Finite Group Databasebeta

← C13×#19034 #15705373

Subgroups — C13×#19034 #15705373

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic
3C13×#3165C211yesmaximal, characteristic, complemented
4C2×C13×#501C211yesmaximal, characteristic, complemented
5C13×#1663C214yesmaximal, complemented
6C13×#1660C214yesmaximal, complemented
7C13×#1531C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic
10C13×#564C2212yes—
11C13×#563C2212yes—
12C13×#557—21no—
13C13×#554—21no—
14C13×#552—21no—
15C13×#552—22no—
16C13×#552—21no—
17C13×#544—21no—
18C13×#544—21no—
19C13×#541—21no—
20C13×#541—22no—
21C13×#539—21no—
22C13×#533C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#501—22no—
27C13×#501C2214yes—
28C13×#501C2214yes—
29C13×#500—21no—
30C13×#498—21no—
31C13×#497C2212yes—
32C13×#491C2212yes—
33C13×#462—21no—
34C13×#461—21no—
35C13×#451—21no—
36C13×#448—21no—
37C13×#432C2211yescharacteristic
38C13×#428—22no—
39C2×C13×#107—21no—
40C2×C13×#106—21no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yes—
44C13×#330C2214yes—
45C13×#330C2214yes—
46C13×#329C2212yes—
47C22×Q8×C13—21no—
48C2×C13×Q16—22no—
49C2×C13×SD16—22no—
50C2×C13×M16—21no—
51C22×C8×C13—21no—
52C13×C4⋊Q8—22no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8D411yescharacteristic
59C13×C4⋊Q8D411yescharacteristic
60C13×C4⋊Q8C2312yes—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—21no—
66C13×#125—22no—
67C13×#125—22no—
68C13×#125—21no—
69C13×#125—22no—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125—21no—
76C13×#125—21no—
77C13×#125D412yes—
78C13×#125C2311yescharacteristic
79C13×#125C2312yes—
80C13×#125C2312yes—
81C13×#124C2311yescharacteristic
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—21no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8D411yescharacteristic
94C13×#121D411yescharacteristic
95C4×Q8×C13—21no—
96C4×Q8×C13—22no—
97C4×Q8×C13—21no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13D411yescharacteristic
101C4×D4×C13—22no—
102C4×D4×C13—21no—
103C4×D4×C13D411yescharacteristic
104C13×#117—22no—
105C13×#117—21no—
106C13×#117—22no—
107C13×#117—21no—
108C13×#117D412yes—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4D411yescharacteristic
116C2×C42×C13C2311yescharacteristic
117C13×#107—24no—
118C13×#107—24no—
119C13×#106—24no—
120C13×#106—24no—
121C13×C4⋊C8—21no—
122C13×#103—22no—
123C13×#103—22no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19034C1311yesmaximal, characteristic, direct product factor, Sylow
131C2×Q8×C13—22no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—22no—
135C2×Q8×C13—41no—
136C2×Q8×C13—82no—
137C2×Q8×C13C2×D411yescharacteristic
138C2×D4×C13—21no—
139C2×D4×C13C2×D411yescharacteristic
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—41no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C13×Q16—82no—
149C13×SD16—82no—
150C13×M16—24no—
151C2×C8×C13—24no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C2×C8×C13—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
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—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4C2×D411yescharacteristic
182C13×C4⋊C4C2×D411yescharacteristic
183C13×C4⋊C4C2×D412yes—
184C13×C4⋊C4C2×D412yes—
185C13×C4⋊C4C2×D412yes—
186C13×C4⋊C4C2×D412yes—
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—21no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C42×C13—22no—
197C42×C13—22no—
198C42×C13—22no—
199C42×C13—22no—
200C42×C13—21no—
201C42×C13C2×D411yescharacteristic
202C42×C13C2×D411yescharacteristic
203C42×C13C2×D411yescharacteristic
204C42×C13C2411yescharacteristic
205#3563C2×C1311yescharacteristic
206#3218C2×C1311yescharacteristic
207#3165C2×C1311yescharacteristic, complemented
208C2×#501C2×C1311yescharacteristic, complemented
209#1663C2×C1314yescomplemented
210#1660C2×C1314yescomplemented
211#1531C2×C1311yescharacteristic, complemented
212#1528C2×C1311yescharacteristic, complemented
213#1524C2×C1311yescharacteristic
214C23×C13—21no—
215C23×C13#12011yescharacteristic
216Q8×C13—41no—
217Q8×C13—42no—
218Q8×C13—42no—
219Q8×C13—42no—
220Q8×C13—81no—
221Q8×C13—82no—
222Q8×C13—82no—
223D4×C13—41no—
224D4×C13—42no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—41no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—81no—
239C2×C4×C13—82no—
240C2×C4×C13—82no—
241C2×C4×C13#12011yescharacteristic
242C2×C4×C13#12011yescharacteristic
243C2×C4×C13#12011yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C8×C13—24no—
248C8×C13—24no—
249C8×C13—42no—
250#564C22×C1312yes—
251#563C22×C1312yes—
252#557—21no—
253#554—21no—
254#552—21no—
255#552—22no—
256#552—21no—
257#544—21no—
258#544—21no—
259#541—21no—
260#541—22no—
261#539—21no—
262#533C22×C1311yescharacteristic
