Finite Group Databasebeta

← C13×#19026 #15705365

Subgroups — C13×#19026 #15705365

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C2×C13×#496C211yesmaximal, characteristic, complemented
4C13×#3138C211yesmaximal, characteristic, complemented
5C13×#1657C214yesmaximal, complemented
6C13×#1656C214yesmaximal, complemented
7C13×#1531C211yesmaximal, characteristic, complemented
8C13×#1527C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C22×C13×SD16—21no—
11C22×C13×D8—21no—
12C13×#563C2212yescomplemented
13C13×#562C2212yescomplemented
14C13×#556—21no—
15C13×#551—22no—
16D4×Q8×C13—21no—
17C13×#548—21no—
18C13×#546—21no—
19C13×#543—21no—
20C13×#542—21no—
21C13×#542—22no—
22C13×#538—21no—
23C13×#536—21no—
24C13×#533C2211yescharacteristic
25C2×C13×#127C2211yescharacteristic
26C13×#529C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#496—22no—
29C13×#496C2214yes—
30C13×#496C2212yescomplemented
31C13×#490C2214yescomplemented
32C13×#490C2212yescomplemented
33C13×#486—21no—
34C13×#486—21no—
35C13×#460—21no—
36C13×#459—21no—
37C13×#450—21no—
38C13×#447—21no—
39C13×#432C2211yescharacteristic
40C13×#418—22no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yescomplemented
44C13×#330C2214yescomplemented
45C13×#329C2212yescomplemented
46C13×#329C2214yescomplemented
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13D411yescharacteristic
50C22×D4×C13—21no—
51C22×D4×C13—21no—
52C22×D4×C13—21no—
53C22×D4×C13D411yescharacteristic
54C2×C13×SD16—24no—
55C2×C13×SD16—22no—
56C2×C13×SD16—44no—
57C2×C13×D8—24no—
58C2×C13×D8—22no—
59C2×C13×D8—44no—
60C2×C13×M16—21no—
61C22×C8×C13—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—22no—
64C13×C4⋊Q8D411yescharacteristic
65C13×C4⋊Q8D411yescharacteristic
66C13×#127—21no—
67C13×#127—21no—
68C13×#127—21no—
69C13×#127C2312yes—
70C13×#126—22no—
71C13×#126—22no—
72C13×#126—22no—
73C13×#126—21no—
74C13×#125C2311yescharacteristic
75C13×#125C2312yes—
76C13×#124—21no—
77C13×#124—22no—
78C13×#124—22no—
79C13×#124—21no—
80C13×#124—21no—
81C13×#124D412yes—
82C13×#124C2312yes—
83C13×#124C2311yescharacteristic
84C13×#123—22no—
85C13×#123—22no—
86C13×#123—21no—
87C13×#123—22no—
88C13×#123—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8D411yescharacteristic
100C13×#121—21no—
101C13×#121—22no—
102C13×#121—22no—
103C13×#121D411yescharacteristic
104C13×#120—22no—
105C4×Q8×C13—21no—
106C4×Q8×C13—21no—
107C4×Q8×C13—21no—
108C4×Q8×C13D411yescharacteristic
109C4×D4×C13—22no—
110C4×D4×C13—21no—
111C4×D4×C13—22no—
112C4×D4×C13—21no—
113C4×D4×C13D411yescharacteristic
114C13×#117—22no—
115C13×#117—21no—
116C13×#117D412yes—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C42×C13C2311yescharacteristic
121C13×C4⋊C8—21no—
122C13×#102—24no—
123C13×#102—24no—
124C13×#102—22no—
125C13×#102—22no—
126C13×C22⋊C8—21no—
127C13×#97—21no—
128C13×#97C2312yes—
129C13×#97C2312yes—
130C13×#97C2312yes—
131C4×C8×C13—21no—
132#19026C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—21no—
134C24×C13—41no—
135C13×#41—82no—
136C2×Q8×C13—22no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—42no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—42no—
152C2×D4×C13—42no—
153C2×D4×C13—42no—
154C2×D4×C13—44no—
155C2×D4×C13—41no—
156C2×D4×C13—41no—
157C2×D4×C13—41no—
158C2×D4×C13—82no—
159C2×D4×C13C2×D411yescharacteristic
160C2×D4×C13C2×D412yes—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C13×SD16—48no—
170C13×SD16—82no—
171C13×D8—48no—
172C13×D8—82no—
173C13×M16—42no—
174C2×C8×C13—24no—
175C2×C8×C13—22no—
176C2×C8×C13—22no—
177C2×C8×C13—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
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—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—21no—
208C13×C22⋊C4—21no—
209C42×C13—22no—
210C42×C13—22no—
211C42×C13—21no—
212C42×C13C2×D411yescharacteristic
