Finite Group Databasebeta

← C13×#19016 #15705355

Subgroups — C13×#19016 #15705355

Order 3328.

1008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C13×#3151C211yesmaximal, characteristic, complemented
4C2×C13×#490C211yesmaximal, characteristic, complemented
5C13×#1657C214yesmaximal, complemented
6C13×#1656C214yesmaximal, complemented
7C13×#1530C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C2×C13×AGL(1,ℤ/8)—22no—
11C13×#563C2212yescomplemented
12C13×#562C2212yescomplemented
13C13×#554—21no—
14C13×#553—21no—
15C13×#553—21no—
16C13×#547—22no—
17C13×#547—21no—
18C13×#544—21no—
19C13×#540—21no—
20C13×#539—22no—
21C13×#539—21no—
22C13×#537—21no—
23C13×#532C2211yescharacteristic
24C2×C13×#127C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C13×#496C2214yes—
28C13×#496C2212yes—
29C13×#493—21no—
30C13×#492—21no—
31C13×#490—22no—
32C13×#490C2214yes—
33C13×#490C2212yes—
34C13×#460—21no—
35C13×#459—21no—
36C13×#450—21no—
37C13×#447—21no—
38C13×#432C2211yescharacteristic
39C2×C13×#102—21no—
40C2×C13×#102—21no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yescomplemented
44C13×#330C2214yescomplemented
45C13×#329C2212yescomplemented
46C13×#329C2214yescomplemented
47C2×C13×#41—22no—
48C2×C13×#41D412yes—
49C22×D4×C13—21no—
50C22×D4×C13—21no—
51C22×D4×C13—21no—
52C13×AGL(1,ℤ/8)—48no—
53C2×C13×SD16—24no—
54C2×C13×SD16—22no—
55C2×C13×D8—24no—
56C2×C13×D8—22no—
57C2×C13×M16—21no—
58C22×C8×C13—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8D411yescharacteristic
62C13×#127—21no—
63C13×#127—21no—
64C13×#127—21no—
65C13×#127D411yescharacteristic
66C13×#127C2312yes—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—21no—
70C13×#125—22no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—21no—
74C13×#125D412yes—
75C13×#125C2312yes—
76C13×#125C2311yescharacteristic
77C13×#124C2311yescharacteristic
78C13×#124C2312yes—
79C13×#123—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—21no—
84C13×#123—22no—
85C13×#123—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8D411yescharacteristic
93C13×#121—22no—
94C13×#121—22no—
95C13×#121—21no—
96C13×#121—21no—
97C13×#121—22no—
98C13×#121—22no—
99C13×#121—21no—
100C13×#121—21no—
101C13×#121D411yescharacteristic
102C4×Q8×C13D411yescharacteristic
103C4×D4×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13—21no—
106C4×D4×C13—21no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C4×D4×C13—21no—
110C4×D4×C13D411yescharacteristic
111C13×#117—21no—
112C13×#117—21no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C42×C13C2311yescharacteristic
120C13×C4⋊C8—21no—
121C13×#102—24no—
122C13×#102—24no—
123C13×#102—22no—
124C13×#102—22no—
125C13×C22⋊C8—21no—
126C13×#97—21no—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C13×#97C2312yes—
130C4×C8×C13—21no—
131#19016C1311yesmaximal, characteristic, direct product factor, Sylow
132C24×C13—41no—
133C13×#41—44no—
134C13×#41—84no—
135C2×Q8×C13—22no—
136C2×Q8×C13C2×D411yescharacteristic
137C2×Q8×C13C2×D412yes—
138C2×D4×C13—22no—
139C2×D4×C13—21no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—44no—
148C2×D4×C13—44no—
149C2×D4×C13—41no—
150C2×D4×C13—41no—
151C2×D4×C13—41no—
152C2×D4×C13—82no—
153C2×D4×C13C2×D411yescharacteristic
154C2×D4×C13C2×D412yes—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C13×SD16—48no—
166C13×SD16—82no—
167C13×D8—48no—
168C13×D8—82no—
169C13×M16—24no—
170C2×C8×C13—22no—
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—42no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4C2×D412yes—
191C13×C4⋊C4C2×D412yes—
