Finite Group Databasebeta

← C59×#18416 #28430525

Subgroups — C59×#18416 #28430525

Order 15104.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3535C211yesmaximal, characteristic, complemented
2C59×#3194C211yesmaximal, characteristic, complemented
3C59×#3187C211yesmaximal, characteristic, complemented
4C59×#2661C211yesmaximal, characteristic, complemented
5C59×#1612C211yesmaximal, characteristic, complemented
6C59×#1611C211yesmaximal, characteristic, complemented
7C59×#1609C211yesmaximal, characteristic, complemented
8C59×#1608C211yesmaximal, characteristic, complemented
9C59×#1600C211yesmaximal, characteristic, complemented
10C59×#1599C211yesmaximal, characteristic, complemented
11C59×#1597C211yesmaximal, characteristic, complemented
12C59×#1596C211yesmaximal, characteristic, complemented
13C59×#1508C211yesmaximal, characteristic, complemented
14C59×#1501C211yesmaximal, characteristic, complemented
15C59×#1468C211yesmaximal, characteristic, complemented
16C59×#563—21no—
17C59×#562—21no—
18C59×#554—21no—
19C59×#552—21no—
20C59×#551—21no—
21C59×#551—21no—
22C59×#547—21no—
23C59×#546—21no—
24C59×#544C2211yescharacteristic
25C59×#543C2211yescharacteristic
26C59×#542—21no—
27C59×#539—21no—
28C59×#539—21no—
29C59×#539C2211yescharacteristic
30C59×#538C2211yescharacteristic
31C59×#536—21no—
32C59×#525C2211yescharacteristic
33C2×#123×C59C2211yescharacteristic
34C2×C22⋊Q8×C59C2211yescharacteristic
35C2×#121×C59C2211yescharacteristic
36C59×#483C2211yescharacteristic
37C59×#483C2211yescharacteristic
38C59×#483C2211yescharacteristic
39C59×#482—21no—
40C59×#481—21no—
41C59×#480C2211yescharacteristic
42C59×#469—21no—
43C59×#468—21no—
44C59×#465—21no—
45C59×#465—21no—
46C59×#450C2211yescharacteristic
47C59×#450C2211yescharacteristic
48C59×#450C2211yescharacteristic
49C59×#449—21no—
50C59×#448—21no—
51C59×#447C2211yescharacteristic
52C59×#407C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C59×#398C2211yescharacteristic
55C59×#397C2211yescharacteristic
56C59×#394—21no—
57C59×#394C2211yescharacteristic
58C59×#392—21no—
59C59×#392C2211yescharacteristic
60C59×#390—21no—
61C59×#388—21no—
62C4×C22⋊C4×C59C2211yescharacteristic
63C59×#328C2211yescharacteristic
64C59×#328C2211yescharacteristic
65C59×#328C2211yescharacteristic
66C59×#328C2211yescharacteristic
67C59×#328C2211yescharacteristic
68C59×#328C2211yescharacteristic
69C59×#327C2211yescharacteristic
70C59×#327C2211yescharacteristic
71C59×#324C2211yescharacteristic
72C59×#324C2211yescharacteristic
73C59×#323C2211yescharacteristic
74C59×#323C2211yescharacteristic
75C2×#41×C59—21no—
76C2×#41×C59D411yescharacteristic, complemented
77C22×Q8×C59D411yescharacteristic, complemented
78C22×D4×C59—21no—
79C22×D4×C59—21no—
80C22×D4×C59D411yescharacteristic
81C22×D4×C59C2311yescharacteristic
82C23×C4×C59C2311yescharacteristic
83C2×SD16×C59—21no—
84C2×SD16×C59—21no—
85C2×SD16×C59—21no—
86C2×D8×C59—21no—
87C2×M16×C59—21no—
88C22×C8×C59—21no—
89C4⋊Q8×C59—21no—
90C4⋊Q8×C59—21no—
91C4⋊Q8×C59—21no—
92#126×C59—21no—
93#126×C59—21no—
94#126×C59—21no—
95#126×C59—21no—
96#126×C59—21no—
97#126×C59—21no—
98#125×C59—21no—
99#125×C59—21no—
100#125×C59—21no—
101#125×C59—21no—
102#125×C59—21no—
103#124×C59—21no—
104#124×C59—21no—
105#124×C59—21no—
106#124×C59—21no—
107#123×C59—21no—
108#123×C59—21no—
109#123×C59—21no—
110#123×C59—21no—
111#123×C59—21no—
112#123×C59—21no—
113#123×C59—21no—
