Finite Group Databasebeta

← C13×#18259 #15704598

Subgroups — C13×#18259 #15704598

Order 3328.

1132 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic
2C13×#3004C211yesmaximal, characteristic
3C2×C13×#451C211yesmaximal, characteristic, complemented
4C13×#2434C211yesmaximal, characteristic, complemented
5C13×#1605C214yesmaximal, complemented
6C13×#1603C214yesmaximal, complemented
7C13×#1508C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic
9C13×#1472C211yesmaximal, characteristic, complemented
10C23×Q8×C13C2211yescharacteristic
11C2×C13×#137—21no—
12C22×C13×Q16—21no—
13C13×#563—22no—
14C13×#552—21no—
15C13×#552—21no—
16C13×#551—22no—
17D4×Q8×C13—21no—
18D4×Q8×C13—21no—
19C13×#544—21no—
20C13×#544C2212yes—
21C13×#541—21no—
22C13×#539—21no—
23C13×#539C2212yes—
24C13×#536—21no—
25C2×C13×C4⋊Q8—21no—
26C13×#525C2211yescharacteristic
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×C22⋊Q8C2211yescharacteristic
29C13×#451—22no—
30C13×#451—21no—
31C13×#451C2214yes—
32C13×#451C2212yes—
33C13×#448—21no—
34C13×#448C2212yes—
35C13×#419—21no—
36C2×C13×#103—21no—
37C13×#407C2211yescharacteristic
38C2×C13×C22⋊C8C2211yescharacteristic
39C13×#395C2214yes—
40C13×#391—21no—
41C13×#385—22no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#324C2214yes—
47C2×C13×#41D411yescharacteristic
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13—21no—
51C22×Q8×C13—21no—
52C22×Q8×C13—21no—
53C22×Q8×C13—21no—
54C22×Q8×C13—44no—
55C22×Q8×C13D411yescharacteristic
56C22×Q8×C13D411yescharacteristic
57C22×Q8×C13C2312yes—
58C23×C4×C13—21no—
59C23×C4×C13C2311yescharacteristic
60C13×#137—44no—
61C2×C13×Q16—24no—
62C2×C13×Q16—22no—
63C2×C13×Q16—44no—
64C2×C13×SD16—22no—
65C2×C13×M16—21no—
66C22×C8×C13—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×C4⋊Q8—44no—
72C13×#126—22no—
73C13×#126—22no—
74C13×#126—22no—
75C13×#126—22no—
76C13×#125—21no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#125—22no—
81C13×#124—22no—
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—22no—
85C13×#123—21no—
86C13×#123—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8D412yes—
100C13×C22⋊Q8D411yescharacteristic
101C13×C22⋊Q8C2312yes—
102C13×C22⋊Q8C2311yescharacteristic
103C13×#121D411yescharacteristic
104C13×#121C2311yescharacteristic
105C13×#120—21no—
106C4×Q8×C13—21no—
107C4×Q8×C13—21no—
108C4×D4×C13—22no—
109C4×D4×C13—21no—
110C4×D4×C13—21no—
111C4×D4×C13—22no—
112C13×#117—21no—
113C13×#117—22no—
114C13×#117—22no—
115C13×#117D411yescharacteristic
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—24no—
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C4⋊C4C2312yes—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4D412yes—
124C2×C42×C13—21no—
125C13×#103—24no—
126C13×#103—22no—
127C13×#103—22no—
128C13×C22⋊C8—21no—
129C13×C22⋊C8—21no—
130C13×C22⋊C8C2312yes—
131C13×C22⋊C8C2312yes—
132C13×#95—24no—
133C13×#95C2312yes—
134#18259C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13C2×D411yescharacteristic
136C13×#41—42no—
137C2×Q8×C13—24no—
138C2×Q8×C13—22no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—24no—
143C2×Q8×C13—24no—
144C2×Q8×C13—22no—
145C2×Q8×C13—22no—
146C2×Q8×C13—44no—
147C2×Q8×C13—42no—
148C2×Q8×C13—42no—
149C2×Q8×C13—42no—
150C2×Q8×C13—42no—
151C2×Q8×C13—42no—
152C2×Q8×C13—44no—
153C2×Q8×C13—44no—
154C2×Q8×C13—41no—
155C2×Q8×C13—41no—
156C2×Q8×C13—82no—
157C2×Q8×C13C2×D412yes—
158C2×Q8×C13C2×D411yescharacteristic
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13C2×D411yescharacteristic
163C22×C4×C13—21no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—42no—
170C22×C4×C13—44no—
171C22×C4×C13—41no—
