Finite Group Databasebeta

← C13×#18279 #15704618

Subgroups — C13×#18279 #15704618

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3113C211yesmaximal, characteristic, complemented
3C13×#3108C211yesmaximal, characteristic
4C13×#2584C211yesmaximal, characteristic, complemented
5C13×#1611C212yesmaximal, complemented
6C13×#1609C212yesmaximal
7C13×#1605C212yesmaximal, complemented
8C13×#1603C212yesmaximal
9C13×#1509C211yesmaximal, characteristic
10C13×#1503C211yesmaximal, characteristic, complemented
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#564—21no—
13C13×#563—21no—
14C13×#557—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—22no—
18C13×#552—21no—
19C13×#544—21no—
20C13×#544C2212yes—
21C13×#541—21no—
22C13×#541—22no—
23C13×#539C2212yes—
24C13×#533C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C13×#483C2211yescharacteristic
29C13×#483C2212yes—
30C13×#480C2211yescharacteristic
31C13×#479—21no—
32C13×#475—21no—
33C13×#464—21no—
34C13×#462—21no—
35C13×#451C2211yescharacteristic
36C13×#451C2212yes—
37C13×#448C2211yescharacteristic
38C13×#441—22no—
39C4×C13×Q16—21no—
40C4×C13×SD16—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#398C2212yes—
44C13×#395C2212yes—
45C13×#389—21no—
46C13×#389—22no—
47C13×#389—21no—
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C22×Q8×C13C2311yescharacteristic
56C2×C13×Q16—21no—
57C2×C13×Q16—22no—
58C2×C13×SD16—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8—22no—
62C13×C4⋊Q8D411yescharacteristic
63C13×C4⋊Q8D411yescharacteristic
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—22no—
67C13×#126—22no—
68C13×#126—21no—
69C13×#125—22no—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—21no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—21no—
79C13×#125—21no—
80C13×#125—21no—
81C13×#125—21no—
82C13×#125—21no—
83C13×#125D411yescharacteristic
84C13×#124D411yescharacteristic
85C13×#123—22no—
86C13×#123—21no—
87C13×#123—22no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8C2311yescharacteristic
96C13×C22⋊Q8C2312yes—
97C13×#121C2311yescharacteristic
98C4×Q8×C13—21no—
99C4×Q8×C13—22no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×Q8×C13—21no—
103C4×Q8×C13—21no—
104C4×Q8×C13—21no—
105C4×Q8×C13—21no—
106C4×Q8×C13D411yescharacteristic
107C4×Q8×C13D412yes—
108C4×D4×C13—21no—
109C4×D4×C13—22no—
110C4×D4×C13D411yescharacteristic
111C13×#117—22no—
112C13×#117—21no—
113C13×#117—21no—
114C13×#117—22no—
115C13×#117—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—22no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—22no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4D412yes—
123C2×C13×C4⋊C4D411yescharacteristic
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C4⋊C4C2312yes—
126C2×C42×C13—21no—
127C2×C42×C13—21no—
128C2×C42×C13C2311yescharacteristic
129C13×#107—21no—
130C13×#106—21no—
131C13×#106—22no—
132C13×C4⋊C8—21no—
133C13×C4⋊C8—21no—
134C13×#103—21no—
135C13×#103—22no—
136C13×#103—21no—
137C13×#103—21no—
138C13×#103—22no—
139C13×#102—21no—
140C13×C22⋊C8C2312yes—
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2311yescharacteristic
143C13×#97—21no—
144C4×C8×C13—21no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18279C1311yesmaximal, characteristic, direct product factor, Sylow
149C2×Q8×C13—22no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—42no—
154C2×Q8×C13C2×D412yes—
155C2×Q8×C13C2×D411yescharacteristic
156C2×D4×C13—21no—
157C2×D4×C13C2×D411yescharacteristic
158C22×C4×C13—22no—
159C22×C4×C13—21no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2411yescharacteristic
168C13×Q16—42no—
169C13×Q16—44no—
