Finite Group Databasebeta

← C59×#26354 #28438463

Subgroups — C59×#26354 #28438463

Order 15104.

904 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#476C211yesmaximal, characteristic, complemented
2C2×C59×#428C211yesmaximal, characteristic, complemented
3C59×#2439C211yesmaximal, characteristic, complemented
4C59×#2361C211yesmaximal, characteristic
5C59×#2092C211yesmaximal, characteristic, complemented
6C59×#2086C211yesmaximal, characteristic, complemented
7C59×#2065C211yesmaximal, characteristic, complemented
8C59×#2058C211yesmaximal, characteristic, complemented
9C59×#1949C211yesmaximal, characteristic, complemented
10C59×#1919C211yesmaximal, characteristic, complemented
11C59×#1895C211yesmaximal, characteristic
12C59×#1875C211yesmaximal, characteristic
13C59×#1862C211yesmaximal, characteristic, complemented
14C59×#1853C211yesmaximal, characteristic, complemented
15C59×#1851C211yesmaximal, characteristic, complemented
16C22×M16×C59C2211yescharacteristic
17C2×C4⋊Q8×C59C2211yescharacteristic
18C2×#121×C59C2211yescharacteristic
19C2×C4×D4×C59—21no—
20C2×C4×D4×C59C2211yescharacteristic
21C2×#117×C59C2211yescharacteristic
22C22×C4⋊C4×C59C2211yescharacteristic
23C59×#476—24no—
24C59×#428—24no—
25C2×#107×C59C2211yescharacteristic
26C2×#107×C59C2211yescharacteristic
27C2×#106×C59C2211yescharacteristic
28C2×#106×C59C2211yescharacteristic
29C2×#106×C59C2211yescharacteristic
30C2×#106×C59C2211yescharacteristic
31C2×C4⋊C8×C59C2211yescharacteristic
32C2×C4⋊C8×C59C2211yescharacteristic
33C2×#102×C59C2211yescharacteristic
34C2×#102×C59C2211yescharacteristic
35C2×#102×C59C2211yescharacteristic
36C2×#102×C59C2211yescharacteristic
37C2×C22⋊C8×C59C2211yescharacteristic
38C59×#396—21no—
39C59×#393—21no—
40C59×#391—21no—
41C59×#390C2211yescharacteristic
42C59×#389C2211yescharacteristic
43C59×#389C2211yescharacteristic
44C59×#389C2211yescharacteristic
45C59×#388—21no—
46C59×#387—21no—
47C59×#386—21no—
48C59×#385—21no—
49C59×#382C2211yescharacteristic
50C59×#380C2211yescharacteristic
51C4×C4⋊C4×C59C2211yescharacteristic
52C4×C22⋊C4×C59C2211yescharacteristic
53C59×#340C2211yescharacteristic
54C59×#340C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C22×Q8×C59—21no—
62C22×D4×C59—21no—
63C22×D4×C59C2311yescharacteristic
64C23×C4×C59—21no—
65C23×C4×C59—21no—
66C23×C4×C59C2311yescharacteristic
67C2×M16×C59—22no—
68C2×M16×C59—22no—
69C2×M16×C59—22no—
70C22×C8×C59C2311yescharacteristic
71C22×C8×C59C2311yescharacteristic
72C22×C8×C59C2311yescharacteristic
73C22×C8×C59C2311yescharacteristic
74C4⋊Q8×C59—22no—
75C4⋊Q8×C59—41no—
76#121×C59—22no—
77#121×C59Q814yescomplemented
78C4×D4×C59—22no—
79C4×D4×C59—41no—
80C4×D4×C59—44no—
81#117×C59—22no—
82#117×C59—41no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—21no—
85C2×C4⋊C4×C59—21no—
86C2×C4⋊C4×C59—21no—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59—21no—
89C2×C4⋊C4×C59—41no—
90C2×C4⋊C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59C2311yescharacteristic
92C2×C4⋊C4×C59C2311yescharacteristic
93C2×C4⋊C4×C59C2311yescharacteristic
94C2×C4⋊C4×C59C2311yescharacteristic
95C2×C4⋊C4×C59C2311yescharacteristic
96C2×C4⋊C4×C59C2311yescharacteristic
97C2×C22⋊C4×C59—21no—
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—21no—
100C2×C22⋊C4×C59—21no—
101C2×C22⋊C4×C59—21no—
102C2×C22⋊C4×C59—21no—
103C2×C22⋊C4×C59D411yescharacteristic
104C2×C22⋊C4×C59D411yescharacteristic
105C2×C42×C59—21no—
106C2×C42×C59—21no—
107C2×C42×C59C2311yescharacteristic
