Finite Group Databasebeta

← C13×#19815 #15706154

Subgroups — C13×#19815 #15706154

Order 3328.

580 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3395C211yesmaximal, characteristic, complemented
2C13×#3386C211yesmaximal, characteristic
3C13×#3381C211yesmaximal, characteristic
4C13×#3299C211yesmaximal, characteristic
5C13×#1723C211yesmaximal, characteristic, complemented
6C13×#1692C211yesmaximal, characteristic, complemented
7C13×#1684C211yesmaximal, characteristic, complemented
8C13×#1674C211yesmaximal, characteristic, complemented
9C13×#1669C211yesmaximal, characteristic
10C13×#1649C211yesmaximal, characteristic
11C13×#1648C211yesmaximal, characteristic, complemented
12C13×#1644C211yesmaximal, characteristic
13C13×#1636C211yesmaximal, characteristic, complemented
14C13×#1584C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic
16C13×#557C2211yescharacteristic
17C13×#557C2211yescharacteristic
18C13×#554C2211yescharacteristic
19D4×Q8×C13C2211yescharacteristic
20C13×#501—21no—
21C13×#500C2211yescharacteristic
22C13×#500C2211yescharacteristic
23C13×#499—21no—
24C13×#498C2211yescharacteristic
25C13×#494—21no—
26C13×#494C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#487C2211yescharacteristic
29C13×#484—21no—
30C13×#479—21no—
31C13×#478—21no—
32C13×#478—21no—
33C13×#477—21no—
34C13×#477C2211yescharacteristic
35C13×#477C2211yescharacteristic
36C13×#475C2211yescharacteristic
37C13×#474C2211yescharacteristic
38C13×#474C2211yescharacteristic
39C13×#467—21no—
40C13×#462—21no—
41C13×#462—21no—
42C13×#462C2211yescharacteristic
43C13×#462C2211yescharacteristic
44C13×#462C2211yescharacteristic
45C13×#451—21no—
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C8×Q8×C13C2211yescharacteristic
49C13×#440—21no—
50C4×C13×Q16—21no—
51C4×C13×Q16C2211yescharacteristic
52C4×C13×SD16—21no—
53C4×C13×SD16C2211yescharacteristic
54C8×D4×C13C2211yescharacteristic
55C2×C13×#103—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
67C22×Q8×C13—21no—
68C2×C13×Q16—21no—
69C2×C13×Q16—21no—
70C2×C13×Q16—21no—
71C2×C13×Q16—21no—
72C2×C13×Q16—21no—
73C2×C13×Q16D411yescharacteristic
74C2×C13×SD16D411yescharacteristic
75C22×C8×C13—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8—21no—
78C13×C4⋊Q8—21no—
79C13×C4⋊Q8C2311yescharacteristic
80C13×C4⋊Q8C2311yescharacteristic
81C13×C4⋊Q8C2311yescharacteristic
82C13×C4⋊Q8C2311yescharacteristic
83C13×#125—21no—
84C13×#125—21no—
85C13×#125—21no—
86C13×#125—41no—
87C13×#125—41no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—41no—
91C13×C22⋊Q8—41no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13—21no—
96C4×Q8×C13C2311yescharacteristic
97C4×Q8×C13C2311yescharacteristic
98C4×Q8×C13C2311yescharacteristic
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13C2311yescharacteristic
102C2×C13×C4⋊C4—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107—21no—
107C13×#107—21no—
108C13×#107—21no—
109C13×#107—41no—
110C13×#107D411yescharacteristic
111C13×#106—21no—
112C13×#106—21no—
113C13×#106—21no—
114C13×#106D411yescharacteristic
115C13×C4⋊C8—21no—
116C13×C4⋊C8—21no—
117C13×C4⋊C8—21no—
118C13×C4⋊C8C2311yescharacteristic
119C13×C4⋊C8C2311yescharacteristic
120C13×C4⋊C8C2311yescharacteristic
121C13×C4⋊C8C2311yescharacteristic
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#19815C1311yesmaximal, 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×C13—42no—
151C2×Q8×C13—81no—
152C2×Q8×C13C2×D411yescharacteristic
153C2×Q8×C13C2×D411yescharacteristic
154C2×Q8×C13C2×D411yescharacteristic
155C2×D4×C13C2×D411yescharacteristic
156C22×C4×C13—21no—
157C22×C4×C13—41no—
158C22×C4×C13—41no—
159C13×Q16—41no—
160C13×Q16—42no—
161C13×Q16—81no—
162C13×Q16—81no—
