Finite Group Databasebeta

← C59×#13873 #28425982

Subgroups — C59×#13873 #28425982

Order 15104.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C59C211yesmaximal, characteristic
2C2×C59×#388C212yesmaximal, complemented
3C2×C59×#380C211yesmaximal, characteristic, complemented
4C2×C59×#379C211yesmaximal, characteristic
5C2×C59×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
7C59×#1440C212yesmaximal, complemented
8C59×#1439C212yesmaximal, complemented
9C59×#1437C212yesmaximal, complemented
10C59×C22⋊#95C211yesmaximal, characteristic, complemented
11C59×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C59C2211yescharacteristic
13C24×C4×C59C2211yescharacteristic
14C24×C4×C59C2211yescharacteristic
15C22×C4⋊C4×C59C2212yescomplemented
16C22×C22⋊C4×C59—28no—
17C22×C22⋊C4×C59C418yescomplemented
18C22×C22⋊C4×C59C2211yescharacteristic
19C22×C22⋊C4×C59C2211yescharacteristic
20C22×C22⋊C4×C59C2212yes—
21C22×C22⋊C4×C59C2212yes—
22C22×C22⋊C4×C59C2212yes—
23C22×C22⋊C4×C59C2212yes—
24C22×C22⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59C2211yescharacteristic
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic
29C22×C22⋊C4×C59C2211yescharacteristic
30C22×C42×C59C2212yescomplemented
31C59×#388—28no—
32C59×#380—24no—
33C59×#379—24no—
34C59×#379—24no—
35C4×C22⋊C4×C59—24no—
36C2×#95×C59C2212yescomplemented
37C2×#95×C59C2212yescomplemented
38C2×#95×C59C2212yescomplemented
39C2×#95×C59C2212yescomplemented
40C2×#95×C59C2212yescomplemented
41C2×#95×C59C2212yescomplemented
42C25×C59—24no—
43C25×C59—24no—
44C25×C59—22no—
45C25×C59—22no—
46C25×C59—22no—
47C25×C59—22no—
48C25×C59—22no—
49C25×C59—22no—
50C25×C59—42no—
51C25×C59—42no—
52C25×C59C2×C414yes—
53C25×C59C2311yescharacteristic
54C25×C59C2311yescharacteristic
55C25×C59C2311yescharacteristic
56C23×C4×C59—22no—
57C23×C4×C59—22no—
58C23×C4×C59—22no—
59C23×C4×C59—22no—
60C23×C4×C59—24no—
61C23×C4×C59—24no—
62C23×C4×C59—42no—
63C23×C4×C59—42no—
64C23×C4×C59C2×C414yes—
65C23×C4×C59C2×C414yes—
66C23×C4×C59C2312yes—
67C23×C4×C59C2312yes—
68C23×C4×C59C2311yescharacteristic
69C23×C4×C59C2311yescharacteristic
70C23×C4×C59C2312yes—
71C23×C4×C59C2312yes—
72C23×C4×C59C2311yescharacteristic
73C23×C4×C59C2311yescharacteristic
74C2×C4⋊C4×C59—24no—
75C2×C4⋊C4×C59—24no—
76C2×C4⋊C4×C59—42no—
77C2×C22⋊C4×C59—22no—
78C2×C22⋊C4×C59—24no—
79C2×C22⋊C4×C59—22no—
80C2×C22⋊C4×C59—22no—
81C2×C22⋊C4×C59—22no—
82C2×C22⋊C4×C59—24no—
83C2×C22⋊C4×C59—24no—
84C2×C22⋊C4×C59—232no—
85C2×C22⋊C4×C59—22no—
86C2×C22⋊C4×C59—22no—
87C2×C22⋊C4×C59—22no—
88C2×C22⋊C4×C59—24no—
89C2×C22⋊C4×C59—24no—
90C2×C22⋊C4×C59—24no—
91C2×C22⋊C4×C59—24no—
92C2×C22⋊C4×C59—22no—
93C2×C22⋊C4×C59—22no—
94C2×C22⋊C4×C59—22no—
95C2×C22⋊C4×C59—24no—
96C2×C22⋊C4×C59—24no—
97C2×C22⋊C4×C59—24no—
98C2×C22⋊C4×C59—24no—
99C2×C22⋊C4×C59—42no—
100C2×C22⋊C4×C59—42no—
101C2×C22⋊C4×C59—42no—
102C2×C22⋊C4×C59—42no—
103C2×C22⋊C4×C59C2×C414yes—
104C2×C22⋊C4×C59C2×C414yes—
105C2×C22⋊C4×C59C2×C414yes—
106C2×C22⋊C4×C59C2×C414yes—
107C2×C22⋊C4×C59D414yes—
108C2×C22⋊C4×C59D414yes—
109C2×C22⋊C4×C59D418yes—
110C2×C42×C59—24no—
111C2×C42×C59—24no—
112C2×C42×C59—42no—
