Finite Group Databasebeta

← C13×#25565 #15711904

Subgroups — C13×#25565 #15711904

Order 3328.

1312 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3490C211yesmaximal, characteristic
2C13×#2483C211yesmaximal, characteristic, complemented
3C13×#2412C212yesmaximal, complemented
4C13×#2062C211yesmaximal, characteristic, complemented
5C13×#2044C211yesmaximal, characteristic, complemented
6C13×#2030C211yesmaximal, characteristic, complemented
7C13×#2022C211yesmaximal, characteristic, complemented
8C13×#1898C212yesmaximal, complemented
9C13×#1890C212yesmaximal, complemented
10C13×#1867C212yesmaximal, complemented
11C2×C13×#342C211yesmaximal, characteristic, complemented
12C13×#551—22no—
13C13×#551—22no—
14C13×#546—22no—
15C13×#546—22no—
16C13×#543C2211yescharacteristic
17C13×#538—21no—
18C13×#538—21no—
19C13×#534C2211yescharacteristic
20C13×#525—21no—
21C13×#525—21no—
22C2×C13×#123C2212yes—
23C2×C13×#120C2212yes—
24C13×#518C2212yes—
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2212yes—
28C2×C13×#99C2212yes—
29C2×C13×#99C2212yes—
30C13×#397—22no—
31C13×#397—21no—
32C13×#397—21no—
33C13×#394—22no—
34C13×#386—22no—
35C13×#386C2212yes—
36C13×#385—21no—
37C13×#385C2211yescharacteristic
38C13×#385C2212yes—
39C13×#385C2211yescharacteristic
40C13×#381—21no—
41C13×#381C2211yescharacteristic
42C13×#381C2212yes—
43C13×#381C2211yescharacteristic
44C13×#380—22no—
45C13×#379C2211yescharacteristic
46C13×#342C2211yescharacteristic
47C13×#342C2211yescharacteristic
48C13×#342C2212yes—
49C13×#342C2212yes—
50C13×#342C2212yes—
51C25×C13C2311yescharacteristic
52C2×C13×#41—21no—
53C2×C13×#41—21no—
54C22×D4×C13D412yes—
55C22×D4×C13D412yes—
56C22×D4×C13C2312yes—
57C23×C4×C13—22no—
58C23×C4×C13D411yescharacteristic
59C23×C4×C13D411yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C13×#126—22no—
63C13×#126—22no—
64C13×#124—22no—
65C13×#124—22no—
66C13×#123—22no—
67C13×#123—22no—
68C13×#123—22no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—24no—
72C13×#123—42no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121—21no—
84C13×#121—21no—
85C13×#120—22no—
86C13×#120—22no—
87C13×#120—22no—
88C13×#120—22no—
89C13×#120—22no—
90C4×D4×C13—22no—
91C4×D4×C13—22no—
92C4×D4×C13—22no—
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C13×#117—21no—
97C13×#117—21no—
98C13×#117—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—21no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—42no—
117C2×C13×C22⋊C4D412yes—
118C2×C13×C22⋊C4D411yescharacteristic
119C2×C13×C22⋊C4D411yescharacteristic
120C2×C13×C22⋊C4D412yes—
121C2×C13×C22⋊C4C2311yescharacteristic
122C2×C13×C22⋊C4C2311yescharacteristic
123C2×C13×C22⋊C4C2312yes—
124C2×C13×C22⋊C4C2311yescharacteristic
125C2×C13×C22⋊C4C2311yescharacteristic
126C2×C13×C22⋊C4C2312yes—
127C2×C13×C22⋊C4C2312yes—
128C13×#99—24no—
129C13×#99—42no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—21no—
133C13×#95—21no—
134C13×#95—21no—
135C13×#95—21no—
136C13×#95—21no—
137C13×#95—21no—
138C13×#95—22no—
139C13×#95—22no—
140#25565C1311yesmaximal, characteristic, direct product factor, Sylow
141C24×C13—22no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—42no—
145C24×C13—81no—
146C24×C13C2×D412yes—
147C24×C13C2×D411yescharacteristic
148C24×C13C2×D412yes—
149C24×C13C2×D412yes—
150C24×C13C2×D411yescharacteristic
151C24×C13C2411yescharacteristic
152C13×#41—82no—
153C13×#41—82no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×D4×C13—22no—
157C2×D4×C13—22no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—22no—
161C2×D4×C13—22no—
162C2×D4×C13—22no—
163C2×D4×C13—22no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13—22no—
167C2×D4×C13—22no—
168C2×D4×C13—44no—
169C2×D4×C13—82no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—21no—
184C22×C4×C13—22no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—44no—
188C22×C4×C13—42no—
189C22×C4×C13—44no—
190C22×C4×C13—81no—
191C22×C4×C13—81no—
192C22×C4×C13—82no—
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D411yescharacteristic
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—44no—
209C13×C4⋊C4—82no—
210C13×C4⋊C4—81no—
