Finite Group Databasebeta

← C13×#18305 #15704644

Subgroups — C13×#18305 #15704644

Order 3328.

934 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×#3455C211yesmaximal, characteristic
2C13×#3209C211yesmaximal, characteristic, complemented
3C13×#3206C211yesmaximal, characteristic, complemented
4C13×#2628C211yesmaximal, characteristic, complemented
5C13×#1606C214yesmaximal, complemented
6C13×#1603C214yesmaximal, complemented
7C13×#1518C211yesmaximal, characteristic, complemented
8C13×#1517C211yesmaximal, characteristic, complemented
9C13×#1458C211yesmaximal, characteristic, complemented
10C13×#542—21no—
11C13×#542—21no—
12C13×#541—21no—
13C13×#540—21no—
14C13×#539—21no—
15C13×#539C2212yes—
16C13×#538—21no—
17C13×#538C2212yes—
18C13×#533C2211yescharacteristic
19C13×#532C2211yescharacteristic
20C2×C13×C4⋊Q8C2211yescharacteristic
21C13×#529—22no—
22C13×#529—22no—
23C13×#525—21no—
24C4×C13×#41—21no—
25C2×C13×#117C2211yescharacteristic
26C13×#494—21no—
27C13×#492—21no—
28C13×#487—21no—
29C13×#487—21no—
30C13×#462—22no—
31C13×#461—22no—
32C13×#451C2214yes—
33C13×#448C2214yes—
34C13×#431C2211yescharacteristic
35C13×#431C2211yescharacteristic
36C13×#400—21no—
37C13×#399—21no—
38C13×#395C2212yes—
39C13×#393C2212yes—
40C13×#389—21no—
41C13×#382C2211yescharacteristic
42C13×#380—21no—
43C13×#328C2214yes—
44C13×#327C2214yes—
45C13×#324C2212yes—
46C13×#323C2212yes—
47C2×C13×#41—21no—
48C22×Q8×C13C2312yes—
49C23×C4×C13D411yescharacteristic
50C2×C13×Q16—24no—
51C2×C13×SD16—24no—
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8D411yescharacteristic
57C13×C4⋊Q8D411yescharacteristic
58C13×C4⋊Q8D411yescharacteristic
59C13×#127D411yescharacteristic
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#125—22no—
65C13×#125—22no—
66C13×#125—21no—
67C13×#124—22no—
68C13×#124—22no—
69C13×#124—21no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—22no—
73C13×#123—22no—
74C13×#123—22no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8C2312yes—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—21no—
86C13×#121C2312yes—
87C13×#120—22no—
88C4×Q8×C13—21no—
89C4×Q8×C13—21no—
90C4×Q8×C13—21no—
91C4×Q8×C13D412yes—
92C4×D4×C13—21no—
93C4×D4×C13—21no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—21no—
99C4×D4×C13D412yes—
100C13×#117—22no—
101C13×#117—21no—
102C13×#117—21no—
103C13×#117—21no—
104C13×#117—21no—
105C13×#117—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4D411yescharacteristic
114C2×C13×C22⋊C4C2311yescharacteristic
115C2×C42×C13—22no—
116C2×C42×C13D411yescharacteristic
117C2×C42×C13C2311yescharacteristic
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—24no—
121C13×#103—24no—
122C13×C22⋊C8C2312yes—
123C13×C22⋊C8C2312yes—
124C4×C8×C13—21no—
125C4×C8×C13—21no—
126C13×#95—22no—
127C13×#95—21no—
128C13×#95—22no—
129C13×#95C2312yes—
130#18305C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13C2×D411yescharacteristic
132C13×#41—42no—
133C13×#41—42no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—22no—
137C2×Q8×C13—22no—
138C2×Q8×C13—82no—
139C2×Q8×C13C2×D412yes—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13C2×D412yes—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2411yescharacteristic
161C13×Q16—84no—
162C13×SD16—84no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—82no—
185C13×C4⋊C4C2×D412yes—
186C13×C4⋊C4C2×D412yes—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—82no—
