Finite Group Databasebeta

← C13×#24056 #15710395

Subgroups — C13×#24056 #15710395

Order 3328.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3484C211yesmaximal, characteristic
2C13×#2849C212yesmaximal, complemented
3C2×C13×#386C211yesmaximal, characteristic, complemented
4C13×#2044C214yesmaximal, complemented
5C13×#1898C212yesmaximal, complemented
6C13×#1867C212yesmaximal, complemented
7C13×#1790C212yesmaximal, complemented
8C13×#1781C211yesmaximal, characteristic, complemented
9C2×C13×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic, complemented
12C13×#546—22no—
13C13×#546—22no—
14D42×C13—22no—
15D42×C13—22no—
16C13×#535—21no—
17C13×#534—21no—
18C13×#534C2212yes—
19C13×#525—21no—
20C2×C13×#123—22no—
21C2×C13×#120—21no—
22C2×C13×#120C2212yes—
23C13×#518C2211yescharacteristic
24C22×C13×C22⋊C4—21no—
25C22×C13×C22⋊C4C2211yescharacteristic, complemented
26C2×C13×#99C2212yes—
27C2×C13×#99C2212yescomplemented
28C2×C13×#99C2214yescomplemented
29C13×#386—21no—
30C13×#386—21no—
31C13×#386—22no—
32C13×#386C2212yes—
33C13×#386C2212yescomplemented
34C13×#386C2214yescomplemented
35C13×#385—22no—
36C13×#385C2214yescomplemented
37C13×#381—22no—
38C13×#379C2212yescomplemented
39C2×C13×#95—21no—
40C13×#342C2214yescomplemented
41C25×C13D411yescharacteristic
42C25×C13C2311yescharacteristic
43C13×H(5,𝔽2)—24no—
44C13×H(5,𝔽2)—42no—
45C2×C13×#41—21no—
46C2×C13×#41—22no—
47C22×D4×C13—21no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13—22no—
51C22×D4×C13—21no—
52C22×D4×C13—21no—
53C22×D4×C13—24no—
54C22×D4×C13—42no—
55C22×D4×C13D411yescharacteristic
56C22×D4×C13D411yescharacteristic
57C22×D4×C13D412yes—
58C22×D4×C13D412yes—
59C22×D4×C13C2312yes—
60C22×D4×C13C2311yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—22no—
63C23×C4×C13—21no—
64C23×C4×C13—22no—
65C23×C4×C13—21no—
66C23×C4×C13—21no—
67C23×C4×C13—44no—
68C23×C4×C13D411yescharacteristic
69C23×C4×C13C2312yes—
70C13×#127—22no—
71C13×#124—22no—
72C13×#123—22no—
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—48no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—21no—
78C13×#121—21no—
79C13×#121—21no—
80C13×#121—22no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#120—22no—
87C13×#120—22no—
88C13×#120—22no—
89C13×#120—22no—
90C13×#120—22no—
91C13×#120—22no—
92C13×#120—22no—
93C13×#120—22no—
94C13×#120—22no—
95C4×D4×C13—22no—
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C13×#117—21no—
100C2×C13×C4⋊C4—24no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4—42no—
111C2×C13×C22⋊C4—44no—
112C2×C13×C22⋊C4D412yes—
113C2×C13×C22⋊C4D412yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C13×C22⋊C4C2312yes—
116C2×C13×C22⋊C4C2312yes—
117C13×#99—24no—
118C13×#99—42no—
119C13×#99—44no—
120C13×#95—24no—
121C13×#95—24no—
122C13×#95—22no—
123C13×#95—22no—
124#24056C1311yesmaximal, characteristic, direct product factor, Sylow
125C24×C13—22no—
126C24×C13—22no—
127C24×C13—21no—
128C24×C13—22no—
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—42no—
132C24×C13—42no—
133C24×C13—41no—
134C24×C13—42no—
135C24×C13—42no—
136C24×C13C2×D411yescharacteristic
137C24×C13C2×D412yes—
138C24×C13C2×D412yes—
139C24×C13C2×D411yescharacteristic
140C24×C13C2×D412yes—
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C24×C13C2411yescharacteristic
144C13×#41—48no—
145C13×#41—42no—
146C13×#41—42no—