211C13×C4⋊C4—81no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
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—22no—
228C13×C22⋊C4—22no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—22no—
231C13×C22⋊C4—21no—
232C13×C22⋊C4—44no—
233C13×C22⋊C4—44no—
234C13×C22⋊C4—42no—
235C13×C22⋊C4—42no—
236C13×C22⋊C4—41no—
237C13×C22⋊C4—41no—
238C13×C22⋊C4—81no—
239C13×C22⋊C4—82no—
240C13×C22⋊C4#4114yescomplemented
241C42×C13—22no—
242C42×C13—22no—
243#3490C2×C1311yescharacteristic
244#2483C2×C1311yescharacteristic, complemented
245#2412C2×C1312yescomplemented
246#2062C2×C1311yescharacteristic, complemented
247#2044C2×C1311yescharacteristic, complemented
248#2030C2×C1311yescharacteristic, complemented
249#2022C2×C1311yescharacteristic, complemented
250#1898C2×C1312yescomplemented
251#1890C2×C1312yescomplemented
252#1867C2×C1312yescomplemented
253C2×#342C2×C1311yescharacteristic, complemented
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—24no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—41no—
268C23×C13—42no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—42no—
273C23×C13—41no—
274C23×C13—42no—
275C23×C13—42no—
276C23×C13—42no—
277C23×C13—84no—
278C23×C13—82no—
279C23×C13—82no—
280C23×C13#12012yes—
281C23×C13#12011yescharacteristic
282C23×C13#12011yescharacteristic
283C23×C13C22×D411yescharacteristic
284C23×C13C22×D412yes—
285C23×C13C2×#4112yes—
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C132−1+411yescharacteristic
288Q8×C13—81no—
289Q8×C13—81no—
290D4×C13—44no—
291D4×C13—42no—
292D4×C13—42no—
293D4×C13—42no—
294D4×C13—42no—
295D4×C13—44no—
296D4×C13—82no—
297D4×C13—82no—
298D4×C13—81no—
299D4×C13—81no—
300C2×C4×C13—22no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—24no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—42no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—42no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—81no—
340C2×C4×C13—81no—
341C2×C4×C13—82no—
342C2×C4×C13—82no—
343C2×C4×C13—88no—
344#551—22no—
345#551—22no—
346#546—22no—
347#546—22no—
348#543C22×C1311yescharacteristic
349#538—21no—
350#538—21no—
351#534C22×C1311yescharacteristic
352#525—21no—
353#525—21no—
354C2×#123C22×C1312yes—
355C2×#120C22×C1312yes—
356#518C22×C1312yes—
357C22×C22⋊C4C22×C1311yescharacteristic
358C22×C22⋊C4C22×C1311yescharacteristic
359C22×C22⋊C4C22×C1312yes—
360C2×#99C22×C1312yes—
361C2×#99C22×C1312yes—
362#397—22no—
363#397—21no—
364#397—21no—
365#394—22no—
366#386—22no—
367#386C22×C1312yes—
368#385—21no—
369#385C22×C1312yes—
370#385C22×C1311yescharacteristic
371#385C22×C1311yescharacteristic
372#381—21no—
373#381C22×C1311yescharacteristic
374#381C22×C1312yes—
375#381C22×C1311yescharacteristic
376#380—22no—
377#379C22×C1311yescharacteristic
378#342C22×C1312yes—
379#342C22×C1311yescharacteristic
380#342C22×C1312yes—
381#342C22×C1312yes—
382#342C22×C1311yescharacteristic
383C22×C13—21no—
384C22×C13—21no—
385C22×C13—22no—
386C22×C13—21no—
387C22×C13—22no—
388C22×C13—21no—
389C22×C13—21no—
390C22×C13—22no—
391C22×C13—21no—
392C22×C13—22no—
393C22×C13—21no—
394C22×C13—22no—
395C22×C13—42no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—44no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—44no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—82no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13—82no—
409C22×C13—82no—
410C22×C13—82no—
411C22×C13#45812yes—
412C22×C13C2×#12011yescharacteristic
413C22×C13#53211yescharacteristic
414C22×C13#53711yescharacteristic
415C22×C13#54612yes—
416C22×C13#54712yes—
417C4×C13—44no—
418C4×C13—42no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—42no—
422C4×C13—41no—
423C4×C13—41no—
424C4×C13—42no—
425C4×C13—81no—
426C4×C13—81no—
427C4×C13—82no—
428C4×C13—81no—
429C4×C13—81no—
430C25C23×C1311yescharacteristic
431C2×#41—21no—
432C2×#41—21no—
433C22×D4D4×C1312yes—
434C22×D4D4×C1312yes—
435C22×D4C23×C1312yes—
436C23×C4—22no—
437C23×C4D4×C1311yescharacteristic
438C23×C4D4×C1311yescharacteristic
439C23×C4C23×C1311yescharacteristic
440C23×C4C23×C1311yescharacteristic
441#126—22no—
442#126—22no—
443#124—22no—
444#124—22no—
445#123—22no—
446#123—22no—
447#123—22no—
448#123—22no—
