Finite Group Databasebeta

← C13×#8538 #15694877

Subgroups — C13×#8538 #15694877

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3505C211yesmaximal, characteristic
2C13×#1901C211yesmaximal, characteristic, complemented
3C13×#1900C211yesmaximal, characteristic, complemented
4C13×#1870C211yesmaximal, characteristic, complemented
5C13×#1472C211yesmaximal, characteristic, complemented
6C13×#1471C211yesmaximal, characteristic, complemented
7C13×#1465C211yesmaximal, characteristic, complemented
8C22×C13×M16C2211yescharacteristic
9C13×#553—22no—
10C13×#553—21no—
11C13×#552—21no—
12C13×#551—22no—
13C13×#548—21no—
14C13×#546—21no—
15C13×#539—21no—
16C13×#538—21no—
17C13×#534C412yes—
18C13×#529—21no—
19C13×#525—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C13×#518C412yes—
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#101—21no—
25C2×C13×#100—21no—
26C13×#407C2211yescharacteristic
27C13×#407C2211yescharacteristic
28C2×C13×C22⋊C8—21no—
29C2×C13×C22⋊C8C2211yescharacteristic
30C13×#343—21no—
31C13×#343—21no—
32C13×#336—21no—
33C13×#324—22no—
34C13×#324—21no—
35C13×#323—22no—
36C13×#323—21no—
37C2×C13×#41—21no—
38C22×Q8×C13D411yescharacteristic
39C22×D4×C13C2×C411yescharacteristic
40C22×D4×C13C2×C412yes—
41C22×D4×C13D411yescharacteristic
42C23×C4×C13D411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C2×C13×M16—21no—
45C2×C13×M16—21no—
46C2×C13×M16—21no—
47C2×C13×M16—21no—
48C2×C13×M16—42no—
49C22×C8×C13—21no—
50C22×C8×C13—21no—
51C13×#126—22no—
52C13×#126—22no—
53C13×#126—22no—
54C13×#125—21no—
55C13×#125—22no—
56C13×#124—21no—
57C13×#124—22no—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—21no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—21no—
68C13×C22⋊Q8—21no—
69C13×#121—21no—
70C13×#121—22no—
71C13×#121—22no—
72C13×#121—22no—
73C13×#121—21no—
74C13×#121—21no—
75C13×#121—21no—
76C13×#121—21no—
77C13×#120—22no—
78C13×#120—22no—
79C4×Q8×C13—21no—
80C4×D4×C13—22no—
81C4×D4×C13—21no—
82C4×D4×C13—22no—
83C4×D4×C13—22no—
84C4×D4×C13—22no—
85C4×D4×C13—22no—
86C4×D4×C13—21no—
87C4×D4×C13—21no—
88C4×D4×C13—21no—
89C4×D4×C13—21no—
90C13×#117—21no—
91C13×#117—22no—
92C13×#117—22no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4D412yes—
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4C2×C411yescharacteristic
99C2×C13×C22⋊C4C2×C412yes—
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C13×C22⋊C4D412yes—
102C2×C42×C13D411yescharacteristic
103C13×#101—42no—
104C13×#100—42no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8—21no—
109C13×C22⋊C8—21no—
110C13×C22⋊C8—21no—
111C13×C22⋊C8—42no—
112#8538C1311yesmaximal, characteristic, direct product factor, Sylow
113C24×C13C22⋊C411yescharacteristic
114C24×C13C22⋊C412yes—
115C24×C13C22×C411yescharacteristic
116C13×#41—81no—
117C13×#41—81no—
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13—41no—
121C2×Q8×C13—41no—
122C2×D4×C13—21no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—21no—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—42no—
135C2×D4×C13—42no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13C22⋊C411yescharacteristic
145C22×C4×C13C22⋊C411yescharacteristic
146C22×C4×C13C22⋊C412yes—
147C22×C4×C13C22⋊C411yescharacteristic
148C22×C4×C13C22⋊C412yes—
149C22×C4×C13C22⋊C412yes—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C13×M16—22no—
157C13×M16—22no—
158C13×M16—41no—
159C13×M16—41no—
160C13×M16—41no—
161C13×M16—41no—
162C13×M16—41no—
163C13×M16—41no—
164C2×C8×C13—22no—
165C2×C8×C13—41no—
166C2×C8×C13—41no—
167C2×C8×C13—41no—
168C2×C8×C13—41no—
169C2×C8×C13—41no—
170C2×C8×C13—41no—
171C2×C8×C13—41no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—21no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—22no—
198C42×C13—22no—
199C42×C13—22no—
200C42×C13—21no—
201C42×C13—21no—
202#3505C2×C1311yescharacteristic
203#1901C2×C1311yescharacteristic, complemented
204#1900C2×C1311yescharacteristic, complemented
205#1870C2×C1311yescharacteristic, complemented
206#1472C2×C1311yescharacteristic, complemented
207#1471C2×C1311yescharacteristic, complemented
208#1465C2×C1311yescharacteristic, complemented
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—22no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13C2×C22⋊C411yescharacteristic
223C23×C13C2×C22⋊C411yescharacteristic
224C23×C13C2×C22⋊C411yescharacteristic
225Q8×C13—41no—
226Q8×C13—41no—
227Q8×C13—81no—
228D4×C13—42no—
229D4×C13—42no—
230D4×C13—44no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—41no—
234D4×C13—41no—
235D4×C13—81no—
236D4×C13—82no—
237D4×C13—82no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—81no—
263C2×C4×C13—82no—
264C2×C4×C13—82no—
265C2×C4×C13#12011yescharacteristic
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13#12011yescharacteristic
269C8×C13—42no—
270C8×C13—81no—
271C8×C13—81no—
272C8×C13—81no—
273C22×M16C22×C1311yescharacteristic
274#553—22no—
275#553—21no—
276#552—21no—
277#551—22no—
278#548—21no—
279#546—21no—
280#539—21no—
