Finite Group Databasebeta

← C13×#14318 #15700657

Subgroups — C13×#14318 #15700657

Order 3328.

1254 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×#400C211yesmaximal, characteristic
2C2×C13×#389C211yesmaximal, characteristic
3C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
4C13×#1445C211yesmaximal, characteristic
5C13×#1444C212yesmaximal
6C13×#1444C211yesmaximal, characteristic
7C13×#1442C212yesmaximal
8C13×#1441C211yesmaximal, characteristic
9C13×#1436C212yesmaximal
10C13×#1434C212yesmaximal
11C13×#1434C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C4⋊C4C2212yes—
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C13×#400C418yescomplemented
22C13×#389—24no—
23C4×C13×C4⋊C4—24no—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2212yes—
38C23×C4×C13C2312yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—24no—
59C2×C13×C4⋊C4—42no—
60C2×C13×C4⋊C4—42no—
61C2×C13×C4⋊C4—42no—
62C2×C13×C4⋊C4—42no—
63C2×C13×C4⋊C4—42no—
64C2×C13×C4⋊C4C2×C414yes—
65C2×C13×C4⋊C4C2×C414yes—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13—42no—
70C2×C42×C13—42no—
71C2×C42×C13D414yes—
72C2×C42×C13Q814yes—
73C13×#95—22no—
74C13×#95—22no—
75C13×#95—24no—
76C13×#95—24no—
77C13×#95—22no—
78C13×#95—24no—
79C13×#95—42no—
80C13×#95—42no—
81C13×#95—42no—
82C13×#95—42no—
83C13×#95—42no—
84C13×#95C2×C414yes—
85C13×#95C2×C418yes—
86C13×#95C2×C418yes—
87#14318C1311yesmaximal, characteristic, direct product factor, Sylow
88C24×C13C2411yescharacteristic
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
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—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×C13C22×C414yes—
140C22×C4×C13C22×C412yes—
141C22×C4×C13C22×C414yes—
142C22×C4×C13C22×C412yes—
143C22×C4×C13C22×C412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×Q812yes—
148C22×C4×C13C2×Q812yes—
149C22×C4×C13C2×Q812yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C13×C4⋊C4—28no—
155C13×C4⋊C4—28no—
156C13×C4⋊C4—28no—
157C13×C4⋊C4—44no—
158C13×C4⋊C4—48no—
159C13×C4⋊C4—48no—
160C42×C13—28no—
161C42×C13—44no—
162C42×C13—44no—
163C2×#400C2×C1311yescharacteristic
164C2×#389C2×C1311yescharacteristic
165C2×C4×C4⋊C4C2×C1311yescharacteristic
166#1445C2×C1311yescharacteristic
167#1444C2×C1312yes—
168#1444C2×C1311yescharacteristic
169#1442C2×C1312yes—
170#1441C2×C1311yescharacteristic
171#1436C2×C1312yes—
172#1434C2×C1311yescharacteristic
173#1434C2×C1312yes—
174C23×C13C23×C411yescharacteristic
175C23×C13C22×D411yescharacteristic
176C23×C13C22×Q811yescharacteristic
177C23×C13C2×#4111yescharacteristic
178C23×C13C2×#4111yescharacteristic
179C23×C13C2×#4111yescharacteristic
180C23×C13C2×#4111yescharacteristic
181C23×C13H(5,𝔽2)12yes—
182C23×C13H(5,𝔽2)12yes—
183C23×C132−1+412yes—
184C23×C132−1+412yes—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—24no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—24no—
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—22no—
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—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—41no—
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—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
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—
248C2×C4×C13C4×Q814yes—
249C2×C4×C13C22⋊Q814yes—
250C22×C4⋊C4C22×C1311yescharacteristic
251C22×C4⋊C4C22×C1311yescharacteristic
252C22×C4⋊C4C22×C1311yescharacteristic
253C22×C4⋊C4C22×C1312yes—
254C22×C4⋊C4C22×C1311yescharacteristic
255C22×C4⋊C4C22×C1312yes—
256C22×C42C22×C1311yescharacteristic
257C22×C42C22×C1311yescharacteristic
258C22×C42C22×C1311yescharacteristic
259#400C4×C1318yescomplemented
260#389—24no—
261C4×C4⋊C4—24no—
262C2×#95C22×C1312yes—
263C2×#95C22×C1312yes—
264C2×#95C22×C1312yes—
265C2×#95C22×C1311yescharacteristic
266C2×#95C22×C1311yescharacteristic
267C2×#95C22×C1311yescharacteristic
268C2×#95C22×C1312yes—
269C2×#95C22×C1312yes—
270C2×#95C22×C1312yes—
271C2×#95C22×C1312yes—
272C2×#95C22×C1312yes—
273C2×#95C22×C1312yes—
274C2×#95C22×C1311yescharacteristic
275C2×#95C22×C1312yes—
276C22×C13C2×C4×D411yescharacteristic
277C22×C13C2×C4×Q811yescharacteristic
278C22×C13C4×#4111yescharacteristic
279C22×C13#52012yes—
280C22×C13#52012yes—
281C22×C13C2×C22⋊Q811yescharacteristic
282C22×C13#52511yescharacteristic
283C22×C13#52911yescharacteristic
284C22×C13#53311yescharacteristic
285C22×C13#53411yescharacteristic
286C22×C13#53511yescharacteristic