114#123×C59—21no—
115#123×C59—21no—
116#123×C59—21no—
117#123×C59—21no—
118#123×C59—21no—
119#123×C59—21no—
120#123×C59—21no—
121C22⋊Q8×C59—21no—
122C22⋊Q8×C59—21no—
123C22⋊Q8×C59—21no—
124C22⋊Q8×C59—21no—
125C22⋊Q8×C59—21no—
126C22⋊Q8×C59—21no—
127C22⋊Q8×C59—21no—
128C22⋊Q8×C59—21no—
129C22⋊Q8×C59—21no—
130C22⋊Q8×C59—21no—
131C22⋊Q8×C59—21no—
132C22⋊Q8×C59—21no—
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C22⋊Q8×C59D411yescharacteristic, complemented
136C22⋊Q8×C59D411yescharacteristic, complemented
137C22⋊Q8×C59D411yescharacteristic, complemented
138C22⋊Q8×C59C2311yescharacteristic
139C22⋊Q8×C59C2311yescharacteristic
140C22⋊Q8×C59C2311yescharacteristic
141#121×C59—21no—
142#121×C59—21no—
143#121×C59—21no—
144#121×C59—21no—
145#121×C59—21no—
146#121×C59—21no—
147#121×C59—21no—
148#121×C59—21no—
149#121×C59D411yescharacteristic, complemented
150#121×C59C2311yescharacteristic
151#120×C59—21no—
152#120×C59—21no—
153C4×Q8×C59—21no—
154C4×D4×C59—21no—
155C4×D4×C59—21no—
156C4×D4×C59—21no—
157C4×D4×C59—21no—
158C4×D4×C59—21no—
159C4×D4×C59—21no—
160C4×D4×C59—21no—
161#117×C59—21no—
162#117×C59—21no—
163#117×C59—21no—
164#117×C59D411yescharacteristic, complemented
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59D411yescharacteristic, complemented
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59D411yescharacteristic
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59C2311yescharacteristic
183C2×C42×C59—21no—
184#107×C59—21no—
185#106×C59—21no—
186#106×C59—21no—
187#106×C59—21no—
188#103×C59—21no—
189#103×C59—21no—
190#103×C59—21no—
191#102×C59—21no—
192#102×C59—21no—
193#102×C59—21no—
194#102×C59—21no—
195#102×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59C2311yescharacteristic
199C22⋊C8×C59C2311yescharacteristic
200C22⋊C8×C59C2311yescharacteristic
201C22⋊C8×C59C2311yescharacteristic
202#95×C59—21no—
203#95×C59—21no—
204#95×C59C2311yescharacteristic
205#95×C59C2311yescharacteristic
206C24×C59—21no—
207C24×C59C2×D411yescharacteristic
208C24×C59C2×D411yescharacteristic
209#41×C59—82no—
210#41×C59—81no—
211C2×Q8×C59—21no—
212C2×Q8×C59—21no—
213C2×Q8×C59—21no—
214C2×Q8×C59—81no—
215C2×Q8×C59C2×D411yescharacteristic
216C2×Q8×C59C2×D411yescharacteristic
217C2×Q8×C59C2×D411yescharacteristic
218C2×D4×C59—21no—
219C2×D4×C59—21no—
220C2×D4×C59—21no—
221C2×D4×C59—21no—
222C2×D4×C59—21no—
223C2×D4×C59—21no—
224C2×D4×C59—21no—
225C2×D4×C59—21no—
226C2×D4×C59—21no—
227C2×D4×C59—42no—
228C2×D4×C59—41no—
229C2×D4×C59—41no—
230C2×D4×C59—81no—
231C2×D4×C59—81no—
232C2×D4×C59—81no—
233C2×D4×C59—81no—
234C2×D4×C59—81no—
235C2×D4×C59—81no—
236C2×D4×C59C2×D411yescharacteristic
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—81no—
248C22×C4×C59C2×D411yescharacteristic
249C22×C4×C59C2×D411yescharacteristic
250C22×C4×C59C2×D411yescharacteristic
251C22×C4×C59C2×D411yescharacteristic
252C22×C4×C59C2×D411yescharacteristic
253C22×C4×C59C2×D411yescharacteristic
254C22×C4×C59C2×D411yescharacteristic
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2411yescharacteristic
257SD16×C59—81no—
258SD16×C59—81no—
259SD16×C59—81no—
260D8×C59—81no—
261M16×C59—81no—
262C2×C8×C59—21no—
263C2×C8×C59—21no—
264C2×C8×C59—21no—
265C2×C8×C59—21no—
266C2×C8×C59—81no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—21no—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59—21no—
273C4⋊C4×C59—21no—