170C13×SD16—42no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—22no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—44no—
203C13×C4⋊C4—41no—
204C13×C4⋊C4—41no—
205C13×C4⋊C4—82no—
206C13×C4⋊C4C2×D411yescharacteristic
207C13×C4⋊C4C2×D412yes—
208C13×C4⋊C4C2×D411yescharacteristic
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—21no—
214C13×C22⋊C4—21no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C42×C13—22no—
219C42×C13—22no—
220C42×C13—22no—
221C42×C13—22no—
222C42×C13—21no—
223C42×C13—41no—
224C42×C13—41no—
225C42×C13—81no—
226C42×C13C2×D411yescharacteristic
227C42×C13C2×D411yescharacteristic
228C42×C13C2×D411yescharacteristic
229C42×C13C2×D411yescharacteristic
230#3563C2×C1311yescharacteristic
231#3113C2×C1311yescharacteristic, complemented
232#3108C2×C1311yescharacteristic
233#2584C2×C1311yescharacteristic, complemented
234#1611C2×C1312yescomplemented
235#1609C2×C1312yes—
236#1605C2×C1312yescomplemented
237#1603C2×C1312yes—
238#1509C2×C1311yescharacteristic
239#1503C2×C1311yescharacteristic, complemented
240#1470C2×C1311yescharacteristic, complemented
241C23×C13—21no—
242C23×C13C22×D411yescharacteristic
243Q8×C13—22no—
244Q8×C13—22no—
245Q8×C13—41no—
246Q8×C13—41no—
247Q8×C13—41no—
248Q8×C13—42no—
249Q8×C13—42no—
250Q8×C13—82no—
251D4×C13—41no—
252D4×C13—41no—
253D4×C13—41no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—24no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—41no—
269C2×C4×C13—42no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—82no—
279C2×C4×C13#12011yescharacteristic
280C2×C4×C13#12011yescharacteristic
281C2×C4×C13#12011yescharacteristic
282C2×C4×C13#12011yescharacteristic
283C2×C4×C13C22×D411yescharacteristic
284C2×C4×C13C22×D411yescharacteristic
285C8×C13—41no—
286C8×C13—41no—
287C8×C13—42no—
288#564—21no—
289#563—21no—
290#557—21no—
291#554—21no—
292#552—21no—
293#552—22no—
294#552—21no—
295#544—21no—
296#544C22×C1312yes—
297#541—21no—
298#541—22no—
299#539C22×C1312yes—
300#533C22×C1311yescharacteristic
301#529C22×C1311yescharacteristic
302C2×#125C22×C1311yescharacteristic
303C2×C4×Q8C22×C1311yescharacteristic
304#483C22×C1311yescharacteristic
305#483C22×C1312yes—
306#480C22×C1311yescharacteristic
307#479—21no—
308#475—21no—
309#464—21no—
310#462—21no—
311#451C22×C1311yescharacteristic
312#451C22×C1312yes—
313#448C22×C1311yescharacteristic
314#441—22no—
315C4×Q16—21no—
316C4×SD16—21no—
317#432C22×C1311yescharacteristic
318#431C22×C1311yescharacteristic
319#398C22×C1312yes—
320#395C22×C1312yes—
321#389—21no—
322#389—22no—
323#389—21no—
324C4×C4⋊C4C22×C1311yescharacteristic
325#328C22×C1312yes—
326#328C22×C1312yes—
327#328C22×C1312yes—
328#327C22×C1312yes—
329#324C22×C1312yes—
330#324C22×C1312yes—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×#12011yescharacteristic
337C22×C13#57711yescharacteristic
338C22×C13#57811yescharacteristic
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—44no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—42no—
352C4×C13—41no—
353C4×C13—81no—
354C4×C13#45612yes—
355C22×Q8C23×C1311yescharacteristic
356C2×Q16—21no—
357C2×Q16—22no—
358C2×SD16—21no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8D4×C1311yescharacteristic
363C4⋊Q8D4×C1311yescharacteristic
364#126—22no—
365#126—22no—
366#126—22no—
367#126—22no—
368#126—21no—
369#125—22no—
370#125—22no—
371#125—22no—
372#125—22no—
373#125—21no—
374#125—22no—
375#125—22no—
376#125—22no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C1311yescharacteristic
384#124D4×C1311yescharacteristic
385#123—22no—
386#123—21no—
387#123—22no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—22no—
