Finite Group Databasebeta

← C13×#61876 #15748215

Subgroups — C13×#61876 #15748215

Order 3328.

1712 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3548C211yesmaximal, characteristic, complemented
2C13×#3504C211yesmaximal, characteristic, complemented
3C13×#3389C214yesmaximal, complemented
4C13×#3388C214yesmaximal, complemented
5C13×#3368C214yesmaximal, complemented
6C13×#3366C214yesmaximal, complemented
7C13×#3241C214yesmaximal, complemented
8C13×#3234C212yesmaximal, complemented
9C13×#3119C214yesmaximal, complemented
10C13×#3115C212yesmaximal, complemented
11C13×#2987C211yesmaximal, characteristic, complemented
12C13×#562—21no—
13C13×#562—21no—
14C13×#557C2214yes—
15C13×#554—24no—
16C13×#554C2214yes—
17C13×#554C2214yes—
18C13×#550C2214yes—
19C13×#547—22no—
20C13×#544—22no—
21C13×#544C2212yes—
22C13×#540C2214yes—
23C13×#537—24no—
24C13×#533—21no—
25C13×#533C2211yescharacteristic
26C13×#532C2212yes—
27C2×C13×#125—21no—
28C2×C13×#125C2211yescharacteristic
29C13×#520C2212yes—
30C4×C13×#41C2211yescharacteristic
31C13×#501C2214yes—
32C13×#501C2214yes—
33C13×#499C2214yes—
34C13×#490C2214yes—
35C13×#490C2214yes—
36C13×#486C2214yes—
37C13×#482C2214yes—
38C13×#481C2214yes—
39C13×#480C2214yes—
40C13×#479C2214yes—
41C13×#478C2214yes—
42C13×#478C2214yes—
43C13×#478C2214yes—
44C13×#478C2214yes—
45C13×#478C2214yes—
46C13×#476C2214yes—
47C13×#475C2212yes—
48C13×#474C2214yes—
49C13×#474C2212yes—
50C13×#460C2212yes—
51C13×#460C2214yes—
52C13×#459C2212yes—
53C13×#459C2214yes—
54C13×#449C2214yes—
55C13×#446C2214yes—
56C13×#446C2214yes—
57C13×#442C2214yes—
58C13×#442C2214yes—
59C13×#440C2214yes—
60C13×#440C2214yes—
61C4×C13×SD16C2214yes—
62C4×C13×D8C2214yes—
63C13×#433C2214yes—
64C13×#432C2212yes—
65C2×C13×#41—24no—
66C2×C13×#41—22no—
67C2×C13×#41C2311yescharacteristic
68C2×C13×SD16C2314yes—
69C2×C13×D8C2314yes—
70C13×C4⋊Q8—24no—
71C13×C4⋊Q8—22no—
72C13×C4⋊Q8D412yes—
73C13×C4⋊Q8C2312yes—
74C13×C4⋊Q8C2314yes—
75C13×#127C2314yes—
76C13×#127C2312yes—
77C13×#125—22no—
78C13×#125—24no—
79C13×#125—24no—
80C13×#125—21no—
81C13×#125—21no—
82C13×#125D411yescharacteristic
83C13×#125D411yescharacteristic
84C13×#125C2314yes—
85C13×#125C2314yes—
86C13×#125C2314yes—
87C13×#124—22no—
88C13×#123—24no—
89C13×#123—24no—
90C13×C22⋊Q8—24no—
91C13×C22⋊Q8—24no—
92C13×C22⋊Q8—24no—
93C13×C22⋊Q8—24no—
94C13×C22⋊Q8—24no—
95C13×C22⋊Q8—24no—
96C13×C22⋊Q8—24no—
97C13×C22⋊Q8D414yes—
98C13×#121—22no—
99C13×#121—24no—
100C13×#121—24no—
101C13×#121—24no—
102C13×#121—24no—
103C13×#121—24no—
104C13×#121C2314yes—
105C4×Q8×C13—24no—
106C4×Q8×C13C2314yes—
107C4×Q8×C13C2312yes—
108C4×Q8×C13C2314yes—
109C4×D4×C13—22no—
110C4×D4×C13—24no—
111C4×D4×C13—22no—
112C4×D4×C13C2314yes—
113C4×D4×C13C2314yes—
114C4×D4×C13C2314yes—
115C4×D4×C13C2314yes—
116C4×D4×C13C2312yes—
117C13×#117—22no—
118C13×#117—21no—
119C13×#117C2311yescharacteristic
120C13×#117C2312yes—
121C2×C13×C4⋊C4—22no—
122C2×C13×C4⋊C4—22no—
123C2×C13×C4⋊C4—24no—
124C2×C13×C4⋊C4—24no—
125C2×C13×C4⋊C4C2312yes—
