Finite Group Databasebeta

← C13×#14626 #15700965

Subgroups — C13×#14626 #15700965

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#395C211yesmaximal, characteristic
2C2×C13×#391C211yesmaximal, characteristic
3C2×C13×#387C211yesmaximal, characteristic
4C13×#1446C211yesmaximal, characteristic
5C13×#1445C212yesmaximal
6C13×#1443C212yesmaximal
7C13×#1443C212yesmaximal
8C13×#1442C211yesmaximal, characteristic
9C13×#1441C211yesmaximal, characteristic
10C13×#1441C212yesmaximal
11C13×#1434C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2212yes—
17C22×C42×C13C2211yescharacteristic
18C13×#395C418yescomplemented
19C13×#391—24no—
20C13×#387—24no—
21C2×C13×#95C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2212yes—
38C22×Q8×C13—22no—
39C22×Q8×C13—22no—
40C22×Q8×C13—42no—
41C22×Q8×C13—42no—
42C22×Q8×C13C2×C414yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—42no—
59C2×C13×C4⋊C4—42no—
60C2×C13×C4⋊C4—42no—
61C2×C13×C4⋊C4—42no—
62C2×C13×C4⋊C4C2×C414yes—
63C2×C13×C4⋊C4C2×C418yes—
64C2×C42×C13—42no—
65C2×C42×C13D414yes—
66C13×#95—22no—
67C13×#95—22no—
68C13×#95—22no—
69C13×#95—22no—
70C13×#95—24no—
71C13×#95—24no—
72C13×#95—22no—
73C13×#95—42no—
74C13×#95—42no—
75C13×#95—42no—
76C13×#95—42no—
77C13×#95—42no—
78C13×#95—42no—
79C13×#95—42no—
80C13×#95—42no—
81C13×#95C2×C418yes—
82C13×#95C2×C414yes—
83#14626C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13C2411yescharacteristic
85C2×Q8×C13—28no—
86C2×Q8×C13—48no—
87C2×Q8×C13—44no—
88C2×Q8×C13—44no—
89C2×Q8×C13—48no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
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—22no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—21no—
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—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C22×C414yes—
148C22×C4×C13C22×C414yes—
149C22×C4×C13C22×C412yes—
150C22×C4×C13C22×C412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13#4112yes—
155C13×C4⋊C4—28no—
156C13×C4⋊C4—48no—
157C13×C4⋊C4—44no—
158C13×C4⋊C4—44no—
159C42×C13—44no—
160C2×#395C2×C1311yescharacteristic
161C2×#391C2×C1311yescharacteristic
162C2×#387C2×C1311yescharacteristic
163#1446C2×C1311yescharacteristic
164#1445C2×C1312yes—
165#1443C2×C1312yes—
166#1443C2×C1312yes—
167#1442C2×C1311yescharacteristic
168#1441C2×C1311yescharacteristic
169#1441C2×C1312yes—
170#1434C2×C1311yescharacteristic
171C23×C13C23×C411yescharacteristic
172C23×C13C22×D411yescharacteristic
173C23×C13C2×#4111yescharacteristic
174C23×C13H(5,𝔽2)12yes—
175C23×C13H(5,𝔽2)12yes—
176C23×C13H(5,𝔽2)11yescharacteristic
177C23×C132−1+412yes—
178C23×C132−1+412yes—
179C23×C132−1+411yescharacteristic
180C23×C132−1+411yescharacteristic
181C23×C132−1+411yescharacteristic
182Q8×C13—416no—
183C2×C4×C13—24no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—24no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—24no—
193C2×C4×C13—24no—
194C2×C4×C13—22no—
195C2×C4×C13—24no—
196C2×C4×C13—22no—
197C2×C4×C13—24no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—41no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—42no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
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—41no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
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—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×C13C4×D414yes—
248C23×Q8C22×C1311yescharacteristic
249C22×C4⋊C4C22×C1311yescharacteristic
250C22×C4⋊C4C22×C1311yescharacteristic
251C22×C4⋊C4C22×C1311yescharacteristic
252C22×C4⋊C4C22×C1312yes—
253C22×C42C22×C1311yescharacteristic
254#395C4×C1318yescomplemented
255#391—24no—
256#387—24no—
257C2×#95C22×C1311yescharacteristic
258C2×#95C22×C1312yes—
259C2×#95C22×C1311yescharacteristic
260C2×#95C22×C1311yescharacteristic
261C2×#95C22×C1311yescharacteristic
262C2×#95C22×C1312yes—
263C2×#95C22×C1311yescharacteristic
264C2×#95C22×C1312yes—
265C2×#95C22×C1312yes—
266C2×#95C22×C1312yes—
267C2×#95C22×C1312yes—
268C2×#95C22×C1312yes—
269C2×#95C22×C1312yes—
270C2×#95C22×C1312yes—
271C2×#95C22×C1312yes—
272C2×#95C22×C1311yescharacteristic
273C2×#95C22×C1312yes—
274C22×C13C2×C4×D411yescharacteristic
275C22×C13#51812yes—
276C22×C13#51911yescharacteristic
277C22×C13#51912yes—
278C22×C13#52011yescharacteristic
279C22×C13#53411yescharacteristic
