Finite Group Databasebeta

← C13×#10431 #15696770

Subgroups — C13×#10431 #15696770

Order 3328.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2537C211yesmaximal, characteristic
2C13×#1834C211yesmaximal, characteristic, complemented
3C13×#1802C211yesmaximal, characteristic, complemented
4C13×#1802C211yesmaximal, characteristic, complemented
5C2×C13×D4⋊C8C211yesmaximal, characteristic, complemented
6C2×C13×D4⋊C8C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×C13×#121—21no—
9C2×C13×#121—21no—
10C2×C4×D4×C13C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×#102—21no—
15C2×C13×#102—21no—
16C2×C4×C8×C13C2211yescharacteristic
17C13×#394—22no—
18C13×#384C2211yescharacteristic
19C13×#384C2211yescharacteristic
20C13×#380—21no—
21C13×#380—21no—
22C13×#340—21no—
23C13×#340—21no—
24C13×#340—22no—
25C13×D4⋊C8—22no—
26C13×D4⋊C8—22no—
27C22×D4×C13—22no—
28C22×D4×C13D411yescharacteristic
29C22×D4×C13D411yescharacteristic
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×#121—42no—
36C13×#121—42no—
37C13×#121—42no—
38C13×#121—42no—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C4⋊C4D411yescharacteristic
54C2×C13×C4⋊C4D412yes—
55C2×C13×C22⋊C4—22no—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C42×C13C2311yescharacteristic
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×#102—42no—
65C13×#102—42no—
66C4×C8×C13—21no—
67C4×C8×C13D412yescomplemented
68C13×#95—22no—
69#10431C1311yesmaximal, characteristic, direct product factor, Sylow
70C24×C13—21no—
71C24×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—44no—
83C2×D4×C13—44no—
84C2×D4×C13—82no—
85C2×D4×C13D812yes—
86C2×D4×C13SD1612yes—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C2×C8×C13—22no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C2×C8×C13—41no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—42no—
120C13×C4⋊C4—42no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—41no—
129C13×C22⋊C4—44no—
130C13×C22⋊C4—44no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C42×C13C2×D411yescharacteristic
136C42×C13#4111yescharacteristic
137C42×C13#4111yescharacteristic
138C42×C13#4111yescharacteristic
139#2537C2×C1311yescharacteristic
140#1834C2×C1311yescharacteristic, complemented
141#1802C2×C1311yescharacteristic, complemented
142#1802C2×C1311yescharacteristic, complemented
143C2×D4⋊C8C2×C1311yescharacteristic, complemented
144C2×D4⋊C8C2×C1311yescharacteristic, complemented
145#1296C2×C1311yescharacteristic, complemented
146C23×C13—22no—
147C23×C13—22no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13#12011yescharacteristic
161D4×C13—22no—
162D4×C13—22no—
163D4×C13—22no—
164D4×C13—22no—
165D4×C13—41no—
166D4×C13—41no—
167D4×C13—41no—
168D4×C13—41no—
169D4×C13—88no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—81no—
182C2×C4×C13—81no—
183C2×C4×C13—81no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13—81no—
188C2×C4×C13—81no—
189C2×C4×C13—81no—
190C2×C4×C13—81no—
191C2×C4×C13—81no—
192C2×C4×C13#12111yescharacteristic
193C2×C4×C13#12111yescharacteristic
194C2×C4×C13#12111yescharacteristic
195C2×C4×C13#12311yescharacteristic
196C2×C4×C13#12311yescharacteristic
197C2×C4×C13#12411yescharacteristic
198C2×C4×C13C2×D811yescharacteristic
199C2×C4×C13C2×SD1611yescharacteristic
200C2×C4×C13#13511yescharacteristic
201C2×C4×C13#13511yescharacteristic
202C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C13#13711yescharacteristic
206C8×C13—42no—
207C8×C13—81no—
208C8×C13—81no—
209C2×#121—21no—
210C2×#121—21no—
211C2×C4×D4C22×C1311yescharacteristic
212C2×C4×D4C22×C1311yescharacteristic
213C2×C4⋊C8C22×C1311yescharacteristic
214C2×C4⋊C8C22×C1311yescharacteristic
215C2×#102—21no—
216C2×#102—21no—
217C2×C4×C8C22×C1311yescharacteristic
218#394—22no—
219#384C22×C1311yescharacteristic
220#384C22×C1311yescharacteristic
221#380—21no—
222#380—21no—
223#340—21no—
224#340—21no—
225#340—22no—
226D4⋊C8—22no—
227D4⋊C8—22no—
228C22×C13—42no—
229C22×C13—42no—
230C22×C13—42no—
231C22×C13—42no—
232C22×C13—42no—
233C22×C13—42no—
234C22×C13—81no—
235C22×C13—81no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13—81no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13#39411yescharacteristic
243C22×C13#44711yescharacteristic
244C22×C13#44911yescharacteristic
