Finite Group Databasebeta

← C59×#24451 #28436560

Subgroups — C59×#24451 #28436560

Order 15104.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#550C211yesmaximal, characteristic, complemented
2C2×C59×#469C211yesmaximal, characteristic, complemented
3C2×C59×#449C211yesmaximal, characteristic, complemented
4C2×C59×#449C211yesmaximal, characteristic, complemented
5C2×C59×#417C211yesmaximal, characteristic, complemented
6C59×#2416C211yesmaximal, characteristic, complemented
7C59×#2041C211yesmaximal, characteristic, complemented
8C59×#2034C211yesmaximal, characteristic, complemented
9C59×#2011C211yesmaximal, characteristic, complemented
10C59×#1999C211yesmaximal, characteristic, complemented
11C59×#1880C211yesmaximal, characteristic, complemented
12C59×#1874C211yesmaximal, characteristic, complemented
13C59×#1870C211yesmaximal, characteristic, complemented
14C59×#1865C211yesmaximal, characteristic, complemented
15C59×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C59C2211yescharacteristic
17C22×#41×C59C2211yescharacteristic
18C22×SD16×C59C2211yescharacteristic
19C22×D8×C59C2211yescharacteristic
20C22×D8×C59C2211yescharacteristic
21C22×M16×C59C2211yescharacteristic
22C59×#550—24no—
23C59×#550—24no—
24C2×#127×C59—21no—
25C2×#127×C59C2211yescharacteristic
26C2×#121×C59—21no—
27C2×#121×C59—21no—
28C2×#121×C59—21no—
29C2×#121×C59C2211yescharacteristic
30C2×#121×C59C2211yescharacteristic
31C2×#121×C59C2211yescharacteristic
32C2×#121×C59C2211yescharacteristic
33C2×C4×Q8×C59C2211yescharacteristic
34C2×C4×D4×C59—21no—
35C2×C4×D4×C59C2211yescharacteristic
36C22×C4⋊C4×C59C2211yescharacteristic
37C59×#469—24no—
38C59×#449—24no—
39C59×#449—24no—
40C2×#106×C59C2211yescharacteristic
41C59×#417—24no—
42C2×#103×C59C2211yescharacteristic
43C2×#103×C59C2211yescharacteristic
44C2×#103×C59C2211yescharacteristic
45C2×#102×C59C2211yescharacteristic
46C2×#102×C59C2211yescharacteristic
47C2×#102×C59C2211yescharacteristic
48C2×#102×C59C2211yescharacteristic
49C2×#102×C59C2211yescharacteristic
50C2×#102×C59C2211yescharacteristic
51C2×#102×C59C2211yescharacteristic
52C2×C22⋊C8×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic
55C59×#396—21no—
56C59×#394—21no—
57C59×#390C2211yescharacteristic
58C59×#389C2211yescharacteristic
59C59×#386—21no—
60C59×#380C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C59×#340C2211yescharacteristic
63C59×#336C2211yescharacteristic
64C59×#336C2211yescharacteristic
65C2×#41×C59—22no—
66C2×#41×C59—22no—
67C2×#41×C59—22no—
68C2×#41×C59—22no—
69C2×#41×C59—22no—
70C2×#41×C59—22no—
71C2×#41×C59—22no—
72C2×#41×C59—41no—
73C2×#41×C59—41no—
74C2×#41×C59—41no—
75C2×#41×C59—41no—
76C2×#41×C59D414yescomplemented
77C22×Q8×C59C2311yescharacteristic
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59—21no—
81C22×D4×C59—21no—
82C22×D4×C59—21no—
83C22×D4×C59—21no—
84C22×D4×C59—21no—
85C22×D4×C59—21no—
86C22×D4×C59D411yescharacteristic
87C22×D4×C59C2311yescharacteristic
88C22×D4×C59C2311yescharacteristic
89C22×D4×C59C2311yescharacteristic
90C23×C4×C59—21no—
91C23×C4×C59—21no—
92C23×C4×C59—21no—
93C23×C4×C59C2311yescharacteristic
94C23×C4×C59C2311yescharacteristic
95C2×SD16×C59—22no—
96C2×SD16×C59—22no—
97C2×SD16×C59—22no—
98C2×D8×C59—22no—
99C2×D8×C59—22no—
100C2×D8×C59—22no—
101C2×D8×C59—41no—
102C2×D8×C59—41no—
103C2×D8×C59—41no—