172C22×C4×C13—41no—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D412yes—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2411yescharacteristic
181C13×Q16—48no—
182C13×Q16—44no—
183C13×SD16—44no—
184C13×M16—42no—
185C2×C8×C13—22no—
186C2×C8×C13—22no—
187C2×C8×C13—42no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—22no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—48no—
206C13×C4⋊C4C2×D412yes—
207C13×C4⋊C4C2×D411yescharacteristic
208C13×C4⋊C4C2×D411yescharacteristic
209C13×C22⋊C4—24no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C42×C13—22no—
223C42×C13—22no—
224C42×C13—22no—
225C42×C13—21no—
226C42×C13—42no—
227#3538C2×C1311yescharacteristic
228#3004C2×C1311yescharacteristic
229C2×#451C2×C1311yescharacteristic, complemented
230#2434C2×C1311yescharacteristic, complemented
231#1605C2×C1314yescomplemented
232#1603C2×C1314yescomplemented
233#1508C2×C1311yescharacteristic, complemented
234#1501C2×C1311yescharacteristic
235#1472C2×C1311yescharacteristic, complemented
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—21no—
239C23×C13—41no—
240C23×C13#12011yescharacteristic
241C23×C13#12011yescharacteristic
242C23×C13C22×D411yescharacteristic
243Q8×C13—24no—
244Q8×C13—24no—
245Q8×C13—42no—
246Q8×C13—42no—
247Q8×C13—44no—
248Q8×C13—42no—
249Q8×C13—41no—
250Q8×C13—44no—
251Q8×C13—42no—
252Q8×C13—42no—
253Q8×C13—81no—
254Q8×C13—82no—
255D4×C13—41no—
256D4×C13—42no—
257D4×C13—42no—
258D4×C13—81no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—24no—
263C2×C4×C13—24no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—24no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—44no—
278C2×C4×C13—44no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—81no—
285C2×C4×C13—82no—
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13#12011yescharacteristic
288C2×C4×C13C22×D411yescharacteristic
289C2×C4×C13C22×D411yescharacteristic
290C8×C13—42no—
291C8×C13—42no—
292C23×Q8C22×C1311yescharacteristic
293C2×#137—21no—
294C22×Q16—21no—
295#563—22no—
296#552—21no—
297#552—21no—
298#551—22no—
299D4×Q8—21no—
300D4×Q8—21no—
301#544—21no—
302#544C22×C1312yes—
303#541—21no—
304#539—21no—
305#539C22×C1312yes—
306#536—21no—
307C2×C4⋊Q8—21no—
308#525C22×C1311yescharacteristic
309C2×C22⋊Q8C22×C1311yescharacteristic
310C2×C22⋊Q8C22×C1311yescharacteristic
311#451—22no—
312#451—21no—
313#451C22×C1314yes—
314#451C22×C1312yes—
315#448—21no—
316#448C22×C1312yes—
317#419—21no—
318C2×#103—21no—
319#407C22×C1311yescharacteristic
320C2×C22⋊C8C22×C1311yescharacteristic
321#395C22×C1314yes—
322#391—21no—
323#385—22no—
324C4×C22⋊C4C22×C1311yescharacteristic
325#328C22×C1314yes—
326#328C22×C1312yes—
327#327C22×C1312yes—
328#324C22×C1314yes—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—44no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13#45612yes—
341C22×C13C2×#12011yescharacteristic
342C22×C13#57812yes—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—21no—
346C4×C13—44no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—41no—
351C4×C13—44no—
352C4×C13—41no—
353C4×C13—42no—
354C4×C13—42no—
355C4×C13B(4,𝔽2)12yes—
356C2×#41D4×C1311yescharacteristic
357C22×Q8—21no—
358C22×Q8—21no—
359C22×Q8—21no—
360C22×Q8—21no—
361C22×Q8—21no—
362C22×Q8—21no—
363C22×Q8—44no—
364C22×Q8D4×C1311yescharacteristic
365C22×Q8D4×C1311yescharacteristic
366C22×Q8C23×C1312yes—
367C23×C4—21no—
368C23×C4C23×C1311yescharacteristic
369#137—44no—
370C2×Q16—24no—
371C2×Q16—22no—
372C2×Q16—44no—
373C2×SD16—22no—
374C2×M16—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—44no—
381#126—22no—
382#126—22no—
383#126—22no—
384#126—22no—
385#125—21no—
386#125—22no—
387#125—22no—
388#125—22no—
389#125—22no—
390#124—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—21no—