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C4⋊C4C2×D411yescharacteristic
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—21no—
206C42×C13—22no—
207C42×C13—21no—
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211C42×C13C2411yescharacteristic
212#3559C2×C1311yescharacteristic, complemented
213#3217C2×C1311yescharacteristic, complemented
214#3151C2×C1311yescharacteristic, complemented
215C2×#490C2×C1311yescharacteristic, complemented
216#1657C2×C1314yescomplemented
217#1656C2×C1314yescomplemented
218#1530C2×C1311yescharacteristic, complemented
219#1528C2×C1311yescharacteristic, complemented
220#1524C2×C1311yescharacteristic, complemented
221C23×C13—22no—
222C23×C13—21no—
223C23×C13—42no—
224C23×C13—82no—
225C23×C13—82no—
226C23×C13—82no—
227C23×C13#12011yescharacteristic
228Q8×C13—42no—
229Q8×C13—41no—
230Q8×C13—82no—
231D4×C13—42no—
232D4×C13—41no—
233D4×C13—44no—
234D4×C13—42no—
235D4×C13—42no—
236D4×C13—44no—
237D4×C13—44no—
238D4×C13—42no—
239D4×C13—42no—
240D4×C13—81no—
241D4×C13—82no—
242D4×C13—82no—
243D4×C13—82no—
244D4×C13—82no—
245D4×C13—82no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—82no—
258C2×C4×C13—81no—
259C2×C4×C13—82no—
260C2×C4×C13—82no—
261C2×C4×C13—82no—
262C2×C4×C13#12011yescharacteristic
263C2×C4×C13#12011yescharacteristic
264C2×C4×C13#12011yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C8×C13—24no—
269C8×C13—42no—
270C8×C13—42no—
271C2×AGL(1,ℤ/8)—22no—
272#563C22×C1312yescomplemented
273#562C22×C1312yescomplemented
274#554—21no—
275#553—21no—
276#553—21no—
277#547—22no—
278#547—21no—
279#544—21no—
280#540—21no—
281#539—22no—
282#539—21no—
283#537—21no—
284#532C22×C1311yescharacteristic
285C2×#127C22×C1311yescharacteristic
286#529C22×C1311yescharacteristic
287C2×#125C22×C1311yescharacteristic
288#496C22×C1314yes—
289#496C22×C1312yes—
290#493—21no—
291#492—21no—
292#490—22no—
293#490C22×C1314yes—
294#490C22×C1312yes—
295#460—21no—
296#459—21no—
297#450—21no—
298#447—21no—
299#432C22×C1311yescharacteristic
300C2×#102—21no—
301C2×#102—21no—
302C4×M16C22×C1311yescharacteristic
303C2×#97C22×C1311yescharacteristic
304#330C22×C1314yescomplemented
305#330C22×C1312yescomplemented
306#329C22×C1312yescomplemented
307#329C22×C1314yescomplemented
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—42no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—41no—
316C22×C13—82no—
317C22×C13—82no—
318C22×C13—82no—
319C22×C13—164no—
320C22×C13#45312yes—
321C22×C13C2×#12011yescharacteristic
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—21no—
327C4×C13—42no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13#45412yes—
334C2×#41—22no—
335C2×#41D4×C1312yes—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339AGL(1,ℤ/8)—48no—
340C2×SD16—24no—
341C2×SD16—22no—
342C2×D8—24no—
343C2×D8—22no—
344C2×M16—21no—
345C22×C8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—22no—
348C4⋊Q8D4×C1311yescharacteristic
349#127—21no—
350#127—21no—
351#127—21no—
352#127D4×C1311yescharacteristic
353#127C23×C1312yes—
354#126—22no—
355#126—22no—
356#126—21no—
357#125—22no—
358#125—21no—
359#125—21no—
360#125—21no—
361#125D4×C1312yes—
362#125C23×C1312yes—
363#125C23×C1311yescharacteristic
364#124C23×C1311yescharacteristic
365#124C23×C1312yes—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370#123—21no—
371#123—22no—
372#123—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8D4×C1311yescharacteristic
380#121—22no—
381#121—22no—
382#121—21no—
383#121—21no—
384#121—22no—
385#121—22no—
386#121—21no—
387#121—21no—
388#121D4×C1311yescharacteristic
