Finite Group Databasebeta

← C13×#24142 #15710481

Subgroups — C13×#24142 #15710481

Order 3328.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3505C211yesmaximal, characteristic, complemented
2C13×#2626C211yesmaximal, characteristic, complemented
3C13×#2617C211yesmaximal, characteristic, complemented
4C13×#2321C211yesmaximal, 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
12C13×#553—22no—
13C13×#553—21no—
14C13×#552—21no—
15C13×#551—22no—
16C13×#548—21no—
17C13×#546—21no—
18C13×#539—21no—
19C13×#538—21no—
20C13×#534C2212yes—
21C13×#529—21no—
22C13×#525—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C13×#120C2211yescharacteristic
26C2×C13×#120C2212yes—
27C13×#518C2212yes—
28C2×C4×D4×C13C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C2×C13×#99C2212yes—
31C2×C13×#99C2212yes—
32C2×C13×#99C2212yes—
33C13×#399—21no—
34C13×#397—21no—
35C13×#396—22no—
36C13×#394—22no—
37C13×#393—21no—
38C13×#392—21no—
39C13×#390—21no—
40C13×#388—21no—
41C13×#388—21no—
42C13×#386—21no—
43C13×#386C2211yescharacteristic
44C13×#386C2212yes—
45C13×#385C2212yes—
46C13×#385C2211yescharacteristic
47C13×#380C2211yescharacteristic
48C13×#380C2211yescharacteristic
49C13×#379C2212yes—
50C13×#379C2211yescharacteristic
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×C13D411yescharacteristic, complemented
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C13×#126—22no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#125—21no—
70C13×#125—22no—
71C13×#124—21no—
72C13×#124—22no—
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×C22⋊Q8—21no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—21no—
84C13×#121—21no—
85C13×#121—22no—
86C13×#121—21no—
87C13×#121—21no—
88C13×#121—21no—
89C13×#121—21no—
90C13×#121—22no—
91C13×#121—22no—
92C13×#120—22no—
93C13×#120—22no—
94C13×#120—22no—
95C13×#120—22no—
96C13×#120—24no—
97C13×#120—42no—
98C4×Q8×C13—21no—
99C4×D4×C13—22no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C4×D4×C13—22no—
107C4×D4×C13—22no—
108C4×D4×C13—22no—
109C13×#117—21no—
110C13×#117—22no—
111C13×#117—22no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4D411yescharacteristic, complemented
117C2×C13×C4⋊C4D412yescomplemented
118C2×C13×C4⋊C4D411yescharacteristic, complemented
119C2×C13×C4⋊C4D411yescharacteristic, complemented
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4—21no—
124C2×C13×C22⋊C4—21no—
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4—22no—
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4—21no—
133C2×C13×C22⋊C4—22no—
134C2×C13×C22⋊C4—22no—
135C2×C13×C22⋊C4D411yescharacteristic, complemented
136C2×C13×C22⋊C4D412yescomplemented
137C2×C13×C22⋊C4C2311yescharacteristic
138C2×C13×C22⋊C4C2312yes—
139C2×C13×C22⋊C4C2312yes—
140C2×C13×C22⋊C4C2311yescharacteristic
141C2×C13×C22⋊C4C2312yes—
142C2×C13×C22⋊C4C2311yescharacteristic
143C2×C42×C13—21no—
144C2×C42×C13D411yescharacteristic, complemented
145C13×#99—24no—
146C13×#99—42no—
147C13×#99—42no—
148C13×#95—21no—
149C13×#95—21no—
150C13×#95—21no—
151C13×#95—21no—
152C13×#95—22no—
153C13×#95—21no—
154C13×#95—22no—
155#24142C1311yesmaximal, characteristic, direct product factor, Sylow
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—81no—
163C24×C13—81no—
164C24×C13C2×D412yes—
165C24×C13C2×D411yescharacteristic
166C24×C13#4112yescomplemented
167C24×C13C2411yescharacteristic
168C13×#41—82no—
169C2×Q8×C13—21no—
170C2×Q8×C13—21no—
171C2×Q8×C13—81no—
172C2×D4×C13—21no—
173C2×D4×C13—22no—
174C2×D4×C13—21no—
175C2×D4×C13—22no—
176C2×D4×C13—22no—
177C2×D4×C13—21no—
178C2×D4×C13—21no—
179C2×D4×C13—22no—
180C2×D4×C13—21no—
181C2×D4×C13—22no—
182C2×D4×C13—21no—
183C2×D4×C13—22no—