274C4⋊C4×C59—21no—
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—21no—
284C4⋊C4×C59—21no—
285C4⋊C4×C59—21no—
286C4⋊C4×C59—21no—
287C4⋊C4×C59—21no—
288C4⋊C4×C59—21no—
289C4⋊C4×C59—21no—
290C4⋊C4×C59—21no—
291C4⋊C4×C59—21no—
292C4⋊C4×C59—81no—
293C4⋊C4×C59C2×D411yescharacteristic
294C4⋊C4×C59C2×D411yescharacteristic
295C4⋊C4×C59C2×D411yescharacteristic
296C4⋊C4×C59C2×D411yescharacteristic
297C22⋊C4×C59—21no—
298C22⋊C4×C59—21no—
299C22⋊C4×C59—21no—
300C22⋊C4×C59—21no—
301C22⋊C4×C59—21no—
302C22⋊C4×C59—21no—
303C22⋊C4×C59—21no—
304C22⋊C4×C59—21no—
305C22⋊C4×C59—21no—
306C22⋊C4×C59—21no—
307C22⋊C4×C59—21no—
308C22⋊C4×C59—21no—
309C22⋊C4×C59—21no—
310C22⋊C4×C59—21no—
311C22⋊C4×C59—21no—
312C22⋊C4×C59—21no—
313C22⋊C4×C59—21no—
314C22⋊C4×C59—21no—
315C22⋊C4×C59—21no—
316C22⋊C4×C59—21no—
317C22⋊C4×C59—21no—
318C22⋊C4×C59—21no—
319C22⋊C4×C59—21no—
320C22⋊C4×C59—42no—
321C22⋊C4×C59—42no—
322C22⋊C4×C59—41no—
323C22⋊C4×C59—41no—
324C22⋊C4×C59—81no—
325C22⋊C4×C59—81no—
326C22⋊C4×C59—81no—
327C42×C59—21no—
328C42×C59—21no—
329C42×C59—21no—
330C42×C59—21no—
331C42×C59—21no—
332C42×C59—81no—
333C23×C59—21no—
334C23×C59—21no—
335C23×C59—21no—
336C23×C59—21no—
337C23×C59—21no—
338C23×C59—21no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59#12011yescharacteristic
351C23×C59#12011yescharacteristic
352C23×C59C22×D411yescharacteristic
353Q8×C59—41no—
354Q8×C59—41no—
355Q8×C59—41no—
356Q8×C59—81no—
357Q8×C59—81no—
358Q8×C59—81no—
359D4×C59—41no—
360D4×C59—41no—
361D4×C59—41no—
362D4×C59—41no—
363D4×C59—41no—
364D4×C59—42no—
365D4×C59—42no—
366D4×C59—41no—
367D4×C59—41no—
368D4×C59—81no—
369D4×C59—81no—
370D4×C59—81no—
371D4×C59—81no—
372D4×C59—84no—
373D4×C59—82no—
374D4×C59—82no—
375C2×C4×C59—22no—
376C2×C4×C59—21no—
377C2×C4×C59—21no—
378C2×C4×C59—21no—
379C2×C4×C59—21no—
380C2×C4×C59—21no—
381C2×C4×C59—21no—
382C2×C4×C59—21no—
383C2×C4×C59—21no—
384C2×C4×C59—21no—
385C2×C4×C59—21no—
386C2×C4×C59—21no—
387C2×C4×C59—21no—
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—42no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—81no—
406C2×C4×C59—81no—
407C2×C4×C59—81no—
408C2×C4×C59—81no—
409C2×C4×C59—81no—
410C2×C4×C59—81no—
411C2×C4×C59#12011yescharacteristic
412C2×C4×C59#12011yescharacteristic
413C2×C4×C59C22×D411yescharacteristic
414C2×C4×C59C22×D411yescharacteristic
415C8×C59—41no—
416C8×C59—41no—
417C8×C59—41no—
418C8×C59—41no—
419#18416C5911yesmaximal, characteristic, direct product factor, Sylow
420C22×C59—21no—
421C22×C59—21no—
422C22×C59—21no—
423C22×C59—21no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—21no—
428C22×C59—41no—
429C22×C59—41no—
430C22×C59—41no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—41no—
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×C59C2×#12011yescharacteristic
446C22×C59#57711yescharacteristic
447C22×C59#57711yescharacteristic
448C4×C59—21no—
449C4×C59—21no—
450C4×C59—21no—
451C4×C59—21no—
452C4×C59—42no—
453C4×C59—41no—
454C4×C59—41no—
455C4×C59—41no—
456C4×C59—41no—
457C4×C59—41no—
458C4×C59—41no—
459C4×C59—41no—
460C4×C59—41no—
461C4×C59—41no—
462C4×C59—41no—
463C4×C59—81no—
464C4×C59—81no—
465#3535C2×C5911yescharacteristic, complemented
466#3194C2×C5911yescharacteristic, complemented
467#3187C2×C5911yescharacteristic, complemented
468#2661C2×C5911yescharacteristic, complemented
469#1612C2×C5911yescharacteristic, complemented
