Finite Group Databasebeta

← C13×#14912 #15701251

Subgroups — C13×#14912 #15701251

Order 3328.

2314 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic
2C2×C13×#386C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic, complemented
5C2×C13×#381C211yesmaximal, characteristic, complemented
6C22×C13×#95C211yesmaximal, characteristic, complemented
7C13×#1442C212yesmaximal, complemented
8C13×#1441C212yesmaximal, complemented
9C13×#1440C212yesmaximal, complemented
10C13×#1439C212yesmaximal, complemented
11C13×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C24×C4×C13C2211yescharacteristic
16C2×C13×#123—24no—
17C2×C13×#123—24no—
18C2×C13×#123—24no—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2212yes—
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2212yes—
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C13×#386—24no—
30C13×#386—24no—
31C13×#385—24no—
32C13×#381—24no—
33C2×C13×#95—24no—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C2×C13×#95C2212yes—
42C2×C13×#95C2212yes—
43C25×C13C2311yescharacteristic
44C25×C13C2311yescharacteristic
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13—22no—
51C22×D4×C13D414yes—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—24no—
61C23×C4×C13—24no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—42no—
67C23×C4×C13—42no—
68C23×C4×C13D414yes—
69C23×C4×C13C2312yes—
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2312yes—
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2312yes—
77C23×C4×C13C2312yes—
78C13×#123—232no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—24no—
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4—42no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—24no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—42no—
106C2×C13×C22⋊C4—42no—
107C2×C13×C22⋊C4D414yes—
108C2×C13×C22⋊C4D414yes—
109C13×#95—24no—
110C13×#95—24no—
111C13×#95—24no—
112C13×#95—24no—
113C13×#95—24no—
114C13×#95—24no—
115C13×#95—24no—
116C13×#95—24no—
117C13×#95—42no—
118#14912C1311yesmaximal, characteristic, direct product factor, Sylow
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—21no—
124C24×C13—21no—
125C24×C13—21no—
126C24×C13—22no—
127C24×C13—22no—
128C24×C13—21no—
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—22no—
132C24×C13—22no—
133C24×C13C2×D412yes—
134C24×C13C2×D412yes—
135C24×C13C2×D412yes—
136C24×C13C2×D412yes—
137C24×C13C2×D412yes—
138C24×C13#4112yes—
139C24×C13#4112yes—
140C24×C13#4112yes—
141C24×C13C2411yescharacteristic
142C2×D4×C13—28no—
143C2×D4×C13—28no—
144C2×D4×C13—28no—
145C2×D4×C13—44no—
146C2×D4×C13—44no—
147C2×D4×C13—44no—
148C2×D4×C13—44no—
149C22×C4×C13—28no—
150C22×C4×C13—28no—
151C22×C4×C13—28no—
152C22×C4×C13—28no—
153C22×C4×C13—28no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—48no—
206C22×C4×C13—48no—
207C22×C4×C13—48no—
208C22×C4×C13—48no—
209C22×C4×C13—44no—
210C22×C4×C13—44no—
211C22×C4×C13—44no—
212C22×C4×C13—44no—
213C22×C4×C13—44no—
214C22×C4×C13—44no—
215C22×C4×C13—44no—
216C22×C4×C13—44no—
217C22×C4×C13C2×D414yes—
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2×D412yes—
220C22×C4×C13C2×D412yes—
221C22×C4×C13C2×D412yes—
222C22×C4×C13C2×D412yes—
223C22×C4×C13#4114yes—
224C22×C4×C13#4114yes—
225C13×C4⋊C4—28no—
226C13×C4⋊C4—28no—
227C13×C4⋊C4—48no—
228C13×C22⋊C4—28no—
229C13×C22⋊C4—28no—
230C13×C22⋊C4—28no—
231C13×C22⋊C4—28no—
232C13×C22⋊C4—48no—
233C13×C22⋊C4—48no—
234C13×C22⋊C4—44no—
235C22×#123C2×C1311yescharacteristic
236C2×#386C2×C1311yescharacteristic
237C2×#386C2×C1311yescharacteristic
238C2×#385C2×C1311yescharacteristic, complemented
239C2×#381C2×C1311yescharacteristic, complemented
240C22×#95C2×C1311yescharacteristic, complemented
241#1442C2×C1312yescomplemented
242#1441C2×C1312yescomplemented
243#1440C2×C1312yescomplemented
244#1439C2×C1312yescomplemented
245C22⋊#95C2×C1311yescharacteristic, complemented
246C23×C13—22no—
247C23×C13—22no—
248C23×C13—24no—
249C23×C13—24no—
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—24no—
255C23×C13—24no—
256C23×C13—24no—
257C23×C13—24no—
258C23×C13—24no—
259C23×C13—24no—
