Finite Group Databasebeta

← C13×#19839 #15706178

Subgroups — C13×#19839 #15706178

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3367C211yesmaximal, characteristic
2C13×#3360C211yesmaximal, characteristic
3C13×#3342C211yesmaximal, characteristic, complemented
4C13×#3299C211yesmaximal, characteristic, complemented
5C13×#1718C211yesmaximal, characteristic, complemented
6C13×#1704C211yesmaximal, characteristic, complemented
7C13×#1683C211yesmaximal, characteristic, complemented
8C13×#1680C211yesmaximal, characteristic, complemented
9C13×#1673C211yesmaximal, characteristic, complemented
10C13×#1652C211yesmaximal, characteristic, complemented
11C13×#1651C211yesmaximal, characteristic, complemented
12C13×#1643C211yesmaximal, characteristic, complemented
13C13×#1638C211yesmaximal, characteristic, complemented
14C13×#1584C211yesmaximal, characteristic, complemented
15C13×#1580C211yesmaximal, characteristic
16C13×#556C2211yescharacteristic
17C13×#556C2211yescharacteristic
18C13×#554C2211yescharacteristic
19D4×Q8×C13C2211yescharacteristic
20C13×#500C2211yescharacteristic
21C13×#498C2211yescharacteristic
22C13×#489—21no—
23C13×#488—21no—
24C13×#487C2211yescharacteristic
25C13×#487C2211yescharacteristic
26C13×#487C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#485—21no—
29C13×#485—21no—
30C13×#484—21no—
31C13×#479—21no—
32C13×#477—21no—
33C13×#477C2211yescharacteristic
34C13×#476C2211yescharacteristic
35C13×#475C2211yescharacteristic
36C13×#475C2211yescharacteristic
37C13×#474C2211yescharacteristic
38C13×#467—21no—
39C13×#467—21no—
40C13×#463—21no—
41C13×#463—21no—
42C13×#462C2211yescharacteristic
43C13×#461C2211yescharacteristic
44C13×#461C2211yescharacteristic
45C13×#451—21no—
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C13×#440—21no—
49C4×C13×Q16C2211yescharacteristic
50C4×C13×SD16—21no—
51C4×C13×D8C2211yescharacteristic
52C8×D4×C13C2211yescharacteristic
53C8×D4×C13C2211yescharacteristic
54C13×#427—21no—
55C2×C13×#103—21no—
56C13×#335C2211yescharacteristic
57C13×#334C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#332C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#332C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×D4⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C22×Q8×C13—21no—
68C2×C13×Q16—21no—
69C2×C13×Q16D411yescharacteristic
70C2×C13×SD16—21no—
71C2×C13×SD16—21no—
72C2×C13×D8D411yescharacteristic
73C22×C8×C13—21no—
74C22×C8×C13—21no—
75C13×C4⋊Q8—21no—
76C13×C4⋊Q8C2311yescharacteristic
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×#126—41no—
81C13×#126—41no—
82C13×#125—21no—
83C13×#124—21no—
84C13×#124—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—41no—
90C13×C22⋊Q8—41no—
91C4×Q8×C13—21no—
92C4×Q8×C13—21no—
93C4×Q8×C13C2311yescharacteristic
94C4×Q8×C13C2311yescharacteristic
95C4×D4×C13—21no—
96C4×D4×C13—21no—
97C4×D4×C13C2311yescharacteristic
98C4×D4×C13C2311yescharacteristic
99C13×#117—21no—
100C13×#117—21no—
101C2×C13×C4⋊C4—21no—
102C13×#107—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107D411yescharacteristic
107C13×#107D411yescharacteristic
108C13×#106—21no—
109C13×#106—21no—
110C13×#106—21no—
111C13×#106—41no—
112C13×C4⋊C8—21no—
113C13×C4⋊C8—21no—
114C13×C4⋊C8C2311yescharacteristic
115C13×C4⋊C8C2311yescharacteristic
116C13×C4⋊C8C2311yescharacteristic
117C13×C4⋊C8C2311yescharacteristic
118C13×#103—21no—
119C13×#103—21no—
120C13×#103—21no—
121C13×#103—21no—
122C13×#103—21no—
123C13×#103—21no—
124C13×#103—21no—
125C13×#103—21no—
126C13×#103—21no—
127C13×#103—21no—
128C13×#103—21no—
129C13×#103—21no—
130C13×#103—41no—
131C13×#103D411yescharacteristic
132C13×#103D411yescharacteristic
133C13×#102—21no—
134C13×#102—21no—
135C13×#102D411yescharacteristic
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×C22⋊C8—21no—
139C13×#97—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19839C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—41no—