126C2×C42×C13—21no—
127C2×C42×C13C2311yescharacteristic
128C13×#107C2314yes—
129C13×#107C2314yes—
130C13×#107C2314yes—
131C13×#106C2314yes—
132C13×#106C2314yes—
133C13×#106C2314yes—
134C13×C4⋊C8C2312yes—
135C13×C4⋊C8C2312yes—
136C13×C4⋊C8C2314yes—
137C13×C4⋊C8C2314yes—
138C13×#103C2314yes—
139C13×#102C2314yes—
140C13×#102C2314yes—
141C13×#102C2314yes—
142C13×#102C2314yes—
143C13×#102C2314yes—
144C13×#102C2314yes—
145C13×#102C2314yes—
146C13×C22⋊C8C2314yes—
147C13×#97C2314yes—
148C13×#97C2314yes—
149C4×C8×C13C2314yes—
150#61876C1311yesmaximal, characteristic, direct product factor, Sylow
151C13×#41—22no—
152C13×#41—22no—
153C13×#41—84no—
154C13×#41—88no—
155C2×Q8×C13—24no—
156C2×Q8×C13—22no—
157C2×Q8×C13C2×D414yes—
158C2×Q8×C13C2411yescharacteristic
159C2×D4×C13—21no—
160C2×D4×C13—24no—
161C2×D4×C13—22no—
162C2×D4×C13—24no—
163C2×D4×C13—24no—
164C2×D4×C13—22no—
165C2×D4×C13C2414yes—
166C2×D4×C13C2411yescharacteristic
167C22×C4×C13—21no—
168C22×C4×C13—22no—
169C22×C4×C13—24no—
170C22×C4×C13—22no—
171C22×C4×C13—24no—
172C22×C4×C13—24no—
173C22×C4×C13—24no—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2411yescharacteristic
176C13×SD16—28no—
177C13×D8—28no—
178C2×C8×C13C2414yes—
179C2×C8×C13C2414yes—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—24no—
191C13×C4⋊C4C2×D412yes—
192C13×C4⋊C4C2×D414yes—
193C13×C4⋊C4C2×D414yes—
194C13×C4⋊C4C2×D412yes—
195C13×C4⋊C4C2×D414yes—
196C13×C4⋊C4C2414yes—
197C13×C4⋊C4C2412yes—
198C13×C4⋊C4C2414yes—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—24no—
202C13×C22⋊C4—24no—
203C13×C22⋊C4—24no—
204C13×C22⋊C4—24no—
205C13×C22⋊C4—24no—
206C13×C22⋊C4C2×D414yes—
207C42×C13—21no—
208C42×C13—22no—
209C42×C13—24no—
210C42×C13C2×D411yescharacteristic
211C42×C13C2×D411yescharacteristic
212C42×C13C2414yes—
213C42×C13C2412yes—
214#3548C2×C1311yescharacteristic, complemented
215#3504C2×C1311yescharacteristic, complemented
216#3389C2×C1314yescomplemented
217#3388C2×C1314yescomplemented
218#3368C2×C1314yescomplemented
219#3366C2×C1314yescomplemented
220#3241C2×C1314yescomplemented
221#3234C2×C1312yescomplemented
222#3119C2×C1314yescomplemented
223#3115C2×C1312yescomplemented
224#2987C2×C1311yescharacteristic, complemented
225C23×C13—21no—
226C23×C13—24no—
227C23×C13C22×D411yescharacteristic
228Q8×C13—21no—
229Q8×C13—44no—
230Q8×C13—84no—
231Q8×C13—82no—
232Q8×C132−1+412yes—
233D4×C13—24no—
234D4×C13—21no—
235D4×C13—24no—
236D4×C13—24no—
237D4×C13—44no—
238D4×C13—82no—
239D4×C13—84no—
240D4×C13—84no—
241D4×C13—84no—
242D4×C132−1+412yes—
243C2×C4×C13—24no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—42no—
251C2×C4×C13—48no—
252C2×C4×C13—82no—
253C2×C4×C13—84no—
254C2×C4×C13—84no—
255C2×C4×C13—84no—
256C2×C4×C13—82no—
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×D412yes—
259C2×C4×C13C22×D414yes—
260C2×C4×C13C22×D412yes—
261C2×C4×C13C22×D414yes—
262C2×C4×C13C2511yescharacteristic
263C8×C13—24no—
264C8×C13—24no—
265#562—21no—
266#562—21no—
267#557C22×C1314yes—
268#554—24no—
