Finite Group Databasebeta

← C13×#14808 #15701147

Subgroups — C13×#14808 #15701147

Order 3328.

1526 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C211yesmaximal, characteristic
2C2×C13×#389C211yesmaximal, characteristic, complemented
3C2×C13×#388C212yesmaximal
4C2×C13×#388C211yesmaximal, characteristic
5C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C13×#1445C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1441C212yesmaximal, complemented
9C13×#1439C211yesmaximal, characteristic
10C13×#1439C212yesmaximal
11C13×#1436C212yesmaximal, complemented
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2212yes—
23C22×C42×C13C2211yescharacteristic
24C13×#397—24no—
25C13×#389—24no—
26C13×#388—28no—
27C13×#388—24no—
28C4×C13×C4⋊C4—24no—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2211yescharacteristic
40C25×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—24no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—24no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—24no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—24no—
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—22no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—42no—
77C2×C13×C22⋊C4D414yes—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—24no—
81C2×C42×C13—24no—
82C2×C42×C13—42no—
83C2×C42×C13D414yes—
84C13×#95—22no—
85C13×#95—24no—
86C13×#95—24no—
87C13×#95—22no—
88C13×#95—22no—
89C13×#95—24no—
90C13×#95—24no—
91C13×#95—24no—
92C13×#95—24no—
93C13×#95—42no—
94C13×#95D414yes—
95#14808C1311yesmaximal, characteristic, direct product factor, Sylow
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—21no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13—22no—
105C24×C13—21no—
106C24×C13C2×D412yes—
107C24×C13C2411yescharacteristic
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
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—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
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—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D414yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13#4114yes—
164C22×C4×C13#4114yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×C4×C13#4114yes—
168C13×C4⋊C4—28no—
169C13×C4⋊C4—216no—
170C13×C4⋊C4—48no—
171C13×C4⋊C4—44no—
172C13×C4⋊C4—44no—
173C13×C22⋊C4—216no—
174C13×C22⋊C4—28no—
175C13×C22⋊C4—48no—
176C13×C22⋊C4—44no—
177C13×C22⋊C4—44no—
178C42×C13—28no—
179C42×C13—48no—
180C2×#397C2×C1311yescharacteristic
181C2×#389C2×C1311yescharacteristic, complemented
182C2×#388C2×C1311yescharacteristic
183C2×#388C2×C1312yes—
184C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
185#1445C2×C1311yescharacteristic, complemented
186#1442C2×C1311yescharacteristic, complemented
187#1441C2×C1312yescomplemented
188#1439C2×C1311yescharacteristic
189#1439C2×C1312yes—
190#1436C2×C1312yescomplemented
191C23×C13—22no—
192C23×C13—24no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—24no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—41no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—41no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13C22×D411yescharacteristic
215C23×C13C22×D411yescharacteristic
216C23×C13C22×D411yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C23×C13C2×#4111yescharacteristic
219C23×C13C2×#4112yes—
220C23×C13C2×#4112yes—
221C23×C13C2×#4112yes—
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C132−1+412yes—
224C23×C132−1+411yescharacteristic
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—41no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—41no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—41no—
269C2×C4×C13—42no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
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#12114yes—
283C2×C4×C13#12114yes—
284C2×C4×C13#12414yes—
285C22×C4⋊C4C22×C1311yescharacteristic
286C22×C4⋊C4C22×C1312yes—
287C22×C4⋊C4C22×C1312yes—
288C22×C4⋊C4C22×C1311yescharacteristic
289C22×C4⋊C4C22×C1311yescharacteristic
290C22×C22⋊C4C22×C1311yescharacteristic
291C22×C22⋊C4C22×C1312yes—
292C22×C22⋊C4C22×C1311yescharacteristic
293C22×C22⋊C4C22×C1312yes—
294C22×C22⋊C4C22×C1311yescharacteristic
295C22×C42C22×C1312yes—
296C22×C42C22×C1311yescharacteristic
297#397—24no—
298#389—24no—
299#388—28no—
300#388—24no—
301C4×C4⋊C4—24no—
302C2×#95C22×C1312yes—
303C2×#95C22×C1311yescharacteristic
304C2×#95C22×C1312yes—
305C2×#95C22×C1312yes—
306C2×#95C22×C1312yes—
307C2×#95C22×C1311yescharacteristic
308C2×#95C22×C1312yes—
309C2×#95C22×C1312yes—
310C2×#95C22×C1311yescharacteristic
311C2×#95C22×C1312yes—
312C2×#95C22×C1311yescharacteristic
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—44no—
316C22×C13—44no—
317C22×C13—42no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—82no—
321C22×C13—81no—
