Finite Group Databasebeta

← C13×#14765 #15701104

Subgroups — C13×#14765 #15701104

Order 3328.

2154 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C13×#393C211yesmaximal, characteristic, complemented
3C2×C13×#388C212yesmaximal, complemented
4C2×C13×#386C211yesmaximal, characteristic
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
6C13×#1446C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1440C212yesmaximal, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1438C212yesmaximal
11C13×#1436C212yesmaximal, complemented
12C23×Q8×C13C2211yescharacteristic
13C23×D4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C2×C13×C22⋊Q8—24no—
16C2×C13×C22⋊Q8—28no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2212yes—
24C22×C13×C22⋊C4C2212yes—
25C22×C13×C22⋊C4C2212yes—
26C22×C42×C13C2212yes—
27C13×#393—24no—
28C13×#388—28no—
29C13×#386—24no—
30C4×C13×C22⋊C4—24no—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2211yescharacteristic
41C25×C13C2311yescharacteristic
42C25×C13C2311yescharacteristic
43C22×Q8×C13—24no—
44C22×Q8×C13—22no—
45C22×Q8×C13—22no—
46C22×Q8×C13—22no—
47C22×Q8×C13—42no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13—24no—
51C22×D4×C13—22no—
52C22×D4×C13—42no—
53C23×C4×C13—22no—
54C23×C4×C13—24no—
55C23×C4×C13—22no—
56C23×C4×C13—42no—
57C23×C4×C13D414yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2312yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2312yes—
63C23×C4×C13C2312yes—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C13×C22⋊Q8—232no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—24no—
72C2×C13×C4⋊C4D418yescomplemented
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4—24no—
80C2×C13×C22⋊C4—24no—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—24no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—24no—
87C2×C13×C22⋊C4—24no—
88C2×C13×C22⋊C4—24no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—42no—
92C2×C42×C13—24no—
93C2×C42×C13—24no—
94C2×C42×C13—42no—
95C13×#95—22no—
96C13×#95—22no—
97C13×#95—22no—
98C13×#95—24no—
99C13×#95—24no—
100C13×#95—24no—
101C13×#95—24no—
102C13×#95—24no—
103C13×#95—42no—
104C13×#95D414yescomplemented
105#14765C1311yesmaximal, characteristic, direct product factor, Sylow
106C24×C13—22no—
107C24×C13—21no—
108C24×C13—22no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—22no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—22no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—22no—
119C24×C13—21no—
120C24×C13—21no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—21no—
124C24×C13—21no—
125C24×C13C2×D412yes—
126C24×C13#4112yes—
127C24×C13#4114yes—
128C24×C13C2411yescharacteristic
129C2×Q8×C13—28no—
130C2×Q8×C13—48no—
131C2×Q8×C13—48no—
132C2×Q8×C13—44no—
133C2×Q8×C13—44no—
134C2×D4×C13—28no—
135C2×D4×C13—48no—
136C2×D4×C13—48no—
137C2×D4×C13—44no—
138C2×D4×C13—44no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—28no—
173C22×C4×C13—28no—
174C22×C4×C13—22no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—22no—
179C22×C4×C13—21no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—44no—
185C22×C4×C13—48no—
186C22×C4×C13—48no—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×D414yes—
189C22×C4×C13C2×D414yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×D414yes—
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2×D412yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4114yes—
196C22×C4×C13#4112yes—
197C13×C4⋊C4—28no—
198C13×C4⋊C4—216no—
199C13×C22⋊C4—216no—
200C13×C22⋊C4—216no—
201C13×C22⋊C4—216no—
202C13×C22⋊C4—48no—
203C13×C22⋊C4—44no—
204C13×C22⋊C4—44no—
205C13×C22⋊C4—44no—
206C42×C13—48no—
207C22×C22⋊Q8C2×C1311yescharacteristic, complemented
208C2×#393C2×C1311yescharacteristic, complemented
209C2×#388C2×C1312yescomplemented
210C2×#386C2×C1311yescharacteristic
211C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
212#1446C2×C1311yescharacteristic, complemented
213#1442C2×C1311yescharacteristic, complemented
214#1440C2×C1312yescomplemented
215#1439C2×C1311yescharacteristic, complemented
216#1438C2×C1312yes—
217#1436C2×C1312yescomplemented
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—24no—
