Finite Group Databasebeta

← C13×#32351 #15718690

Subgroups — C13×#32351 #15718690

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2563C211yesmaximal, characteristic
2C13×#2509C211yesmaximal, characteristic, complemented
3C13×#2101C211yesmaximal, characteristic, complemented
4C13×#2092C211yesmaximal, characteristic
5C13×#2085C211yesmaximal, characteristic, complemented
6C13×#2065C211yesmaximal, characteristic
7C13×#2058C211yesmaximal, characteristic, complemented
8C13×#2057C211yesmaximal, characteristic, complemented
9C13×#1949C211yesmaximal, characteristic, complemented
10C13×#1934C211yesmaximal, characteristic
11C13×#1925C211yesmaximal, characteristic
12C13×#1916C211yesmaximal, characteristic, complemented
13C13×#1864C211yesmaximal, characteristic
14C13×#1862C211yesmaximal, characteristic
15C13×#1846C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#107C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28C2×C13×#102C2211yescharacteristic
29C2×C4×C8×C13C2211yescharacteristic
30C13×#400—21no—
31C13×#400—21no—
32C13×#393—21no—
33C13×#393—21no—
34C13×#390C2211yescharacteristic
35C13×#390C2211yescharacteristic
36C13×#389—21no—
37C13×#389C2211yescharacteristic
38C13×#389C2211yescharacteristic
39C13×#389C2211yescharacteristic
40C13×#389C2211yescharacteristic
41C13×#387—21no—
42C13×#382C2211yescharacteristic
43C13×#382C2211yescharacteristic
44C13×#382C2211yescharacteristic
45C13×#380—21no—
46C13×#380—21no—
47C4×C13×C4⋊C4C2211yescharacteristic
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#336C2211yescharacteristic
56C13×#336C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×C4⋊Q8—41no—
67C13×C4⋊Q8—41no—
68C4×D4×C13—41no—
69C4×D4×C13—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C13×#107—41no—
94C13×#107—41no—
95C13×#107—41no—
96C13×#106—41no—
97C13×#106—41no—
98C13×#106—41no—
99C13×C4⋊C8—22no—
100C13×#102—22no—
101C13×#102—41no—
102C13×#102—41no—
103C13×#102Q814yescomplemented
104C4×C8×C13—22no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95D411yescharacteristic
117C13×#95D411yescharacteristic
118#32351C1311yesmaximal, characteristic, direct product factor, Sylow
119C24×C13—21no—
120C2×Q8×C13—42no—
121C2×Q8×C13—81no—
122C2×Q8×C13—81no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13C2×Q812yes—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C2×Q812yes—
157C2×C8×C13#4112yes—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—41no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—81no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4C2×Q812yes—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—81no—
181C13×C22⋊C4—81no—
182C13×C22⋊C4—81no—
183C13×C22⋊C4—81no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—81no—
191#2563C2×C1311yescharacteristic
192#2509C2×C1311yescharacteristic, complemented
193#2101C2×C1311yescharacteristic, complemented
194#2092C2×C1311yescharacteristic
195#2085C2×C1311yescharacteristic, complemented
196#2065C2×C1311yescharacteristic
197#2058C2×C1311yescharacteristic, complemented
198#2057C2×C1311yescharacteristic, complemented
199#1949C2×C1311yescharacteristic, complemented
200#1934C2×C1311yescharacteristic
201#1925C2×C1311yescharacteristic
202#1916C2×C1311yescharacteristic, complemented
203#1864C2×C1311yescharacteristic
204#1862C2×C1311yescharacteristic
205#1846C2×C1311yescharacteristic, complemented
206C23×C13—22no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13C22×D411yescharacteristic
214Q8×C13—84no—
215D4×C13—22no—
216D4×C13—22no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—84no—
258C2×C4×C13#13512yes—
259C2×C4×C13C22×Q811yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C13H(5,𝔽2)11yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C2×C4×C132−1+411yescharacteristic
265C8×C13—22no—
266C8×C13—22no—
267C8×C13—41no—
268C8×C13—41no—
269C2×C4⋊Q8C22×C1311yescharacteristic
270C2×C4×D4C22×C1311yescharacteristic
271C2×#107C22×C1311yescharacteristic
272C2×#107C22×C1311yescharacteristic
273C2×#107C22×C1311yescharacteristic
274C2×#106C22×C1311yescharacteristic
275C2×#106C22×C1311yescharacteristic
276C2×#106C22×C1311yescharacteristic
277C2×C4⋊C8C22×C1311yescharacteristic
278C2×#102C22×C1311yescharacteristic
279C2×#102C22×C1311yescharacteristic
280C2×#102C22×C1311yescharacteristic
281C2×#102C22×C1311yescharacteristic
282C2×C4×C8C22×C1311yescharacteristic
283#400—21no—
284#400—21no—
285#393—21no—
286#393—21no—
287#390C22×C1311yescharacteristic
288#390C22×C1311yescharacteristic
289#389—21no—
290#389C22×C1311yescharacteristic
291#389C22×C1311yescharacteristic
292#389C22×C1311yescharacteristic
293#389C22×C1311yescharacteristic
294#387—21no—
295#382C22×C1311yescharacteristic
296#382C22×C1311yescharacteristic
297#382C22×C1311yescharacteristic
298#380—21no—
299#380—21no—
300C4×C4⋊C4C22×C1311yescharacteristic