322C22×C13—81no—
323C22×C13—82no—
324C22×C13C2×#12111yescharacteristic
325C22×C13C2×#12111yescharacteristic
326C22×C13#52511yescharacteristic
327C22×C13#52512yes—
328C22×C13#52512yes—
329C22×C13C2×#12411yescharacteristic
330C22×C13#52912yes—
331C22×C13#52912yes—
332C22×C13#53211yescharacteristic
333C22×C13#53611yescharacteristic
334C22×C13#53711yescharacteristic
335C22×C13#53912yes—
336C22×C13#54112yes—
337C22×C13D4211yescharacteristic
338C22×C13#54712yes—
339C22×C13#54711yescharacteristic
340C22×C13#54712yes—
341C22×C13#54811yescharacteristic
342C22×C13#55212yes—
343C22×C13#55311yescharacteristic
344C22×C13#55612yes—
345C22×C13#55612yes—
346C22×C13#55912yes—
347C4×C13—24no—
348C4×C13—24no—
349C4×C13—24no—
350C4×C13—44no—
351C4×C13—44no—
352C4×C13—44no—
353C4×C13—42no—
354C4×C13—81no—
355C4×C13—81no—
356C4×C13—82no—
357C25C23×C1311yescharacteristic
358C23×C4C23×C1312yes—
359C23×C4C23×C1311yescharacteristic
360C23×C4C23×C1311yescharacteristic
361C23×C4C23×C1311yescharacteristic
362C23×C4C23×C1312yes—
363C23×C4C23×C1312yes—
364C23×C4C23×C1312yes—
365C23×C4C23×C1311yescharacteristic
366C23×C4C23×C1311yescharacteristic
367C23×C4C23×C1311yescharacteristic
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4D4×C1314yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42D4×C1314yes—
401#95—22no—
402#95—24no—
403#95—24no—
404#95—22no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—42no—
411#95D4×C1314yes—
412C2×C13—82no—
413C2×C13#239211yescharacteristic
414C2×C13#241311yescharacteristic
415C2×C13#241611yescharacteristic
416C2×C13#245512yes—
417C2×C13#246912yes—
418C2×C13#247812yes—
419C2×C13#254711yescharacteristic
420C2×C13#259211yescharacteristic
421C2×C13#259612yes—
422C2×C13#266411yescharacteristic
423C2×C13#285011yescharacteristic
424C24—21no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24C2×D4×C1312yes—
435C24C24×C1311yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4C2×D4×C1312yes—
485C22×C4C2×D4×C1314yes—
486C22×C4C2×D4×C1312yes—
487C22×C4C2×D4×C1312yes—
488C22×C4C2×D4×C1312yes—
489C22×C4C2×D4×C1312yes—
490C22×C4C2×D4×C1312yes—
491C22×C4C13×#4114yes—
492C22×C4C13×#4114yes—
493C22×C4C13×#4112yes—
494C22×C4C13×#4112yes—
495C22×C4C13×#4114yes—
496C4⋊C4—28no—
497C4⋊C4—216no—
498C4⋊C4—48no—
499C4⋊C4—44no—
500C4⋊C4—44no—
501C22⋊C4—216no—
502C22⋊C4—28no—
503C22⋊C4—48no—
504C22⋊C4—44no—
505C22⋊C4—44no—
506C42—28no—
507C42—48no—
508C13#1480811yescharacteristic, direct product factor, Sylow
509C23—22no—
510C23—24no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23C22×D4×C1311yescharacteristic
533C23C22×D4×C1311yescharacteristic
534C23C22×D4×C1311yescharacteristic
535C23C2×C13×#4111yescharacteristic
536C23C2×C13×#4111yescharacteristic
537C23C2×C13×#4112yes—
538C23C2×C13×#4112yes—
539C23C2×C13×#4112yes—
540C23C13×H(5,𝔽2)11yescharacteristic
541C23C13×2−1+412yes—
542C23C13×2−1+411yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4C13×#12114yes—
601C2×C4C13×#12114yes—
602C2×C4C13×#12414yes—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22—81no—
609C22—81no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—82no—
614C22C2×C13×#12111yescharacteristic
615C22C2×C13×#12111yescharacteristic
616C22C13×#52511yescharacteristic
617C22C13×#52512yes—
618C22C13×#52512yes—
619C22C2×C13×#12411yescharacteristic
620C22C13×#52912yes—
621C22C13×#52912yes—
622C22C13×#53211yescharacteristic
623C22C13×#53611yescharacteristic
624C22C13×#53711yescharacteristic
625C22C13×#53912yes—
626C22C13×#54112yes—
627C22D42×C1311yescharacteristic
628C22C13×#54712yes—
629C22C13×#54712yes—
630C22C13×#54711yescharacteristic
631C22C13×#54811yescharacteristic
632C22C13×#55212yes—
633C22C13×#55311yescharacteristic
634C22C13×#55612yes—
635C22C13×#55612yes—
636C22C13×#55912yes—
637C4—24no—
638C4—24no—
639C4—24no—
640C4—42no—
641C4—44no—
642C4—44no—
643C4—44no—
644C4—81no—
645C4—81no—
646C4—82no—
647C2—82no—
648C2C13×#239211yescharacteristic
649C2C13×#241311yescharacteristic
650C2C13×#241611yescharacteristic
651C2C13×#245512yes—
652C2C13×#246912yes—
653C2C13×#247812yes—
654C2C13×#254711yescharacteristic
655C2C13×#259211yescharacteristic
656C2C13×#259612yes—
657C2C13×#266411yescharacteristic
658C2C13×#285011yescharacteristic
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
2. C2×C13×#389C2semidirect
5. C2×C4×C13×C4⋊C4C2semidirect
6. C13×#1445C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
11. C13×#1436C2semidirect
95. #14808C13direct (N × H)
181. C2×#389C2×C13semidirect
184. C2×C4×C4⋊C4C2×C13semidirect
185. #1445C2×C13semidirect
186. #1442C2×C13semidirect
187. #1441C2×C13semidirect
190. #1436C2×C13semidirect
508. C13#14808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3892
C2×C13×#3882
C2×C4×C13×C4⋊C42
C13×#14452
C13×#14422
C13×#14412
C13×#14392
C13×#14362
#1480813