104C2×M16×C59—22no—
105C2×M16×C59—22no—
106C2×M16×C59—41no—
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111#127×C59—28no—
112#127×C59—22no—
113#127×C59—22no—
114#121×C59—28no—
115#121×C59—28no—
116#121×C59—22no—
117#121×C59—22no—
118#121×C59—22no—
119#121×C59—22no—
120#121×C59—22no—
121#121×C59—22no—
122#121×C59—41no—
123#121×C59—44no—
124#121×C59D414yescomplemented
125C4×Q8×C59—22no—
126C4×Q8×C59—22no—
127C4×D4×C59—28no—
128C4×D4×C59—22no—
129C4×D4×C59—22no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—22no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—41no—
135C2×C4⋊C4×C59D411yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
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×C59D411yescharacteristic
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C42×C59—21no—
150C2×C42×C59C2311yescharacteristic
151#106×C59—22no—
152#103×C59—22no—
153#103×C59—22no—
154#103×C59D414yescomplemented
155#102×C59—22no—
156#102×C59—22no—
157#102×C59—22no—
158#102×C59—22no—
159#102×C59—22no—
160#102×C59—22no—
161#102×C59—41no—
162C22⋊C8×C59—22no—
163C22⋊C8×C59—22no—
164C22⋊C8×C59—41no—
165#95×C59—21no—
166#95×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59C2×D411yescharacteristic
171C24×C59C2×D411yescharacteristic
172#41×C59—28no—
173#41×C59—44no—
174#41×C59—44no—
175#41×C59—44no—
176#41×C59—44no—
177#41×C59—44no—
178#41×C59—44no—
179#41×C59—44no—
180C2×Q8×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59C2×D412yes—
184C2×Q8×C59C2×D412yes—
185C2×Q8×C59#4112yes—
186C2×D4×C59—24no—
187C2×D4×C59—24no—
188C2×D4×C59—22no—
189C2×D4×C59—24no—
190C2×D4×C59—24no—
191C2×D4×C59—24no—
192C2×D4×C59—24no—
193C2×D4×C59—22no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—21no—
197C2×D4×C59—21no—
198C2×D4×C59—21no—
199C2×D4×C59—21no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
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—41no—
211C2×D4×C59—42no—
212C2×D4×C59—42no—
213C2×D4×C59—42no—
214C2×D4×C59—42no—
215C2×D4×C59—42no—
216C2×D4×C59—42no—
217C2×D4×C59—42no—
218C2×D4×C59—42no—
219C2×D4×C59—42no—
220C2×D4×C59—42no—
221C2×D4×C59—42no—
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—24no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—24no—
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—42no—
249C22×C4×C59—42no—
250C22×C4×C59—42no—
251C22×C4×C59—42no—
252C22×C4×C59—42no—
253C22×C4×C59—42no—
254C22×C4×C59—81no—
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D411yescharacteristic
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2×D412yes—
259C22×C4×C59C2×D412yes—
260C22×C4×C59C2×D411yescharacteristic
261C22×C4×C59C2411yescharacteristic
262SD16×C59—44no—
263D8×C59—44no—
264D8×C59—44no—
265M16×C59—44no—
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—21no—
273C2×C8×C59—21no—
274C2×C8×C59—21no—
275C2×C8×C59—21no—
276C2×C8×C59—21no—
277C2×C8×C59C2×D412yes—
278C4⋊C4×C59—24no—
279C4⋊C4×C59—22no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59—21no—
284C4⋊C4×C59—21no—
285C4⋊C4×C59—21no—
286C4⋊C4×C59—42no—
287C4⋊C4×C59—42no—
288C4⋊C4×C59C2×D412yes—
289C4⋊C4×C59C2×D412yes—
290C22⋊C4×C59—24no—
291C22⋊C4×C59—22no—
292C22⋊C4×C59—24no—
293C22⋊C4×C59—22no—
294C22⋊C4×C59—42no—
295C22⋊C4×C59—42no—
296C22⋊C4×C59—42no—
297C22⋊C4×C59—42no—
298C22⋊C4×C59—81no—
299C42×C59—24no—
300C42×C59—21no—
