Finite Group Databasebeta

← C13×#32592 #15718931

Subgroups — C13×#32592 #15718931

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2584C211yesmaximal, characteristic, complemented
2C13×#2580C211yesmaximal, characteristic
3C13×#2101C211yesmaximal, characteristic, complemented
4C13×#2088C211yesmaximal, characteristic, complemented
5C13×#2085C211yesmaximal, characteristic, complemented
6C13×#2067C211yesmaximal, characteristic
7C13×#2059C211yesmaximal, characteristic, complemented
8C13×#2025C211yesmaximal, characteristic
9C13×#1985C211yesmaximal, characteristic, complemented
10C13×#1944C211yesmaximal, characteristic, complemented
11C13×#1936C211yesmaximal, characteristic
12C13×#1926C211yesmaximal, characteristic
13C13×#1918C211yesmaximal, characteristic, complemented
14C13×#1864C211yesmaximal, characteristic
15C13×#1862C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28C2×C13×#97C2211yescharacteristic
29C13×#399—21no—
30C13×#398—21no—
31C13×#395—21no—
32C13×#393—21no—
33C13×#390C2211yescharacteristic
34C13×#390C2211yescharacteristic
35C13×#389—21no—
36C13×#389—21no—
37C13×#389C2211yescharacteristic
38C13×#389C2211yescharacteristic
39C13×#389C2211yescharacteristic
40C13×#389C2211yescharacteristic
41C13×#389C2211yescharacteristic
42C13×#389C2211yescharacteristic
43C13×#385—21no—
44C13×#385—21no—
45C13×#382C2211yescharacteristic
46C4×C13×C4⋊C4C2211yescharacteristic
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×C13D411yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×#125—41no—
67C13×#125—41no—
68C4×Q8×C13—41no—
69C4×Q8×C13—41no—
70C4×D4×C13—41no—
71C4×D4×C13—41no—
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⋊C4D411yescharacteristic
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⋊C4—21no—
95C2×C42×C13—21no—
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C42×C13C2311yescharacteristic
99C13×#107—22no—
100C13×#107—41no—
101C13×#106—22no—
102C13×#106—41no—
103C13×C4⋊C8—41no—
104C13×#102—22no—
105C13×#102—41no—
106C13×#102—41no—
107C13×#102Q814yescomplemented
108C13×#97—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95—21no—
118#32592C1311yesmaximal, characteristic, direct product factor, Sylow
119C24×C13—21no—
120C2×Q8×C13—41no—
121C2×Q8×C13—41no—
122C2×Q8×C13—41no—
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—81no—
138C22×C4×C13—81no—
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×C13—21no—
157C2×C8×C13C2×Q812yes—
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—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4—41no—
172C13×C4⋊C4—41no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4—81no—
180C13×C4⋊C4—81no—
181C13×C4⋊C4C2×Q812yes—
182C13×C4⋊C4#4112yes—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—42no—
185C13×C22⋊C4—42no—
186C13×C22⋊C4—81no—
187C13×C22⋊C4—81no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—81no—
195#2584C2×C1311yescharacteristic, complemented
196#2580C2×C1311yescharacteristic
197#2101C2×C1311yescharacteristic, complemented
198#2088C2×C1311yescharacteristic, complemented
199#2085C2×C1311yescharacteristic, complemented
200#2067C2×C1311yescharacteristic
201#2059C2×C1311yescharacteristic, complemented
202#2025C2×C1311yescharacteristic
203#1985C2×C1311yescharacteristic, complemented
204#1944C2×C1311yescharacteristic, complemented
205#1936C2×C1311yescharacteristic
206#1926C2×C1311yescharacteristic
207#1918C2×C1311yescharacteristic, complemented
208#1864C2×C1311yescharacteristic
209#1862C2×C1311yescharacteristic
210C23×C13—22no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13C22×D411yescharacteristic
218Q8×C13—44no—
219D4×C13—22no—
220D4×C13—22no—
221D4×C13—41no—
222D4×C13—41no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
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—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
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—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—84no—
263C2×C4×C13C22×Q811yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13H(5,𝔽2)11yescharacteristic
266C2×C4×C13H(5,𝔽2)11yescharacteristic
267C2×C4×C132−1+411yescharacteristic
268C2×C4×C132−1+411yescharacteristic
269C8×C13—22no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273C2×#125C22×C1311yescharacteristic
274C2×C4×Q8C22×C1311yescharacteristic
275C2×C4×D4C22×C1311yescharacteristic
276C2×#107C22×C1311yescharacteristic
277C2×#107C22×C1311yescharacteristic
278C2×#106C22×C1311yescharacteristic
279C2×#106C22×C1311yescharacteristic
280C2×C4⋊C8C22×C1311yescharacteristic
281C2×#102C22×C1311yescharacteristic
282C2×#102C22×C1311yescharacteristic
283C2×#102C22×C1311yescharacteristic
284C2×#102C22×C1311yescharacteristic
285C2×#97C22×C1311yescharacteristic
286#399—21no—
287#398—21no—
288#395—21no—
289#393—21no—
290#390C22×C1311yescharacteristic
291#390C22×C1311yescharacteristic
292#389—21no—
293#389—21no—
294#389C22×C1311yescharacteristic
295#389C22×C1311yescharacteristic