184C2×D4×C13—22no—
185C2×D4×C13—22no—
186C2×D4×C13—24no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13—44no—
190C2×D4×C13—81no—
191C2×D4×C13—81no—
192C2×D4×C13—81no—
193C2×D4×C13—82no—
194C2×D4×C13—82no—
195C22×C4×C13—21no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—21no—
206C22×C4×C13—81no—
207C22×C4×C13—81no—
208C22×C4×C13—81no—
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D412yes—
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C13×C4⋊C4—22no—
222C13×C4⋊C4—22no—
223C13×C4⋊C4—22no—
224C13×C4⋊C4—22no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—22no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—22no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—81no—
234C13×C4⋊C4—81no—
235C13×C4⋊C4—81no—
236C13×C4⋊C4—82no—
237C13×C22⋊C4—22no—
238C13×C22⋊C4—22no—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—22no—
241C13×C22⋊C4—22no—
242C13×C22⋊C4—22no—
243C13×C22⋊C4—22no—
244C13×C22⋊C4—21no—
245C13×C22⋊C4—22no—
246C13×C22⋊C4—21no—
247C13×C22⋊C4—22no—
248C13×C22⋊C4—21no—
249C13×C22⋊C4—22no—
250C13×C22⋊C4—21no—
251C13×C22⋊C4—21no—
252C13×C22⋊C4—22no—
253C13×C22⋊C4—22no—
254C13×C22⋊C4—22no—
255C13×C22⋊C4—21no—
256C13×C22⋊C4—22no—
257C13×C22⋊C4—22no—
258C13×C22⋊C4—21no—
259C13×C22⋊C4—44no—
260C13×C22⋊C4—41no—
261C13×C22⋊C4—41no—
262C13×C22⋊C4—41no—
263C13×C22⋊C4—41no—
264C13×C22⋊C4—81no—
265C13×C22⋊C4—82no—
266C13×C22⋊C4—81no—
267C13×C22⋊C4—82no—
268C13×C22⋊C4—81no—
269C13×C22⋊C4—82no—
270C13×C22⋊C4#4112yescomplemented
271C42×C13—22no—
272C42×C13—22no—
273C42×C13—21no—
274C42×C13—21no—
275C42×C13—81no—
276#3505C2×C1311yescharacteristic, complemented
277#2626C2×C1311yescharacteristic, complemented
278#2617C2×C1311yescharacteristic, complemented
279#2321C2×C1311yescharacteristic, complemented
280#2044C2×C1312yescomplemented
281#2021C2×C1312yescomplemented
282#1996C2×C1311yescharacteristic, complemented
283#1964C2×C1311yescharacteristic, complemented
284#1889C2×C1312yescomplemented
285#1867C2×C1312yescomplemented
286#1799C2×C1311yescharacteristic, complemented
287C23×C13—21no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—21no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—21no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—42no—
301C23×C13—41no—
302C23×C13—42no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—42no—
306C23×C13—41no—
307C23×C13—42no—
308C23×C13—42no—
309C23×C13—42no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—82no—
315C23×C13—82no—
316C23×C13—82no—
317C23×C13—82no—
318C23×C13C22×D411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C22×D411yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C132−1+411yescharacteristic
325Q8×C13—42no—
326Q8×C13—81no—
327D4×C13—42no—
328D4×C13—42no—
329D4×C13—42no—
330D4×C13—41no—
331D4×C13—41no—
332D4×C13—41no—
333D4×C13—42no—
334D4×C13—42no—
335D4×C13—41no—
336D4×C13—81no—
337D4×C13—82no—
338D4×C13—84no—
339D4×C13—82no—
340D4×C13—88no—
341C2×C4×C13—21no—
342C2×C4×C13—22no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—21no—
348C2×C4×C13—22no—
349C2×C4×C13—21no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—42no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—42no—
363C2×C4×C13—41no—
364C2×C4×C13—42no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—42no—
368C2×C4×C13—42no—
369C2×C4×C13—41no—
370C2×C4×C13—42no—
371C2×C4×C13—42no—
372C2×C4×C13—42no—
373C2×C4×C13—41no—
374C2×C4×C13—42no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—42no—
378C2×C4×C13—42no—
379C2×C4×C13—81no—
380C2×C4×C13—82no—
381C2×C4×C13—82no—
382C2×C4×C13#12011yescharacteristic
383C2×C4×C13#12011yescharacteristic
384C2×C4×C13#12011yescharacteristic
