Finite Group Databasebeta

← C13×#19023 #15705362

Subgroups — C13×#19023 #15705362

Order 3328.

880 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×#3559C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C13×#3141C211yesmaximal, characteristic, complemented
4C2×C13×#491C211yesmaximal, characteristic, complemented
5C13×#1664C214yesmaximal, complemented
6C13×#1662C214yesmaximal, complemented
7C13×#1530C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C13×#563C2212yes—
11C13×#562C2212yes—
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×#539—21no—
21C13×#537—21no—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#501C2212yes—
27C13×#491—22no—
28C13×#491C2214yes—
29C13×#489C2214yes—
30C13×#489C2212yes—
31C13×#487—21no—
32C13×#486—21no—
33C13×#484—21no—
34C13×#481—21no—
35C13×#475—21no—
36C13×#474—21no—
37C13×#432C2211yescharacteristic
38C13×#417—22no—
39C2×C13×#103—21no—
40C2×C13×#103—21no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yes—
44C13×#330C2214yes—
45C13×#329C2212yes—
46C13×#329C2214yes—
47C2×C13×#41—22no—
48C2×C13×#41D412yes—
49C22×Q8×C13—21no—
50C2×C13×M16—21no—
51C22×C8×C13—21no—
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8D411yescharacteristic
58C13×C4⋊Q8C2312yes—
59C13×#127D411yescharacteristic
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—21no—
63C13×#125—22no—
64C13×#125—21no—
65C13×#125—21no—
66C13×#125—21no—
67C13×#125D412yes—
68C13×#125C2312yes—
69C13×#125C2311yescharacteristic
70C13×#124C2311yescharacteristic
71C13×#124C2312yes—
72C13×#123—22no—
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—21no—
77C13×#123—22no—
78C13×#123—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8D411yescharacteristic
86C13×#121—22no—
87C13×#121—22no—
88C13×#121—21no—
89C13×#121—21no—
90C13×#121—22no—
91C13×#121—22no—
92C13×#121—21no—
93C13×#121—21no—
94C13×#121D411yescharacteristic
95C4×Q8×C13D411yescharacteristic
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13D411yescharacteristic
104C13×#117—21no—
105C13×#117—21no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C42×C13C2311yescharacteristic
115C13×#107—22no—
116C13×#106—22no—
117C13×C4⋊C8—21no—
118C13×#103—24no—
119C13×#103—22no—
120C13×#103—24no—
121C13×#103—24no—
122C13×#102—24no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19023C1311yesmaximal, characteristic, direct product factor, Sylow
131C13×#41—44no—
132C13×#41—84no—
133C2×Q8×C13—22no—
134C2×Q8×C13—22no—
135C2×Q8×C13—44no—
136C2×Q8×C13—41no—
137C2×Q8×C13C2×D411yescharacteristic
138C2×Q8×C13C2×D412yes—
139C2×D4×C13—22no—
140C2×D4×C13—21no—
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—21no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—41no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C13×M16—42no—
159C2×C8×C13—22no—
160C2×C8×C13—22no—
161C2×C8×C13—22no—
162C2×C8×C13—42no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—22no—
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—21no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4C2×D412yes—
184C13×C4⋊C4C2×D412yes—
185C13×C4⋊C4C2×D411yescharacteristic
186C13×C4⋊C4C2×D411yescharacteristic
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—21no—
199C42×C13—22no—
200C42×C13—21no—
201C42×C13C2×D411yescharacteristic
202C42×C13C2×D411yescharacteristic
203C42×C13C2×D411yescharacteristic
204C42×C13C2411yescharacteristic
205#3559C2×C1311yescharacteristic
206#3239C2×C1311yescharacteristic, complemented
207#3141C2×C1311yescharacteristic, complemented
208C2×#491C2×C1311yescharacteristic, complemented
209#1664C2×C1314yescomplemented
210#1662C2×C1314yescomplemented
211#1530C2×C1311yescharacteristic, complemented
212#1528C2×C1311yescharacteristic, complemented
213#1524C2×C1311yescharacteristic, complemented
214C23×C13—22no—
215C23×C13—21no—
216C23×C13#12011yescharacteristic
217Q8×C13—41no—
218Q8×C13—42no—
219Q8×C13—44no—
220Q8×C13—82no—
221Q8×C13—82no—
222D4×C13—41no—
223D4×C13—42no—
224D4×C13—44no—
225D4×C13—42no—
226D4×C13—42no—
227D4×C13—81no—
228D4×C13—82no—
229D4×C13—82no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—82no—
243C2×C4×C13—81no—
244C2×C4×C13—82no—
245C2×C4×C13—82no—
246C2×C4×C13—82no—
247C2×C4×C13—82no—
248C2×C4×C13#12011yescharacteristic
249C2×C4×C13#12011yescharacteristic
250C2×C4×C13#12011yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C8×C13—42no—
255C8×C13—42no—
256C8×C13—42no—
257#563C22×C1312yes—
258#562C22×C1312yes—
259#554—21no—
260#553—21no—
261#553—21no—
262#547—22no—
263#547—21no—
264#544—21no—
265#540—21no—
266#539—22no—
267#539—21no—
268#537—21no—
269#532C22×C1311yescharacteristic
270C2×C4⋊Q8C22×C1311yescharacteristic
271#529C22×C1311yescharacteristic
272C2×#125C22×C1311yescharacteristic
273#501C22×C1312yes—
274#491—22no—
275#491C22×C1314yes—
