Finite Group Databasebeta

← C13×#15429 #15701768

Subgroups — C13×#15429 #15701768

Order 3328.

2090 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C212yesmaximal, complemented
2C2×C13×#386C212yesmaximal
3C2×C13×#385C212yesmaximal, complemented
4C2×C13×#380C212yesmaximal, complemented
5C13×#1444C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1441C212yesmaximal, complemented
8C13×#1439C212yesmaximal, complemented
9C13×#1438C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2212yes—
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2212yes—
21C22×C13×C22⋊C4C2212yes—
22C13×#396—28no—
23C13×#386—28no—
24C13×#385—28no—
25C13×#380—28no—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C25×C13C2312yes—
36C22×D4×C13—24no—
37C22×D4×C13—24no—
38C22×D4×C13—41no—
39C22×D4×C13—41no—
40C22×D4×C13Q814yes—
41C23×C4×C13—24no—
42C23×C4×C13—24no—
43C23×C4×C13—24no—
44C23×C4×C13—24no—
45C23×C4×C13—24no—
46C23×C4×C13—42no—
47C23×C4×C13—42no—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2312yes—
56C2×C13×C4⋊C4—24no—
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—24no—
64C2×C13×C4⋊C4—42no—
65C2×C13×C4⋊C4—42no—
66C2×C13×C4⋊C4—41no—
67C2×C13×C4⋊C4—41no—
68C2×C13×C4⋊C4—42no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4—42no—
80C2×C13×C22⋊C4—42no—
81C2×C13×C22⋊C4—42no—
82C2×C13×C22⋊C4—42no—
83C2×C13×C22⋊C4D418yes—
84C13×#95—24no—
85C13×#95—24no—
86C13×#95—24no—
87C13×#95—24no—
88C13×#95—24no—
89C13×#95—41no—
90C13×#95—41no—
91C13×#95D414yescomplemented
92C13×#95D414yescomplemented
93#15429C1311yesmaximal, characteristic, direct product factor, Sylow
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13C2×D414yes—
107C24×C13C2×Q814yes—
108C24×C13#4114yes—
109C24×C13C2411yescharacteristic
110C2×D4×C13—216no—
111C2×D4×C13—44no—
112C2×D4×C13—44no—
113C2×D4×C13—48no—
114C2×D4×C13—44no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—216no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
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—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
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—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—48no—
159C22×C4×C13—48no—
160C22×C4×C13—48no—
161C22×C4×C13—48no—
162C22×C4×C13—48no—
163C22×C4×C13—48no—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D414yes—
166C22×C4×C13C2×D414yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D414yes—
169C22×C4×C13C2×D414yes—
170C22×C4×C13C2×Q812yes—
171C22×C4×C13#4114yes—
172C13×C4⋊C4—48no—
173C13×C4⋊C4—48no—
174C13×C4⋊C4—44no—
175C13×C4⋊C4—44no—
176C13×C4⋊C4—48no—
177C13×C22⋊C4—216no—
178C13×C22⋊C4—48no—
179C13×C22⋊C4—48no—
180C13×C22⋊C4—48no—
181C13×C22⋊C4—48no—
182C2×#396C2×C1312yescomplemented
183C2×#386C2×C1312yes—
184C2×#385C2×C1312yescomplemented
185C2×#380C2×C1312yescomplemented
186#1444C2×C1311yescharacteristic, complemented
187#1442C2×C1311yescharacteristic, complemented
188#1441C2×C1312yescomplemented
189#1439C2×C1312yescomplemented
190#1438C2×C1311yescharacteristic
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—24no—
196C23×C13—24no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—24no—
205C23×C13—24no—
206C23×C13—24no—
207C23×C13—24no—
208C23×C13—24no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13C22⋊Q818yes—
226C23×C13C22×D411yescharacteristic
227C23×C13C22×D412yes—
