Finite Group Databasebeta

← C13×#18469 #15704808

Subgroups — C13×#18469 #15704808

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3236C211yesmaximal, characteristic, complemented
3C13×#3232C211yesmaximal, characteristic
4C13×#2822C211yesmaximal, characteristic, complemented
5C13×#1617C212yesmaximal, complemented
6C13×#1615C212yesmaximal
7C13×#1611C212yesmaximal, complemented
8C13×#1609C212yesmaximal
9C13×#1518C211yesmaximal, characteristic, complemented
10C13×#1512C211yesmaximal, characteristic
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#564—21no—
13C13×#563—21no—
14C13×#557—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—22no—
18C13×#552—21no—
19C13×#544—21no—
20C13×#544C2212yes—
21C13×#541—21no—
22C13×#541—22no—
23C13×#539C2212yes—
24C13×#533C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C13×#125C2211yescharacteristic
28C13×#501—21no—
29C13×#499—21no—
30C13×#491—21no—
31C13×#488—21no—
32C13×#484C2212yes—
33C13×#484C2211yescharacteristic
34C13×#483C2212yes—
35C13×#483C2211yescharacteristic
36C13×#481C2211yescharacteristic
37C13×#480C2211yescharacteristic
38C13×#479—21no—
39C13×#479—22no—
40C13×#478—21no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#400—21no—
44C13×#400C2212yes—
45C13×#398—21no—
46C13×#398—22no—
47C13×#398C2212yes—
48C13×#382C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—22no—
58C13×C4⋊Q8D411yescharacteristic
59C13×C4⋊Q8D411yescharacteristic
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—21no—
65C13×#125—22no—
66C13×#125—22no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#125—21no—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#125—21no—
77C13×#125—21no—
78C13×#125—21no—
79C13×#125—21no—
80C13×#125—21no—
81C13×#125—21no—
82C13×#125—21no—
83C13×#125D411yescharacteristic
84C13×#124D411yescharacteristic
85C13×#123—22no—
86C13×#123—21no—
87C13×#123—22no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8C2311yescharacteristic
96C13×C22⋊Q8C2312yes—
97C13×#121C2311yescharacteristic
98C4×Q8×C13—21no—
99C4×Q8×C13—22no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×Q8×C13D411yescharacteristic
103C4×Q8×C13D412yes—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C4×D4×C13D411yescharacteristic
107C13×#117—22no—
108C13×#117—21no—
109C13×#117—21no—
110C13×#117—22no—
111C13×#117—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D412yes—
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C4⋊C4C2311yescharacteristic
122C2×C13×C4⋊C4C2312yes—
123C2×C42×C13C2311yescharacteristic
124C13×#107—21no—
125C13×#107—21no—
126C13×#107—22no—
127C13×#106—21no—
128C13×#106—21no—
129C13×#106—22no—
130C13×C4⋊C8—21no—
131C13×C4⋊C8—21no—
132C13×#103—21no—
133C13×#103—22no—
134C13×#103—21no—
135C13×#103—22no—
136C13×#102—21no—
137C13×#102—21no—
138C13×C22⋊C8C2312yes—
139C13×C22⋊C8C2311yescharacteristic
140C13×C22⋊C8C2311yescharacteristic
141C13×#97—21no—
142C4×C8×C13—21no—
143C13×#95—21no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18469C1311yesmaximal, characteristic, direct product factor, Sylow
149C2×Q8×C13—22no—
150C2×Q8×C13—21no—
151C2×Q8×C13C2×D412yes—
152C2×Q8×C13C2×D411yescharacteristic
153C2×D4×C13—21no—
154C2×D4×C13C2×D411yescharacteristic
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2411yescharacteristic
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—41no—
