Finite Group Databasebeta

← C13×#24140 #15710479

Subgroups — C13×#24140 #15710479

Order 3328.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3505C211yesmaximal, characteristic, complemented
2C13×#2848C211yesmaximal, characteristic, complemented
3C13×#2847C211yesmaximal, characteristic, complemented
4C4×C13×#120C211yesmaximal, characteristic, complemented
5C13×#2044C212yesmaximal, complemented
6C13×#2021C212yesmaximal, complemented
7C13×#1996C211yesmaximal, characteristic, complemented
8C13×#1964C211yesmaximal, characteristic, complemented
9C13×#1889C212yesmaximal, complemented
10C13×#1867C212yesmaximal, complemented
11C13×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C13×#553—21no—
14C13×#553—22no—
15C13×#552—21no—
16C13×#551—22no—
17C13×#548—21no—
18C13×#546—21no—
19C13×#539—21no—
20C13×#538—21no—
21C13×#534C2212yes—
22C13×#529—21no—
23C13×#525—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×#121—21no—
27C2×C13×#121C2211yescharacteristic
28C2×C13×#120C2211yescharacteristic
29C2×C13×#120C2212yes—
30C13×#518C2212yes—
31C2×C4×D4×C13—21no—
32C2×C4×D4×C13C2211yescharacteristic
33C2×C13×#99C2212yes—
34C2×C13×#99C2212yes—
35C2×C13×#99C2212yes—
36C13×#386—21no—
37C13×#386—22no—
38C13×#386C2211yescharacteristic
39C13×#386C2212yes—
40C13×#385—21no—
41C13×#385—22no—
42C13×#385C2211yescharacteristic
43C13×#385C2212yes—
44C13×#380—21no—
45C13×#380—21no—
46C13×#380C2211yescharacteristic
47C13×#380C2211yescharacteristic
48C13×#379C2212yes—
49C13×#379C2211yescharacteristic
50C4×C13×C22⋊C4—21no—
51C4×C13×C22⋊C4C2211yescharacteristic
52C13×#342C2212yes—
53C13×#342C2212yes—
54C13×#342C2212yes—
55C25×C13C2311yescharacteristic
56C2×C13×#41—21no—
57C22×Q8×C13D411yescharacteristic, complemented
58C22×D4×C13—21no—
59C22×D4×C13—22no—
60C22×D4×C13D411yescharacteristic, complemented
61C22×D4×C13C2311yescharacteristic
62C22×D4×C13C2312yes—
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13—21no—
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C23×C4×C13—21no—
69C23×C4×C13—44no—
70C23×C4×C13D411yescharacteristic, complemented
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C13×#126—22no—
74C13×#126—22no—
75C13×#126—22no—
76C13×#125—21no—
77C13×#125—22no—
78C13×#124—21no—
79C13×#124—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—22no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—44no—
92C13×#121—21no—
93C13×#121—22no—
94C13×#121—21no—
95C13×#121—21no—
96C13×#121—21no—
97C13×#121—21no—
98C13×#121—22no—
99C13×#121—22no—
100C13×#121—44no—
101C13×#120—22no—
102C13×#120—22no—
103C13×#120—22no—
104C13×#120—22no—
105C13×#120—24no—
106C13×#120—42no—
107C4×Q8×C13—21no—
108C4×D4×C13—22no—
109C4×D4×C13—21no—
110C4×D4×C13—21no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—22no—
115C4×D4×C13—22no—
116C4×D4×C13—22no—
117C4×D4×C13—22no—
118C4×D4×C13—44no—
119C13×#117—21no—
120C13×#117—22no—
121C13×#117—22no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4—22no—
126C2×C13×C4⋊C4D411yescharacteristic, complemented
127C2×C13×C4⋊C4D411yescharacteristic, complemented
128C2×C13×C4⋊C4D411yescharacteristic, complemented
129C2×C13×C4⋊C4D412yescomplemented
130C2×C13×C22⋊C4—22no—
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4—21no—
133C2×C13×C22⋊C4—22no—
