Finite Group Databasebeta

← C13×#32793 #15719132

Subgroups — C13×#32793 #15719132

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2629C211yesmaximal, characteristic
2C13×#2628C211yesmaximal, characteristic
3C13×#2101C211yesmaximal, characteristic, complemented
4C13×#2101C211yesmaximal, characteristic, complemented
5C13×#2100C211yesmaximal, characteristic, complemented
6C13×#2099C211yesmaximal, characteristic, complemented
7C13×#2077C211yesmaximal, characteristic
8C13×#2077C211yesmaximal, characteristic
9C13×#2076C211yesmaximal, characteristic
10C13×#2075C211yesmaximal, characteristic
11C13×#2059C211yesmaximal, characteristic, complemented
12C13×#2059C211yesmaximal, characteristic, complemented
13C13×#2058C211yesmaximal, characteristic, complemented
14C13×#2057C211yesmaximal, characteristic, complemented
15C13×#1818C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#125C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C13×#400—21no—
26C13×#399—21no—
27C13×#398—21no—
28C13×#398—21no—
29C13×#396—21no—
30C13×#396—21no—
31C13×#395—21no—
32C13×#393—21no—
33C13×#389C2211yescharacteristic
34C13×#389C2211yescharacteristic
35C13×#389C2211yescharacteristic
36C13×#389C2211yescharacteristic
37C13×#384C2211yescharacteristic
38C13×#382C2211yescharacteristic
39C13×#380C2211yescharacteristic
40C13×#380C2211yescharacteristic
41C13×#380C2211yescharacteristic
42C13×#380C2211yescharacteristic
43C13×#340C2211yescharacteristic
44C13×#340C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#336C2211yescharacteristic
56C13×#336C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×Q8×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C4⋊Q8—41no—
66C13×C4⋊Q8—41no—
67C13×#125—41no—
68C13×#125—41no—
69C13×#117—41no—
70C13×#117—41no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4D411yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C13×C22⋊C4D411yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C13×#107—41no—
99C13×#107—41no—
100C13×#106—41no—
101C13×#106—41no—
102C13×C22⋊C8—41no—
103C13×C22⋊C8—41no—
104C13×#95—21no—
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—
114#32793C1311yesmaximal, characteristic, direct product factor, Sylow
115C24×C13C2×D411yescharacteristic
116C2×Q8×C13—42no—
117C2×Q8×C13—81no—
118C2×Q8×C13—81no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C2×C8×C13—21no—
140C2×C8×C13—21no—
141C2×C8×C13—21no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
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—41no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—81no—
173C13×C4⋊C4—81no—
174C13×C4⋊C4—81no—
175C13×C4⋊C4—81no—
176C13×C4⋊C4—81no—
177C13×C4⋊C4—81no—
178C13×C22⋊C4—41no—
179C13×C22⋊C4—41no—
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—
188#2629C2×C1311yescharacteristic
189#2628C2×C1311yescharacteristic
190#2101C2×C1311yescharacteristic, complemented
191#2101C2×C1311yescharacteristic, complemented
192#2100C2×C1311yescharacteristic, complemented
193#2099C2×C1311yescharacteristic, complemented
194#2077C2×C1311yescharacteristic
195#2077C2×C1311yescharacteristic
196#2076C2×C1311yescharacteristic
197#2075C2×C1311yescharacteristic
198#2059C2×C1311yescharacteristic, complemented
199#2059C2×C1311yescharacteristic, complemented
200#2058C2×C1311yescharacteristic, complemented
201#2057C2×C1311yescharacteristic, complemented
202#1818C2×C1311yescharacteristic
203C23×C13—21no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13C22×D411yescharacteristic
211Q8×C13—84no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
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—21no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
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×C13H(5,𝔽2)11yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C2×C4×C132−1+411yescharacteristic
258C2×C4×C132−1+411yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C2×C4×C132−1+411yescharacteristic
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265C2×C4⋊Q8C22×C1311yescharacteristic
266C2×#125C22×C1311yescharacteristic
267C2×#117C22×C1311yescharacteristic
268C2×#107C22×C1311yescharacteristic
269C2×#107C22×C1311yescharacteristic
270C2×#106C22×C1311yescharacteristic
271C2×#106C22×C1311yescharacteristic
272C2×C22⋊C8C22×C1311yescharacteristic
273C2×C22⋊C8C22×C1311yescharacteristic
274#400—21no—
275#399—21no—
276#398—21no—
277#398—21no—
278#396—21no—
279#396—21no—
280#395—21no—
281#393—21no—
282#389C22×C1311yescharacteristic
283#389C22×C1311yescharacteristic
284#389C22×C1311yescharacteristic
285#389C22×C1311yescharacteristic
286#384C22×C1311yescharacteristic
287#382C22×C1311yescharacteristic
