Finite Group Databasebeta

← C13×#12793 #15699132

Subgroups — C13×#12793 #15699132

Order 3328.

808 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C13×#120C211yesmaximal, characteristic
2C2×C13×AΣL(1,𝔽16)C212yesmaximal
3C13×#1800C211yesmaximal, characteristic, complemented
4C13×#1799C211yesmaximal, characteristic, complemented
5C13×#1390C212yesmaximal, complemented
6C24×C4×C13C411yescharacteristic, complemented
7C2×C13×#120C2211yescharacteristic
8C2×C4×D4×C13—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#423—21no—
11C2×C13×#100C2212yes—
12C2×C13×#99C2212yes—
13C13×#386—21no—
14C13×#386C2211yescharacteristic
15C13×#385—21no—
16C13×#385C411yescharacteristic, complemented
17C13×#380—21no—
18C13×#379C411yescharacteristic, complemented
19C4×C13×C22⋊C4—21no—
20C4×C13×C22⋊C4C411yescharacteristic, complemented
21C13×AΣL(1,𝔽16)—24no—
22C13×#343—21no—
23C13×#342—21no—
24C25×C13C2×C411yescharacteristic
25C22×D4×C13—21no—
26C22×D4×C13C2311yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13—21no—
29C23×C4×C13—44no—
30C23×C4×C13—41no—
31C23×C4×C13—41no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C2×C13×M16—22no—
36C13×#120—21no—
37C13×#120—21no—
38C13×#120D412yes—
39C13×#120Q812yes—
40C4×D4×C13—41no—
41C4×D4×C13—41no—
42C4×D4×C13—44no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—41no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—22no—
51C2×C13×C22⋊C4C2×C411yescharacteristic
52C2×C13×C22⋊C4C2×C411yescharacteristic
53C2×C13×C22⋊C4C2×C411yescharacteristic
54C2×C13×C22⋊C4D411yescharacteristic
55C2×C42×C13—21no—
56C2×C42×C13D411yescharacteristic
57C13×C4⋊C8—41no—
58C13×C4⋊C8—41no—
59C13×#100—22no—
60C13×#100—22no—
61C13×#99—22no—
62C13×#99—22no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95—21no—
66C13×#95—41no—
67#12793C1311yesmaximal, characteristic, direct product factor, Sylow
68C24×C13—21no—
69C24×C13—21no—
70C24×C13—42no—
71C24×C13—41no—
72C24×C13—42no—
73C24×C13—41no—
74C24×C13C4⋊C412yescomplemented
75C24×C13C22×C411yescharacteristic
76C24×C13C2×D411yescharacteristic
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—42no—
82C2×D4×C13—42no—
83C2×D4×C13C2×D411yescharacteristic
84C2×D4×C13C2×Q811yescharacteristic
85C2×D4×C13#4111yescharacteristic
86C2×D4×C13#4111yescharacteristic
87C22×C4×C13—24no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—42no—
102C22×C4×C13—44no—
103C22×C4×C13—44no—
104C22×C4×C13—44no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—44no—
109C22×C4×C13—42no—
110C22×C4×C13C22⋊C411yescharacteristic
111C22×C4×C13C22⋊C411yescharacteristic
112C22×C4×C13C22⋊C411yescharacteristic
113C22×C4×C13C22⋊C411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C13×M16—42no—
116C13×M16—42no—
117C2×C8×C13—42no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—42no—
120C13×C4⋊C4—82no—
121C13×C22⋊C4—21no—
122C13×C22⋊C4—22no—
123C13×C22⋊C4—22no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—42no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—42no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4—42no—
132C13×C22⋊C4C4⋊C412yescomplemented
133C42×C13—21no—
134C42×C13—21no—
135C42×C13—42no—
136C4×#120C2×C1311yescharacteristic
137C2×AΣL(1,𝔽16)C2×C1312yes—
138#1800C2×C1311yescharacteristic, complemented
139#1799C2×C1311yescharacteristic, complemented
140#1390C2×C1312yescomplemented