470#1611C2×C5911yescharacteristic, complemented
471#1609C2×C5911yescharacteristic, complemented
472#1608C2×C5911yescharacteristic, complemented
473#1600C2×C5911yescharacteristic, complemented
474#1599C2×C5911yescharacteristic, complemented
475#1597C2×C5911yescharacteristic, complemented
476#1596C2×C5911yescharacteristic, complemented
477#1508C2×C5911yescharacteristic, complemented
478#1501C2×C5911yescharacteristic, complemented
479#1468C2×C5911yescharacteristic, complemented
480C2×C59—21no—
481C2×C59—21no—
482C2×C59—41no—
483C2×C59—41no—
484C2×C59—81no—
485C2×C59—81no—
486C2×C59—161no—
487C2×C59#301011yescharacteristic
488C2×C59#301811yescharacteristic
489C2×C59#302611yescharacteristic
490#563—21no—
491#562—21no—
492#554—21no—
493#552—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#544C22×C5911yescharacteristic
499#543C22×C5911yescharacteristic
500#542—21no—
501#539—21no—
502#539—21no—
503#539C22×C5911yescharacteristic
504#538C22×C5911yescharacteristic
505#536—21no—
506#525C22×C5911yescharacteristic
507C2×#123C22×C5911yescharacteristic
508C2×C22⋊Q8C22×C5911yescharacteristic
509C2×#121C22×C5911yescharacteristic
510#483C22×C5911yescharacteristic
511#483C22×C5911yescharacteristic
512#483C22×C5911yescharacteristic
513#482—21no—
514#481—21no—
515#480C22×C5911yescharacteristic
516#469—21no—
517#468—21no—
518#465—21no—
519#465—21no—
520#450C22×C5911yescharacteristic
521#450C22×C5911yescharacteristic
522#450C22×C5911yescharacteristic
523#449—21no—
524#448—21no—
525#447C22×C5911yescharacteristic
526#407C22×C5911yescharacteristic
527C2×C22⋊C8C22×C5911yescharacteristic
528#398C22×C5911yescharacteristic
529#397C22×C5911yescharacteristic
530#394—21no—
531#394C22×C5911yescharacteristic
532#392—21no—
533#392C22×C5911yescharacteristic
534#390—21no—
535#388—21no—
536C4×C22⋊C4C22×C5911yescharacteristic
537#328C22×C5911yescharacteristic
538#328C22×C5911yescharacteristic
539#328C22×C5911yescharacteristic
540#328C22×C5911yescharacteristic
541#328C22×C5911yescharacteristic
542#328C22×C5911yescharacteristic
543#327C22×C5911yescharacteristic
544#327C22×C5911yescharacteristic
545#324C22×C5911yescharacteristic
546#324C22×C5911yescharacteristic
547#323C22×C5911yescharacteristic
548#323C22×C5911yescharacteristic
549C59#1841611yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41D4×C5911yescharacteristic, complemented
552C22×Q8D4×C5911yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C5911yescharacteristic
556C22×D4C23×C5911yescharacteristic
557C23×C4C23×C5911yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C5911yescharacteristic, complemented
611C22⋊Q8D4×C5911yescharacteristic, complemented
612C22⋊Q8D4×C5911yescharacteristic, complemented
613C22⋊Q8C23×C5911yescharacteristic
614C22⋊Q8C23×C5911yescharacteristic
615C22⋊Q8C23×C5911yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C5911yescharacteristic, complemented
625#121C23×C5911yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C5911yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C5911yescharacteristic
644C2×C4⋊C4D4×C5911yescharacteristic, complemented
645C2×C4⋊C4C23×C5911yescharacteristic
646C2×C4⋊C4C23×C5911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C5911yescharacteristic
656C2×C22⋊C4D4×C5911yescharacteristic
657C2×C22⋊C4C23×C5911yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C5911yescharacteristic
674C22⋊C8C23×C5911yescharacteristic