147C2×Q8×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—21no—
152C2×D4×C13—22no—
153C2×D4×C13—22no—
154C2×D4×C13—22no—
155C2×D4×C13—22no—
156C2×D4×C13—22no—
157C2×D4×C13—22no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—22no—
161C2×D4×C13—24no—
162C2×D4×C13—22no—
163C2×D4×C13—24no—
164C2×D4×C13—22no—
165C2×D4×C13—22no—
166C2×D4×C13—22no—
167C2×D4×C13—22no—
168C2×D4×C13—22no—
169C2×D4×C13—41no—
170C2×D4×C13—41no—
171C2×D4×C13—48no—
172C2×D4×C13—48no—
173C2×D4×C13—48no—
174C2×D4×C13—42no—
175C2×D4×C13—42no—
176C2×D4×C13—44no—
177C2×D4×C13—44no—
178C2×D4×C13—82no—
179C2×D4×C13—82no—
180C2×D4×C13#4114yes—
181C22×C4×C13—21no—
182C22×C4×C13—24no—
183C22×C4×C13—22no—
184C22×C4×C13—28no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—22no—
188C22×C4×C13—24no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—22no—
192C22×C4×C13—24no—
193C22×C4×C13—22no—
194C22×C4×C13—44no—
195C22×C4×C13—41no—
196C22×C4×C13—44no—
197C22×C4×C13—48no—
198C22×C4×C13—42no—
199C22×C4×C13—44no—
200C22×C4×C13—42no—
201C22×C4×C13—41no—
202C22×C4×C13—41no—
203C22×C4×C13—42no—
204C22×C4×C13—42no—
205C22×C4×C13—42no—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×D412yes—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—22no—
214C13×C4⋊C4—22no—
215C13×C4⋊C4—48no—
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—22no—
226C13×C22⋊C4—22no—
227C13×C22⋊C4—24no—
228C13×C22⋊C4—24no—
229C13×C22⋊C4—24no—
230C13×C22⋊C4—44no—
231C13×C22⋊C4—44no—
232C13×C22⋊C4—48no—
233C13×C22⋊C4—44no—
234C13×C22⋊C4—42no—
235C13×C22⋊C4—44no—
236C42×C13—22no—
237#3484C2×C1311yescharacteristic
238#2849C2×C1312yescomplemented
239C2×#386C2×C1311yescharacteristic, complemented
240#2044C2×C1314yescomplemented
241#1898C2×C1312yescomplemented
242#1867C2×C1312yescomplemented
243#1790C2×C1312yescomplemented
244#1781C2×C1311yescharacteristic, complemented
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—22no—
248C23×C13—22no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—24no—
255C23×C13—24no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—22no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—24no—
262C23×C13—42no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—42no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—42no—
269C23×C13—42no—
270C23×C13—48no—
271C23×C13—48no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—48no—
277C23×C13—42no—
278C23×C13—42no—
279C23×C13—42no—
280C23×C13—42no—
281C23×C13—42no—
282C23×C13—81no—
283C23×C13—81no—
284C23×C13—84no—
285C23×C13—81no—
286C23×C13—81no—
287C23×C13#12012yes—
288C23×C13#12011yescharacteristic
289C23×C13#12011yescharacteristic
290C23×C13#12312yescomplemented
291C23×C13C22×D411yescharacteristic
292C23×C13C22×D412yes—
293C23×C13C2×#4112yes—
294C23×C13H(5,𝔽2)12yes—
295Q8×C13—42no—
296D4×C13—28no—
297D4×C13—44no—
298D4×C13—42no—
299D4×C13—44no—
300D4×C13—44no—
301D4×C13—42no—
302D4×C13—42no—
303D4×C13—44no—
304D4×C13—44no—
305D4×C13—44no—
306D4×C13—44no—
307D4×C13—82no—
308D4×C13—82no—
309D4×C13—82no—
310D4×C13—82no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—24no—
314C2×C4×C13—28no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—24no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—44no—
325C2×C4×C13—44no—
326C2×C4×C13—42no—
327C2×C4×C13—44no—
