Finite Group Databasebeta

← C13×#24350 #15710689

Subgroups — C13×#24350 #15710689

Order 3328.

1462 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic, complemented
2C13×#2848C212yesmaximal, complemented
3C4×C13×#120C211yesmaximal, characteristic
4C13×#2062C212yesmaximal, complemented
5C13×#2029C212yesmaximal, complemented
6C13×#1996C212yesmaximal, complemented
7C13×#1889C212yesmaximal
8C13×#1867C212yesmaximal, complemented
9C13×#1799C211yesmaximal, characteristic, complemented
10C24×C4×C13C2211yescharacteristic
11C13×#554—22no—
12C13×#554—24no—
13D4×Q8×C13—22no—
14C13×#544—21no—
15C13×#543—21no—
16C13×#543C2212yes—
17C13×#533—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—22no—
20C2×C13×C22⋊Q8C2212yes—
21C2×C13×#120C2211yescharacteristic
22C13×#518C2212yes—
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C2×C13×#99C2212yes—
26C13×#386—21no—
27C13×#386C2211yescharacteristic
28C13×#385—21no—
29C13×#385—24no—
30C13×#385C2211yescharacteristic
31C13×#385C2214yes—
32C13×#380—22no—
33C13×#380C2212yes—
34C13×#379C2211yescharacteristic
35C13×#379C2214yes—
36C4×C13×C22⋊C4—21no—
37C4×C13×C22⋊C4C2211yescharacteristic
38C13×#342C2214yes—
39C13×#342C2214yes—
40C13×#342C2212yes—
41C25×C13C2311yescharacteristic
42C22×Q8×C13—21no—
43C22×Q8×C13D412yescomplemented
44C22×D4×C13—21no—
45C22×D4×C13C2311yescharacteristic
46C23×C4×C13—21no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—21no—
50C23×C4×C13—44no—
51C23×C4×C13D411yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—24no—
57C13×#125—22no—
58C13×#125—24no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8—24no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8—24no—
70C13×C22⋊Q8—24no—
71C13×C22⋊Q8—48no—
72C13×#120—22no—
73C13×#120Q814yescomplemented
74C4×Q8×C13—22no—
75C4×Q8×C13—22no—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C4×D4×C13—24no—
79C4×D4×C13—24no—
80C4×D4×C13—44no—
81C13×#117—22no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4D411yescharacteristic
88C2×C13×C4⋊C4D412yescomplemented
89C2×C13×C4⋊C4D414yescomplemented
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—24no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C13×C22⋊C4C2311yescharacteristic
99C2×C13×C22⋊C4C2314yes—
100C2×C13×C22⋊C4C2311yescharacteristic
101C2×C13×C22⋊C4C2314yes—
102C2×C13×C22⋊C4C2311yescharacteristic
103C2×C42×C13—21no—
104C2×C42×C13D411yescharacteristic
105C13×#99—24no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—24no—
110C13×#95—22no—
111#24350C1311yesmaximal, characteristic, direct product factor, Sylow
112C24×C13—22no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—22no—
116C24×C13—42no—
117C24×C13—42no—
118C24×C13C2×D411yescharacteristic
119C24×C13C2×Q812yescomplemented
120C24×C13C2411yescharacteristic
121C2×Q8×C13—22no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—44no—
126C2×Q8×C13—82no—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13—24no—
130C2×D4×C13—42no—
131C2×D4×C13—42no—
132C2×D4×C13C2×Q812yes—
133C2×D4×C13#4112yes—
134C22×C4×C13—24no—
135C22×C4×C13—28no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—44no—
149C22×C4×C13—42no—
150C22×C4×C13—44no—
151C22×C4×C13—42no—
152C22×C4×C13—44no—
153C22×C4×C13—42no—
154C22×C4×C13—41no—
155C22×C4×C13—42no—
156C22×C4×C13—41no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D414yes—
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D414yes—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D412yes—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—24no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—24no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—44no—
179C13×C4⋊C4—48no—
180C13×C22⋊C4—24no—
181C13×C22⋊C4—24no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—24no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—24no—
187C13×C22⋊C4—24no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—24no—
190C13×C22⋊C4—42no—
191C13×C22⋊C4—48no—
192C13×C22⋊C4—42no—
193C13×C22⋊C4—42no—
194C13×C22⋊C4—48no—
195C13×C22⋊C4C2×Q812yescomplemented
196C42×C13—24no—
197C42×C13—21no—
198C42×C13—21no—
199C42×C13—42no—
200#3501C2×C1311yescharacteristic, complemented
201#2848C2×C1312yescomplemented
202C4×#120C2×C1311yescharacteristic