134C2×C13×C22⋊C4—21no—
135C2×C13×C22⋊C4—22no—
136C2×C13×C22⋊C4—21no—
137C2×C13×C22⋊C4—22no—
138C2×C13×C22⋊C4—22no—
139C2×C13×C22⋊C4D411yescharacteristic, complemented
140C2×C13×C22⋊C4D412yescomplemented
141C2×C13×C22⋊C4C2311yescharacteristic
142C2×C13×C22⋊C4C2312yes—
143C2×C13×C22⋊C4C2312yes—
144C2×C13×C22⋊C4C2311yescharacteristic
145C2×C13×C22⋊C4C2312yes—
146C2×C13×C22⋊C4C2311yescharacteristic
147C2×C42×C13—21no—
148C2×C42×C13D411yescharacteristic, complemented
149C13×#99—24no—
150C13×#99—42no—
151C13×#99—42no—
152C13×#95—21no—
153C13×#95—21no—
154C13×#95—21no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—21no—
158C13×#95—21no—
159#24140C1311yesmaximal, characteristic, direct product factor, Sylow
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—42no—
167C24×C13—42no—
168C24×C13C2×D412yes—
169C24×C13C2×D411yescharacteristic
170C24×C13#4112yescomplemented
171C24×C13C2411yescharacteristic
172C13×#41—82no—
173C2×Q8×C13—21no—
174C2×Q8×C13—21no—
175C2×Q8×C13—42no—
176C2×D4×C13—24no—
177C2×D4×C13—21no—
178C2×D4×C13—22no—
179C2×D4×C13—21no—
180C2×D4×C13—22no—
181C2×D4×C13—22no—
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—22no—
185C2×D4×C13—21no—
186C2×D4×C13—22no—
187C2×D4×C13—21no—
188C2×D4×C13—22no—
189C2×D4×C13—22no—
190C2×D4×C13—22no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—42no—
194C2×D4×C13—42no—
195C2×D4×C13—42no—
196C2×D4×C13—44no—
197C2×D4×C13—44no—
198C2×D4×C13—44no—
199C22×C4×C13—24no—
200C22×C4×C13—24no—
201C22×C4×C13—24no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—42no—
214C22×C4×C13—42no—
215C22×C4×C13—42no—
216C22×C4×C13—42no—
217C22×C4×C13—42no—
218C22×C4×C13—42no—
219C22×C4×C13—42no—
220C22×C4×C13—42no—
221C22×C4×C13—42no—
222C22×C4×C13—42no—
223C22×C4×C13—42no—
224C22×C4×C13—42no—
225C22×C4×C13—41no—
226C22×C4×C13—41no—
227C22×C4×C13—41no—
228C22×C4×C13—41no—
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D412yes—
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D412yes—
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2×D411yescharacteristic
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C13×C4⋊C4—22no—
242C13×C4⋊C4—22no—
243C13×C4⋊C4—22no—
244C13×C4⋊C4—22no—
245C13×C4⋊C4—21no—
246C13×C4⋊C4—22no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4—21no—
249C13×C4⋊C4—21no—
250C13×C4⋊C4—21no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—42no—
254C13×C4⋊C4—42no—
255C13×C4⋊C4—42no—
256C13×C4⋊C4—44no—
257C13×C22⋊C4—22no—
258C13×C22⋊C4—22no—
259C13×C22⋊C4—24no—
260C13×C22⋊C4—22no—
261C13×C22⋊C4—22no—
262C13×C22⋊C4—22no—
263C13×C22⋊C4—22no—
264C13×C22⋊C4—21no—
265C13×C22⋊C4—22no—
266C13×C22⋊C4—21no—
267C13×C22⋊C4—22no—
268C13×C22⋊C4—21no—
269C13×C22⋊C4—22no—
270C13×C22⋊C4—21no—
271C13×C22⋊C4—21no—
272C13×C22⋊C4—22no—
273C13×C22⋊C4—22no—
274C13×C22⋊C4—22no—
275C13×C22⋊C4—21no—
276C13×C22⋊C4—22no—
277C13×C22⋊C4—22no—
278C13×C22⋊C4—21no—
279C13×C22⋊C4—44no—
280C13×C22⋊C4—42no—
281C13×C22⋊C4—44no—
282C13×C22⋊C4—44no—
283C13×C22⋊C4—42no—
284C13×C22⋊C4—42no—
285C13×C22⋊C4—44no—
286C13×C22⋊C4#4112yescomplemented
287C42×C13—22no—
288C42×C13—22no—
289C42×C13—21no—
290C42×C13—21no—
291C42×C13—42no—
292#3505C2×C1311yescharacteristic, complemented
293#2848C2×C1311yescharacteristic, complemented