276#489C22×C1314yes—
277#489C22×C1312yes—
278#487—21no—
279#486—21no—
280#484—21no—
281#481—21no—
282#475—21no—
283#474—21no—
284#432C22×C1311yescharacteristic
285#417—22no—
286C2×#103—21no—
287C2×#103—21no—
288C4×M16C22×C1311yescharacteristic
289C2×#97C22×C1311yescharacteristic
290#330C22×C1314yes—
291#330C22×C1312yes—
292#329C22×C1312yes—
293#329C22×C1314yes—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—42no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—41no—
302C22×C13#45512yes—
303C22×C13C2×#12011yescharacteristic
304C4×C13—21no—
305C4×C13—21no—
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—42no—
310C4×C13—42no—
311C4×C13—41no—
312C4×C13—41no—
313C4×C13—42no—
314C4×C13—41no—
315C4×C13—82no—
316C4×C13#45412yes—
317C2×#41—22no—
318C2×#41D4×C1312yes—
319C22×Q8—21no—
320C2×M16—21no—
321C22×C8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—22no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8D4×C1311yescharacteristic
328C4⋊Q8C23×C1312yes—
329#127D4×C1311yescharacteristic
330#126—22no—
331#126—22no—
332#126—21no—
333#125—22no—
334#125—21no—
335#125—21no—
336#125—21no—
337#125D4×C1312yes—
338#125C23×C1312yes—
339#125C23×C1311yescharacteristic
340#124C23×C1311yescharacteristic
341#124C23×C1312yes—
342#123—22no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123—21no—
347#123—22no—
348#123—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8D4×C1311yescharacteristic
356#121—22no—
357#121—22no—
358#121—21no—
359#121—21no—
360#121—22no—
361#121—22no—
362#121—21no—
363#121—21no—
364#121D4×C1311yescharacteristic
365C4×Q8D4×C1311yescharacteristic
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4D4×C1311yescharacteristic
374#117—21no—
375#117—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4D4×C1311yescharacteristic
383C2×C4⋊C4D4×C1311yescharacteristic
384C2×C42C23×C1311yescharacteristic
385#107—22no—
386#106—22no—
387C4⋊C8—21no—
388#103—24no—
389#103—22no—
390#103—24no—
391#103—24no—
392#102—24no—
393#102—22no—
394C22⋊C8—21no—
395#97—21no—
396#97C23×C1312yes—
397#97C23×C1312yes—
398#97C23×C1312yes—
399C4×C8—21no—
400C2×C13—22no—
401C2×C13—82no—
402C2×C13—81no—
403C2×C13C2×#45511yescharacteristic
404C2×C13C2×#45411yescharacteristic
405C2×C13#302211yescharacteristic
406#41—44no—
407#41—84no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—41no—
412C2×Q8C2×D4×C1311yescharacteristic
413C2×Q8C2×D4×C1312yes—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4C2×D4×C1311yescharacteristic
421C2×D4C2×D4×C1312yes—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4C2×D4×C1311yescharacteristic
431C22×C4C2×D4×C1311yescharacteristic
432C22×C4C2×D4×C1311yescharacteristic
433M16—42no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—42no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4C2×D4×C1312yes—
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—22no—
473C22⋊C4—21no—
474C42—22no—
475C42—21no—
476C42C2×D4×C1311yescharacteristic
477C42C2×D4×C1311yescharacteristic
478C42C2×D4×C1311yescharacteristic
479C42C24×C1311yescharacteristic
480C13#1902311yescharacteristic, direct product factor, Sylow
481C23—22no—
482C23—21no—
483C23C13×#12011yescharacteristic
484Q8—42no—
485Q8—41no—
486Q8—44no—
487Q8—82no—
488Q8—82no—
489D4—41no—
490D4—42no—
491D4—44no—
492D4—42no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—81no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4C13×#12011yescharacteristic
516C2×C4C13×#12011yescharacteristic
517C2×C4C13×#12011yescharacteristic
518C2×C4C22×D4×C1311yescharacteristic
519C2×C4C22×D4×C1311yescharacteristic
520C2×C4C22×D4×C1311yescharacteristic
521C8—42no—
522C8—42no—
523C8—42no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22C13×#45512yes—
533C22C2×C13×#12011yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—42no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—41no—
545C4—82no—
546C4C13×#45412yes—
547C2—22no—
548C2—82no—
549C2—81no—
550C2C2×C13×#45511yescharacteristic
551C2C2×C13×#45411yescharacteristic
552C2C13×#302211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3559C2
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
2. C13×#3239C2semidirect
3. C13×#3141C2semidirect
4. C2×C13×#491C2semidirect
5. C13×#1664C2semidirect
6. C13×#1662C2semidirect
7. C13×#1530C2semidirect
8. C13×#1528C2semidirect
9. C13×#1524C2semidirect
130. #19023C13direct (N × H)
206. #3239C2×C13semidirect
207. #3141C2×C13semidirect
208. C2×#491C2×C13semidirect
209. #1664C2×C13semidirect
210. #1662C2×C13semidirect
211. #1530C2×C13semidirect
212. #1528C2×C13semidirect
213. #1524C2×C13semidirect
480. C13#19023direct (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×#31412
C2×C13×#4912
C13×#16642
C13×#16622
C13×#15302
C13×#15282
C13×#15242
#1902313