301C42×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—22no—
310C23×C59—22no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—21no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59—41no—
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—41no—
335C23×C59—41no—
336C23×C59#12012yes—
337C23×C59C22×D411yescharacteristic
338Q8×C59—22no—
339Q8×C59—22no—
340Q8×C59—22no—
341Q8×C59#12114yescomplemented
342D4×C59—22no—
343D4×C59—22no—
344D4×C59—22no—
345D4×C59—22no—
346D4×C59—44no—
347D4×C59—48no—
348D4×C59—48no—
349D4×C59—48no—
350D4×C59—41no—
351D4×C59—41no—
352D4×C59—41no—
353D4×C59—41no—
354D4×C59—41no—
355D4×C59—41no—
356D4×C59—41no—
357D4×C59—41no—
358D4×C59—84no—
359D4×C59—84no—
360D4×C59—84no—
361D4×C59—84no—
362D4×C59—84no—
363C2×C4×C59—21no—
364C2×C4×C59—22no—
365C2×C4×C59—21no—
366C2×C4×C59—22no—
367C2×C4×C59—21no—
368C2×C4×C59—22no—
369C2×C4×C59—21no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—21no—
375C2×C4×C59—22no—
376C2×C4×C59—21no—
377C2×C4×C59—21no—
378C2×C4×C59—22no—
379C2×C4×C59—21no—
380C2×C4×C59—21no—
381C2×C4×C59—21no—
382C2×C4×C59—48no—
383C2×C4×C59—48no—
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—84no—
399C2×C4×C59#12012yes—
400C2×C4×C59AGL(1,ℤ/8)12yes—
401C2×C4×C59C22×D411yescharacteristic
402C2×C4×C59C22×D411yescharacteristic
403C2×C4×C59C22×D411yescharacteristic
404C2×C4×C59C2×#4111yescharacteristic
405C2×C4×C59H(5,𝔽2)11yescharacteristic
406C2×C4×C59H(5,𝔽2)11yescharacteristic
407C8×C59—22no—
408C8×C59—41no—
409C8×C59—41no—
410C8×C59—41no—
411#24451C5911yesmaximal, characteristic, direct product factor, Sylow
412C22×C59—22no—
413C22×C59—22no—
414C22×C59—22no—
415C22×C59—41no—
416C22×C59—41no—
417C22×C59—41no—
418C22×C59—41no—
419C22×C59—41no—
420C22×C59—42no—
421C22×C59—42no—
422C22×C59—41no—
423C22×C59—41no—
424C22×C59—42no—
425C22×C59—42no—
426C22×C59—41no—
427C22×C59—42no—
428C22×C59—42no—
429C22×C59—41no—
430C22×C59—41no—
431C22×C59—41no—
432C22×C59—81no—
433C22×C59—81no—
434C22×C59—81no—
435C22×C59—81no—
436C22×C59—81no—
437C22×C59—81no—
438C22×C59—81no—
439C22×C59—81no—
440C22×C59—81no—
441C22×C59—81no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59—81no—
447C22×C59C2×#12011yescharacteristic
448C22×C59D4211yescharacteristic
449C22×C59#54611yescharacteristic
450C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C59#57511yescharacteristic
452C22×C59#57611yescharacteristic
453C22×C59#57711yescharacteristic
454C4×C59—22no—
455C4×C59—24no—
456C4×C59—22no—
457C4×C59—41no—
458C4×C59—41no—
459C4×C59—42no—
460C4×C59—42no—
461C4×C59—81no—
462C4×C59—81no—
463C4×C59C2×#12111yescharacteristic
464C4×C59#53411yescharacteristic
465C4×C59D4211yescharacteristic
466C4×C59#54611yescharacteristic
467C2×#550C2×C5911yescharacteristic, complemented
468C2×#469C2×C5911yescharacteristic, complemented
469C2×#449C2×C5911yescharacteristic, complemented
470C2×#449C2×C5911yescharacteristic, complemented
471C2×#417C2×C5911yescharacteristic, complemented
472#2416C2×C5911yescharacteristic, complemented
473#2041C2×C5911yescharacteristic, complemented
474#2034C2×C5911yescharacteristic, complemented
475#2011C2×C5911yescharacteristic, complemented
476#1999C2×C5911yescharacteristic, complemented
477#1880C2×C5911yescharacteristic, complemented
478#1874C2×C5911yescharacteristic, complemented
479#1870C2×C5911yescharacteristic, complemented