675C22⋊C8C23×C5911yescharacteristic
676C22⋊C8C23×C5911yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C5911yescharacteristic
680#95C23×C5911yescharacteristic
681C24—21no—
682C24C2×D4×C5911yescharacteristic
683C24C2×D4×C5911yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C5911yescharacteristic
691C2×Q8C2×D4×C5911yescharacteristic
692C2×Q8C2×D4×C5911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C5911yescharacteristic
712C22×C4—21no—
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—81no—
723C22×C4C2×D4×C5911yescharacteristic
724C22×C4C2×D4×C5911yescharacteristic
725C22×C4C2×D4×C5911yescharacteristic
726C22×C4C2×D4×C5911yescharacteristic
727C22×C4C2×D4×C5911yescharacteristic
728C22×C4C2×D4×C5911yescharacteristic
729C22×C4C2×D4×C5911yescharacteristic
730C22×C4C2×D4×C5911yescharacteristic
731C22×C4C24×C5911yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
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—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C5911yescharacteristic
769C4⋊C4C2×D4×C5911yescharacteristic
770C4⋊C4C2×D4×C5911yescharacteristic
771C4⋊C4C2×D4×C5911yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C5911yescharacteristic
826C23#120×C5911yescharacteristic
827C23C22×D4×C5911yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
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—42no—
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—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C5911yescharacteristic
887C2×C4#120×C5911yescharacteristic
888C2×C4C22×D4×C5911yescharacteristic
889C2×C4C22×D4×C5911yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C5911yescharacteristic
920C22C59×#57711yescharacteristic
921C22C59×#57711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C59×#301011yescharacteristic
947C2C59×#301811yescharacteristic
948C2C59×#302611yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3535C2semidirect
2. C59×#3194C2semidirect
3. C59×#3187C2semidirect
4. C59×#2661C2semidirect
5. C59×#1612C2semidirect
6. C59×#1611C2semidirect
7. C59×#1609C2semidirect
8. C59×#1608C2semidirect
9. C59×#1600C2semidirect
10. C59×#1599C2semidirect
11. C59×#1597C2semidirect
12. C59×#1596C2semidirect
13. C59×#1508C2semidirect
14. C59×#1501C2semidirect
15. C59×#1468C2semidirect
76. C2×#41×C59D4semidirect
77. C22×Q8×C59D4semidirect
135. C22⋊Q8×C59D4semidirect
136. C22⋊Q8×C59D4semidirect
137. C22⋊Q8×C59D4semidirect
149. #121×C59D4semidirect
164. #117×C59D4semidirect
169. C2×C4⋊C4×C59D4semidirect
419. #18416C59direct (N × H)
465. #3535C2×C59semidirect
466. #3194C2×C59semidirect
467. #3187C2×C59semidirect
468. #2661C2×C59semidirect
469. #1612C2×C59semidirect
470. #1611C2×C59semidirect
471. #1609C2×C59semidirect
472. #1608C2×C59semidirect
473. #1600C2×C59semidirect
474. #1599C2×C59semidirect
475. #1597C2×C59semidirect
476. #1596C2×C59semidirect
477. #1508C2×C59semidirect
478. #1501C2×C59semidirect
479. #1468C2×C59semidirect
549. C59#18416direct (N × H)
551. C2×#41D4×C59semidirect
552. C22×Q8D4×C59semidirect
610. C22⋊Q8D4×C59semidirect
611. C22⋊Q8D4×C59semidirect
612. C22⋊Q8D4×C59semidirect
624. #121D4×C59semidirect
639. #117D4×C59semidirect
644. C2×C4⋊C4D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#35352
C59×#31942
C59×#31872
C59×#26612
C59×#16122
C59×#16112
C59×#16092
C59×#16082
C59×#16002
C59×#15992
C59×#15972
C59×#15962
C59×#15082
C59×#15012
C59×#14682
#1841659