263C2×C4⋊Q8C22×C1311yescharacteristic
264#529C22×C1311yescharacteristic
265C2×#125C22×C1311yescharacteristic
266#501—22no—
267#501C22×C1314yes—
268#501C22×C1314yes—
269#500—21no—
270#498—21no—
271#497C22×C1312yes—
272#491C22×C1312yes—
273#462—21no—
274#461—21no—
275#451—21no—
276#448—21no—
277#432C22×C1311yescharacteristic
278#428—22no—
279C2×#107—21no—
280C2×#106—21no—
281C4×M16C22×C1311yescharacteristic
282C2×#97C22×C1311yescharacteristic
283#330C22×C1314yes—
284#330C22×C1314yes—
285#330C22×C1312yes—
286#329C22×C1312yes—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—41no—
290C22×C13—41no—
291C22×C13—41no—
292C22×C13#45612yes—
293C22×C13C2×#12011yescharacteristic
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—42no—
300C4×C13—41no—
301C4×C13—41no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—41no—
306C4×C13—82no—
307C4×C13#45612yes—
308C22×Q8—21no—
309C2×Q16—22no—
310C2×SD16—22no—
311C2×M16—21no—
312C22×C8—21no—
313C4⋊Q8—22no—
314C4⋊Q8—21no—
315C4⋊Q8—22no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8D4×C1311yescharacteristic
320C4⋊Q8D4×C1311yescharacteristic
321C4⋊Q8C23×C1312yes—
322#126—22no—
323#126—22no—
324#126—22no—
325#126—22no—
326#126—21no—
327#125—22no—
328#125—22no—
329#125—21no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125—22no—
334#125—22no—
335#125—22no—
336#125—21no—
337#125—21no—
338#125D4×C1312yes—
339#125C23×C1312yes—
340#125C23×C1311yescharacteristic
341#125C23×C1312yes—
342#124C23×C1311yescharacteristic
343#123—22no—
344#123—22no—
345#123—21no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8D4×C1311yescharacteristic
355#121D4×C1311yescharacteristic
356C4×Q8—21no—
357C4×Q8—22no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8D4×C1311yescharacteristic
362C4×D4—22no—
363C4×D4—21no—
364C4×D4D4×C1311yescharacteristic
365#117—22no—
366#117—21no—
367#117—22no—
368#117—21no—
369#117D4×C1312yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C1311yescharacteristic
376C2×C4⋊C4D4×C1311yescharacteristic
377C2×C42C23×C1311yescharacteristic
378#107—24no—
379#107—24no—
380#106—24no—
381#106—24no—
382C4⋊C8—21no—
383#103—22no—
384#103—22no—
385C22⋊C8—21no—
386#97—21no—
387#97C23×C1312yes—
388#97C23×C1312yes—
389#97C23×C1312yes—
390C4×C8—21no—
391C2×C13—22no—
392C2×C13—81no—
393C2×C13C2×#45611yescharacteristic
394C2×C13C2×#45611yescharacteristic
395C2×C13#302111yescharacteristic
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—41no—
401C2×Q8—82no—
402C2×Q8C2×D4×C1311yescharacteristic
403C2×D4—21no—
404C2×D4C2×D4×C1311yescharacteristic
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1311yescharacteristic
413Q16—82no—
414SD16—82no—
415M16—24no—
416C2×C8—24no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4C2×D4×C1311yescharacteristic
447C4⋊C4C2×D4×C1311yescharacteristic
448C4⋊C4C2×D4×C1312yes—
449C4⋊C4C2×D4×C1312yes—
450C4⋊C4C2×D4×C1312yes—
451C4⋊C4C2×D4×C1312yes—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—21no—
456C22⋊C4—22no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C42—22no—
462C42—22no—
463C42—22no—
464C42—22no—
465C42—21no—
466C42C2×D4×C1311yescharacteristic
467C42C2×D4×C1311yescharacteristic
468C42C2×D4×C1311yescharacteristic
469C42C24×C1311yescharacteristic
470C13#1903411yescharacteristic, direct product factor, Sylow
471C23—21no—
472C23C13×#12011yescharacteristic
473Q8—41no—
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—81no—
478Q8—82no—
479Q8—82no—
480D4—41no—
481D4—42no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—81no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12011yescharacteristic
500C2×C4C13×#12011yescharacteristic
501C2×C4C22×D4×C1311yescharacteristic
502C2×C4C22×D4×C1311yescharacteristic
503C2×C4C22×D4×C1311yescharacteristic
504C8—24no—
505C8—24no—
506C8—42no—
507C22—21no—
508C22—21no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22C13×#45612yes—
513C22C2×C13×#12011yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—82no—
527C4C13×#45612yes—
528C2—22no—
529C2—81no—
530C2C2×C13×#45611yescharacteristic
531C2C2×C13×#45611yescharacteristic
532C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#121D4
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
3. C13×#3165C2semidirect
4. C2×C13×#501C2semidirect
5. C13×#1663C2semidirect
6. C13×#1660C2semidirect
7. C13×#1531C2semidirect
8. C13×#1528C2semidirect
130. #19034C13direct (N × H)
207. #3165C2×C13semidirect
208. C2×#501C2×C13semidirect
209. #1663C2×C13semidirect
210. #1660C2×C13semidirect
211. #1531C2×C13semidirect
212. #1528C2×C13semidirect
470. C13#19034direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#32182
C13×#31652
C2×C13×#5012
C13×#16632
C13×#16602
C13×#15312
C13×#15282
C13×#15242
#1903413