Finite Group Databasebeta

← C59×#24394 #28436503

Subgroups — C59×#24394 #28436503

Order 15104.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#535C211yesmaximal, characteristic
2C2×C59×#468C211yesmaximal, characteristic, complemented
3C2×C59×#465C211yesmaximal, characteristic, complemented
4C2×C59×#450C211yesmaximal, characteristic, complemented
5C2×C59×#408C211yesmaximal, characteristic, complemented
6C59×#2616C211yesmaximal, characteristic, complemented
7C59×#2034C211yesmaximal, characteristic, complemented
8C59×#2033C211yesmaximal, characteristic, complemented
9C59×#2000C211yesmaximal, characteristic, complemented
10C59×#2000C211yesmaximal, characteristic, complemented
11C59×#1895C211yesmaximal, characteristic, complemented
12C59×#1893C211yesmaximal, characteristic, complemented
13C59×#1873C211yesmaximal, characteristic, complemented
14C59×#1854C211yesmaximal, characteristic, complemented
15C59×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C23×D4×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic
19C22×SD16×C59C2211yescharacteristic
20C22×M16×C59C2211yescharacteristic, complemented
21C23×C8×C59C2211yescharacteristic, complemented
22C59×#535—24no—
23C59×#535—24no—
24C2×#127×C59—21no—
25C2×#124×C59—21no—
26C2×C22⋊Q8×C59C2211yescharacteristic
27C2×C22⋊Q8×C59C2211yescharacteristic, complemented
28C2×C22⋊Q8×C59C2211yescharacteristic, complemented
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C2×#121×C59C2211yescharacteristic
32C2×#121×C59C2211yescharacteristic
33C2×#120×C59—21no—
34C2×#120×C59—21no—
35C2×#117×C59C2211yescharacteristic
36C59×#468—24no—
37C59×#465—24no—
38C59×#450—24no—
39C2×#107×C59C2211yescharacteristic, complemented
40C2×#106×C59C2211yescharacteristic, complemented
41C2×#103×C59C2211yescharacteristic, complemented
42C2×#103×C59C2211yescharacteristic, complemented
43C2×#102×C59C2211yescharacteristic
44C2×#102×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×#102×C59C2211yescharacteristic
48C2×#102×C59C2211yescharacteristic
49C59×#408—24no—
50C2×C22⋊C8×C59C2211yescharacteristic
51C2×C22⋊C8×C59C2211yescharacteristic
52C2×C22⋊C8×C59C2211yescharacteristic, complemented
53C2×C22⋊C8×C59C2211yescharacteristic, complemented
54C59×#395—21no—
55C59×#394—21no—
56C59×#394—21no—
57C59×#394—21no—
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic, complemented
60C59×#380C2211yescharacteristic, complemented
61C59×#340C2211yescharacteristic, complemented
62C59×#340C2211yescharacteristic, complemented
63C59×#340C2211yescharacteristic, complemented
64C59×#340C2211yescharacteristic, complemented
65C25×C59—21no—
66C2×#41×C59—22no—
67C2×#41×C59—22no—
68C2×#41×C59—22no—
69C2×#41×C59—22no—
70C2×#41×C59—41no—
71C2×#41×C59—41no—
72C22×Q8×C59D411yescharacteristic
73C22×Q8×C59C2311yescharacteristic
74C22×D4×C59—21no—
75C22×D4×C59—21no—
76C22×D4×C59—21no—
77C22×D4×C59—21no—
78C22×D4×C59—22no—
79C22×D4×C59—22no—
80C22×D4×C59—21no—
81C22×D4×C59—22no—
82C22×D4×C59—22no—
83C22×D4×C59—41no—
84C22×D4×C59—41no—
85C22×D4×C59D411yescharacteristic
86C22×D4×C59D411yescharacteristic
87C22×D4×C59D411yescharacteristic
88C22×D4×C59C2311yescharacteristic
89C22×D4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2311yescharacteristic
93C2×SD16×C59—22no—
94C2×SD16×C59—22no—
95C2×SD16×C59—22no—
96C2×SD16×C59—22no—
97C2×SD16×C59—41no—
98C2×SD16×C59—41no—
99C2×M16×C59—22no—
100C2×M16×C59—22no—
101C2×M16×C59—41no—