269#554C22×C1314yes—
270#554C22×C1314yes—
271#550C22×C1314yes—
272#547—22no—
273#544—22no—
274#544C22×C1312yes—
275#540C22×C1314yes—
276#537—24no—
277#533—21no—
278#533C22×C1311yescharacteristic
279#532C22×C1312yes—
280C2×#125—21no—
281C2×#125C22×C1311yescharacteristic
282#520C22×C1312yes—
283C4×#41C22×C1311yescharacteristic
284#501C22×C1314yes—
285#501C22×C1314yes—
286#499C22×C1314yes—
287#490C22×C1314yes—
288#490C22×C1314yes—
289#486C22×C1314yes—
290#482C22×C1314yes—
291#481C22×C1314yes—
292#480C22×C1314yes—
293#479C22×C1314yes—
294#478C22×C1314yes—
295#478C22×C1314yes—
296#478C22×C1314yes—
297#478C22×C1314yes—
298#478C22×C1314yes—
299#476C22×C1314yes—
300#475C22×C1312yes—
301#474C22×C1314yes—
302#474C22×C1312yes—
303#460C22×C1312yes—
304#460C22×C1314yes—
305#459C22×C1312yes—
306#459C22×C1314yes—
307#449C22×C1314yes—
308#446C22×C1314yes—
309#446C22×C1314yes—
310#442C22×C1314yes—
311#442C22×C1314yes—
312#440C22×C1314yes—
313#440C22×C1314yes—
314C4×SD16C22×C1314yes—
315C4×D8C22×C1314yes—
316#433C22×C1314yes—
317#432C22×C1312yes—
318C22×C13—22no—
319C22×C13—21no—
320C22×C13—22no—
321C22×C13—42no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13C23×D411yescharacteristic
326C4×C13—22no—
327C4×C13—22no—
328C4×C13—24no—
329C4×C13—24no—
330C4×C13—21no—
331C4×C13—22no—
332C4×C13—44no—
333C4×C13—44no—
334C4×C13—42no—
335C4×C13C2×2−1+411yescharacteristic
336C4×C13C2×2−1+411yescharacteristic
337C2×#41—24no—
338C2×#41—22no—
339C2×#41C23×C1311yescharacteristic
340C2×SD16C23×C1314yes—
341C2×D8C23×C1314yes—
342C4⋊Q8—24no—
343C4⋊Q8—22no—
344C4⋊Q8D4×C1312yes—
345C4⋊Q8C23×C1312yes—
346C4⋊Q8C23×C1314yes—
347#127C23×C1312yes—
348#127C23×C1314yes—
349#125—22no—
350#125—24no—
351#125—24no—
352#125—21no—
353#125—21no—
354#125D4×C1311yescharacteristic
355#125D4×C1311yescharacteristic
356#125C23×C1314yes—
357#125C23×C1314yes—
358#125C23×C1314yes—
359#124—22no—
360#123—24no—
361#123—24no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369C22⋊Q8D4×C1314yes—
370#121—22no—
371#121—24no—
372#121—24no—
373#121—24no—
374#121—24no—
375#121—24no—
376#121C23×C1314yes—
377C4×Q8—24no—
378C4×Q8C23×C1312yes—
379C4×Q8C23×C1314yes—
380C4×Q8C23×C1314yes—
381C4×D4—22no—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4C23×C1312yes—
385C4×D4C23×C1314yes—
386C4×D4C23×C1314yes—
387C4×D4C23×C1314yes—
388C4×D4C23×C1314yes—
389#117—22no—
390#117—21no—
391#117C23×C1311yescharacteristic
392#117C23×C1312yes—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4C23×C1312yes—
398C2×C42—21no—
399C2×C42C23×C1311yescharacteristic
400#107C23×C1314yes—
401#107C23×C1314yes—
402#107C23×C1314yes—
403#106C23×C1314yes—
404#106C23×C1314yes—
405#106C23×C1314yes—
406C4⋊C8C23×C1312yes—
407C4⋊C8C23×C1312yes—
408C4⋊C8C23×C1314yes—
409C4⋊C8C23×C1314yes—
410#103C23×C1314yes—
411#102C23×C1314yes—
412#102C23×C1314yes—
413#102C23×C1314yes—
414#102C23×C1314yes—
415#102C23×C1314yes—
416#102C23×C1314yes—
417#102C23×C1314yes—
418C22⋊C8C23×C1314yes—
419#97C23×C1314yes—
420#97C23×C1314yes—
