Finite Group Databasebeta

← C13×#18268 #15704607

Subgroups — C13×#18268 #15704607

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic
3C2×C13×#483C211yesmaximal, characteristic, complemented
4C13×#2502C211yesmaximal, characteristic, complemented
5C13×#1611C214yesmaximal, complemented
6C13×#1609C214yesmaximal, complemented
7C13×#1508C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic
9C13×#1472C211yesmaximal, characteristic, complemented
10C13×#563—22no—
11C13×#552—21no—
12C13×#552—21no—
13C13×#551—22no—
14D4×Q8×C13—21no—
15D4×Q8×C13—21no—
16C13×#544—21no—
17C13×#544C2212yes—
18C13×#541—21no—
19C13×#539—21no—
20C13×#539C2212yes—
21C13×#536—21no—
22C13×#525C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×C22⋊Q8C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C13×#484—21no—
27C13×#483—22no—
28C13×#483C2214yes—
29C13×#483C2212yes—
30C13×#481—21no—
31C13×#480C2212yes—
32C13×#428—21no—
33C2×C13×#106—21no—
34C13×#417—21no—
35C2×C13×#103—21no—
36C13×#407C2211yescharacteristic
37C2×C13×C22⋊C8C2211yescharacteristic
38C13×#398C2214yes—
39C13×#391—21no—
40C13×#385—22no—
41C13×#384—21no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#324C2214yes—
47C2×C13×#41D411yescharacteristic
48C22×Q8×C13—21no—
49C22×Q8×C13D411yescharacteristic
50C22×Q8×C13D411yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13C2311yescharacteristic
53C2×C13×M16—21no—
54C22×C8×C13—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—22no—
58C13×C4⋊Q8—22no—
59C13×#126—22no—
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#125—21no—
64C13×#125—22no—
65C13×#125—22no—
66C13×#125—22no—
67C13×#125—22no—
68C13×#124—22no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—21no—
73C13×#123—22no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8D412yes—
87C13×C22⋊Q8D411yescharacteristic
88C13×C22⋊Q8C2312yes—
89C13×C22⋊Q8C2311yescharacteristic
90C13×#121D411yescharacteristic
91C13×#121C2311yescharacteristic
92C13×#120—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×D4×C13—22no—
96C4×D4×C13—21no—
97C4×D4×C13—21no—
98C4×D4×C13—22no—
99C13×#117—21no—
100C13×#117—22no—
101C13×#117—22no—
102C13×#117D411yescharacteristic
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—24no—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4C2312yes—
113C2×C13×C4⋊C4C2312yes—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4D412yes—
117C2×C42×C13—21no—
118C13×#107—22no—
119C13×#106—24no—
120C13×#106—22no—
121C13×#103—24no—
122C13×#103—22no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×C22⋊C8—21no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C13×#95—24no—
129C13×#95C2312yes—
130#18268C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13C2×D411yescharacteristic
132C13×#41—42no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—42no—
138C2×Q8×C13—42no—
139C2×Q8×C13—82no—
140C2×Q8×C13C2×D412yes—
141C2×Q8×C13C2×D411yescharacteristic
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13C2×D411yescharacteristic
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—42no—
153C22×C4×C13—41no—
154C22×C4×C13—41no—
155C22×C4×C13—82no—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2411yescharacteristic
164C13×M16—42no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—42no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—84no—
190C13×C4⋊C4C2×D412yes—
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C22⋊C4—24no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—21no—
206C42×C13—22no—
207C42×C13—22no—
208C42×C13—22no—
209C42×C13—21no—
210C42×C13—42no—
211#3538C2×C1311yescharacteristic
212#3092C2×C1311yescharacteristic
213C2×#483C2×C1311yescharacteristic, complemented
214#2502C2×C1311yescharacteristic, complemented
215#1611C2×C1314yescomplemented
216#1609C2×C1314yescomplemented
217#1508C2×C1311yescharacteristic, complemented
218#1501C2×C1311yescharacteristic
219#1472C2×C1311yescharacteristic, complemented
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—21no—
223C23×C13—41no—
224C23×C13#12011yescharacteristic
225C23×C13#12011yescharacteristic
226C23×C13C22×D411yescharacteristic
227Q8×C13—42no—
228Q8×C13—41no—
229Q8×C13—42no—
230Q8×C13—42no—
231Q8×C13—81no—
232Q8×C13—82no—
233D4×C13—41no—
234D4×C13—42no—
235D4×C13—42no—
236D4×C13—81no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—24no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—44no—
259C2×C4×C13—81no—
260C2×C4×C13—82no—
261C2×C4×C13—82no—
262C2×C4×C13—82no—
263C2×C4×C13#12011yescharacteristic
264C2×C4×C13#12011yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C8×C13—42no—
268C8×C13—42no—
269#563—22no—
270#552—21no—
271#552—21no—
272#551—22no—
273D4×Q8—21no—
274D4×Q8—21no—
275#544—21no—
276#544C22×C1312yes—
277#541—21no—
278#539—21no—
279#539C22×C1312yes—
280#536—21no—
281#525C22×C1311yescharacteristic
282C2×C22⋊Q8C22×C1311yescharacteristic
283C2×C22⋊Q8C22×C1311yescharacteristic
284C22×C4⋊C4C22×C1311yescharacteristic
285#484—21no—
286#483—22no—
287#483C22×C1314yes—