108C2×C42×C59C2311yescharacteristic
109#107×C59—22no—
110#107×C59—22no—
111#106×C59—22no—
112#106×C59—22no—
113#106×C59—41no—
114#106×C59D414yescomplemented
115C4⋊C8×C59—22no—
116C4⋊C8×C59—22no—
117#102×C59—22no—
118#102×C59—22no—
119#102×C59—22no—
120#102×C59—41no—
121C22⋊C8×C59—22no—
122#95×C59—21no—
123#95×C59—21no—
124#95×C59—21no—
125#95×C59—21no—
126#95×C59—21no—
127#95×C59—21no—
128#95×C59—21no—
129#95×C59D411yescharacteristic
130#95×C59D411yescharacteristic
131C24×C59—21no—
132C24×C59C2×D411yescharacteristic
133C2×Q8×C59—42no—
134C2×Q8×C59—42no—
135C2×Q8×C59—81no—
136C2×D4×C59—24no—
137C2×D4×C59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—42no—
143C2×D4×C59—42no—
144C2×D4×C59C2×Q812yes—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—81no—
161C22×C4×C59—81no—
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×Q812yes—
168C22×C4×C59#4112yes—
169C22×C4×C59C2411yescharacteristic
170M16×C59—28no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—21no—
178C2×C8×C59—21no—
179C2×C8×C59—21no—
180C2×C8×C59—21no—
181C2×C8×C59C2×D412yes—
182C2×C8×C59#4112yes—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59—42no—
196C4⋊C4×C59—42no—
197C4⋊C4×C59—42no—
198C4⋊C4×C59—81no—
199C4⋊C4×C59C2×D412yes—
200C4⋊C4×C59C2×D412yes—
201C4⋊C4×C59C2×Q812yes—
202C22⋊C4×C59—24no—
203C22⋊C4×C59—22no—
204C22⋊C4×C59—41no—
205C22⋊C4×C59—42no—
206C22⋊C4×C59—42no—
207C22⋊C4×C59—42no—
208C22⋊C4×C59—81no—
209C22⋊C4×C59—81no—
210C42×C59—21no—
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—42no—
215C42×C59—42no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—21no—
219C23×C59—21no—
220C23×C59—21no—
221C23×C59—21no—
222C23×C59—22no—
223C23×C59—41no—
224C23×C59—41no—
225C23×C59—41no—
226C23×C59—41no—
227C23×C59—41no—
228C23×C59—41no—
229C23×C59C22⋊Q812yes—
230C23×C59C22×D411yescharacteristic
231Q8×C59—84no—
232D4×C59—22no—
233D4×C59—22no—
234D4×C59—48no—
235D4×C59—41no—
236D4×C59—41no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—21no—
241C2×C4×C59—22no—
242C2×C4×C59—22no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—22no—
246C2×C4×C59—21no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—84no—
276C2×C4×C59—84no—
277C2×C4×C59C22⋊Q812yes—
278C2×C4×C59AGL(1,ℤ/8)12yes—
279C2×C4×C59C22×D411yescharacteristic
280C2×C4×C59C22×Q811yescharacteristic
281C2×C4×C59C2×#4111yescharacteristic
282C2×C4×C59C2×#4111yescharacteristic
283C2×C4×C59H(5,𝔽2)11yescharacteristic
284C2×C4×C592−1+411yescharacteristic
285C8×C59—22no—
286C8×C59—22no—
287C8×C59—41no—
288C8×C59—41no—
289#26354C5911yesmaximal, characteristic, direct product factor, Sylow
290C22×C59—22no—
291C22×C59—22no—
292C22×C59—22no—
293C22×C59—41no—
294C22×C59—41no—
295C22×C59—41no—
296C22×C59—41no—
297C22×C59—42no—
298C22×C59—42no—
299C22×C59—42no—
300C22×C59—81no—
301C22×C59—81no—
302C22×C59—81no—
303C22×C59—81no—
304C22×C59C2×C22⋊Q811yescharacteristic
305C22×C59D4211yescharacteristic
306C22×C59#54711yescharacteristic
307C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C59#57511yescharacteristic
309C22×C59#57711yescharacteristic
310C22×C59#57711yescharacteristic
311C4×C59—22no—
312C4×C59—22no—
313C4×C59—42no—
314C4×C59—41no—
315C4×C59—41no—
316C4×C59—42no—
317C4×C59—41no—
318C4×C59—42no—
319C4×C59—81no—
320C4×C59—81no—
321C4×C59—81no—
322C4×C59—81no—
323C4×C59#52511yescharacteristic
324C4×C59#53911yescharacteristic
325C4×C59D4×Q811yescharacteristic
326C4×C59#55411yescharacteristic
327C2×#476C2×C5911yescharacteristic, complemented