260C23×C13—24no—
261C23×C13—24no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—24no—
266C23×C13—24no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—42no—
274C23×C13—42no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—42no—
278C23×C13—42no—
279C23×C13—42no—
280C23×C13—42no—
281C23×C13—42no—
282C23×C13—42no—
283C23×C13—42no—
284C23×C13—42no—
285C23×C13#12014yes—
286C23×C13#12114yes—
287C23×C13#12114yes—
288C23×C13#12114yes—
289C23×C13#12314yes—
290C23×C13#12314yes—
291C23×C13#12414yes—
292C23×C13C22×D411yescharacteristic
293C23×C13C22×D411yescharacteristic
294C23×C13C22×D411yescharacteristic
295C23×C13C22×D411yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13C2×#4111yescharacteristic
299C23×C13C2×#4112yes—
300C23×C13C2×#4112yes—
301C23×C13H(5,𝔽2)12yes—
302C23×C132−1+412yes—
303D4×C13—416no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—24no—
317C2×C4×C13—24no—
318C2×C4×C13—24no—
319C2×C4×C13—24no—
320C2×C4×C13—24no—
321C2×C4×C13—24no—
322C2×C4×C13—24no—
323C2×C4×C13—24no—
324C2×C4×C13—24no—
325C2×C4×C13—24no—
326C2×C4×C13—416no—
327C2×C4×C13—416no—
328C2×C4×C13—42no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—42no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—42no—
345C2×C4×C13—41no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13—41no—
349C2×C4×C13—42no—
350C2×C4×C13—42no—
351C2×C4×C13—42no—
352C2×C4×C13—42no—
353C2×C4×C13—42no—
354C2×C4×C13—42no—
355C2×C4×C13—42no—
356C2×C4×C13—42no—
357C2×C4×C13—42no—
358C2×C4×C13—416no—
359C2×C4×C13—42no—
360C2×C4×C13—42no—
361C2×C4×C13—42no—
362C2×C4×C13—42no—
363C2×C4×C13—42no—
364C2×C4×C13—42no—
365C2×C4×C13—42no—
366C23×D4C22×C1311yescharacteristic
367C24×C4C22×C1311yescharacteristic
368C24×C4C22×C1311yescharacteristic
369C24×C4C22×C1311yescharacteristic
370C2×#123—24no—
371C2×#123—24no—
372C2×#123—24no—
373C22×C4⋊C4C22×C1311yescharacteristic
374C22×C4⋊C4C22×C1311yescharacteristic
375C22×C4⋊C4C22×C1312yes—
376C22×C22⋊C4C22×C1311yescharacteristic
377C22×C22⋊C4C22×C1311yescharacteristic
378C22×C22⋊C4C22×C1311yescharacteristic
379C22×C22⋊C4C22×C1312yes—
380C22×C22⋊C4C22×C1312yes—
381C22×C22⋊C4C22×C1311yescharacteristic
382C22×C22⋊C4C22×C1311yescharacteristic
383#386—24no—
384#386—24no—
385#385—24no—
386#381—24no—
387C2×#95—24no—
388C2×#95C22×C1312yes—
389C2×#95C22×C1312yes—
390C2×#95C22×C1312yes—
391C2×#95C22×C1312yes—
392C2×#95C22×C1312yes—
393C2×#95C22×C1312yes—
394C2×#95C22×C1312yes—
395C2×#95C22×C1312yes—
396C2×#95C22×C1312yes—
397C22×C13—24no—
398C22×C13—24no—
399C22×C13—24no—
400C22×C13—24no—
401C22×C13—24no—
402C22×C13—24no—
403C22×C13—28no—
404C22×C13—28no—
405C22×C13—28no—
406C22×C13—28no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13—42no—
410C22×C13—44no—
411C22×C13—44no—
412C22×C13—81no—
413C22×C13—81no—
414C22×C13—81no—
415C22×C13—81no—
416C22×C13—82no—
417C22×C13—82no—
418C22×C13#39418yes—
419C22×C13C2×#12011yescharacteristic
420C22×C13C2×#12111yescharacteristic
421C22×C13C2×#12111yescharacteristic
422C22×C13C2×#12111yescharacteristic
423C22×C13C2×#12311yescharacteristic
424C22×C13C2×#12311yescharacteristic
425C22×C13#52511yescharacteristic
426C22×C13#52511yescharacteristic
427C22×C13C2×#12411yescharacteristic
428C22×C13#52912yes—
429C22×C13#52912yes—
430C22×C13#53511yescharacteristic
431C22×C13#53611yescharacteristic
432C22×C13#53912yes—
433C22×C13#53912yes—
434C22×C13#54612yes—
435C22×C13#54612yes—
436C22×C13#54612yes—
437C22×C13#54712yes—
438C22×C13#54712yes—
439C22×C13#54712yes—
440C22×C13#55112yes—
441C22×C13#55212yes—
442C4×C13—42no—
443C4×C13—42no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13—44no—
447C4×C13—42no—
448C4×C13—44no—
449C4×C13—44no—
450C4×C13—82no—
451C25C23×C1311yescharacteristic
452C25C23×C1311yescharacteristic
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4D4×C1314yes—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—42no—
475C23×C4—42no—
476C23×C4D4×C1314yes—
477C23×C4C23×C1312yes—
478C23×C4C23×C1311yescharacteristic
479C23×C4C23×C1312yes—
480C23×C4C23×C1311yescharacteristic
481C23×C4C23×C1311yescharacteristic
482C23×C4C23×C1311yescharacteristic