288#380C22×C1311yescharacteristic
289#380C22×C1311yescharacteristic
290#380C22×C1311yescharacteristic
291#380C22×C1311yescharacteristic
292#340C22×C1311yescharacteristic
293#340C22×C1311yescharacteristic
294#340C22×C1311yescharacteristic
295#340C22×C1311yescharacteristic
296#340C22×C1311yescharacteristic
297#340C22×C1311yescharacteristic
298#340C22×C1311yescharacteristic
299#340C22×C1311yescharacteristic
300#340C22×C1311yescharacteristic
301#340C22×C1311yescharacteristic
302#340C22×C1311yescharacteristic
303#340C22×C1311yescharacteristic
304#336C22×C1311yescharacteristic
305#336C22×C1311yescharacteristic
306#336C22×C1311yescharacteristic
307#336C22×C1311yescharacteristic
308C22×C13—41no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13—41no—
314C22×C13—41no—
315C22×C13#53411yescharacteristic
316C22×C13#53611yescharacteristic
317C22×C13#53611yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C22×C13#57711yescharacteristic
321C22×C13#57811yescharacteristic
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—81no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13#56311yescharacteristic
336C4×C13#56311yescharacteristic
337C4×C13#56311yescharacteristic
338C4×C13#56311yescharacteristic
339C22×Q8—21no—
340C23×C4C23×C1311yescharacteristic
341C22×C8C23×C1311yescharacteristic
342C22×C8C23×C1311yescharacteristic
343C22×C8C23×C1311yescharacteristic
344C22×C8C23×C1311yescharacteristic
345C4⋊Q8—41no—
346C4⋊Q8—41no—
347#125—41no—
348#125—41no—
349#117—41no—
350#117—41no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4D4×C1311yescharacteristic
361C2×C4⋊C4D4×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×C4⋊C4C23×C1311yescharacteristic
369C2×C4⋊C4C23×C1311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4D4×C1311yescharacteristic
375C2×C22⋊C4D4×C1311yescharacteristic
376C2×C42C23×C1311yescharacteristic
377C2×C42C23×C1311yescharacteristic
378#107—41no—
379#107—41no—
380#106—41no—
381#106—41no—
382C22⋊C8—41no—
383C22⋊C8—41no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394C2×C13—81no—
395C2×C13#281711yescharacteristic
396C2×C13#319811yescharacteristic
397C2×C13#320111yescharacteristic
398C2×C13#324111yescharacteristic
399C2×C13#324211yescharacteristic
400C2×C13#324311yescharacteristic
401C2×C13#324411yescharacteristic
402C24C2×D4×C1311yescharacteristic
403C2×Q8—42no—
404C2×Q8—81no—
405C2×Q8—81no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4C2×D4×C1311yescharacteristic
421C22×C4C2×D4×C1311yescharacteristic
422C22×C4C2×D4×C1311yescharacteristic
423C22×C4C2×D4×C1311yescharacteristic
424C22×C4C2×D4×C1311yescharacteristic
425C22×C4C24×C1311yescharacteristic
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—81no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C13#3279311yescharacteristic, direct product factor, Sylow
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23C22×D4×C1311yescharacteristic
484Q8—84no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
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×C4C13×H(5,𝔽2)11yescharacteristic
529C2×C4C13×H(5,𝔽2)11yescharacteristic
530C2×C4C13×2−1+411yescharacteristic
531C2×C4C13×2−1+411yescharacteristic
532C2×C4C13×2−1+411yescharacteristic
533C2×C4C13×2−1+411yescharacteristic
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22C13×#53411yescharacteristic
546C22C13×#53611yescharacteristic
547C22C13×#53611yescharacteristic
548C22C13×#57611yescharacteristic
549C22C13×#57711yescharacteristic
550C22C13×#57711yescharacteristic
551C22C13×#57811yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C13×#56311yescharacteristic
566C4C13×#56311yescharacteristic
567C4C13×#56311yescharacteristic
568C4C13×#56311yescharacteristic
569C2—81no—
570C2C13×#281711yescharacteristic
571C2C13×#319811yescharacteristic
572C2C13×#320111yescharacteristic
573C2C13×#324111yescharacteristic
574C2C13×#324211yescharacteristic
575C2C13×#324311yescharacteristic
576C2C13×#324411yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2101C2semidirect
4. C13×#2101C2semidirect
5. C13×#2100C2semidirect
6. C13×#2099C2semidirect
11. C13×#2059C2semidirect
12. C13×#2059C2semidirect
13. C13×#2058C2semidirect
14. C13×#2057C2semidirect
114. #32793C13direct (N × H)
190. #2101C2×C13semidirect
191. #2101C2×C13semidirect
192. #2100C2×C13semidirect
193. #2099C2×C13semidirect
198. #2059C2×C13semidirect
199. #2059C2×C13semidirect
200. #2058C2×C13semidirect
201. #2057C2×C13semidirect
475. C13#32793direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26292
C13×#26282
C13×#21012
C13×#21002
C13×#20992
C13×#20772
C13×#20762
C13×#20752
C13×#20592
C13×#20582
C13×#20572
C13×#18182
#3279313