328C2×C4×C13—48no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—44no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—44no—
335C2×C4×C13—42no—
336C2×C4×C13—44no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—44no—
340C2×C4×C13—81no—
341C2×C4×C13—81no—
342C2×C4×C13—84no—
343C2×C4×C13#12312yescomplemented
344C2×H(5,𝔽2)C22×C1311yescharacteristic
345C23×D4C22×C1311yescharacteristic
346C24×C4C22×C1311yescharacteristic, complemented
347#546—22no—
348#546—22no—
349D42—22no—
350D42—22no—
351#535—21no—
352#534—21no—
353#534C22×C1312yes—
354#525—21no—
355C2×#123—22no—
356C2×#120—21no—
357C2×#120C22×C1312yes—
358#518C22×C1311yescharacteristic
359C22×C22⋊C4—21no—
360C22×C22⋊C4C22×C1311yescharacteristic, complemented
361C2×#99C22×C1312yes—
362C2×#99C22×C1314yescomplemented
363C2×#99C22×C1312yescomplemented
364#386—22no—
365#386—21no—
366#386—21no—
367#386C22×C1312yes—
368#386C22×C1314yescomplemented
369#386C22×C1312yescomplemented
370#385—22no—
371#385C22×C1314yescomplemented
372#381—22no—
373#379C22×C1312yescomplemented
374C2×#95—21no—
375#342C22×C1314yescomplemented
376C22×C13—24no—
377C22×C13—24no—
378C22×C13—21no—
379C22×C13—21no—
380C22×C13—22no—
381C22×C13—21no—
382C22×C13—21no—
383C22×C13—22no—
384C22×C13—21no—
385C22×C13—21no—
386C22×C13—22no—
387C22×C13—22no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—48no—
393C22×C13—48no—
394C22×C13—42no—
395C22×C13—42no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—42no—
401C22×C13—41no—
402C22×C13—42no—
403C22×C13—41no—
404C22×C13—42no—
405C22×C13—41no—
406C22×C13—81no—
407C22×C13—84no—
408C22×C13—84no—
409C22×C13—84no—
410C22×C13—81no—
411C22×C13—162no—
412C22×C13B(4,𝔽2)12yes—
413C22×C13#45812yes—
414C22×C13C2×#12011yescharacteristic
415C22×C13C2×#12311yescharacteristic
416C22×C13#53411yescharacteristic
417C22×C13#54614yes—
418C4×C13—22no—
419C4×C13—41no—
420C4×C13—42no—
421C4×C13—44no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13—84no—
425C4×C13—82no—
426C25D4×C1311yescharacteristic
427C25C23×C1311yescharacteristic
428H(5,𝔽2)—24no—
429H(5,𝔽2)—42no—
430C2×#41—21no—
431C2×#41—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—24no—
439C22×D4—42no—
440C22×D4D4×C1311yescharacteristic
441C22×D4D4×C1311yescharacteristic
442C22×D4D4×C1312yes—
443C22×D4D4×C1312yes—
444C22×D4C23×C1312yes—
445C22×D4C23×C1311yescharacteristic
446C22×D4C23×C1311yescharacteristic
447C23×C4—21no—
448C23×C4—22no—
449C23×C4—21no—
450C23×C4—22no—
451C23×C4—21no—
452C23×C4—44no—
453C23×C4D4×C1311yescharacteristic
454C23×C4C23×C1312yes—
455#127—22no—
456#124—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—48no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463#121—21no—
464#121—21no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—22no—
469#121—22no—
470#121—22no—
471#120—22no—
472#120—22no—
473#120—22no—
474#120—22no—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—22no—
479#120—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484#117—21no—
485C2×C4⋊C4—24no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—44no—
497C2×C22⋊C4D4×C1312yes—
498C2×C22⋊C4D4×C1312yes—
499C2×C22⋊C4C23×C1312yes—
500C2×C22⋊C4C23×C1314yes—
501C2×C22⋊C4C23×C1312yes—
502#99—24no—
503#99—42no—
504#99—44no—
505#95—22no—
506#95—22no—
507#95—24no—
508#95—24no—
509C2×C13—21no—
510C2×C13—24no—
511C2×C13—21no—
512C2×C13—22no—
513C2×C13—22no—
514C2×C13—42no—
515C2×C13—42no—