480#1865C2×C5911yescharacteristic, complemented
481#1788C2×C5911yescharacteristic, complemented
482C2×C59—42no—
483C2×C59—81no—
484C2×C59—82no—
485C2×C59—82no—
486C2×C59—161no—
487C2×C59#241011yescharacteristic
488C2×C59#300611yescharacteristic
489C2×C59#301211yescharacteristic
490C2×C59#327111yescharacteristic
491C2×C59#327411yescharacteristic
492C2×C59#330911yescharacteristic
493C2×C59#333211yescharacteristic
494C22×#41C22×C5911yescharacteristic
495C22×#41C22×C5911yescharacteristic
496C22×SD16C22×C5911yescharacteristic
497C22×D8C22×C5911yescharacteristic
498C22×D8C22×C5911yescharacteristic
499C22×M16C22×C5911yescharacteristic
500#550—24no—
501#550—24no—
502C2×#127—21no—
503C2×#127C22×C5911yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—21no—
507C2×#121C22×C5911yescharacteristic
508C2×#121C22×C5911yescharacteristic
509C2×#121C22×C5911yescharacteristic
510C2×#121C22×C5911yescharacteristic
511C2×C4×Q8C22×C5911yescharacteristic
512C2×C4×D4—21no—
513C2×C4×D4C22×C5911yescharacteristic
514C22×C4⋊C4C22×C5911yescharacteristic
515#469—24no—
516#449—24no—
517#449—24no—
518C2×#106C22×C5911yescharacteristic
519#417—24no—
520C2×#103C22×C5911yescharacteristic
521C2×#103C22×C5911yescharacteristic
522C2×#103C22×C5911yescharacteristic
523C2×#102C22×C5911yescharacteristic
524C2×#102C22×C5911yescharacteristic
525C2×#102C22×C5911yescharacteristic
526C2×#102C22×C5911yescharacteristic
527C2×#102C22×C5911yescharacteristic
528C2×#102C22×C5911yescharacteristic
529C2×#102C22×C5911yescharacteristic
530C2×C22⋊C8C22×C5911yescharacteristic
531C2×C22⋊C8C22×C5911yescharacteristic
532C2×C22⋊C8C22×C5911yescharacteristic
533#396—21no—
534#394—21no—
535#390C22×C5911yescharacteristic
536#389C22×C5911yescharacteristic
537#386—21no—
538#380C22×C5911yescharacteristic
539#340C22×C5911yescharacteristic
540#340C22×C5911yescharacteristic
541#336C22×C5911yescharacteristic
542#336C22×C5911yescharacteristic
543C59#2445111yescharacteristic, direct product factor, Sylow
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C5914yescomplemented
556C22×Q8C23×C5911yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C5911yescharacteristic
566C22×D4C23×C5911yescharacteristic
567C22×D4C23×C5911yescharacteristic
568C22×D4C23×C5911yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C5911yescharacteristic
573C23×C4C23×C5911yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—22no—
584C2×M16—22no—
585C2×M16—41no—
586C22×C8C23×C5911yescharacteristic
587C22×C8C23×C5911yescharacteristic
588C22×C8C23×C5911yescharacteristic
589C22×C8C23×C5911yescharacteristic
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121D4×C5914yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×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⋊C4D4×C5911yescharacteristic
627C2×C22⋊C4D4×C5911yescharacteristic
628C2×C42—21no—
629C2×C42C23×C5911yescharacteristic
630#106—22no—
631#103—22no—
632#103—22no—
633#103D4×C5914yescomplemented
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C5911yescharacteristic
650C24C2×D4×C5911yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C5912yes—
663C2×Q8C2×D4×C5912yes—
664C2×Q8#41×C5912yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C5912yes—
709C2×D4C2×D4×C5912yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