203#2062C2×C1312yescomplemented
204#2029C2×C1312yescomplemented
205#1996C2×C1312yescomplemented
206#1889C2×C1312yes—
207#1867C2×C1312yescomplemented
208#1799C2×C1311yescharacteristic, complemented
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—21no—
214C23×C13—22no—
215C23×C13—24no—
216C23×C13—21no—
217C23×C13—41no—
218C23×C13—44no—
219C23×C13—41no—
220C23×C13—42no—
221C23×C13—41no—
222C23×C13—42no—
223C23×C13—41no—
224C23×C13—44no—
225C23×C13—48no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—42no—
231C23×C13C22⋊Q812yescomplemented
232C23×C13C22×D411yescharacteristic
233C23×C13C22×D412yes—
234C23×C13C22×Q811yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C132−1+412yes—
237Q8×C13—44no—
238Q8×C13—82no—
239Q8×C13—82no—
240Q8×C13—82no—
241D4×C13—24no—
242D4×C13—24no—
243D4×C13—48no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—24no—
250C2×C4×C13—21no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—42no—
256C2×C4×C13—41no—
257C2×C4×C13—44no—
258C2×C4×C13—48no—
259C2×C4×C13—41no—
260C2×C4×C13—42no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—44no—
265C2×C4×C13—42no—
266C2×C4×C13—41no—
267C2×C4×C13—44no—
268C2×C4×C13—44no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—44no—
272C2×C4×C13—44no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—44no—
276C2×C4×C13—81no—
277C2×C4×C13—82no—
278C2×C4×C13—82no—
279C2×C4×C13#12011yescharacteristic
280C2×C4×C13#12012yes—
281C2×C4×C13#12011yescharacteristic
282C2×C4×C13C22⋊Q812yescomplemented
283C24×C4C22×C1311yescharacteristic
284#554—22no—
285#554—24no—
286D4×Q8—22no—
287#544—21no—
288#543—21no—
289#543C22×C1312yes—
290#533—21no—
291C2×C22⋊Q8—21no—
292C2×C22⋊Q8—22no—
293C2×C22⋊Q8C22×C1312yes—
294C2×#120C22×C1311yescharacteristic
295#518C22×C1312yes—
296C2×C4×D4—21no—
297C2×C4×D4C22×C1311yescharacteristic
298C2×#99C22×C1312yes—
299#386—21no—
300#386C22×C1311yescharacteristic
301#385—21no—
302#385—24no—
303#385C22×C1311yescharacteristic
304#385C22×C1314yes—
305#380—22no—
306#380C22×C1312yes—
307#379C22×C1314yes—
308#379C22×C1311yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4C22×C1311yescharacteristic
311#342C22×C1312yes—
312#342C22×C1314yes—
313#342C22×C1314yes—
314C22×C13—22no—
315C22×C13—21no—
316C22×C13—22no—
317C22×C13—21no—
318C22×C13—24no—
319C22×C13—28no—
320C22×C13—22no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—44no—
327C22×C13—44no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—44no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—42no—
336C22×C13—81no—
337C22×C13C2×#12011yescharacteristic
338C22×C13C2×C22⋊Q811yescharacteristic
339C22×C13#53611yescharacteristic
340C22×C13#54812yes—
341C22×C13D4×Q812yes—
342C4×C13—22no—
343C4×C13—21no—
344C4×C13—22no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13—41no—
348C4×C13—44no—
349C4×C13—44no—
350C4×C13—41no—
351C4×C13—84no—
352C4×C13—81no—
353C4×C13B(4,𝔽2)12yes—
354C25C23×C1311yescharacteristic
355C22×Q8—21no—
356C22×Q8D4×C1312yescomplemented
357C22×D4—21no—
358C22×D4C23×C1311yescharacteristic
359C23×C4—21no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—21no—
363C23×C4—44no—
364C23×C4D4×C1311yescharacteristic
365C23×C4C23×C1311yescharacteristic
366C23×C4C23×C1311yescharacteristic
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—24no—
370#125—22no—
371#125—24no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—24no—
383C22⋊Q8—24no—
384C22⋊Q8—48no—
385#120—22no—
386#120Q8×C1314yescomplemented
387C4×Q8—22no—
388C4×Q8—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—24no—
392C4×D4—24no—
393C4×D4—44no—
394#117—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4D4×C1311yescharacteristic
401C2×C4⋊C4D4×C1312yescomplemented
402C2×C4⋊C4D4×C1314yescomplemented
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4D4×C1311yescharacteristic
411C2×C22⋊C4C23×C1311yescharacteristic
412C2×C22⋊C4C23×C1314yes—
413C2×C22⋊C4C23×C1311yescharacteristic
414C2×C22⋊C4C23×C1314yes—
415C2×C22⋊C4C23×C1311yescharacteristic
416C2×C42—21no—
417C2×C42D4×C1311yescharacteristic
418#99—24no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—24no—
423#95—22no—
424C2×C13—21no—
425C2×C13—22no—
426C2×C13—21no—
427C2×C13—22no—
428C2×C13—44no—
429C2×C13—42no—
