Finite Group Databasebeta

← C13×#15406 #15701745

Subgroups — C13×#15406 #15701745

Order 3328.

1674 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic
2C2×C13×#389C212yesmaximal, complemented
3C2×C13×#385C211yesmaximal, characteristic
4C2×C13×#385C212yesmaximal
5C13×#1444C212yesmaximal, complemented
6C13×#1444C212yesmaximal, complemented
7C13×#1442C212yesmaximal, complemented
8C13×#1439C212yesmaximal
9C13×#1437C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C13×#399—24no—
23C13×#389—28no—
24C13×#385—24no—
25C13×#385—28no—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C25×C13C2311yescharacteristic
36C23×C4×C13—22no—
37C23×C4×C13—24no—
38C23×C4×C13—41no—
39C23×C4×C13—42no—
40C23×C4×C13—41no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C2×C13×C4⋊C4—24no—
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—24no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—42no—
61C2×C13×C4⋊C4—42no—
62C2×C13×C4⋊C4—42no—
63C2×C13×C4⋊C4—42no—
64C2×C13×C4⋊C4—42no—
65C2×C13×C4⋊C4—41no—
66C2×C13×C4⋊C4—41no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—24no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—41no—
74C2×C13×C22⋊C4—41no—
75C2×C13×C22⋊C4—42no—
76C2×C13×C22⋊C4D414yes—
77C2×C13×C22⋊C4Q818yes—
78C2×C42×C13—24no—
79C2×C42×C13—41no—
80C13×#95—24no—
81C13×#95—24no—
82C13×#95—24no—
83C13×#95—22no—
84C13×#95—24no—
85C13×#95—24no—
86C13×#95—41no—
87C13×#95—42no—
88C13×#95D418yes—
89#15406C1311yesmaximal, characteristic, direct product factor, Sylow
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—21no—
94C24×C13—21no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13C2×D412yes—
98C24×C13C2×Q814yes—
99C24×C13C2411yescharacteristic
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
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—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
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—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—44no—
144C22×C4×C13—48no—
145C22×C4×C13—48no—
146C22×C4×C13—44no—
147C22×C4×C13—44no—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D414yes—
150C22×C4×C13C2×D414yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D414yes—
153C22×C4×C13C2×Q814yes—
154C22×C4×C13C2×Q814yes—
155C22×C4×C13#4114yes—
156C22×C4×C13#4114yes—
157C13×C4⋊C4—216no—
158C13×C4⋊C4—48no—
159C13×C4⋊C4—48no—
160C13×C4⋊C4—48no—
161C13×C4⋊C4—44no—
162C13×C4⋊C4—48no—
163C13×C22⋊C4—28no—
164C13×C22⋊C4—216no—
165C13×C22⋊C4—44no—
166C13×C22⋊C4—48no—
167C42×C13—44no—
168C2×#399C2×C1311yescharacteristic
169C2×#389C2×C1312yescomplemented
170C2×#385C2×C1311yescharacteristic
171C2×#385C2×C1312yes—
172#1444C2×C1312yescomplemented
173#1444C2×C1312yescomplemented
174#1442C2×C1312yescomplemented
175#1439C2×C1312yes—
176#1437C2×C1311yescharacteristic
177C23×C13—24no—
178C23×C13—22no—
179C23×C13—22no—
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—41no—
192C23×C13—42no—
193C23×C13—41no—
194C23×C13—42no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13C4⋊Q814yes—
198C23×C13C22×D412yes—
199C23×C13C22×D411yescharacteristic
200C23×C13C22×Q812yes—
201C23×C13C2×#4112yes—
202C23×C13C2×#4112yes—
203C23×C13H(5,𝔽2)11yescharacteristic
204C23×C13H(5,𝔽2)11yescharacteristic
205C23×C13H(5,𝔽2)12yes—
206C23×C132−1+412yes—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—416no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13C22⋊Q818yes—
260C24×C4C22×C1311yescharacteristic
261C22×C4⋊C4C22×C1312yes—
262C22×C4⋊C4C22×C1312yes—
263C22×C4⋊C4C22×C1312yes—
264C22×C4⋊C4C22×C1312yes—
265C22×C4⋊C4C22×C1311yescharacteristic
266C22×C4⋊C4C22×C1312yes—
267C22×C22⋊C4C22×C1311yescharacteristic
268C22×C22⋊C4C22×C1312yes—
269C22×C22⋊C4C22×C1312yes—
270C22×C22⋊C4C22×C1311yescharacteristic
271C22×C42C22×C1311yescharacteristic
272#399—24no—
273#389—28no—
274#385—24no—
275#385—28no—
276C2×#95C22×C1311yescharacteristic
277C2×#95C22×C1312yes—
278C2×#95C22×C1312yes—
279C2×#95C22×C1312yes—
280C2×#95C22×C1312yes—
281C2×#95C22×C1312yes—
282C2×#95C22×C1311yescharacteristic
283C2×#95C22×C1312yes—
284C2×#95C22×C1312yes—
285C22×C13—24no—
286C22×C13—28no—
287C22×C13—44no—
288C22×C13—42no—
289C22×C13—44no—