294#2847C2×C1311yescharacteristic, complemented
295C4×#120C2×C1311yescharacteristic, complemented
296#2044C2×C1312yescomplemented
297#2021C2×C1312yescomplemented
298#1996C2×C1311yescharacteristic, complemented
299#1964C2×C1311yescharacteristic, complemented
300#1889C2×C1312yescomplemented
301#1867C2×C1312yescomplemented
302#1799C2×C1311yescharacteristic, complemented
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—21no—
313C23×C13—22no—
314C23×C13—21no—
315C23×C13—21no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—41no—
319C23×C13—44no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13—44no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—42no—
333C23×C13—42no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13C22×D411yescharacteristic
339C23×C13C22×D411yescharacteristic
340C23×C13C22×D411yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C132−1+411yescharacteristic
345Q8×C13—42no—
346Q8×C13—81no—
347D4×C13—48no—
348D4×C13—42no—
349D4×C13—42no—
350D4×C13—41no—
351D4×C13—41no—
352D4×C13—41no—
353D4×C13—42no—
354D4×C13—42no—
355D4×C13—41no—
356D4×C13—42no—
357D4×C13—81no—
358D4×C13—82no—
359D4×C13—82no—
360D4×C13—88no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—21no—
368C2×C4×C13—22no—
369C2×C4×C13—21no—
370C2×C4×C13—21no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—21no—
374C2×C4×C13—22no—
375C2×C4×C13—21no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—44no—
382C2×C4×C13—44no—
383C2×C4×C13—44no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—44no—
391C2×C4×C13—42no—
392C2×C4×C13—41no—
393C2×C4×C13—42no—
394C2×C4×C13—41no—
395C2×C4×C13—42no—
396C2×C4×C13—41no—
397C2×C4×C13—42no—
398C2×C4×C13—42no—
399C2×C4×C13—42no—
400C2×C4×C13—41no—
401C2×C4×C13—42no—
402C2×C4×C13—41no—
403C2×C4×C13—42no—
404C2×C4×C13—42no—
405C2×C4×C13—81no—
406C2×C4×C13—82no—
407C2×C4×C13—82no—
408C2×C4×C13#12011yescharacteristic
409C2×C4×C13#12011yescharacteristic
410C2×C4×C13#12011yescharacteristic
411C2×C4×C13#12011yescharacteristic
412C24×C4C22×C1311yescharacteristic
413#553—21no—
414#553—22no—
415#552—21no—
416#551—22no—
417#548—21no—
418#546—21no—
419#539—21no—
420#538—21no—
421#534C22×C1312yes—
422#529—21no—
423#525—21no—
424C2×C22⋊Q8—21no—
425C2×C22⋊Q8C22×C1311yescharacteristic
426C2×#121—21no—
427C2×#121C22×C1311yescharacteristic
428C2×#120C22×C1311yescharacteristic
429C2×#120C22×C1312yes—
430#518C22×C1312yes—
431C2×C4×D4—21no—
432C2×C4×D4C22×C1311yescharacteristic
433C2×#99C22×C1312yes—
434C2×#99C22×C1312yes—
435C2×#99C22×C1312yes—
436#386—22no—
437#386—21no—
438#386C22×C1312yes—
439#386C22×C1311yescharacteristic
440#385—22no—
441#385—21no—
442#385C22×C1312yes—
443#385C22×C1311yescharacteristic
444#380—21no—
445#380—21no—
446#380C22×C1311yescharacteristic
447#380C22×C1311yescharacteristic
448#379C22×C1312yes—
449#379C22×C1311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4C22×C1311yescharacteristic
452#342C22×C1312yes—
453#342C22×C1312yes—
454#342C22×C1312yes—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—41no—
465C22×C13—41no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—41no—
482C22×C13—42no—
483C22×C13—41no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—41no—
487C22×C13—82no—
488C22×C13—81no—
489C22×C13—82no—
