Finite Group Databasebeta

← C13×#9523 #15695862

Subgroups — C13×#9523 #15695862

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3006C211yesmaximal, characteristic
2C13×#2333C211yesmaximal, characteristic, complemented
3C13×#1789C211yesmaximal, characteristic, complemented
4C13×#1782C211yesmaximal, characteristic, complemented
5C13×#1510C211yesmaximal, characteristic, complemented
6C13×#1306C211yesmaximal, characteristic, complemented
7C13×#1284C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×AGL(1,ℤ/8)—21no—
10C2×C13×#121C2211yescharacteristic
11C13×#449—22no—
12C13×#448C412yescomplemented
13C13×#447C412yescomplemented
14C2×C13×#104—21no—
15C2×C13×#104—21no—
16C13×#417—21no—
17C2×C13×#99—21no—
18C2×C13×#99—21no—
19C13×#407C2211yescharacteristic
20C13×#407C2211yescharacteristic
21C13×#390—21no—
22C13×#388—21no—
23C13×#387—21no—
24C13×#386—21no—
25C13×#386—21no—
26C13×#381C2211yescharacteristic
27C13×#381C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#327—22no—
31C2×C13×#41—21no—
32C2×C13×#41—21no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—42no—
36C2×C13×#41—42no—
37C22×Q8×C13C2×C411yescharacteristic, complemented
38C22×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13C2×C411yescharacteristic, complemented
41C22×D4×C13D411yescharacteristic
42C23×C4×C13—21no—
43C23×C4×C13—21no—
44C23×C4×C13C2311yescharacteristic
45C13×AGL(1,ℤ/8)—42no—
46C13×AGL(1,ℤ/8)—42no—
47C2×C13×SD16—22no—
48C2×C13×D8—22no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C13×#121—21no—
52C13×#121—21no—
53C13×#121C2×C412yes—
54C13×#121D412yes—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13D411yescharacteristic
67C2×C42×C13D411yescharacteristic
68C13×#104—42no—
69C13×#104—42no—
70C13×#103—22no—
71C13×#102—22no—
72C13×#99—42no—
73C13×#99—42no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8C2×C412yescomplemented
78C13×#95—21no—
79C13×#95—21no—
80C13×#95—21no—
81C13×#95—21no—
82C13×#95—21no—
83C13×#95—21no—
84C13×#95—21no—
85#9523C1311yesmaximal, characteristic, direct product factor, Sylow
86C24×C13—21no—
87C24×C13—21no—
88C24×C13C2×D411yescharacteristic
89C13×#41—22no—
90C13×#41—22no—
91C13×#41—22no—
92C13×#41—22no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—41no—
97C13×#41—42no—
98C13×#41—42no—
99C13×#41—42no—
100C13×#41—42no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—42no—
104C2×D4×C13—22no—
105C2×D4×C13—22no—
106C2×D4×C13—22no—
107C2×D4×C13—22no—
108C2×D4×C13—21no—
109C2×D4×C13—21no—
110C2×D4×C13—21no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—42no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C2×D4×C13—41no—
118C2×D4×C13—81no—
119C2×D4×C13—81no—
120C2×D4×C13C22⋊C412yes—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13—81no—
136C22×C4×C13—81no—
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13#4111yescharacteristic
142C22×C4×C13#4111yescharacteristic
143C13×SD16—44no—
144C13×D8—44no—
145C13×M16—41no—
146C13×M16—41no—
147C13×M16—41no—
148C13×M16—41no—
149C2×C8×C13—22no—
150C2×C8×C13—41no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—81no—
153C13×C4⋊C4C22⋊C412yes—
154C13×C22⋊C4—22no—
155C13×C22⋊C4—22no—
156C13×C22⋊C4—42no—
157C13×C22⋊C4—42no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—81no—
163C13×C22⋊C4—81no—
164C42×C13—41no—
165C42×C13—41no—
166C42×C13—81no—
167#3006C2×C1311yescharacteristic
168#2333C2×C1311yescharacteristic, complemented
169#1789C2×C1311yescharacteristic, complemented
170#1782C2×C1311yescharacteristic, complemented
171#1510C2×C1311yescharacteristic, complemented
172#1306C2×C1311yescharacteristic, complemented
173#1284C2×C1311yescharacteristic, complemented
174C23×C13—21no—
175C23×C13—21no—
176C23×C13—22no—
177C23×C13—22no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—41no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13C4×D411yescharacteristic
191C23×C13#12011yescharacteristic
192C23×C13#12111yescharacteristic
193Q8×C13—22no—
194Q8×C13—22no—
195Q8×C13—41no—
196Q8×C13—41no—
197D4×C13—22no—
198D4×C13—22no—
199D4×C13—41no—
200D4×C13—41no—
201D4×C13—42no—
202D4×C13—42no—
203D4×C13—42no—
204D4×C13—42no—
205D4×C13—42no—
206D4×C13—81no—
207D4×C13—82no—
208D4×C13—82no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—84no—
240C2×C4×C13—81no—
241C2×C4×C13—81no—
242C2×C4×C13—81no—
243C2×C4×C13C2×C22⋊C411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13#12111yescharacteristic
246C2×C4×C13#12311yescharacteristic
247C8×C13—42no—
248C8×C13—81no—
249C22×#41C22×C1311yescharacteristic
250C2×AGL(1,ℤ/8)—21no—
251C2×#121C22×C1311yescharacteristic
252#449—22no—
253#448C4×C1312yescomplemented
254#447C4×C1312yescomplemented
255C2×#104—21no—
256C2×#104—21no—
