Finite Group Databasebeta

← C13×#32373 #15718712

Subgroups — C13×#32373 #15718712

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2563C211yesmaximal, characteristic
2C13×#2507C211yesmaximal, characteristic, complemented
3C13×#2101C211yesmaximal, characteristic, complemented
4C13×#2093C211yesmaximal, characteristic
5C13×#2085C211yesmaximal, characteristic, complemented
6C13×#2067C211yesmaximal, characteristic
7C13×#2057C211yesmaximal, characteristic, complemented
8C13×#2057C211yesmaximal, characteristic, complemented
9C13×#1949C211yesmaximal, characteristic, complemented
10C13×#1936C211yesmaximal, characteristic
11C13×#1925C211yesmaximal, characteristic
12C13×#1917C211yesmaximal, characteristic, complemented
13C13×#1864C211yesmaximal, characteristic
14C13×#1864C211yesmaximal, characteristic
15C13×#1847C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#107C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#107C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28C2×C13×#102C2211yescharacteristic
29C2×C13×#97C2211yescharacteristic
30C13×#398—21no—
31C13×#398—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×#384C2211yescharacteristic
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⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C42×C13—21no—
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C13×#107—41no—
96C13×#107—41no—
97C13×#107—41no—
98C13×#107—41no—
99C13×#106—41no—
100C13×#106—41no—
101C13×C4⋊C8—22no—
102C13×#102—22no—
103C13×#102—41no—
104C13×#102—41no—
105C13×#102Q814yescomplemented
106C13×#97—22no—
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#32373C1311yesmaximal, 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—81no—
176C13×C4⋊C4—81no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4—81no—
180C13×C4⋊C4C2×Q812yes—
181C13×C22⋊C4—42no—
182C13×C22⋊C4—81no—
183C13×C22⋊C4—81no—
184C13×C22⋊C4—81no—
185C13×C22⋊C4—81no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—81no—
193#2563C2×C1311yescharacteristic
194#2507C2×C1311yescharacteristic, complemented
195#2101C2×C1311yescharacteristic, complemented
196#2093C2×C1311yescharacteristic
197#2085C2×C1311yescharacteristic, complemented
198#2067C2×C1311yescharacteristic
199#2057C2×C1311yescharacteristic, complemented
200#2057C2×C1311yescharacteristic, complemented
201#1949C2×C1311yescharacteristic, complemented
202#1936C2×C1311yescharacteristic
203#1925C2×C1311yescharacteristic
204#1917C2×C1311yescharacteristic, complemented
205#1864C2×C1311yescharacteristic
206#1864C2×C1311yescharacteristic
207#1847C2×C1311yescharacteristic, complemented
208C23×C13—22no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13C22×D411yescharacteristic
216Q8×C13—84no—
217D4×C13—22no—
218D4×C13—22no—
219D4×C13—41no—
220D4×C13—41no—
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—21no—
228C2×C4×C13—22no—
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—21no—
238C2×C4×C13—21no—
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—41no—
258C2×C4×C13—41no—
259C2×C4×C13—84no—
260C2×C4×C13#13712yes—
261C2×C4×C13C22×Q811yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13H(5,𝔽2)11yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C8×C13—22no—
268C8×C13—22no—
269C8×C13—41no—
270C8×C13—41no—
271C2×C4⋊Q8C22×C1311yescharacteristic
272C2×C4×D4C22×C1311yescharacteristic
273C2×#107C22×C1311yescharacteristic
274C2×#107C22×C1311yescharacteristic
275C2×#107C22×C1311yescharacteristic
276C2×#107C22×C1311yescharacteristic
277C2×#106C22×C1311yescharacteristic
278C2×#106C22×C1311yescharacteristic
279C2×C4⋊C8C22×C1311yescharacteristic
280C2×#102C22×C1311yescharacteristic
281C2×#102C22×C1311yescharacteristic
282C2×#102C22×C1311yescharacteristic
283C2×#102C22×C1311yescharacteristic
284C2×#97C22×C1311yescharacteristic
285#398—21no—
286#398—21no—
287#393—21no—
288#393—21no—
289#390C22×C1311yescharacteristic
290#390C22×C1311yescharacteristic
291#389—21no—
292#389C22×C1311yescharacteristic
293#389C22×C1311yescharacteristic
294#389C22×C1311yescharacteristic
295#389C22×C1311yescharacteristic
296#387—21no—
297#384C22×C1311yescharacteristic
298#382C22×C1311yescharacteristic
299#382C22×C1311yescharacteristic
300#380—21no—
301#380—21no—
302C4×C4⋊C4C22×C1311yescharacteristic
303C4×C4⋊C4C22×C1311yescharacteristic
304#340C22×C1311yescharacteristic
305#340C22×C1311yescharacteristic
306#340C22×C1311yescharacteristic
307#340C22×C1311yescharacteristic
308#340C22×C1311yescharacteristic
309#340C22×C1311yescharacteristic
310#336C22×C1311yescharacteristic
311#336C22×C1311yescharacteristic
312#336C22×C1311yescharacteristic