113#95×C59—24no—
114#95×C59—24no—
115#95×C59—24no—
116#95×C59—24no—
117#95×C59—42no—
118#95×C59—42no—
119C24×C59—22no—
120C24×C59—22no—
121C24×C59—22no—
122C24×C59—22no—
123C24×C59—216no—
124C24×C59—216no—
125C24×C59—28no—
126C24×C59—28no—
127C24×C59—28no—
128C24×C59—22no—
129C24×C59—21no—
130C24×C59—21no—
131C24×C59—21no—
132C24×C59—21no—
133C24×C59—21no—
134C24×C59—21no—
135C24×C59—22no—
136C24×C59—21no—
137C24×C59—21no—
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—21no—
141C24×C59—21no—
142C24×C59—22no—
143C24×C59—22no—
144C24×C59—22no—
145C24×C59—22no—
146C24×C59—28no—
147C24×C59—28no—
148C24×C59—44no—
149C24×C59—44no—
150C24×C59—48no—
151C24×C59—48no—
152C24×C59—48no—
153C24×C59—48no—
154C24×C59—48no—
155C24×C59—48no—
156C24×C59—48no—
157C24×C59—48no—
158C24×C59—48no—
159C24×C59—48no—
160C24×C59—44no—
161C24×C59—44no—
162C24×C59—44no—
163C24×C59—44no—
164C24×C59C22×C412yes—
165C24×C59C22×C412yes—
166C24×C59C22×C412yes—
167C24×C59C2×D414yes—
168C24×C59C2×D412yes—
169C24×C59C2×D412yes—
170C24×C59#4114yes—
171C24×C59#4112yes—
172C24×C59#4112yes—
173C24×C59#4112yes—
174C24×C59#4112yes—
175C24×C59C2411yescharacteristic
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—28no—
183C22×C4×C59—28no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—28no—
205C22×C4×C59—28no—
206C22×C4×C59—22no—
207C22×C4×C59—22no—
208C22×C4×C59—22no—
209C22×C4×C59—22no—
210C22×C4×C59—22no—
211C22×C4×C59—22no—
212C22×C4×C59—22no—
213C22×C4×C59—22no—
214C22×C4×C59—22no—
215C22×C4×C59—22no—
216C22×C4×C59—22no—
217C22×C4×C59—22no—
218C22×C4×C59—22no—
219C22×C4×C59—22no—
220C22×C4×C59—44no—
221C22×C4×C59—44no—
222C22×C4×C59—48no—
223C22×C4×C59—48no—
224C22×C4×C59—48no—
225C22×C4×C59—48no—
226C22×C4×C59C22×C412yes—
227C22×C4×C59C22×C412yes—
228C22×C4×C59C22×C412yes—
229C22×C4×C59C22×C412yes—
230C22×C4×C59C2×D414yes—
231C22×C4×C59C2×D414yes—
232C22×C4×C59C2×D414yes—
233C22×C4×C59C2×D414yes—
234C4⋊C4×C59—48no—
235C22⋊C4×C59—28no—
236C22⋊C4×C59—28no—
237C22⋊C4×C59—28no—
238C22⋊C4×C59—28no—
239C22⋊C4×C59—28no—
240C22⋊C4×C59—48no—
241C22⋊C4×C59—48no—
242C22⋊C4×C59—48no—
243C22⋊C4×C59—48no—
244C22⋊C4×C59—44no—
245C22⋊C4×C59—44no—
246C22⋊C4×C59C22⋊C4116yescomplemented
247C42×C59—48no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—24no—
253C23×C59—24no—
254C23×C59—24no—
255C23×C59—24no—
256C23×C59—24no—
257C23×C59—24no—
258C23×C59—24no—
259C23×C59—24no—
260C23×C59—24no—
261C23×C59—24no—
262C23×C59—24no—
263C23×C59—24no—
264C23×C59—232no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—24no—
278C23×C59—24no—
279C23×C59—24no—
280C23×C59—24no—
281C23×C59—24no—
282C23×C59—24no—
283C23×C59—24no—
284C23×C59—24no—
285C23×C59—24no—
286C23×C59—24no—
287C23×C59—24no—
288C23×C59—24no—
289C23×C59—416no—
290C23×C59—416no—
291C23×C59—416no—
292C23×C59—416no—
293C23×C59—416no—
294C23×C59—432no—
295C23×C59—432no—
296C23×C59—432no—
297C23×C59—432no—
298C23×C59—41no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—42no—
307C23×C59—42no—
308C23×C59—42no—
309C23×C59—42no—
310C23×C59—42no—
311C23×C59—42no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59—42no—
