Finite Group Databasebeta

← C13×#15078 #15701417

Subgroups — C13×#15078 #15701417

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#388C212yesmaximal
2C2×C13×#388C211yesmaximal, characteristic
3C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
4C13×#1444C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1441C212yesmaximal, complemented
7C13×#1440C212yesmaximal
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1434C212yesmaximal, complemented
11C13×#1434C211yesmaximal, characteristic, complemented
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2212yes—
22C22×C42×C13C2211yescharacteristic
23C13×#388—28no—
24C13×#388—24no—
25C4×C13×C4⋊C4—24no—
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2212yes—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C25×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—42no—
57C2×C13×C4⋊C4—42no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—42no—
70C2×C13×C22⋊C4—42no—
71C2×C13×C22⋊C4D414yes—
72C2×C42×C13—22no—
73C2×C42×C13—22no—
74C2×C42×C13—24no—
75C2×C42×C13—24no—
76C2×C42×C13—24no—
77C2×C42×C13D414yes—
78C13×#95—24no—
79C13×#95—24no—
80C13×#95—24no—
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—22no—
84C13×#95—24no—
85C13×#95—24no—
86C13×#95—24no—
87C13×#95—22no—
88C13×#95—42no—
89C13×#95—42no—
90#15078C1311yesmaximal, characteristic, direct product factor, Sylow
91C24×C13—21no—
92C24×C13—21no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13—21no—
100C24×C13—21no—
101C24×C13C2×D412yes—
102C24×C13C2411yescharacteristic
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
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—21no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13#4114yes—
158C22×C4×C13#4114yes—
159C22×C4×C13#4114yes—
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
162C22×C4×C13#4112yes—
163C13×C4⋊C4—28no—
164C13×C4⋊C4—28no—
165C13×C4⋊C4—48no—
166C13×C4⋊C4—44no—
167C13×C22⋊C4—216no—
168C13×C22⋊C4—28no—
169C13×C22⋊C4—48no—
170C13×C22⋊C4—44no—
171C13×C22⋊C4—44no—
172C42×C13—28no—
173C42×C13—48no—
174C2×#388C2×C1311yescharacteristic
175C2×#388C2×C1312yes—
176C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
177#1444C2×C1311yescharacteristic, complemented
178#1442C2×C1311yescharacteristic, complemented
179#1441C2×C1312yescomplemented
180#1440C2×C1312yes—
181#1439C2×C1311yescharacteristic
182#1439C2×C1311yescharacteristic
183#1434C2×C1312yescomplemented
184#1434C2×C1311yescharacteristic, complemented
185C23×C13—22no—
186C23×C13—24no—
187C23×C13—24no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—42no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13C22×D411yescharacteristic
209C23×C13C22×D411yescharacteristic
210C23×C13C2×#4111yescharacteristic
211C23×C13C2×#4111yescharacteristic
212C23×C13C2×#4111yescharacteristic
213C23×C13C2×#4112yes—
214C23×C13C2×#4112yes—
215C23×C13C2×#4112yes—
216C23×C13H(5,𝔽2)12yes—
217C23×C132−1+411yescharacteristic
218C23×C132−1+411yescharacteristic
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
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—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—41no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—41no—
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—42no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13#12114yes—
278C2×C4×C13#12314yes—
279C22×C4⋊C4C22×C1311yescharacteristic
280C22×C4⋊C4C22×C1311yescharacteristic
281C22×C4⋊C4C22×C1312yes—
282C22×C4⋊C4C22×C1311yescharacteristic
283C22×C22⋊C4C22×C1311yescharacteristic
284C22×C22⋊C4C22×C1312yes—
285C22×C22⋊C4C22×C1312yes—
286C22×C22⋊C4C22×C1311yescharacteristic
287C22×C22⋊C4C22×C1311yescharacteristic
288C22×C42C22×C1312yes—
289C22×C42C22×C1311yescharacteristic
290#388—28no—
291#388—24no—
292C4×C4⋊C4—24no—
293C2×#95C22×C1311yescharacteristic
294C2×#95C22×C1312yes—
295C2×#95C22×C1312yes—
296C2×#95C22×C1311yescharacteristic
297C2×#95C22×C1311yescharacteristic
298C2×#95C22×C1312yes—
299C2×#95C22×C1312yes—
300C2×#95C22×C1312yes—
301C2×#95C22×C1312yes—
302C2×#95C22×C1311yescharacteristic
303C2×#95C22×C1312yes—
304C2×#95C22×C1312yes—
305C22×C13—42no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13C2×#12111yescharacteristic
317C22×C13C2×#12311yescharacteristic
318C22×C13#52511yescharacteristic
319C22×C13#52511yescharacteristic
320C22×C13#52512yes—
321C22×C13#52912yes—
322C22×C13#52912yes—
323C22×C13#52912yes—
324C22×C13#53211yescharacteristic
325C22×C13#53511yescharacteristic
326C22×C13#53611yescharacteristic
