Finite Group Databasebeta

← C59×#11087 #28423196

Subgroups — C59×#11087 #28423196

Order 15104.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C59C211yesmaximal, characteristic
2C59×#2308C211yesmaximal, characteristic
3C2×C59×#386C211yesmaximal, characteristic
4C2×C59×#385C211yesmaximal, characteristic, complemented
5C2×C59×#342C211yesmaximal, characteristic, complemented
6C2×C59×#342C211yesmaximal, characteristic, complemented
7C59×C22⋊#95C211yesmaximal, characteristic, complemented
8C23×D4×C59C2211yescharacteristic
9C24×C4×C59C2211yescharacteristic
10C22×C4⋊C4×C59—21no—
11C22×C22⋊C4×C59—21no—
12C22×C22⋊C4×C59C2211yescharacteristic
13C22×C22⋊C4×C59C2211yescharacteristic
14C22×C22⋊C4×C59C2211yescharacteristic
15C22×C22⋊C4×C59C2211yescharacteristic
16C22×C22⋊C4×C59C2211yescharacteristic
17C2×#99×C59—22no—
18C2×#99×C59—22no—
19C2×#99×C59C414yescomplemented
20C59×#386—22no—
21C59×#386—21no—
22C59×#386—22no—
23C59×#386—21no—
24C59×#386—22no—
25C59×#385—22no—
26C59×#385—22no—
27C59×#381—21no—
28C59×#379—21no—
29C2×#95×C59—21no—
30C2×#95×C59—21no—
31C2×#95×C59—22no—
32C59×#342—22no—
33C59×#342—22no—
34C25×C59D411yescharacteristic
35C25×C59C2311yescharacteristic
36C22×D4×C59—21no—
37C22×D4×C59—21no—
38C22×D4×C59—21no—
39C22×D4×C59—21no—
40C22×D4×C59—21no—
41C22×D4×C59—21no—
42C22×D4×C59—21no—
43C22×D4×C59—21no—
44C22×D4×C59—21no—
45C22×D4×C59—21no—
46C22×D4×C59—21no—
47C22×D4×C59—21no—
48C22×D4×C59C2×C412yes—
49C22×D4×C59Q812yes—
50C23×C4×C59—21no—
51C23×C4×C59—21no—
52C23×C4×C59—21no—
53C23×C4×C59—21no—
54C23×C4×C59—21no—
55C23×C4×C59—21no—
56C23×C4×C59—21no—
57C23×C4×C59—21no—
58C23×C4×C59—21no—
59C23×C4×C59—44no—
60C23×C4×C59D411yescharacteristic
61C23×C4×C59D411yescharacteristic
62C23×C4×C59D412yes—
63C23×C4×C59D412yes—
64C23×C4×C59D411yescharacteristic
65C2×C4⋊C4×C59—24no—
66C2×C4⋊C4×C59—44no—
67C2×C22⋊C4×C59—21no—
68C2×C22⋊C4×C59—21no—
69C2×C22⋊C4×C59—21no—
70C2×C22⋊C4×C59—21no—
71C2×C22⋊C4×C59—21no—
72C2×C22⋊C4×C59—21no—
73C2×C22⋊C4×C59—21no—
74C2×C22⋊C4×C59—21no—
75C2×C22⋊C4×C59—21no—
76C2×C22⋊C4×C59—21no—
77C2×C22⋊C4×C59—21no—
78C2×C22⋊C4×C59—24no—
79C2×C22⋊C4×C59—21no—
80C2×C22⋊C4×C59—21no—
81C2×C22⋊C4×C59—21no—
82C2×C22⋊C4×C59—21no—
83C2×C22⋊C4×C59—21no—
84C2×C22⋊C4×C59—21no—
85C2×C22⋊C4×C59—21no—
86C2×C22⋊C4×C59—21no—
87C2×C22⋊C4×C59—21no—
88C2×C22⋊C4×C59—21no—
89C2×C22⋊C4×C59—21no—
90C2×C22⋊C4×C59—21no—
91C2×C22⋊C4×C59—21no—
92C2×C22⋊C4×C59—21no—
93C2×C22⋊C4×C59—22no—
94C2×C22⋊C4×C59—22no—
95C2×C22⋊C4×C59—44no—
96C2×C22⋊C4×C59C2×C412yes—
97C2×C22⋊C4×C59C2×C412yes—
98C2×C22⋊C4×C59D412yes—
99C2×C22⋊C4×C59D412yes—
100C2×C22⋊C4×C59D412yes—
101#99×C59—28no—
102#95×C59—24no—
103#95×C59—24no—
104#95×C59—22no—
105#95×C59—22no—
106#95×C59—44no—
107C24×C59—21no—
108C24×C59—21no—
109C24×C59—21no—
110C24×C59—21no—
111C24×C59—21no—
112C24×C59—21no—
113C24×C59—42no—
114C24×C59—42no—
115C24×C59—42no—
116C24×C59—42no—
117C24×C59C4⋊C412yescomplemented
118C24×C59C22×C411yescharacteristic
119C24×C59C2×D411yescharacteristic
120C24×C59C2×D411yescharacteristic
121C24×C59C2×D411yescharacteristic
