Finite Group Databasebeta

← C13×#14409 #15700748

Subgroups — C13×#14409 #15700748

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#387C212yesmaximal, complemented
2C2×C13×#385C211yesmaximal, characteristic
3C2×C13×#380C212yesmaximal
4C13×#1442C212yesmaximal, complemented
5C13×#1441C212yesmaximal, complemented
6C13×#1440C212yesmaximal
7C13×#1437C211yesmaximal, characteristic
8C13×#1437C211yesmaximal, characteristic
9C13×#1436C212yesmaximal, complemented
10C24×C4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C13×#387—28no—
21C13×#385C418yescomplemented
22C13×#380—28no—
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C25×C13C2311yescharacteristic
35C23×C4×C13—24no—
36C23×C4×C13—24no—
37C23×C4×C13—41no—
38C23×C4×C13—41no—
39C23×C4×C13C2×C414yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C2×C13×C4⋊C4—24no—
49C2×C13×C4⋊C4—24no—
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4C2×C418yes—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—41no—
63C2×C13×C22⋊C4—41no—
64C2×C13×C22⋊C4—42no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4C2×C414yes—
67C2×C13×C22⋊C4C2×C414yes—
68C2×C42×C13—24no—
69C2×C42×C13—41no—
70C2×C42×C13—42no—
71C2×C42×C13—41no—
72C13×#95—24no—
73C13×#95—24no—
74C13×#95—24no—
75C13×#95—24no—
76C13×#95—42no—
77C13×#95—42no—
78C13×#95—42no—
79C13×#95—41no—
80C13×#95—41no—
81C13×#95C2×C418yes—
82C13×#95D418yes—
83#14409C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13—22no—
85C24×C13—22no—
86C24×C13—22no—
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13C22×C412yes—
92C24×C13#4114yes—
93C24×C13C2411yescharacteristic
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
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—216no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—44no—
140C22×C4×C13—44no—
141C22×C4×C13—48no—
142C22×C4×C13—44no—
143C22×C4×C13C22×C412yes—
144C22×C4×C13C22×C414yes—
145C22×C4×C13C22×C412yes—
146C22×C4×C13C22×C414yes—
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2×D414yes—
150C22×C4×C13#4114yes—
151C13×C4⋊C4—216no—
152C13×C4⋊C4—48no—
153C13×C4⋊C4—48no—
154C13×C22⋊C4—28no—
155C13×C22⋊C4—44no—
156C13×C22⋊C4—48no—
157C13×C22⋊C4—48no—
158C42×C13—44no—
159C42×C13—44no—
160C2×#387C2×C1312yescomplemented
161C2×#385C2×C1311yescharacteristic
162C2×#380C2×C1312yes—
163#1442C2×C1312yescomplemented
164#1441C2×C1312yescomplemented
165#1440C2×C1312yes—
166#1437C2×C1311yescharacteristic
167#1437C2×C1311yescharacteristic
168#1436C2×C1312yescomplemented
169C23×C13—24no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—24no—
173C23×C13—24no—
174C23×C13—24no—
175C23×C13—24no—
176C23×C13—24no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—41no—
184C23×C13—42no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—42no—
188C23×C13—41no—
189C23×C13#11714yes—
190C23×C13C23×C411yescharacteristic
191C23×C13C22×D412yes—
192C23×C13C2×#4112yes—
193C23×C13C2×#4112yes—
194C23×C13H(5,𝔽2)11yescharacteristic
195C23×C13H(5,𝔽2)11yescharacteristic
196C23×C13H(5,𝔽2)12yes—
197C23×C132−1+412yes—
198C23×C132−1+412yes—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—416no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—41no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
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—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13C4×D418yes—
252C24×C4C22×C1311yescharacteristic
253C22×C4⋊C4C22×C1312yes—
254C22×C4⋊C4C22×C1312yes—
255C22×C4⋊C4C22×C1312yes—
256C22×C22⋊C4C22×C1312yes—
257C22×C22⋊C4C22×C1312yes—
258C22×C22⋊C4C22×C1311yescharacteristic
259C22×C22⋊C4C22×C1311yescharacteristic
260C22×C42C22×C1311yescharacteristic
261C22×C42C22×C1311yescharacteristic
262#387—28no—
263#385C4×C1318yescomplemented
264#380—28no—
265C2×#95C22×C1312yes—
266C2×#95C22×C1312yes—
267C2×#95C22×C1312yes—
268C2×#95C22×C1312yes—
269C2×#95C22×C1312yes—
270C2×#95C22×C1312yes—
271C2×#95C22×C1311yescharacteristic
272C2×#95C22×C1311yescharacteristic
273C2×#95C22×C1312yes—
274C2×#95C22×C1312yes—
275C2×#95C22×C1312yes—
276C22×C13—24no—
277C22×C13—28no—
278C22×C13—44no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—44no—
282C22×C13—44no—
283C22×C13—44no—
284C22×C13—44no—
285C22×C13C2×#11711yescharacteristic
286C22×C13C2×C4×D412yes—