395#123—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—22no—
408C22⋊Q8D4×C1312yes—
409C22⋊Q8D4×C1311yescharacteristic
410C22⋊Q8C23×C1312yes—
411C22⋊Q8C23×C1311yescharacteristic
412#121D4×C1311yescharacteristic
413#121C23×C1311yescharacteristic
414#120—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—22no—
421#117—21no—
422#117—22no—
423#117—22no—
424#117D4×C1311yescharacteristic
425C2×C4⋊C4—21no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4D4×C1311yescharacteristic
428C2×C4⋊C4D4×C1311yescharacteristic
429C2×C4⋊C4C23×C1312yes—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4D4×C1312yes—
433C2×C42—21no—
434#103—24no—
435#103—22no—
436#103—22no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8C23×C1312yes—
440C22⋊C8C23×C1312yes—
441#95—24no—
442#95C23×C1312yes—
443C2×C13—22no—
444C2×C13—22no—
445C2×C13—41no—
446C2×C13—81no—
447C2×C13#301111yescharacteristic
448C2×C13C2×#45611yescharacteristic
449C2×C13C2×B(4,𝔽2)11yescharacteristic
450C24C2×D4×C1311yescharacteristic
451#41—42no—
452C2×Q8—24no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—44no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—82no—
472C2×Q8C2×D4×C1312yes—
473C2×Q8C2×D4×C1311yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4C2×D4×C1311yescharacteristic
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—44no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4C2×D4×C1312yes—
489C22×C4C2×D4×C1311yescharacteristic
490C22×C4C2×D4×C1311yescharacteristic
491C22×C4C2×D4×C1311yescharacteristic
492C22×C4C2×D4×C1312yes—
493C22×C4C2×D4×C1311yescharacteristic
494C22×C4C2×D4×C1311yescharacteristic
495C22×C4C24×C1311yescharacteristic
496Q16—48no—
497Q16—44no—
498SD16—44no—
499M16—42no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—42no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—48no—
521C4⋊C4C2×D4×C1312yes—
522C4⋊C4C2×D4×C1311yescharacteristic
523C4⋊C4C2×D4×C1311yescharacteristic
524C22⋊C4—24no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—21no—
541C42—42no—
542C13#1825911yescharacteristic, direct product factor, Sylow
543C23—22no—
544C23—22no—
545C23—21no—
546C23—41no—
547C23C13×#12011yescharacteristic
548C23C13×#12011yescharacteristic
549C23C22×D4×C1311yescharacteristic
550Q8—24no—
551Q8—24no—
552Q8—42no—
553Q8—41no—
554Q8—42no—
555Q8—42no—
556Q8—44no—
557Q8—44no—
558Q8—42no—
559Q8—42no—
560Q8—81no—
561Q8—82no—
562D4—41no—
563D4—42no—
564D4—42no—
565D4—81no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4C13×#12011yescharacteristic
594C2×C4C13×#12011yescharacteristic
595C2×C4C22×D4×C1311yescharacteristic
596C2×C4C22×D4×C1311yescharacteristic
597C8—42no—
598C8—42no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—44no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22C13×#45612yes—
611C22C2×C13×#12011yescharacteristic
612C22C13×#57812yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—44no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—44no—
622C4—41no—
623C4—42no—
624C4—42no—
625C4C13×B(4,𝔽2)12yes—
626C2—22no—
627C2—22no—
628C2—41no—
629C2—81no—
630C2C13×#301111yescharacteristic
631C2C2×C13×#45611yescharacteristic
632C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#451C2semidirect
4. C13×#2434C2semidirect
5. C13×#1605C2semidirect
6. C13×#1603C2semidirect
7. C13×#1508C2semidirect
9. C13×#1472C2semidirect
134. #18259C13direct (N × H)
229. C2×#451C2×C13semidirect
230. #2434C2×C13semidirect
231. #1605C2×C13semidirect
232. #1603C2×C13semidirect
233. #1508C2×C13semidirect
235. #1472C2×C13semidirect
542. C13#18259direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35382
C13×#30042
C2×C13×#4512
C13×#24342
C13×#16052
C13×#16032
C13×#15082
C13×#15012
C13×#14722
#1825913