301C4×C4⋊C4C22×C1311yescharacteristic
302#340C22×C1311yescharacteristic
303#340C22×C1311yescharacteristic
304#340C22×C1311yescharacteristic
305#340C22×C1311yescharacteristic
306#340C22×C1311yescharacteristic
307#340C22×C1311yescharacteristic
308#336C22×C1311yescharacteristic
309#336C22×C1311yescharacteristic
310#336C22×C1311yescharacteristic
311#336C22×C1311yescharacteristic
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13#53511yescharacteristic
320C22×C13#54711yescharacteristic
321C22×C13D4×Q811yescharacteristic
322C22×C13C2×#13511yescharacteristic
323C22×C13#57511yescharacteristic
324C22×C13#57611yescharacteristic
325C22×C13#57711yescharacteristic
326C4×C13—22no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13#53911yescharacteristic
340C4×C13#54411yescharacteristic
341C4×C13#55411yescharacteristic
342C4×C13#56311yescharacteristic
343C22×Q8—21no—
344C22×D4C23×C1311yescharacteristic
345C23×C4—21no—
346C22×C8C23×C1311yescharacteristic
347C22×C8C23×C1311yescharacteristic
348C22×C8C23×C1311yescharacteristic
349C22×C8C23×C1311yescharacteristic
350C4⋊Q8—41no—
351C4⋊Q8—41no—
352C4×D4—41no—
353C4×D4—41no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4D4×C1311yescharacteristic
360C2×C4⋊C4D4×C1311yescharacteristic
361C2×C4⋊C4C23×C1311yescharacteristic
362C2×C4⋊C4C23×C1311yescharacteristic
363C2×C4⋊C4C23×C1311yescharacteristic
364C2×C4⋊C4C23×C1311yescharacteristic
365C2×C4⋊C4C23×C1311yescharacteristic
366C2×C4⋊C4C23×C1311yescharacteristic
367C2×C4⋊C4C23×C1311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42C23×C1311yescharacteristic
375C2×C42C23×C1311yescharacteristic
376C2×C42C23×C1311yescharacteristic
377#107—41no—
378#107—41no—
379#107—41no—
380#106—41no—
381#106—41no—
382#106—41no—
383C4⋊C8—22no—
384#102—22no—
385#102—41no—
386#102—41no—
387#102Q8×C1314yescomplemented
388C4×C8—22no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95D4×C1311yescharacteristic
401#95D4×C1311yescharacteristic
402C2×C13—82no—
403C2×C13#272011yescharacteristic
404C2×C13#321111yescharacteristic
405C2×C13#322411yescharacteristic
406C2×C13#334011yescharacteristic
407C2×C13#334711yescharacteristic
408C2×C13#338011yescharacteristic
409C2×C13#338811yescharacteristic
410C24—21no—
411C2×Q8—42no—
412C2×Q8—81no—
413C2×Q8—81no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4C2×Q8×C1312yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×D4×C1311yescharacteristic
431C22×C4C2×D4×C1311yescharacteristic
432C22×C4C2×D4×C1311yescharacteristic
433C22×C4C2×D4×C1311yescharacteristic
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C24×C1311yescharacteristic
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8C2×Q8×C1312yes—
448C2×C8C13×#4112yes—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4C2×Q8×C1312yes—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—81no—
482C13#3235111yescharacteristic, direct product factor, Sylow
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C22×D4×C1311yescharacteristic
491Q8—84no—
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—84no—
535C2×C4C13×#13512yes—
536C2×C4C22×Q8×C1311yescharacteristic
537C2×C4C2×C13×#4111yescharacteristic
538C2×C4C13×H(5,𝔽2)11yescharacteristic
539C2×C4C13×H(5,𝔽2)11yescharacteristic
540C2×C4C13×2−1+411yescharacteristic
541C2×C4C13×2−1+411yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C13×#53511yescharacteristic
554C22C13×#54711yescharacteristic
555C22D4×Q8×C1311yescharacteristic
556C22C2×C13×#13511yescharacteristic
557C22C13×#57511yescharacteristic
558C22C13×#57611yescharacteristic
559C22C13×#57711yescharacteristic
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C13×#53911yescharacteristic
574C4C13×#54411yescharacteristic
575C4C13×#55411yescharacteristic
576C4C13×#56311yescharacteristic
577C2—82no—
578C2C13×#272011yescharacteristic
579C2C13×#321111yescharacteristic
580C2C13×#322411yescharacteristic
581C2C13×#334011yescharacteristic
582C2C13×#334711yescharacteristic
583C2C13×#338011yescharacteristic
584C2C13×#338811yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2509C2semidirect
3. C13×#2101C2semidirect
5. C13×#2085C2semidirect
7. C13×#2058C2semidirect
8. C13×#2057C2semidirect
9. C13×#1949C2semidirect
12. C13×#1916C2semidirect
15. C13×#1846C2semidirect
103. C13×#102Q8semidirect
118. #32351C13direct (N × H)
192. #2509C2×C13semidirect
193. #2101C2×C13semidirect
195. #2085C2×C13semidirect
197. #2058C2×C13semidirect
198. #2057C2×C13semidirect
199. #1949C2×C13semidirect
202. #1916C2×C13semidirect
205. #1846C2×C13semidirect
387. #102Q8×C13semidirect
482. C13#32351direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25632
C13×#25092
C13×#21012
C13×#20922
C13×#20852
C13×#20652
C13×#20582
C13×#20572
C13×#19492
C13×#19342
C13×#19252
C13×#19162
C13×#18642
C13×#18622
C13×#18462
#3235113