5911yescharacteristic
736C23×C4C23×C5911yescharacteristic
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C4⋊C4—41no—
743C2×C4⋊C4—41no—
744C2×C4⋊C4—41no—
745C2×C4⋊C4—41no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
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—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
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—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—41no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95D4×C5914yescomplemented
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
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—
847C24C2×D4×C5912yes—
848C24C2×D4×C5912yes—
849C24#41×C5912yes—
850C24C24×C5911yescharacteristic
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
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—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
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×C4C2×D4×C5912yes—
951C22×C4C2×D4×C5912yes—
952C22×C4C2×D4×C5912yes—
953C22×C4C2×D4×C5912yes—
954C22×C4#41×C5912yes—
955C22×C4#41×C5912yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
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—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
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—
1079C23C22×D4×C5911yescharacteristic
1080C23C22×D4×C5911yescharacteristic
1081C23C2×#41×C5911yescharacteristic
1082C23C2×#41×C5911yescharacteristic
1083C23C2×#41×C5911yescharacteristic
1084C23H(5,𝔽2)×C5911yescharacteristic
1085C23H(5,𝔽2)×C5911yescharacteristic
1086C23H(5,𝔽2)×C5911yescharacteristic
1087C23H(5,𝔽2)×C5911yescharacteristic
1088C23H(5,𝔽2)×C5911yescharacteristic
1089C23H(5,𝔽2)×C5911yescharacteristic
1090C23H(5,𝔽2)×C5911yescharacteristic
1091C23H(5,𝔽2)×C5911yescharacteristic
1092C23H(5,𝔽2)×C5911yescharacteristic
1093C232−1+4×C5911yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
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—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
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—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C59×#53411yescharacteristic
1227C22C59×#53411yescharacteristic
1228C22C59×#53411yescharacteristic
1229C22C59×#53511yescharacteristic
1230C22C59×#53511yescharacteristic
1231C22C59×#53711yescharacteristic
1232C22C59×#53811yescharacteristic
1233C22C59×#53811yescharacteristic
1234C22C59×#53811yescharacteristic
1235C22C59×#53811yescharacteristic
1236C22C59×#53911yescharacteristic
1237C22C59×#54011yescharacteristic
1238C22C59×#54011yescharacteristic
1239C22C59×#54011yescharacteristic
1240C22C59×#54211yescharacteristic
1241C22D42×C5911yescharacteristic
1242C22C59×#54611yescharacteristic
1243C22C59×#54611yescharacteristic
1244C22C59×#54611yescharacteristic
1245C22C59×#54611yescharacteristic
1246C22C59×#54711yescharacteristic
1247C22C59×#55011yescharacteristic
1248C22C59×#55111yescharacteristic
1249C22C59×#55311yescharacteristic
1250C22C59×#55311yescharacteristic
1251C22C59×#56011yescharacteristic
1252C22C59×#56011yescharacteristic
1253C22C59×#56011yescharacteristic
1254C22C59×#56011yescharacteristic
1255C22C59×#56011yescharacteristic
1256C22C59×H(3,𝔽4)11yescharacteristic
1257C22C59×H(3,𝔽4)11yescharacteristic
1258C22C59×#56211yescharacteristic
1259C22C59×#56211yescharacteristic
1260C22C59×#56211yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C59×#267111yescharacteristic
1277C2C59×#267311yescharacteristic
1278C2C59×#267811yescharacteristic
1279C2C59×#268411yescharacteristic
1280C2C59×#270111yescharacteristic
1281C2C59×#270311yescharacteristic
1282C2C59×#270511yescharacteristic
1283C2C59×#270811yescharacteristic
1284C2C59×#271411yescharacteristic
1285C2C59×#275311yescharacteristic
1286C2C59×#281211yescharacteristic
1287C2C59×#281911yescharacteristic
1288C2C59×#282611yescharacteristic
1289C2C59×#282811yescharacteristic
1290C2C59×#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
5. C59×#1442C2semidirect
6. C59×#1442C2semidirect
7. C59×#1440C2semidirect
8. C59×#1439C2semidirect
9. C59×#1439C2semidirect
10. C59×#1439C2semidirect
11. C59×#1439C2semidirect
12. C59×#1438C2semidirect
13. C59×#1438C2semidirect
14. C59×#1438C2semidirect
15. C59×#1438C2semidirect
158. #95×C59D4semidirect
535. #17094C59direct (N × H)
628. C2×#397C2×C59semidirect
629. C2×#394C2×C59semidirect
630. C2×#394C2×C59semidirect
632. #1442C2×C59semidirect
633. #1442C2×C59semidirect
634. #1440C2×C59semidirect
635. #1439C2×C59semidirect
636. #1439C2×C59semidirect
637. #1439C2×C59semidirect
638. #1439C2×C59semidirect
639. #1438C2×C59semidirect
640. #1438C2×C59semidirect
641. #1438C2×C59semidirect
642. #1438C2×C59semidirect
700. C59#17094direct (N × H)
804. #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
C59×#14422
C59×#14402
C59×#14392
C59×#14382
#1709459