Finite Group Databasebeta

← C13×#18361 #15704700

Subgroups — C13×#18361 #15704700

Order 3328.

930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic
2C13×#3238C212yesmaximal, complemented
3C13×#2621C211yesmaximal, characteristic, complemented
4C13×#1609C214yesmaximal, complemented
5C13×#1608C212yesmaximal, complemented
6C13×#1607C212yesmaximal
7C13×#1512C212yesmaximal, complemented
8C13×#1464C211yesmaximal, characteristic, complemented
9C13×#552—22no—
10C13×#552—22no—
11C13×#551—22no—
12C13×#551—22no—
13C13×#543C2211yescharacteristic
14C13×#539—21no—
15C13×#539C2212yes—
16C13×#534C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic, complemented
18C13×#529—21no—
19C13×#529C2212yes—
20C2×C13×#123—21no—
21C2×C13×C22⋊Q8—21no—
22C13×#518—21no—
23C2×C13×#117C2211yescharacteristic
24C13×#501—22no—
25C13×#489—22no—
26C13×#483C2214yescomplemented
27C13×#480C2214yes—
28C13×#477—22no—
29C13×#476—22no—
30C13×#432C2212yescomplemented
31C13×#398—21no—
32C13×#398C2212yescomplemented
33C13×#397—21no—
34C13×#397C2212yes—
35C13×#391—21no—
36C13×#382C2211yescharacteristic, complemented
37C13×#328C2214yescomplemented
38C13×#327C2214yes—
39C13×#324C2212yescomplemented
40C13×#323C2212yes—
41C22×Q8×C13—21no—
42C22×D4×C13—21no—
43C23×C4×C13D411yescharacteristic
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8—22no—
46C13×#126—22no—
47C13×#126—22no—
48C13×#126—22no—
49C13×#126—22no—
50C13×#125—21no—
51C13×#125—22no—
52C13×#125—22no—
53C13×#125D412yes—
54C13×#124—21no—
55C13×#124D412yes—
56C13×#123—22no—
57C13×#123—22no—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—44no—
69C13×C22⋊Q8C2312yes—
70C13×#121—21no—
71C13×#121C2312yes—
72C13×#120—22no—
73C4×Q8×C13—21no—
74C4×Q8×C13D412yes—
75C4×D4×C13—22no—
76C4×D4×C13—22no—
77C4×D4×C13—21no—
78C4×D4×C13—22no—
79C4×D4×C13—22no—
80C4×D4×C13D412yes—
81C13×#117—22no—
82C13×#117—22no—
83C13×#117—22no—
84C13×#117—22no—
85C13×#117—22no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4D411yescharacteristic
92C2×C13×C4⋊C4C2312yes—
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4D411yescharacteristic
100C2×C13×C22⋊C4C2311yescharacteristic
101C2×C42×C13D411yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C13×#107—24no—
104C13×#106—24no—
105C13×C4⋊C8—22no—
106C13×#103—24no—
107C13×#102—24no—
108C13×C22⋊C8C2314yes—
109C13×#97—22no—
110C13×#95—21no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95C2312yes—
114#18361C1311yesmaximal, characteristic, direct product factor, Sylow
115C24×C13—21no—
116C24×C13C2×D411yescharacteristic
117C2×Q8×C13—21no—
118C2×Q8×C13—42no—
119C2×Q8×C13—42no—
120C2×Q8×C13—41no—
121C2×Q8×C13—41no—
122C2×Q8×C13C2×D412yes—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—21no—
126C2×D4×C13—42no—
127C2×D4×C13—42no—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—41no—
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—24no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—44no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4C2×D412yes—
164C13×C4⋊C4C2×D412yes—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—44no—
178C42×C13—22no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—22no—
182C42×C13C2×D412yes—
183C42×C13C2×D412yes—
184#3491C2×C1311yescharacteristic
185#3238C2×C1312yescomplemented
186#2621C2×C1311yescharacteristic, complemented
187#1609C2×C1314yescomplemented
188#1608C2×C1312yescomplemented
189#1607C2×C1312yes—
190#1512C2×C1312yescomplemented
191#1464C2×C1311yescharacteristic, complemented
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—22no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—42no—
198C23×C13—81no—
199C23×C13—81no—
200C23×C13AGL(1,ℤ/8)12yes—
201C23×C13C22×D411yescharacteristic
202Q8×C13—42no—
203Q8×C13—82no—
204Q8×C13—82no—
205Q8×C13—81no—
206D4×C13—42no—
207D4×C13—44no—
208D4×C13—42no—
209D4×C13—42no—
210D4×C13—81no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—82no—
235C2×C4×C13—81no—
236C2×C4×C13—82no—
237C2×C4×C13—81no—
238C2×C4×C13#12012yes—
239C2×C4×C13#12011yescharacteristic
240C2×C4×C13#12011yescharacteristic
241C2×C4×C13C22×D412yes—
242C8×C13—44no—
243#552—22no—
244#552—22no—
245#551—22no—
246#551—22no—
247#543C22×C1311yescharacteristic
248#539—21no—
249#539C22×C1312yes—
250#534C22×C1311yescharacteristic
251C2×C4⋊Q8C22×C1311yescharacteristic, complemented
252#529—21no—
253#529C22×C1312yes—
254C2×#123—21no—
255C2×C22⋊Q8—21no—
256#518—21no—
257C2×#117C22×C1311yescharacteristic
258#501—22no—
259#489—22no—
260#483C22×C1314yescomplemented
261#480C22×C1314yes—
262#477—22no—
263#476—22no—
264#432C22×C1312yescomplemented
265#398—21no—
266#398C22×C1312yescomplemented
267#397—21no—
