Finite Group Databasebeta

← C13×#12689 #15699028

Subgroups — C13×#12689 #15699028

Order 3328.

1160 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#525C211yesmaximal, characteristic
2C2×C13×#352C212yesmaximal, complemented
3C2×C13×AΣL(1,𝔽16)C212yesmaximal, complemented
4C13×#1785C211yesmaximal, characteristic, complemented
5C13×#1782C211yesmaximal, characteristic, complemented
6C22×C13×#41C2211yescharacteristic
7C24×C4×C13C411yescharacteristic, complemented
8C13×#525—24no—
9C13×#525—24no—
10C2×C13×#123C411yescharacteristic, complemented
11C2×C13×#123C2211yescharacteristic
12C2×C13×C22⋊Q8—21no—
13C2×C13×#121—21no—
14C2×C13×#120C411yescharacteristic, complemented
15C2×C13×#120C2211yescharacteristic
16C2×C4×D4×C13—21no—
17C2×C4×D4×C13—21no—
18C2×C13×#117C411yescharacteristic, complemented
19C2×C13×#101—21no—
20C2×C13×#100C2212yes—
21C2×C13×#99—21no—
22C2×C13×#99C2212yes—
23C13×#407—21no—
24C13×#381—21no—
25C13×#352—24no—
26C13×AΣL(1,𝔽16)—24no—
27C25×C13C2×C411yescharacteristic
28C2×C13×#41—22no—
29C2×C13×#41—22no—
30C2×C13×#41—42no—
31C2×C13×#41—42no—
32C22×Q8×C13D411yescharacteristic
33C22×D4×C13—21no—
34C22×D4×C13—21no—
35C22×D4×C13C2×C411yescharacteristic
36C22×D4×C13D411yescharacteristic
37C22×D4×C13C2311yescharacteristic
38C23×C4×C13—22no—
39C23×C4×C13—21no—
40C23×C4×C13—22no—
41C23×C4×C13—21no—
42C23×C4×C13—42no—
43C23×C4×C13—42no—
44C23×C4×C13C2×C411yescharacteristic
45C23×C4×C13C2×C411yescharacteristic
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C2×C13×M16—22no—
49C13×#123—22no—
50C13×#123—22no—
51C13×#123—22no—
52C13×#123D414yes—
53C13×C22⋊Q8—28no—
54C13×#121—28no—
55C13×#120—22no—
56C13×#120—22no—
57C13×#120—22no—
58C13×#120D414yes—
59C4×D4×C13—28no—
60C4×D4×C13—28no—
61C13×#117—22no—
62C13×#117—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4C2×C411yescharacteristic
72C2×C13×C22⋊C4C2×C411yescharacteristic
73C2×C42×C13—21no—
74C13×#101—42no—
75C13×#100—22no—
76C13×#100—22no—
77C13×#99—22no—
78C13×#99—22no—
79C13×#99—42no—
80C13×C22⋊C8—42no—
81C13×#95—42no—
82#12689C1311yesmaximal, characteristic, direct product factor, Sylow
83C24×C13—21no—
84C24×C13—21no—
85C24×C13—41no—
86C24×C13—41no—
87C24×C13—44no—
88C24×C13C22⋊C411yescharacteristic
89C24×C13C22⋊C412yes—
90C24×C13C22×C411yescharacteristic
91C24×C13C2×D411yescharacteristic
92C13×#41—48no—
93C13×#41—48no—
94C2×Q8×C13—22no—
95C2×Q8×C13—22no—
96C2×Q8×C13—41no—
97C2×D4×C13—24no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—24no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—41no—
107C2×D4×C13—41no—
108C2×D4×C13—44no—
109C2×D4×C13—44no—
110C2×D4×C13C2×D412yes—
111C2×D4×C13C2×D412yes—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—24no—
117C22×C4×C13—24no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—48no—
129C22×C4×C13—48no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—41no—
135C22×C4×C13—41no—
136C22×C4×C13—42no—
137C22×C4×C13C22⋊C411yescharacteristic
138C22×C4×C13C22⋊C411yescharacteristic
139C22×C4×C13C22⋊C412yes—
140C22×C4×C13C22⋊C411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C13×M16—42no—
143C13×M16—42no—
144C2×C8×C13—42no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C22⋊C4—24no—
149C13×C22⋊C4—24no—
150C13×C22⋊C4—21no—
151C13×C22⋊C4—21no—
152C13×C22⋊C4—24no—
153C13×C22⋊C4—24no—
