Finite Group Databasebeta

← C13×#10405 #15696744

Subgroups — C13×#10405 #15696744

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2639C211yesmaximal, characteristic
2C13×#1874C211yesmaximal, characteristic
3C13×#1872C211yesmaximal, characteristic, complemented
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C2×C13×#327C211yesmaximal, characteristic
6C13×#1444C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4—21no—
11C22×C13×C4⋊C4C2211yescharacteristic
12C2×C13×#103—21no—
13C2×C13×#102—21no—
14C2×C13×C22⋊C8C2211yescharacteristic
15C2×C13×C22⋊C8C2211yescharacteristic
16C13×#400—21no—
17C13×#397—21no—
18C13×#394—21no—
19C13×#393—21no—
20C13×#386—21no—
21C13×#386—21no—
22C2×C13×#95—21no—
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2211yescharacteristic
25C13×#340—21no—
26C13×#340—21no—
27C13×#328—22no—
28C13×#327—22no—
29C22×Q8×C13D411yescharacteristic
30C22×D4×C13—21no—
31C22×D4×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13—21no—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×#121—21no—
44C13×#121—21no—
45C13×#121—21no—
46C13×#121—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—42no—
51C2×C13×C4⋊C4—42no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C13×#103—42no—
63C13×#102—42no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8—21no—
67C13×C22⋊C8—21no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75C13×#95—42no—
76C13×#95D412yes—
77#10405C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C22×C4×C13#4111yescharacteristic
128C22×C4×C13#4111yescharacteristic
129C2×C8×C13—41no—
130C2×C8×C13—41no—
131C2×C8×C13—41no—
132C2×C8×C13—41no—
133C2×C8×C13—41no—
134C2×C8×C13—41no—
135C13×C4⋊C4—22no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4—41no—
143C13×C4⋊C4—48no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—81no—
151C13×C22⋊C4—81no—
152C13×C22⋊C4—81no—
153C13×C22⋊C4—81no—
154#2639C2×C1311yescharacteristic
155#1874C2×C1311yescharacteristic
156#1872C2×C1311yescharacteristic, complemented
157C2×#328C2×C1311yescharacteristic, complemented
158C2×#327C2×C1311yescharacteristic
159#1444C2×C1311yescharacteristic, complemented
160#1280C2×C1311yescharacteristic, complemented
161C23×C13—21no—
162C23×C13—21no—
163C23×C13—21no—
164C23×C13—21no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13#12011yescharacteristic
173C23×C13#12111yescharacteristic
174C23×C13#12411yescharacteristic
175C23×C13#13511yescharacteristic
176C23×C13#13511yescharacteristic
177C23×C13AGL(1,ℤ/8)11yescharacteristic
178C23×C13#13711yescharacteristic
179Q8×C13—42no—
180Q8×C13—81no—
181D4×C13—42no—
182D4×C13—81no—
183D4×C13—81no—
184D4×C13—81no—
185D4×C13—81no—
186D4×C13—81no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—24no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—42no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—81no—
223C2×C4×C13—81no—
224C2×C4×C13—81no—
225C2×C4×C13—81no—
226C2×C4×C13—81no—
227C2×C4×C13—81no—
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12311yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C8×C13—81no—
233C8×C13—81no—
234C2×C22⋊Q8C22×C1311yescharacteristic
235C2×#121C22×C1311yescharacteristic
236C22×C4⋊C4—21no—
237C22×C4⋊C4C22×C1311yescharacteristic
238C2×#103—21no—
239C2×#102—21no—
240C2×C22⋊C8C22×C1311yescharacteristic
241C2×C22⋊C8C22×C1311yescharacteristic
242#400—21no—
243#397—21no—
244#394—21no—
245#393—21no—
246#386—21no—
247#386—21no—
248C2×#95—21no—
249C2×#95C22×C1311yescharacteristic
250C2×#95C22×C1311yescharacteristic
251#340—21no—
252#340—21no—
253#328—22no—
254#327—22no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13#39411yescharacteristic
