Finite Group Databasebeta

← C13×#8427 #15694766

Subgroups — C13×#8427 #15694766

Order 3328.

700 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3509C211yesmaximal, characteristic
2C13×#1988C211yesmaximal, characteristic, complemented
3C13×#1806C211yesmaximal, characteristic
4C13×#1550C211yesmaximal, characteristic, complemented
5C13×#1546C211yesmaximal, characteristic, complemented
6C13×#1503C211yesmaximal, characteristic, complemented
7C13×#1477C211yesmaximal, characteristic
8C13×#557—21no—
9C13×#557C412yescomplemented
10C13×#556—21no—
11C13×#556C412yescomplemented
12C13×#552—22no—
13C13×#552—22no—
14C13×#541—22no—
15C13×#536—21no—
16C13×#533—21no—
17C13×#533—21no—
18C13×#533C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#519—21no—
21C4×C13×#41C2211yescharacteristic
22C13×#431C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#104—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C13×#340—22no—
28C13×#339—21no—
29C13×#333—21no—
30C13×#332—22no—
31C13×#332—21no—
32C13×#328—22no—
33C13×Q8⋊C8—21no—
34C13×D4⋊C8—21no—
35C2×C13×#41D411yescharacteristic
36C22×Q8×C13—21no—
37C2×C13×M16—21no—
38C22×C8×C13—21no—
39C13×C4⋊Q8—22no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8C2×C412yes—
43C13×C4⋊Q8D411yescharacteristic
44C13×C4⋊Q8D412yes—
45C13×C4⋊Q8D411yescharacteristic
46C13×#126—24no—
47C13×#126—24no—
48C13×#125—22no—
49C13×#125—24no—
50C13×#125—22no—
51C13×#125—24no—
52C13×#125—21no—
53C13×#124—22no—
54C13×#123—24no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—22no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—21no—
60C13×C22⋊Q8D412yes—
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—21no—
68C4×Q8×C13C2×C411yescharacteristic
69C4×Q8×C13C2×C412yes—
70C4×Q8×C13D411yescharacteristic
71C4×D4×C13—21no—
72C4×D4×C13—21no—
73C4×D4×C13C2×C411yescharacteristic
74C4×D4×C13D411yescharacteristic
75C13×#117—24no—
76C13×#117—22no—
77C13×#117—21no—
78C13×#117—22no—
79C13×#117—21no—
80C13×#117D411yescharacteristic
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4D412yes—
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C13×C4⋊C8—21no—
88C13×C4⋊C8—21no—
89C13×C4⋊C8—21no—
90C13×C4⋊C8—21no—
91C13×C4⋊C8—21no—
92C13×#104—42no—
93C13×C22⋊C8—21no—
94C4×C8×C13—21no—
95C13×#95—21no—
96#8427C1311yesmaximal, characteristic, direct product factor, Sylow
97C13×#41—21no—
98C13×#41—21no—
99C13×#41—21no—
100C13×#41—21no—
101C2×Q8×C13—22no—
102C2×Q8×C13—21no—
103C2×Q8×C13—22no—
104C2×Q8×C13—41no—
105C2×Q8×C13—41no—
106C2×Q8×C13—41no—
107C2×Q8×C13—41no—
108C2×Q8×C13C22⋊C411yescharacteristic
109C2×Q8×C13C22⋊C412yes—
110C2×D4×C13—21no—
111C2×D4×C13C22⋊C411yescharacteristic
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—41no—
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C13×M16—41no—
121C13×M16—41no—
122C2×C8×C13—42no—
123C2×C8×C13—41no—
124C2×C8×C13—41no—
125C2×C8×C13—41no—
126C13×C4⋊C4—24no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—24no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4C22⋊C414yes—
143C13×C4⋊C4C22⋊C412yes—
144C13×C4⋊C4C22⋊C411yescharacteristic
145C13×C4⋊C4C22⋊C411yescharacteristic
146C13×C22⋊C4—24no—
147C13×C22⋊C4—24no—
148C13×C22⋊C4—21no—
149C13×C22⋊C4—22no—
150C13×C22⋊C4—21no—
151C13×C22⋊C4—21no—
152C42×C13—24no—
153C42×C13—24no—
154C42×C13—21no—
