Finite Group Databasebeta

← C13×#19017 #15705356

Subgroups — C13×#19017 #15705356

Order 3328.

944 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic, complemented
3C2×C13×#501C211yesmaximal, characteristic, complemented
4C13×#3152C211yesmaximal, characteristic, complemented
5C13×#1661C214yesmaximal, complemented
6C13×#1660C214yesmaximal, complemented
7C13×#1530C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C2×C13×#137—22no—
11C13×#563C2212yes—
12C13×#562C2212yes—
13C13×#554—21no—
14C13×#553—21no—
15C13×#553—21no—
16C13×#547—22no—
17C13×#547—21no—
18C13×#544—21no—
19C13×#540—21no—
20C13×#539—22no—
21C13×#539—21no—
22C13×#537—21no—
23C13×#532C2211yescharacteristic
24C2×C13×C4⋊Q8C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C13×#501—22no—
28C13×#501C2214yes—
29C13×#501C2212yes—
30C13×#497C2214yes—
31C13×#494—21no—
32C13×#492—21no—
33C13×#489C2212yes—
34C13×#483—21no—
35C13×#480—21no—
36C13×#477—21no—
37C13×#476—21no—
38C13×#432C2211yescharacteristic
39C2×C13×#107—21no—
40C2×C13×#106—21no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yes—
44C13×#330C2214yes—
45C13×#329C2212yes—
46C13×#329C2214yes—
47C2×C13×#41—22no—
48C2×C13×#41D412yes—
49C22×Q8×C13—21no—
50C13×#137—48no—
51C2×C13×Q16—24no—
52C2×C13×SD16—24no—
53C2×C13×M16—21no—
54C22×C8×C13—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8D411yescharacteristic
61C13×C4⋊Q8C2312yes—
62C13×#127D411yescharacteristic
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—21no—
66C13×#125—22no—
67C13×#125—21no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#125D412yes—
71C13×#125C2312yes—
72C13×#125C2311yescharacteristic
73C13×#124C2311yescharacteristic
74C13×#124C2312yes—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—21no—
80C13×#123—22no—
81C13×#123—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8D411yescharacteristic
89C13×#121—22no—
90C13×#121—22no—
91C13×#121—21no—
92C13×#121—21no—
93C13×#121—22no—
94C13×#121—22no—
95C13×#121—21no—
96C13×#121—21no—
97C13×#121D411yescharacteristic
98C4×Q8×C13D411yescharacteristic
99C4×D4×C13—22no—
100C4×D4×C13—22no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13—21no—
106C4×D4×C13D411yescharacteristic
107C13×#117—21no—
108C13×#117—21no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4D411yescharacteristic
116C2×C13×C4⋊C4D411yescharacteristic
117C2×C42×C13C2311yescharacteristic
118C13×#107—24no—
119C13×#107—22no—
120C13×#106—24no—
121C13×#106—22no—
122C13×C4⋊C8—21no—
123C13×#103—22no—
124C13×#102—22no—
125C13×C22⋊C8—21no—
126C13×#97—21no—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C13×#97C2312yes—
130C4×C8×C13—21no—
131#19017C1311yesmaximal, characteristic, direct product factor, Sylow
132C13×#41—44no—
133C13×#41—84no—
134C2×Q8×C13—22no—
135C2×Q8×C13—22no—
136C2×Q8×C13—44no—
137C2×Q8×C13—41no—
138C2×Q8×C13C2×D411yescharacteristic
139C2×Q8×C13C2×D412yes—
140C2×D4×C13—22no—
141C2×D4×C13—21no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—21no—
146C2×D4×C13C2×D411yescharacteristic
147C2×D4×C13C2×D412yes—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—41no—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C13×Q16—48no—
160C13×SD16—48no—
161C13×M16—24no—
162C2×C8×C13—24no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4C2×D412yes—
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C4⋊C4C2×D412yes—
189C13×C4⋊C4C2×D411yescharacteristic
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C42×C13—22no—
203C42×C13—21no—
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2411yescharacteristic
208#3559C2×C1311yescharacteristic
209#3238C2×C1311yescharacteristic, complemented
210C2×#501C2×C1311yescharacteristic, complemented
211#3152C2×C1311yescharacteristic, complemented
212#1661C2×C1314yescomplemented
213#1660C2×C1314yescomplemented
214#1530C2×C1311yescharacteristic, complemented
215#1528C2×C1311yescharacteristic, complemented
216#1524C2×C1311yescharacteristic, complemented
217C23×C13—22no—
218C23×C13—21no—
219C23×C13#12011yescharacteristic
220Q8×C13—42no—
221Q8×C13—41no—
222Q8×C13—44no—
223Q8×C13—82no—
224Q8×C13—82no—
225D4×C13—42no—
226D4×C13—41no—
227D4×C13—44no—
228D4×C13—42no—
229D4×C13—42no—
230D4×C13—81no—
231D4×C13—82no—
232D4×C13—82no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—82no—
246C2×C4×C13—81no—
247C2×C4×C13—82no—
248C2×C4×C13—82no—
249C2×C4×C13—82no—
250C2×C4×C13—82no—
251C2×C4×C13#12011yescharacteristic
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C8×C13—24no—
258C8×C13—24no—
259C8×C13—42no—
260C2×#137—22no—
261#563C22×C1312yes—
262#562C22×C1312yes—
263#554—21no—
264#553—21no—
265#553—21no—
266#547—22no—
267#547—21no—
268#544—21no—
269#540—21no—
270#539—22no—
271#539—21no—
272#537—21no—
273#532C22×C1311yescharacteristic
274C2×C4⋊Q8C22×C1311yescharacteristic
275#529C22×C1311yescharacteristic