430C2×C13#240911yescharacteristic
431C2×C13C2×B(4,𝔽2)11yescharacteristic
432C2×C13#302511yescharacteristic
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—42no—
438C24—42no—
439C24C2×D4×C1311yescharacteristic
440C24C2×Q8×C1312yescomplemented
441C24C24×C1311yescharacteristic
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—44no—
447C2×Q8—82no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—24no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4C2×Q8×C1312yes—
454C2×D4C13×#4112yes—
455C22×C4—24no—
456C22×C4—28no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—44no—
474C22×C4—42no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4C2×D4×C1311yescharacteristic
479C22×C4C2×D4×C1312yes—
480C22×C4C2×D4×C1311yescharacteristic
481C22×C4C2×D4×C1311yescharacteristic
482C22×C4C2×D4×C1314yes—
483C22×C4C2×D4×C1311yescharacteristic
484C22×C4C2×D4×C1314yes—
485C22×C4C2×D4×C1311yescharacteristic
486C22×C4C2×D4×C1312yes—
487C4⋊C4—22no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—24no—
492C4⋊C4—22no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—24no—
498C4⋊C4—42no—
499C4⋊C4—44no—
500C4⋊C4—48no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—24no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—24no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—48no—
514C22⋊C4—48no—
515C22⋊C4—42no—
516C22⋊C4C2×Q8×C1312yescomplemented
517C42—24no—
518C42—21no—
519C42—21no—
520C42—42no—
521C13#2435011yescharacteristic, direct product factor, Sylow
522C23—24no—
523C23—24no—
524C23—22no—
525C23—22no—
526C23—21no—
527C23—22no—
528C23—24no—
529C23—21no—
530C23—41no—
531C23—44no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—41no—
537C23—44no—
538C23—48no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—42no—
544C23C13×C22⋊Q812yescomplemented
545C23C22×D4×C1311yescharacteristic
546C23C22×D4×C1312yes—
547C23C22×Q8×C1311yescharacteristic
548C23C2×C13×#4111yescharacteristic
549C23C13×2−1+412yes—
550Q8—44no—
551Q8—82no—
552Q8—82no—
553Q8—82no—
554D4—24no—
555D4—24no—
556D4—48no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—44no—
571C2×C4—48no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—44no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—44no—
589C2×C4—81no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4C13×#12011yescharacteristic
593C2×C4C13×#12012yes—
594C2×C4C13×#12011yescharacteristic
595C2×C4C13×C22⋊Q812yescomplemented
596C22—22no—
597C22—21no—
598C22—22no—
599C22—21no—
600C22—24no—
601C22—28no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—44no—
613C22—42no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22C2×C13×#12011yescharacteristic
620C22C2×C13×C22⋊Q811yescharacteristic
621C22C13×#53611yescharacteristic
622C22C13×#54812yes—
623C22D4×Q8×C1312yes—
624C4—21no—
625C4—22no—
626C4—22no—
627C4—42no—
628C4—42no—
629C4—41no—
630C4—44no—
631C4—44no—
632C4—41no—
633C4—84no—
634C4—81no—
635C4C13×B(4,𝔽2)12yes—
636C2—21no—
637C2—22no—
638C2—21no—
639C2—22no—
640C2—44no—
641C2—42no—
642C2C13×#240911yescharacteristic
643C2C2×C13×B(4,𝔽2)11yescharacteristic
644C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#120C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3501C2semidirect
2. C13×#2848C2semidirect
4. C13×#2062C2semidirect
5. C13×#2029C2semidirect
6. C13×#1996C2semidirect
8. C13×#1867C2semidirect
9. C13×#1799C2semidirect
43. C22×Q8×C13D4semidirect
73. C13×#120Q8semidirect
88. C2×C13×C4⋊C4D4semidirect
89. C2×C13×C4⋊C4D4semidirect
111. #24350C13direct (N × H)
119. C24×C13C2×Q8semidirect
195. C13×C22⋊C4C2×Q8semidirect
200. #3501C2×C13semidirect
201. #2848C2×C13semidirect
203. #2062C2×C13semidirect
204. #2029C2×C13semidirect
205. #1996C2×C13semidirect
207. #1867C2×C13semidirect
208. #1799C2×C13semidirect
231. C23×C13C22⋊Q8semidirect
282. C2×C4×C13C22⋊Q8semidirect
356. C22×Q8D4×C13semidirect
386. #120Q8×C13semidirect
401. C2×C4⋊C4D4×C13semidirect
402. C2×C4⋊C4D4×C13semidirect
440. C24C2×Q8×C13semidirect
516. C22⋊C4C2×Q8×C13semidirect
521. C13#24350direct (N × H)
544. C23C13×C22⋊Q8semidirect
595. C2×C4C13×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C13×#35012
C13×#28482
C4×C13×#1202
C13×#20622
C13×#20292
C13×#19962
C13×#18892
C13×#18672
C13×#17992
#2435013