385C2×C4×C13#12011yescharacteristic
386#553—22no—
387#553—21no—
388#552—21no—
389#551—22no—
390#548—21no—
391#546—21no—
392#539—21no—
393#538—21no—
394#534C22×C1312yes—
395#529—21no—
396#525—21no—
397C2×C22⋊Q8C22×C1311yescharacteristic
398C2×#121C22×C1311yescharacteristic
399C2×#120C22×C1311yescharacteristic
400C2×#120C22×C1312yes—
401#518C22×C1312yes—
402C2×C4×D4C22×C1311yescharacteristic
403C22×C22⋊C4C22×C1311yescharacteristic
404C2×#99C22×C1312yes—
405C2×#99C22×C1312yes—
406C2×#99C22×C1312yes—
407#399—21no—
408#397—21no—
409#396—22no—
410#394—22no—
411#393—21no—
412#392—21no—
413#390—21no—
414#388—21no—
415#388—21no—
416#386—21no—
417#386C22×C1311yescharacteristic
418#386C22×C1312yes—
419#385C22×C1311yescharacteristic
420#385C22×C1312yes—
421#380C22×C1311yescharacteristic
422#380C22×C1311yescharacteristic
423#379C22×C1311yescharacteristic
424#379C22×C1312yes—
425C4×C22⋊C4C22×C1311yescharacteristic
426#342C22×C1312yes—
427#342C22×C1312yes—
428#342C22×C1312yes—
429C22×C13—21no—
430C22×C13—21no—
431C22×C13—21no—
432C22×C13—21no—
433C22×C13—21no—
434C22×C13—21no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13—41no—
438C22×C13—41no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—44no—
442C22×C13—42no—
443C22×C13—44no—
444C22×C13—41no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—41no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—41no—
451C22×C13—82no—
452C22×C13—81no—
453C22×C13—82no—
454C22×C13—82no—
455C22×C13—81no—
456C22×C13—81no—
457C22×C13—82no—
458C22×C13—81no—
459C22×C13—81no—
460C22×C13C2×#12011yescharacteristic
461C22×C13#52511yescharacteristic
462C22×C13#53711yescharacteristic
463C22×C13#54611yescharacteristic
464C22×C13#54711yescharacteristic
465C22×C13#54811yescharacteristic
466C22×C13#55011yescharacteristic
467C4×C13—21no—
468C4×C13—21no—
469C4×C13—21no—
470C4×C13—21no—
471C4×C13—42no—
472C4×C13—41no—
473C4×C13—42no—
474C4×C13—41no—
475C4×C13—42no—
476C4×C13—41no—
477C4×C13—42no—
478C4×C13—82no—
479C4×C13—81no—
480C4×C13—82no—
481C4×C13—81no—
482C25C23×C1311yescharacteristic
483C2×#41—21no—
484C22×Q8D4×C1311yescharacteristic, complemented
485C22×D4—21no—
486C22×D4—22no—
487C22×D4D4×C1311yescharacteristic, complemented
488C22×D4C23×C1311yescharacteristic
489C22×D4C23×C1312yes—
490C23×C4D4×C1311yescharacteristic, complemented
491C23×C4C23×C1311yescharacteristic
492C23×C4C23×C1311yescharacteristic
493#126—22no—
494#126—22no—
495#126—22no—
496#125—21no—
497#125—22no—
498#124—21no—
499#124—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8—21no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511#121—21no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121—22no—
519#120—22no—
520#120—22no—
521#120—22no—
522#120—22no—
523#120—24no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4D4×C1311yescharacteristic, complemented
544C2×C4⋊C4D4×C1311yescharacteristic, complemented
545C2×C4⋊C4D4×C1312yescomplemented
546C2×C4⋊C4D4×C1311yescharacteristic, complemented
547C2×C22⋊C4—22no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4D4×C1311yescharacteristic, complemented
563C2×C22⋊C4D4×C1312yescomplemented
564C2×C22⋊C4C23×C1312yes—
565C2×C22⋊C4C23×C1311yescharacteristic
566C2×C22⋊C4C23×C1312yes—
567C2×C22⋊C4C23×C1311yescharacteristic
568C2×C22⋊C4C23×C1312yes—
569C2×C22⋊C4C23×C1311yescharacteristic
570C2×C42—21no—
571C2×C42D4×C1311yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C2×C13—21no—
583C2×C13—21no—
584C2×C13—21no—
585C2×C13—21no—
586C2×C13—21no—
587C2×C13—21no—
588C2×C13—82no—
589C2×C13—81no—
590C2×C13—82no—
591C2×C13#240711yescharacteristic
592C2×C13#302611yescharacteristic
593C2×C13#302711yescharacteristic
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—81no—
