Finite Group Databasebeta

← C13×#25947 #15712286

Subgroups — C13×#25947 #15712286

Order 3328.

1490 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic, complemented
2C13×#2435C212yesmaximal, complemented
3C13×#2408C211yesmaximal, characteristic
4C13×#2029C214yesmaximal, complemented
5C13×#1996C212yesmaximal, complemented
6C13×#1889C214yesmaximal, complemented
7C4×C13×#99C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C13×#554—22no—
10C13×#554—24no—
11D4×Q8×C13—22no—
12C13×#544—21no—
13C13×#543—21no—
14C13×#543C2212yes—
15C13×#533—21no—
16C2×C13×#124—22no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8C2212yes—
19C2×C13×#121—21no—
20C2×C13×#120C2212yes—
21C13×#518C2212yes—
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#99C2212yes—
24C13×#394—21no—
25C13×#394—24no—
26C13×#392—21no—
27C13×#390—22no—
28C13×#390—21no—
29C13×#380C2211yescharacteristic
30C13×#379C2212yes—
31C13×#379C2218yes—
32C4×C13×C22⋊C4C2212yes—
33C13×#342C2218yes—
34C13×#342C2212yes—
35C25×C13C2312yes—
36C22×Q8×C13—21no—
37C22×Q8×C13D412yescomplemented
38C22×D4×C13—22no—
39C22×D4×C13—21no—
40C22×D4×C13—22no—
41C22×D4×C13—21no—
42C22×D4×C13—22no—
43C22×D4×C13—44no—
44C22×D4×C13C2311yescharacteristic
45C23×C4×C13D411yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—24no—
50C13×#125—22no—
51C13×#125—24no—
52C13×#124—48no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—24no—
56C13×C22⋊Q8—24no—
57C13×C22⋊Q8—22no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—24no—
64C13×C22⋊Q8—24no—
65C13×#121—44no—
66C13×#120—28no—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—24no—
72C4×D4×C13—24no—
73C13×#117—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D412yescomplemented
79C2×C13×C4⋊C4D414yescomplemented
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—28no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—28no—
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C13×C22⋊C4C2314yes—
88C2×C13×C22⋊C4C2312yes—
89C2×C13×C22⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4C2314yes—
91C2×C42×C13—22no—
92C2×C42×C13D411yescharacteristic
93C13×#99—24no—
94C13×#95—22no—
95C13×#95—21no—
96#25947C1311yesmaximal, characteristic, direct product factor, Sylow
97C24×C13—24no—
98C24×C13—22no—
99C24×C13—24no—
100C24×C13—24no—
101C24×C13—44no—
102C24×C13—82no—
103C24×C13C2×D411yescharacteristic
104C24×C13C2411yescharacteristic
105C2×Q8×C13—22no—
106C2×Q8×C13—22no—
107C2×Q8×C13—22no—
108C2×Q8×C13—22no—
109C2×Q8×C13—44no—
110C2×Q8×C13—82no—
111C2×D4×C13—22no—
112C2×D4×C13—22no—
113C2×D4×C13—24no—
114C2×D4×C13—28no—
115C2×D4×C13—44no—
116C2×D4×C13—42no—
117C2×D4×C13—48no—
118C2×D4×C13—44no—
119C2×D4×C13—44no—
120C2×D4×C13—44no—
121C2×D4×C13—41no—
122C2×D4×C13—42no—
123C2×D4×C13—41no—
124C2×D4×C13—82no—
125C2×D4×C13#4114yes—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—24no—
131C22×C4×C13—22no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D414yes—
140C22×C4×C13C2×D414yes—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D412yes—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—42no—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—22no—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—22no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—44no—
164C13×C22⋊C4—416no—
165C13×C22⋊C4—44no—
166C13×C22⋊C4—88no—
167C13×C22⋊C4—82no—
168C42×C13—24no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—44no—
172#3501C2×C1311yescharacteristic, complemented
173#2435C2×C1312yescomplemented