163C13×Q16—81no—
164C13×Q16—81no—
165C13×SD16Q1614yescomplemented
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—81no—
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4—41no—
191C13×C4⋊C4—41no—
192C13×C4⋊C4—41no—
193C13×C4⋊C4—41no—
194C13×C4⋊C4—41no—
195C13×C4⋊C4—41no—
196C13×C4⋊C4C2×D411yescharacteristic
197C13×C4⋊C4C2×D411yescharacteristic
198C13×C4⋊C4C2×D411yescharacteristic
199C13×C4⋊C4C2×D411yescharacteristic
200C13×C22⋊C4—21no—
201C13×C22⋊C4—41no—
202C13×C22⋊C4—41no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—41no—
207C42×C13—41no—
208C42×C13C2411yescharacteristic
209#3395C2×C1311yescharacteristic, complemented
210#3386C2×C1311yescharacteristic
211#3381C2×C1311yescharacteristic
212#3299C2×C1311yescharacteristic
213#1723C2×C1311yescharacteristic, complemented
214#1692C2×C1311yescharacteristic, complemented
215#1684C2×C1311yescharacteristic, complemented
216#1674C2×C1311yescharacteristic, complemented
217#1669C2×C1311yescharacteristic
218#1649C2×C1311yescharacteristic
219#1648C2×C1311yescharacteristic, complemented
220#1644C2×C1311yescharacteristic
221#1636C2×C1311yescharacteristic, complemented
222#1584C2×C1311yescharacteristic, complemented
223SD16⋊C8C2×C1311yescharacteristic
224C23×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—41no—
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—41no—
235Q8×C13—41no—
236Q8×C13—81no—
237Q8×C13—82no—
238Q8×C13C2×Q1612yes—
239D4×C13—21no—
240D4×C13C2×Q1612yes—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—82no—
255C2×C4×C13—161no—
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13H(5,𝔽2)11yescharacteristic
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13C2×Q1612yes—
268#557C22×C1311yescharacteristic
269#557C22×C1311yescharacteristic
270#554C22×C1311yescharacteristic
271D4×Q8C22×C1311yescharacteristic
272#501—21no—
273#500C22×C1311yescharacteristic
274#500C22×C1311yescharacteristic
275#499—21no—
276#498C22×C1311yescharacteristic
277#494—21no—
278#494C22×C1311yescharacteristic
279#487C22×C1311yescharacteristic
280#487C22×C1311yescharacteristic
281#484—21no—
282#479—21no—
283#478—21no—
284#478—21no—
285#477—21no—
286#477C22×C1311yescharacteristic
287#477C22×C1311yescharacteristic
288#475C22×C1311yescharacteristic
289#474C22×C1311yescharacteristic
290#474C22×C1311yescharacteristic
291#467—21no—
292#462—21no—
293#462—21no—
294#462C22×C1311yescharacteristic
295#462C22×C1311yescharacteristic
296#462C22×C1311yescharacteristic
297#451—21no—
298#446C22×C1311yescharacteristic
299C8×Q8C22×C1311yescharacteristic
300C8×Q8C22×C1311yescharacteristic
301#440—21no—
302C4×Q16—21no—
303C4×Q16C22×C1311yescharacteristic
304C4×SD16—21no—
305C4×SD16C22×C1311yescharacteristic
306C8×D4C22×C1311yescharacteristic
307C2×#103—21no—
308#335C22×C1311yescharacteristic
309#335C22×C1311yescharacteristic
310#333C22×C1311yescharacteristic
311#332C22×C1311yescharacteristic
312#332C22×C1311yescharacteristic
313#332C22×C1311yescharacteristic
314Q8⋊C8C22×C1311yescharacteristic
315Q8⋊C8C22×C1311yescharacteristic
316Q8⋊C8C22×C1311yescharacteristic
317D4⋊C8C22×C1311yescharacteristic
318#322C22×C1311yescharacteristic
319C22×C13—22no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13D4211yescharacteristic
323C4×C13—22no—
324C4×C13—21no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13C22×Q1611yescharacteristic
336C4×C13#57511yescharacteristic
337C4×C13#57611yescharacteristic
338C4×C13#57811yescharacteristic
339C22×Q8—21no—
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16D4×C1311yescharacteristic
346C2×SD16D4×C1311yescharacteristic
347C22×C8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8C23×C1311yescharacteristic
