Finite Group Databasebeta

← C13×#18313 #15704652

Subgroups — C13×#18313 #15704652

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3455C211yesmaximal, characteristic
2C13×#3230C211yesmaximal, characteristic, complemented
3C13×#3227C211yesmaximal, characteristic, complemented
4C13×#2628C211yesmaximal, characteristic, complemented
5C13×#1618C214yesmaximal, complemented
6C13×#1615C214yesmaximal, 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×#500—21no—
27C13×#498—21no—
28C13×#487—21no—
29C13×#486—21no—
30C13×#484C2214yes—
31C13×#481C2214yes—
32C13×#477—22no—
33C13×#476—22no—
34C13×#431C2211yescharacteristic
35C13×#431C2211yescharacteristic
36C13×#400C2212yes—
37C13×#399C2212yes—
38C13×#395—21no—
39C13×#393—21no—
40C13×#389—21no—
41C13×#382C2211yescharacteristic
42C13×#380—21no—
43C13×#328C2214yes—
44C13×#327C2214yes—
45C13×#324C2212yes—
46C13×#323C2212yes—
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C23×C4×C13D411yescharacteristic
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8—21no—
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8D411yescharacteristic
55C13×C4⋊Q8D411yescharacteristic
56C13×C4⋊Q8D411yescharacteristic
57C13×#127D411yescharacteristic
58C13×#126—22no—
59C13×#126—22no—
60C13×#126—22no—
61C13×#126—22no—
62C13×#125—22no—
63C13×#125—22no—
64C13×#125—21no—
65C13×#124—22no—
66C13×#124—22no—
67C13×#124—21no—
68C13×#123—22no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—22no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—21no—
78C13×C22⋊Q8C2312yes—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121—21no—
84C13×#121C2312yes—
85C13×#120—22no—
86C4×Q8×C13—21no—
87C4×Q8×C13—21no—
88C4×Q8×C13—21no—
89C4×Q8×C13D412yes—
90C4×D4×C13—21no—
91C4×D4×C13—21no—
92C4×D4×C13—22no—
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—21no—
97C4×D4×C13D412yes—
98C13×#117—22no—
99C13×#117—21no—
100C13×#117—21no—
101C13×#117—21no—
102C13×#117—21no—
103C13×#117—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4C2312yes—
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C13×C22⋊C4C2311yescharacteristic
113C2×C42×C13—22no—
114C2×C42×C13D411yescharacteristic
115C2×C42×C13C2311yescharacteristic
116C13×#107—24no—
117C13×#106—24no—
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—24no—
121C13×#102—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#18313C1311yesmaximal, 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—41no—
137C2×Q8×C13—41no—
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
161C2×C8×C13—22no—
162C2×C8×C13—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—42no—
182C13×C4⋊C4—82no—
183C13×C4⋊C4C2×D412yes—
184C13×C4⋊C4C2×D412yes—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—82no—
199C42×C13—22no—
200C42×C13—22no—
201C42×C13—21no—
202C42×C13—22no—
203C42×C13—21no—
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208#3455C2×C1311yescharacteristic
209#3230C2×C1311yescharacteristic, complemented
210#3227C2×C1311yescharacteristic, complemented
211#2628C2×C1311yescharacteristic, complemented
212#1618C2×C1314yescomplemented
213#1615C2×C1314yescomplemented
214#1518C2×C1311yescharacteristic, complemented
215#1517C2×C1311yescharacteristic, complemented
216#1458C2×C1311yescharacteristic, complemented
217C23×C13—21no—
218C23×C13—22no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13C22×D411yescharacteristic
224Q8×C13—42no—
225Q8×C13—42no—
226Q8×C13—81no—
227Q8×C13—82no—
228Q8×C13—82no—
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—81no—
234D4×C13—82no—
235D4×C13—82no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—44no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—82no—
258C2×C4×C13—82no—
259C2×C4×C13#12011yescharacteristic
260C2×C4×C13#12011yescharacteristic
261C2×C4×C13#12011yescharacteristic
262C2×C4×C13#12011yescharacteristic
263C2×C4×C13#13512yes—
264C2×C4×C13#13712yes—
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C8×C13—42no—
268C8×C13—42no—
269#542—21no—
270#542—21no—
271#541—21no—
272#540—21no—
273#539—21no—
274#539C22×C1312yes—
275#538—21no—
276#538C22×C1312yes—
277#533C22×C1311yescharacteristic
278#532C22×C1311yescharacteristic
279C2×C4⋊Q8C22×C1311yescharacteristic
280#529—22no—
281#529—22no—
282#525—21no—
283C4×#41—21no—
284C2×#117C22×C1311yescharacteristic
285#500—21no—
286#498—21no—
287#487—21no—
288#486—21no—
289#484C22×C1314yes—
290#481C22×C1314yes—
291#477—22no—
292#476—22no—
293#431C22×C1311yescharacteristic
294#431C22×C1311yescharacteristic
295#400C22×C1312yes—
296#399C22×C1312yes—
297#395—21no—
298#393—21no—
299#389—21no—
300#382C22×C1311yescharacteristic