318C23×C59—416no—
319C23×C59C2×C22⋊C414yes—
320C23×C59#11714yes—
321C23×C59#11714yes—
322C23×C59C4×D414yes—
323C23×C59C4×D414yes—
324C23×C59#12114yes—
325C23×C59#12314yes—
326C23×C59#12414yes—
327C23×C59#12614yes—
328C23×C59C23×C411yescharacteristic
329C23×C59C22×D412yes—
330C23×C59C22×D411yescharacteristic
331C23×C59C22×D411yescharacteristic
332C23×C59C2×#4111yescharacteristic
333C23×C59C2×#4111yescharacteristic
334C23×C59C2×#4112yes—
335C23×C59C2×#4111yescharacteristic
336C23×C59C2×#4111yescharacteristic
337C23×C59H(5,𝔽2)12yes—
338C23×C59H(5,𝔽2)12yes—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—24no—
344C2×C4×C59—24no—
345C2×C4×C59—24no—
346C2×C4×C59—24no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—24no—
354C2×C4×C59—24no—
355C2×C4×C59—24no—
356C2×C4×C59—24no—
357C2×C4×C59—24no—
358C2×C4×C59—24no—
359C2×C4×C59—416no—
360C2×C4×C59—416no—
361C2×C4×C59—42no—
362C2×C4×C59—42no—
363C2×C4×C59—42no—
364C2×C4×C59—42no—
365C2×C4×C59—42no—
366C2×C4×C59—42no—
367C2×C4×C59—42no—
368C2×C4×C59—42no—
369C2×C4×C59—42no—
370C2×C4×C59—42no—
371C2×C4×C59—42no—
372C2×C4×C59—42no—
373C2×C4×C59—42no—
374C2×C4×C59—42no—
375C2×C4×C59—42no—
376C2×C4×C59—42no—
377C2×C4×C59—42no—
378C2×C4×C59—42no—
379C2×C4×C59—42no—
380C2×C4×C59—42no—
381C2×C4×C59—42no—
382C2×C4×C59—42no—
383C2×C4×C59—42no—
384C2×C4×C59—42no—
385C2×C4×C59—42no—
386C2×C4×C59—42no—
387C2×C4×C59C2×C22⋊C414yes—
388C2×C4×C59C2×C22⋊C414yes—
389#13873C5911yesmaximal, characteristic, direct product factor, Sylow
390C22×C59—24no—
391C22×C59—24no—
392C22×C59—24no—
393C22×C59—24no—
394C22×C59—24no—
395C22×C59—28no—
396C22×C59—28no—
397C22×C59—28no—
398C22×C59—28no—
399C22×C59—24no—
400C22×C59—24no—
401C22×C59—24no—
402C22×C59—24no—
403C22×C59—24no—
404C22×C59—24no—
405C22×C59—24no—
406C22×C59—464no—
407C22×C59—42no—
408C22×C59—42no—
409C22×C59—42no—
410C22×C59—42no—
411C22×C59—42no—
412C22×C59—42no—
413C22×C59—44no—
414C22×C59—44no—
415C22×C59—44no—
416C22×C59—44no—
417C22×C59—44no—
418C22×C59—44no—
419C22×C59—44no—
420C22×C59—44no—
421C22×C59—42no—
422C22×C59—42no—
423C22×C59#38818yescomplemented
424C22×C59C22×C22⋊C411yescharacteristic
425C22×C59C2×#11711yescharacteristic
426C22×C59C2×#11711yescharacteristic
427C22×C59C2×C4×D411yescharacteristic
428C22×C59C2×C4×D411yescharacteristic
429C22×C59#51811yescharacteristic
430C22×C59#51811yescharacteristic
431C22×C59C2×#12111yescharacteristic
432C22×C59C2×#12311yescharacteristic
433C22×C59#52512yes—
434C22×C59#52512yes—
435C22×C59C2×#12411yescharacteristic
436C22×C59C2×#12611yescharacteristic
437C22×C59#53812yes—
438C22×C59#53812yes—
439C22×C59D4212yes—
440C22×C59D4212yes—
441C22×C59#54612yes—
442C22×C59#54612yes—
443C22×C59#54612yes—
444C22×C59#54612yes—
445C22×C59#55112yes—
446C22×C59#55112yes—
447C4×C59—24no—
448C4×C59—24no—
449C4×C59—42no—
450C4×C59—42no—
451C4×C59—44no—
452C4×C59—44no—
453C4×C59—82no—
454C4×C59—82no—
455C23×C22⋊C4C2×C5911yescharacteristic
456C2×#388C2×C5912yescomplemented
457C2×#380C2×C5911yescharacteristic, complemented
458C2×#379C2×C5911yescharacteristic
459C2×#379C2×C5911yescharacteristic