257#417—21no—
258C2×#99—21no—
259C2×#99—21no—
260#407C22×C1311yescharacteristic
261#407C22×C1311yescharacteristic
262#390—21no—
263#388—21no—
264#387—21no—
265#386—21no—
266#386—21no—
267#381C22×C1311yescharacteristic
268#381C22×C1311yescharacteristic
269C4×C22⋊C4—21no—
270C4×C22⋊C4C22×C1311yescharacteristic
271#327—22no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—82no—
291C22×C13—82no—
292C22×C13—81no—
293C22×C13—81no—
294C22×C13#38611yescharacteristic
295C22×C13B(4,𝔽2)11yescharacteristic
296C22×C13B(4,𝔽2)11yescharacteristic
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13—81no—
307C4×C13—161no—
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—42no—
313C2×#41—42no—
314C22×Q8C2×C4×C1311yescharacteristic, complemented
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C2×C4×C1311yescharacteristic, complemented
318C22×D4D4×C1311yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C1311yescharacteristic
322AGL(1,ℤ/8)—42no—
323AGL(1,ℤ/8)—42no—
324C2×SD16—22no—
325C2×D8—22no—
326C2×M16—21no—
327C2×M16—21no—
328#121—21no—
329#121—21no—
330#121C2×C4×C1312yes—
331#121D4×C1312yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4D4×C1311yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4D4×C1311yescharacteristic
341C2×C22⋊C4D4×C1311yescharacteristic
342C2×C42—21no—
343C2×C42D4×C1311yescharacteristic
344C2×C42D4×C1311yescharacteristic
345#104—42no—
346#104—42no—
347#103—22no—
348#102—22no—
349#99—42no—
350#99—42no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8C2×C4×C1312yescomplemented
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362C2×C13—21no—
363C2×C13—21no—
364C2×C13—41no—
365C2×C13—41no—
366C2×C13—82no—
367C2×C13—82no—
368C2×C13#188911yescharacteristic
369C2×C13#190411yescharacteristic
370C2×C13#190611yescharacteristic
371C24—21no—
372C24—21no—
373C24C2×D4×C1311yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—42no—
383#41—42no—
384#41—42no—
385#41—42no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—42no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—81no—
404C2×D4—81no—
405C2×D4C13×C22⋊C412yes—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4C22×C4×C1311yescharacteristic
423C22×C4C2×D4×C1311yescharacteristic
424C22×C4C2×D4×C1311yescharacteristic
425C22×C4C2×D4×C1311yescharacteristic
426C22×C4C13×#4111yescharacteristic
427C22×C4C13×#4111yescharacteristic
428SD16—44no—
429D8—44no—
430M16—41no—
431M16—41no—
432M16—41no—
433M16—41no—
434C2×C8—22no—
435C2×C8—41no—
436C4⋊C4—21no—
437C4⋊C4—81no—
438C4⋊C4C13×C22⋊C412yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—42no—
442C22⋊C4—42no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—81no—
448C22⋊C4—81no—
449C42—41no—
450C42—41no—
451C42—81no—
452C13#952311yescharacteristic, direct product factor, Sylow
453C23—21no—
454C23—21no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—81no—
468C23—81no—
469C23C4×D4×C1311yescharacteristic
470C23C13×#12011yescharacteristic
471C23C13×#12111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—41no—
475Q8—41no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—81no—
486D4—82no—
487D4—82no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—84no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4C2×C13×C22⋊C411yescharacteristic
523C2×C4C4×D4×C1311yescharacteristic
524C2×C4C13×#12111yescharacteristic
525C2×C4C13×#12311yescharacteristic
526C8—42no—
527C8—81no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—81no—
549C22—81no—
550C22C13×#38611yescharacteristic
551C22C13×B(4,𝔽2)11yescharacteristic
552C22C13×B(4,𝔽2)11yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—161no—
564C2—21no—
565C2—21no—
566C2—41no—
567C2—41no—
568C2—82no—
569C2—82no—
570C2C13×#188911yescharacteristic
571C2C13×#190411yescharacteristic
572C2C13×#190611yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#3006C2
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
2. C13×#2333C2semidirect
3. C13×#1789C2semidirect
4. C13×#1782C2semidirect
5. C13×#1510C2semidirect
6. C13×#1306C2semidirect
7. C13×#1284C2semidirect
12. C13×#448C4semidirect
13. C13×#447C4semidirect
37. C22×Q8×C13C2×C4semidirect
40. C22×D4×C13C2×C4semidirect
77. C13×C22⋊C8C2×C4semidirect
85. #9523C13direct (N × H)
168. #2333C2×C13semidirect
169. #1789C2×C13semidirect
170. #1782C2×C13semidirect
171. #1510C2×C13semidirect
172. #1306C2×C13semidirect
173. #1284C2×C13semidirect
253. #448C4×C13semidirect
254. #447C4×C13semidirect
314. C22×Q8C2×C4×C13semidirect
317. C22×D4C2×C4×C13semidirect
354. C22⋊C8C2×C4×C13semidirect
452. C13#9523direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30062
C13×#23332
C13×#17892
C13×#17822
C13×#15102
C13×#13062
C13×#12842
#952313