Finite Group Databasebeta

← C13×#24003 #15710342

Subgroups — C13×#24003 #15710342

Order 3328.

1500 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#483C212yesmaximal, complemented
3C2×C13×#380C211yesmaximal, characteristic
4C13×#2035C214yesmaximal, complemented
5C13×#1872C212yesmaximal, complemented
6C13×#1853C212yesmaximal, complemented
7C13×#1787C212yesmaximal, complemented
8C13×#1779C211yesmaximal, characteristic
9C23×Q8×C13C2211yescharacteristic
10C24×C4×C13C2211yescharacteristic
11C2×C13×C22⋊Q8—21no—
12C2×C13×C22⋊Q8—21no—
13C2×C13×C22⋊Q8—28no—
14C2×C13×C22⋊Q8C2212yes—
15C2×C13×C22⋊Q8C2212yes—
16C22×C13×C4⋊C4—21no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4—21no—
21C22×C13×C22⋊C4—21no—
22C13×#483—28no—
23C2×C13×#106C2214yescomplemented
24C2×C13×#103C2214yescomplemented
25C2×C13×#103C2214yescomplemented
26C2×C13×C22⋊C8C2212yes—
27C2×C13×C22⋊C8C2212yes—
28C2×C13×C22⋊C8C2212yes—
29C13×#380—21no—
30C13×#380—21no—
31C13×#380C2212yes—
32C13×#380C2212yes—
33C2×C13×#95—21no—
34C13×#340C2214yescomplemented
35C25×C13D411yescharacteristic
36C22×Q8×C13—24no—
37C22×Q8×C13—21no—
38C22×Q8×C13—24no—
39C22×Q8×C13—42no—
40C22×Q8×C13C2312yes—
41C23×C4×C13—21no—
42C23×C4×C13—21no—
43C23×C4×C13—24no—
44C23×C4×C13—24no—
45C23×C4×C13—21no—
46C23×C4×C13—21no—
47C23×C4×C13—42no—
48C23×C4×C13D411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C22×C8×C13C2314yes—
55C13×C22⋊Q8—28no—
56C13×C22⋊Q8—28no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—24no—
59C13×C22⋊Q8—24no—
60C13×C22⋊Q8D418yes—
61C2×C13×C4⋊C4—28no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—24no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—42no—
70C2×C13×C4⋊C4C2312yes—
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C22⋊C4—28no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—44no—
79C13×#106—28no—
80C13×#103—28no—
81C13×#103—44no—
82C13×C22⋊C8—24no—
83C13×C22⋊C8—24no—
84C13×C22⋊C8—42no—
85C13×#95—22no—
86C13×#95—22no—
87#24003C1311yesmaximal, characteristic, direct product factor, Sylow
88C24×C13—22no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—41no—
93C24×C13—41no—
94C24×C13SD1614yes—
95C24×C13C2×D411yescharacteristic
96C24×C13C2×D411yescharacteristic
97C24×C13C2×D411yescharacteristic
98C2×Q8×C13—24no—
99C2×Q8×C13—22no—
100C2×Q8×C13—24no—
101C2×Q8×C13—24no—
102C2×Q8×C13—416no—
103C2×Q8×C13—42no—
104C2×Q8×C13—42no—
105C2×Q8×C13C2×D414yes—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—24no—
111C22×C4×C13—24no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—416no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D414yes—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13#4114yes—
144C22×C4×C13C2411yescharacteristic
145C2×C8×C13—24no—
146C2×C8×C13—24no—
147C2×C8×C13—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—28no—
150C13×C4⋊C4—28no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4C2×D414yes—
157C13×C22⋊C4—28no—
158C13×C22⋊C4—28no—
159C13×C22⋊C4—44no—
160C13×C22⋊C4—44no—
161C22×C22⋊Q8C2×C1311yescharacteristic
162C2×#483C2×C1312yescomplemented
163C2×#380C2×C1311yescharacteristic
164#2035C2×C1314yescomplemented
165#1872C2×C1312yescomplemented
166#1853C2×C1312yescomplemented
167#1787C2×C1312yescomplemented
168#1779C2×C1311yescharacteristic
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13—21no—
173C23×C13—21no—
174C23×C13—21no—
175C23×C13—21no—
176C23×C13—21no—
177C23×C13—21no—
