Finite Group Databasebeta

← C13×#15103 #15701442

Subgroups — C13×#15103 #15701442

Order 3328.

1462 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#400C211yesmaximal, characteristic, complemented
2C2×C13×#399C211yesmaximal, characteristic
3C2×C13×#388C211yesmaximal, characteristic
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5C13×#1441C211yesmaximal, characteristic, complemented
6C13×#1441C212yesmaximal, complemented
7C13×#1439C211yesmaximal, characteristic
8C13×#1439C212yesmaximal
9C13×#1437C212yesmaximal
10C13×#1436C212yesmaximal, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2212yes—
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2212yes—
24C13×#400—24no—
25C13×#399—24no—
26C13×#388—24no—
27C4×C13×C4⋊C4—24no—
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C25×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—24no—
59C2×C13×C4⋊C4—24no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—42no—
62C2×C13×C4⋊C4—42no—
63C2×C13×C4⋊C4D414yes—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—24no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—42no—
75C2×C13×C22⋊C4—42no—
76C2×C13×C22⋊C4—42no—
77C2×C13×C22⋊C4Q814yes—
78C2×C42×C13—24no—
79C2×C42×C13—24no—
80C2×C42×C13—42no—
81C2×C42×C13—42no—
82C2×C42×C13D414yes—
83C13×#95—24no—
84C13×#95—22no—
85C13×#95—22no—
86C13×#95—22no—
87C13×#95—24no—
88C13×#95—22no—
89C13×#95—24no—
90C13×#95—24no—
91C13×#95—24no—
92C13×#95—42no—
93C13×#95—42no—
94#15103C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—21no—
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—21no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13C2×Q812yes—
106C24×C13C2411yescharacteristic
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
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—21no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13C2×D414yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×Q812yes—
161C22×C4×C13C2×Q812yes—
162C22×C4×C13#4114yes—
163C22×C4×C13#4114yes—
164C22×C4×C13#4112yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4114yes—
167C13×C4⋊C4—28no—
168C13×C4⋊C4—28no—
169C13×C4⋊C4—48no—
170C13×C4⋊C4—48no—
171C13×C4⋊C4—44no—
172C13×C22⋊C4—28no—
173C13×C22⋊C4—48no—
174C13×C22⋊C4—48no—
175C13×C22⋊C4—44no—
176C13×C22⋊C4—44no—
177C42×C13—28no—
178C42×C13—48no—
179C2×#400C2×C1311yescharacteristic, complemented
180C2×#399C2×C1311yescharacteristic
181C2×#388C2×C1311yescharacteristic
182C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
183#1441C2×C1311yescharacteristic, complemented
184#1441C2×C1312yescomplemented
185#1439C2×C1311yescharacteristic
186#1439C2×C1312yes—
187#1437C2×C1312yes—
188#1436C2×C1312yescomplemented
189C4⋊#95C2×C1311yescharacteristic, complemented
190C23×C13—22no—
191C23×C13—24no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—24no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—41no—
201C23×C13—42no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—41no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—42no—
213C23×C13C22×D411yescharacteristic
214C23×C13C22×D411yescharacteristic
215C23×C13C22×Q811yescharacteristic
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C23×C13C2×#4112yes—
219C23×C13C2×#4112yes—
220C23×C13C2×#4112yes—
221C23×C13H(5,𝔽2)12yes—
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C132−1+411yescharacteristic
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—22no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—41no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—41no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—41no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13#12114yes—
282C2×C4×C13C22⋊Q814yes—
283C2×C4×C13#12314yes—
284C22×C4⋊C4C22×C1311yescharacteristic
285C22×C4⋊C4C22×C1311yescharacteristic
286C22×C4⋊C4C22×C1312yes—
287C22×C4⋊C4C22×C1312yes—
288C22×C4⋊C4C22×C1311yescharacteristic
289C22×C22⋊C4C22×C1311yescharacteristic
290C22×C22⋊C4C22×C1311yescharacteristic
291C22×C22⋊C4C22×C1312yes—
292C22×C22⋊C4C22×C1311yescharacteristic
293C22×C22⋊C4C22×C1312yes—
294C22×C42C22×C1311yescharacteristic
295C22×C42C22×C1312yes—
296#400—24no—
297#399—24no—
298#388—24no—
299C4×C4⋊C4—24no—
300C2×#95C22×C1311yescharacteristic
301C2×#95C22×C1311yescharacteristic
302C2×#95C22×C1312yes—
303C2×#95C22×C1312yes—
304C2×#95C22×C1312yes—
305C2×#95C22×C1311yescharacteristic
306C2×#95C22×C1312yes—
307C2×#95C22×C1312yes—
308C2×#95C22×C1311yescharacteristic
309C2×#95C22×C1312yes—
310C2×#95C22×C1312yes—
311C22×C13—44no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—44no—
316C22×C13—82no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13—82no—
322C22×C13C2×#12111yescharacteristic
323C22×C13C2×C22⋊Q811yescharacteristic