122C24×C59C2×D411yescharacteristic
123C24×C59C2×D411yescharacteristic
124C24×C59C2×D411yescharacteristic
125C24×C59C2×D411yescharacteristic
126C24×C59C2×Q811yescharacteristic
127C24×C59#4111yescharacteristic
128C24×C59#4111yescharacteristic
129C24×C59#4111yescharacteristic
130C24×C59#4111yescharacteristic
131C24×C59#4111yescharacteristic
132C24×C59#4111yescharacteristic
133C2×D4×C59—22no—
134C2×D4×C59—22no—
135C2×D4×C59—22no—
136C2×D4×C59—22no—
137C2×D4×C59—22no—
138C2×D4×C59—22no—
139C2×D4×C59—22no—
140C2×D4×C59—22no—
141C2×D4×C59—22no—
142C2×D4×C59—22no—
143C2×D4×C59—22no—
144C2×D4×C59—22no—
145C2×D4×C59—41no—
146C2×D4×C59—41no—
147C2×D4×C59—41no—
148C2×D4×C59—41no—
149C2×D4×C59—41no—
150C2×D4×C59—41no—
151C2×D4×C59—41no—
152C2×D4×C59—41no—
153C2×D4×C59—41no—
154C2×D4×C59—41no—
155C2×D4×C59—41no—
156C2×D4×C59—41no—
157C2×D4×C59—41no—
158C2×D4×C59—41no—
159C2×D4×C59—41no—
160C2×D4×C59—41no—
161C22×C4×C59—24no—
162C22×C4×C59—24no—
163C22×C4×C59—24no—
164C22×C4×C59—22no—
165C22×C4×C59—21no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—21no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—22no—
177C22×C4×C59—21no—
178C22×C4×C59—22no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—22no—
187C22×C4×C59—44no—
188C22×C4×C59—44no—
189C22×C4×C59—44no—
190C22×C4×C59—44no—
191C22×C4×C59—42no—
192C22×C4×C59—42no—
193C22×C4×C59—42no—
194C22×C4×C59—42no—
195C22×C4×C59—42no—
196C22×C4×C59—41no—
197C22×C4×C59—41no—
198C22×C4×C59—41no—
199C22×C4×C59—41no—
200C22×C4×C59—42no—
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—42no—
208C22×C4×C59—41no—
209C22×C4×C59—41no—
210C22×C4×C59—41no—
211C22×C4×C59—41no—
212C22×C4×C59C4⋊C412yescomplemented
213C4⋊C4×C59—48no—
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—22no—
221C22⋊C4×C59—48no—
222C22⋊C4×C59—41no—
223C22⋊C4×C59—41no—
224C22⋊C4×C59—41no—
225C22⋊C4×C59—41no—
226C22⋊C4×C59—41no—
227C22⋊C4×C59—41no—
228C22⋊C4×C59—41no—
229C22⋊C4×C59—41no—
230C22⋊C4×C59—41no—
231C22⋊C4×C59—41no—
232C22⋊C4×C59—41no—
233C22⋊C4×C59—41no—
234C22⋊C4×C59—82no—
235C22⋊C4×C59—82no—
236C22⋊C4×C59C22⋊C414yescomplemented
237C23×C59—22no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—22no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—42no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—42no—
255C23×C59—42no—
256C23×C59—42no—
257C23×C59—42no—
258C23×C59—41no—
259C23×C59—42no—
260C23×C59—42no—
261C23×C59—42no—
262C23×C59—44no—
263C23×C59—42no—
264C23×C59—42no—
265C23×C59—44no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59—82no—
273C23×C59—81no—
274C23×C59—81no—
275C23×C59—82no—
276C23×C59C2×C22⋊C411yescharacteristic
277C23×C59C2×C4⋊C411yescharacteristic
278C23×C59#11711yescharacteristic
279C23×C59C4×D411yescharacteristic
280C23×C59C4×D411yescharacteristic
281C23×C59C4×D411yescharacteristic
282C23×C59C4×D411yescharacteristic
283C23×C59#12011yescharacteristic
284C23×C59#12011yescharacteristic
285C23×C59#12011yescharacteristic
286C23×C59#12111yescharacteristic
287C23×C59#12111yescharacteristic
288C23×C59#12111yescharacteristic
