Finite Group Databasebeta

← C13×#24107 #15710446

Subgroups — C13×#24107 #15710446

Order 3328.

1082 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#556C211yesmaximal, characteristic
2C2×C13×#484C211yesmaximal, characteristic, complemented
3C2×C13×#428C211yesmaximal, characteristic, complemented
4C13×#2486C211yesmaximal, characteristic
5C13×#2057C212yesmaximal, complemented
6C13×#2036C212yesmaximal, complemented
7C13×#1894C211yesmaximal, characteristic, complemented
8C13×#1870C211yesmaximal, characteristic
9C13×#1865C212yesmaximal, complemented
10C13×#1854C212yesmaximal, complemented
11C13×#1825C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C13×#556—24no—
14C13×#556—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#126—21no—
17C2×C13×#126—21no—
18C2×C13×#124—21no—
19C2×C13×#123—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C13—21no—
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×D4×C13C2211yescharacteristic
25C2×C13×#117C2211yescharacteristic
26C2×C13×#117C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C13×#484—24no—
29C13×#428—24no—
30C2×C13×#107C2212yes—
31C2×C13×#107C2212yes—
32C2×C13×#106C2212yes—
33C2×C13×#103C2212yes—
34C2×C13×#103C2212yes—
35C2×C13×C22⋊C8C2212yes—
36C2×C13×C22⋊C8C2211yescharacteristic
37C13×#398—21no—
38C13×#397—21no—
39C13×#389C2212yes—
40C13×#381—21no—
41C13×#380C2212yes—
42C13×#380C2211yescharacteristic
43C13×#340C2212yes—
44C13×#340C2212yes—
45C13×#340C2212yes—
46C13×#336C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13C2311yescharacteristic
49C22×D4×C13D411yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C2×C13×M16—22no—
54C2×C13×M16—24no—
55C22×C8×C13C2312yes—
56C22×C8×C13C2312yes—
57C13×C4⋊Q8—22no—
58C13×C4⋊Q8—22no—
59C13×#126—28no—
60C13×#126—28no—
61C13×#124—28no—
62C13×#123—44no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8D414yes—
67C4×Q8×C13—28no—
68C4×Q8×C13—22no—
69C4×Q8×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C13×#117—22no—
73C13×#117—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—21no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C4⋊C4C2312yes—
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4D411yescharacteristic
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C42×C13—21no—
99C2×C42×C13—21no—
100C2×C42×C13—21no—
101C2×C42×C13C2311yescharacteristic
102C13×#107—24no—
103C13×#107—24no—
104C13×#106—24no—
105C13×#103—24no—
106C13×#103—24no—
107C13×C22⋊C8—22no—
108C13×C22⋊C8—24no—
109C13×#95—22no—
110C13×#95—21no—
111C13×#95—22no—
112#24107C1311yesmaximal, characteristic, direct product factor, Sylow
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C2×Q8×C13—24no—
116C2×Q8×C13—21no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—42no—
120C2×Q8×C13—42no—
121C2×Q8×C13C2×D412yes—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—41no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C13×M16—28no—
148C2×C8×C13—22no—
149C2×C8×C13—22no—
150C2×C8×C13—22no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13#4114yes—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—44no—
168C13×C4⋊C4C2×D412yes—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×D412yes—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—44no—
179C42×C13—24no—
180C42×C13—24no—
181C42×C13—24no—
182C42×C13—21no—
183C42×C13—21no—
184C2×#556C2×C1311yescharacteristic
185C2×#484C2×C1311yescharacteristic, complemented
186C2×#428C2×C1311yescharacteristic, complemented
187#2486C2×C1311yescharacteristic
188#2057C2×C1312yescomplemented
189#2036C2×C1312yescomplemented
190#1894C2×C1311yescharacteristic, complemented
191#1870C2×C1311yescharacteristic
192#1865C2×C1312yescomplemented
193#1854C2×C1312yescomplemented
194#1825C2×C1311yescharacteristic, complemented
195C23×C13—22no—
196C23×C13—21no—
197C23×C13—21no—
198C23×C13—22no—
199C23×C13—21no—
200C23×C13—22no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—22no—
204C23×C13#12012yes—
205C23×C13C22×D411yescharacteristic
206Q8×C13—24no—
207Q8×C13—48no—
208Q8×C13—41no—
209Q8×C13—41no—
210D4×C13—44no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—84no—
241C2×C4×C13#12012yes—
242C2×C4×C13AGL(1,ℤ/8)12yes—
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4112yes—
246C2×C4×C132−1+412yes—
247C8×C13—24no—
248C8×C13—42no—
249C22×M16C22×C1311yescharacteristic
250#556—24no—
251#556—24no—
252C2×C4⋊Q8C22×C1311yescharacteristic
253C2×#126—21no—
254C2×#126—21no—
255C2×#124—21no—
256C2×#123—21no—
257C2×C22⋊Q8C22×C1311yescharacteristic
258C2×C22⋊Q8C22×C1311yescharacteristic
259C2×C4×Q8—21no—
260C2×C4×Q8C22×C1311yescharacteristic
261C2×C4×D4C22×C1311yescharacteristic
262C2×#117C22×C1311yescharacteristic
263C2×#117C22×C1311yescharacteristic
264C22×C4⋊C4C22×C1311yescharacteristic
265#484—24no—
266#428—24no—
267C2×#107C22×C1312yes—
268C2×#107C22×C1312yes—
269C2×#106C22×C1312yes—
270C2×#103C22×C1312yes—
271C2×#103C22×C1312yes—
272C2×C22⋊C8C22×C1311yescharacteristic