201C42×C13—22no—
202C42×C13—22no—
203C42×C13—21no—
204C42×C13—22no—
205C42×C13—21no—
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210#3455C2×C1311yescharacteristic
211#3209C2×C1311yescharacteristic, complemented
212#3206C2×C1311yescharacteristic, complemented
213#2628C2×C1311yescharacteristic, complemented
214#1606C2×C1314yescomplemented
215#1603C2×C1314yescomplemented
216#1518C2×C1311yescharacteristic, complemented
217#1517C2×C1311yescharacteristic, complemented
218#1458C2×C1311yescharacteristic, complemented
219C23×C13—21no—
220C23×C13—22no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226Q8×C13—42no—
227Q8×C13—44no—
228Q8×C13—44no—
229Q8×C13—42no—
230Q8×C13—81no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—42no—
234D4×C13—42no—
235D4×C13—81no—
236D4×C13—82no—
237D4×C13—82no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—44no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—82no—
260C2×C4×C13—82no—
261C2×C4×C13#12011yescharacteristic
262C2×C4×C13#12011yescharacteristic
263C2×C4×C13#12011yescharacteristic
264C2×C4×C13#12011yescharacteristic
265C2×C4×C13#13512yes—
266C2×C4×C13#13712yes—
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C8×C13—42no—
270C8×C13—42no—
271#542—21no—
272#542—21no—
273#541—21no—
274#540—21no—
275#539—21no—
276#539C22×C1312yes—
277#538—21no—
278#538C22×C1312yes—
279#533C22×C1311yescharacteristic
280#532C22×C1311yescharacteristic
281C2×C4⋊Q8C22×C1311yescharacteristic
282#529—22no—
283#529—22no—
284#525—21no—
285C4×#41—21no—
286C2×#117C22×C1311yescharacteristic
287#494—21no—
288#492—21no—
289#487—21no—
290#487—21no—
291#462—22no—
292#461—22no—
293#451C22×C1314yes—
294#448C22×C1314yes—
295#431C22×C1311yescharacteristic
296#431C22×C1311yescharacteristic
297#400—21no—
298#399—21no—
299#395C22×C1312yes—
300#393C22×C1312yes—
301#389—21no—
302#382C22×C1311yescharacteristic
303#380—21no—
304#328C22×C1314yes—
305#327C22×C1314yes—
306#324C22×C1312yes—
307#323C22×C1312yes—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—42no—
311C22×C13—41no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—41no—
315C22×C13—42no—
316C22×C13—41no—
317C22×C13—81no—
318C22×C13C2×#12011yescharacteristic
319C22×C13C2×#13511yescharacteristic
320C22×C13C2×#13711yescharacteristic
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13—41no—
326C4×C13—42no—
327C4×C13—41no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—42no—
331C4×C13—82no—
332C4×C13—82no—
333C4×C13#45212yes—
334C4×C13#45212yes—
335C2×#41—21no—
336C22×Q8C23×C1312yes—
337C23×C4D4×C1311yescharacteristic
338C2×Q16—24no—
339C2×SD16—24no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8D4×C1311yescharacteristic
345C4⋊Q8D4×C1311yescharacteristic
346C4⋊Q8D4×C1311yescharacteristic
347#127D4×C1311yescharacteristic
348#126—22no—
349#126—22no—
350#126—22no—
351#126—22no—
352#125—22no—
353#125—22no—
354#125—21no—
355#124—22no—
356#124—22no—
357#124—21no—
358#123—22no—
359#123—22no—
360#123—22no—
361#123—22no—
362#123—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—21no—
368C22⋊Q8C23×C1312yes—
369#121—21no—
370#121—21no—
371#121—22no—
372#121—22no—
373#121—21no—
374#121C23×C1312yes—
375#120—22no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8D4×C1312yes—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4D4×C1312yes—