213C42×C13C2×D411yescharacteristic
214C42×C13C2×D411yescharacteristic
215C42×C13C2411yescharacteristic
216#3561C2×C1311yescharacteristic, complemented
217#3217C2×C1311yescharacteristic, complemented
218C2×#496C2×C1311yescharacteristic, complemented
219#3138C2×C1311yescharacteristic, complemented
220#1657C2×C1314yescomplemented
221#1656C2×C1314yescomplemented
222#1531C2×C1311yescharacteristic, complemented
223#1527C2×C1311yescharacteristic, complemented
224#1524C2×C1311yescharacteristic, complemented
225C23×C13—22no—
226C23×C13—21no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13—81no—
230C23×C13—81no—
231C23×C13—82no—
232C23×C13—82no—
233C23×C13—82no—
234C23×C13#12011yescharacteristic
235Q8×C13—42no—
236Q8×C13—41no—
237Q8×C13—42no—
238Q8×C13—42no—
239Q8×C13—81no—
240Q8×C13—82no—
241D4×C13—42no—
242D4×C13—41no—
243D4×C13—42no—
244D4×C13—42no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—44no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—82no—
251D4×C13—82no—
252D4×C13—82no—
253D4×C13—82no—
254D4×C13—82no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—41no—
264C2×C4×C13—42no—
265C2×C4×C13—81no—
266C2×C4×C13—82no—
267C2×C4×C13—82no—
268C2×C4×C13—82no—
269C2×C4×C13#12011yescharacteristic
270C2×C4×C13#12011yescharacteristic
271C2×C4×C13#12011yescharacteristic
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C8×C13—24no—
276C8×C13—42no—
277C8×C13—42no—
278C22×SD16—21no—
279C22×D8—21no—
280#563C22×C1312yescomplemented
281#562C22×C1312yescomplemented
282#556—21no—
283#551—22no—
284D4×Q8—21no—
285#548—21no—
286#546—21no—
287#543—21no—
288#542—21no—
289#542—22no—
290#538—21no—
291#536—21no—
292#533C22×C1311yescharacteristic
293C2×#127C22×C1311yescharacteristic
294#529C22×C1311yescharacteristic
295C2×#124C22×C1311yescharacteristic
296#496—22no—
297#496C22×C1314yes—
298#496C22×C1312yescomplemented
299#490C22×C1314yescomplemented
300#490C22×C1312yescomplemented
301#486—21no—
302#486—21no—
303#460—21no—
304#459—21no—
305#450—21no—
306#447—21no—
307#432C22×C1311yescharacteristic
308#418—22no—
309C4×M16C22×C1311yescharacteristic
310C2×#97C22×C1311yescharacteristic
311#330C22×C1314yescomplemented
312#330C22×C1312yescomplemented
313#329C22×C1312yescomplemented
314#329C22×C1314yescomplemented
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—41no—
318C22×C13—42no—
319C22×C13—41no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—41no—
323C22×C13—82no—
324C22×C13—82no—
325C22×C13—82no—
326C22×C13—162no—
327C22×C13—164no—
328C22×C13#45412yes—
329C22×C13C2×#12011yescharacteristic
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—41no—
336C4×C13—42no—
337C4×C13—42no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—42no—
341C4×C13#45312yes—
342C2×#41—21no—
343C22×Q8—21no—
344C22×Q8D4×C1311yescharacteristic
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4D4×C1311yescharacteristic
349C2×SD16—24no—
350C2×SD16—22no—
351C2×SD16—44no—
352C2×D8—24no—
353C2×D8—22no—
354C2×D8—44no—
355C2×M16—21no—
356C22×C8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—22no—
359C4⋊Q8D4×C1311yescharacteristic
360C4⋊Q8D4×C1311yescharacteristic
361#127—21no—
362#127—21no—
363#127—21no—
364#127C23×C1312yes—
365#126—22no—
366#126—22no—
367#126—22no—
368#126—21no—
369#125C23×C1311yescharacteristic
370#125C23×C1312yes—
371#124—21no—
372#124—22no—
373#124—22no—
374#124—21no—
375#124—21no—
376#124D4×C1312yes—
377#124C23×C1312yes—
378#124C23×C1311yescharacteristic
379#123—22no—
380#123—22no—
381#123—21no—
382#123—22no—
383#123—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—21no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8D4×C1311yescharacteristic
395#121—21no—
396#121—22no—
397#121—22no—
398#121D4×C1311yescharacteristic
399#120—22no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8D4×C1311yescharacteristic
