Finite Group Databasebeta

← C13×#24057 #15710396

Subgroups — C13×#24057 #15710396

Order 3328.

1392 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3485C211yesmaximal, characteristic
2C13×#2853C212yesmaximal, complemented
3C13×#2297C211yesmaximal, characteristic, complemented
4C13×#2044C214yesmaximal, complemented
5C13×#1899C212yesmaximal, complemented
6C13×#1867C212yesmaximal, complemented
7C13×#1790C212yesmaximal, complemented
8C13×#1782C211yesmaximal, characteristic, complemented
9C2×C13×H(5,𝔽2)C2211yescharacteristic
10C22×C13×#41C2211yescharacteristic
11C13×#547—24no—
12C13×#546—24no—
13C13×#536—21no—
14C13×#534—21no—
15C13×#534C2212yes—
16C13×#525—21no—
17C2×C13×#123—21no—
18C2×C13×#123C2212yes—
19C13×#518C2211yescharacteristic
20C2×C13×#117C2211yescharacteristic, complemented
21C22×C42×C13C2211yescharacteristic, complemented
22C2×C13×#99C2212yes—
23C2×C13×#99C2214yes—
24C2×C13×#99C2212yescomplemented
25C13×#391—21no—
26C13×#390—21no—
27C13×#388—24no—
28C13×#387—24no—
29C13×#386C2212yes—
30C13×#386C2214yes—
31C13×#386C2212yescomplemented
32C13×#385C2214yescomplemented
33C13×#381C2212yescomplemented
34C4×C13×C22⋊C4—21no—
35C4×C13×C22⋊C4—21no—
36C13×#342C2214yescomplemented
37C13×H(5,𝔽2)—24no—
38C13×H(5,𝔽2)—42no—
39C2×C13×#41—24no—
40C2×C13×#41—21no—
41C2×C13×#41—24no—
42C2×C13×#41—22no—
43C2×C13×#41—42no—
44C22×Q8×C13D411yescharacteristic
45C22×D4×C13—21no—
46C22×D4×C13—22no—
47C22×D4×C13D411yescharacteristic
48C22×D4×C13C2312yes—
49C22×D4×C13C2311yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C13×C4⋊Q8—22no—
56C13×#124—22no—
57C13×#123—24no—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—24no—
63C13×#123—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—24no—
66C13×#121—22no—
67C13×#121—24no—
68C13×#121—24no—
69C13×#120—22no—
70C13×#120—22no—
71C13×#120—22no—
72C4×D4×C13—24no—
73C4×D4×C13—24no—
74C13×#117—21no—
75C13×#117—42no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4D414yes—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—24no—
85C2×C13×C22⋊C4D414yes—
86C2×C13×C22⋊C4C2314yes—
87C2×C13×C22⋊C4C2312yes—
88C2×C13×C22⋊C4C2312yes—
89C2×C42×C13—21no—
90C2×C42×C13—21no—
91C2×C42×C13—24no—
92C2×C42×C13—21no—
93C13×#99—24no—
94C13×#99—44no—
95C13×#99—42no—
96C13×#95—22no—
97C13×#95—22no—
98C13×#95—24no—
99C13×#95—24no—
100C13×#95—24no—
101#24057C1311yesmaximal, characteristic, direct product factor, Sylow
102C24×C13—21no—
103C24×C13C2×D412yes—
104C24×C13C2×D411yescharacteristic
105C24×C13C2×D411yescharacteristic
106C24×C13C2411yescharacteristic
107C13×#41—416no—
108C13×#41—48no—
109C13×#41—42no—
110C13×#41—42no—
111C2×Q8×C13—21no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13—41no—
115C2×D4×C13—22no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—21no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—24no—
125C2×D4×C13—22no—
126C2×D4×C13—24no—
127C2×D4×C13—24no—
128C2×D4×C13—22no—
129C2×D4×C13—41no—
130C2×D4×C13—48no—
131C2×D4×C13—42no—
132C2×D4×C13—42no—
133C2×D4×C13#4114yes—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—24no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—24no—
146C22×C4×C13—22no—
147C22×C4×C13—44no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D414yes—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D414yes—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—48no—
162C13×C4⋊C4—42no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—24no—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—44no—
174C13×C22⋊C4—44no—
175C13×C22⋊C4—48no—
176C42×C13—22no—
177C42×C13—42no—