289C23×C59#12111yescharacteristic
290C23×C59#12111yescharacteristic
291C23×C59#12111yescharacteristic
292C23×C59#12111yescharacteristic
293C23×C59#12111yescharacteristic
294C23×C59C22⋊Q811yescharacteristic
295C23×C59C22⋊Q811yescharacteristic
296C23×C59C22⋊Q811yescharacteristic
297C23×C59C22⋊Q811yescharacteristic
298C23×C59C22⋊Q811yescharacteristic
299C23×C59C22⋊Q811yescharacteristic
300C23×C59#12311yescharacteristic
301C23×C59#12311yescharacteristic
302C23×C59#12311yescharacteristic
303C23×C59#12311yescharacteristic
304C23×C59#12311yescharacteristic
305C23×C59#12411yescharacteristic
306C23×C59#12411yescharacteristic
307C23×C59#12411yescharacteristic
308C23×C59#12611yescharacteristic
309C23×C59#12611yescharacteristic
310C23×C59#12711yescharacteristic
311D4×C59—42no—
312D4×C59—42no—
313D4×C59—42no—
314D4×C59—42no—
315D4×C59—42no—
316D4×C59—42no—
317D4×C59—42no—
318D4×C59—42no—
319C2×C4×C59—24no—
320C2×C4×C59—24no—
321C2×C4×C59—24no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—24no—
326C2×C4×C59—42no—
327C2×C4×C59—44no—
328C2×C4×C59—42no—
329C2×C4×C59—44no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—42no—
333C2×C4×C59—44no—
334C2×C4×C59—44no—
335C2×C4×C59—44no—
336C2×C4×C59—42no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—44no—
342C2×C4×C59—42no—
343C2×C4×C59—42no—
344C2×C4×C59—44no—
345C2×C4×C59—42no—
346C2×C4×C59—42no—
347C2×C4×C59—44no—
348C2×C4×C59—42no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59—42no—
352C2×C4×C59—42no—
353C2×C4×C59—42no—
354C2×C4×C59—42no—
355C2×C4×C59—42no—
356C2×C4×C59—42no—
357C2×C4×C59—82no—
358C2×C4×C59—81no—
359C2×C4×C59—81no—
360C2×C4×C59—82no—
361C2×C4×C59—82no—
362C2×C4×C59—81no—
363C2×C4×C59—81no—
364C2×C4×C59—82no—
365#11087C5911yesmaximal, characteristic, direct product factor, Sylow
366C22×C59—22no—
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—22no—
372C22×C59—21no—
373C22×C59—21no—
374C22×C59—21no—
375C22×C59—21no—
376C22×C59—21no—
377C22×C59—21no—
378C22×C59—21no—
379C22×C59—21no—
380C22×C59—21no—
381C22×C59—21no—
382C22×C59—21no—
383C22×C59—21no—
384C22×C59—22no—
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—22no—
388C22×C59—22no—
389C22×C59—22no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59—41no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—41no—
400C22×C59—41no—
401C22×C59—41no—
402C22×C59—41no—
403C22×C59—41no—
404C22×C59—41no—
405C22×C59—41no—
406C22×C59—44no—
407C22×C59—44no—
408C22×C59—42no—
409C22×C59—82no—
410C22×C59—82no—
411C22×C59—82no—
412C22×C59—81no—
413C22×C59—81no—
414C22×C59—82no—
415C22×C59#38011yescharacteristic
416C22×C59#38511yescharacteristic
417C22×C59#38511yescharacteristic
418C22×C59#38611yescharacteristic
419C22×C59#38811yescharacteristic
420C22×C59#38811yescharacteristic
421C22×C59#39011yescharacteristic
422C22×C59#39211yescharacteristic
423C22×C59#39311yescharacteristic
424C22×C59#39411yescharacteristic
425C22×C59#39411yescharacteristic
426C22×C59#39611yescharacteristic
427C22×C59#39611yescharacteristic
428C22×C59#39711yescharacteristic
429C22×C59#39911yescharacteristic