388#117—22no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4D4×C1311yescharacteristic
399C2×C4⋊C4C23×C1311yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4D4×C1311yescharacteristic
402C2×C22⋊C4C23×C1311yescharacteristic
403C2×C42—22no—
404C2×C42D4×C1311yescharacteristic
405C2×C42C23×C1311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—21no—
408#103—24no—
409#103—24no—
410C22⋊C8C23×C1312yes—
411C22⋊C8C23×C1312yes—
412C4×C8—21no—
413C4×C8—21no—
414#95—22no—
415#95—21no—
416#95—22no—
417#95C23×C1312yes—
418C2×C13—21no—
419C2×C13—21no—
420C2×C13—82no—
421C2×C13—81no—
422C2×C13C2×#45211yescharacteristic
423C2×C13#302211yescharacteristic
424C2×C13#302711yescharacteristic
425C24C2×D4×C1311yescharacteristic
426#41—42no—
427#41—42no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—82no—
433C2×Q8C2×D4×C1312yes—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C2×D4×C1312yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4C2×D4×C1311yescharacteristic
450C22×C4C2×D4×C1311yescharacteristic
451C22×C4C2×D4×C1311yescharacteristic
452C22×C4C2×D4×C1311yescharacteristic
453C22×C4C2×D4×C1311yescharacteristic
454C22×C4C24×C1311yescharacteristic
455Q16—84no—
456SD16—84no—
457C2×C8—22no—
458C2×C8—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—42no—
478C4⋊C4—82no—
479C4⋊C4C2×D4×C1312yes—
480C4⋊C4C2×D4×C1312yes—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—82no—
495C42—22no—
496C42—22no—
497C42—21no—
498C42—22no—
499C42—21no—
500C42C2×D4×C1311yescharacteristic
501C42C2×D4×C1311yescharacteristic
502C42C2×D4×C1311yescharacteristic
503C42C2×D4×C1311yescharacteristic
504C13#1830511yescharacteristic, direct product factor, Sylow
505C23—21no—
506C23—22no—
507C23—21no—
508C23—21no—
509C23—41no—
510C23—41no—
511C23C22×D4×C1311yescharacteristic
512Q8—42no—
513Q8—44no—
514Q8—44no—
515Q8—42no—
516Q8—81no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522D4—82no—
523D4—82no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C13×#12011yescharacteristic
548C2×C4C13×#12011yescharacteristic
549C2×C4C13×#12011yescharacteristic
550C2×C4C13×#12011yescharacteristic
551C2×C4C13×#13512yes—
552C2×C4C13×#13712yes—
553C2×C4C22×D4×C1311yescharacteristic
554C2×C4C22×D4×C1311yescharacteristic
555C8—42no—
556C8—42no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—42no—
566C22—81no—
567C22C2×C13×#12011yescharacteristic
568C22C2×C13×#13511yescharacteristic
569C22C2×C13×#13711yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—82no—
581C4—82no—
582C4C13×#45212yes—
583C4C13×#45212yes—
584C2—21no—
585C2—21no—
586C2—81no—
587C2—82no—
588C2C2×C13×#45211yescharacteristic
589C2C13×#302211yescharacteristic
590C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3455C2
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×#3209C2semidirect
3. C13×#3206C2semidirect
4. C13×#2628C2semidirect
5. C13×#1606C2semidirect
6. C13×#1603C2semidirect
7. C13×#1518C2semidirect
8. C13×#1517C2semidirect
9. C13×#1458C2semidirect
130. #18305C13direct (N × H)
211. #3209C2×C13semidirect
212. #3206C2×C13semidirect
213. #2628C2×C13semidirect
214. #1606C2×C13semidirect
215. #1603C2×C13semidirect
216. #1518C2×C13semidirect
217. #1517C2×C13semidirect
218. #1458C2×C13semidirect
504. C13#18305direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34552
C13×#32092
C13×#32062
C13×#26282
C13×#16062
C13×#16032
C13×#15182
C13×#15172
C13×#14582
#1830513