449#123—22no—
450#123—24no—
451#123—42no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458#121—21no—
459#121—21no—
460#121—22no—
461#121—22no—
462#121—21no—
463#121—21no—
464#120—22no—
465#120—22no—
466#120—22no—
467#120—22no—
468#120—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475#117—21no—
476#117—21no—
477#117—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4D4×C1311yescharacteristic
497C2×C22⋊C4D4×C1311yescharacteristic
498C2×C22⋊C4D4×C1312yes—
499C2×C22⋊C4D4×C1312yes—
500C2×C22⋊C4C23×C1312yes—
501C2×C22⋊C4C23×C1311yescharacteristic
502C2×C22⋊C4C23×C1311yescharacteristic
503C2×C22⋊C4C23×C1311yescharacteristic
504C2×C22⋊C4C23×C1311yescharacteristic
505C2×C22⋊C4C23×C1312yes—
506C2×C22⋊C4C23×C1312yes—
507#99—24no—
508#99—42no—
509#95—22no—
510#95—22no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—22no—
519C2×C13—22no—
520C2×C13—21no—
521C2×C13—21no—
522C2×C13—22no—
523C2×C13—22no—
524C2×C13—41no—
525C2×C13—42no—
526C2×C13—82no—
527C2×C13#243011yescharacteristic
528C2×C13C2×#45811yescharacteristic
529C2×C13#302611yescharacteristic
530C24—22no—
531C24—21no—
532C24—21no—
533C24—42no—
534C24—81no—
535C24C2×D4×C1312yes—
536C24C2×D4×C1311yescharacteristic
537C24C2×D4×C1312yes—
538C24C2×D4×C1312yes—
539C24C2×D4×C1311yescharacteristic
540C24C24×C1311yescharacteristic
541#41—82no—
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—44no—
558C2×D4—82no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—44no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—82no—
582C22×C4C2×D4×C1312yes—
583C22×C4C2×D4×C1311yescharacteristic
584C22×C4C2×D4×C1312yes—
585C22×C4C2×D4×C1311yescharacteristic
586C22×C4C2×D4×C1311yescharacteristic
587C22×C4C2×D4×C1312yes—
588C22×C4C2×D4×C1311yescharacteristic
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—44no—
598C4⋊C4—82no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—81no—
628C22⋊C4—82no—
629C22⋊C4C13×#4114yescomplemented
630C42—22no—
631C42—22no—
632C13#2556511yescharacteristic, direct product factor, Sylow
633C23—22no—
634C23—24no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—84no—
657C23—82no—
658C23—82no—
659C23C13×#12012yes—
660C23C13×#12011yescharacteristic
661C23C13×#12011yescharacteristic
662C23C22×D4×C1311yescharacteristic
663C23C22×D4×C1312yes—
664C23C2×C13×#4112yes—
665C23C13×H(5,𝔽2)11yescharacteristic
666C23C13×2−1+411yescharacteristic
667Q8—81no—
668Q8—81no—
669D4—44no—
670D4—44no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—82no—
676D4—82no—
677D4—81no—
678D4—81no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—88no—
723C22—21no—
724C22—22no—
725C22—21no—
726C22—22no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—21no—
732C22—22no—
733C22—21no—
734C22—22no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22C13×#45812yes—
752C22C2×C13×#12011yescharacteristic
753C22C13×#53211yescharacteristic
754C22C13×#53711yescharacteristic
755C22C13×#54612yes—
756C22C13×#54712yes—
757C4—44no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4—82no—
768C4—81no—
769C4—81no—
770C2—22no—
771C2—21no—
772C2—21no—
773C2—22no—
774C2—22no—
775C2—41no—
776C2—42no—
777C2—82no—
778C2C13×#243011yescharacteristic
779C2C2×C13×#45811yescharacteristic
780C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3490C2
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×#2483C2semidirect
3. C13×#2412C2semidirect
4. C13×#2062C2semidirect
5. C13×#2044C2semidirect
6. C13×#2030C2semidirect
7. C13×#2022C2semidirect
8. C13×#1898C2semidirect
9. C13×#1890C2semidirect
10. C13×#1867C2semidirect
11. C2×C13×#342C2semidirect
140. #25565C13direct (N × H)
240. C13×C22⋊C4#41semidirect
244. #2483C2×C13semidirect
245. #2412C2×C13semidirect
246. #2062C2×C13semidirect
247. #2044C2×C13semidirect
248. #2030C2×C13semidirect
249. #2022C2×C13semidirect
250. #1898C2×C13semidirect
251. #1890C2×C13semidirect
252. #1867C2×C13semidirect
253. C2×#342C2×C13semidirect
629. C22⋊C4C13×#41semidirect
632. C13#25565direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34902
C13×#24832
C13×#24122
C13×#20622
C13×#20442
C13×#20302
C13×#20222
C13×#18982
C13×#18902
C13×#18672
C2×C13×#3422
#2556513