290C22×C13—44no—
291C22×C13—44no—
292C22×C13—42no—
293C22×C13—44no—
294C22×C13C2×C22⋊Q812yes—
295C22×C13#52512yes—
296C22×C13#52511yescharacteristic
297C22×C13C2×C4⋊Q811yescharacteristic
298C22×C13#53411yescharacteristic
299C22×C13#53512yes—
300C22×C13#53912yes—
301C22×C13#53912yes—
302C22×C13#54412yes—
303C22×C13D4212yes—
304C22×C13D4211yescharacteristic
305C22×C13#54712yes—
306C22×C13#54712yes—
307C22×C13D4×Q812yes—
308C22×C13#55412yes—
309C22×C13#55412yes—
310C22×C13#55412yes—
311C22×C13#55911yescharacteristic
312C22×C13#55912yes—
313C22×C13#56011yescharacteristic
314C22×C13#56311yescharacteristic
315C4×C13—28no—
316C4×C13—44no—
317C4×C13—42no—
318C4×C13—44no—
319C4×C13—44no—
320C4×C13—44no—
321C4×C13—42no—
322C4×C13—82no—
323C25C23×C1311yescharacteristic
324C23×C4—22no—
325C23×C4—24no—
326C23×C4—41no—
327C23×C4—42no—
328C23×C4—41no—
329C23×C4C23×C1312yes—
330C23×C4C23×C1311yescharacteristic
331C23×C4C23×C1312yes—
332C23×C4C23×C1311yescharacteristic
333C23×C4C23×C1312yes—
334C23×C4C23×C1312yes—
335C23×C4C23×C1312yes—
336C23×C4C23×C1312yes—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4D4×C1314yes—
365C2×C22⋊C4Q8×C1318yes—
366C2×C42—24no—
367C2×C42—41no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—22no—
372#95—24no—
373#95—24no—
374#95—41no—
375#95—42no—
376#95D4×C1318yes—
377C2×C13—44no—
378C2×C13#244012yes—
379C2×C13#244912yes—
380C2×C13#245512yes—
381C2×C13#258012yes—
382C2×C13#258311yescharacteristic
383C2×C13#266911yescharacteristic
384C2×C13#272012yes—
385C2×C13#272411yescharacteristic
386C2×C13#280712yes—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24C2×D4×C1312yes—
395C24C2×Q8×C1314yes—
396C24C24×C1311yescharacteristic
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—44no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4C2×D4×C1312yes—
446C22×C4C2×D4×C1314yes—
447C22×C4C2×D4×C1314yes—
448C22×C4C2×D4×C1312yes—
449C22×C4C2×D4×C1314yes—
450C22×C4C2×Q8×C1314yes—
451C22×C4C2×Q8×C1314yes—
452C22×C4C13×#4114yes—
453C22×C4C13×#4114yes—
454C4⋊C4—216no—
455C4⋊C4—48no—
456C4⋊C4—48no—
457C4⋊C4—48no—
458C4⋊C4—44no—
459C4⋊C4—48no—
460C22⋊C4—28no—
461C22⋊C4—216no—
462C22⋊C4—44no—
463C22⋊C4—48no—
464C42—44no—
465C13#1540611yescharacteristic, direct product factor, Sylow
466C23—24no—
467C23—22no—
468C23—22no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23C13×C4⋊Q814yes—
487C23C22×D4×C1312yes—
488C23C22×D4×C1311yescharacteristic
489C23C22×Q8×C1312yes—
490C23C2×C13×#4112yes—
491C23C2×C13×#4112yes—
492C23C13×H(5,𝔽2)11yescharacteristic
493C23C13×H(5,𝔽2)11yescharacteristic
494C23C13×H(5,𝔽2)12yes—
495C23C13×2−1+412yes—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—416no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4C13×C22⋊Q818yes—
549C22—24no—
550C22—28no—
551C22—44no—
552C22—44no—
553C22—42no—
554C22—44no—
555C22—44no—
556C22—44no—
557C22—42no—
558C22C2×C13×C22⋊Q812yes—
559C22C13×#52512yes—
560C22C13×#52511yescharacteristic
561C22C2×C13×C4⋊Q811yescharacteristic
562C22C13×#53411yescharacteristic
563C22C13×#53512yes—
564C22C13×#53912yes—
565C22C13×#53912yes—
566C22C13×#54412yes—
567C22D42×C1312yes—
568C22D42×C1311yescharacteristic
569C22C13×#54712yes—
570C22C13×#54712yes—
571C22D4×Q8×C1312yes—
572C22C13×#55412yes—
573C22C13×#55412yes—
574C22C13×#55412yes—
575C22C13×#55912yes—
576C22C13×#55911yescharacteristic
577C22C13×#56011yescharacteristic
578C22C13×#56311yescharacteristic
579C4—28no—
580C4—44no—
581C4—42no—
582C4—44no—
583C4—44no—
584C4—44no—
585C4—42no—
586C4—82no—
587C2—44no—
588C2C13×#244012yes—
589C2C13×#244912yes—
590C2C13×#245512yes—
591C2C13×#258012yes—
592C2C13×#258311yescharacteristic
593C2C13×#266911yescharacteristic
594C2C13×#272012yes—
595C2C13×#272411yescharacteristic
596C2C13×#280712yes—
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. C13×#1444C2semidirect
6. C13×#1444C2semidirect
7. C13×#1442C2semidirect
89. #15406C13direct (N × H)
169. C2×#389C2×C13semidirect
172. #1444C2×C13semidirect
173. #1444C2×C13semidirect
174. #1442C2×C13semidirect
465. C13#15406direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3992
C2×C13×#3892
C2×C13×#3852
C13×#14442
C13×#14422
C13×#14392
C13×#14372
#1540613