430C22×C59B(4,𝔽2)12yes—
431C22×C59#45812yes—
432C4×C59—44no—
433C4×C59—42no—
434C4×C59—44no—
435C4×C59—82no—
436C4×C59—82no—
437C4×C59—81no—
438C4×C59—81no—
439C4×C59—82no—
440C22×#99C2×C5911yescharacteristic
441#2308C2×C5911yescharacteristic
442C2×#386C2×C5911yescharacteristic
443C2×#385C2×C5911yescharacteristic, complemented
444C2×#342C2×C5911yescharacteristic, complemented
445C2×#342C2×C5911yescharacteristic, complemented
446C22⋊#95C2×C5911yescharacteristic, complemented
447C2×C59—21no—
448C2×C59—21no—
449C2×C59—21no—
450C2×C59—21no—
451C2×C59—21no—
452C2×C59—21no—
453C2×C59—21no—
454C2×C59—21no—
455C2×C59—21no—
456C2×C59—21no—
457C2×C59—21no—
458C2×C59—21no—
459C2×C59—82no—
460C2×C59#143911yescharacteristic
461C2×C59#186712yes—
462C2×C59#202111yescharacteristic
463C2×C59#202211yescharacteristic
464C2×C59#204412yes—
465C23×D4C22×C5911yescharacteristic
466C24×C4C22×C5911yescharacteristic
467C22×C4⋊C4—21no—
468C22×C22⋊C4—21no—
469C22×C22⋊C4C22×C5911yescharacteristic
470C22×C22⋊C4C22×C5911yescharacteristic
471C22×C22⋊C4C22×C5911yescharacteristic
472C22×C22⋊C4C22×C5911yescharacteristic
473C22×C22⋊C4C22×C5911yescharacteristic
474C2×#99—22no—
475C2×#99—22no—
476C2×#99C4×C5914yescomplemented
477#386—21no—
478#386—21no—
479#386—22no—
480#386—22no—
481#386—22no—
482#385—22no—
483#385—22no—
484#381—21no—
485#379—21no—
486C2×#95—21no—
487C2×#95—21no—
488C2×#95—22no—
489#342—22no—
490#342—22no—
491C59#1108711yescharacteristic, direct product factor, Sylow
492C25D4×C5911yescharacteristic
493C25C23×C5911yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2×C4×C5912yes—
507C22×D4Q8×C5912yes—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—44no—
518C23×C4D4×C5911yescharacteristic
519C23×C4D4×C5911yescharacteristic
520C23×C4D4×C5911yescharacteristic
521C23×C4D4×C5912yes—
522C23×C4D4×C5912yes—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—44no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—44no—
554C2×C22⋊C4C2×C4×C5912yes—
555C2×C22⋊C4C2×C4×C5912yes—
556C2×C22⋊C4D4×C5912yes—
557C2×C22⋊C4D4×C5912yes—
558C2×C22⋊C4D4×C5912yes—
559#99—28no—
560#95—24no—
561#95—24no—
562#95—22no—
563#95—22no—
564#95—44no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24C4⋊C4×C5912yescomplemented
576C24C22×C4×C5911yescharacteristic
577C24C2×D4×C5911yescharacteristic
578C24C2×D4×C5911yescharacteristic
579C24C2×D4×C5911yescharacteristic
580C24C2×D4×C5911yescharacteristic
581C24C2×D4×C5911yescharacteristic
582C24C2×D4×C5911yescharacteristic
583C24C2×D4×C5911yescharacteristic
584C24C2×Q8×C5911yescharacteristic
585C24#41×C5911yescharacteristic
586C24#41×C5911yescharacteristic
587C24#41×C5911yescharacteristic
588C24#41×C5911yescharacteristic
589C24#41×C5911yescharacteristic
590C24#41×C5911yescharacteristic
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4C4⋊C4×C5912yescomplemented
671C4⋊C4—48no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—48no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4C22⋊C4×C5914yescomplemented
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—82no—
731C23—81no—