328C2×#428C2×C5911yescharacteristic, complemented
329#2439C2×C5911yescharacteristic, complemented
330#2361C2×C5911yescharacteristic
331#2092C2×C5911yescharacteristic, complemented
332#2086C2×C5911yescharacteristic, complemented
333#2065C2×C5911yescharacteristic, complemented
334#2058C2×C5911yescharacteristic, complemented
335#1949C2×C5911yescharacteristic, complemented
336#1919C2×C5911yescharacteristic, complemented
337#1895C2×C5911yescharacteristic
338#1875C2×C5911yescharacteristic
339#1862C2×C5911yescharacteristic, complemented
340#1853C2×C5911yescharacteristic, complemented
341#1851C2×C5911yescharacteristic, complemented
342C2×C59—42no—
343C2×C59—82no—
344C2×C59#244911yescharacteristic
345C2×C59#307711yescharacteristic
346C2×C59#308411yescharacteristic
347C2×C59#326511yescharacteristic
348C2×C59#327511yescharacteristic
349C2×C59#335011yescharacteristic
350C2×C59#335411yescharacteristic
351C22×M16C22×C5911yescharacteristic
352C2×C4⋊Q8C22×C5911yescharacteristic
353C2×#121C22×C5911yescharacteristic
354C2×C4×D4—21no—
355C2×C4×D4C22×C5911yescharacteristic
356C2×#117C22×C5911yescharacteristic
357C22×C4⋊C4C22×C5911yescharacteristic
358#476—24no—
359#428—24no—
360C2×#107C22×C5911yescharacteristic
361C2×#107C22×C5911yescharacteristic
362C2×#106C22×C5911yescharacteristic
363C2×#106C22×C5911yescharacteristic
364C2×#106C22×C5911yescharacteristic
365C2×#106C22×C5911yescharacteristic
366C2×C4⋊C8C22×C5911yescharacteristic
367C2×C4⋊C8C22×C5911yescharacteristic
368C2×#102C22×C5911yescharacteristic
369C2×#102C22×C5911yescharacteristic
370C2×#102C22×C5911yescharacteristic
371C2×#102C22×C5911yescharacteristic
372C2×C22⋊C8C22×C5911yescharacteristic
373#396—21no—
374#393—21no—
375#391—21no—
376#390C22×C5911yescharacteristic
377#389C22×C5911yescharacteristic
378#389C22×C5911yescharacteristic
379#389C22×C5911yescharacteristic
380#388—21no—
381#387—21no—
382#386—21no—
383#385—21no—
384#382C22×C5911yescharacteristic
385#380C22×C5911yescharacteristic
386C4×C4⋊C4C22×C5911yescharacteristic
387C4×C22⋊C4C22×C5911yescharacteristic
388#340C22×C5911yescharacteristic
389#340C22×C5911yescharacteristic
390#340C22×C5911yescharacteristic
391#340C22×C5911yescharacteristic
392#340C22×C5911yescharacteristic
393#340C22×C5911yescharacteristic
394#336C22×C5911yescharacteristic
395#336C22×C5911yescharacteristic
396C59#2635411yescharacteristic, direct product factor, Sylow
397C22×Q8—21no—
398C22×D4—21no—
399C22×D4C23×C5911yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C23×C5911yescharacteristic
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C22×C8C23×C5911yescharacteristic
407C22×C8C23×C5911yescharacteristic
408C22×C8C23×C5911yescharacteristic
409C22×C8C23×C5911yescharacteristic
410C4⋊Q8—22no—
411C4⋊Q8—41no—
412#121—22no—
413#121Q8×C5914yescomplemented
414C4×D4—22no—
415C4×D4—41no—
416C4×D4—44no—
417#117—22no—
418#117—41no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4C23×C5911yescharacteristic
427C2×C4⋊C4C23×C5911yescharacteristic
428C2×C4⋊C4C23×C5911yescharacteristic
429C2×C4⋊C4C23×C5911yescharacteristic
430C2×C4⋊C4C23×C5911yescharacteristic
431C2×C4⋊C4C23×C5911yescharacteristic
432C2×C4⋊C4C23×C5911yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C5911yescharacteristic
440C2×C22⋊C4D4×C5911yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C5911yescharacteristic
444C2×C42C23×C5911yescharacteristic
445#107—22no—
446#107—22no—
447#106—22no—
448#106—22no—
449#106—41no—
450#106D4×C5914yescomplemented
451C4⋊C8—22no—