490C22×C13C2×#12011yescharacteristic
491C22×C13#52511yescharacteristic
492C22×C13#53711yescharacteristic
493C22×C13#54611yescharacteristic
494C22×C13#54711yescharacteristic
495C22×C13#54811yescharacteristic
496C22×C13#55011yescharacteristic
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—42no—
501C4×C13—41no—
502C4×C13—42no—
503C4×C13—42no—
504C4×C13—41no—
505C4×C13—42no—
506C4×C13—41no—
507C4×C13—42no—
508C4×C13—82no—
509C4×C13—81no—
510C4×C13—82no—
511C4×C13B(4,𝔽2)12yes—
512C25C23×C1311yescharacteristic
513C2×#41—21no—
514C22×Q8D4×C1311yescharacteristic, complemented
515C22×D4—21no—
516C22×D4—22no—
517C22×D4D4×C1311yescharacteristic, complemented
518C22×D4C23×C1311yescharacteristic
519C22×D4C23×C1312yes—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—44no—
527C23×C4D4×C1311yescharacteristic, complemented
528C23×C4C23×C1311yescharacteristic
529C23×C4C23×C1311yescharacteristic
530#126—22no—
531#126—22no—
532#126—22no—
533#125—21no—
534#125—22no—
535#124—21no—
536#124—22no—
537#123—22no—
538#123—22no—
539#123—22no—
540#123—22no—
541#123—22no—
542C22⋊Q8—21no—
543C22⋊Q8—22no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—44no—
549#121—21no—
550#121—22no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121—22no—
556#121—22no—
557#121—44no—
558#120—22no—
559#120—22no—
560#120—22no—
561#120—22no—
562#120—24no—
563#120—42no—
564C4×Q8—21no—
565C4×D4—22no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—44no—
576#117—21no—
577#117—22no—
578#117—22no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4D4×C1311yescharacteristic, complemented
584C2×C4⋊C4D4×C1311yescharacteristic, complemented
585C2×C4⋊C4D4×C1311yescharacteristic, complemented
586C2×C4⋊C4D4×C1312yescomplemented
587C2×C22⋊C4—22no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4D4×C1311yescharacteristic, complemented
597C2×C22⋊C4D4×C1312yescomplemented
598C2×C22⋊C4C23×C1312yes—
599C2×C22⋊C4C23×C1311yescharacteristic
600C2×C22⋊C4C23×C1312yes—
601C2×C22⋊C4C23×C1311yescharacteristic
602C2×C22⋊C4C23×C1312yes—
603C2×C22⋊C4C23×C1311yescharacteristic
604C2×C42—21no—
605C2×C42D4×C1311yescharacteristic, complemented
606#99—24no—
607#99—42no—
608#99—42no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95—22no—
613#95—22no—
614#95—21no—
615#95—21no—
616C2×C13—21no—
617C2×C13—21no—
618C2×C13—21no—
619C2×C13—21no—
620C2×C13—21no—
621C2×C13—21no—
622C2×C13—44no—
623C2×C13—81no—
624C2×C13—82no—
625C2×C13#240711yescharacteristic
626C2×C13C2×B(4,𝔽2)11yescharacteristic
627C2×C13#302511yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—42no—
635C24—42no—
636C24C2×D4×C1312yes—
637C24C2×D4×C1311yescharacteristic
638C24C13×#4112yescomplemented
639C24C24×C1311yescharacteristic
640#41—82no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—42no—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4C2×D4×C1311yescharacteristic
698C22×C4C2×D4×C1312yes—
699C22×C4C2×D4×C1311yescharacteristic
700C22×C4C2×D4×C1311yescharacteristic
701C22×C4C2×D4×C1311yescharacteristic
702C22×C4C2×D4×C1311yescharacteristic
703C22×C4C2×D4×C1312yes—
704C22×C4C2×D4×C1311yescharacteristic
705C22×C4C2×D4×C1312yes—
706C22×C4C2×D4×C1311yescharacteristic
707C22×C4C2×D4×C1311yescharacteristic
708C22×C4C2×D4×C1311yescharacteristic