421C4×C8C23×C1314yes—
422C2×C13—41no—
423C2×C13—42no—
424C2×C13—84no—
425C2×C13#348611yescharacteristic
426C2×C13#358512yes—
427#41—22no—
428#41—22no—
429#41—84no—
430#41—88no—
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8C2×D4×C1314yes—
434C2×Q8C24×C1311yescharacteristic
435C2×D4—21no—
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4C24×C1314yes—
442C2×D4C24×C1311yescharacteristic
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4C2×D4×C1312yes—
451C22×C4C24×C1311yescharacteristic
452SD16—28no—
453D8—28no—
454C2×C8C24×C1314yes—
455C2×C8C24×C1314yes—
456C4⋊C4—22no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—24no—
467C4⋊C4C2×D4×C1312yes—
468C4⋊C4C2×D4×C1314yes—
469C4⋊C4C2×D4×C1314yes—
470C4⋊C4C2×D4×C1312yes—
471C4⋊C4C2×D4×C1314yes—
472C4⋊C4C24×C1314yes—
473C4⋊C4C24×C1312yes—
474C4⋊C4C24×C1314yes—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4C2×D4×C1314yes—
483C42—21no—
484C42—22no—
485C42—24no—
486C42C2×D4×C1311yescharacteristic
487C42C2×D4×C1311yescharacteristic
488C42C24×C1314yes—
489C42C24×C1312yes—
490C13#6187611yescharacteristic, direct product factor, Sylow
491C23—21no—
492C23—24no—
493C23C22×D4×C1311yescharacteristic
494Q8—21no—
495Q8—44no—
496Q8—82no—
497Q8—84no—
498Q8C13×2−1+412yes—
499D4—24no—
500D4—21no—
501D4—24no—
502D4—24no—
503D4—44no—
504D4—82no—
505D4—84no—
506D4—84no—
507D4—84no—
508D4C13×2−1+412yes—
509C2×C4—24no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—42no—
517C2×C4—48no—
518C2×C4—82no—
519C2×C4—84no—
520C2×C4—84no—
521C2×C4—84no—
522C2×C4—82no—
523C2×C4C22×D4×C1311yescharacteristic
524C2×C4C22×D4×C1312yes—
525C2×C4C22×D4×C1314yes—
526C2×C4C22×D4×C1312yes—
527C2×C4C22×D4×C1314yes—
528C2×C4C25×C1311yescharacteristic
529C8—24no—
530C8—24no—
531C22—22no—
532C22—21no—
533C22—22no—
534C22—42no—
535C22—44no—
536C22—44no—
537C22—44no—
538C22C23×D4×C1311yescharacteristic
539C4—22no—
540C4—22no—
541C4—24no—
542C4—24no—
543C4—21no—
544C4—22no—
545C4—44no—
546C4—44no—
547C4—42no—
548C4C2×C13×2−1+411yescharacteristic
549C4C2×C13×2−1+411yescharacteristic
550C2—41no—
551C2—42no—
552C2—84no—
553C2C13×#348611yescharacteristic
554C2C13×#358512yes—
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3548C2semidirect
2. C13×#3504C2semidirect
3. C13×#3389C2semidirect
4. C13×#3388C2semidirect
5. C13×#3368C2semidirect
6. C13×#3366C2semidirect
7. C13×#3241C2semidirect
8. C13×#3234C2semidirect
9. C13×#3119C2semidirect
10. C13×#3115C2semidirect
11. C13×#2987C2semidirect
150. #61876C13direct (N × H)
214. #3548C2×C13semidirect
215. #3504C2×C13semidirect
216. #3389C2×C13semidirect
217. #3388C2×C13semidirect
218. #3368C2×C13semidirect
219. #3366C2×C13semidirect
220. #3241C2×C13semidirect
221. #3234C2×C13semidirect
222. #3119C2×C13semidirect
223. #3115C2×C13semidirect
224. #2987C2×C13semidirect
490. C13#61876direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35482
C13×#35042
C13×#33892
C13×#33882
C13×#33682
C13×#33662
C13×#32412
C13×#32342
C13×#31192
C13×#31152
C13×#29872
#6187613