174#2408C2×C1311yescharacteristic
175#2029C2×C1314yescomplemented
176#1996C2×C1312yescomplemented
177#1889C2×C1314yescomplemented
178C4×#99C2×C1311yescharacteristic, complemented
179C23×C13—21no—
180C23×C13—21no—
181C23×C13—28no—
182C23×C13—24no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—48no—
188C23×C13—42no—
189C23×C13—44no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—48no—
196C23×C13—88no—
197C23×C13—88no—
198C23×C13#12412yescomplemented
199C23×C13C22×D411yescharacteristic
200C23×C13C22×D412yes—
201C23×C13C2×#4112yes—
202C23×C132−1+412yes—
203Q8×C13—44no—
204Q8×C13—82no—
205Q8×C13—82no—
206Q8×C13—82no—
207D4×C13—28no—
208D4×C13—44no—
209D4×C13—48no—
210D4×C13—44no—
211D4×C13—88no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—24no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—21no—
220C2×C4×C13—42no—
221C2×C4×C13—41no—
222C2×C4×C13—42no—
223C2×C4×C13—41no—
224C2×C4×C13—44no—
225C2×C4×C13—44no—
226C2×C4×C13—41no—
227C2×C4×C13—44no—
228C2×C4×C13—42no—
229C2×C4×C13—44no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—44no—
233C2×C4×C13—81no—
234C2×C4×C13—82no—
235C2×C4×C13—82no—
236C2×C4×C13#12011yescharacteristic
237C2×C4×C13#12012yes—
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#12412yescomplemented
240C23×D4C22×C1311yescharacteristic
241#554—22no—
242#554—24no—
243D4×Q8—22no—
244#544—21no—
245#543—21no—
246#543C22×C1312yes—
247#533—21no—
248C2×#124—22no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C22×C1312yes—
251C2×#121—21no—
252C2×#120C22×C1312yes—
253#518C22×C1312yes—
254C2×C4×D4C22×C1311yescharacteristic
255C2×#99C22×C1312yes—
256#394—21no—
257#394—24no—
258#392—21no—
259#390—22no—
260#390—21no—
261#380C22×C1311yescharacteristic
262#379C22×C1318yes—
263#379C22×C1312yes—
264C4×C22⋊C4C22×C1312yes—
265#342C22×C1318yes—
266#342C22×C1312yes—
267C22×C13—22no—
268C22×C13—21no—
269C22×C13—22no—
270C22×C13—21no—
271C22×C13—22no—
272C22×C13—42no—
273C22×C13—42no—
274C22×C13—42no—
275C22×C13—44no—
276C22×C13—416no—
277C22×C13—44no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—44no—
281C22×C13—81no—
282C22×C13—82no—
283C22×C13—88no—
284C22×C13—82no—
285C22×C13—82no—
286C22×C13—82no—
287C22×C13C2×#12011yescharacteristic
288C22×C13C2×#12411yescharacteristic
289C22×C13#53611yescharacteristic
290C22×C13#54814yes—
291C4×C13—22no—
292C4×C13—21no—
293C4×C13—22no—
294C4×C13—41no—
295C4×C13—44no—
296C4×C13—44no—
297C4×C13—41no—
298C4×C13—84no—
299C4×C13—82no—
300C4×C13B(4,𝔽2)12yes—
301C25C23×C1312yes—
302C22×Q8—21no—
303C22×Q8D4×C1312yescomplemented
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—22no—
307C22×D4—21no—
308C22×D4—22no—
309C22×D4—44no—
310C22×D4C23×C1311yescharacteristic
311C23×C4D4×C1311yescharacteristic
312C23×C4C23×C1311yescharacteristic
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—24no—
316#125—22no—
317#125—24no—
318#124—48no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331#121—44no—
332#120—28no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—24no—
338C4×D4—24no—
339#117—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4D4×C1311yescharacteristic
344C2×C4⋊C4D4×C1312yescomplemented
345C2×C4⋊C4D4×C1314yescomplemented
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4D4×C1311yescharacteristic
353C2×C22⋊C4C23×C1312yes—
354C2×C22⋊C4C23×C1314yes—
355C2×C22⋊C4C23×C1311yescharacteristic
356C2×C22⋊C4C23×C1314yes—
357C2×C42—22no—
358C2×C42D4×C1311yescharacteristic
359#99—24no—
360#95—22no—