102C22×C8×C59—22no—
103C22×C8×C59—22no—
104C22×C8×C59—41no—
105C22×C8×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109#127×C59—28no—
110#124×C59—28no—
111C22⋊Q8×C59—22no—
112C22⋊Q8×C59—22no—
113C22⋊Q8×C59—22no—
114C22⋊Q8×C59—22no—
115C22⋊Q8×C59—41no—
116C22⋊Q8×C59—41no—
117#121×C59—22no—
118#121×C59—22no—
119#121×C59—22no—
120#121×C59—22no—
121#121×C59—22no—
122#121×C59—22no—
123#121×C59D414yes—
124#121×C59D414yes—
125#120×C59—28no—
126#120×C59—28no—
127#117×C59—22no—
128#117×C59—22no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C22⋊C4×C59—21no—
138C2×C22⋊C4×C59—21no—
139C2×C22⋊C4×C59—21no—
140C2×C22⋊C4×C59—21no—
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145C2×C22⋊C4×C59—21no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59—21no—
148C2×C42×C59—21no—
149#107×C59—22no—
150#106×C59—22no—
151#103×C59—22no—
152#103×C59—22no—
153#102×C59—22no—
154#102×C59—22no—
155#102×C59—22no—
156#102×C59—22no—
157#102×C59—41no—
158#102×C59—41no—
159C22⋊C8×C59—22no—
160C22⋊C8×C59—22no—
161C22⋊C8×C59—22no—
162C22⋊C8×C59D414yescomplemented
163#95×C59—21no—
164#95×C59—21no—
165#95×C59—21no—
166C24×C59—24no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—42no—
170C24×C59—42no—
171C24×C59—81no—
172C24×C59—81no—
173C24×C59—81no—
174C24×C59—81no—
175C24×C59C2×D411yescharacteristic
176C24×C59C2×D411yescharacteristic
177C24×C59C2×D411yescharacteristic
178#41×C59—44no—
179#41×C59—44no—
180#41×C59—44no—
181#41×C59—44no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—41no—
191C2×D4×C59—24no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—22no—
196C2×D4×C59—24no—
197C2×D4×C59—24no—
198C2×D4×C59—24no—
199C2×D4×C59—24no—
200C2×D4×C59—22no—
201C2×D4×C59—22no—
202C2×D4×C59—21no—
203C2×D4×C59—21no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—21no—
208C2×D4×C59—21no—
209C2×D4×C59—21no—
210C2×D4×C59—21no—
211C2×D4×C59—21no—
212C2×D4×C59—44no—
213C2×D4×C59—44no—
214C2×D4×C59—44no—
215C2×D4×C59—44no—
216C2×D4×C59—41no—
217C2×D4×C59—41no—
218C2×D4×C59—41no—
219C2×D4×C59—42no—
220C2×D4×C59—42no—
221C2×D4×C59—81no—
222C2×D4×C59—81no—
223C2×D4×C59—81no—
224C2×D4×C59—81no—
225C2×D4×C59—81no—
226C2×D4×C59—81no—
227C2×D4×C59—81no—
228C2×D4×C59—81no—
229C2×D4×C59C2×D412yes—
230C2×D4×C59C2×D412yes—
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×C59C2×D411yescharacteristic
252C22×C4×C59C2×D411yescharacteristic
253C22×C4×C59C2×D412yes—
254C22×C4×C59C2×D412yes—
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D412yes—
257C22×C4×C59#4112yes—
258C22×C4×C59C2411yescharacteristic
259SD16×C59—44no—
260SD16×C59—44no—
261M16×C59—44no—
262C2×C8×C59—21no—
263C2×C8×C59—21no—
264C2×C8×C59—21no—
265C2×C8×C59—21no—
266C2×C8×C59—21no—
267C2×C8×C59—21no—
268C2×C8×C59—21no—
269C2×C8×C59—21no—
270C2×C8×C59—21no—
271C2×C8×C59—21no—
272C2×C8×C59—44no—
273C2×C8×C59C2×D412yes—
274C2×C8×C59C2×D412yes—
275C4⋊C4×C59—21no—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—42no—
284C4⋊C4×C59—42no—
285C4⋊C4×C59—42no—
286C4⋊C4×C59C2×D412yes—
287C4⋊C4×C59C2×D412yes—
288C22⋊C4×C59—24no—
289C22⋊C4×C59—24no—
290C22⋊C4×C59—24no—
291C22⋊C4×C59—24no—
292C22⋊C4×C59—24no—
293C22⋊C4×C59—42no—
294C22⋊C4×C59—42no—
295C22⋊C4×C59—42no—
296C22⋊C4×C59—81no—
297C22⋊C4×C59—81no—
298C22⋊C4×C59—81no—
299C42×C59—24no—
300C23×C59—21no—
301C23×C59—21no—
302C23×C59—21no—
303C23×C59—21no—
304C23×C59—21no—
305C23×C59—21no—
306C23×C59—21no—