155C42×C13—22no—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13—41no—
159C42×C13—41no—
160C42×C13C22×C411yescharacteristic
161C42×C13C2×D411yescharacteristic
162C42×C13C2×D411yescharacteristic
163C42×C13C2×D411yescharacteristic
164#3509C2×C1311yescharacteristic
165#1988C2×C1311yescharacteristic, complemented
166#1806C2×C1311yescharacteristic
167#1550C2×C1311yescharacteristic, complemented
168#1546C2×C1311yescharacteristic, complemented
169#1503C2×C1311yescharacteristic, complemented
170#1477C2×C1311yescharacteristic
171C23×C13—21no—
172C23×C13#12011yescharacteristic
173Q8×C13—21no—
174Q8×C13—21no—
175Q8×C13—42no—
176Q8×C13—42no—
177Q8×C13—42no—
178Q8×C13—42no—
179Q8×C13—42no—
180Q8×C13—41no—
181Q8×C13—41no—
182D4×C13—21no—
183D4×C13—21no—
184D4×C13—41no—
185D4×C13—41no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—24no—
193C2×C4×C13—21no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13—81no—
204C2×C4×C13—81no—
205C2×C4×C13C2×C22⋊C411yescharacteristic
206C2×C4×C13C2×C22⋊C411yescharacteristic
207C2×C4×C13C2×C22⋊C411yescharacteristic
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12011yescharacteristic
210C2×C4×C13#12011yescharacteristic
211C2×C4×C13#13511yescharacteristic
212C2×C4×C13#13511yescharacteristic
213C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
214C2×C4×C13#13711yescharacteristic
215C8×C13—81no—
216C8×C13—81no—
217C8×C13—81no—
218#557—21no—
219#557C4×C1312yescomplemented
220#556—21no—
221#556C4×C1312yescomplemented
222#552—22no—
223#552—22no—
224#541—22no—
225#536—21no—
226#533—21no—
227#533—21no—
228#533C22×C1311yescharacteristic
229C2×C4⋊Q8C22×C1311yescharacteristic
230#519—21no—
231C4×#41C22×C1311yescharacteristic
232#431C22×C1311yescharacteristic
233#423C22×C1311yescharacteristic
234C2×C4⋊C8C22×C1311yescharacteristic
235C2×#104—21no—
236C4×C4⋊C4C22×C1311yescharacteristic
237#340—22no—
238#339—21no—
239#333—21no—
240#332—22no—
241#332—21no—
242#328—22no—
243Q8⋊C8—21no—
244D4⋊C8—21no—
245C22×C13—21no—
246C22×C13—21no—
247C22×C13—41no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13#37911yescharacteristic
251C22×C13#44911yescharacteristic
252C22×C13#45211yescharacteristic
253C4×C13—21no—
254C4×C13—21no—
255C4×C13—21no—
256C4×C13—41no—
257C4×C13—42no—
258C4×C13—41no—
259C4×C13—42no—
260C4×C13—41no—
261C4×C13—44no—
262C4×C13—82no—
263C4×C13#41611yescharacteristic
264C4×C13#41711yescharacteristic
265C4×C13#44911yescharacteristic
266C4×C13#45211yescharacteristic
267C4×C13#45411yescharacteristic
268C4×C13#45611yescharacteristic
269C2×#41D4×C1311yescharacteristic
270C22×Q8—21no—
271C2×M16—21no—
272C22×C8—21no—
273C4⋊Q8—22no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8C2×C4×C1312yes—
277C4⋊Q8D4×C1311yescharacteristic
278C4⋊Q8D4×C1312yes—
279C4⋊Q8D4×C1311yescharacteristic
280#126—24no—
281#126—24no—
282#125—22no—
283#125—24no—
284#125—22no—
285#125—24no—
286#125—21no—
287#124—22no—
288#123—24no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—21no—
294C22⋊Q8D4×C1312yes—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—21no—
302C4×Q8C2×C4×C1311yescharacteristic
303C4×Q8C2×C4×C1312yes—
304C4×Q8D4×C1311yescharacteristic
305C4×D4—21no—
306C4×D4—21no—
307C4×D4C2×C4×C1311yescharacteristic
308C4×D4D4×C1311yescharacteristic
309#117—24no—
310#117—22no—
311#117—21no—
312#117—22no—
313#117—21no—