275C22×C13#44911yescharacteristic
276C22×C13#45211yescharacteristic
277C22×C13#45311yescharacteristic
278C22×C13#45611yescharacteristic
279C22×C13B(4,𝔽2)11yescharacteristic
280C22×C13#45811yescharacteristic
281C22×C13#46311yescharacteristic
282C22×C13#46411yescharacteristic
283C22×C13#48811yescharacteristic
284C22×C13#48911yescharacteristic
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—44no—
290C4×C13—81no—
291C4×C13—82no—
292C4×C13—81no—
293C4×C13—81no—
294C4×C13—81no—
295C4×C13—81no—
296C22×Q8D4×C1311yescharacteristic
297C22×D4—21no—
298C22×D4D4×C1311yescharacteristic
299C23×C4—21no—
300C23×C4—21no—
301C23×C4D4×C1311yescharacteristic
302C23×C4D4×C1311yescharacteristic
303C23×C4C23×C1311yescharacteristic
304C22×C8—21no—
305C22×C8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4D4×C1311yescharacteristic
322C2×C4⋊C4D4×C1311yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329#103—42no—
330#102—42no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—42no—
343#95D4×C1312yes—
344C2×C13—21no—
345C2×C13—21no—
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—161no—
349C2×C13#160011yescharacteristic
350C2×C13#160311yescharacteristic
351C2×C13#160911yescharacteristic
352C2×C13#161811yescharacteristic
353C2×C13#203911yescharacteristic
354C2×C13#204211yescharacteristic
355C2×C13#204411yescharacteristic
356C24—21no—
357C24C2×D4×C1311yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C2×D4×C1311yescharacteristic
402C22×C4C2×D4×C1311yescharacteristic
403C22×C4C2×D4×C1311yescharacteristic
404C22×C4C13×#4111yescharacteristic
405C22×C4C13×#4111yescharacteristic
406C22×C4C13×#4111yescharacteristic
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—48no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C22⋊C4—81no—
432C13#1040511yescharacteristic, direct product factor, Sylow
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23C13×#12011yescharacteristic
445C23C13×#12111yescharacteristic
446C23C13×#12411yescharacteristic
447C23C13×#13511yescharacteristic
448C23C13×#13511yescharacteristic
449C23C13×AGL(1,ℤ/8)11yescharacteristic
450C23C13×#13711yescharacteristic
451Q8—42no—
452Q8—81no—
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4C13×#12111yescharacteristic
501C2×C4C13×#12111yescharacteristic
502C2×C4C13×#12311yescharacteristic
503C2×C4C13×#12311yescharacteristic
504C8—81no—
505C8—81no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22C13×#39411yescharacteristic
526C22C13×#44911yescharacteristic
527C22C13×#45211yescharacteristic
528C22C13×#45311yescharacteristic
529C22C13×#45611yescharacteristic
530C22C13×B(4,𝔽2)11yescharacteristic
531C22C13×#45811yescharacteristic
532C22C13×#46311yescharacteristic
533C22C13×#46411yescharacteristic
534C22C13×#48811yescharacteristic
535C22C13×#48911yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—44no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—82no—
546C4—81no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—161no—
552C2C13×#160011yescharacteristic
553C2C13×#160311yescharacteristic
554C2C13×#160911yescharacteristic
555C2C13×#161811yescharacteristic
556C2C13×#203911yescharacteristic
557C2C13×#204211yescharacteristic
558C2C13×#204411yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1872C2semidirect
4. C2×C13×#328C2semidirect
6. C13×#1444C2semidirect
7. C13×#1280C2semidirect
77. #10405C13direct (N × H)
156. #1872C2×C13semidirect
157. C2×#328C2×C13semidirect
159. #1444C2×C13semidirect
160. #1280C2×C13semidirect
432. C13#10405direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26392
C13×#18742
C13×#18722
C2×C13×#3282
C2×C13×#3272
C13×#14442
C13×#12802
#1040513