154C13×C22⋊C4—42no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4C22⋊C412yes—
157C13×C22⋊C4C22⋊C412yes—
158C42×C13—24no—
159C2×#525C2×C1311yescharacteristic
160C2×#352C2×C1312yescomplemented
161C2×AΣL(1,𝔽16)C2×C1312yescomplemented
162#1785C2×C1311yescharacteristic, complemented
163#1782C2×C1311yescharacteristic, complemented
164C23×C13—24no—
165C23×C13—22no—
166C23×C13—21no—
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13—21no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—44no—
176C23×C13—42no—
177C23×C13—44no—
178C23×C13—42no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—48no—
182C23×C13—44no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—44no—
186C23×C13C2×C22⋊C411yescharacteristic
187C23×C13C2×C22⋊C411yescharacteristic
188C23×C13C2×C22⋊C411yescharacteristic
189C23×C13#12012yes—
190Q8×C13—44no—
191D4×C13—42no—
192D4×C13—42no—
193D4×C13—44no—
194D4×C13—48no—
195D4×C13—48no—
196D4×C13—42no—
197D4×C13—42no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—44no—
213C2×C4×C13—44no—
214C2×C4×C13—48no—
215C2×C4×C13—48no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—42no—
222C2×C4×C13—82no—
223C2×C4×C13—84no—
224C2×C4×C13#9912yes—
225C2×C4×C13#9912yes—
226C2×C4×C13#12012yes—
227C8×C13—82no—
228C22×#41C22×C1311yescharacteristic
229C24×C4C4×C1311yescharacteristic, complemented
230#525—24no—
231#525—24no—
232C2×#123C4×C1311yescharacteristic, complemented
233C2×#123C22×C1311yescharacteristic
234C2×C22⋊Q8—21no—
235C2×#121—21no—
236C2×#120C4×C1311yescharacteristic, complemented
237C2×#120C22×C1311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×#117C4×C1311yescharacteristic, complemented
241C2×#101—21no—
242C2×#100C22×C1312yes—
243C2×#99—21no—
244C2×#99C22×C1312yes—
245#407—21no—
246#381—21no—
247#352—24no—
248AΣL(1,𝔽16)—24no—
249C22×C13—22no—
250C22×C13—24no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—22no—
254C22×C13—42no—
255C22×C13—41no—
256C22×C13—41no—
257C22×C13—42no—
258C22×C13—44no—
259C22×C13—42no—
260C22×C13—42no—
261C22×C13—44no—
262C22×C13—48no—
263C22×C13—44no—
264C22×C13—42no—
265C22×C13—44no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—41no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13#37911yescharacteristic
273C22×C13C2×#9911yescharacteristic
274C22×C13C2×#9911yescharacteristic
275C4×C13—22no—
276C4×C13—22no—
277C4×C13—22no—
278C4×C13—42no—
279C4×C13—42no—
280C4×C13—41no—
281C4×C13—42no—
282C4×C13—162no—
283C25C2×C4×C1311yescharacteristic
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—42no—
287C2×#41—42no—
288C22×Q8D4×C1311yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×C4×C1311yescharacteristic
292C22×D4D4×C1311yescharacteristic
293C22×D4C23×C1311yescharacteristic
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—22no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×C4×C1311yescharacteristic
301C23×C4C2×C4×C1311yescharacteristic
302C23×C4D4×C1311yescharacteristic
303C23×C4D4×C1311yescharacteristic
304C2×M16—22no—
305#123—22no—
306#123—22no—
307#123—22no—
308#123D4×C1314yes—
309C22⋊Q8—28no—
310#121—28no—
311#120—22no—
312#120—22no—
313#120—22no—
314#120D4×C1314yes—
315C4×D4—28no—
316C4×D4—28no—
317#117—22no—
318#117—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4C2×C4×C1311yescharacteristic