324C22×C13C2×#12311yescharacteristic
325C22×C13#52511yescharacteristic
326C22×C13#52912yes—
327C22×C13#52912yes—
328C22×C13#53212yes—
329C22×C13#53211yescharacteristic
330C22×C13#53312yes—
331C22×C13#53511yescharacteristic
332C22×C13#53711yescharacteristic
333C22×C13#53812yes—
334C22×C13#53912yes—
335C22×C13#54612yes—
336C22×C13D4×Q811yescharacteristic
337C22×C13#55011yescharacteristic
338C22×C13#55112yes—
339C22×C13#55212yes—
340C22×C13#55312yes—
341C22×C13#55411yescharacteristic
342C22×C13#55412yes—
343C22×C13#55611yescharacteristic
344C22×C13#55912yes—
345C4×C13—24no—
346C4×C13—24no—
347C4×C13—24no—
348C4×C13—44no—
349C4×C13—42no—
350C4×C13—44no—
351C4×C13—44no—
352C4×C13—81no—
353C4×C13—81no—
354C4×C13—82no—
355C25C23×C1311yescharacteristic
356C23×C4C23×C1311yescharacteristic
357C23×C4C23×C1312yes—
358C23×C4C23×C1311yescharacteristic
359C23×C4C23×C1312yes—
360C23×C4C23×C1311yescharacteristic
361C23×C4C23×C1312yes—
362C23×C4C23×C1312yes—
363C23×C4C23×C1311yescharacteristic
364C23×C4C23×C1311yescharacteristic
365C23×C4C23×C1311yescharacteristic
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4D4×C1314yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4Q8×C1314yes—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42D4×C1314yes—
399#95—24no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—24no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—42no—
409#95—42no—
410C2×C13—82no—
411C2×C13#239611yescharacteristic
412C2×C13#248711yescharacteristic
413C2×C13#249811yescharacteristic
414C2×C13#253811yescharacteristic
415C2×C13#254411yescharacteristic
416C2×C13#255412yes—
417C2×C13#255612yes—
418C2×C13#258912yes—
419C2×C13#259612yes—
420C2×C13#263611yescharacteristic
421C2×C13#285411yescharacteristic
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24C2×Q8×C1312yes—
433C24C24×C1311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4C2×D4×C1314yes—
483C22×C4C2×D4×C1312yes—
484C22×C4C2×D4×C1312yes—
485C22×C4C2×D4×C1312yes—
486C22×C4C2×D4×C1312yes—
487C22×C4C2×Q8×C1312yes—
488C22×C4C2×Q8×C1312yes—
489C22×C4C13×#4114yes—
490C22×C4C13×#4114yes—
491C22×C4C13×#4112yes—
492C22×C4C13×#4112yes—
493C22×C4C13×#4114yes—
494C4⋊C4—28no—
495C4⋊C4—28no—
496C4⋊C4—48no—
497C4⋊C4—48no—
498C4⋊C4—44no—
499C22⋊C4—28no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C42—28no—
505C42—48no—
506C13#1510311yescharacteristic, direct product factor, Sylow
507C23—22no—
508C23—24no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23C22×D4×C1311yescharacteristic
531C23C22×D4×C1311yescharacteristic
532C23C22×Q8×C1311yescharacteristic
533C23C2×C13×#4111yescharacteristic
534C23C2×C13×#4111yescharacteristic
535C23C2×C13×#4112yes—
536C23C2×C13×#4112yes—
537C23C2×C13×#4112yes—
538C23C13×H(5,𝔽2)12yes—
539C23C13×H(5,𝔽2)11yescharacteristic
540C23C13×2−1+411yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4C13×#12114yes—
599C2×C4C13×C22⋊Q814yes—
600C2×C4C13×#12314yes—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—81no—
607C22—81no—
608C22—82no—
609C22—82no—
610C22—81no—
611C22—81no—
612C22C2×C13×#12111yescharacteristic
613C22C2×C13×C22⋊Q811yescharacteristic
614C22C2×C13×#12311yescharacteristic
615C22C13×#52511yescharacteristic
616C22C13×#52912yes—
617C22C13×#52912yes—
618C22C13×#53211yescharacteristic
619C22C13×#53212yes—
620C22C13×#53312yes—
621C22C13×#53511yescharacteristic
622C22C13×#53711yescharacteristic
623C22C13×#53812yes—
624C22C13×#53912yes—
625C22C13×#54612yes—
626C22D4×Q8×C1311yescharacteristic
627C22C13×#55011yescharacteristic
628C22C13×#55112yes—
629C22C13×#55212yes—
630C22C13×#55312yes—
631C22C13×#55411yescharacteristic
632C22C13×#55412yes—
633C22C13×#55611yescharacteristic
634C22C13×#55912yes—
635C4—24no—
636C4—24no—
637C4—24no—
638C4—42no—
639C4—44no—
640C4—44no—
641C4—44no—
642C4—81no—
643C4—82no—
644C4—81no—
645C2—82no—
646C2C13×#239611yescharacteristic
647C2C13×#248711yescharacteristic
648C2C13×#249811yescharacteristic
649C2C13×#253811yescharacteristic
650C2C13×#254411yescharacteristic
651C2C13×#255412yes—
652C2C13×#255612yes—
653C2C13×#258912yes—
654C2C13×#259612yes—
655C2C13×#263611yescharacteristic
656C2C13×#285411yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#400C2semidirect
4. C2×C4×C13×C4⋊C4C2semidirect
5. C13×#1441C2semidirect
6. C13×#1441C2semidirect
10. C13×#1436C2semidirect
11. C13×C4⋊#95C2semidirect
94. #15103C13direct (N × H)
179. C2×#400C2×C13semidirect
182. C2×C4×C4⋊C4C2×C13semidirect
183. #1441C2×C13semidirect
184. #1441C2×C13semidirect
188. #1436C2×C13semidirect
189. C4⋊#95C2×C13semidirect
506. C13#15103direct (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×#3992
C2×C13×#3882
C2×C4×C13×C4⋊C42
C13×#14412
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
#1510313