288#483C22×C1312yes—
289#481—21no—
290#480C22×C1312yes—
291#428—21no—
292C2×#106—21no—
293#417—21no—
294C2×#103—21no—
295#407C22×C1311yescharacteristic
296C2×C22⋊C8C22×C1311yescharacteristic
297#398C22×C1314yes—
298#391—21no—
299#385—22no—
300#384—21no—
301C4×C22⋊C4C22×C1311yescharacteristic
302#328C22×C1314yes—
303#328C22×C1312yes—
304#327C22×C1312yes—
305#324C22×C1314yes—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—21no—
311C22×C13—21no—
312C22×C13—21no—
313C22×C13—44no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13#45612yes—
318C22×C13C2×#12011yescharacteristic
319C22×C13#57712yes—
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—44no—
324C4×C13—42no—
325C4×C13—41no—
326C4×C13—42no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—42no—
330C4×C13—42no—
331C4×C13—82no—
332C4×C13#45812yes—
333C2×#41D4×C1311yescharacteristic
334C22×Q8—21no—
335C22×Q8D4×C1311yescharacteristic
336C22×Q8D4×C1311yescharacteristic
337C23×C4—21no—
338C23×C4C23×C1311yescharacteristic
339C2×M16—21no—
340C22×C8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345#126—22no—
346#126—22no—
347#126—22no—
348#126—22no—
349#125—21no—
350#125—22no—
351#125—22no—
352#125—22no—
353#125—22no—
354#124—22no—
355#123—22no—
356#123—22no—
357#123—22no—
358#123—21no—
359#123—22no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8D4×C1312yes—
373C22⋊Q8D4×C1311yescharacteristic
374C22⋊Q8C23×C1312yes—
375C22⋊Q8C23×C1311yescharacteristic
376#121D4×C1311yescharacteristic
377#121C23×C1311yescharacteristic
378#120—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—22no—
385#117—21no—
386#117—22no—
387#117—22no—
388#117D4×C1311yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4D4×C1311yescharacteristic
397C2×C4⋊C4D4×C1311yescharacteristic
398C2×C4⋊C4C23×C1312yes—
399C2×C4⋊C4C23×C1312yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4D4×C1312yes—
403C2×C42—21no—
404#107—22no—
405#106—24no—
406#106—22no—
407#103—24no—
408#103—22no—
409#102—22no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8C23×C1312yes—
413C22⋊C8C23×C1312yes—
414#95—24no—
415#95C23×C1312yes—
416C2×C13—22no—
417C2×C13—22no—
418C2×C13—41no—
419C2×C13—81no—
420C2×C13#301011yescharacteristic
421C2×C13C2×#45611yescharacteristic
422C2×C13C2×#45811yescharacteristic
423C24C2×D4×C1311yescharacteristic
424#41—42no—
425C2×Q8—22no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—42no—
430C2×Q8—42no—
431C2×Q8—82no—
432C2×Q8C2×D4×C1312yes—
433C2×Q8C2×D4×C1311yescharacteristic
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×D4×C1311yescharacteristic
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—82no—
448C22×C4C2×D4×C1312yes—
449C22×C4C2×D4×C1311yescharacteristic
450C22×C4C2×D4×C1311yescharacteristic
451C22×C4C2×D4×C1311yescharacteristic
452C22×C4C2×D4×C1312yes—
453C22×C4C2×D4×C1311yescharacteristic
454C22×C4C2×D4×C1311yescharacteristic
455C22×C4C24×C1311yescharacteristic
456M16—42no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—42no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—84no—
482C4⋊C4C2×D4×C1312yes—
483C4⋊C4C2×D4×C1311yescharacteristic
484C4⋊C4C2×D4×C1311yescharacteristic
485C22⋊C4—24no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C42—22no—
499C42—22no—
500C42—22no—
501C42—21no—
502C42—42no—
503C13#1826811yescharacteristic, direct product factor, Sylow
504C23—22no—
505C23—22no—
506C23—21no—
507C23—41no—
508C23C13×#12011yescharacteristic
509C23C13×#12011yescharacteristic
510C23C22×D4×C1311yescharacteristic
511Q8—42no—
512Q8—41no—
513Q8—42no—
514Q8—42no—
515Q8—81no—
516Q8—82no—
517D4—41no—
518D4—42no—
519D4—42no—
520D4—81no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—44no—
543C2×C4—81no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C13×#12011yescharacteristic
548C2×C4C13×#12011yescharacteristic
549C2×C4C22×D4×C1311yescharacteristic
550C2×C4C22×D4×C1311yescharacteristic
551C8—42no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—44no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22C13×#45612yes—
565C22C2×C13×#12011yescharacteristic
566C22C13×#57712yes—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—44no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—41no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4C13×#45812yes—
580C2—22no—
581C2—22no—
582C2—41no—
583C2—81no—
584C2C13×#301011yescharacteristic
585C2C2×C13×#45611yescharacteristic
586C2C2×C13×#45811yescharacteristic
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×#483C2semidirect
4. C13×#2502C2semidirect
5. C13×#1611C2semidirect
6. C13×#1609C2semidirect
7. C13×#1508C2semidirect
9. C13×#1472C2semidirect
130. #18268C13direct (N × H)
213. C2×#483C2×C13semidirect
214. #2502C2×C13semidirect
215. #1611C2×C13semidirect
216. #1609C2×C13semidirect
217. #1508C2×C13semidirect
219. #1472C2×C13semidirect
503. C13#18268direct (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×#30922
C2×C13×#4832
C13×#25022
C13×#16112
C13×#16092
C13×#15082
C13×#15012
C13×#14722
#1826813