296#389C22×C1311yescharacteristic
297#389C22×C1311yescharacteristic
298#389C22×C1311yescharacteristic
299#389C22×C1311yescharacteristic
300#385—21no—
301#385—21no—
302#382C22×C1311yescharacteristic
303C4×C4⋊C4C22×C1311yescharacteristic
304#340C22×C1311yescharacteristic
305#340C22×C1311yescharacteristic
306#340C22×C1311yescharacteristic
307#340C22×C1311yescharacteristic
308#340C22×C1311yescharacteristic
309#340C22×C1311yescharacteristic
310#340C22×C1311yescharacteristic
311#340C22×C1311yescharacteristic
312#336C22×C1311yescharacteristic
313#336C22×C1311yescharacteristic
314#336C22×C1311yescharacteristic
315#336C22×C1311yescharacteristic
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13—81no—
322C22×C13—81no—
323C22×C13#53411yescharacteristic
324C22×C13#54811yescharacteristic
325C22×C13D4×Q811yescharacteristic
326C22×C13#57511yescharacteristic
327C22×C13#57511yescharacteristic
328C22×C13#57611yescharacteristic
329C22×C13#57711yescharacteristic
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13#54211yescharacteristic
344C4×C13#54411yescharacteristic
345C4×C13#55411yescharacteristic
346C4×C13#56311yescharacteristic
347C22×Q8D4×C1311yescharacteristic
348C22×D4C23×C1311yescharacteristic
349C23×C4—21no—
350C22×C8C23×C1311yescharacteristic
351C22×C8C23×C1311yescharacteristic
352C22×C8C23×C1311yescharacteristic
353C22×C8C23×C1311yescharacteristic
354#125—41no—
355#125—41no—
356C4×Q8—41no—
357C4×Q8—41no—
358C4×D4—41no—
359C4×D4—41no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C1311yescharacteristic
369C2×C4⋊C4D4×C1311yescharacteristic
370C2×C4⋊C4D4×C1311yescharacteristic
371C2×C4⋊C4C23×C1311yescharacteristic
372C2×C4⋊C4C23×C1311yescharacteristic
373C2×C4⋊C4C23×C1311yescharacteristic
374C2×C4⋊C4C23×C1311yescharacteristic
375C2×C4⋊C4C23×C1311yescharacteristic
376C2×C4⋊C4C23×C1311yescharacteristic
377C2×C4⋊C4C23×C1311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42C23×C1311yescharacteristic
385C2×C42C23×C1311yescharacteristic
386C2×C42C23×C1311yescharacteristic
387#107—22no—
388#107—41no—
389#106—22no—
390#106—41no—
391C4⋊C8—41no—
392#102—22no—
393#102—41no—
394#102—41no—
395#102Q8×C1314yescomplemented
396#97—41no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406C2×C13—82no—
407C2×C13#272911yescharacteristic
408C2×C13#319711yescharacteristic
409C2×C13#319811yescharacteristic
410C2×C13#337011yescharacteristic
411C2×C13#337111yescharacteristic
412C2×C13#338811yescharacteristic
413C2×C13#338911yescharacteristic
414C24—21no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4C2×Q8×C1312yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C2×D4×C1311yescharacteristic
440C22×C4C24×C1311yescharacteristic
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×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8C2×Q8×C1312yes—
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—41no—
467C4⋊C4—41no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4C2×Q8×C1312yes—
477C4⋊C4C13×#4112yes—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—81no—
490C13#3259211yescharacteristic, direct product factor, Sylow
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C22×D4×C1311yescharacteristic
499Q8—44no—
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—84no—
544C2×C4C22×Q8×C1311yescharacteristic
545C2×C4C2×C13×#4111yescharacteristic
546C2×C4C13×H(5,𝔽2)11yescharacteristic
547C2×C4C13×H(5,𝔽2)11yescharacteristic
548C2×C4C13×2−1+411yescharacteristic
549C2×C4C13×2−1+411yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C13×#53411yescharacteristic
562C22C13×#54811yescharacteristic
563C22D4×Q8×C1311yescharacteristic
564C22C13×#57511yescharacteristic
565C22C13×#57511yescharacteristic
566C22C13×#57611yescharacteristic
567C22C13×#57711yescharacteristic
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C13×#54211yescharacteristic
582C4C13×#54411yescharacteristic
583C4C13×#55411yescharacteristic
584C4C13×#56311yescharacteristic
585C2—82no—
586C2C13×#272911yescharacteristic
587C2C13×#319711yescharacteristic
588C2C13×#319811yescharacteristic
589C2C13×#337011yescharacteristic
590C2C13×#337111yescharacteristic
591C2C13×#338811yescharacteristic
592C2C13×#338911yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2584C2semidirect
3. C13×#2101C2semidirect
4. C13×#2088C2semidirect
5. C13×#2085C2semidirect
7. C13×#2059C2semidirect
9. C13×#1985C2semidirect
10. C13×#1944C2semidirect
13. C13×#1918C2semidirect
107. C13×#102Q8semidirect
118. #32592C13direct (N × H)
195. #2584C2×C13semidirect
197. #2101C2×C13semidirect
198. #2088C2×C13semidirect
199. #2085C2×C13semidirect
201. #2059C2×C13semidirect
203. #1985C2×C13semidirect
204. #1944C2×C13semidirect
207. #1918C2×C13semidirect
395. #102Q8×C13semidirect
490. C13#32592direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25842
C13×#25802
C13×#21012
C13×#20882
C13×#20852
C13×#20672
C13×#20592
C13×#20252
C13×#19852
C13×#19442
C13×#19362
C13×#19262
C13×#19182
C13×#18642
C13×#18622
#3259213