732C23—81no—
733C23—82no—
734C23C2×C22⋊C4×C5911yescharacteristic
735C23C2×C4⋊C4×C5911yescharacteristic
736C23#117×C5911yescharacteristic
737C23C4×D4×C5911yescharacteristic
738C23C4×D4×C5911yescharacteristic
739C23C4×D4×C5911yescharacteristic
740C23C4×D4×C5911yescharacteristic
741C23#120×C5911yescharacteristic
742C23#120×C5911yescharacteristic
743C23#120×C5911yescharacteristic
744C23#121×C5911yescharacteristic
745C23#121×C5911yescharacteristic
746C23#121×C5911yescharacteristic
747C23#121×C5911yescharacteristic
748C23#121×C5911yescharacteristic
749C23#121×C5911yescharacteristic
750C23#121×C5911yescharacteristic
751C23#121×C5911yescharacteristic
752C23C22⋊Q8×C5911yescharacteristic
753C23C22⋊Q8×C5911yescharacteristic
754C23C22⋊Q8×C5911yescharacteristic
755C23C22⋊Q8×C5911yescharacteristic
756C23C22⋊Q8×C5911yescharacteristic
757C23C22⋊Q8×C5911yescharacteristic
758C23#123×C5911yescharacteristic
759C23#123×C5911yescharacteristic
760C23#123×C5911yescharacteristic
761C23#123×C5911yescharacteristic
762C23#123×C5911yescharacteristic
763C23#124×C5911yescharacteristic
764C23#124×C5911yescharacteristic
765C23#124×C5911yescharacteristic
766C23#126×C5911yescharacteristic
767C23#126×C5911yescharacteristic
768C23#127×C5911yescharacteristic
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—82no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—81no—
870C22—81no—
871C22—82no—
872C22C59×#38011yescharacteristic
873C22C59×#38511yescharacteristic
874C22C59×#38511yescharacteristic
875C22C59×#38611yescharacteristic
876C22C59×#38811yescharacteristic
877C22C59×#38811yescharacteristic
878C22C59×#39011yescharacteristic
879C22C59×#39211yescharacteristic
880C22C59×#39311yescharacteristic
881C22C59×#39411yescharacteristic
882C22C59×#39411yescharacteristic
883C22C59×#39611yescharacteristic
884C22C59×#39611yescharacteristic
885C22C59×#39711yescharacteristic
886C22C59×#39911yescharacteristic
887C22C59×B(4,𝔽2)12yes—
888C22C59×#45812yes—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—82no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2C59×#143911yescharacteristic
911C2C59×#186712yes—
912C2C59×#202111yescharacteristic
913C2C59×#202211yescharacteristic
914C2C59×#204412yes—
subgroupG/H
center, socleC23×C59#120
commutatorC24C22×C4×C59
Frattini, cosocleC25C23×C59
prime radicalC23×D4×C59C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C25×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C59×#385C2semidirect
5. C2×C59×#342C2semidirect
6. C2×C59×#342C2semidirect
7. C59×C22⋊#95C2semidirect
19. C2×#99×C59C4semidirect
117. C24×C59C4⋊C4semidirect
212. C22×C4×C59C4⋊C4semidirect
236. C22⋊C4×C59C22⋊C4semidirect
365. #11087C59direct (N × H)
443. C2×#385C2×C59semidirect
444. C2×#342C2×C59semidirect
445. C2×#342C2×C59semidirect
446. C22⋊#95C2×C59semidirect
476. C2×#99C4×C59semidirect
491. C59#11087direct (N × H)
575. C24C4⋊C4×C59semidirect
670. C22×C4C4⋊C4×C59semidirect
694. C22⋊C4C22⋊C4×C59semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C592
C59×#23082
C2×C59×#3862
C2×C59×#3852
C2×C59×#3422
C59×C22⋊#952
#1108759