198C13×C4⋊C4—41no—
199C13×C4⋊C4—41no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—81no—
202C13×C4⋊C4—82no—
203C13×C4⋊C4C2×D411yescharacteristic
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C4⋊C4C2×D412yes—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—21no—
211C13×C22⋊C4—21no—
212C13×C22⋊C4—21no—
213C13×C22⋊C4—21no—
214C13×C22⋊C4—21no—
215C42×C13—22no—
216C42×C13—22no—
217C42×C13—22no—
218C42×C13—22no—
219C42×C13—21no—
220C42×C13C2×D411yescharacteristic
221C42×C13C2×D411yescharacteristic
222C42×C13C2×D411yescharacteristic
223C42×C13C2×D411yescharacteristic
224#3563C2×C1311yescharacteristic
225#3236C2×C1311yescharacteristic, complemented
226#3232C2×C1311yescharacteristic
227#2822C2×C1311yescharacteristic, complemented
228#1617C2×C1312yescomplemented
229#1615C2×C1312yes—
230#1611C2×C1312yescomplemented
231#1609C2×C1312yes—
232#1518C2×C1311yescharacteristic, complemented
233#1512C2×C1311yescharacteristic
234#1470C2×C1311yescharacteristic, complemented
235C23×C13—21no—
236C23×C13C22×D411yescharacteristic
237Q8×C13—42no—
238Q8×C13—41no—
239Q8×C13—42no—
240Q8×C13—82no—
241D4×C13—41no—
242D4×C13—41no—
243D4×C13—41no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—42no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—82no—
268C2×C4×C13#12011yescharacteristic
269C2×C4×C13#12011yescharacteristic
270C2×C4×C13#12011yescharacteristic
271C2×C4×C13#12011yescharacteristic
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—42no—
277#564—21no—
278#563—21no—
279#557—21no—
280#554—21no—
281#552—21no—
282#552—22no—
283#552—21no—
284#544—21no—
285#544C22×C1312yes—
286#541—21no—
287#541—22no—
288#539C22×C1312yes—
289#533C22×C1311yescharacteristic
290#529C22×C1311yescharacteristic
291C2×#125C22×C1311yescharacteristic
292C2×#125C22×C1311yescharacteristic
293#501—21no—
294#499—21no—
295#491—21no—
296#488—21no—
297#484C22×C1312yes—
298#484C22×C1311yescharacteristic
299#483C22×C1312yes—
300#483C22×C1311yescharacteristic
301#481C22×C1311yescharacteristic
302#480C22×C1311yescharacteristic
303#479—21no—
304#479—22no—
305#478—21no—
306#432C22×C1311yescharacteristic
307#431C22×C1311yescharacteristic
308#400—21no—
309#400C22×C1312yes—
310#398—21no—
311#398—22no—
312#398C22×C1312yes—
313#382C22×C1311yescharacteristic
314#328C22×C1312yes—
315#328C22×C1312yes—
316#328C22×C1312yes—
317#327C22×C1312yes—
318#324C22×C1312yes—
319#324C22×C1312yes—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C2×#12011yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57811yescharacteristic
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—42no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—42no—
338C4×C13—42no—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—82no—
342C4×C13—81no—
343C4×C13—81no—
344C4⋊Q8—21no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8D4×C1311yescharacteristic
348C4⋊Q8D4×C1311yescharacteristic
349#126—22no—
350#126—22no—
351#126—22no—
352#126—22no—
353#126—21no—
354#125—22no—
355#125—22no—
356#125—22no—
357#125—22no—
358#125—21no—
359#125—22no—
360#125—22no—
361#125—22no—
362#125—22no—
363#125—21no—
364#125—21no—
365#125—21no—
366#125—21no—
367#125—21no—
368#125—21no—
369#125—21no—
370#125—21no—
371#125—21no—
372#125D4×C1311yescharacteristic
373#124D4×C1311yescharacteristic
374#123—22no—
375#123—21no—