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—22no—
407C4×D4—21no—
408C4×D4D4×C1311yescharacteristic
409#117—22no—
410#117—21no—
411#117D4×C1312yes—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C42C23×C1311yescharacteristic
416C4⋊C8—21no—
417#102—24no—
418#102—24no—
419#102—22no—
420#102—22no—
421C22⋊C8—21no—
422#97—21no—
423#97C23×C1312yes—
424#97C23×C1312yes—
425#97C23×C1312yes—
426C4×C8—21no—
427C2×C13—22no—
428C2×C13—81no—
429C2×C13—82no—
430C2×C13—162no—
431C2×C13C2×#45311yescharacteristic
432C2×C13C2×#45411yescharacteristic
433C2×C13#302111yescharacteristic
434C24—21no—
435C24—41no—
436#41—82no—
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—42no—
442C2×Q8—82no—
443C2×Q8C2×D4×C1311yescharacteristic
444C2×Q8C2×D4×C1312yes—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—44no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—82no—
460C2×D4C2×D4×C1311yescharacteristic
461C2×D4C2×D4×C1312yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4C2×D4×C1311yescharacteristic
468C22×C4C2×D4×C1311yescharacteristic
469C22×C4C2×D4×C1311yescharacteristic
470SD16—48no—
471SD16—82no—
472D8—48no—
473D8—82no—
474M16—42no—
475C2×C8—24no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4C2×D4×C1312yes—
492C4⋊C4C2×D4×C1312yes—
493C4⋊C4C2×D4×C1311yescharacteristic
494C4⋊C4C2×D4×C1311yescharacteristic
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42C2×D4×C1311yescharacteristic
514C42C2×D4×C1311yescharacteristic
515C42C2×D4×C1311yescharacteristic
516C42C24×C1311yescharacteristic
517C13#1902611yescharacteristic, direct product factor, Sylow
518C23—22no—
519C23—21no—
520C23—42no—
521C23—42no—
522C23—81no—
523C23—81no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23C13×#12011yescharacteristic
528Q8—42no—
529Q8—41no—
530Q8—42no—
531Q8—42no—
532Q8—81no—
533Q8—82no—
534D4—42no—
535D4—41no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—82no—
544D4—82no—
545D4—82no—
546D4—82no—
547D4—82no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C13×#12011yescharacteristic
563C2×C4C13×#12011yescharacteristic
564C2×C4C13×#12011yescharacteristic
565C2×C4C22×D4×C1311yescharacteristic
566C2×C4C22×D4×C1311yescharacteristic
567C2×C4C22×D4×C1311yescharacteristic
568C8—24no—
569C8—42no—
570C8—42no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—42no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—162no—
583C22—164no—
584C22C13×#45412yes—
585C22C2×C13×#12011yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4C13×#45312yes—
598C2—22no—
599C2—82no—
600C2—81no—
601C2—162no—
602C2C2×C13×#45311yescharacteristic
603C2C2×C13×#45411yescharacteristic
604C2C13×#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×#3561C2semidirect
2. C13×#3217C2semidirect
3. C2×C13×#496C2semidirect
4. C13×#3138C2semidirect
5. C13×#1657C2semidirect
6. C13×#1656C2semidirect
7. C13×#1531C2semidirect
8. C13×#1527C2semidirect
9. C13×#1524C2semidirect
12. C13×#563C22semidirect
13. C13×#562C22semidirect
30. C13×#496C22semidirect
31. C13×#490C22semidirect
32. C13×#490C22semidirect
43. C13×#330C22semidirect
44. C13×#330C22semidirect
45. C13×#329C22semidirect
46. C13×#329C22semidirect
132. #19026C13direct (N × H)
216. #3561C2×C13semidirect
217. #3217C2×C13semidirect
218. C2×#496C2×C13semidirect
219. #3138C2×C13semidirect
220. #1657C2×C13semidirect
221. #1656C2×C13semidirect
222. #1531C2×C13semidirect
223. #1527C2×C13semidirect
224. #1524C2×C13semidirect
280. #563C22×C13semidirect
281. #562C22×C13semidirect
298. #496C22×C13semidirect
299. #490C22×C13semidirect
300. #490C22×C13semidirect
311. #330C22×C13semidirect
312. #330C22×C13semidirect
313. #329C22×C13semidirect
314. #329C22×C13semidirect
517. C13#19026direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#32172
C2×C13×#4962
C13×#31382
C13×#16572
C13×#16562
C13×#15312
C13×#15272
C13×#15242
#1902613