Finite Group Databasebeta

← C13×#19848 #15706187

Subgroups — C13×#19848 #15706187

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3369C211yesmaximal, characteristic
2C13×#3364C211yesmaximal, characteristic
3C13×#3363C211yesmaximal, characteristic, complemented
4C13×#3342C211yesmaximal, characteristic
5C13×#1718C211yesmaximal, characteristic, complemented
6C13×#1700C211yesmaximal, characteristic, complemented
7C13×#1684C211yesmaximal, characteristic, complemented
8C13×#1683C211yesmaximal, characteristic
9C13×#1674C211yesmaximal, characteristic, complemented
10C13×#1653C211yesmaximal, characteristic, complemented
11C13×#1652C211yesmaximal, characteristic
12C13×#1645C211yesmaximal, characteristic, complemented
13C13×#1638C211yesmaximal, characteristic
14C13×#1584C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic
16Q82×C13C2211yescharacteristic
17C13×#557C2211yescharacteristic
18C13×#556C2211yescharacteristic
19C13×#556C2211yescharacteristic
20C13×#500C2211yescharacteristic
21C13×#498C2211yescharacteristic
22C13×#489—21no—
23C13×#488—21no—
24C13×#487—21no—
25C13×#487C2211yescharacteristic
26C13×#487C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#487C2211yescharacteristic
29C13×#485—21no—
30C13×#485—21no—
31C13×#479—21no—
32C13×#477—21no—
33C13×#477C2211yescharacteristic
34C13×#476C2211yescharacteristic
35C13×#475—21no—
36C13×#475C2211yescharacteristic
37C13×#475C2211yescharacteristic
38C13×#474C2211yescharacteristic
39C13×#467—21no—
40C13×#464—21no—
41C13×#464—21no—
42C13×#462—21no—
43C13×#462C2211yescharacteristic
44C13×#462C2211yescharacteristic
45C13×#462C2211yescharacteristic
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C8×Q8×C13C2211yescharacteristic
49C13×#441—21no—
50C4×C13×Q16—21no—
51C4×C13×Q16—21no—
52C4×C13×Q16C2211yescharacteristic
53C4×C13×SD16C2211yescharacteristic
54C8×D4×C13C2211yescharacteristic
55C13×#427—21no—
56C13×#335C2211yescharacteristic
57C13×#335C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#332C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#332C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×Q8⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C2×C13×Q16—21no—
68C2×C13×Q16—21no—
69C2×C13×Q16—21no—
70C2×C13×Q16D411yescharacteristic
71C2×C13×SD16D411yescharacteristic
72C22×C8×C13—21no—
73C13×C4⋊Q8—21no—
74C13×C4⋊Q8—21no—
75C13×C4⋊Q8—21no—
76C13×C4⋊Q8—41no—
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×C4⋊Q8C2311yescharacteristic
81C13×#126—41no—
82C13×#126—41no—
83C13×#125—21no—
84C13×#125—41no—
85C13×#124—21no—
86C13×#124—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C4×Q8×C13—21no—
90C4×Q8×C13—21no—
91C4×Q8×C13—21no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13C2311yescharacteristic
96C4×Q8×C13C2311yescharacteristic
97C4×Q8×C13C2311yescharacteristic
98C4×D4×C13C2311yescharacteristic
99C13×#117—21no—
100C13×#117—21no—
101C13×#107—21no—
102C13×#107—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107D411yescharacteristic
106C13×#106—21no—
107C13×#106—21no—
108C13×#106—21no—
109C13×#106—41no—
110C13×#106D411yescharacteristic
111C13×C4⋊C8—21no—
112C13×C4⋊C8—21no—
113C13×C4⋊C8—21no—
114C13×C4⋊C8C2311yescharacteristic
115C13×C4⋊C8C2311yescharacteristic
116C13×C4⋊C8C2311yescharacteristic
117C13×C4⋊C8C2311yescharacteristic
118C13×#103—21no—
119C13×#103—21no—
120C13×#103—21no—
121C13×#103—21no—
122C13×#103—21no—
123C13×#103—21no—
124C13×#103—21no—
125C13×#103—21no—
126C13×#103—21no—
127C13×#103—21no—
128C13×#103—21no—
129C13×#103—21no—
130C13×#103—41no—
131C13×#103D411yescharacteristic
132C13×#103D411yescharacteristic
133C13×#103D411yescharacteristic
134C13×#102—21no—
135C13×#102—21no—
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×#97—21no—
139C4×C8×C13—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19848C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—41no—