307C23×C59—21no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—21no—
311C23×C59—21no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—21no—
318C23×C59—21no—
319C23×C59—21no—
320C23×C59—21no—
321C23×C59—48no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—84no—
335C23×C59—84no—
336C23×C59—84no—
337C23×C59—84no—
338C23×C59—84no—
339C23×C59—84no—
340C23×C59#12012yes—
341C23×C59#12112yes—
342C23×C59C22×D411yescharacteristic
343Q8×C59—44no—
344Q8×C59—41no—
345Q8×C59—41no—
346Q8×C59—41no—
347Q8×C59—41no—
348D4×C59—22no—
349D4×C59—22no—
350D4×C59—22no—
351D4×C59—22no—
352D4×C59—44no—
353D4×C59—44no—
354D4×C59—48no—
355D4×C59—44no—
356D4×C59—41no—
357D4×C59—41no—
358D4×C59—41no—
359D4×C59—41no—
360D4×C59—84no—
361D4×C59—84no—
362D4×C59—84no—
363D4×C59—84no—
364C2×C4×C59—21no—
365C2×C4×C59—21no—
366C2×C4×C59—21no—
367C2×C4×C59—21no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—21no—
379C2×C4×C59—21no—
380C2×C4×C59—21no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59#12012yes—
402C2×C4×C59#12112yes—
403C2×C4×C59C22×D411yescharacteristic
404C2×C4×C59C22×D411yescharacteristic
405C2×C4×C59C22×D411yescharacteristic
406C2×C4×C59C2×#4111yescharacteristic
407C2×C4×C59H(5,𝔽2)11yescharacteristic
408C2×C4×C59H(5,𝔽2)11yescharacteristic
409C8×C59—22no—
410C8×C59—22no—
411C8×C59—41no—
412C8×C59—41no—
413#24394C5911yesmaximal, characteristic, direct product factor, Sylow
414C22×C59—22no—
415C22×C59—22no—
416C22×C59—22no—
417C22×C59—22no—
418C22×C59—22no—
419C22×C59—22no—
420C22×C59—41no—
421C22×C59—41no—
422C22×C59—41no—
423C22×C59—41no—
424C22×C59—41no—
425C22×C59—41no—
426C22×C59—41no—
427C22×C59—41no—
428C22×C59—41no—
429C22×C59—42no—
430C22×C59—42no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—42no—
435C22×C59—42no—
436C22×C59—41no—
437C22×C59—42no—
438C22×C59—42no—
439C22×C59—41no—
440C22×C59—41no—
441C22×C59—816no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59—81no—
448C22×C59—81no—
449C22×C59—81no—
450C22×C59C2×#12011yescharacteristic
451C22×C59C2×#12111yescharacteristic
452C22×C59#53411yescharacteristic
453C22×C59#57611yescharacteristic
454C22×C59#57711yescharacteristic
455C22×C59#57711yescharacteristic
456C22×C59#57711yescharacteristic
457C4×C59—22no—
458C4×C59—22no—
459C4×C59—41no—
460C4×C59—42no—
461C4×C59—42no—
462C4×C59—81no—
463C4×C59—81no—
464C4×C59—81no—
465C4×C59—81no—
466C4×C59D4211yescharacteristic
467C4×C59D4211yescharacteristic
468C4×C59#54611yescharacteristic
469C4×C59#54611yescharacteristic
470C2×#535C2×C5911yescharacteristic
471C2×#468C2×C5911yescharacteristic, complemented
472C2×#465C2×C5911yescharacteristic, complemented
473C2×#450C2×C5911yescharacteristic, complemented
474C2×#408C2×C5911yescharacteristic, complemented
475#2616C2×C5911yescharacteristic, complemented
476#2034C2×C5911yescharacteristic, complemented
477#2033C2×C5911yescharacteristic, complemented
478#2000C2×C5911yescharacteristic, complemented
479#2000C2×C5911yescharacteristic, complemented
480#1895C2×C5911yescharacteristic, complemented
481#1893C2×C5911yescharacteristic, complemented
482#1873C2×C5911yescharacteristic, complemented
483#1854C2×C5911yescharacteristic, complemented
484#1786C2×C5911yescharacteristic, complemented
485C2×C59—42no—
486C2×C59—42no—
487C2×C59—81no—
488C2×C59—82no—
489C2×C59—82no—
490C2×C59#241011yescharacteristic
491C2×C59#300911yescharacteristic
492C2×C59#301211yescharacteristic
493C2×C59#305711yescharacteristic