178C42×C13—42no—
179C42×C13—42no—
180#3485C2×C1311yescharacteristic
181#2853C2×C1312yescomplemented
182#2297C2×C1311yescharacteristic, complemented
183#2044C2×C1314yescomplemented
184#1899C2×C1312yescomplemented
185#1867C2×C1312yescomplemented
186#1790C2×C1312yescomplemented
187#1782C2×C1311yescharacteristic, complemented
188C23×C13—21no—
189C23×C13—21no—
190C23×C13—22no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—24no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—44no—
200C23×C13—82no—
201C23×C13#12312yes—
202C23×C13C22×D411yescharacteristic
203C23×C13C22×D412yes—
204C23×C13C2×#4112yes—
205C23×C13H(5,𝔽2)12yes—
206Q8×C13—44no—
207Q8×C13—42no—
208D4×C13—28no—
209D4×C13—44no—
210D4×C13—42no—
211D4×C13—44no—
212D4×C13—42no—
213D4×C13—42no—
214D4×C13—44no—
215D4×C13—44no—
216D4×C13—84no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—28no—
224C2×C4×C13—24no—
225C2×C4×C13—28no—
226C2×C4×C13—24no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—24no—
232C2×C4×C13—44no—
233C2×C4×C13—44no—
234C2×C4×C13—44no—
235C2×C4×C13—44no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—44no—
240C2×C4×C13—44no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—44no—
244C2×C4×C13—42no—
245C2×C4×C13—44no—
246C2×C4×C13—82no—
247C2×C4×C13#12012yes—
248C2×C4×C13#12012yes—
249C2×C4×C13#12312yes—
250C2×H(5,𝔽2)C22×C1311yescharacteristic
251C22×#41C22×C1311yescharacteristic
252#547—24no—
253#546—24no—
254#536—21no—
255#534—21no—
256#534C22×C1312yes—
257#525—21no—
258C2×#123—21no—
259C2×#123C22×C1312yes—
260#518C22×C1311yescharacteristic
261C2×#117C22×C1311yescharacteristic, complemented
262C22×C42C22×C1311yescharacteristic, complemented
263C2×#99C22×C1312yes—
264C2×#99C22×C1314yes—
265C2×#99C22×C1312yescomplemented
266#391—21no—
267#390—21no—
268#388—24no—
269#387—24no—
270#386C22×C1314yes—
271#386C22×C1312yes—
272#386C22×C1312yescomplemented
273#385C22×C1314yescomplemented
274#381C22×C1312yescomplemented
275C4×C22⋊C4—21no—
276C4×C22⋊C4—21no—
277#342C22×C1314yescomplemented
278C22×C13—24no—
279C22×C13—22no—
280C22×C13—22no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—42no—
285C22×C13—42no—
286C22×C13—41no—
287C22×C13—42no—
288C22×C13—42no—
289C22×C13—44no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13—84no—
293C22×C13—162no—
294C22×C13C2×#12011yescharacteristic
295C22×C13C2×#12311yescharacteristic
296C22×C13#53411yescharacteristic
297C22×C13#54614yes—
298C4×C13—22no—
299C4×C13—22no—
300C4×C13—22no—
301C4×C13—42no—
302C4×C13—41no—
303C4×C13—44no—
304C4×C13—44no—
305C4×C13—82no—
306C4×C13—84no—
307H(5,𝔽2)—24no—
308H(5,𝔽2)—42no—
309C2×#41—24no—
310C2×#41—21no—
311C2×#41—24no—
312C2×#41—22no—
313C2×#41—42no—
314C22×Q8D4×C1311yescharacteristic
315C22×D4—21no—
316C22×D4—22no—
317C22×D4D4×C1311yescharacteristic
318C22×D4C23×C1312yes—
319C22×D4C23×C1311yescharacteristic
320C22×D4C23×C1311yescharacteristic
321C23×C4D4×C1311yescharacteristic
322C23×C4D4×C1311yescharacteristic
323C23×C4C23×C1311yescharacteristic
324C23×C4C23×C1312yes—
325C4⋊Q8—22no—
326#124—22no—
327#123—24no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—22no—
332#123—24no—
333#123—22no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336#121—22no—
337#121—24no—
338#121—24no—
339#120—22no—
340#120—22no—
341#120—22no—
342C4×D4—24no—
343C4×D4—24no—
344#117—21no—
345#117—42no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4D4×C1314yes—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4D4×C1314yes—
356C2×C22⋊C4C23×C1312yes—
357C2×C22⋊C4C23×C1314yes—