280C22×C13#53511yescharacteristic
281C22×C13#53611yescharacteristic
282C22×C13#53611yescharacteristic
283C22×C13#53611yescharacteristic
284C22×C13#53711yescharacteristic
285C22×C13#53812yes—
286C22×C13#54112yes—
287C22×C13#54111yescharacteristic
288C22×C13#54211yescharacteristic
289C22×C13#56212yes—
290C22×C13#56212yes—
291C22×C13#56312yes—
292C22×C13#56312yes—
293C22×C13#56312yes—
294C22×C13#56312yes—
295C22×C13#56312yes—
296C22×C13#56312yes—
297C4×C13—24no—
298C4×C13—42no—
299C4×C13—42no—
300C4×C13—44no—
301C4×C13—42no—
302C4×C13—44no—
303C4×C13—42no—
304C4×C13—82no—
305C4×C13—81no—
306C4×C13—82no—
307C4×C13—81no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—42no—
311C22×Q8—42no—
312C22×Q8C2×C4×C1314yes—
313C23×C4C23×C1311yescharacteristic
314C23×C4C23×C1312yes—
315C23×C4C23×C1311yescharacteristic
316C23×C4C23×C1312yes—
317C23×C4C23×C1311yescharacteristic
318C23×C4C23×C1312yes—
319C23×C4C23×C1311yescharacteristic
320C23×C4C23×C1312yes—
321C23×C4C23×C1311yescharacteristic
322C23×C4C23×C1311yescharacteristic
323C23×C4C23×C1311yescharacteristic
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4C2×C4×C1314yes—
333C2×C4⋊C4C2×C4×C1318yes—
334C2×C42—42no—
335C2×C42D4×C1314yes—
336#95—22no—
337#95—22no—
338#95—22no—
339#95—22no—
340#95—24no—
341#95—24no—
342#95—22no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95C2×C4×C1318yes—
352#95C2×C4×C1314yes—
353C2×C13#232111yescharacteristic
354C2×C13#232311yescharacteristic
355C2×C13#232711yescharacteristic
356C2×C13#237812yes—
357C2×C13#238112yes—
358C2×C13#281411yescharacteristic
359C2×C13#281711yescharacteristic
360C2×C13#282011yescharacteristic
361C2×C13#282111yescharacteristic
362C2×C13#283112yes—
363C2×C13#283312yes—
364C24C24×C1311yescharacteristic
365C2×Q8—28no—
366C2×Q8—48no—
367C2×Q8—44no—
368C2×Q8—44no—
369C2×Q8—48no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
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—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
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—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4C22×C4×C1312yes—
427C22×C4C22×C4×C1314yes—
428C22×C4C22×C4×C1314yes—
429C22×C4C22×C4×C1312yes—
430C22×C4C22×C4×C1312yes—
431C22×C4C2×D4×C1312yes—
432C22×C4C2×D4×C1312yes—
433C22×C4C2×D4×C1312yes—
434C22×C4C13×#4112yes—
435C4⋊C4—28no—
436C4⋊C4—48no—
437C4⋊C4—44no—
438C4⋊C4—44no—
439C42—44no—
440C13#1462611yescharacteristic, direct product factor, Sylow
441C23C23×C4×C1311yescharacteristic
442C23C22×D4×C1311yescharacteristic
443C23C2×C13×#4111yescharacteristic
444C23C13×H(5,𝔽2)12yes—
445C23C13×H(5,𝔽2)12yes—
446C23C13×H(5,𝔽2)11yescharacteristic
447C23C13×2−1+412yes—
448C23C13×2−1+412yes—
449C23C13×2−1+411yescharacteristic
450C23C13×2−1+411yescharacteristic
451C23C13×2−1+411yescharacteristic
452Q8—416no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4C4×D4×C1314yes—
518C22C2×C4×D4×C1311yescharacteristic
519C22C13×#51812yes—
520C22C13×#51911yescharacteristic
521C22C13×#51912yes—
522C22C13×#52011yescharacteristic
523C22C13×#53411yescharacteristic
524C22C13×#53511yescharacteristic
525C22C13×#53611yescharacteristic
526C22C13×#53611yescharacteristic
527C22C13×#53611yescharacteristic
528C22C13×#53711yescharacteristic
529C22C13×#53812yes—
530C22C13×#54112yes—
531C22C13×#54111yescharacteristic
532C22C13×#54211yescharacteristic
533C22C13×#56212yes—
534C22C13×#56212yes—
535C22C13×#56312yes—
536C22C13×#56312yes—
537C22C13×#56312yes—
538C22C13×#56312yes—
539C22C13×#56312yes—
540C22C13×#56312yes—
541C4—24no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—44no—
546C4—42no—
547C4—44no—
548C4—81no—
549C4—82no—
550C4—81no—
551C4—82no—
552C2C13×#232111yescharacteristic
553C2C13×#232311yescharacteristic
554C2C13×#232711yescharacteristic
555C2C13×#237812yes—
556C2C13×#238112yes—
557C2C13×#281411yescharacteristic
558C2C13×#281711yescharacteristic
559C2C13×#282011yescharacteristic
560C2C13×#282111yescharacteristic
561C2C13×#283112yes—
562C2C13×#283312yes—
subgroupG/H
center, socle, prime radicalC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
18. C13×#395C4semidirect
83. #14626C13direct (N × H)
254. #395C4×C13semidirect
440. C13#14626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3952
C2×C13×#3912
C2×C13×#3872
C13×#14462
C13×#14452
C13×#14432
C13×#14422
C13×#14412
C13×#14342
#1462613