494C2×C59#306211yescharacteristic
495C2×C59#319811yescharacteristic
496C2×C59#320011yescharacteristic
497C22×#41C22×C5911yescharacteristic
498C23×D4C22×C5911yescharacteristic
499C22×SD16C22×C5911yescharacteristic
500C22×SD16C22×C5911yescharacteristic
501C22×M16C22×C5911yescharacteristic, complemented
502C23×C8C22×C5911yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127—21no—
506C2×#124—21no—
507C2×C22⋊Q8C22×C5911yescharacteristic
508C2×C22⋊Q8C22×C5911yescharacteristic, complemented
509C2×C22⋊Q8C22×C5911yescharacteristic, complemented
510C2×#121C22×C5911yescharacteristic
511C2×#121C22×C5911yescharacteristic
512C2×#121C22×C5911yescharacteristic
513C2×#121C22×C5911yescharacteristic
514C2×#120—21no—
515C2×#120—21no—
516C2×#117C22×C5911yescharacteristic
517#468—24no—
518#465—24no—
519#450—24no—
520C2×#107C22×C5911yescharacteristic, complemented
521C2×#106C22×C5911yescharacteristic, complemented
522C2×#103C22×C5911yescharacteristic, complemented
523C2×#103C22×C5911yescharacteristic, complemented
524C2×#102C22×C5911yescharacteristic
525C2×#102C22×C5911yescharacteristic
526C2×#102C22×C5911yescharacteristic
527C2×#102C22×C5911yescharacteristic
528C2×#102C22×C5911yescharacteristic
529C2×#102C22×C5911yescharacteristic
530#408—24no—
531C2×C22⋊C8C22×C5911yescharacteristic
532C2×C22⋊C8C22×C5911yescharacteristic
533C2×C22⋊C8C22×C5911yescharacteristic, complemented
534C2×C22⋊C8C22×C5911yescharacteristic, complemented
535#395—21no—
536#394—21no—
537#394—21no—
538#394—21no—
539#380C22×C5911yescharacteristic
540#380C22×C5911yescharacteristic, complemented
541#380C22×C5911yescharacteristic, complemented
542#340C22×C5911yescharacteristic, complemented
543#340C22×C5911yescharacteristic, complemented
544#340C22×C5911yescharacteristic, complemented
545#340C22×C5911yescharacteristic, complemented
546C59#2439411yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C5911yescharacteristic
555C22×Q8C23×C5911yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C5911yescharacteristic
568C22×D4D4×C5911yescharacteristic
569C22×D4D4×C5911yescharacteristic
570C22×D4C23×C5911yescharacteristic
571C22×D4C23×C5911yescharacteristic
572C23×C4C23×C5911yescharacteristic
573C23×C4C23×C5911yescharacteristic
574C23×C4C23×C5911yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C5911yescharacteristic
588C22×C8C23×C5911yescharacteristic
589C22×C8C23×C5911yescharacteristic
590C22×C8C23×C5911yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C5914yes—
606#121D4×C5914yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C5911yescharacteristic
615C2×C4⋊C4C23×C5911yescharacteristic
616C2×C4⋊C4C23×C5911yescharacteristic
617C2×C4⋊C4C23×C5911yescharacteristic
618C2×C4⋊C4C23×C5911yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C5914yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C5911yescharacteristic
658C24C2×D4×C5911yescharacteristic
659C24C2×D4×C5911yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C5912yes—
712C2×D4C2×D4×C5912yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C5911yescharacteristic
734C22×C4C2×D4×C5911yescharacteristic
735C22×C4C2×D4×C5912yes—
736C22×C4C2×D4×C5912yes—
737C22×C4C2×D4×C5911yescharacteristic
738C22×C4C2×D4×C5912yes—
739C22×C4#41×C5912yes—
740C22×C4C24×C5911yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C5912yes—
756C2×C8C2×D4×C5912yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C5912yes—