245C22×C13#45011yescharacteristic
246C22×C13#45211yescharacteristic
247C22×C13#45411yescharacteristic
248C22×C13#45511yescharacteristic
249C4×C13—21no—
250C4×C13—21no—
251C4×C13—82no—
252C4×C13—81no—
253C4×C13—81no—
254C4×C13—161no—
255C4×C13#46511yescharacteristic
256C4×C13#46611yescharacteristic
257C4×C13#46811yescharacteristic
258C4×C13#46911yescharacteristic
259C4×C13#48011yescharacteristic
260C4×C13#48111yescharacteristic
261C4×C13#48211yescharacteristic
262C4×C13#48211yescharacteristic
263C22×D4—22no—
264C22×D4D4×C1311yescharacteristic
265C22×D4D4×C1311yescharacteristic
266C23×C4—21no—
267C23×C4—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271#121—42no—
272#121—42no—
273#121—42no—
274#121—42no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4D4×C1311yescharacteristic
289C2×C4⋊C4D4×C1311yescharacteristic
290C2×C4⋊C4D4×C1312yes—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C42C23×C1311yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300#102—42no—
301#102—42no—
302C4×C8—21no—
303C4×C8D4×C1312yescomplemented
304#95—22no—
305C2×C13—82no—
306C2×C13—82no—
307C2×C13#162511yescharacteristic
308C2×C13#163511yescharacteristic
309C2×C13#163911yescharacteristic
310C2×C13#164611yescharacteristic
311C2×C13#203311yescharacteristic
312C2×C13#203411yescharacteristic
313C2×C13#204011yescharacteristic
314C24—21no—
315C24—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—44no—
327C2×D4—44no—
328C2×D4—82no—
329C2×D4C13×D812yes—
330C2×D4C13×SD1612yes—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4C2×D4×C1311yescharacteristic
348C22×C4C2×D4×C1311yescharacteristic
349C22×C4C2×D4×C1311yescharacteristic
350C2×C8—22no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42C2×D4×C1311yescharacteristic
380C42C13×#4111yescharacteristic
381C42C13×#4111yescharacteristic
382C42C13×#4111yescharacteristic
383C13#1043111yescharacteristic, direct product factor, Sylow
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23C13×#12011yescharacteristic
399D4—22no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—88no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4C13×#12111yescharacteristic
431C2×C4C13×#12111yescharacteristic
432C2×C4C13×#12111yescharacteristic
433C2×C4C13×#12311yescharacteristic
434C2×C4C13×#12311yescharacteristic
435C2×C4C13×#12411yescharacteristic
436C2×C4C2×C13×D811yescharacteristic
437C2×C4C2×C13×SD1611yescharacteristic
438C2×C4C13×#13511yescharacteristic
439C2×C4C13×#13511yescharacteristic
440C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
441C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
442C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
443C2×C4C13×#13711yescharacteristic
444C8—42no—
445C8—81no—
446C8—81no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22C13×#39411yescharacteristic
462C22C13×#44711yescharacteristic
463C22C13×#44911yescharacteristic
464C22C13×#45011yescharacteristic
465C22C13×#45211yescharacteristic
466C22C13×#45411yescharacteristic
467C22C13×#45511yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—81no—
472C4—82no—
473C4—161no—
474C4C13×#46511yescharacteristic
475C4C13×#46611yescharacteristic
476C4C13×#46811yescharacteristic
477C4C13×#46911yescharacteristic
478C4C13×#48011yescharacteristic
479C4C13×#48111yescharacteristic
480C4C13×#48211yescharacteristic
481C4C13×#48211yescharacteristic
482C2—82no—
483C2—82no—
484C2C13×#162511yescharacteristic
485C2C13×#163511yescharacteristic
486C2C13×#163911yescharacteristic
487C2C13×#164611yescharacteristic
488C2C13×#203311yescharacteristic
489C2C13×#203411yescharacteristic
490C2C13×#204011yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#2537C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1834C2semidirect
3. C13×#1802C2semidirect
4. C13×#1802C2semidirect
5. C2×C13×D4⋊C8C2semidirect
6. C2×C13×D4⋊C8C2semidirect
7. C13×#1296C2semidirect
67. C4×C8×C13D4semidirect
69. #10431C13direct (N × H)
140. #1834C2×C13semidirect
141. #1802C2×C13semidirect
142. #1802C2×C13semidirect
143. C2×D4⋊C8C2×C13semidirect
144. C2×D4⋊C8C2×C13semidirect
145. #1296C2×C13semidirect
303. C4×C8D4×C13semidirect
383. C13#10431direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25372
C13×#18342
C13×#18022
C2×C13×D4⋊C82
C13×#12962
#1043113