273C2×C22⋊C8C22×C1312yes—
274#398—21no—
275#397—21no—
276#389C22×C1312yes—
277#381—21no—
278#380C22×C1311yescharacteristic
279#380C22×C1312yes—
280#340C22×C1312yes—
281#340C22×C1312yes—
282#340C22×C1312yes—
283#336C22×C1312yes—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—22no—
287C22×C13—42no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—41no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13C2×#12011yescharacteristic
295C22×C13#54712yes—
296C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C13#57511yescharacteristic
298C22×C13#57812yes—
299C4×C13—22no—
300C4×C13—22no—
301C4×C13—41no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—41no—
306C4×C13—42no—
307C4×C13—82no—
308C4×C13—82no—
309C4×C13#52511yescharacteristic
310C4×C13#53611yescharacteristic
311C4×C13#54712yes—
312C22×Q8—21no—
313C22×Q8C23×C1311yescharacteristic
314C22×D4D4×C1311yescharacteristic
315C23×C4—21no—
316C23×C4C23×C1311yescharacteristic
317C23×C4C23×C1311yescharacteristic
318C2×M16—22no—
319C2×M16—24no—
320C22×C8C23×C1312yes—
321C22×C8C23×C1312yes—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324#126—28no—
325#126—28no—
326#124—28no—
327#123—44no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8D4×C1314yes—
332C4×Q8—28no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×D4—22no—
336C4×D4—22no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117D4×C1314yes—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4D4×C1311yescharacteristic
350C2×C4⋊C4C23×C1312yes—
351C2×C4⋊C4C23×C1312yes—
352C2×C4⋊C4C23×C1311yescharacteristic
353C2×C4⋊C4C23×C1311yescharacteristic
354C2×C4⋊C4C23×C1311yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4D4×C1311yescharacteristic
362C2×C22⋊C4D4×C1311yescharacteristic
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42C23×C1311yescharacteristic
367#107—24no—
368#107—24no—
369#106—24no—
370#103—24no—
371#103—24no—
372C22⋊C8—22no—
373C22⋊C8—24no—
374#95—22no—
375#95—21no—
376#95—22no—
377C2×C13—42no—
378C2×C13—81no—
379C2×C13#240611yescharacteristic
380C2×C13#300611yescharacteristic
381C2×C13#301111yescharacteristic
382C2×C13#334912yes—
383C2×C13#335312yes—
384C24C2×D4×C1311yescharacteristic
385C24C2×D4×C1311yescharacteristic
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8C2×D4×C1312yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—41no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4C2×D4×C1311yescharacteristic
412C22×C4C2×D4×C1311yescharacteristic
413C22×C4C2×D4×C1311yescharacteristic
414C22×C4C2×D4×C1312yes—
415C22×C4C2×D4×C1312yes—
416C22×C4C2×D4×C1311yescharacteristic
417C22×C4C24×C1311yescharacteristic
418M16—28no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8C13×#4114yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—42no—
438C4⋊C4—44no—
439C4⋊C4C2×D4×C1312yes—
440C4⋊C4C2×D4×C1312yes—
441C4⋊C4C2×D4×C1312yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—42no—
449C22⋊C4—44no—
450C42—24no—
451C42—24no—
452C42—24no—
453C42—21no—
454C42—21no—
455C13#2410711yescharacteristic, direct product factor, Sylow
456C23—22no—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—21no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23C13×#12012yes—
466C23C22×D4×C1311yescharacteristic
467Q8—24no—
468Q8—48no—
469Q8—41no—
470Q8—41no—
471D4—44no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4C13×#12012yes—
503C2×C4C13×AGL(1,ℤ/8)12yes—
504C2×C4C22×D4×C1311yescharacteristic
505C2×C4C22×D4×C1311yescharacteristic
506C2×C4C2×C13×#4112yes—
507C2×C4C13×2−1+412yes—
508C8—24no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—41no—
517C22—42no—
518C22—42no—
519C22—41no—
520C22C2×C13×#12011yescharacteristic
521C22C13×#54712yes—
522C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
523C22C13×#57511yescharacteristic
524C22C13×#57812yes—
525C4—22no—
526C4—22no—
527C4—42no—
528C4—42no—
529C4—41no—
530C4—42no—
531C4—41no—
532C4—42no—
533C4—82no—
534C4—82no—
535C4C13×#52511yescharacteristic
536C4C13×#53611yescharacteristic
537C4C13×#54712yes—
538C2—42no—
539C2—81no—
540C2C13×#240611yescharacteristic
541C2C13×#300611yescharacteristic
542C2C13×#301111yescharacteristic
543C2C13×#334912yes—
544C2C13×#335312yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×D4×C13D4
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×#484C2semidirect
3. C2×C13×#428C2semidirect
5. C13×#2057C2semidirect
6. C13×#2036C2semidirect
7. C13×#1894C2semidirect
9. C13×#1865C2semidirect
10. C13×#1854C2semidirect
11. C13×#1825C2semidirect
112. #24107C13direct (N × H)
185. C2×#484C2×C13semidirect
186. C2×#428C2×C13semidirect
188. #2057C2×C13semidirect
189. #2036C2×C13semidirect
190. #1894C2×C13semidirect
192. #1865C2×C13semidirect
193. #1854C2×C13semidirect
194. #1825C2×C13semidirect
455. C13#24107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5562
C2×C13×#4842
C2×C13×#4282
C13×#24862
C13×#20572
C13×#20362
C13×#18942
C13×#18702
C13×#18652
C13×#18542
C13×#18252
#2410713