327C22×C13#54212yes—
328C22×C13#54212yes—
329C22×C13#54612yes—
330C22×C13#54711yescharacteristic
331C22×C13#54711yescharacteristic
332C22×C13#55212yes—
333C22×C13#55211yescharacteristic
334C22×C13#55211yescharacteristic
335C22×C13#55312yes—
336C22×C13#55312yes—
337C22×C13#55512yes—
338C22×C13#55612yes—
339C4×C13—24no—
340C4×C13—24no—
341C4×C13—44no—
342C4×C13—44no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—44no—
346C4×C13—81no—
347C4×C13—82no—
348C4×C13—81no—
349C25C23×C1311yescharacteristic
350C23×C4C23×C1311yescharacteristic
351C23×C4C23×C1312yes—
352C23×C4C23×C1311yescharacteristic
353C23×C4C23×C1311yescharacteristic
354C23×C4C23×C1311yescharacteristic
355C23×C4C23×C1312yes—
356C23×C4C23×C1312yes—
357C23×C4C23×C1312yes—
358C23×C4C23×C1311yescharacteristic
359C23×C4C23×C1311yescharacteristic
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4D4×C1314yes—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42D4×C1314yes—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—22no—
399#95—42no—
400#95—42no—
401C2×C13—82no—
402C2×C13#239211yescharacteristic
403C2×C13#246812yes—
404C2×C13#247412yes—
405C2×C13#248611yescharacteristic
406C2×C13#250011yescharacteristic
407C2×C13#252512yes—
408C2×C13#252912yes—
409C2×C13#253511yescharacteristic
410C2×C13#260411yescharacteristic
411C2×C13#263211yescharacteristic
412C2×C13#285311yescharacteristic
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24C2×D4×C1312yes—
424C24C24×C1311yescharacteristic
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
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—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4C2×D4×C1312yes—
475C22×C4C2×D4×C1312yes—
476C22×C4C2×D4×C1312yes—
477C22×C4C2×D4×C1312yes—
478C22×C4C2×D4×C1312yes—
479C22×C4C13×#4114yes—
480C22×C4C13×#4114yes—
481C22×C4C13×#4114yes—
482C22×C4C13×#4112yes—
483C22×C4C13×#4112yes—
484C22×C4C13×#4112yes—
485C4⋊C4—28no—
486C4⋊C4—28no—
487C4⋊C4—48no—
488C4⋊C4—44no—
489C22⋊C4—216no—
490C22⋊C4—28no—
491C22⋊C4—48no—
492C22⋊C4—44no—
493C22⋊C4—44no—
494C42—28no—
495C42—48no—
496C13#1507811yescharacteristic, direct product factor, Sylow
497C23—22no—
498C23—24no—
499C23—24no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23C22×D4×C1311yescharacteristic
521C23C22×D4×C1311yescharacteristic
522C23C2×C13×#4111yescharacteristic
523C23C2×C13×#4111yescharacteristic
524C23C2×C13×#4111yescharacteristic
525C23C2×C13×#4112yes—
526C23C2×C13×#4112yes—
527C23C2×C13×#4112yes—
528C23C13×H(5,𝔽2)12yes—
529C23C13×2−1+411yescharacteristic
530C23C13×2−1+411yescharacteristic
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4C13×#12114yes—
590C2×C4C13×#12314yes—
591C22—42no—
592C22—42no—
593C22—44no—
594C22—44no—
595C22—42no—
596C22—81no—
597C22—82no—
598C22—82no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22C2×C13×#12111yescharacteristic
603C22C2×C13×#12311yescharacteristic
604C22C13×#52511yescharacteristic
605C22C13×#52511yescharacteristic
606C22C13×#52512yes—
607C22C13×#52912yes—
608C22C13×#52912yes—
609C22C13×#52912yes—
610C22C13×#53211yescharacteristic
611C22C13×#53511yescharacteristic
612C22C13×#53611yescharacteristic
613C22C13×#54212yes—
614C22C13×#54212yes—
615C22C13×#54612yes—
616C22C13×#54711yescharacteristic
617C22C13×#54711yescharacteristic
618C22C13×#55211yescharacteristic
619C22C13×#55211yescharacteristic
620C22C13×#55212yes—
621C22C13×#55312yes—
622C22C13×#55312yes—
623C22C13×#55512yes—
624C22C13×#55612yes—
625C4—24no—
626C4—24no—
627C4—42no—
628C4—42no—
629C4—44no—
630C4—44no—
631C4—44no—
632C4—81no—
633C4—81no—
634C4—82no—
635C2—82no—
636C2C13×#239211yescharacteristic
637C2C13×#246812yes—
638C2C13×#247412yes—
639C2C13×#248611yescharacteristic
640C2C13×#250011yescharacteristic
641C2C13×#252512yes—
642C2C13×#252912yes—
643C2C13×#253511yescharacteristic
644C2C13×#260411yescharacteristic
645C2C13×#263211yescharacteristic
646C2C13×#285311yescharacteristic
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
3. C2×C4×C13×C4⋊C4C2semidirect
4. C13×#1444C2semidirect
5. C13×#1442C2semidirect
6. C13×#1441C2semidirect
10. C13×#1434C2semidirect
11. C13×#1434C2semidirect
90. #15078C13direct (N × H)
176. C2×C4×C4⋊C4C2×C13semidirect
177. #1444C2×C13semidirect
178. #1442C2×C13semidirect
179. #1441C2×C13semidirect
183. #1434C2×C13semidirect
184. #1434C2×C13semidirect
496. C13#15078direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3882
C2×C4×C13×C4⋊C42
C13×#14442
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14342
#1507813