287C22×C13#51811yescharacteristic
288C22×C13#51911yescharacteristic
289C22×C13#52012yes—
290C22×C13#53612yes—
291C22×C13#53712yes—
292C22×C13#53912yes—
293C22×C13#53912yes—
294C22×C13#54112yes—
295C22×C13#54212yes—
296C22×C13D4211yescharacteristic
297C22×C13#54612yes—
298C22×C13#54612yes—
299C22×C13#54812yes—
300C22×C13#55111yescharacteristic
301C22×C13#55212yes—
302C22×C13#55312yes—
303C22×C13#56011yescharacteristic
304C22×C13#56212yes—
305C22×C13#56311yescharacteristic
306C4×C13—28no—
307C4×C13—44no—
308C4×C13—42no—
309C4×C13—42no—
310C4×C13—44no—
311C4×C13—44no—
312C4×C13—82no—
313C4×C13—82no—
314C25C23×C1311yescharacteristic
315C23×C4—24no—
316C23×C4—24no—
317C23×C4—41no—
318C23×C4—41no—
319C23×C4C2×C4×C1314yes—
320C23×C4C23×C1312yes—
321C23×C4C23×C1312yes—
322C23×C4C23×C1311yescharacteristic
323C23×C4C23×C1312yes—
324C23×C4C23×C1311yescharacteristic
325C23×C4C23×C1312yes—
326C23×C4C23×C1312yes—
327C23×C4C23×C1312yes—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4C2×C4×C1318yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4C2×C4×C1314yes—
347C2×C22⋊C4C2×C4×C1314yes—
348C2×C42—24no—
349C2×C42—41no—
350C2×C42—42no—
351C2×C42—41no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—41no—
360#95—41no—
361#95C2×C4×C1318yes—
362#95D4×C1318yes—
363C2×C13—44no—
364C2×C13#231311yescharacteristic
365C2×C13#232312yes—
366C2×C13#235212yes—
367C2×C13#235811yescharacteristic
368C2×C13#237611yescharacteristic
369C2×C13#268112yes—
370C2×C13#269012yes—
371C2×C13#269112yes—
372C2×C13#274712yes—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—22no—
379C24—22no—
380C24C22×C4×C1312yes—
381C24C13×#4114yes—
382C24C24×C1311yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
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—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—216no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—48no—
431C22×C4—44no—
432C22×C4C22×C4×C1312yes—
433C22×C4C22×C4×C1314yes—
434C22×C4C22×C4×C1312yes—
435C22×C4C22×C4×C1314yes—
436C22×C4C2×D4×C1314yes—
437C22×C4C2×D4×C1314yes—
438C22×C4C2×D4×C1314yes—
439C22×C4C13×#4114yes—
440C4⋊C4—216no—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C22⋊C4—28no—
444C22⋊C4—44no—
445C22⋊C4—48no—
446C22⋊C4—48no—
447C42—44no—
448C42—44no—
449C13#1440911yescharacteristic, direct product factor, Sylow
450C23—24no—
451C23—22no—
452C23—22no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—41no—
470C23C13×#11714yes—
471C23C23×C4×C1311yescharacteristic
472C23C22×D4×C1312yes—
473C23C2×C13×#4112yes—
474C23C2×C13×#4112yes—
475C23C13×H(5,𝔽2)11yescharacteristic
476C23C13×H(5,𝔽2)11yescharacteristic
477C23C13×H(5,𝔽2)12yes—
478C23C13×2−1+412yes—
479C23C13×2−1+412yes—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4C4×D4×C1318yes—
533C22—24no—
534C22—28no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22C2×C13×#11711yescharacteristic
543C22C2×C4×D4×C1312yes—
544C22C13×#51811yescharacteristic
545C22C13×#51911yescharacteristic
546C22C13×#52012yes—
547C22C13×#53612yes—
548C22C13×#53712yes—
549C22C13×#53912yes—
550C22C13×#53912yes—
551C22C13×#54112yes—
552C22C13×#54212yes—
553C22D42×C1311yescharacteristic
554C22C13×#54612yes—
555C22C13×#54612yes—
556C22C13×#54812yes—
557C22C13×#55111yescharacteristic
558C22C13×#55212yes—
559C22C13×#55312yes—
560C22C13×#56011yescharacteristic
561C22C13×#56212yes—
562C22C13×#56311yescharacteristic
563C4—28no—
564C4—44no—
565C4—42no—
566C4—42no—
567C4—44no—
568C4—44no—
569C4—82no—
570C4—82no—
571C2—44no—
572C2C13×#231311yescharacteristic
573C2C13×#232312yes—
574C2C13×#235212yes—
575C2C13×#235811yescharacteristic
576C2C13×#237611yescharacteristic
577C2C13×#268112yes—
578C2C13×#269012yes—
579C2C13×#269112yes—
580C2C13×#274712yes—
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#387C2semidirect
4. C13×#1442C2semidirect
5. C13×#1441C2semidirect
9. C13×#1436C2semidirect
21. C13×#385C4semidirect
83. #14409C13direct (N × H)
160. C2×#387C2×C13semidirect
163. #1442C2×C13semidirect
164. #1441C2×C13semidirect
168. #1436C2×C13semidirect
263. #385C4×C13semidirect
449. C13#14409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3872
C2×C13×#3852
C2×C13×#3802
C13×#14422
C13×#14412
C13×#14402
C13×#14372
C13×#14362
#1440913