Finite Group Databasebeta

← C59×#26488 #28438597

Subgroups — C59×#26488 #28438597

Order 15104.

870 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×#501C211yesmaximal, characteristic, complemented
2C2×C4×D8×C59C211yesmaximal, characteristic
3C59×#2454C211yesmaximal, characteristic, complemented
4C59×#2452C211yesmaximal, characteristic, complemented
5C59×#2067C211yesmaximal, characteristic, complemented
6C59×#2065C211yesmaximal, characteristic, complemented
7C59×#2025C211yesmaximal, characteristic, complemented
8C59×#2023C211yesmaximal, characteristic, complemented
9C59×#1972C211yesmaximal, characteristic
10C59×#1972C211yesmaximal, characteristic
11C59×#1943C211yesmaximal, characteristic, complemented
12C59×#1941C211yesmaximal, characteristic, complemented
13C59×#1864C211yesmaximal, characteristic, complemented
14C59×#1862C211yesmaximal, characteristic, complemented
15C59×#1771C211yesmaximal, characteristic, complemented
16C22×D8×C59C2211yescharacteristic
17C2×C4⋊Q8×C59C2211yescharacteristic
18C2×#125×C59C2211yescharacteristic
19C2×C22⋊Q8×C59—21no—
20C2×C4×D4×C59C2211yescharacteristic
21C2×C4×D4×C59C2211yescharacteristic
22C59×#501—24no—
23C4×D8×C59—24no—
24C2×#107×C59C2211yescharacteristic
25C2×#107×C59C2211yescharacteristic
26C2×#106×C59C2211yescharacteristic
27C2×#106×C59C2211yescharacteristic
28C2×#106×C59C2211yescharacteristic
29C2×C4⋊C8×C59C2211yescharacteristic
30C2×#102×C59C2211yescharacteristic
31C2×#102×C59C2211yescharacteristic
32C2×#102×C59C2211yescharacteristic
33C2×#102×C59C2211yescharacteristic
34C2×#102×C59C2211yescharacteristic
35C2×#102×C59C2211yescharacteristic
36C2×#97×C59C2211yescharacteristic
37C2×#97×C59C2211yescharacteristic
38C2×C4×C8×C59C2211yescharacteristic
39C59×#399—21no—
40C59×#396—21no—
41C59×#396—21no—
42C59×#393—21no—
43C59×#390C2211yescharacteristic
44C59×#390C2211yescharacteristic
45C59×#390C2211yescharacteristic
46C59×#390C2211yescharacteristic
47C59×#389C2211yescharacteristic
48C59×#389C2211yescharacteristic
49C59×#389C2211yescharacteristic
50C59×#389C2211yescharacteristic
51C59×#385—21no—
52C59×#385—21no—
53C59×#380—21no—
54C4×C4⋊C4×C59C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C22×Q8×C59—21no—
62C22×D4×C59C2311yescharacteristic
63C22×D4×C59C2311yescharacteristic
64C23×C4×C59—21no—
65C23×C4×C59—21no—
66C2×D8×C59—22no—
67C2×D8×C59—22no—
68C2×D8×C59Q814yescomplemented
69C22×C8×C59C2311yescharacteristic
70C22×C8×C59C2311yescharacteristic
71C22×C8×C59C2311yescharacteristic
72C22×C8×C59C2311yescharacteristic
73C4⋊Q8×C59—22no—
74C4⋊Q8×C59—41no—
75#125×C59—22no—
76#125×C59—41no—
77C22⋊Q8×C59—44no—
78C4×D4×C59—22no—
79C4×D4×C59—22no—
80C4×D4×C59—41no—
81C4×D4×C59—41no—
82C2×C4⋊C4×C59—21no—
83C2×C4⋊C4×C59—21no—
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×C59D411yescharacteristic
90C2×C4⋊C4×C59D411yescharacteristic
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×C59—21no—
104C2×C22⋊C4×C59—21no—
105C2×C22⋊C4×C59—21no—
106C2×C22⋊C4×C59—21no—
107C2×C42×C59C2311yescharacteristic
108C2×C42×C59C2311yescharacteristic
109C2×C42×C59C2311yescharacteristic
110#107×C59—22no—
111#107×C59D414yes—
112#106×C59—22no—
113#106×C59—22no—
114#106×C59—22no—
115C4⋊C8×C59—22no—
116#102×C59—22no—
117#102×C59—22no—
118#102×C59—22no—
119#102×C59—22no—