361#95—21no—
362C2×C13—21no—
363C2×C13—24no—
364C2×C13—21no—
365C2×C13—42no—
366C2×C13—84no—
367C2×C13#243611yescharacteristic
368C2×C13C2×B(4,𝔽2)11yescharacteristic
369C2×C13#302711yescharacteristic
370C24—24no—
371C24—22no—
372C24—24no—
373C24—24no—
374C24—44no—
375C24—82no—
376C24C2×D4×C1311yescharacteristic
377C24C24×C1311yescharacteristic
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—44no—
383C2×Q8—82no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—24no—
387C2×D4—28no—
388C2×D4—44no—
389C2×D4—42no—
390C2×D4—48no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—82no—
398C2×D4C13×#4114yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4C2×D4×C1312yes—
408C22×C4C2×D4×C1311yescharacteristic
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1314yes—
413C22×C4C2×D4×C1314yes—
414C22×C4C2×D4×C1311yescharacteristic
415C22×C4C2×D4×C1312yes—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—42no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—44no—
437C22⋊C4—416no—
438C22⋊C4—44no—
439C22⋊C4—88no—
440C22⋊C4—82no—
441C42—24no—
442C42—21no—
443C42—21no—
444C42—44no—
445C13#2594711yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—21no—
448C23—28no—
449C23—24no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—48no—
455C23—42no—
456C23—44no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—48no—
463C23—88no—
464C23—88no—
465C23C13×#12412yescomplemented
466C23C22×D4×C1311yescharacteristic
467C23C22×D4×C1312yes—
468C23C2×C13×#4112yes—
469C23C13×2−1+412yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—28no—
475D4—44no—
476D4—48no—
477D4—44no—
478D4—88no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—21no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4C13×#12011yescharacteristic
504C2×C4C13×#12012yes—
505C2×C4C13×#12011yescharacteristic
506C2×C4C13×#12412yescomplemented
507C22—22no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—22no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—44no—
516C22—416no—
517C22—44no—
518C22—41no—
519C22—41no—
520C22—44no—
521C22—81no—
522C22—82no—
523C22—88no—
524C22—82no—
525C22—82no—
526C22—82no—
527C22C2×C13×#12011yescharacteristic
528C22C2×C13×#12411yescharacteristic
529C22C13×#53611yescharacteristic
530C22C13×#54814yes—
531C4—21no—
532C4—22no—
533C4—22no—
534C4—41no—
535C4—44no—
536C4—44no—
537C4—41no—
538C4—84no—
539C4—82no—
540C4C13×B(4,𝔽2)12yes—
541C2—21no—
542C2—24no—
543C2—21no—
544C2—42no—
545C2—84no—
546C2C13×#243611yescharacteristic
547C2C2×C13×B(4,𝔽2)11yescharacteristic
548C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#2408C2
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
1. C13×#3501C2semidirect
2. C13×#2435C2semidirect
4. C13×#2029C2semidirect
5. C13×#1996C2semidirect
6. C13×#1889C2semidirect
7. C4×C13×#99C2semidirect
37. C22×Q8×C13D4semidirect
78. C2×C13×C4⋊C4D4semidirect
79. C2×C13×C4⋊C4D4semidirect
96. #25947C13direct (N × H)
172. #3501C2×C13semidirect
173. #2435C2×C13semidirect
175. #2029C2×C13semidirect
176. #1996C2×C13semidirect
177. #1889C2×C13semidirect
178. C4×#99C2×C13semidirect
198. C23×C13#124semidirect
239. C2×C4×C13#124semidirect
303. C22×Q8D4×C13semidirect
344. C2×C4⋊C4D4×C13semidirect
345. C2×C4⋊C4D4×C13semidirect
445. C13#25947direct (N × H)
465. C23C13×#124semidirect
506. C2×C4C13×#124semidirect

Maximal subgroups

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

subgroupindex
C13×#35012
C13×#24352
C13×#24082
C13×#20292
C13×#19962
C13×#18892
C4×C13×#992
#2594713