452C4⋊C8—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—41no—
457C22⋊C8—22no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C5911yescharacteristic
466#95D4×C5911yescharacteristic
467C24—21no—
468C24C2×D4×C5911yescharacteristic
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×D4—24no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×Q8×C5912yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4C2×D4×C5911yescharacteristic
499C22×C4C2×D4×C5911yescharacteristic
500C22×C4C2×D4×C5911yescharacteristic
501C22×C4C2×D4×C5911yescharacteristic
502C22×C4C2×D4×C5911yescharacteristic
503C22×C4C2×Q8×C5912yes—
504C22×C4#41×C5912yes—
505C22×C4C24×C5911yescharacteristic
506M16—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8C2×D4×C5912yes—
518C2×C8#41×C5912yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4C2×D4×C5912yes—
536C4⋊C4C2×D4×C5912yes—
537C4⋊C4C2×Q8×C5912yes—
538C22⋊C4—24no—
539C22⋊C4—22no—
540C22⋊C4—41no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C22⋊Q8×C5912yes—
566C23C22×D4×C5911yescharacteristic
567Q8—84no—
568D4—22no—
569D4—22no—
570D4—48no—
571D4—41no—
572D4—41no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—84no—
613C2×C4C22⋊Q8×C5912yes—
614C2×C4AGL(1,ℤ/8)×C5912yes—
615C2×C4C22×D4×C5911yescharacteristic
616C2×C4C22×Q8×C5911yescharacteristic
617C2×C4C2×#41×C5911yescharacteristic
618C2×C4C2×#41×C5911yescharacteristic
619C2×C4H(5,𝔽2)×C5911yescharacteristic
620C2×C42−1+4×C5911yescharacteristic
621C8—22no—
622C8—22no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×C22⋊Q8×C5911yescharacteristic
640C22D42×C5911yescharacteristic
641C22C59×#54711yescharacteristic
642C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
643C22C59×#57511yescharacteristic
644C22C59×#57711yescharacteristic
645C22C59×#57711yescharacteristic
646C4—22no—
647C4—22no—
648C4—42no—
649C4—41no—
650C4—42no—
651C4—42no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C59×#52511yescharacteristic
659C4C59×#53911yescharacteristic
660C4D4×Q8×C5911yescharacteristic
661C4C59×#55411yescharacteristic
662C2—42no—
663C2—82no—
664C2C59×#244911yescharacteristic
665C2C59×#307711yescharacteristic
666C2C59×#308411yescharacteristic
667C2C59×#326511yescharacteristic
668C2C59×#327511yescharacteristic
669C2C59×#335011yescharacteristic
670C2C59×#335411yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC2×#121×C59C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C4×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#476C2semidirect
2. C2×C59×#428C2semidirect
3. C59×#2439C2semidirect
5. C59×#2092C2semidirect
6. C59×#2086C2semidirect
7. C59×#2065C2semidirect
8. C59×#2058C2semidirect
9. C59×#1949C2semidirect
10. C59×#1919C2semidirect
13. C59×#1862C2semidirect
14. C59×#1853C2semidirect
15. C59×#1851C2semidirect
77. #121×C59Q8semidirect
114. #106×C59D4semidirect
289. #26354C59direct (N × H)
327. C2×#476C2×C59semidirect
328. C2×#428C2×C59semidirect
329. #2439C2×C59semidirect
331. #2092C2×C59semidirect
332. #2086C2×C59semidirect
333. #2065C2×C59semidirect
334. #2058C2×C59semidirect
335. #1949C2×C59semidirect
336. #1919C2×C59semidirect
339. #1862C2×C59semidirect
340. #1853C2×C59semidirect
341. #1851C2×C59semidirect
396. C59#26354direct (N × H)
413. #121Q8×C59semidirect
450. #106D4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#4762
C2×C59×#4282
C59×#24392
C59×#23612
C59×#20922
C59×#20862
C59×#20652
C59×#20582
C59×#19492
C59×#19192
C59×#18952
C59×#18752
C59×#18622
C59×#18532
C59×#18512
#2635459