376#123—22no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8C23×C1311yescharacteristic
385C22⋊Q8C23×C1312yes—
386#121C23×C1311yescharacteristic
387C4×Q8—21no—
388C4×Q8—22no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8D4×C1311yescharacteristic
392C4×Q8D4×C1312yes—
393C4×D4—21no—
394C4×D4—22no—
395C4×D4D4×C1311yescharacteristic
396#117—22no—
397#117—21no—
398#117—21no—
399#117—22no—
400#117—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4D4×C1311yescharacteristic
407C2×C4⋊C4D4×C1312yes—
408C2×C4⋊C4D4×C1311yescharacteristic
409C2×C4⋊C4C23×C1311yescharacteristic
410C2×C4⋊C4C23×C1311yescharacteristic
411C2×C4⋊C4C23×C1312yes—
412C2×C42C23×C1311yescharacteristic
413#107—21no—
414#107—21no—
415#107—22no—
416#106—21no—
417#106—21no—
418#106—22no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421#103—21no—
422#103—22no—
423#103—21no—
424#103—22no—
425#102—21no—
426#102—21no—
427C22⋊C8C23×C1312yes—
428C22⋊C8C23×C1311yescharacteristic
429C22⋊C8C23×C1311yescharacteristic
430#97—21no—
431C4×C8—21no—
432#95—21no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95C23×C1312yes—
437C2×C13—21no—
438C2×C13—21no—
439C2×C13—81no—
440C2×C13#301311yescharacteristic
441C2×C13#302011yescharacteristic
442C2×C13#302811yescharacteristic
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8C2×D4×C1312yes—
446C2×Q8C2×D4×C1311yescharacteristic
447C2×D4—21no—
448C2×D4C2×D4×C1311yescharacteristic
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4C2×D4×C1312yes—
455C22×C4C2×D4×C1311yescharacteristic
456C22×C4C2×D4×C1312yes—
457C22×C4C2×D4×C1311yescharacteristic
458C22×C4C24×C1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—81no—
496C4⋊C4—82no—
497C4⋊C4C2×D4×C1311yescharacteristic
498C4⋊C4C2×D4×C1311yescharacteristic
499C4⋊C4C2×D4×C1312yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42C2×D4×C1311yescharacteristic
515C42C2×D4×C1311yescharacteristic
516C42C2×D4×C1311yescharacteristic
517C42C2×D4×C1311yescharacteristic
518C13#1846911yescharacteristic, direct product factor, Sylow
519C23—21no—
520C23C22×D4×C1311yescharacteristic
521Q8—41no—
522Q8—42no—
523Q8—42no—
524Q8—82no—
525D4—41no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4C13×#12011yescharacteristic
553C2×C4C13×#12011yescharacteristic
554C2×C4C13×#12011yescharacteristic
555C2×C4C13×#12011yescharacteristic
556C2×C4C22×D4×C1311yescharacteristic
557C2×C4C22×D4×C1311yescharacteristic
558C8—41no—
559C8—41no—
560C8—42no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×C13×#12011yescharacteristic
567C22C13×#57711yescharacteristic
568C22C13×#57811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—82no—
583C4—81no—
584C4—81no—
585C2—21no—
586C2—21no—
587C2—81no—
588C2C13×#301311yescharacteristic
589C2C13×#302011yescharacteristic
590C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3236C2semidirect
4. C13×#2822C2semidirect
5. C13×#1617C2semidirect
7. C13×#1611C2semidirect
9. C13×#1518C2semidirect
11. C13×#1470C2semidirect
148. #18469C13direct (N × H)
225. #3236C2×C13semidirect
227. #2822C2×C13semidirect
228. #1617C2×C13semidirect
230. #1611C2×C13semidirect
232. #1518C2×C13semidirect
234. #1470C2×C13semidirect
518. C13#18469direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#32362
C13×#32322
C13×#28222
C13×#16172
C13×#16152
C13×#16112
C13×#16092
C13×#15182
C13×#15122
C13×#14702
#1846913