Finite Group Databasebeta

← C13×#14969 #15701308

Subgroups — C13×#14969 #15701308

Order 3328.

1686 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#389C211yesmaximal, characteristic, complemented
2C2×C13×#387C212yesmaximal, complemented
3C2×C13×#385C212yesmaximal
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
5C13×#1445C212yesmaximal, complemented
6C13×#1444C211yesmaximal, characteristic, complemented
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1439C212yesmaximal
9C13×#1439C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1434C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2212yes—
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C13×#389—24no—
25C13×#387—28no—
26C13×#385—28no—
27C4×C13×C22⋊C4—24no—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C25×C13C2311yescharacteristic
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—24no—
44C23×C4×C13—42no—
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—24no—
59C2×C13×C4⋊C4—24no—
60C2×C13×C4⋊C4—24no—
61C2×C13×C4⋊C4—24no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—24no—
66C2×C13×C4⋊C4—42no—
67C2×C13×C4⋊C4—42no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—42no—
79C2×C13×C22⋊C4Q814yes—
80C2×C42×C13—22no—
81C2×C42×C13—24no—
82C2×C42×C13—42no—
83C2×C42×C13D414yes—
84C13×#95—22no—
85C13×#95—22no—
86C13×#95—24no—
87C13×#95—24no—
88C13×#95—24no—
89C13×#95—24no—
90C13×#95—24no—
91C13×#95—22no—
92C13×#95—22no—
93C13×#95—42no—
94C13×#95D418yes—
95#14969C1311yesmaximal, characteristic, direct product factor, Sylow
96C24×C13—21no—
97C24×C13—22no—
98C24×C13—21no—
99C24×C13—21no—
100C24×C13—22no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13C2×Q812yes—
105C24×C13#4112yes—
106C24×C13#4112yes—
107C24×C13C2411yescharacteristic
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—28no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
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—48no—
156C22×C4×C13—48no—
157C22×C4×C13—44no—
158C22×C4×C13—44no—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D414yes—
161C22×C4×C13C2×D414yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D414yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×Q812yes—
166C22×C4×C13C2×Q812yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4114yes—
169C22×C4×C13#4112yes—
170C22×C4×C13#4112yes—
171C13×C4⋊C4—28no—
172C13×C4⋊C4—216no—
173C13×C4⋊C4—48no—
174C13×C4⋊C4—44no—
175C13×C4⋊C4—48no—
176C13×C22⋊C4—28no—
177C13×C22⋊C4—216no—
178C13×C22⋊C4—28no—
179C13×C22⋊C4—48no—
180C42×C13—44no—
181C42×C13—44no—
182C2×#389C2×C1311yescharacteristic, complemented
183C2×#387C2×C1312yescomplemented
184C2×#385C2×C1312yes—
185C2×C4×C22⋊C4C2×C1311yescharacteristic
186#1445C2×C1312yescomplemented
187#1444C2×C1311yescharacteristic, complemented
188#1444C2×C1311yescharacteristic, complemented
189#1439C2×C1312yes—
190#1439C2×C1311yescharacteristic
191#1439C2×C1311yescharacteristic
192#1434C2×C1311yescharacteristic, complemented
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—24no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—24no—
205C23×C13—41no—
206C23×C13—42no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13#12514yes—
216C23×C13C22×D411yescharacteristic
217C23×C13C22×D412yes—
218C23×C13C22×Q811yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13C2×#4112yes—
223C23×C13C2×#4111yescharacteristic
224C23×C13C2×#4111yescharacteristic
225C23×C13H(5,𝔽2)12yes—
226C23×C132−1+412yes—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—416no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—42no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—42no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13C22⋊Q814yes—
285C2×C4×C13#12714yes—
286C24×C4C22×C1311yescharacteristic
287C22×C4⋊C4C22×C1312yes—
288C22×C4⋊C4C22×C1311yescharacteristic
289C22×C4⋊C4C22×C1312yes—
290C22×C4⋊C4C22×C1312yes—
291C22×C4⋊C4C22×C1311yescharacteristic
292C22×C22⋊C4C22×C1311yescharacteristic
293C22×C22⋊C4C22×C1312yes—
294C22×C22⋊C4C22×C1312yes—
295C22×C22⋊C4C22×C1311yescharacteristic
296C22×C42C22×C1311yescharacteristic
297C22×C42C22×C1311yescharacteristic
298#389—24no—
299#387—28no—
300#385—28no—
301C4×C22⋊C4—24no—
302C2×#95C22×C1311yescharacteristic
303C2×#95C22×C1311yescharacteristic
304C2×#95C22×C1312yes—
305C2×#95C22×C1312yes—
306C2×#95C22×C1312yes—
307C2×#95C22×C1312yes—
308C2×#95C22×C1311yescharacteristic
309C2×#95C22×C1312yes—
310C2×#95C22×C1311yescharacteristic
311C2×#95C22×C1312yes—
312C2×#95C22×C1312yes—
313C22×C13—24no—
314C22×C13—28no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—44no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13C2×C22⋊Q811yescharacteristic
325C22×C13#52511yescharacteristic
326C22×C13#52511yescharacteristic
327C22×C13#52511yescharacteristic