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—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C5911yescharacteristic
735C22×C4C2×D4×C5911yescharacteristic
736C22×C4C2×D4×C5911yescharacteristic
737C22×C4C2×D4×C5912yes—
738C22×C4C2×D4×C5912yes—
739C22×C4C2×D4×C5911yescharacteristic
740C22×C4C24×C5911yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
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—21no—
755C2×C8—21no—
756C2×C8C2×D4×C5912yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
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⋊C4C2×D4×C5912yes—
768C4⋊C4C2×D4×C5912yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#120×C5912yes—
816C23C22×D4×C5911yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#121×C5914yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
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—84no—
878C2×C4#120×C5912yes—
879C2×C4AGL(1,ℤ/8)×C5912yes—
880C2×C4C22×D4×C5911yescharacteristic
881C2×C4C22×D4×C5911yescharacteristic
882C2×C4C22×D4×C5911yescharacteristic
883C2×C4C2×#41×C5911yescharacteristic
884C2×C4H(5,𝔽2)×C5911yescharacteristic
885C2×C4H(5,𝔽2)×C5911yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—42no—
908C22—42no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×#120×C5911yescharacteristic
926C22D42×C5911yescharacteristic
927C22C59×#54611yescharacteristic
928C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
929C22C59×#57511yescharacteristic
930C22C59×#57611yescharacteristic
931C22C59×#57711yescharacteristic
932C4—22no—
933C4—22no—
934C4—24no—
935C4—41no—
936C4—42no—
937C4—42no—
938C4—41no—
939C4—81no—
940C4—81no—
941C4C2×#121×C5911yescharacteristic
942C4C59×#53411yescharacteristic
943C4D42×C5911yescharacteristic
944C4C59×#54611yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C59×#241011yescharacteristic
951C2C59×#300611yescharacteristic
952C2C59×#301211yescharacteristic
953C2C59×#327111yescharacteristic
954C2C59×#327411yescharacteristic
955C2C59×#330911yescharacteristic
956C2C59×#333211yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#550C2semidirect
2. C2×C59×#469C2semidirect
3. C2×C59×#449C2semidirect
4. C2×C59×#449C2semidirect
5. C2×C59×#417C2semidirect
6. C59×#2416C2semidirect
7. C59×#2041C2semidirect
8. C59×#2034C2semidirect
9. C59×#2011C2semidirect
10. C59×#1999C2semidirect
11. C59×#1880C2semidirect
12. C59×#1874C2semidirect
13. C59×#1870C2semidirect
14. C59×#1865C2semidirect
15. C59×#1788C2semidirect
76. C2×#41×C59D4semidirect
124. #121×C59D4semidirect
154. #103×C59D4semidirect
341. Q8×C59#121semidirect
411. #24451C59direct (N × H)
467. C2×#550C2×C59semidirect
468. C2×#469C2×C59semidirect
469. C2×#449C2×C59semidirect
470. C2×#449C2×C59semidirect
471. C2×#417C2×C59semidirect
472. #2416C2×C59semidirect
473. #2041C2×C59semidirect
474. #2034C2×C59semidirect
475. #2011C2×C59semidirect
476. #1999C2×C59semidirect
477. #1880C2×C59semidirect
478. #1874C2×C59semidirect
479. #1870C2×C59semidirect
480. #1865C2×C59semidirect
481. #1788C2×C59semidirect
543. C59#24451direct (N × H)
555. C2×#41D4×C59semidirect
603. #121D4×C59semidirect
633. #103D4×C59semidirect
820. Q8#121×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5502
C2×C59×#4692
C2×C59×#4492
C2×C59×#4172
C59×#24162
C59×#20412
C59×#20342
C59×#20112
C59×#19992
C59×#18802
C59×#18742
C59×#18702
C59×#18652
C59×#17882
#2445159