460C2×C4×C22⋊C4C2×C5911yescharacteristic, complemented
461#1440C2×C5912yescomplemented
462#1439C2×C5912yescomplemented
463#1437C2×C5912yescomplemented
464C22⋊#95C2×C5911yescharacteristic, complemented
465C22⋊#95C2×C5911yescharacteristic, complemented
466C2×C59—28no—
467C2×C59—44no—
468C2×C59—44no—
469C2×C59#228011yescharacteristic
470C2×C59C2×#38811yescharacteristic
471C2×C59#231211yescharacteristic
472C2×C59D4×C22⋊C411yescharacteristic
473C2×C59D4×C22⋊C411yescharacteristic
474C2×C59#234211yescharacteristic
475C2×C59#234211yescharacteristic
476C2×C59#241812yes—
477C2×C59#242412yes—
478C2×C59#247212yes—
479C2×C59#248012yes—
480C26C22×C5911yescharacteristic
481C24×C4C22×C5911yescharacteristic
482C24×C4C22×C5911yescharacteristic
483C22×C4⋊C4C22×C5912yescomplemented
484C22×C22⋊C4—28no—
485C22×C22⋊C4C4×C5918yescomplemented
486C22×C22⋊C4C22×C5911yescharacteristic
487C22×C22⋊C4C22×C5911yescharacteristic
488C22×C22⋊C4C22×C5912yes—
489C22×C22⋊C4C22×C5912yes—
490C22×C22⋊C4C22×C5912yes—
491C22×C22⋊C4C22×C5912yes—
492C22×C22⋊C4C22×C5911yescharacteristic
493C22×C22⋊C4C22×C5911yescharacteristic
494C22×C22⋊C4C22×C5911yescharacteristic
495C22×C22⋊C4C22×C5911yescharacteristic
496C22×C22⋊C4C22×C5911yescharacteristic
497C22×C22⋊C4C22×C5911yescharacteristic
498C22×C42C22×C5912yescomplemented
499#388—28no—
500#380—24no—
501#379—24no—
502#379—24no—
503C4×C22⋊C4—24no—
504C2×#95C22×C5912yescomplemented
505C2×#95C22×C5912yescomplemented
506C2×#95C22×C5912yescomplemented
507C2×#95C22×C5912yescomplemented
508C2×#95C22×C5912yescomplemented
509C2×#95C22×C5912yescomplemented
510C59#1387311yescharacteristic, direct product factor, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C5914yes—
522C25C23×C5911yescharacteristic
523C25C23×C5911yescharacteristic
524C25C23×C5911yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C5914yes—
534C23×C4C2×C4×C5914yes—
535C23×C4C23×C5912yes—
536C23×C4C23×C5912yes—
537C23×C4C23×C5911yescharacteristic
538C23×C4C23×C5911yescharacteristic
539C23×C4C23×C5912yes—
540C23×C4C23×C5912yes—
541C23×C4C23×C5911yescharacteristic
542C23×C4C23×C5911yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C5914yes—
573C2×C22⋊C4C2×C4×C5914yes—
574C2×C22⋊C4C2×C4×C5914yes—
575C2×C22⋊C4C2×C4×C5914yes—
576C2×C22⋊C4D4×C5914yes—
577C2×C22⋊C4D4×C5914yes—
578C2×C22⋊C4D4×C5918yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C5912yes—
634C24C22×C4×C5912yes—
635C24C22×C4×C5912yes—
636C24C2×D4×C5914yes—
637C24C2×D4×C5912yes—
638C24C2×D4×C5912yes—
639C24#41×C5914yes—
640C24#41×C5912yes—
641C24#41×C5912yes—
642C24#41×C5912yes—
643C24#41×C5912yes—
644C24C24×C5911yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C5912yes—
696C22×C4C22×C4×C5912yes—
697C22×C4C22×C4×C5912yes—
698C22×C4C22×C4×C5912yes—
699C22×C4C2×D4×C5914yes—
700C22×C4C2×D4×C5914yes—
701C22×C4C2×D4×C5914yes—
702C22×C4C2×D4×C5914yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C59116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—416no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23C2×C22⋊C4×C5914yes—
789C23#117×C5914yes—
790C23#117×C5914yes—
791C23C4×D4×C5914yes—
792C23C4×D4×C5914yes—