769C4⋊C4C2×D4×C5912yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C5912yes—
823C23#121×C5912yes—
824C23C22×D4×C5911yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C5912yes—
884C2×C4#121×C5912yes—
885C2×C4C22×D4×C5911yescharacteristic
886C2×C4C22×D4×C5911yescharacteristic
887C2×C4C22×D4×C5911yescharacteristic
888C2×C4C2×#41×C5911yescharacteristic
889C2×C4H(5,𝔽2)×C5911yescharacteristic
890C2×C4H(5,𝔽2)×C5911yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—42no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C5911yescharacteristic
932C22C2×#121×C5911yescharacteristic
933C22C59×#53411yescharacteristic
934C22C59×#57611yescharacteristic
935C22C59×#57711yescharacteristic
936C22C59×#57711yescharacteristic
937C22C59×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—42no—
941C4—42no—
942C4—41no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C5911yescharacteristic
948C4D42×C5911yescharacteristic
949C4C59×#54611yescharacteristic
950C4C59×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C59×#241011yescharacteristic
957C2C59×#300911yescharacteristic
958C2C59×#301211yescharacteristic
959C2C59×#305711yescharacteristic
960C2C59×#306211yescharacteristic
961C2C59×#319811yescharacteristic
962C2C59×#320011yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×C59×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C22×#41×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#468C2semidirect
3. C2×C59×#465C2semidirect
4. C2×C59×#450C2semidirect
5. C2×C59×#408C2semidirect
6. C59×#2616C2semidirect
7. C59×#2034C2semidirect
8. C59×#2033C2semidirect
9. C59×#2000C2semidirect
10. C59×#2000C2semidirect
11. C59×#1895C2semidirect
12. C59×#1893C2semidirect
13. C59×#1873C2semidirect
14. C59×#1854C2semidirect
15. C59×#1786C2semidirect
20. C22×M16×C59C22semidirect
21. C23×C8×C59C22semidirect
27. C2×C22⋊Q8×C59C22semidirect
28. C2×C22⋊Q8×C59C22semidirect
39. C2×#107×C59C22semidirect
40. C2×#106×C59C22semidirect
41. C2×#103×C59C22semidirect
42. C2×#103×C59C22semidirect
52. C2×C22⋊C8×C59C22semidirect
53. C2×C22⋊C8×C59C22semidirect
59. C59×#380C22semidirect
60. C59×#380C22semidirect
61. C59×#340C22semidirect
62. C59×#340C22semidirect
63. C59×#340C22semidirect
64. C59×#340C22semidirect
162. C22⋊C8×C59D4semidirect
413. #24394C59direct (N × H)
471. C2×#468C2×C59semidirect
472. C2×#465C2×C59semidirect
473. C2×#450C2×C59semidirect
474. C2×#408C2×C59semidirect
475. #2616C2×C59semidirect
476. #2034C2×C59semidirect
477. #2033C2×C59semidirect
478. #2000C2×C59semidirect
479. #2000C2×C59semidirect
480. #1895C2×C59semidirect
481. #1893C2×C59semidirect
482. #1873C2×C59semidirect
483. #1854C2×C59semidirect
484. #1786C2×C59semidirect
501. C22×M16C22×C59semidirect
502. C23×C8C22×C59semidirect
508. C2×C22⋊Q8C22×C59semidirect
509. C2×C22⋊Q8C22×C59semidirect
520. C2×#107C22×C59semidirect
521. C2×#106C22×C59semidirect
522. C2×#103C22×C59semidirect
523. C2×#103C22×C59semidirect
533. C2×C22⋊C8C22×C59semidirect
534. C2×C22⋊C8C22×C59semidirect
540. #380C22×C59semidirect
541. #380C22×C59semidirect
542. #340C22×C59semidirect
543. #340C22×C59semidirect
544. #340C22×C59semidirect
545. #340C22×C59semidirect
546. C59#24394direct (N × H)
644. C22⋊C8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5352
C2×C59×#4682
C2×C59×#4652
C2×C59×#4502
C2×C59×#4082
C59×#26162
C59×#20342
C59×#20332
C59×#20002
C59×#18952
C59×#18932
C59×#18732
C59×#18542
C59×#17862
#2439459