Finite Group Databasebeta

← C13×#24102 #15710441

Subgroups — C13×#24102 #15710441

Order 3328.

1132 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#553C211yesmaximal, characteristic
2C2×C13×#480C211yesmaximal, characteristic, complemented
3C2×C13×#428C211yesmaximal, characteristic, complemented
4C13×#2487C211yesmaximal, characteristic, complemented
5C13×#2059C212yesmaximal, complemented
6C13×#2034C212yesmaximal, complemented
7C13×#1895C211yesmaximal, characteristic, complemented
8C13×#1870C211yesmaximal, characteristic, complemented
9C13×#1862C212yesmaximal, complemented
10C13×#1852C212yesmaximal, complemented
11C13×#1825C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C13×#553—24no—
14C13×#553—24no—
15C2×C13×#126—21no—
16C2×C13×#125C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×#121—21no—
19C2×C13×#121C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C13×#480—24no—
28C13×#428—24no—
29C2×C13×#107C2212yes—
30C2×C13×#107C2212yes—
31C2×C13×#106C2212yes—
32C2×C13×#102C2212yes—
33C2×C13×#102C2212yes—
34C2×C13×C22⋊C8C2212yes—
35C2×C13×C22⋊C8C2211yescharacteristic
36C13×#400—21no—
37C13×#399—21no—
38C13×#389C2212yes—
39C13×#386—21no—
40C13×#385—21no—
41C13×#380C2212yes—
42C13×#380C2211yescharacteristic
43C13×#340C2212yes—
44C13×#340C2212yes—
45C13×#340C2212yes—
46C13×#336C2212yes—
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13D411yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13—21no—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C2×C13×M16—22no—
57C2×C13×M16—24no—
58C22×C8×C13C2312yes—
59C22×C8×C13C2312yes—
60C13×#126—28no—
61C13×#125—22no—
62C13×#125—22no—
63C13×#123—28no—
64C13×#121—28no—
65C13×#121—22no—
66C13×#121—22no—
67C13×#121—22no—
68C13×#121D414yes—
69C4×D4×C13—28no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C13×#117—22no—
75C13×#117D414yes—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4D411yescharacteristic
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C42×C13—21no—
100C2×C42×C13C2311yescharacteristic
101C13×#107—24no—
102C13×#107—24no—
103C13×#106—24no—
104C13×#102—24no—
105C13×#102—24no—
106C13×C22⋊C8—22no—
107C13×C22⋊C8—24no—
108C13×#95—22no—
109C13×#95—21no—
110C13×#95—22no—
111#24102C1311yesmaximal, characteristic, direct product factor, Sylow
112C24×C13—21no—
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C2×D4×C13—24no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—24no—
119C2×D4×C13—21no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—41no—
123C2×D4×C13—42no—
124C2×D4×C13—42no—
125C2×D4×C13—82no—
126C2×D4×C13C2×D412yes—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—42no—
141C22×C4×C13—82no—
142C22×C4×C13—82no—
143C22×C4×C13—82no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2411yescharacteristic
151C13×M16—28no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C2×C8×C13—22no—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C2×C8×C13#4114yes—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—82no—
171C13×C4⋊C4C2×D412yes—
172C13×C4⋊C4C2×D412yes—
173C13×C4⋊C4C2×D412yes—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—24no—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—24no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—42no—
181C13×C22⋊C4—82no—
182C42×C13—24no—
183C42×C13—21no—
184C42×C13—21no—
185C2×#553C2×C1311yescharacteristic
186C2×#480C2×C1311yescharacteristic, complemented
187C2×#428C2×C1311yescharacteristic, complemented
188#2487C2×C1311yescharacteristic, complemented
189#2059C2×C1312yescomplemented
190#2034C2×C1312yescomplemented
191#1895C2×C1311yescharacteristic, complemented
192#1870C2×C1311yescharacteristic, complemented
193#1862C2×C1312yescomplemented
194#1852C2×C1312yescomplemented
195#1825C2×C1311yescharacteristic, complemented
196C23×C13—21no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—42no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—42no—
209C23×C13#12012yes—
210C23×C13#13712yes—
211C23×C13C22×D411yescharacteristic
212D4×C13—24no—
213D4×C13—44no—
214D4×C13—48no—
215D4×C13—41no—
216D4×C13—41no—
217D4×C13—84no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—22no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—84no—
246C2×C4×C13—84no—
247C2×C4×C13—84no—
248C2×C4×C13#12012yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C2×#4112yes—
252C2×C4×C132−1+412yes—
253C8×C13—24no—
254C8×C13—42no—
255C22×M16C22×C1311yescharacteristic
256#553—24no—
257#553—24no—
258C2×#126—21no—
259C2×#125C22×C1311yescharacteristic
260C2×#123—21no—
261C2×#121—21no—
262C2×#121C22×C1311yescharacteristic
263C2×#121C22×C1311yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C22×C1311yescharacteristic
266C2×C4×D4C22×C1311yescharacteristic
267C2×#117C22×C1311yescharacteristic
268C22×C4⋊C4C22×C1311yescharacteristic
269C22×C4⋊C4C22×C1311yescharacteristic
270#480—24no—
271#428—24no—
272C2×#107C22×C1312yes—
273C2×#107C22×C1312yes—
274C2×#106C22×C1312yes—
275C2×#102C22×C1312yes—
276C2×#102C22×C1312yes—