281#538—21no—
282#534C4×C1312yes—
283#529—21no—
284#525—21no—
285C2×C22⋊Q8C22×C1311yescharacteristic
286C2×#121C22×C1311yescharacteristic
287#518C4×C1312yes—
288C2×C4×D4C22×C1311yescharacteristic
289C2×#101—21no—
290C2×#100—21no—
291#407C22×C1311yescharacteristic
292#407C22×C1311yescharacteristic
293C2×C22⋊C8—21no—
294C2×C22⋊C8C22×C1311yescharacteristic
295#343—21no—
296#343—21no—
297#336—21no—
298#324—21no—
299#324—22no—
300#323—21no—
301#323—22no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—42no—
311C22×C13—41no—
312C22×C13—42no—
313C22×C13—41no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—41no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—162no—
321C22×C13#37911yescharacteristic
322C22×C13#41311yescharacteristic
323C22×C13#41311yescharacteristic
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—21no—
327C4×C13—41no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—42no—
331C4×C13—41no—
332C4×C13—42no—
333C4×C13B(4,𝔽2)11yescharacteristic
334C4×C13#45811yescharacteristic
335C2×#41—21no—
336C22×Q8D4×C1311yescharacteristic
337C22×D4C2×C4×C1311yescharacteristic
338C22×D4C2×C4×C1312yes—
339C22×D4D4×C1311yescharacteristic
340C23×C4D4×C1311yescharacteristic
341C23×C4C23×C1311yescharacteristic
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—42no—
347C22×C8—21no—
348C22×C8—21no—
349#126—22no—
350#126—22no—
351#126—22no—
352#125—21no—
353#125—22no—
354#124—21no—
355#124—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359#123—22no—
360#123—22no—
361C22⋊Q8—21no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367#121—21no—
368#121—22no—
369#121—22no—
370#121—22no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—21no—
375#120—22no—
376#120—22no—
377C4×Q8—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388#117—21no—
389#117—22no—
390#117—22no—
391C2×C4⋊C4D4×C1311yescharacteristic
392C2×C4⋊C4D4×C1311yescharacteristic
393C2×C4⋊C4D4×C1312yes—
394C2×C4⋊C4D4×C1311yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4C2×C4×C1311yescharacteristic
397C2×C22⋊C4C2×C4×C1312yes—
398C2×C22⋊C4D4×C1311yescharacteristic
399C2×C22⋊C4D4×C1312yes—
400C2×C42D4×C1311yescharacteristic
401#101—42no—
402#100—42no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—42no—
410C2×C13—21no—
411C2×C13—21no—
412C2×C13—41no—
413C2×C13—41no—
414C2×C13—81no—
415C2×C13—82no—
416C2×C13#178511yescharacteristic
417C2×C13#179011yescharacteristic
418C2×C13#179111yescharacteristic
419C24C13×C22⋊C411yescharacteristic
420C24C13×C22⋊C412yes—
421C24C22×C4×C1311yescharacteristic
422#41—81no—
423#41—81no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—42no—
441C2×D4—42no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C13×C22⋊C411yescharacteristic
451C22×C4C13×C22⋊C411yescharacteristic
452C22×C4C13×C22⋊C412yes—
453C22×C4C13×C22⋊C411yescharacteristic
454C22×C4C13×C22⋊C412yes—
455C22×C4C13×C22⋊C412yes—
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C2×D4×C1311yescharacteristic
458C22×C4C2×D4×C1311yescharacteristic
459C22×C4C2×D4×C1311yescharacteristic
460C22×C4C2×D4×C1311yescharacteristic
461C22×C4C2×D4×C1311yescharacteristic
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—22no—
504C42—22no—
505C42—22no—
506C42—21no—
507C42—21no—
508C13#853811yescharacteristic, direct product factor, Sylow
509C23—21no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—21no—
514C23—21no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C2×C13×C22⋊C411yescharacteristic
523C23C2×C13×C22⋊C411yescharacteristic
524C23C2×C13×C22⋊C411yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—81no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—81no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4C13×#12011yescharacteristic
566C2×C4C13×#12011yescharacteristic
567C2×C4C13×#12011yescharacteristic
568C2×C4C13×#12011yescharacteristic
569C8—42no—
570C8—81no—
571C8—81no—
572C8—81no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—162no—
592C22C13×#37911yescharacteristic
593C22C13×#41311yescharacteristic
594C22C13×#41311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4C13×B(4,𝔽2)11yescharacteristic
605C4C13×#45811yescharacteristic
606C2—21no—
607C2—21no—
608C2—41no—
609C2—41no—
610C2—81no—
611C2—82no—
612C2C13×#178511yescharacteristic
613C2C13×#179011yescharacteristic
614C2C13×#179111yescharacteristic
subgroupG/H
center, socleC22×C13#379
commutatorC24C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#3505C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1901C2semidirect
3. C13×#1900C2semidirect
4. C13×#1870C2semidirect
5. C13×#1472C2semidirect
6. C13×#1471C2semidirect
7. C13×#1465C2semidirect
112. #8538C13direct (N × H)
203. #1901C2×C13semidirect
204. #1900C2×C13semidirect
205. #1870C2×C13semidirect
206. #1472C2×C13semidirect
207. #1471C2×C13semidirect
208. #1465C2×C13semidirect
508. C13#8538direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35052
C13×#19012
C13×#19002
C13×#18702
C13×#14722
C13×#14712
C13×#14652
#853813