228C23×C13C22×D411yescharacteristic
229C23×C13C22×Q811yescharacteristic
230C23×C13C2×#4112yes—
231C23×C13C2×#4112yes—
232C23×C13H(5,𝔽2)11yescharacteristic
233C23×C13H(5,𝔽2)12yes—
234C23×C13H(5,𝔽2)11yescharacteristic
235C23×C132−1+411yescharacteristic
236C23×C132−1+411yescharacteristic
237D4×C13—416no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
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—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—432no—
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—41no—
264C2×C4×C13—41no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—42no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
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×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13#12118yes—
289C23×D4C22×C1311yescharacteristic
290C24×C4C22×C1312yes—
291C22×C4⋊C4C22×C1312yes—
292C22×C4⋊C4C22×C1311yescharacteristic
293C22×C4⋊C4C22×C1312yes—
294C22×C4⋊C4C22×C1312yes—
295C22×C4⋊C4C22×C1311yescharacteristic
296C22×C22⋊C4C22×C1312yes—
297C22×C22⋊C4C22×C1312yes—
298C22×C22⋊C4C22×C1312yes—
299C22×C22⋊C4C22×C1312yes—
300C22×C22⋊C4C22×C1312yes—
301#396—28no—
302#386—28no—
303#385—28no—
304#380—28no—
305C2×#95C22×C1312yes—
306C2×#95C22×C1312yes—
307C2×#95C22×C1312yes—
308C2×#95C22×C1312yes—
309C2×#95C22×C1312yes—
310C2×#95C22×C1311yescharacteristic
311C2×#95C22×C1311yescharacteristic
312C2×#95C22×C1311yescharacteristic
313C2×#95C22×C1311yescharacteristic
314C22×C13—28no—
315C22×C13—28no—
316C22×C13—28no—
317C22×C13—44no—
318C22×C13—44no—
319C22×C13—44no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13—44no—
326C22×C13—44no—
327C22×C13—44no—
328C22×C13—44no—
329C22×C13C2×#12112yes—
330C22×C13C2×C22⋊Q812yes—
331C22×C13#52512yes—
332C22×C13#53711yescharacteristic
333C22×C13#53712yes—
334C22×C13#53711yescharacteristic
335C22×C13#53812yes—
336C22×C13#53912yes—
337C22×C13#54311yescharacteristic
338C22×C13D4212yes—
339C22×C13D4211yescharacteristic
340C22×C13D4211yescharacteristic
341C22×C13#54612yes—
342C22×C13#54612yes—
343C22×C13#54712yes—
344C22×C13D4×Q811yescharacteristic
345C22×C13D4×Q811yescharacteristic
346C22×C13#55111yescharacteristic
347C22×C13#55212yes—
348C22×C13#55412yes—
349C22×C13#55511yescharacteristic
350C22×C13#56011yescharacteristic
351C22×C13#56311yescharacteristic
352C4×C13—28no—
353C4×C13—42no—
354C4×C13—44no—
355C4×C13—42no—
356C4×C13—42no—
357C4×C13—44no—
358C4×C13—82no—
359C4×C13—82no—
360C25C23×C1312yes—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4Q8×C1314yes—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4C23×C1312yes—
374C23×C4C23×C1312yes—
375C23×C4C23×C1311yescharacteristic
376C23×C4C23×C1312yes—
377C23×C4C23×C1311yescharacteristic
378C23×C4C23×C1312yes—
379C23×C4C23×C1311yescharacteristic
380C23×C4C23×C1312yes—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—42no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4D4×C1318yes—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—41no—
415#95—41no—
416#95D4×C1314yescomplemented
417#95D4×C1314yescomplemented
418C2×C13—48no—
419C2×C13#241712yes—
420C2×C13#242412yes—
421C2×C13#243711yescharacteristic
422C2×C13#244912yes—
423C2×C13#253711yescharacteristic
424C2×C13#260911yescharacteristic
425C2×C13#267511yescharacteristic
426C2×C13#268311yescharacteristic
427C2×C13#269311yescharacteristic