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—21no—
714C4⋊C4—22no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—22no—
720C4⋊C4—21no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—44no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—24no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—21no—
733C22⋊C4—22no—
734C22⋊C4—21no—
735C22⋊C4—22no—
736C22⋊C4—21no—
737C22⋊C4—22no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—21no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—44no—
750C22⋊C4—42no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—42no—
754C22⋊C4C13×#4112yescomplemented
755C42—22no—
756C42—22no—
757C42—21no—
758C42—21no—
759C42—42no—
760C13#2414011yescharacteristic, direct product factor, Sylow
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C1311yescharacteristic
797C23C22×D4×C1311yescharacteristic
798C23C22×D4×C1311yescharacteristic
799C23C2×C13×#4111yescharacteristic
800C23C2×C13×#4111yescharacteristic
801C23C13×H(5,𝔽2)11yescharacteristic
802C23C13×2−1+411yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4C13×#12011yescharacteristic
867C2×C4C13×#12011yescharacteristic
868C2×C4C13×#12011yescharacteristic
869C2×C4C13×#12011yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×C13×#12011yescharacteristic
906C22C13×#52511yescharacteristic
907C22C13×#53711yescharacteristic
908C22C13×#54611yescharacteristic
909C22C13×#54711yescharacteristic
910C22C13×#54811yescharacteristic
911C22C13×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—81no—
925C4—82no—
926C4C13×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C13×#240711yescharacteristic
937C2C2×C13×B(4,𝔽2)11yescharacteristic
938C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3505C2semidirect
2. C13×#2848C2semidirect
3. C13×#2847C2semidirect
4. C4×C13×#120C2semidirect
5. C13×#2044C2semidirect
6. C13×#2021C2semidirect
7. C13×#1996C2semidirect
8. C13×#1964C2semidirect
9. C13×#1889C2semidirect
10. C13×#1867C2semidirect
11. C13×#1799C2semidirect
57. C22×Q8×C13D4semidirect
60. C22×D4×C13D4semidirect
70. C23×C4×C13D4semidirect
126. C2×C13×C4⋊C4D4semidirect
127. C2×C13×C4⋊C4D4semidirect
128. C2×C13×C4⋊C4D4semidirect
129. C2×C13×C4⋊C4D4semidirect
139. C2×C13×C22⋊C4D4semidirect
140. C2×C13×C22⋊C4D4semidirect
148. C2×C42×C13D4semidirect
159. #24140C13direct (N × H)
170. C24×C13#41semidirect
286. C13×C22⋊C4#41semidirect
292. #3505C2×C13semidirect
293. #2848C2×C13semidirect
294. #2847C2×C13semidirect
295. C4×#120C2×C13semidirect
296. #2044C2×C13semidirect
297. #2021C2×C13semidirect
298. #1996C2×C13semidirect
299. #1964C2×C13semidirect
300. #1889C2×C13semidirect
301. #1867C2×C13semidirect
302. #1799C2×C13semidirect
514. C22×Q8D4×C13semidirect
517. C22×D4D4×C13semidirect
527. C23×C4D4×C13semidirect
583. C2×C4⋊C4D4×C13semidirect
584. C2×C4⋊C4D4×C13semidirect
585. C2×C4⋊C4D4×C13semidirect
586. C2×C4⋊C4D4×C13semidirect
596. C2×C22⋊C4D4×C13semidirect
597. C2×C22⋊C4D4×C13semidirect
605. C2×C42D4×C13semidirect
638. C24C13×#41semidirect
754. C22⋊C4C13×#41semidirect
760. C13#24140direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35052
C13×#28482
C13×#28472
C4×C13×#1202
C13×#20442
C13×#20212
C13×#19962
C13×#19642
C13×#18892
C13×#18672
C13×#17992
#2414013