793C23#121×C5914yes—
794C23#123×C5914yes—
795C23#124×C5914yes—
796C23#126×C5914yes—
797C23C23×C4×C5911yescharacteristic
798C23C22×D4×C5912yes—
799C23C22×D4×C5911yescharacteristic
800C23C22×D4×C5911yescharacteristic
801C23C2×#41×C5911yescharacteristic
802C23C2×#41×C5911yescharacteristic
803C23C2×#41×C5912yes—
804C23C2×#41×C5911yescharacteristic
805C23C2×#41×C5911yescharacteristic
806C23H(5,𝔽2)×C5912yes—
807C23H(5,𝔽2)×C5912yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C5914yes—
857C2×C4C2×C22⋊C4×C5914yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22C59×#38818yescomplemented
892C22C22×C22⋊C4×C5911yescharacteristic
893C22C2×#117×C5911yescharacteristic
894C22C2×#117×C5911yescharacteristic
895C22C2×C4×D4×C5911yescharacteristic
896C22C2×C4×D4×C5911yescharacteristic
897C22C59×#51811yescharacteristic
898C22C59×#51811yescharacteristic
899C22C2×#121×C5911yescharacteristic
900C22C2×#123×C5911yescharacteristic
901C22C59×#52512yes—
902C22C59×#52512yes—
903C22C2×#124×C5911yescharacteristic
904C22C2×#126×C5911yescharacteristic
905C22C59×#53812yes—
906C22C59×#53812yes—
907C22D42×C5912yes—
908C22D42×C5912yes—
909C22C59×#54612yes—
910C22C59×#54612yes—
911C22C59×#54612yes—
912C22C59×#54612yes—
913C22C59×#55112yes—
914C22C59×#55112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C59×#228011yescharacteristic
927C2C2×C59×#38811yescharacteristic
928C2C59×#231211yescharacteristic
929C2D4×C22⋊C4×C5911yescharacteristic
930C2D4×C22⋊C4×C5911yescharacteristic
931C2C59×#234211yescharacteristic
932C2C59×#234211yescharacteristic
933C2C59×#241812yes—
934C2C59×#242412yes—
935C2C59×#247212yes—
936C2C59×#248012yes—
subgroupG/H
center, socleC24×C59C24
commutatorC23C23×C4×C59
Frattini, cosocleC24C24×C59
prime radicalC26×C59C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#388C2semidirect
3. C2×C59×#380C2semidirect
6. C2×C4×C22⋊C4×C59C2semidirect
7. C59×#1440C2semidirect
8. C59×#1439C2semidirect
9. C59×#1437C2semidirect
10. C59×C22⋊#95C2semidirect
11. C59×C22⋊#95C2semidirect
15. C22×C4⋊C4×C59C22semidirect
17. C22×C22⋊C4×C59C4semidirect
30. C22×C42×C59C22semidirect
36. C2×#95×C59C22semidirect
37. C2×#95×C59C22semidirect
38. C2×#95×C59C22semidirect
39. C2×#95×C59C22semidirect
40. C2×#95×C59C22semidirect
41. C2×#95×C59C22semidirect
246. C22⋊C4×C59C22⋊C4semidirect
389. #13873C59direct (N × H)
423. C22×C59#388semidirect
456. C2×#388C2×C59semidirect
457. C2×#380C2×C59semidirect
460. C2×C4×C22⋊C4C2×C59semidirect
461. #1440C2×C59semidirect
462. #1439C2×C59semidirect
463. #1437C2×C59semidirect
464. C22⋊#95C2×C59semidirect
465. C22⋊#95C2×C59semidirect
483. C22×C4⋊C4C22×C59semidirect
485. C22×C22⋊C4C4×C59semidirect
498. C22×C42C22×C59semidirect
504. C2×#95C22×C59semidirect
505. C2×#95C22×C59semidirect
506. C2×#95C22×C59semidirect
507. C2×#95C22×C59semidirect
508. C2×#95C22×C59semidirect
509. C2×#95C22×C59semidirect
510. C59#13873direct (N × H)
715. C22⋊C4C22⋊C4×C59semidirect
891. C22C59×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C592
C2×C59×#3882
C2×C59×#3802
C2×C59×#3792
C2×C4×C22⋊C4×C592
C59×#14402
C59×#14392
C59×#14372
C59×C22⋊#952
#1387359