150C2×Q8×C13—42no—
151C2×Q8×C13—81no—
152C2×Q8×C13C2×D411yescharacteristic
153C2×Q8×C13C2×D411yescharacteristic
154C2×D4×C13C2×D411yescharacteristic
155C2×D4×C13C2×D411yescharacteristic
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—41no—
159C22×C4×C13—41no—
160C13×Q16—41no—
161C13×Q16—81no—
162C13×SD16—42no—
163C13×SD16—42no—
164C13×D8—22no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—42no—
171C2×C8×C13—81no—
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4—41no—
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C4⋊C4C2×D411yescharacteristic
194C13×C4⋊C4C2×D411yescharacteristic
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4—41no—
200C13×C22⋊C4—41no—
201C13×C22⋊C4—41no—
202C13×C22⋊C4—41no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—41no—
206C42×C13—41no—
207C42×C13C2411yescharacteristic
208#3367C2×C1311yescharacteristic
209#3360C2×C1311yescharacteristic
210#3342C2×C1311yescharacteristic, complemented
211#3299C2×C1311yescharacteristic, complemented
212#1718C2×C1311yescharacteristic, complemented
213#1704C2×C1311yescharacteristic, complemented
214#1683C2×C1311yescharacteristic, complemented
215#1680C2×C1311yescharacteristic, complemented
216#1673C2×C1311yescharacteristic, complemented
217#1652C2×C1311yescharacteristic, complemented
218#1651C2×C1311yescharacteristic, complemented
219#1643C2×C1311yescharacteristic, complemented
220#1638C2×C1311yescharacteristic, complemented
221#1584C2×C1311yescharacteristic, complemented
222#1580C2×C1311yescharacteristic
223C23×C13—21no—
224C23×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—41no—
230Q8×C13—41no—
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—41no—
235Q8×C13—81no—
236Q8×C13—82no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13#13512yes—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—82no—
256C2×C4×C13—161no—
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—41no—
269#556C22×C1311yescharacteristic
270#556C22×C1311yescharacteristic
271#554C22×C1311yescharacteristic
272D4×Q8C22×C1311yescharacteristic
273#500C22×C1311yescharacteristic
274#498C22×C1311yescharacteristic
275#489—21no—
276#488—21no—
277#487C22×C1311yescharacteristic
278#487C22×C1311yescharacteristic
279#487C22×C1311yescharacteristic
280#487C22×C1311yescharacteristic
281#485—21no—
282#485—21no—
283#484—21no—
284#479—21no—
285#477—21no—
286#477C22×C1311yescharacteristic
287#476C22×C1311yescharacteristic
288#475C22×C1311yescharacteristic
289#475C22×C1311yescharacteristic
290#474C22×C1311yescharacteristic
291#467—21no—
292#467—21no—
293#463—21no—
294#463—21no—
295#462C22×C1311yescharacteristic
296#461C22×C1311yescharacteristic
297#461C22×C1311yescharacteristic
298#451—21no—
299#446C22×C1311yescharacteristic
300C8×Q8C22×C1311yescharacteristic
301#440—21no—
302C4×Q16C22×C1311yescharacteristic
303C4×SD16—21no—
304C4×D8C22×C1311yescharacteristic
305C8×D4C22×C1311yescharacteristic
306C8×D4C22×C1311yescharacteristic
307#427—21no—
308C2×#103—21no—
309#335C22×C1311yescharacteristic
310#334C22×C1311yescharacteristic
311#333C22×C1311yescharacteristic
312#332C22×C1311yescharacteristic
313#332C22×C1311yescharacteristic
314#332C22×C1311yescharacteristic
315Q8⋊C8C22×C1311yescharacteristic
316Q8⋊C8C22×C1311yescharacteristic
317D4⋊C8C22×C1311yescharacteristic
318D4⋊C8C22×C1311yescharacteristic
319#322C22×C1311yescharacteristic
320C22×C13—22no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13D4211yescharacteristic
327C4×C13—21no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13C2×#13511yescharacteristic
339C4×C13#57511yescharacteristic
340C4×C13#57711yescharacteristic
341C4×C13#57811yescharacteristic
342C22×Q8—21no—
343C2×Q16—21no—
344C2×Q16D4×C1311yescharacteristic
345C2×SD16—21no—
346C2×SD16—21no—
347C2×D8D4×C1311yescharacteristic
348C22×C8—21no—
349C22×C8—21no—