313#336C22×C1311yescharacteristic
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13#53511yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13D4×Q811yescharacteristic
324C22×C13C2×#13711yescharacteristic
325C22×C13#57511yescharacteristic
326C22×C13#57611yescharacteristic
327C22×C13#57611yescharacteristic
328C4×C13—22no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13#53911yescharacteristic
342C4×C13#54411yescharacteristic
343C4×C13#55411yescharacteristic
344C4×C13#56311yescharacteristic
345C22×Q8—21no—
346C22×D4C23×C1311yescharacteristic
347C23×C4—21no—
348C22×C8C23×C1311yescharacteristic
349C22×C8C23×C1311yescharacteristic
350C22×C8C23×C1311yescharacteristic
351C22×C8C23×C1311yescharacteristic
352C4⋊Q8—41no—
353C4⋊Q8—41no—
354C4×D4—41no—
355C4×D4—41no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C1311yescharacteristic
364C2×C4⋊C4D4×C1311yescharacteristic
365C2×C4⋊C4C23×C1311yescharacteristic
366C2×C4⋊C4C23×C1311yescharacteristic
367C2×C4⋊C4C23×C1311yescharacteristic
368C2×C4⋊C4C23×C1311yescharacteristic
369C2×C4⋊C4C23×C1311yescharacteristic
370C2×C4⋊C4C23×C1311yescharacteristic
371C2×C4⋊C4C23×C1311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—21no—
378C2×C42C23×C1311yescharacteristic
379C2×C42C23×C1311yescharacteristic
380C2×C42C23×C1311yescharacteristic
381#107—41no—
382#107—41no—
383#107—41no—
384#107—41no—
385#106—41no—
386#106—41no—
387C4⋊C8—22no—
388#102—22no—
389#102—41no—
390#102—41no—
391#102Q8×C1314yescomplemented
392#97—22no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95D4×C1311yescharacteristic
403#95D4×C1311yescharacteristic
404C2×C13—82no—
405C2×C13#272011yescharacteristic
406C2×C13#321511yescharacteristic
407C2×C13#322011yescharacteristic
408C2×C13#334711yescharacteristic
409C2×C13#335711yescharacteristic
410C2×C13#338511yescharacteristic
411C2×C13#338911yescharacteristic
412C24—21no—
413C2×Q8—42no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×Q8×C1312yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4C2×D4×C1311yescharacteristic
433C22×C4C2×D4×C1311yescharacteristic
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C24×C1311yescharacteristic
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×C8—21no—
448C2×C8—21no—
449C2×C8C2×Q8×C1312yes—
450C2×C8C13×#4112yes—
451C4⋊C4—22no—
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—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4C2×Q8×C1312yes—
474C22⋊C4—42no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—81no—
486C13#3237311yescharacteristic, direct product factor, Sylow
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×D4×C1311yescharacteristic
495Q8—84no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
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—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—84no—
539C2×C4C13×#13712yes—
540C2×C4C22×Q8×C1311yescharacteristic
541C2×C4C2×C13×#4111yescharacteristic
542C2×C4C13×H(5,𝔽2)11yescharacteristic
543C2×C4C13×H(5,𝔽2)11yescharacteristic
544C2×C4C13×2−1+411yescharacteristic
545C2×C4C13×2−1+411yescharacteristic
546C8—22no—
547C8—22no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C13×#53511yescharacteristic
558C22C13×#54711yescharacteristic
559C22D4×Q8×C1311yescharacteristic
560C22C2×C13×#13711yescharacteristic
561C22C13×#57511yescharacteristic
562C22C13×#57611yescharacteristic
563C22C13×#57611yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C13×#53911yescharacteristic
578C4C13×#54411yescharacteristic
579C4C13×#55411yescharacteristic
580C4C13×#56311yescharacteristic
581C2—82no—
582C2C13×#272011yescharacteristic
583C2C13×#321511yescharacteristic
584C2C13×#322011yescharacteristic
585C2C13×#334711yescharacteristic
586C2C13×#335711yescharacteristic
587C2C13×#338511yescharacteristic
588C2C13×#338911yescharacteristic
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×#2507C2semidirect
3. C13×#2101C2semidirect
5. C13×#2085C2semidirect
7. C13×#2057C2semidirect
8. C13×#2057C2semidirect
9. C13×#1949C2semidirect
12. C13×#1917C2semidirect
15. C13×#1847C2semidirect
105. C13×#102Q8semidirect
118. #32373C13direct (N × H)
194. #2507C2×C13semidirect
195. #2101C2×C13semidirect
197. #2085C2×C13semidirect
199. #2057C2×C13semidirect
200. #2057C2×C13semidirect
201. #1949C2×C13semidirect
204. #1917C2×C13semidirect
207. #1847C2×C13semidirect
391. #102Q8×C13semidirect
486. C13#32373direct (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×#25072
C13×#21012
C13×#20932
C13×#20852
C13×#20672
C13×#20572
C13×#19492
C13×#19362
C13×#19252
C13×#19172
C13×#18642
C13×#18472
#3237313