276C2×#125C22×C1311yescharacteristic
277#501—22no—
278#501C22×C1314yes—
279#501C22×C1312yes—
280#497C22×C1314yes—
281#494—21no—
282#492—21no—
283#489C22×C1312yes—
284#483—21no—
285#480—21no—
286#477—21no—
287#476—21no—
288#432C22×C1311yescharacteristic
289C2×#107—21no—
290C2×#106—21no—
291C4×M16C22×C1311yescharacteristic
292C2×#97C22×C1311yescharacteristic
293#330C22×C1312yes—
294#330C22×C1314yes—
295#329C22×C1314yes—
296#329C22×C1312yes—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—42no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—41no—
305C22×C13#45312yes—
306C22×C13C2×#12011yescharacteristic
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—42no—
313C4×C13—42no—
314C4×C13—41no—
315C4×C13—41no—
316C4×C13—42no—
317C4×C13—41no—
318C4×C13—82no—
319C4×C13#45612yes—
320C2×#41—22no—
321C2×#41D4×C1312yes—
322C22×Q8—21no—
323#137—48no—
324C2×Q16—24no—
325C2×SD16—24no—
326C2×M16—21no—
327C22×C8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—22no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8D4×C1311yescharacteristic
334C4⋊Q8C23×C1312yes—
335#127D4×C1311yescharacteristic
336#126—22no—
337#126—22no—
338#126—21no—
339#125—22no—
340#125—21no—
341#125—21no—
342#125—21no—
343#125D4×C1312yes—
344#125C23×C1312yes—
345#125C23×C1311yescharacteristic
346#124C23×C1311yescharacteristic
347#124C23×C1312yes—
348#123—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352#123—21no—
353#123—22no—
354#123—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8D4×C1311yescharacteristic
362#121—22no—
363#121—22no—
364#121—21no—
365#121—21no—
366#121—22no—
367#121—22no—
368#121—21no—
369#121—21no—
370#121D4×C1311yescharacteristic
371C4×Q8D4×C1311yescharacteristic
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C1311yescharacteristic
380#117—21no—
381#117—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C1311yescharacteristic
389C2×C4⋊C4D4×C1311yescharacteristic
390C2×C42C23×C1311yescharacteristic
391#107—24no—
392#107—22no—
393#106—24no—
394#106—22no—
395C4⋊C8—21no—
396#103—22no—
397#102—22no—
398C22⋊C8—21no—
399#97—21no—
400#97C23×C1312yes—
401#97C23×C1312yes—
402#97C23×C1312yes—
403C4×C8—21no—
404C2×C13—22no—
405C2×C13—82no—
406C2×C13—81no—
407C2×C13C2×#45311yescharacteristic
408C2×C13C2×#45611yescharacteristic
409C2×C13#302211yescharacteristic
410#41—44no—
411#41—84no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—44no—
415C2×Q8—41no—
416C2×Q8C2×D4×C1311yescharacteristic
417C2×Q8C2×D4×C1312yes—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×D4×C1311yescharacteristic
425C2×D4C2×D4×C1312yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437Q16—48no—
438SD16—48no—
439M16—24no—
440C2×C8—24no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C1312yes—
465C4⋊C4C2×D4×C1311yescharacteristic
466C4⋊C4C2×D4×C1312yes—
467C4⋊C4C2×D4×C1311yescharacteristic
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C42—22no—
481C42—21no—
482C42C2×D4×C1311yescharacteristic
483C42C2×D4×C1311yescharacteristic
484C42C2×D4×C1311yescharacteristic
485C42C24×C1311yescharacteristic
486C13#1901711yescharacteristic, direct product factor, Sylow
487C23—22no—
488C23—21no—
489C23C13×#12011yescharacteristic
490Q8—42no—
491Q8—41no—
492Q8—44no—
493Q8—82no—
494Q8—82no—
495D4—42no—
496D4—41no—
497D4—44no—
498D4—42no—
499D4—42no—
500D4—81no—
501D4—82no—
502D4—82no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4C13×#12011yescharacteristic
522C2×C4C13×#12011yescharacteristic
523C2×C4C13×#12011yescharacteristic
524C2×C4C22×D4×C1311yescharacteristic
525C2×C4C22×D4×C1311yescharacteristic
526C2×C4C22×D4×C1311yescharacteristic
527C8—24no—
528C8—24no—
529C8—42no—
530C22—21no—
531C22—21no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22C13×#45312yes—
539C22C2×C13×#12011yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—42no—
546C4—42no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—82no—
552C4C13×#45612yes—
553C2—22no—
554C2—82no—
555C2—81no—
556C2C2×C13×#45311yescharacteristic
557C2C2×C13×#45611yescharacteristic
558C2C13×#302211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3559C2
LCSG ▷ C42 ▷ 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×#3238C2semidirect
3. C2×C13×#501C2semidirect
4. C13×#3152C2semidirect
5. C13×#1661C2semidirect
6. C13×#1660C2semidirect
7. C13×#1530C2semidirect
8. C13×#1528C2semidirect
9. C13×#1524C2semidirect
131. #19017C13direct (N × H)
209. #3238C2×C13semidirect
210. C2×#501C2×C13semidirect
211. #3152C2×C13semidirect
212. #1661C2×C13semidirect
213. #1660C2×C13semidirect
214. #1530C2×C13semidirect
215. #1528C2×C13semidirect
216. #1524C2×C13semidirect
486. C13#19017direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32382
C2×C13×#5012
C13×#31522
C13×#16612
C13×#16602
C13×#15302
C13×#15282
C13×#15242
#1901713