328C2×C22⋊C4C2×C4×C1311yescharacteristic
329C2×C42—21no—
330#101—42no—
331#100—22no—
332#100—22no—
333#99—22no—
334#99—22no—
335#99—42no—
336C22⋊C8—42no—
337#95—42no—
338C2×C13—21no—
339C2×C13—21no—
340C2×C13—42no—
341C2×C13—44no—
342C2×C13—41no—
343C2×C13—41no—
344C2×C13—81no—
345C2×C13#178111yescharacteristic
346C2×C13#212012yes—
347C24—21no—
348C24—21no—
349C24—41no—
350C24—41no—
351C24—44no—
352C24C13×C22⋊C411yescharacteristic
353C24C13×C22⋊C412yes—
354C24C22×C4×C1311yescharacteristic
355C24C2×D4×C1311yescharacteristic
356#41—48no—
357#41—48no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×D4—24no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4C2×D4×C1312yes—
375C2×D4C2×D4×C1312yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—48no—
393C22×C4—48no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—42no—
401C22×C4C13×C22⋊C411yescharacteristic
402C22×C4C13×C22⋊C411yescharacteristic
403C22×C4C13×C22⋊C411yescharacteristic
404C22×C4C13×C22⋊C412yes—
405C22×C4C2×D4×C1311yescharacteristic
406M16—42no—
407M16—42no—
408C2×C8—42no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4C13×C22⋊C412yes—
421C22⋊C4C13×C22⋊C412yes—
422C42—24no—
423C13#1268911yescharacteristic, direct product factor, Sylow
424C23—24no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—42no—
434C23—44no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—44no—
439C23—42no—
440C23—42no—
441C23—44no—
442C23—48no—
443C23—44no—
444C23—41no—
445C23—41no—
446C23C2×C13×C22⋊C411yescharacteristic
447C23C2×C13×C22⋊C411yescharacteristic
448C23C2×C13×C22⋊C411yescharacteristic
449C23C13×#12012yes—
450Q8—44no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—48no—
455D4—48no—
456D4—42no—
457D4—42no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—48no—
475C2×C4—48no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—84no—
484C2×C4C13×#9912yes—
485C2×C4C13×#9912yes—
486C2×C4C13×#12012yes—
487C8—82no—
488C22—22no—
489C22—24no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—42no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—44no—
498C22—42no—
499C22—42no—
500C22—44no—
501C22—44no—
502C22—48no—
503C22—42no—
504C22—42no—
505C22—44no—
506C22—42no—
507C22—41no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22C13×#37911yescharacteristic
512C22C2×C13×#9911yescharacteristic
513C22C2×C13×#9911yescharacteristic
514C4—22no—
515C4—22no—
516C4—22no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—162no—
522C2—21no—
523C2—21no—
524C2—42no—
525C2—44no—
526C2—41no—
527C2—41no—
528C2—81no—
529C2C13×#178111yescharacteristic
530C2C13×#212012yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#525C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#352C2semidirect
3. C2×C13×AΣL(1,𝔽16)C2semidirect
4. C13×#1785C2semidirect
5. C13×#1782C2semidirect
7. C24×C4×C13C4semidirect
10. C2×C13×#123C4semidirect
14. C2×C13×#120C4semidirect
18. C2×C13×#117C4semidirect
82. #12689C13direct (N × H)
160. C2×#352C2×C13semidirect
161. C2×AΣL(1,𝔽16)C2×C13semidirect
162. #1785C2×C13semidirect
163. #1782C2×C13semidirect
229. C24×C4C4×C13semidirect
232. C2×#123C4×C13semidirect
236. C2×#120C4×C13semidirect
240. C2×#117C4×C13semidirect
423. C13#12689direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5252
C2×C13×#3522
C2×C13×AΣL(1,𝔽16)2
C13×#17852
C13×#17822
#1268913