358C2×C22⋊C4C23×C1312yes—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—24no—
362C2×C42—21no—
363#99—24no—
364#99—44no—
365#99—42no—
366#95—22no—
367#95—22no—
368#95—24no—
369#95—24no—
370#95—24no—
371C2×C13—21no—
372C2×C13—24no—
373C2×C13—21no—
374C2×C13—42no—
375C2×C13—81no—
376C2×C13—82no—
377C2×C13#240511yescharacteristic
378C2×C13#302512yes—
379C24—21no—
380C24C2×D4×C1312yes—
381C24C2×D4×C1311yescharacteristic
382C24C2×D4×C1311yescharacteristic
383C24C24×C1311yescharacteristic
384#41—416no—
385#41—48no—
386#41—42no—
387#41—42no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—41no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—22no—
406C2×D4—41no—
407C2×D4—48no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4C13×#4114yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—44no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4C2×D4×C1312yes—
428C22×C4C2×D4×C1311yescharacteristic
429C22×C4C2×D4×C1314yes—
430C22×C4C2×D4×C1311yescharacteristic
431C22×C4C2×D4×C1311yescharacteristic
432C22×C4C2×D4×C1311yescharacteristic
433C22×C4C2×D4×C1314yes—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—42no—
439C4⋊C4—48no—
440C22⋊C4—22no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—44no—
451C22⋊C4—44no—
452C22⋊C4—48no—
453C42—22no—
454C42—42no—
455C42—42no—
456C42—42no—
457C13#2405711yescharacteristic, direct product factor, Sylow
458C23—21no—
459C23—21no—
460C23—22no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—24no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—44no—
470C23—82no—
471C23C13×#12312yes—
472C23C22×D4×C1311yescharacteristic
473C23C22×D4×C1312yes—
474C23C2×C13×#4112yes—
475C23C13×H(5,𝔽2)12yes—
476Q8—44no—
477Q8—42no—
478D4—28no—
479D4—44no—
480D4—42no—
481D4—44no—
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—84no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—28no—
494C2×C4—24no—
495C2×C4—28no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—82no—
517C2×C4C13×#12012yes—
518C2×C4C13×#12012yes—
519C2×C4C13×#12312yes—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—41no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—84no—
535C22—162no—
536C22C2×C13×#12011yescharacteristic
537C22C2×C13×#12311yescharacteristic
538C22C13×#53411yescharacteristic
539C22C13×#54614yes—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—44no—
544C4—44no—
545C4—42no—
546C4—41no—
547C4—82no—
548C4—84no—
549C2—21no—
550C2—24no—
551C2—21no—
552C2—42no—
553C2—81no—
554C2—82no—
555C2C13×#240511yescharacteristic
556C2C13×#302512yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3485C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2853C2semidirect
3. C13×#2297C2semidirect
4. C13×#2044C2semidirect
5. C13×#1899C2semidirect
6. C13×#1867C2semidirect
7. C13×#1790C2semidirect
8. C13×#1782C2semidirect
20. C2×C13×#117C22semidirect
21. C22×C42×C13C22semidirect
24. C2×C13×#99C22semidirect
31. C13×#386C22semidirect
32. C13×#385C22semidirect
33. C13×#381C22semidirect
36. C13×#342C22semidirect
101. #24057C13direct (N × H)
181. #2853C2×C13semidirect
182. #2297C2×C13semidirect
183. #2044C2×C13semidirect
184. #1899C2×C13semidirect
185. #1867C2×C13semidirect
186. #1790C2×C13semidirect
187. #1782C2×C13semidirect
261. C2×#117C22×C13semidirect
262. C22×C42C22×C13semidirect
265. C2×#99C22×C13semidirect
272. #386C22×C13semidirect
273. #385C22×C13semidirect
274. #381C22×C13semidirect
277. #342C22×C13semidirect
457. C13#24057direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34852
C13×#28532
C13×#22972
C13×#20442
C13×#18992
C13×#18672
C13×#17902
C13×#17822
#2405713