141C23×C13—22no—
142C23×C13—22no—
143C23×C13—22no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—44no—
151C23×C13—42no—
152C23×C13—41no—
153C23×C13—44no—
154C23×C13—42no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—42no—
159C23×C13—48no—
160C23×C13—42no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—42no—
164C23×C13—42no—
165C23×C13C2×C22⋊C411yescharacteristic
166C23×C13C2×C4⋊C411yescharacteristic
167C23×C13#11711yescharacteristic
168C23×C13#12111yescharacteristic
169C23×C13C22⋊Q811yescharacteristic
170D4×C13—41no—
171D4×C13—41no—
172D4×C13—41no—
173D4×C13—41no—
174D4×C13—44no—
175D4×C13—44no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—22no—
179C2×C4×C13—22no—
180C2×C4×C13—22no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—44no—
185C2×C4×C13—42no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—48no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—44no—
194C2×C4×C13—42no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—81no—
203C2×C4×C13—82no—
204C2×C4×C13—82no—
205C2×C4×C13—82no—
206C2×C4×C13#9911yescharacteristic
207C2×C4×C13#9911yescharacteristic
208C2×C4×C13#12111yescharacteristic
209C2×C4×C13C22⋊Q811yescharacteristic
210C8×C13—82no—
211C24×C4C4×C1311yescharacteristic, complemented
212C2×#120C22×C1311yescharacteristic
213C2×C4×D4—21no—
214C2×C4×D4C22×C1311yescharacteristic
215#423—21no—
216C2×#100C22×C1312yes—
217C2×#99C22×C1312yes—
218#386—21no—
219#386C22×C1311yescharacteristic
220#385—21no—
221#385C4×C1311yescharacteristic, complemented
222#380—21no—
223#379C4×C1311yescharacteristic, complemented
224C4×C22⋊C4—21no—
225C4×C22⋊C4C4×C1311yescharacteristic, complemented
226AΣL(1,𝔽16)—24no—
227#343—21no—
228#342—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—24no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—42no—
241C22×C13—42no—
242C22×C13—42no—
243C22×C13—42no—
244C22×C13—44no—
245C22×C13—44no—
246C22×C13—44no—
247C22×C13—44no—
248C22×C13—42no—
249C22×C13—42no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—42no—
254C22×C13—41no—
255C22×C13—81no—
256C22×C13#38011yescharacteristic
257C22×C13C2×#9911yescharacteristic
258C22×C13#41011yescharacteristic
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—21no—
262C4×C13—42no—
263C4×C13—42no—
264C4×C13—41no—
265C4×C13—41no—
266C4×C13—41no—
267C4×C13—81no—
268C4×C13—162no—
269C4×C13AΣL(1,𝔽16)12yescomplemented
270C25C2×C4×C1311yescharacteristic
271C22×D4—21no—
272C22×D4C23×C1311yescharacteristic
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—44no—
276C23×C4—41no—
277C23×C4—41no—
278C23×C4C2×C4×C1311yescharacteristic
279C23×C4C2×C4×C1311yescharacteristic
280C23×C4D4×C1311yescharacteristic
281C2×M16—22no—
282#120—21no—
283#120—21no—
284#120D4×C1312yes—
285#120Q8×C1312yes—
286C4×D4—41no—
287C4×D4—41no—
288C4×D4—44no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4D4×C1311yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C1311yescharacteristic
298C2×C22⋊C4C2×C4×C1311yescharacteristic
299C2×C22⋊C4C2×C4×C1311yescharacteristic
300C2×C22⋊C4D4×C1311yescharacteristic
301C2×C42—21no—
302C2×C42D4×C1311yescharacteristic
303C4⋊C8—41no—
304C4⋊C8—41no—
305#100—22no—
306#100—22no—
307#99—22no—
308#99—22no—
309#95—21no—
310#95—21no—
311#95—21no—
312#95—41no—
313C2×C13—21no—
314C2×C13—21no—
315C2×C13—41no—
