Finite Group Databasebeta

← C13×#18441 #15704780

Subgroups — C13×#18441 #15704780

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C13×#3227C211yesmaximal, characteristic, complemented
4C13×#2642C211yesmaximal, characteristic, complemented
5C13×#1616C214yesmaximal, complemented
6C13×#1615C214yesmaximal, complemented
7C13×#1505C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1470C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#554—21no—
13C13×#553—21no—
14C13×#553—21no—
15C13×#547—22no—
16C13×#547—21no—
17C13×#544—21no—
18C13×#540—21no—
19C13×#539—22no—
20C13×#539C2212yes—
21C13×#537C2212yes—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#501—21no—
27C13×#498—21no—
28C13×#489—21no—
29C13×#486—21no—
30C13×#484C2212yes—
31C13×#481C2214yes—
32C13×#481C2212yes—
33C13×#476—22no—
34C13×#475—21no—
35C13×#474—21no—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#400—22no—
39C13×#400C2214yes—
40C13×#391—21no—
41C13×#391—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#327C2212yes—
45C13×#327C2214yes—
46C13×#324C2214yes—
47C2×C13×#41—21no—
48C2×C13×#41—22no—
49C22×Q8×C13—21no—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8—22no—
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8D411yescharacteristic
57C13×#127D411yescharacteristic
58C13×#126—22no—
59C13×#126—22no—
60C13×#126—21no—
61C13×#125—21no—
62C13×#125—22no—
63C13×#125—21no—
64C13×#125—21no—
65C13×#125—21no—
66C13×#125—21no—
67C13×#125D411yescharacteristic
68C13×#124—21no—
69C13×#124D411yescharacteristic
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—22no—
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—21no—
76C13×#123—22no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8C2311yescharacteristic
84C13×#121—21no—
85C13×#121—22no—
86C13×#121—21no—
87C13×#121—22no—
88C13×#121—22no—
89C13×#121—21no—
90C13×#121—22no—
91C13×#121C2311yescharacteristic
92C13×#121C2312yes—
93C4×Q8×C13D411yescharacteristic
94C4×D4×C13—22no—
95C4×D4×C13—21no—
96C4×D4×C13—21no—
97C4×D4×C13—21no—
98C4×D4×C13—22no—
99C4×D4×C13—21no—
100C4×D4×C13D411yescharacteristic
101C4×D4×C13D412yes—
102C13×#117—21no—
103C13×#117—21no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4D412yes—
110C2×C13×C4⋊C4C2312yes—
111C2×C13×C4⋊C4C2312yes—
112C2×C42×C13—21no—
113C2×C42×C13C2311yescharacteristic
114C13×#107—22no—
115C13×#106—22no—
116C13×#106—24no—
117C13×C4⋊C8—21no—
118C13×C4⋊C8—21no—
119C13×#103—22no—
120C13×#102—22no—
121C13×#102—24no—
122C13×C22⋊C8C2312yes—
123C13×C22⋊C8C2312yes—
124C13×#97—21no—
125C4×C8×C13—21no—
126C13×#95—24no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18441C1311yesmaximal, characteristic, direct product factor, Sylow
131C13×#41—82no—
132C13×#41—84no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—44no—
136C2×Q8×C13—41no—
137C2×Q8×C13—41no—
138C2×Q8×C13C2×D411yescharacteristic
139C2×D4×C13—21no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13C2×D411yescharacteristic
146C2×D4×C13C2×D412yes—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2411yescharacteristic
159C2×C8×C13—22no—
160C2×C8×C13—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4C2×D412yes—
183C13×C4⋊C4C2×D411yescharacteristic
184C13×C4⋊C4C2×D411yescharacteristic
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—21no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C42×C13—22no—
198C42×C13—21no—
199C42×C13—42no—
200C42×C13C2×D411yescharacteristic
201C42×C13C2×D411yescharacteristic
202C42×C13C2×D411yescharacteristic
203C42×C13C2×D411yescharacteristic
204#3559C2×C1311yescharacteristic
205#3239C2×C1311yescharacteristic, complemented
206#3227C2×C1311yescharacteristic, complemented
207#2642C2×C1311yescharacteristic, complemented
208#1616C2×C1314yescomplemented
209#1615C2×C1314yescomplemented
210#1505C2×C1311yescharacteristic, complemented
211#1500C2×C1311yescharacteristic, complemented
212#1470C2×C1311yescharacteristic, complemented
213C23×C13—21no—
214C23×C13—22no—
215C23×C13C22×D411yescharacteristic
216Q8×C13—41no—
217Q8×C13—81no—
218Q8×C13—82no—
219Q8×C13—82no—
220Q8×C13—82no—
221D4×C13—42no—
222D4×C13—41no—
223D4×C13—44no—
224D4×C13—42no—
225D4×C13—42no—
226D4×C13—81no—
227D4×C13—82no—
228D4×C13—82no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—44no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—82no—
247C2×C4×C13—82no—
248C2×C4×C13—82no—
249C2×C4×C13—82no—
250C2×C4×C13#12011yescharacteristic
251C2×C4×C13#12011yescharacteristic
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C8×C13—42no—
257C8×C13—42no—
258#563—21no—
259#562—21no—
260#554—21no—
261#553—21no—
262#553—21no—
263#547—22no—
264#547—21no—
265#544—21no—
266#540—21no—
267#539—22no—
268#539C22×C1312yes—
269#537C22×C1312yes—
270#532C22×C1311yescharacteristic
271C2×C4⋊Q8C22×C1311yescharacteristic
272#529C22×C1311yescharacteristic
273C2×#125C22×C1311yescharacteristic
274#501—21no—
275#498—21no—