120#102×C59—41no—
121#102×C59—41no—
122#97×C59—22no—
123#97×C59—22no—
124C4×C8×C59—22no—
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×C59—21no—
133C2×Q8×C59—42no—
134C2×Q8×C59—42no—
135C2×Q8×C59—81no—
136C2×D4×C59—21no—
137C2×D4×C59—21no—
138C2×D4×C59—21no—
139C2×D4×C59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59C2×Q812yes—
147C2×D4×C59C2×Q812yes—
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—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—81no—
159C22×C4×C59—81no—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2411yescharacteristic
167D8×C59—28no—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59C2×D412yes—
177C2×C8×C59C2×Q812yes—
178C2×C8×C59#4112yes—
179C2×C8×C59#4112yes—
180C4⋊C4×C59—22no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
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—41no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59—42no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59—42no—
196C4⋊C4×C59—42no—
197C4⋊C4×C59—81no—
198C4⋊C4×C59—81no—
199C4⋊C4×C59C2×D412yes—
200C4⋊C4×C59C2×D412yes—
201C22⋊C4×C59—42no—
202C22⋊C4×C59—42no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—42no—
205C22⋊C4×C59—42no—
206C22⋊C4×C59—42no—
207C22⋊C4×C59—81no—
208C22⋊C4×C59—81no—
209C22⋊C4×C59—81no—
210C22⋊C4×C59—81no—
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—21no—
216C42×C59—21no—
217C23×C59—22no—
218C23×C59—22no—
219C23×C59—41no—
220C23×C59—41no—
221C23×C59—41no—
222C23×C59—41no—
223C23×C59—41no—
224C23×C59—41no—
225C23×C59—41no—
226C23×C59—41no—
227C23×C59—41no—
228C23×C59—41no—
229C23×C59—41no—
230C23×C59—41no—
231C23×C59C22×D411yescharacteristic
232Q8×C59—84no—
233D4×C59—22no—
234D4×C59—22no—
235D4×C59—22no—
236D4×C59—22no—
237D4×C59—41no—
238D4×C59—41no—
239D4×C59—41no—
240D4×C59—41no—
241C2×C4×C59—21no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—22no—
249C2×C4×C59—22no—
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—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
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—41no—
276C2×C4×C59—84no—
277C2×C4×C59—84no—
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—41no—
287C8×C59—41no—
288C8×C59C22⋊Q814yescomplemented
289#26488C5911yesmaximal, characteristic, direct product factor, Sylow
290C22×C59—42no—
291C22×C59—42no—
292C22×C59—42no—
293C22×C59—42no—
294C22×C59—42no—
295C22×C59—42no—
296C22×C59—81no—
297C22×C59—81no—
298C22×C59—81no—
299C22×C59—81no—
300C22×C59—81no—
301C22×C59—81no—
302C22×C59—81no—
303C22×C59—81no—
304C22×C59#53211yescharacteristic
305C22×C59D4211yescharacteristic
306C22×C59D4×Q811yescharacteristic
307C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C59#57511yescharacteristic
309C22×C59#57611yescharacteristic
310C22×C59#57711yescharacteristic
311C4×C59—22no—
312C4×C59—41no—
313C4×C59—41no—
314C4×C59—41no—
315C4×C59—42no—
316C4×C59—42no—
317C4×C59—41no—
318C4×C59—41no—
319C4×C59—81no—
320C4×C59—81no—
321C4×C59—81no—
322C4×C59—81no—
323C4×C59C2×C22⋊Q811yescharacteristic
324C4×C59#54211yescharacteristic
325C4×C59#54811yescharacteristic
326C4×C59#55411yescharacteristic
327C2×#501C2×C5911yescharacteristic, complemented
328C2×C4×D8C2×C5911yescharacteristic
329#2454C2×C5911yescharacteristic, complemented