350C4⋊Q8—21no—
351C4⋊Q8C23×C1311yescharacteristic
352C4⋊Q8C23×C1311yescharacteristic
353C4⋊Q8C23×C1311yescharacteristic
354C4⋊Q8C23×C1311yescharacteristic
355#126—41no—
356#126—41no—
357#125—21no—
358#124—21no—
359#124—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—41no—
365C22⋊Q8—41no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C1311yescharacteristic
369C4×Q8C23×C1311yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4C23×C1311yescharacteristic
373C4×D4C23×C1311yescharacteristic
374#117—21no—
375#117—21no—
376C2×C4⋊C4—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107D4×C1311yescharacteristic
382#107D4×C1311yescharacteristic
383#106—21no—
384#106—21no—
385#106—21no—
386#106—41no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C23×C1311yescharacteristic
390C4⋊C8C23×C1311yescharacteristic
391C4⋊C8C23×C1311yescharacteristic
392C4⋊C8C23×C1311yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—41no—
406#103D4×C1311yescharacteristic
407#103D4×C1311yescharacteristic
408#102—21no—
409#102—21no—
410#102D4×C1311yescharacteristic
411#102D4×C1311yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8C23×C1311yescharacteristic
417C4×C8C23×C1311yescharacteristic
418C4×C8C23×C1311yescharacteristic
419C2×C13—42no—
420C2×C13—81no—
421C2×C13#326711yescharacteristic
422C2×C13#328511yescharacteristic
423C2×C13#328911yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—42no—
430C2×Q8—81no—
431C2×Q8C2×D4×C1311yescharacteristic
432C2×Q8C2×D4×C1311yescharacteristic
433C2×D4C2×D4×C1311yescharacteristic
434C2×D4C2×D4×C1311yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439Q16—41no—
440Q16—81no—
441SD16—42no—
442SD16—42no—
443D8—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—42no—
450C2×C8—81no—
451C2×C8C2×D4×C1311yescharacteristic
452C2×C8C2×D4×C1311yescharacteristic
453C2×C8C2×D4×C1311yescharacteristic
454C2×C8C2×D4×C1311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4C2×D4×C1311yescharacteristic
471C4⋊C4C2×D4×C1311yescharacteristic
472C4⋊C4C2×D4×C1311yescharacteristic
473C4⋊C4C2×D4×C1311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42C24×C1311yescharacteristic
487C13#1983911yescharacteristic, direct product factor, Sylow
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—82no—
502D4—21no—
503D4—21no—
504D4—21no—
505D4C13×#13512yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—82no—
521C2×C4—161no—
522C2×C4C22×D4×C1311yescharacteristic
523C2×C4C22×D4×C1311yescharacteristic
524C2×C4C13×H(5,𝔽2)11yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C1311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×C13×#13511yescharacteristic
553C4C13×#57511yescharacteristic
554C4C13×#57711yescharacteristic
555C4C13×#57811yescharacteristic
556C2—42no—
557C2—81no—
558C2C13×#326711yescharacteristic
559C2C13×#328511yescharacteristic
560C2C13×#328911yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC2×C13×D8D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#3342C2semidirect
4. C13×#3299C2semidirect
5. C13×#1718C2semidirect
6. C13×#1704C2semidirect
7. C13×#1683C2semidirect
8. C13×#1680C2semidirect
9. C13×#1673C2semidirect
10. C13×#1652C2semidirect
11. C13×#1651C2semidirect
12. C13×#1643C2semidirect
13. C13×#1638C2semidirect
14. C13×#1584C2semidirect
144. #19839C13direct (N × H)
210. #3342C2×C13semidirect
211. #3299C2×C13semidirect
212. #1718C2×C13semidirect
213. #1704C2×C13semidirect
214. #1683C2×C13semidirect
215. #1680C2×C13semidirect
216. #1673C2×C13semidirect
217. #1652C2×C13semidirect
218. #1651C2×C13semidirect
219. #1643C2×C13semidirect
220. #1638C2×C13semidirect
221. #1584C2×C13semidirect
487. C13#19839direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33672
C13×#33602
C13×#33422
C13×#32992
C13×#17182
C13×#17042
C13×#16832
C13×#16802
C13×#16732
C13×#16522
C13×#16512
C13×#16432
C13×#16382
C13×#15842
C13×#15802
#1983913