150C2×Q8×C13C2×D411yescharacteristic
151C2×Q8×C13C2×D411yescharacteristic
152C2×Q8×C13C2×D411yescharacteristic
153C2×D4×C13C2×D411yescharacteristic
154C22×C4×C13—21no—
155C13×Q16—41no—
156C13×Q16—42no—
157C13×Q16—42no—
158C13×Q16—42no—
159C13×SD16—22no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—42no—
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—41no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4C2×D411yescharacteristic
189C13×C4⋊C4C2×D411yescharacteristic
190C13×C4⋊C4C2×D411yescharacteristic
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C22⋊C4—21no—
193C13×C22⋊C4—41no—
194C13×C22⋊C4—41no—
195C13×C22⋊C4—41no—
196C13×C22⋊C4—41no—
197C42×C13—21no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—41no—
201C42×C13—41no—
202C42×C13—41no—
203C42×C13—41no—
204C42×C13C2411yescharacteristic
205#3369C2×C1311yescharacteristic
206#3364C2×C1311yescharacteristic
207#3363C2×C1311yescharacteristic, complemented
208#3342C2×C1311yescharacteristic
209#1718C2×C1311yescharacteristic, complemented
210#1700C2×C1311yescharacteristic, complemented
211#1684C2×C1311yescharacteristic, complemented
212#1683C2×C1311yescharacteristic
213#1674C2×C1311yescharacteristic, complemented
214#1653C2×C1311yescharacteristic, complemented
215#1652C2×C1311yescharacteristic
216#1645C2×C1311yescharacteristic, complemented
217#1638C2×C1311yescharacteristic
218#1584C2×C1311yescharacteristic, complemented
219SD16⋊C8C2×C1311yescharacteristic
220C23×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—41no—
227Q8×C13—41no—
228Q8×C13—41no—
229Q8×C13—41no—
230Q8×C13—41no—
231Q8×C13—41no—
232Q8×C13—81no—
233Q8×C13—161no—
234Q8×C13#13512yes—
235D4×C13—21no—
236D4×C13—21no—
237C2×C4×C13—21no—
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—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13H(5,𝔽2)11yescharacteristic
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—41no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13—41no—
262Q82C22×C1311yescharacteristic
263#557C22×C1311yescharacteristic
264#556C22×C1311yescharacteristic
265#556C22×C1311yescharacteristic
266#500C22×C1311yescharacteristic
267#498C22×C1311yescharacteristic
268#489—21no—
269#488—21no—
270#487—21no—
271#487C22×C1311yescharacteristic
272#487C22×C1311yescharacteristic
273#487C22×C1311yescharacteristic
274#487C22×C1311yescharacteristic
275#485—21no—
276#485—21no—
277#479—21no—
278#477—21no—
279#477C22×C1311yescharacteristic
280#476C22×C1311yescharacteristic
281#475—21no—
282#475C22×C1311yescharacteristic
283#475C22×C1311yescharacteristic
284#474C22×C1311yescharacteristic
285#467—21no—
286#464—21no—
287#464—21no—
288#462—21no—
289#462C22×C1311yescharacteristic
290#462C22×C1311yescharacteristic
291#462C22×C1311yescharacteristic
292#446C22×C1311yescharacteristic
293C8×Q8C22×C1311yescharacteristic
294C8×Q8C22×C1311yescharacteristic
295#441—21no—
296C4×Q16—21no—
297C4×Q16—21no—
298C4×Q16C22×C1311yescharacteristic
299C4×SD16C22×C1311yescharacteristic
300C8×D4C22×C1311yescharacteristic
301#427—21no—
302#335C22×C1311yescharacteristic
303#335C22×C1311yescharacteristic
304#333C22×C1311yescharacteristic
305#332C22×C1311yescharacteristic
306#332C22×C1311yescharacteristic
307#332C22×C1311yescharacteristic
308Q8⋊C8C22×C1311yescharacteristic
309Q8⋊C8C22×C1311yescharacteristic
310Q8⋊C8C22×C1311yescharacteristic
311D4⋊C8C22×C1311yescharacteristic
312#322C22×C1311yescharacteristic
313C22×C13—41no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13D4211yescharacteristic
317C4×C13—22no—
318C4×C13—21no—
319C4×C13—41no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—81no—
326C4×C13—81no—
327C4×C13—81no—
328C4×C13—81no—
329C4×C13C2×#13511yescharacteristic
330C4×C13#57511yescharacteristic
331C4×C13#57811yescharacteristic
332C4×C13#57811yescharacteristic
333C2×Q16—21no—