389C4×Q8D4×C1311yescharacteristic
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4D4×C1311yescharacteristic
398#117—21no—
399#117—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4D4×C1311yescharacteristic
405C2×C4⋊C4D4×C1311yescharacteristic
406C2×C42C23×C1311yescharacteristic
407C4⋊C8—21no—
408#102—24no—
409#102—24no—
410#102—22no—
411#102—22no—
412C22⋊C8—21no—
413#97—21no—
414#97C23×C1312yes—
415#97C23×C1312yes—
416#97C23×C1312yes—
417C4×C8—21no—
418C2×C13—22no—
419C2×C13—82no—
420C2×C13—81no—
421C2×C13—162no—
422C2×C13C2×#45311yescharacteristic
423C2×C13C2×#45411yescharacteristic
424C2×C13#302111yescharacteristic
425C24—41no—
426#41—44no—
427#41—84no—
428C2×Q8—22no—
429C2×Q8C2×D4×C1311yescharacteristic
430C2×Q8C2×D4×C1312yes—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—82no—
446C2×D4C2×D4×C1311yescharacteristic
447C2×D4C2×D4×C1312yes—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4C2×D4×C1311yescharacteristic
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C2×D4×C1311yescharacteristic
458SD16—48no—
459SD16—82no—
460D8—48no—
461D8—82no—
462M16—24no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—42no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4C2×D4×C1312yes—
484C4⋊C4C2×D4×C1312yes—
485C4⋊C4C2×D4×C1311yescharacteristic
486C4⋊C4C2×D4×C1311yescharacteristic
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C42—22no—
500C42—21no—
501C42C2×D4×C1311yescharacteristic
502C42C2×D4×C1311yescharacteristic
503C42C2×D4×C1311yescharacteristic
504C42C24×C1311yescharacteristic
505C13#1901611yescharacteristic, direct product factor, Sylow
506C23—22no—
507C23—21no—
508C23—42no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23C13×#12011yescharacteristic
513Q8—42no—
514Q8—41no—
515Q8—82no—
516D4—42no—
517D4—41no—
518D4—44no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—82no—
543C2×C4—81no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C13×#12011yescharacteristic
548C2×C4C13×#12011yescharacteristic
549C2×C4C13×#12011yescharacteristic
550C2×C4C22×D4×C1311yescharacteristic
551C2×C4C22×D4×C1311yescharacteristic
552C2×C4C22×D4×C1311yescharacteristic
553C8—24no—
554C8—42no—
555C8—42no—
556C22—21no—
557C22—21no—
558C22—42no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—164no—
568C22C13×#45312yes—
569C22C2×C13×#12011yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4C13×#45412yes—
582C2—22no—
583C2—82no—
584C2—81no—
585C2—162no—
586C2C2×C13×#45311yescharacteristic
587C2C2×C13×#45411yescharacteristic
588C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3559C2semidirect
2. C13×#3217C2semidirect
3. C13×#3151C2semidirect
4. C2×C13×#490C2semidirect
5. C13×#1657C2semidirect
6. C13×#1656C2semidirect
7. C13×#1530C2semidirect
8. C13×#1528C2semidirect
9. C13×#1524C2semidirect
11. C13×#563C22semidirect
12. C13×#562C22semidirect
43. C13×#330C22semidirect
44. C13×#330C22semidirect
45. C13×#329C22semidirect
46. C13×#329C22semidirect
131. #19016C13direct (N × H)
212. #3559C2×C13semidirect
213. #3217C2×C13semidirect
214. #3151C2×C13semidirect
215. C2×#490C2×C13semidirect
216. #1657C2×C13semidirect
217. #1656C2×C13semidirect
218. #1530C2×C13semidirect
219. #1528C2×C13semidirect
220. #1524C2×C13semidirect
272. #563C22×C13semidirect
273. #562C22×C13semidirect
304. #330C22×C13semidirect
305. #330C22×C13semidirect
306. #329C22×C13semidirect
307. #329C22×C13semidirect
505. C13#19016direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32172
C13×#31512
C2×C13×#4902
C13×#16572
C13×#16562
C13×#15302
C13×#15282
C13×#15242
#1901613