330#2452C2×C5911yescharacteristic, complemented
331#2067C2×C5911yescharacteristic, complemented
332#2065C2×C5911yescharacteristic, complemented
333#2025C2×C5911yescharacteristic, complemented
334#2023C2×C5911yescharacteristic, complemented
335#1972C2×C5911yescharacteristic
336#1972C2×C5911yescharacteristic
337#1943C2×C5911yescharacteristic, complemented
338#1941C2×C5911yescharacteristic, complemented
339#1864C2×C5911yescharacteristic, complemented
340#1862C2×C5911yescharacteristic, complemented
341#1771C2×C5911yescharacteristic, complemented
342C2×C59—82no—
343C2×C59—82no—
344C2×C59#245211yescharacteristic
345C2×C59#317111yescharacteristic
346C2×C59#317911yescharacteristic
347C2×C59#326411yescharacteristic
348C2×C59#327111yescharacteristic
349C2×C59#338411yescharacteristic
350C2×C59#338911yescharacteristic
351C22×D8C22×C5911yescharacteristic
352C2×C4⋊Q8C22×C5911yescharacteristic
353C2×#125C22×C5911yescharacteristic
354C2×C22⋊Q8—21no—
355C2×C4×D4C22×C5911yescharacteristic
356C2×C4×D4C22×C5911yescharacteristic
357#501—24no—
358C4×D8—24no—
359C2×#107C22×C5911yescharacteristic
360C2×#107C22×C5911yescharacteristic
361C2×#106C22×C5911yescharacteristic
362C2×#106C22×C5911yescharacteristic
363C2×#106C22×C5911yescharacteristic
364C2×C4⋊C8C22×C5911yescharacteristic
365C2×#102C22×C5911yescharacteristic
366C2×#102C22×C5911yescharacteristic
367C2×#102C22×C5911yescharacteristic
368C2×#102C22×C5911yescharacteristic
369C2×#102C22×C5911yescharacteristic
370C2×#102C22×C5911yescharacteristic
371C2×#97C22×C5911yescharacteristic
372C2×#97C22×C5911yescharacteristic
373C2×C4×C8C22×C5911yescharacteristic
374#399—21no—
375#396—21no—
376#396—21no—
377#393—21no—
378#390C22×C5911yescharacteristic
379#390C22×C5911yescharacteristic
380#390C22×C5911yescharacteristic
381#390C22×C5911yescharacteristic
382#389C22×C5911yescharacteristic
383#389C22×C5911yescharacteristic
384#389C22×C5911yescharacteristic
385#389C22×C5911yescharacteristic
386#385—21no—
387#385—21no—
388#380—21no—
389C4×C4⋊C4C22×C5911yescharacteristic
390#340C22×C5911yescharacteristic
391#340C22×C5911yescharacteristic
392#340C22×C5911yescharacteristic
393#340C22×C5911yescharacteristic
394#336C22×C5911yescharacteristic
395#336C22×C5911yescharacteristic
396C59#2648811yescharacteristic, direct product factor, Sylow
397C22×Q8—21no—
398C22×D4C23×C5911yescharacteristic
399C22×D4C23×C5911yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C2×D8—22no—
403C2×D8—22no—
404C2×D8Q8×C5914yescomplemented
405C22×C8C23×C5911yescharacteristic
406C22×C8C23×C5911yescharacteristic
407C22×C8C23×C5911yescharacteristic
408C22×C8C23×C5911yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—41no—
411#125—22no—
412#125—41no—
413C22⋊Q8—44no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—41no—
417C4×D4—41no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4D4×C5911yescharacteristic
426C2×C4⋊C4D4×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⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C42C23×C5911yescharacteristic
444C2×C42C23×C5911yescharacteristic
445C2×C42C23×C5911yescharacteristic
446#107—22no—
447#107D4×C5914yes—
448#106—22no—
449#106—22no—
450#106—22no—
451C4⋊C8—22no—
452#102—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—41no—
457#102—41no—