178C23×C13—21no—
179C23×C13—21no—
180C23×C13—21no—
181C23×C13—21no—
182C23×C13—21no—
183C23×C13—28no—
184C23×C13—28no—
185C23×C13—44no—
186C23×C13—44no—
187C23×C13—44no—
188C23×C13—44no—
189C23×C13—44no—
190C23×C13#12012yes—
191C23×C13#12312yes—
192C23×C13C2×SD1612yes—
193C23×C13C2×SD1612yes—
194C23×C13C2×SD1612yes—
195C23×C13#13712yes—
196C23×C13#13712yes—
197C23×C13C22×D411yescharacteristic
198Q8×C13—28no—
199Q8×C13—48no—
200Q8×C13—44no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—28no—
206C2×C4×C13—28no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—44no—
213C2×C4×C13—44no—
214C2×C4×C13—44no—
215C2×C4×C13—48no—
216C2×C4×C13—48no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—44no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—84no—
229C2×C4×C13—84no—
230C2×C4×C13#12012yes—
231C2×C4×C13#12312yes—
232C2×C4×C13C22×D412yes—
233C2×C4×C13C2×#4112yes—
234C2×C4×C13H(5,𝔽2)12yes—
235C8×C13—44no—
236C23×Q8C22×C1311yescharacteristic
237C24×C4C22×C1311yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—28no—
241C2×C22⋊Q8C22×C1312yes—
242C2×C22⋊Q8C22×C1312yes—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C22×C1311yescharacteristic
245C22×C4⋊C4C22×C1311yescharacteristic
246C22×C4⋊C4C22×C1311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249#483—28no—
250C2×#106C22×C1314yescomplemented
251C2×#103C22×C1314yescomplemented
252C2×#103C22×C1314yescomplemented
253C2×C22⋊C8C22×C1312yes—
254C2×C22⋊C8C22×C1312yes—
255C2×C22⋊C8C22×C1312yes—
256#380—21no—
257#380—21no—
258#380C22×C1312yes—
259#380C22×C1312yes—
260C2×#95—21no—
261#340C22×C1314yescomplemented
262C22×C13—22no—
263C22×C13—22no—
264C22×C13—22no—
265C22×C13—22no—
266C22×C13—22no—
267C22×C13—22no—
268C22×C13—22no—
269C22×C13—22no—
270C22×C13—22no—
271C22×C13—22no—
272C22×C13—22no—
273C22×C13—22no—
274C22×C13—22no—
275C22×C13—22no—
276C22×C13—22no—
277C22×C13—416no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13#44814yes—
283C22×C13#48314yescomplemented
284C22×C13C2×#12011yescharacteristic
285C22×C13C2×#12311yescharacteristic
286C22×C13#53411yescharacteristic
287C22×C13C22×SD1611yescharacteristic
288C22×C13C2×#13711yescharacteristic
289C22×C13C2×#13711yescharacteristic
290C22×C13#57511yescharacteristic
291C4×C13—22no—
292C4×C13—22no—
293C4×C13—41no—
294C4×C13—44no—
295C4×C13—44no—
296C4×C13—82no—
297C4×C13—82no—
298C4×C13#54614yes—
299C25D4×C1311yescharacteristic
300C22×Q8—24no—
301C22×Q8—21no—
302C22×Q8—24no—
303C22×Q8—42no—
304C22×Q8C23×C1312yes—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—24no—
308C23×C4—24no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—42no—
312C23×C4D4×C1311yescharacteristic
313C23×C4D4×C1311yescharacteristic
314C23×C4D4×C1311yescharacteristic
315C23×C4C23×C1311yescharacteristic
316C23×C4C23×C1311yescharacteristic
317C23×C4C23×C1311yescharacteristic
318C22×C8C23×C1314yes—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8D4×C1318yes—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4C23×C1312yes—
335C2×C4⋊C4C23×C1312yes—
336C2×C4⋊C4C23×C1312yes—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—44no—
343#106—28no—
344#103—28no—
345#103—44no—
346C22⋊C8—24no—
347C22⋊C8—24no—
348C22⋊C8—42no—
349#95—22no—
350#95—22no—
351C2×C13—24no—
352C2×C13—24no—
353C2×C13—42no—
354C2×C13#240511yescharacteristic
355C2×C13C2×#44811yescharacteristic
356C2×C13#300711yescharacteristic
357C2×C13C2×#48311yescharacteristic