221C23×C13—22no—
222C23×C13—24no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—24no—
234C23×C13—22no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13—42no—
238C23×C13—42no—
239C23×C13—42no—
240C23×C13—42no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—42no—
248C23×C13—41no—
249C23×C13—42no—
250C23×C13—42no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—42no—
255C23×C13—42no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13—41no—
259C23×C13—42no—
260C23×C13—42no—
261C23×C13—42no—
262C23×C13—41no—
263C23×C13#12414yes—
264C23×C13C22×D411yescharacteristic
265C23×C13C22×D412yes—
266C23×C13C22×D411yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C23×C13C2×#4112yes—
270C23×C13C2×#4112yes—
271C23×C13C2×#4111yescharacteristic
272C23×C13H(5,𝔽2)12yes—
273C23×C132−1+411yescharacteristic
274C23×C132−1+411yescharacteristic
275Q8×C13—416no—
276D4×C13—416no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—24no—
282C2×C4×C13—24no—
283C2×C4×C13—24no—
284C2×C4×C13—24no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—22no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—24no—
298C2×C4×C13—24no—
299C2×C4×C13—416no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—41no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—41no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—42no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—42no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13#12014yes—
330C2×C4×C13#12114yes—
331C23×Q8C22×C1311yescharacteristic
332C23×D4C22×C1311yescharacteristic
333C24×C4C22×C1311yescharacteristic
334C2×C22⋊Q8—24no—
335C2×C22⋊Q8—28no—
336C22×C4⋊C4C22×C1311yescharacteristic
337C22×C4⋊C4C22×C1312yes—
338C22×C22⋊C4C22×C1311yescharacteristic
339C22×C22⋊C4C22×C1312yes—
340C22×C22⋊C4C22×C1312yes—
341C22×C22⋊C4C22×C1312yes—
342C22×C22⋊C4C22×C1311yescharacteristic
343C22×C22⋊C4C22×C1311yescharacteristic
344C22×C22⋊C4C22×C1312yes—
345C22×C42C22×C1312yes—
346#393—24no—
347#388—28no—
348#386—24no—
349C4×C22⋊C4—24no—
350C2×#95C22×C1312yes—
351C2×#95C22×C1311yescharacteristic
352C2×#95C22×C1312yes—
353C2×#95C22×C1312yes—
354C2×#95C22×C1311yescharacteristic
355C2×#95C22×C1312yes—
356C2×#95C22×C1312yes—
357C2×#95C22×C1311yescharacteristic
358C2×#95C22×C1312yes—
359C2×#95C22×C1311yescharacteristic
360C22×C13—24no—
361C22×C13—24no—
362C22×C13—24no—
363C22×C13—44no—
364C22×C13—42no—
365C22×C13—42no—
366C22×C13—42no—
367C22×C13—42no—
368C22×C13—44no—
369C22×C13—44no—
370C22×C13—44no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—42no—
374C22×C13—44no—
375C22×C13—44no—
376C22×C13—82no—
377C22×C13—81no—
378C22×C13—81no—
379C22×C13—81no—
380C22×C13—81no—
381C22×C13—82no—
382C22×C13C2×#12011yescharacteristic
383C22×C13C2×#12111yescharacteristic
384C22×C13#52511yescharacteristic
385C22×C13#52512yes—
386C22×C13#52512yes—
387C22×C13C2×#12411yescharacteristic
388C22×C13#52912yes—
389C22×C13#53212yes—
390C22×C13#53211yescharacteristic
391C22×C13#53411yescharacteristic
392C22×C13#53611yescharacteristic
393C22×C13#53912yes—
394C22×C13#54212yes—
395C22×C13D4212yes—
396C22×C13#54612yes—
397C22×C13#54711yescharacteristic
398C22×C13#54812yes—
399C22×C13#54811yescharacteristic
400C22×C13#54812yes—
401C22×C13#55112yes—
402C22×C13#55112yes—
403C22×C13#55211yescharacteristic
404C22×C13#55611yescharacteristic
405C4×C13—24no—
406C4×C13—24no—
407C4×C13—42no—
408C4×C13—44no—
409C4×C13—44no—
410C4×C13—44no—
411C4×C13—44no—
412C4×C13—81no—
413C4×C13—81no—
414C25C23×C1311yescharacteristic
415C25C23×C1311yescharacteristic
416C22×Q8—24no—
417C22×Q8—22no—
418C22×Q8—22no—
419C22×Q8—22no—
420C22×Q8—42no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—24no—
424C22×D4—22no—
425C22×D4—42no—
426C23×C4—24no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—42no—
430C23×C4D4×C1314yes—
431C23×C4C23×C1311yescharacteristic
432C23×C4C23×C1311yescharacteristic
433C23×C4C23×C1312yes—
434C23×C4C23×C1312yes—
435C23×C4C23×C1312yes—
436C23×C4C23×C1312yes—
437C23×C4C23×C1311yescharacteristic
438C23×C4C23×C1311yescharacteristic
439C23×C4C23×C1311yescharacteristic
440C22⋊Q8—232no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4D4×C1318yescomplemented