352C4⋊Q8C23×C1311yescharacteristic
353C4⋊Q8C23×C1311yescharacteristic
354C4⋊Q8C23×C1311yescharacteristic
355#125—21no—
356#125—21no—
357#125—21no—
358#125—41no—
359#125—41no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C1311yescharacteristic
369C4×Q8C23×C1311yescharacteristic
370C4×Q8C23×C1311yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C23×C1311yescharacteristic
374C2×C4⋊C4—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—41no—
382#107D4×C1311yescharacteristic
383#106—21no—
384#106—21no—
385#106—21no—
386#106D4×C1311yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8C23×C1311yescharacteristic
391C4⋊C8C23×C1311yescharacteristic
392C4⋊C8C23×C1311yescharacteristic
393C4⋊C8C23×C1311yescharacteristic
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—41no—
403#103D4×C1311yescharacteristic
404#103D4×C1311yescharacteristic
405#103D4×C1311yescharacteristic
406#102—21no—
407#102—21no—
408#102D4×C1311yescharacteristic
409C22⋊C8—21no—
410#97—21no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8C23×C1311yescharacteristic
414C4×C8C23×C1311yescharacteristic
415C4×C8C23×C1311yescharacteristic
416C2×C13—42no—
417C2×C13#326811yescharacteristic
418C2×C13D4×Q1611yescharacteristic
419C2×C13#328911yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C1311yescharacteristic
428C2×Q8C2×D4×C1311yescharacteristic
429C2×Q8C2×D4×C1311yescharacteristic
430C2×D4C2×D4×C1311yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434Q16—41no—
435Q16—42no—
436Q16—81no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440SD16C13×Q1614yescomplemented
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8C2×D4×C1311yescharacteristic
448C2×C8C2×D4×C1311yescharacteristic
449C2×C8C2×D4×C1311yescharacteristic
450C2×C8C2×D4×C1311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C1311yescharacteristic
472C4⋊C4C2×D4×C1311yescharacteristic
473C4⋊C4C2×D4×C1311yescharacteristic
474C4⋊C4C2×D4×C1311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42C24×C1311yescharacteristic
484C13#1981511yescharacteristic, direct product factor, Sylow
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—81no—
498Q8—82no—
499Q8C2×C13×Q1612yes—
500D4—21no—
501D4C2×C13×Q1612yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—161no—
517C2×C4C22×D4×C1311yescharacteristic
518C2×C4C22×D4×C1311yescharacteristic
519C2×C4C13×H(5,𝔽2)11yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8C2×C13×Q1612yes—
529C22—22no—
530C22—41no—
531C22—41no—
532C22D42×C1311yescharacteristic
533C4—22no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4C22×C13×Q1611yescharacteristic
546C4C13×#57511yescharacteristic
547C4C13×#57611yescharacteristic
548C4C13×#57811yescharacteristic
549C2—42no—
550C2C13×#326811yescharacteristic
551C2D4×C13×Q1611yescharacteristic
552C2C13×#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
1. C13×#3395C2semidirect
5. C13×#1723C2semidirect
6. C13×#1692C2semidirect
7. C13×#1684C2semidirect
8. C13×#1674C2semidirect
11. C13×#1648C2semidirect
13. C13×#1636C2semidirect
14. C13×#1584C2semidirect
144. #19815C13direct (N × H)
165. C13×SD16Q16semidirect
209. #3395C2×C13semidirect
213. #1723C2×C13semidirect
214. #1692C2×C13semidirect
215. #1684C2×C13semidirect
216. #1674C2×C13semidirect
219. #1648C2×C13semidirect
221. #1636C2×C13semidirect
222. #1584C2×C13semidirect
440. SD16C13×Q16semidirect
484. C13#19815direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33952
C13×#33862
C13×#33812
C13×#32992
C13×#17232
C13×#16922
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C13×#16742
C13×#16692
C13×#16492
C13×#16482
C13×#16442
C13×#16362
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C13×SD16⋊C82
#1981513