268#397C22×C1312yes—
269#391—21no—
270#382C22×C1311yescharacteristic, complemented
271#328C22×C1314yescomplemented
272#327C22×C1314yes—
273#324C22×C1312yescomplemented
274#323C22×C1312yes—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—22no—
278C22×C13—42no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—81no—
285C22×C13—162no—
286C22×C13C2×#12011yescharacteristic
287C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C13#57511yescharacteristic
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—22no—
292C4×C13—22no—
293C4×C13—41no—
294C4×C13—42no—
295C4×C13—41no—
296C4×C13—42no—
297C4×C13—41no—
298C4×C13—42no—
299C4×C13—82no—
300C4×C13—82no—
301C22×Q8—21no—
302C22×D4—21no—
303C23×C4D4×C1311yescharacteristic
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#126—22no—
307#126—22no—
308#126—22no—
309#126—22no—
310#125—21no—
311#125—22no—
312#125—22no—
313#125D4×C1312yes—
314#124—21no—
315#124D4×C1312yes—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322#123—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—21no—
327C22⋊Q8—22no—
328C22⋊Q8—44no—
329C22⋊Q8C23×C1312yes—
330#121—21no—
331#121C23×C1312yes—
332#120—22no—
333C4×Q8—21no—
334C4×Q8D4×C1312yes—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4D4×C1312yes—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4D4×C1311yescharacteristic
352C2×C4⋊C4C23×C1312yes—
353C2×C4⋊C4C23×C1311yescharacteristic
354C2×C22⋊C4—22no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4D4×C1311yescharacteristic
360C2×C22⋊C4C23×C1311yescharacteristic
361C2×C42D4×C1311yescharacteristic
362C2×C42C23×C1311yescharacteristic
363#107—24no—
364#106—24no—
365C4⋊C8—22no—
366#103—24no—
367#102—24no—
368C22⋊C8C23×C1314yes—
369#97—22no—
370#95—21no—
371#95—22no—
372#95—22no—
373#95C23×C1312yes—
374C2×C13—21no—
375C2×C13—21no—
376C2×C13—42no—
377C2×C13—82no—
378C2×C13#300611yescharacteristic
379C2×C13#302211yescharacteristic
380C2×C13#302811yescharacteristic
381C24—21no—
382C24C2×D4×C1311yescharacteristic
383C2×Q8—21no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8C2×D4×C1312yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4C2×D4×C1312yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—41no—
406C22×C4C2×D4×C1311yescharacteristic
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C2×D4×C1311yescharacteristic
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C24×C1311yescharacteristic
412C2×C8—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—42no—
427C4⋊C4—44no—
428C4⋊C4—42no—
429C4⋊C4C2×D4×C1312yes—
430C4⋊C4C2×D4×C1312yes—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—44no—
444C42—22no—
445C42—21no—
446C42—21no—
447C42—22no—
448C42C2×D4×C1312yes—
449C42C2×D4×C1312yes—
450C13#1836111yescharacteristic, direct product factor, Sylow
451C23—21no—
452C23—21no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—81no—
458C23—81no—
459C23C13×AGL(1,ℤ/8)12yes—
460C23C22×D4×C1311yescharacteristic
461Q8—42no—
462Q8—82no—
463Q8—82no—
464Q8—81no—
465D4—42no—
466D4—44no—
467D4—42no—
468D4—42no—
469D4—81no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4C13×#12012yes—
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12011yescharacteristic
500C2×C4C22×D4×C1312yes—
501C8—44no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—162no—
513C22C2×C13×#12011yescharacteristic
514C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
515C22C13×#57511yescharacteristic
516C4—21no—
517C4—21no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—82no—
527C4—82no—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—82no—
532C2C13×#300611yescharacteristic
533C2C13×#302211yescharacteristic
534C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#534C22
LCSG ▷ C22×C4 ▷ 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×#3238C2semidirect
3. C13×#2621C2semidirect
4. C13×#1609C2semidirect
5. C13×#1608C2semidirect
7. C13×#1512C2semidirect
8. C13×#1464C2semidirect
17. C2×C13×C4⋊Q8C22semidirect
26. C13×#483C22semidirect
30. C13×#432C22semidirect
32. C13×#398C22semidirect
36. C13×#382C22semidirect
37. C13×#328C22semidirect
39. C13×#324C22semidirect
114. #18361C13direct (N × H)
185. #3238C2×C13semidirect
186. #2621C2×C13semidirect
187. #1609C2×C13semidirect
188. #1608C2×C13semidirect
190. #1512C2×C13semidirect
191. #1464C2×C13semidirect
251. C2×C4⋊Q8C22×C13semidirect
260. #483C22×C13semidirect
264. #432C22×C13semidirect
266. #398C22×C13semidirect
270. #382C22×C13semidirect
271. #328C22×C13semidirect
273. #324C22×C13semidirect
450. C13#18361direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34912
C13×#32382
C13×#26212
C13×#16092
C13×#16082
C13×#16072
C13×#15122
C13×#14642
#1836113