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—42no—
465C2×C42—24no—
466C2×C42—24no—
467C2×C42—42no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—42no—
477#95D4×C1314yescomplemented
478C2×C13—44no—
479C2×C13—82no—
480C2×C13#238811yescharacteristic
481C2×C13#241011yescharacteristic
482C2×C13#241511yescharacteristic
483C2×C13#243611yescharacteristic
484C2×C13#246112yes—
485C2×C13#246312yes—
486C2×C13#247712yes—
487C2×C13#256012yes—
488C2×C13#256111yescharacteristic
489C2×C13#266311yescharacteristic
490C2×C13#285011yescharacteristic
491C24—22no—
492C24—21no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24C2×D4×C1312yes—
511C24C13×#4112yes—
512C24C13×#4114yes—
513C24C24×C1311yescharacteristic
514C2×Q8—28no—
515C2×Q8—48no—
516C2×Q8—48no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×D4—28no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—44no—
523C2×D4—44no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4C2×D4×C1314yes—
573C22×C4C2×D4×C1314yes—
574C22×C4C2×D4×C1314yes—
575C22×C4C2×D4×C1312yes—
576C22×C4C2×D4×C1314yes—
577C22×C4C2×D4×C1312yes—
578C22×C4C2×D4×C1312yes—
579C22×C4C13×#4112yes—
580C22×C4C13×#4114yes—
581C22×C4C13×#4112yes—
582C4⋊C4—28no—
583C4⋊C4—216no—
584C22⋊C4—216no—
585C22⋊C4—216no—
586C22⋊C4—216no—
587C22⋊C4—48no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C42—48no—
592C13#1476511yescharacteristic, direct product factor, Sylow
593C23—22no—
594C23—22no—
595C23—24no—
596C23—22no—
597C23—24no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23C13×#12414yes—
639C23C22×D4×C1311yescharacteristic
640C23C22×D4×C1312yes—
641C23C22×D4×C1311yescharacteristic
642C23C2×C13×#4111yescharacteristic
643C23C2×C13×#4111yescharacteristic
644C23C2×C13×#4112yes—
645C23C2×C13×#4112yes—
646C23C2×C13×#4111yescharacteristic
647C23C13×H(5,𝔽2)12yes—
648C23C13×2−1+411yescharacteristic
649C23C13×2−1+411yescharacteristic
650Q8—416no—
651D4—416no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4C13×#12014yes—
705C2×C4C13×#12114yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—82no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—82no—
728C22C2×C13×#12011yescharacteristic
729C22C2×C13×#12111yescharacteristic
730C22C13×#52511yescharacteristic
731C22C13×#52512yes—
732C22C13×#52512yes—
733C22C2×C13×#12411yescharacteristic
734C22C13×#52912yes—
735C22C13×#53212yes—
736C22C13×#53211yescharacteristic
737C22C13×#53411yescharacteristic
738C22C13×#53611yescharacteristic
739C22C13×#53912yes—
740C22C13×#54212yes—
741C22D42×C1312yes—
742C22C13×#54612yes—
743C22C13×#54711yescharacteristic
744C22C13×#54812yes—
745C22C13×#54811yescharacteristic
746C22C13×#54812yes—
747C22C13×#55112yes—
748C22C13×#55112yes—
749C22C13×#55211yescharacteristic
750C22C13×#55611yescharacteristic
751C4—24no—
752C4—24no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—44no—
757C4—44no—
758C4—81no—
759C4—81no—
760C2—44no—
761C2—82no—
762C2C13×#238811yescharacteristic
763C2C13×#241011yescharacteristic
764C2C13×#241511yescharacteristic
765C2C13×#243611yescharacteristic
766C2C13×#246112yes—
767C2C13×#246312yes—
768C2C13×#247712yes—
769C2C13×#256012yes—
770C2C13×#256111yescharacteristic
771C2C13×#266311yescharacteristic
772C2C13×#285011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×C22⋊Q8C2semidirect
2. C2×C13×#393C2semidirect
3. C2×C13×#388C2semidirect
5. C2×C4×C13×C22⋊C4C2semidirect
6. C13×#1446C2semidirect
7. C13×#1442C2semidirect
8. C13×#1440C2semidirect
9. C13×#1439C2semidirect
11. C13×#1436C2semidirect
72. C2×C13×C4⋊C4D4semidirect
104. C13×#95D4semidirect
105. #14765C13direct (N × H)
207. C22×C22⋊Q8C2×C13semidirect
208. C2×#393C2×C13semidirect
209. C2×#388C2×C13semidirect
211. C2×C4×C22⋊C4C2×C13semidirect
212. #1446C2×C13semidirect
213. #1442C2×C13semidirect
214. #1440C2×C13semidirect
215. #1439C2×C13semidirect
217. #1436C2×C13semidirect
445. C2×C4⋊C4D4×C13semidirect
477. #95D4×C13semidirect
592. C13#14765direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#3932
C2×C13×#3882
C2×C13×#3862
C2×C4×C13×C22⋊C42
C13×#14462
C13×#14422
C13×#14402
C13×#14392
C13×#14382
C13×#14362
#1476513