395C22⋊Q8C23×C1311yescharacteristic
396C22⋊Q8C23×C1312yes—
397#121C23×C1311yescharacteristic
398C4×Q8—21no—
399C4×Q8—22no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8D4×C1311yescharacteristic
407C4×Q8D4×C1312yes—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4D4×C1311yescharacteristic
411#117—22no—
412#117—21no—
413#117—21no—
414#117—22no—
415#117—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4D4×C1311yescharacteristic
422C2×C4⋊C4D4×C1312yes—
423C2×C4⋊C4D4×C1311yescharacteristic
424C2×C4⋊C4C23×C1311yescharacteristic
425C2×C4⋊C4C23×C1312yes—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42C23×C1311yescharacteristic
429#107—21no—
430#106—21no—
431#106—22no—
432C4⋊C8—21no—
433C4⋊C8—21no—
434#103—21no—
435#103—22no—
436#103—21no—
437#103—21no—
438#103—22no—
439#102—21no—
440C22⋊C8C23×C1312yes—
441C22⋊C8C23×C1311yescharacteristic
442C22⋊C8C23×C1311yescharacteristic
443#97—21no—
444C4×C8—21no—
445#95—22no—
446#95—22no—
447#95C23×C1312yes—
448C2×C13—21no—
449C2×C13—21no—
450C2×C13—81no—
451C2×C13#301311yescharacteristic
452C2×C13C2×#45611yescharacteristic
453C2×C13#302511yescharacteristic
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—42no—
459C2×Q8C2×D4×C1312yes—
460C2×Q8C2×D4×C1311yescharacteristic
461C2×D4—21no—
462C2×D4C2×D4×C1311yescharacteristic
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4C2×D4×C1312yes—
469C22×C4C2×D4×C1311yescharacteristic
470C22×C4C2×D4×C1311yescharacteristic
471C22×C4C2×D4×C1312yes—
472C22×C4C24×C1311yescharacteristic
473Q16—42no—
474Q16—44no—
475SD16—42no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—22no—
479C4⋊C4—22no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—44no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—82no—
511C4⋊C4C2×D4×C1311yescharacteristic
512C4⋊C4C2×D4×C1312yes—
513C4⋊C4C2×D4×C1311yescharacteristic
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—21no—
528C42—41no—
529C42—41no—
530C42—81no—
531C42C2×D4×C1311yescharacteristic
532C42C2×D4×C1311yescharacteristic
533C42C2×D4×C1311yescharacteristic
534C42C2×D4×C1311yescharacteristic
535C13#1827911yescharacteristic, direct product factor, Sylow
536C23—21no—
537C23C22×D4×C1311yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—41no—
541Q8—42no—
542Q8—41no—
543Q8—41no—
544Q8—42no—
545Q8—82no—
546D4—41no—
547D4—41no—
548D4—41no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—82no—
574C2×C4C13×#12011yescharacteristic
575C2×C4C13×#12011yescharacteristic
576C2×C4C13×#12011yescharacteristic
577C2×C4C13×#12011yescharacteristic
578C2×C4C22×D4×C1311yescharacteristic
579C2×C4C22×D4×C1311yescharacteristic
580C8—41no—
581C8—41no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C2×C13×#12011yescharacteristic
589C22C13×#57711yescharacteristic
590C22C13×#57811yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—44no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—41no—
605C4—81no—
606C4C13×#45612yes—
607C2—21no—
608C2—21no—
609C2—81no—
610C2C13×#301311yescharacteristic
611C2C2×C13×#45611yescharacteristic
612C2C13×#302511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3113C2semidirect
4. C13×#2584C2semidirect
5. C13×#1611C2semidirect
7. C13×#1605C2semidirect
10. C13×#1503C2semidirect
11. C13×#1470C2semidirect
148. #18279C13direct (N × H)
231. #3113C2×C13semidirect
233. #2584C2×C13semidirect
234. #1611C2×C13semidirect
236. #1605C2×C13semidirect
239. #1503C2×C13semidirect
240. #1470C2×C13semidirect
535. C13#18279direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#31132
C13×#31082
C13×#25842
C13×#16112
C13×#16092
C13×#16052
C13×#16032
C13×#15092
C13×#15032
C13×#14702
#1827913