516C2×C13—81no—
517C2×C13—82no—
518C2×C13#240511yescharacteristic
519C2×C13C2×B(4,𝔽2)11yescharacteristic
520C2×C13C2×#45811yescharacteristic
521C24—22no—
522C24—22no—
523C24—21no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—42no—
528C24—42no—
529C24—41no—
530C24—42no—
531C24—42no—
532C24C2×D4×C1311yescharacteristic
533C24C2×D4×C1312yes—
534C24C2×D4×C1312yes—
535C24C2×D4×C1311yescharacteristic
536C24C2×D4×C1312yes—
537C24C2×D4×C1311yescharacteristic
538C24C2×D4×C1311yescharacteristic
539C24C24×C1311yescharacteristic
540#41—48no—
541#41—42no—
542#41—42no—
543C2×Q8—21no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—24no—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4C13×#4114yes—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—41no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C1312yes—
603C22×C4C2×D4×C1311yescharacteristic
604C22×C4C2×D4×C1311yescharacteristic
605C22×C4C2×D4×C1312yes—
606C22×C4C2×D4×C1312yes—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—48no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—48no—
629C22⋊C4—42no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C42—22no—
633C13#2405611yescharacteristic, direct product factor, Sylow
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23C13×#12012yes—
677C23C13×#12011yescharacteristic
678C23C13×#12011yescharacteristic
679C23C13×#12312yescomplemented
680C23C22×D4×C1311yescharacteristic
681C23C22×D4×C1312yes—
682C23C2×C13×#4112yes—
683C23C13×H(5,𝔽2)12yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4C13×#12312yescomplemented
733C22—24no—
734C22—24no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—84no—
767C22—81no—
768C22—162no—
769C22C13×B(4,𝔽2)12yes—
770C22C13×#45812yes—
771C22C2×C13×#12011yescharacteristic
772C22C2×C13×#12311yescharacteristic
773C22C13×#53411yescharacteristic
774C22C13×#54614yes—
775C4—22no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—84no—
782C4—82no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C13×#240511yescharacteristic
793C2C2×C13×B(4,𝔽2)11yescharacteristic
794C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2849C2semidirect
3. C2×C13×#386C2semidirect
4. C13×#2044C2semidirect
5. C13×#1898C2semidirect
6. C13×#1867C2semidirect
7. C13×#1790C2semidirect
8. C13×#1781C2semidirect
11. C24×C4×C13C22semidirect
25. C22×C13×C22⋊C4C22semidirect
27. C2×C13×#99C22semidirect
28. C2×C13×#99C22semidirect
33. C13×#386C22semidirect
34. C13×#386C22semidirect
36. C13×#385C22semidirect
38. C13×#379C22semidirect
40. C13×#342C22semidirect
124. #24056C13direct (N × H)
238. #2849C2×C13semidirect
239. C2×#386C2×C13semidirect
240. #2044C2×C13semidirect
241. #1898C2×C13semidirect
242. #1867C2×C13semidirect
243. #1790C2×C13semidirect
244. #1781C2×C13semidirect
290. C23×C13#123semidirect
343. C2×C4×C13#123semidirect
346. C24×C4C22×C13semidirect
360. C22×C22⋊C4C22×C13semidirect
362. C2×#99C22×C13semidirect
363. C2×#99C22×C13semidirect
368. #386C22×C13semidirect
369. #386C22×C13semidirect
371. #385C22×C13semidirect
373. #379C22×C13semidirect
375. #342C22×C13semidirect
633. C13#24056direct (N × H)
679. C23C13×#123semidirect
732. C2×C4C13×#123semidirect

Maximal subgroups

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

subgroupindex
C13×#34842
C13×#28492
C2×C13×#3862
C13×#20442
C13×#18982
C13×#18672
C13×#17902
C13×#17812
#2405613