358C2×C13#309511yescharacteristic
359C2×C13#318711yescharacteristic
360C2×C13#319511yescharacteristic
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—41no—
366C24—41no—
367C24C13×SD1614yes—
368C24C2×D4×C1311yescharacteristic
369C24C2×D4×C1311yescharacteristic
370C24C2×D4×C1311yescharacteristic
371C2×Q8—24no—
372C2×Q8—22no—
373C2×Q8—24no—
374C2×Q8—24no—
375C2×Q8—416no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8C2×D4×C1314yes—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—416no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4C2×D4×C1311yescharacteristic
413C22×C4C2×D4×C1311yescharacteristic
414C22×C4C2×D4×C1314yes—
415C22×C4C2×D4×C1311yescharacteristic
416C22×C4C13×#4114yes—
417C22×C4C24×C1311yescharacteristic
418C2×C8—24no—
419C2×C8—24no—
420C2×C8—24no—
421C4⋊C4—24no—
422C4⋊C4—28no—
423C4⋊C4—28no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—42no—
428C4⋊C4—42no—
429C4⋊C4C2×D4×C1314yes—
430C22⋊C4—28no—
431C22⋊C4—28no—
432C22⋊C4—44no—
433C22⋊C4—44no—
434C13#2400311yescharacteristic, direct product factor, Sylow
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—28no—
444C23—28no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—44no—
452C23—44no—
453C23—44no—
454C23—44no—
455C23—44no—
456C23C13×#12012yes—
457C23C13×#12312yes—
458C23C2×C13×SD1612yes—
459C23C2×C13×SD1612yes—
460C23C2×C13×SD1612yes—
461C23C13×#13712yes—
462C23C13×#13712yes—
463C23C22×D4×C1311yescharacteristic
464Q8—28no—
465Q8—48no—
466Q8—44no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—28no—
472C2×C4—28no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—48no—
482C2×C4—48no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4—84no—
496C2×C4C13×#12012yes—
497C2×C4C13×#12312yes—
498C2×C4C22×D4×C1312yes—
499C2×C4C2×C13×#4112yes—
500C2×C4C13×H(5,𝔽2)12yes—
501C8—44no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—416no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22C13×#44814yes—
523C22C13×#48314yescomplemented
524C22C2×C13×#12011yescharacteristic
525C22C2×C13×#12311yescharacteristic
526C22C13×#53411yescharacteristic
527C22C22×C13×SD1611yescharacteristic
528C22C2×C13×#13711yescharacteristic
529C22C2×C13×#13711yescharacteristic
530C22C13×#57511yescharacteristic
531C4—22no—
532C4—22no—
533C4—44no—
534C4—41no—
535C4—44no—
536C4—82no—
537C4—82no—
538C4C13×#54614yes—
539C2—24no—
540C2—24no—
541C2—42no—
542C2C13×#240511yescharacteristic
543C2C2×C13×#44811yescharacteristic
544C2C13×#300711yescharacteristic
545C2C2×C13×#48311yescharacteristic
546C2C13×#309511yescharacteristic
547C2C13×#318711yescharacteristic
548C2C13×#319511yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#483C2semidirect
4. C13×#2035C2semidirect
5. C13×#1872C2semidirect
6. C13×#1853C2semidirect
7. C13×#1787C2semidirect
23. C2×C13×#106C22semidirect
24. C2×C13×#103C22semidirect
25. C2×C13×#103C22semidirect
34. C13×#340C22semidirect
87. #24003C13direct (N × H)
162. C2×#483C2×C13semidirect
164. #2035C2×C13semidirect
165. #1872C2×C13semidirect
166. #1853C2×C13semidirect
167. #1787C2×C13semidirect
250. C2×#106C22×C13semidirect
251. C2×#103C22×C13semidirect
252. C2×#103C22×C13semidirect
261. #340C22×C13semidirect
283. C22×C13#483semidirect
434. C13#24003direct (N × H)
523. C22C13×#483semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#4832
C2×C13×#3802
C13×#20352
C13×#18722
C13×#18532
C13×#17872
C13×#17792
#2400313