601C24—81no—
602C24C2×D4×C1312yes—
603C24C2×D4×C1311yescharacteristic
604C24C13×#4112yescomplemented
605C24C24×C1311yescharacteristic
606#41—82no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—81no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—44no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—82no—
632C2×D4—82no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4C2×D4×C1311yescharacteristic
648C22×C4C2×D4×C1312yes—
649C22×C4C2×D4×C1311yescharacteristic
650C22×C4C2×D4×C1312yes—
651C22×C4C2×D4×C1311yescharacteristic
652C22×C4C2×D4×C1312yes—
653C22×C4C2×D4×C1311yescharacteristic
654C22×C4C2×D4×C1311yescharacteristic
655C22×C4C2×D4×C1311yescharacteristic
656C22×C4C2×D4×C1311yescharacteristic
657C22×C4C2×D4×C1311yescharacteristic
658C22×C4C2×D4×C1311yescharacteristic
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—21no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—22no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—21no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—21no—
697C22⋊C4—44no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—81no—
703C22⋊C4—82no—
704C22⋊C4—81no—
705C22⋊C4—82no—
706C22⋊C4—81no—
707C22⋊C4—82no—
708C22⋊C4C13×#4112yescomplemented
709C42—22no—
710C42—22no—
711C42—21no—
712C42—21no—
713C42—81no—
714C13#2414211yescharacteristic, direct product factor, Sylow
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C1311yescharacteristic
747C23C22×D4×C1311yescharacteristic
748C23C22×D4×C1311yescharacteristic
749C23C2×C13×#4111yescharacteristic
750C23C2×C13×#4111yescharacteristic
751C23C13×H(5,𝔽2)11yescharacteristic
752C23C13×2−1+411yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4C13×#12011yescharacteristic
811C2×C4C13×#12011yescharacteristic
812C2×C4C13×#12011yescharacteristic
813C2×C4C13×#12011yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×C13×#12011yescharacteristic
846C22C13×#52511yescharacteristic
847C22C13×#53711yescharacteristic
848C22C13×#54611yescharacteristic
849C22C13×#54711yescharacteristic
850C22C13×#54811yescharacteristic
851C22C13×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—81no—
865C4—82no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C13×#240711yescharacteristic
877C2C13×#302611yescharacteristic
878C2C13×#302711yescharacteristic
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×#2626C2semidirect
3. C13×#2617C2semidirect
4. C13×#2321C2semidirect
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
63. C23×C4×C13D4semidirect
116. C2×C13×C4⋊C4D4semidirect
117. C2×C13×C4⋊C4D4semidirect
118. C2×C13×C4⋊C4D4semidirect
119. C2×C13×C4⋊C4D4semidirect
135. C2×C13×C22⋊C4D4semidirect
136. C2×C13×C22⋊C4D4semidirect
144. C2×C42×C13D4semidirect
155. #24142C13direct (N × H)
166. C24×C13#41semidirect
270. C13×C22⋊C4#41semidirect
276. #3505C2×C13semidirect
277. #2626C2×C13semidirect
278. #2617C2×C13semidirect
279. #2321C2×C13semidirect
280. #2044C2×C13semidirect
281. #2021C2×C13semidirect
282. #1996C2×C13semidirect
283. #1964C2×C13semidirect
284. #1889C2×C13semidirect
285. #1867C2×C13semidirect
286. #1799C2×C13semidirect
484. C22×Q8D4×C13semidirect
487. C22×D4D4×C13semidirect
490. C23×C4D4×C13semidirect
543. C2×C4⋊C4D4×C13semidirect
544. C2×C4⋊C4D4×C13semidirect
545. C2×C4⋊C4D4×C13semidirect
546. C2×C4⋊C4D4×C13semidirect
562. C2×C22⋊C4D4×C13semidirect
563. C2×C22⋊C4D4×C13semidirect
571. C2×C42D4×C13semidirect
604. C24C13×#41semidirect
708. C22⋊C4C13×#41semidirect
714. C13#24142direct (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×#26262
C13×#26172
C13×#23212
C13×#20442
C13×#20212
C13×#19962
C13×#19642
C13×#18892
C13×#18672
C13×#17992
#2414213