316C2×C13—44no—
317C2×C13—41no—
318C2×C13—41no—
319C2×C13—41no—
320C2×C13#179911yescharacteristic
321C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
322C2×C13#212011yescharacteristic
323C24—21no—
324C24—21no—
325C24—42no—
326C24—41no—
327C24—42no—
328C24—41no—
329C24C13×C4⋊C412yescomplemented
330C24C22×C4×C1311yescharacteristic
331C24C2×D4×C1311yescharacteristic
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4C2×D4×C1311yescharacteristic
339C2×D4C2×Q8×C1311yescharacteristic
340C2×D4C13×#4111yescharacteristic
341C2×D4C13×#4111yescharacteristic
342C22×C4—24no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—44no—
364C22×C4—42no—
365C22×C4C13×C22⋊C411yescharacteristic
366C22×C4C13×C22⋊C411yescharacteristic
367C22×C4C13×C22⋊C411yescharacteristic
368C22×C4C13×C22⋊C411yescharacteristic
369C22×C4C2×D4×C1311yescharacteristic
370M16—42no—
371M16—42no—
372C2×C8—42no—
373C4⋊C4—41no—
374C4⋊C4—42no—
375C4⋊C4—82no—
376C22⋊C4—21no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—41no—
385C22⋊C4—42no—
386C22⋊C4—42no—
387C22⋊C4C13×C4⋊C412yescomplemented
388C42—21no—
389C42—21no—
390C42—42no—
391C13#1279311yescharacteristic, direct product factor, Sylow
392C23—22no—
393C23—22no—
394C23—22no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—41no—
400C23—44no—
401C23—42no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—44no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—48no—
413C23—42no—
414C23—41no—
415C23—41no—
416C23C2×C13×C22⋊C411yescharacteristic
417C23C2×C13×C4⋊C411yescharacteristic
418C23C13×#11711yescharacteristic
419C23C13×#12111yescharacteristic
420C23C13×C22⋊Q811yescharacteristic
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—44no—
426D4—44no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4C13×#9911yescharacteristic
458C2×C4C13×#9911yescharacteristic
459C2×C4C13×#12111yescharacteristic
460C2×C4C13×C22⋊Q811yescharacteristic
461C8—82no—
462C22—21no—
463C22—21no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—42no—
482C22—42no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—42no—
487C22—41no—
488C22—81no—
489C22C13×#38011yescharacteristic
490C22C2×C13×#9911yescharacteristic
491C22C13×#41011yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—81no—
501C4—162no—
502C4C13×AΣL(1,𝔽16)12yescomplemented
503C2—21no—
504C2—21no—
505C2—41no—
506C2—44no—
507C2—41no—
508C2—41no—
509C2—41no—
510C2C13×#179911yescharacteristic
511C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
512C2C13×#212011yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#120C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1800C2semidirect
4. C13×#1799C2semidirect
5. C13×#1390C2semidirect
6. C24×C4×C13C4semidirect
16. C13×#385C4semidirect
18. C13×#379C4semidirect
20. C4×C13×C22⋊C4C4semidirect
67. #12793C13direct (N × H)
74. C24×C13C4⋊C4semidirect
132. C13×C22⋊C4C4⋊C4semidirect
138. #1800C2×C13semidirect
139. #1799C2×C13semidirect
140. #1390C2×C13semidirect
211. C24×C4C4×C13semidirect
221. #385C4×C13semidirect
223. #379C4×C13semidirect
225. C4×C22⋊C4C4×C13semidirect
269. C4×C13AΣL(1,𝔽16)semidirect
329. C24C13×C4⋊C4semidirect
387. C22⋊C4C13×C4⋊C4semidirect
391. C13#12793direct (N × H)
502. C4C13×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C4×C13×#1202
C2×C13×AΣL(1,𝔽16)2
C13×#18002
C13×#17992
C13×#13902
#1279313