287C22×C13#53611yescharacteristic
288C22×C13#53611yescharacteristic
289C22×C13#53812yes—
290C22×C13#53912yes—
291C22×C13#53912yes—
292C22×C13#54012yes—
293C22×C13#54112yes—
294C22×C13#54112yes—
295C22×C13#54212yes—
296C22×C13#54212yes—
297C22×C13#54412yes—
298C22×C13#54412yes—
299C4×C13—24no—
300C4×C13—24no—
301C4×C13—24no—
302C4×C13—42no—
303C4×C13—44no—
304C4×C13—44no—
305C4×C13—42no—
306C4×C13—42no—
307C4×C13—42no—
308C4×C13—82no—
309C4×C13—82no—
310C23×C4C23×C1312yes—
311C23×C4C23×C1312yes—
312C23×C4C23×C1312yes—
313C23×C4C23×C1312yes—
314C23×C4C23×C1311yescharacteristic
315C23×C4C23×C1311yescharacteristic
316C23×C4C23×C1311yescharacteristic
317C23×C4C23×C1311yescharacteristic
318C23×C4C23×C1311yescharacteristic
319C23×C4C23×C1311yescharacteristic
320C23×C4C23×C1311yescharacteristic
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4C2×C4×C1314yes—
337C2×C4⋊C4C2×C4×C1314yes—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42D4×C1314yes—
344C2×C42Q8×C1314yes—
345#95—22no—
346#95—22no—
347#95—24no—
348#95—24no—
349#95—22no—
350#95—24no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95C2×C4×C1314yes—
357#95C2×C4×C1318yes—
358#95C2×C4×C1318yes—
359C2×C13C4×C22⋊Q811yescharacteristic
360C2×C13#232211yescharacteristic
361C2×C13#232611yescharacteristic
362C2×C13#233012yes—
363C2×C13#233412yes—
364C2×C13#262711yescharacteristic
365C2×C13#262811yescharacteristic
366C2×C13#263411yescharacteristic
367C2×C13#263511yescharacteristic
368C2×C13#265412yes—
369C2×C13#266612yes—
370C24C24×C1311yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
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—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
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—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4C22×C4×C1314yes—
422C22×C4C22×C4×C1314yes—
423C22×C4C22×C4×C1312yes—
424C22×C4C22×C4×C1312yes—
425C22×C4C22×C4×C1312yes—
426C22×C4C2×D4×C1312yes—
427C22×C4C2×D4×C1312yes—
428C22×C4C2×D4×C1312yes—
429C22×C4C2×Q8×C1312yes—
430C22×C4C2×Q8×C1312yes—
431C22×C4C2×Q8×C1312yes—
432C22×C4C13×#4112yes—
433C22×C4C13×#4112yes—
434C22×C4C13×#4112yes—
435C22×C4C13×#4112yes—
436C4⋊C4—28no—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—44no—
440C4⋊C4—48no—
441C4⋊C4—48no—
442C42—28no—
443C42—44no—
444C42—44no—
445C13#1431811yescharacteristic, direct product factor, Sylow
446C23C23×C4×C1311yescharacteristic
447C23C22×D4×C1311yescharacteristic
448C23C22×Q8×C1311yescharacteristic
449C23C2×C13×#4111yescharacteristic
450C23C2×C13×#4111yescharacteristic
451C23C2×C13×#4111yescharacteristic
452C23C2×C13×#4111yescharacteristic
453C23C13×H(5,𝔽2)12yes—
454C23C13×H(5,𝔽2)12yes—
455C23C13×2−1+412yes—
456C23C13×2−1+412yes—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
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—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×C4—42no—
518C2×C4—42no—
519C2×C4C4×D4×C1314yes—
520C2×C4C4×Q8×C1314yes—
521C2×C4C13×C22⋊Q814yes—
522C22C2×C4×D4×C1311yescharacteristic
523C22C2×C4×Q8×C1311yescharacteristic
524C22C4×C13×#4111yescharacteristic
525C22C13×#52012yes—
526C22C13×#52012yes—
527C22C2×C13×C22⋊Q811yescharacteristic
528C22C13×#52511yescharacteristic
529C22C13×#52911yescharacteristic
530C22C13×#53311yescharacteristic
531C22C13×#53411yescharacteristic
532C22C13×#53511yescharacteristic
533C22C13×#53611yescharacteristic
534C22C13×#53611yescharacteristic
535C22C13×#53812yes—
536C22C13×#53912yes—
537C22C13×#53912yes—
538C22C13×#54012yes—
539C22C13×#54112yes—
540C22C13×#54112yes—
541C22C13×#54212yes—
542C22C13×#54212yes—
543C22C13×#54412yes—
544C22C13×#54412yes—
545C4—24no—
546C4—24no—
547C4—24no—
548C4—42no—
549C4—44no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—82no—
556C2C4×C13×C22⋊Q811yescharacteristic
557C2C13×#232211yescharacteristic
558C2C13×#232611yescharacteristic
559C2C13×#233012yes—
560C2C13×#233412yes—
561C2C13×#262711yescharacteristic
562C2C13×#262811yescharacteristic
563C2C13×#263411yescharacteristic
564C2C13×#263511yescharacteristic
565C2C13×#265412yes—
566C2C13×#266612yes—
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
21. C13×#400C4semidirect
87. #14318C13direct (N × H)
259. #400C4×C13semidirect
445. C13#14318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4002
C2×C13×#3892
C2×C4×C13×C4⋊C42
C13×#14452
C13×#14442
C13×#14422
C13×#14412
C13×#14362
C13×#14342
#1431813