277C2×C22⋊C8C22×C1311yescharacteristic
278C2×C22⋊C8C22×C1312yes—
279#400—21no—
280#399—21no—
281#389C22×C1312yes—
282#386—21no—
283#385—21no—
284#380C22×C1311yescharacteristic
285#380C22×C1312yes—
286#340C22×C1312yes—
287#340C22×C1312yes—
288#340C22×C1312yes—
289#336C22×C1312yes—
290C22×C13—24no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13—22no—
294C22×C13—22no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—82no—
304C22×C13—82no—
305C22×C13C2×#12011yescharacteristic
306C22×C13#54712yes—
307C22×C13C2×#13711yescharacteristic
308C22×C13#57511yescharacteristic
309C22×C13#57612yes—
310C4×C13—22no—
311C4×C13—41no—
312C4×C13—41no—
313C4×C13—42no—
314C4×C13—41no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—82no—
318C4×C13—82no—
319C4×C13#52511yescharacteristic
320C4×C13#53611yescharacteristic
321C4×C13#54712yes—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4D4×C1311yescharacteristic
325C22×D4C23×C1311yescharacteristic
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4C23×C1311yescharacteristic
330C23×C4C23×C1311yescharacteristic
331C2×M16—22no—
332C2×M16—24no—
333C22×C8C23×C1312yes—
334C22×C8C23×C1312yes—
335#126—28no—
336#125—22no—
337#125—22no—
338#123—28no—
339#121—28no—
340#121—22no—
341#121—22no—
342#121—22no—
343#121D4×C1314yes—
344C4×D4—28no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349#117—22no—
350#117D4×C1314yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4D4×C1311yescharacteristic
361C2×C4⋊C4C23×C1312yes—
362C2×C4⋊C4C23×C1312yes—
363C2×C4⋊C4C23×C1311yescharacteristic
364C2×C4⋊C4C23×C1311yescharacteristic
365C2×C4⋊C4C23×C1311yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4D4×C1311yescharacteristic
373C2×C22⋊C4D4×C1311yescharacteristic
374C2×C42—21no—
375C2×C42C23×C1311yescharacteristic
376#107—24no—
377#107—24no—
378#106—24no—
379#102—24no—
380#102—24no—
381C22⋊C8—22no—
382C22⋊C8—24no—
383#95—22no—
384#95—21no—
385#95—22no—
386C2×C13—42no—
387C2×C13—42no—
388C2×C13—82no—
389C2×C13#240611yescharacteristic
390C2×C13#300711yescharacteristic
391C2×C13#300811yescharacteristic
392C2×C13#334612yes—
393C2×C13#335512yes—
394C24—21no—
395C24C2×D4×C1311yescharacteristic
396C24C2×D4×C1311yescharacteristic
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—24no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—82no—
408C2×D4C2×D4×C1312yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—82no—
424C22×C4—82no—
425C22×C4—82no—
426C22×C4C2×D4×C1311yescharacteristic
427C22×C4C2×D4×C1311yescharacteristic
428C22×C4C2×D4×C1311yescharacteristic
429C22×C4C2×D4×C1311yescharacteristic
430C22×C4C2×D4×C1312yes—
431C22×C4C2×D4×C1312yes—
432C22×C4C24×C1311yescharacteristic
433M16—28no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8C13×#4114yes—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—82no—
453C4⋊C4C2×D4×C1312yes—
454C4⋊C4C2×D4×C1312yes—
455C4⋊C4C2×D4×C1312yes—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—42no—
463C22⋊C4—82no—
464C42—24no—
465C42—21no—
466C42—21no—
467C13#2410211yescharacteristic, direct product factor, Sylow
468C23—21no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—42no—
481C23C13×#12012yes—
482C23C13×#13712yes—
483C23C22×D4×C1311yescharacteristic
484D4—24no—
485D4—44no—
486D4—48no—
487D4—41no—
488D4—41no—
489D4—84no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4C13×#12012yes—
521C2×C4C22×D4×C1311yescharacteristic
522C2×C4C22×D4×C1311yescharacteristic
523C2×C4C2×C13×#4112yes—
524C2×C4C13×2−1+412yes—
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—24no—
531C22—22no—
532C22—41no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—82no—
541C22—82no—
542C22C2×C13×#12011yescharacteristic
543C22C13×#54712yes—
544C22C2×C13×#13711yescharacteristic
545C22C13×#57511yescharacteristic
546C22C13×#57612yes—
547C4—22no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—42no—
552C4—42no—
553C4—41no—
554C4—82no—
555C4—82no—
556C4C13×#52511yescharacteristic
557C4C13×#53611yescharacteristic
558C4C13×#54712yes—
559C2—42no—
560C2—42no—
561C2—82no—
562C2C13×#240611yescharacteristic
563C2C13×#300711yescharacteristic
564C2C13×#300811yescharacteristic
565C2C13×#334612yes—
566C2C13×#335512yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#480C2semidirect
3. C2×C13×#428C2semidirect
4. C13×#2487C2semidirect
5. C13×#2059C2semidirect
6. C13×#2034C2semidirect
7. C13×#1895C2semidirect
8. C13×#1870C2semidirect
9. C13×#1862C2semidirect
10. C13×#1852C2semidirect
11. C13×#1825C2semidirect
111. #24102C13direct (N × H)
186. C2×#480C2×C13semidirect
187. C2×#428C2×C13semidirect
188. #2487C2×C13semidirect
189. #2059C2×C13semidirect
190. #2034C2×C13semidirect
191. #1895C2×C13semidirect
192. #1870C2×C13semidirect
193. #1862C2×C13semidirect
194. #1852C2×C13semidirect
195. #1825C2×C13semidirect
467. C13#24102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5532
C2×C13×#4802
C2×C13×#4282
C13×#24872
C13×#20592
C13×#20342
C13×#18952
C13×#18702
C13×#18622
C13×#18522
C13×#18252
#2410213