428C2×C13#269512yes—
429C2×C13#278411yescharacteristic
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24C2×D4×C1314yes—
443C24C2×Q8×C1314yes—
444C24C13×#4114yes—
445C24C24×C1311yescharacteristic
446C2×D4—216no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—48no—
450C2×D4—44no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—216no—
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—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4C2×D4×C1312yes—
501C22×C4C2×D4×C1314yes—
502C22×C4C2×D4×C1314yes—
503C22×C4C2×D4×C1312yes—
504C22×C4C2×D4×C1314yes—
505C22×C4C2×D4×C1314yes—
506C22×C4C2×Q8×C1312yes—
507C22×C4C13×#4114yes—
508C4⋊C4—48no—
509C4⋊C4—48no—
510C4⋊C4—44no—
511C4⋊C4—44no—
512C4⋊C4—48no—
513C22⋊C4—216no—
514C22⋊C4—48no—
515C22⋊C4—48no—
516C22⋊C4—48no—
517C22⋊C4—48no—
518C13#1542911yescharacteristic, direct product factor, Sylow
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23C13×C22⋊Q818yes—
554C23C22×D4×C1311yescharacteristic
555C23C22×D4×C1312yes—
556C23C22×D4×C1311yescharacteristic
557C23C22×Q8×C1311yescharacteristic
558C23C2×C13×#4112yes—
559C23C2×C13×#4112yes—
560C23C13×H(5,𝔽2)11yescharacteristic
561C23C13×H(5,𝔽2)12yes—
562C23C13×H(5,𝔽2)11yescharacteristic
563C23C13×2−1+411yescharacteristic
564C23C13×2−1+411yescharacteristic
565D4—416no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—432no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4C13×#12118yes—
617C22—28no—
618C22—28no—
619C22—28no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22C2×C13×#12112yes—
633C22C2×C13×C22⋊Q812yes—
634C22C13×#52512yes—
635C22C13×#53711yescharacteristic
636C22C13×#53711yescharacteristic
637C22C13×#53712yes—
638C22C13×#53812yes—
639C22C13×#53912yes—
640C22C13×#54311yescharacteristic
641C22D42×C1311yescharacteristic
642C22D42×C1312yes—
643C22D42×C1311yescharacteristic
644C22C13×#54612yes—
645C22C13×#54612yes—
646C22C13×#54712yes—
647C22D4×Q8×C1311yescharacteristic
648C22D4×Q8×C1311yescharacteristic
649C22C13×#55111yescharacteristic
650C22C13×#55212yes—
651C22C13×#55412yes—
652C22C13×#55511yescharacteristic
653C22C13×#56011yescharacteristic
654C22C13×#56311yescharacteristic
655C4—28no—
656C4—44no—
657C4—42no—
658C4—44no—
659C4—42no—
660C4—42no—
661C4—82no—
662C4—82no—
663C2—48no—
664C2C13×#241712yes—
665C2C13×#242412yes—
666C2C13×#243711yescharacteristic
667C2C13×#244912yes—
668C2C13×#253711yescharacteristic
669C2C13×#260911yescharacteristic
670C2C13×#267511yescharacteristic
671C2C13×#268311yescharacteristic
672C2C13×#269311yescharacteristic
673C2C13×#269512yes—
674C2C13×#278411yescharacteristic
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
1. C2×C13×#396C2semidirect
3. C2×C13×#385C2semidirect
4. C2×C13×#380C2semidirect
5. C13×#1444C2semidirect
6. C13×#1442C2semidirect
7. C13×#1441C2semidirect
8. C13×#1439C2semidirect
91. C13×#95D4semidirect
92. C13×#95D4semidirect
93. #15429C13direct (N × H)
182. C2×#396C2×C13semidirect
184. C2×#385C2×C13semidirect
185. C2×#380C2×C13semidirect
186. #1444C2×C13semidirect
187. #1442C2×C13semidirect
188. #1441C2×C13semidirect
189. #1439C2×C13semidirect
416. #95D4×C13semidirect
417. #95D4×C13semidirect
518. C13#15429direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3962
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C13×#14442
C13×#14422
C13×#14412
C13×#14392
C13×#14382
#1542913