458#97—22no—
459#97—22no—
460C4×C8—22no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C5911yescharacteristic
466#95D4×C5911yescharacteristic
467C24—21no—
468C24—21no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4C2×Q8×C5912yes—
483C2×D4C2×Q8×C5912yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4C2×D4×C5911yescharacteristic
497C22×C4C2×D4×C5911yescharacteristic
498C22×C4C2×D4×C5911yescharacteristic
499C22×C4C2×D4×C5911yescharacteristic
500C22×C4C2×D4×C5911yescharacteristic
501C22×C4C2×D4×C5911yescharacteristic
502C22×C4C24×C5911yescharacteristic
503D8—28no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8C2×D4×C5912yes—
513C2×C8C2×Q8×C5912yes—
514C2×C8#41×C5912yes—
515C2×C8#41×C5912yes—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
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—41no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4C2×D4×C5912yes—
536C4⋊C4C2×D4×C5912yes—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C22×D4×C5911yescharacteristic
568Q8—84no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
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—41no—
612C2×C4—84no—
613C2×C4—84no—
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—41no—
623C8—41no—
624C8C22⋊Q8×C5914yescomplemented
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C59×#53211yescharacteristic
640C22D42×C5911yescharacteristic
641C22D4×Q8×C5911yescharacteristic
642C22C2×AGL(1,ℤ/8)×C5911yescharacteristic
643C22C59×#57511yescharacteristic
644C22C59×#57611yescharacteristic
645C22C59×#57711yescharacteristic
646C4—22no—
647C4—41no—
648C4—42no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C2×C22⋊Q8×C5911yescharacteristic
659C4C59×#54211yescharacteristic
660C4C59×#54811yescharacteristic
661C4C59×#55411yescharacteristic
662C2—82no—
663C2—82no—
664C2C59×#245211yescharacteristic
665C2C59×#317111yescharacteristic
666C2C59×#317911yescharacteristic
667C2C59×#326411yescharacteristic
668C2C59×#327111yescharacteristic
669C2C59×#338411yescharacteristic
670C2C59×#338911yescharacteristic
subgroupG/H
center, socleC23×C59C22×D4
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC22×D8×C59C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C4×C4⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#501C2semidirect
3. C59×#2454C2semidirect
4. C59×#2452C2semidirect
5. C59×#2067C2semidirect
6. C59×#2065C2semidirect
7. C59×#2025C2semidirect
8. C59×#2023C2semidirect
11. C59×#1943C2semidirect
12. C59×#1941C2semidirect
13. C59×#1864C2semidirect
14. C59×#1862C2semidirect
15. C59×#1771C2semidirect
68. C2×D8×C59Q8semidirect
288. C8×C59C22⋊Q8semidirect
289. #26488C59direct (N × H)
327. C2×#501C2×C59semidirect
329. #2454C2×C59semidirect
330. #2452C2×C59semidirect
331. #2067C2×C59semidirect
332. #2065C2×C59semidirect
333. #2025C2×C59semidirect
334. #2023C2×C59semidirect
337. #1943C2×C59semidirect
338. #1941C2×C59semidirect
339. #1864C2×C59semidirect
340. #1862C2×C59semidirect
341. #1771C2×C59semidirect
396. C59#26488direct (N × H)
404. C2×D8Q8×C59semidirect
624. C8C22⋊Q8×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C59×#5012
C2×C4×D8×C592
C59×#24542
C59×#24522
C59×#20672
C59×#20652
C59×#20252
C59×#20232
C59×#19722
C59×#19432
C59×#19412
C59×#18642
C59×#18622
C59×#17712
#2648859