334C2×Q16—21no—
335C2×Q16—21no—
336C2×Q16D4×C1311yescharacteristic
337C2×SD16D4×C1311yescharacteristic
338C22×C8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—41no—
343C4⋊Q8C23×C1311yescharacteristic
344C4⋊Q8C23×C1311yescharacteristic
345C4⋊Q8C23×C1311yescharacteristic
346C4⋊Q8C23×C1311yescharacteristic
347#126—41no—
348#126—41no—
349#125—21no—
350#125—41no—
351#124—21no—
352#124—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C23×C1311yescharacteristic
362C4×Q8C23×C1311yescharacteristic
363C4×Q8C23×C1311yescharacteristic
364C4×D4C23×C1311yescharacteristic
365#117—21no—
366#117—21no—
367#107—21no—
368#107—21no—
369#107—21no—
370#107—21no—
371#107D4×C1311yescharacteristic
372#106—21no—
373#106—21no—
374#106—21no—
375#106—41no—
376#106D4×C1311yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8C23×C1311yescharacteristic
381C4⋊C8C23×C1311yescharacteristic
382C4⋊C8C23×C1311yescharacteristic
383C4⋊C8C23×C1311yescharacteristic
384#103—21no—
385#103—21no—
386#103—21no—
387#103—21no—
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—41no—
397#103D4×C1311yescharacteristic
398#103D4×C1311yescharacteristic
399#103D4×C1311yescharacteristic
400#102—21no—
401#102—21no—
402#102D4×C1311yescharacteristic
403C22⋊C8—21no—
404#97—21no—
405C4×C8—21no—
406C4×C8—21no—
407C4×C8C23×C1311yescharacteristic
408C4×C8C23×C1311yescharacteristic
409C4×C8C23×C1311yescharacteristic
410C2×C13—81no—
411C2×C13#326911yescharacteristic
412C2×C13#328511yescharacteristic
413C2×C13#328911yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—41no—
419C2×Q8C2×D4×C1311yescharacteristic
420C2×Q8C2×D4×C1311yescharacteristic
421C2×Q8C2×D4×C1311yescharacteristic
422C2×D4C2×D4×C1311yescharacteristic
423C22×C4—21no—
424Q16—41no—
425Q16—42no—
426Q16—42no—
427Q16—42no—
428SD16—22no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—42no—
435C2×C8C2×D4×C1311yescharacteristic
436C2×C8C2×D4×C1311yescharacteristic
437C2×C8C2×D4×C1311yescharacteristic
438C2×C8C2×D4×C1311yescharacteristic
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4C2×D4×C1311yescharacteristic
458C4⋊C4C2×D4×C1311yescharacteristic
459C4⋊C4C2×D4×C1311yescharacteristic
460C4⋊C4C2×D4×C1311yescharacteristic
461C22⋊C4—21no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—41no—
470C42—41no—
471C42—41no—
472C42—41no—
473C42C24×C1311yescharacteristic
474C13#1984811yescharacteristic, direct product factor, Sylow
475C23—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—161no—
489Q8C13×#13512yes—
490D4—21no—
491D4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4C22×D4×C1311yescharacteristic
506C2×C4C22×D4×C1311yescharacteristic
507C2×C4C13×H(5,𝔽2)11yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22D42×C1311yescharacteristic
521C4—22no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4C2×C13×#13511yescharacteristic
534C4C13×#57511yescharacteristic
535C4C13×#57811yescharacteristic
536C4C13×#57811yescharacteristic
537C2—81no—
538C2C13×#326911yescharacteristic
539C2C13×#328511yescharacteristic
540C2C13×#328911yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC2×D4×C13C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#3363C2semidirect
5. C13×#1718C2semidirect
6. C13×#1700C2semidirect
7. C13×#1684C2semidirect
9. C13×#1674C2semidirect
10. C13×#1653C2semidirect
12. C13×#1645C2semidirect
14. C13×#1584C2semidirect
144. #19848C13direct (N × H)
207. #3363C2×C13semidirect
209. #1718C2×C13semidirect
210. #1700C2×C13semidirect
211. #1684C2×C13semidirect
213. #1674C2×C13semidirect
214. #1653C2×C13semidirect
216. #1645C2×C13semidirect
218. #1584C2×C13semidirect
474. C13#19848direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33692
C13×#33642
C13×#33632
C13×#33422
C13×#17182
C13×#17002
C13×#16842
C13×#16832
C13×#16742
C13×#16532
C13×#16522
C13×#16452
C13×#16382
C13×#15842
C13×SD16⋊C82
#1984813