276#489—21no—
277#486—21no—
278#484C22×C1312yes—
279#481C22×C1314yes—
280#481C22×C1312yes—
281#476—22no—
282#475—21no—
283#474—21no—
284#432C22×C1311yescharacteristic
285#431C22×C1311yescharacteristic
286#400—22no—
287#400C22×C1314yes—
288#391—21no—
289#391—21no—
290#376C22×C1311yescharacteristic
291#328C22×C1312yes—
292#327C22×C1314yes—
293#327C22×C1312yes—
294#324C22×C1314yes—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13C2×#12011yescharacteristic
304C22×C13#57712yes—
305C4×C13—21no—
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—42no—
311C4×C13—42no—
312C4×C13—41no—
313C4×C13—41no—
314C4×C13—42no—
315C4×C13—41no—
316C4×C13—82no—
317C4×C13—82no—
318C4×C13#45412yes—
319C2×#41—21no—
320C2×#41—22no—
321C22×Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—22no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8D4×C1311yescharacteristic
329#127D4×C1311yescharacteristic
330#126—22no—
331#126—22no—
332#126—21no—
333#125—21no—
334#125—22no—
335#125—21no—
336#125—21no—
337#125—21no—
338#125—21no—
339#125D4×C1311yescharacteristic
340#124—21no—
341#124D4×C1311yescharacteristic
342#123—22no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123—22no—
347#123—21no—
348#123—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8C23×C1311yescharacteristic
356#121—21no—
357#121—22no—
358#121—21no—
359#121—22no—
360#121—22no—
361#121—21no—
362#121—22no—
363#121C23×C1311yescharacteristic
364#121C23×C1312yes—
365C4×Q8D4×C1311yescharacteristic
366C4×D4—22no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—22no—
371C4×D4—21no—
372C4×D4D4×C1311yescharacteristic
373C4×D4D4×C1312yes—
374#117—21no—
375#117—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C1311yescharacteristic
380C2×C4⋊C4D4×C1312yes—
381C2×C4⋊C4D4×C1311yescharacteristic
382C2×C4⋊C4C23×C1312yes—
383C2×C4⋊C4C23×C1312yes—
384C2×C42—21no—
385C2×C42C23×C1311yescharacteristic
386#107—22no—
387#106—22no—
388#106—24no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391#103—22no—
392#102—22no—
393#102—24no—
394C22⋊C8C23×C1312yes—
395C22⋊C8C23×C1312yes—
396#97—21no—
397C4×C8—21no—
398#95—21no—
399#95—24no—
400#95—24no—
401#95C23×C1312yes—
402C2×C13—22no—
403C2×C13—81no—
404C2×C13—82no—
405C2×C13#300911yescharacteristic
406C2×C13C2×#45411yescharacteristic
407C2×C13#302811yescharacteristic
408#41—82no—
409#41—84no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—44no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8C2×D4×C1311yescharacteristic
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×D4×C1311yescharacteristic
423C2×D4C2×D4×C1312yes—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4C2×D4×C1312yes—
432C22×C4C2×D4×C1311yescharacteristic
433C22×C4C2×D4×C1311yescharacteristic
434C22×C4C2×D4×C1312yes—
435C22×C4C24×C1311yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4C2×D4×C1312yes—
460C4⋊C4C2×D4×C1311yescharacteristic
461C4⋊C4C2×D4×C1311yescharacteristic
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C42—22no—
475C42—21no—
476C42—42no—
477C42C2×D4×C1311yescharacteristic
478C42C2×D4×C1311yescharacteristic
479C42C2×D4×C1311yescharacteristic
480C42C2×D4×C1311yescharacteristic
481C13#1844111yescharacteristic, direct product factor, Sylow
482C23—21no—
483C23—22no—
484C23C22×D4×C1311yescharacteristic
485Q8—41no—
486Q8—81no—
487Q8—82no—
488Q8—82no—
489Q8—82no—
490D4—42no—
491D4—41no—
492D4—44no—
493D4—42no—
494D4—42no—
495D4—81no—
496D4—82no—
497D4—82no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4C13×#12011yescharacteristic
520C2×C4C13×#12011yescharacteristic
521C2×C4C13×#12011yescharacteristic
522C2×C4C13×#12011yescharacteristic
523C2×C4C22×D4×C1311yescharacteristic
524C2×C4C22×D4×C1311yescharacteristic
525C8—42no—
526C8—42no—
527C22—21no—
528C22—21no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—42no—
533C22—42no—
534C22—41no—
535C22C2×C13×#12011yescharacteristic
536C22C13×#57712yes—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—42no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—41no—
548C4—82no—
549C4—82no—
550C4C13×#45412yes—
551C2—22no—
552C2—81no—
553C2—82no—
554C2C13×#300911yescharacteristic
555C2C2×C13×#45411yescharacteristic
556C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3559C2
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×#3239C2semidirect
3. C13×#3227C2semidirect
4. C13×#2642C2semidirect
5. C13×#1616C2semidirect
6. C13×#1615C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1470C2semidirect
130. #18441C13direct (N × H)
205. #3239C2×C13semidirect
206. #3227C2×C13semidirect
207. #2642C2×C13semidirect
208. #1616C2×C13semidirect
209. #1615C2×C13semidirect
210. #1505C2×C13semidirect
211. #1500C2×C13semidirect
212. #1470C2×C13semidirect
481. C13#18441direct (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×#32392
C13×#32272
C13×#26422
C13×#16162
C13×#16152
C13×#15052
C13×#15002
C13×#14702
#1844113