301#380—21no—
302#328C22×C1314yes—
303#327C22×C1314yes—
304#324C22×C1312yes—
305#323C22×C1312yes—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—42no—
309C22×C13—41no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—41no—
313C22×C13—42no—
314C22×C13—41no—
315C22×C13—81no—
316C22×C13C2×#12011yescharacteristic
317C22×C13C2×#13511yescharacteristic
318C22×C13C2×#13711yescharacteristic
319C4×C13—21no—
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—41no—
324C4×C13—42no—
325C4×C13—41no—
326C4×C13—42no—
327C4×C13—41no—
328C4×C13—42no—
329C4×C13—82no—
330C4×C13—82no—
331C4×C13#45212yes—
332C4×C13#45212yes—
333C2×#41—21no—
334C22×Q8—21no—
335C23×C4D4×C1311yescharacteristic
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8D4×C1311yescharacteristic
341C4⋊Q8D4×C1311yescharacteristic
342C4⋊Q8D4×C1311yescharacteristic
343#127D4×C1311yescharacteristic
344#126—22no—
345#126—22no—
346#126—22no—
347#126—22no—
348#125—22no—
349#125—22no—
350#125—21no—
351#124—22no—
352#124—22no—
353#124—21no—
354#123—22no—
355#123—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8C23×C1312yes—
365#121—21no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121C23×C1312yes—
371#120—22no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C1312yes—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4D4×C1312yes—
384#117—22no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4D4×C1311yescharacteristic
394C2×C4⋊C4C23×C1312yes—
395C2×C4⋊C4C23×C1311yescharacteristic
396C2×C22⋊C4—22no—
397C2×C22⋊C4D4×C1311yescharacteristic
398C2×C22⋊C4C23×C1311yescharacteristic
399C2×C42—22no—
400C2×C42D4×C1311yescharacteristic
401C2×C42C23×C1311yescharacteristic
402#107—24no—
403#106—24no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406#103—24no—
407#102—24no—
408C22⋊C8C23×C1312yes—
409C22⋊C8C23×C1312yes—
410C4×C8—21no—
411C4×C8—21no—
412#95—22no—
413#95—21no—
414#95—22no—
415#95C23×C1312yes—
416C2×C13—21no—
417C2×C13—21no—
418C2×C13—82no—
419C2×C13—81no—
420C2×C13C2×#45211yescharacteristic
421C2×C13#302111yescharacteristic
422C2×C13#302811yescharacteristic
423C24C2×D4×C1311yescharacteristic
424#41—42no—
425#41—42no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—82no—
431C2×Q8C2×D4×C1312yes—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×D4×C1312yes—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4C2×D4×C1311yescharacteristic
448C22×C4C2×D4×C1311yescharacteristic
449C22×C4C2×D4×C1311yescharacteristic
450C22×C4C2×D4×C1311yescharacteristic
451C22×C4C2×D4×C1311yescharacteristic
452C22×C4C24×C1311yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—42no—
474C4⋊C4—82no—
475C4⋊C4C2×D4×C1312yes—
476C4⋊C4C2×D4×C1312yes—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—22no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—82no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42—22no—
495C42—21no—
496C42C2×D4×C1311yescharacteristic
497C42C2×D4×C1311yescharacteristic
498C42C2×D4×C1311yescharacteristic
499C42C2×D4×C1311yescharacteristic
500C13#1831311yescharacteristic, direct product factor, Sylow
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—41no—
506C23—41no—
507C23C22×D4×C1311yescharacteristic
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C13×#12011yescharacteristic
544C2×C4C13×#12011yescharacteristic
545C2×C4C13×#12011yescharacteristic
546C2×C4C13×#12011yescharacteristic
547C2×C4C13×#13512yes—
548C2×C4C13×#13712yes—
549C2×C4C22×D4×C1311yescharacteristic
550C2×C4C22×D4×C1311yescharacteristic
551C8—42no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—81no—
563C22C2×C13×#12011yescharacteristic
564C22C2×C13×#13511yescharacteristic
565C22C2×C13×#13711yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—82no—
577C4—82no—
578C4C13×#45212yes—
579C4C13×#45212yes—
580C2—21no—
581C2—21no—
582C2—81no—
583C2—82no—
584C2C2×C13×#45211yescharacteristic
585C2C13×#302111yescharacteristic
586C2C13×#302811yescharacteristic
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×#3230C2semidirect
3. C13×#3227C2semidirect
4. C13×#2628C2semidirect
5. C13×#1618C2semidirect
6. C13×#1615C2semidirect
7. C13×#1518C2semidirect
8. C13×#1517C2semidirect
9. C13×#1458C2semidirect
130. #18313C13direct (N × H)
209. #3230C2×C13semidirect
210. #3227C2×C13semidirect
211. #2628C2×C13semidirect
212. #1618C2×C13semidirect
213. #1615C2×C13semidirect
214. #1518C2×C13semidirect
215. #1517C2×C13semidirect
216. #1458C2×C13semidirect
500. C13#18313direct (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×#32302
C13×#32272
C13×#26282
C13×#16182
C13×#16152
C13×#15182
C13×#15172
C13×#14582
#1831313