483C23×C4C23×C1311yescharacteristic
484C23×C4C23×C1312yes—
485C23×C4C23×C1312yes—
486#123—232no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—42no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4D4×C1314yes—
516C2×C22⋊C4D4×C1314yes—
517#95—24no—
518#95—24no—
519#95—24no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—42no—
526C2×C13—28no—
527C2×C13—82no—
528C2×C13C2×#39411yescharacteristic
529C2×C13#240411yescharacteristic
530C2×C13#240611yescharacteristic
531C2×C13#241111yescharacteristic
532C2×C13#241311yescharacteristic
533C2×C13#241912yes—
534C2×C13#242512yes—
535C2×C13#242512yes—
536C2×C13#248812yes—
537C2×C13#262311yescharacteristic
538C2×C13#285311yescharacteristic
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—22no—
547C24—22no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24C2×D4×C1312yes—
554C24C2×D4×C1312yes—
555C24C2×D4×C1312yes—
556C24C2×D4×C1312yes—
557C24C2×D4×C1312yes—
558C24C13×#4112yes—
559C24C13×#4112yes—
560C24C13×#4112yes—
561C24C24×C1311yescharacteristic
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
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—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4C2×D4×C1314yes—
638C22×C4C2×D4×C1312yes—
639C22×C4C2×D4×C1312yes—
640C22×C4C2×D4×C1312yes—
641C22×C4C2×D4×C1312yes—
642C22×C4C2×D4×C1312yes—
643C22×C4C13×#4114yes—
644C22×C4C13×#4114yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—48no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—44no—
655C13#1491211yescharacteristic, direct product factor, Sylow
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23C13×#12014yes—
696C23C13×#12114yes—
697C23C13×#12114yes—
698C23C13×#12114yes—
699C23C13×#12314yes—
700C23C13×#12314yes—
701C23C13×#12414yes—
702C23C22×D4×C1311yescharacteristic
703C23C22×D4×C1311yescharacteristic
704C23C22×D4×C1311yescharacteristic
705C23C22×D4×C1311yescharacteristic
706C23C2×C13×#4111yescharacteristic
707C23C2×C13×#4111yescharacteristic
708C23C2×C13×#4111yescharacteristic
709C23C2×C13×#4112yes—
710C23C2×C13×#4112yes—
711C23C13×H(5,𝔽2)12yes—
712C23C13×2−1+412yes—
713D4—416no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—28no—
783C22—28no—
784C22—28no—
785C22—28no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—82no—
796C22—82no—
797C22C13×#39418yes—
798C22C2×C13×#12011yescharacteristic
799C22C2×C13×#12111yescharacteristic
800C22C2×C13×#12111yescharacteristic
801C22C2×C13×#12111yescharacteristic
802C22C2×C13×#12311yescharacteristic
803C22C2×C13×#12311yescharacteristic
804C22C13×#52511yescharacteristic
805C22C13×#52511yescharacteristic
806C22C2×C13×#12411yescharacteristic
807C22C13×#52912yes—
808C22C13×#52912yes—
809C22C13×#53511yescharacteristic
810C22C13×#53611yescharacteristic
811C22C13×#53912yes—
812C22C13×#53912yes—
813C22C13×#54612yes—
814C22C13×#54612yes—
815C22C13×#54612yes—
816C22C13×#54712yes—
817C22C13×#54712yes—
818C22C13×#54712yes—
819C22C13×#55112yes—
820C22C13×#55212yes—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—82no—
830C2—28no—
831C2—82no—
832C2C2×C13×#39411yescharacteristic
833C2C13×#240411yescharacteristic
834C2C13×#240611yescharacteristic
835C2C13×#241111yescharacteristic
836C2C13×#241311yescharacteristic
837C2C13×#241912yes—
838C2C13×#242512yes—
839C2C13×#242512yes—
840C2C13×#248812yes—
841C2C13×#262311yescharacteristic
842C2C13×#285311yescharacteristic
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
4. C2×C13×#385C2semidirect
5. C2×C13×#381C2semidirect
6. C22×C13×#95C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
9. C13×#1440C2semidirect
10. C13×#1439C2semidirect
11. C13×C22⋊#95C2semidirect
118. #14912C13direct (N × H)
238. C2×#385C2×C13semidirect
239. C2×#381C2×C13semidirect
240. C22×#95C2×C13semidirect
241. #1442C2×C13semidirect
242. #1441C2×C13semidirect
243. #1440C2×C13semidirect
244. #1439C2×C13semidirect
245. C22⋊#95C2×C13semidirect
655. C13#14912direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C2×C13×#3862
C2×C13×#3852
C2×C13×#3812
C22×C13×#952
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×C22⋊#952
#1491213