328C22×C13#52512yes—
329C22×C13#52512yes—
330C22×C13C2×#12511yescharacteristic
331C22×C13#52911yescharacteristic
332C22×C13#52911yescharacteristic
333C22×C13C2×#12711yescharacteristic
334C22×C13#53311yescharacteristic
335C22×C13#53411yescharacteristic
336C22×C13#53611yescharacteristic
337C22×C13#53912yes—
338C22×C13#54212yes—
339C22×C13#54612yes—
340C22×C13#54612yes—
341C22×C13#54712yes—
342C22×C13D4×Q812yes—
343C22×C13#55212yes—
344C22×C13#55312yes—
345C22×C13#55412yes—
346C22×C13#55612yes—
347C4×C13—24no—
348C4×C13—24no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—44no—
352C4×C13—44no—
353C4×C13—44no—
354C4×C13—42no—
355C4×C13—42no—
356C4×C13—82no—
357C25C23×C1311yescharacteristic
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—42no—
363C23×C4C23×C1312yes—
364C23×C4C23×C1312yes—
365C23×C4C23×C1312yes—
366C23×C4C23×C1311yescharacteristic
367C23×C4C23×C1311yescharacteristic
368C23×C4C23×C1312yes—
369C23×C4C23×C1311yescharacteristic
370C23×C4C23×C1311yescharacteristic
371C23×C4C23×C1311yescharacteristic
372C23×C4C23×C1311yescharacteristic
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4Q8×C1314yes—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42D4×C1314yes—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—22no—
410#95—22no—
411#95—42no—
412#95D4×C1318yes—
413C2×C13—44no—
414C2×C13#239711yescharacteristic
415C2×C13#246512yes—
416C2×C13#246612yes—
417C2×C13#247012yes—
418C2×C13#247312yes—
419C2×C13#253911yescharacteristic
420C2×C13#254211yescharacteristic
421C2×C13#257911yescharacteristic
422C2×C13#259911yescharacteristic
423C2×C13#263811yescharacteristic
424C2×C13#285111yescharacteristic
425C24—21no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24C2×Q8×C1312yes—
434C24C13×#4112yes—
435C24C13×#4112yes—
436C24C24×C1311yescharacteristic
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4C2×D4×C1312yes—
489C22×C4C2×D4×C1314yes—
490C22×C4C2×D4×C1314yes—
491C22×C4C2×D4×C1312yes—
492C22×C4C2×D4×C1314yes—
493C22×C4C2×D4×C1312yes—
494C22×C4C2×Q8×C1312yes—
495C22×C4C2×Q8×C1312yes—
496C22×C4C13×#4112yes—
497C22×C4C13×#4114yes—
498C22×C4C13×#4112yes—
499C22×C4C13×#4112yes—
500C4⋊C4—28no—
501C4⋊C4—216no—
502C4⋊C4—48no—
503C4⋊C4—44no—
504C4⋊C4—48no—
505C22⋊C4—28no—
506C22⋊C4—216no—
507C22⋊C4—28no—
508C22⋊C4—48no—
509C42—44no—
510C42—44no—
511C13#1496911yescharacteristic, direct product factor, Sylow
512C23—22no—
513C23—22no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—41no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23C13×#12514yes—
535C23C22×D4×C1311yescharacteristic
536C23C22×D4×C1312yes—
537C23C22×Q8×C1311yescharacteristic
538C23C2×C13×#4111yescharacteristic
539C23C2×C13×#4111yescharacteristic
540C23C2×C13×#4111yescharacteristic
541C23C2×C13×#4112yes—
542C23C2×C13×#4111yescharacteristic
543C23C2×C13×#4111yescharacteristic
544C23C13×H(5,𝔽2)12yes—
545C23C13×2−1+412yes—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—416no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4C13×C22⋊Q814yes—
604C2×C4C13×#12714yes—
605C22—24no—
606C22—28no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22C2×C13×C22⋊Q811yescharacteristic
617C22C13×#52511yescharacteristic
618C22C13×#52511yescharacteristic
619C22C13×#52511yescharacteristic
620C22C13×#52512yes—
621C22C13×#52512yes—
622C22C2×C13×#12511yescharacteristic
623C22C13×#52911yescharacteristic
624C22C13×#52911yescharacteristic
625C22C2×C13×#12711yescharacteristic
626C22C13×#53311yescharacteristic
627C22C13×#53411yescharacteristic
628C22C13×#53611yescharacteristic
629C22C13×#53912yes—
630C22C13×#54212yes—
631C22C13×#54612yes—
632C22C13×#54612yes—
633C22C13×#54712yes—
634C22D4×Q8×C1312yes—
635C22C13×#55212yes—
636C22C13×#55312yes—
637C22C13×#55412yes—
638C22C13×#55612yes—
639C4—24no—
640C4—24no—
641C4—42no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—44no—
646C4—44no—
647C4—44no—
648C4—82no—
649C2—44no—
650C2C13×#239711yescharacteristic
651C2C13×#246512yes—
652C2C13×#246612yes—
653C2C13×#247012yes—
654C2C13×#247312yes—
655C2C13×#253911yescharacteristic
656C2C13×#254211yescharacteristic
657C2C13×#257911yescharacteristic
658C2C13×#259911yescharacteristic
659C2C13×#263811yescharacteristic
660C2C13×#285111yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#389C2semidirect
2. C2×C13×#387C2semidirect
5. C13×#1445C2semidirect
6. C13×#1444C2semidirect
7. C13×#1444C2semidirect
11. C13×#1434C2semidirect
95. #14969C13direct (N × H)
182. C2×#389C2×C13semidirect
183. C2×#387C2×C13semidirect
186. #1445C2×C13semidirect
187. #1444C2×C13semidirect
188. #1444C2×C13semidirect
192. #1434C2×C13semidirect
511. C13#14969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3892
C2×C13×#3872
C2×C13×#3852
C2×C4×C13×C22⋊C42
C13×#14452
C13×#14442
C13×#14392
C13×#14342
#1496913