314#117D4×C1311yescharacteristic
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C1312yes—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42C23×C1311yescharacteristic
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326#104—42no—
327C22⋊C8—21no—
328C4×C8—21no—
329#95—21no—
330C2×C13—21no—
331C2×C13—21no—
332C2×C13—81no—
333C2×C13#178811yescharacteristic
334C2×C13#179311yescharacteristic
335C2×C13#179611yescharacteristic
336#41—21no—
337#41—21no—
338#41—21no—
339#41—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8C13×C22⋊C411yescharacteristic
348C2×Q8C13×C22⋊C412yes—
349C2×D4—21no—
350C2×D4C13×C22⋊C411yescharacteristic
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4C2×D4×C1311yescharacteristic
357C22×C4C2×D4×C1311yescharacteristic
358C22×C4C2×D4×C1311yescharacteristic
359M16—41no—
360M16—41no—
361C2×C8—42no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—41no—
381C4⋊C4C13×C22⋊C414yes—
382C4⋊C4C13×C22⋊C412yes—
383C4⋊C4C13×C22⋊C411yescharacteristic
384C4⋊C4C13×C22⋊C411yescharacteristic
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—21no—
388C22⋊C4—22no—
389C22⋊C4—21no—
390C22⋊C4—21no—
391C42—24no—
392C42—24no—
393C42—21no—
394C42—22no—
395C42—21no—
396C42—21no—
397C42—41no—
398C42—41no—
399C42C22×C4×C1311yescharacteristic
400C42C2×D4×C1311yescharacteristic
401C42C2×D4×C1311yescharacteristic
402C42C2×D4×C1311yescharacteristic
403C13#842711yescharacteristic, direct product factor, Sylow
404C23—21no—
405C23C13×#12011yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—42no—
412Q8—42no—
413Q8—41no—
414Q8—41no—
415D4—21no—
416D4—21no—
417D4—41no—
418D4—41no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4C2×C13×C22⋊C411yescharacteristic
439C2×C4C2×C13×C22⋊C411yescharacteristic
440C2×C4C2×C13×C22⋊C411yescharacteristic
441C2×C4C13×#12011yescharacteristic
442C2×C4C13×#12011yescharacteristic
443C2×C4C13×#12011yescharacteristic
444C2×C4C13×#13511yescharacteristic
445C2×C4C13×#13511yescharacteristic
446C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
447C2×C4C13×#13711yescharacteristic
448C8—81no—
449C8—81no—
450C8—81no—
451C22—21no—
452C22—21no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22C13×#37911yescharacteristic
457C22C13×#44911yescharacteristic
458C22C13×#45211yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—44no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—42no—
468C4—82no—
469C4C13×#41611yescharacteristic
470C4C13×#41711yescharacteristic
471C4C13×#44911yescharacteristic
472C4C13×#45211yescharacteristic
473C4C13×#45411yescharacteristic
474C4C13×#45611yescharacteristic
475C2—21no—
476C2—21no—
477C2—81no—
478C2C13×#178811yescharacteristic
479C2C13×#179311yescharacteristic
480C2C13×#179611yescharacteristic
subgroupG/H
center, socleC22×C13#379
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1988C2semidirect
4. C13×#1550C2semidirect
5. C13×#1546C2semidirect
6. C13×#1503C2semidirect
9. C13×#557C4semidirect
11. C13×#556C4semidirect
96. #8427C13direct (N × H)
165. #1988C2×C13semidirect
167. #1550C2×C13semidirect
168. #1546C2×C13semidirect
169. #1503C2×C13semidirect
219. #557C4×C13semidirect
221. #556C4×C13semidirect
403. C13#8427direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35092
C13×#19882
C13×#18062
C13×#15502
C13×#15462
C13×#15032
C13×#14772
#842713