Finite Group Databasebeta

← C13×#18344 #15704683

Subgroups — C13×#18344 #15704683

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3461C211yesmaximal, characteristic
2C13×#3238C212yesmaximal, complemented
3C13×#2546C211yesmaximal, characteristic, complemented
4C13×#1611C212yesmaximal, complemented
5C13×#1610C212yesmaximal
6C13×#1609C214yesmaximal, complemented
7C13×#1509C212yesmaximal, complemented
8C13×#1467C211yesmaximal, characteristic, complemented
9C13×#544C2211yescharacteristic
10C13×#542—22no—
11C13×#541—22no—
12C13×#539—21no—
13C13×#539C2212yes—
14C13×#537C2211yescharacteristic
15C13×#536—21no—
16C13×#533—22no—
17C2×C13×C4⋊Q8—21no—
18C2×C13×C4⋊Q8C2211yescharacteristic
19C13×#529—22no—
20C13×#529—21no—
21C13×#529C2212yes—
22C4×C13×#41—21no—
23C2×C4×Q8×C13C2211yescharacteristic
24C13×#501—22no—
25C13×#489—22no—
26C13×#483C2214yes—
27C13×#480C2214yes—
28C13×#477—22no—
29C13×#476—22no—
30C13×#432C2212yes—
31C13×#398C2212yes—
32C13×#398C2212yes—
33C13×#391—21no—
34C13×#389—21no—
35C13×#389—21no—
36C4×C13×C4⋊C4C2211yescharacteristic
37C13×#328C2214yes—
38C13×#327C2214yes—
39C13×#324C2212yes—
40C13×#324C2212yes—
41C2×C13×#41—21no—
42C22×Q8×C13—21no—
43C22×Q8×C13D411yescharacteristic
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8—22no—
46C13×C4⋊Q8—22no—
47C13×C4⋊Q8—22no—
48C13×C4⋊Q8—44no—
49C13×#126—22no—
50C13×#126—22no—
51C13×#126—22no—
52C13×#126—22no—
53C13×#125—21no—
54C13×#125—22no—
55C13×#125—22no—
56C13×#125—22no—
57C13×#125D412yes—
58C13×#124—22no—
59C13×#124—21no—
60C13×#124D412yes—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8—22no—
71C13×C22⋊Q8C2312yes—
72C13×#121—22no—
73C13×#121—21no—
74C13×#121C2312yes—
75C4×Q8×C13—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C4×Q8×C13—22no—
79C4×Q8×C13—22no—
80C4×Q8×C13D412yes—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13—22no—
85C4×D4×C13—22no—
86C4×D4×C13D412yes—
87C13×#117—22no—
88C13×#117—22no—
89C13×#117—21no—
90C13×#117—22no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C4⋊C4C2312yes—
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C42×C13—22no—
100C2×C42×C13—21no—
101C2×C42×C13D411yescharacteristic
102C2×C42×C13D411yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C13×#107—24no—
105C13×#106—24no—
106C13×C4⋊C8—22no—
107C13×#103—24no—
108C13×#102—24no—
109C13×C22⋊C8C2314yes—
110C13×#97—22no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95C2312yes—
114#18344C1311yesmaximal, characteristic, direct product factor, Sylow
115C13×#41—42no—
116C13×#41—42no—
117C2×Q8×C13—21no—
118C2×Q8×C13—21no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—41no—
122C2×Q8×C13—42no—
123C2×Q8×C13—42no—
124C2×Q8×C13—42no—
125C2×Q8×C13C2×D412yes—
126C2×D4×C13—21no—
127C2×D4×C13—22no—
128C2×D4×C13—21no—
129C2×D4×C13C2×D412yes—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C2×C8×C13—24no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
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—44no—
161C13×C4⋊C4—41no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4—44no—
164C13×C4⋊C4C2×D412yes—
165C13×C4⋊C4C2×D412yes—
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—
175C42×C13—22no—
176C42×C13—22no—
177C42×C13—21no—
178C42×C13—22no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—42no—
183C42×C13C2×D412yes—
184C42×C13C2×D412yes—
185#3461C2×C1311yescharacteristic
186#3238C2×C1312yescomplemented
187#2546C2×C1311yescharacteristic, complemented
188#1611C2×C1312yescomplemented
189#1610C2×C1312yes—
190#1609C2×C1314yescomplemented
191#1509C2×C1312yescomplemented
192#1467C2×C1311yescharacteristic, complemented
193C23×C13—22no—
194C23×C13C22×D411yescharacteristic
195Q8×C13—44no—
196Q8×C13—42no—
197Q8×C13—42no—
198Q8×C13—84no—
199Q8×C13—81no—
200D4×C13—42no—
201D4×C13—42no—
202D4×C13—42no—
203D4×C13—42no—
204D4×C13—81no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—41no—
220C2×C4×C13—44no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—44no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—82no—
230C2×C4×C13#12011yescharacteristic
231C2×C4×C13#12012yes—
232C2×C4×C13#12011yescharacteristic
233C2×C4×C13AGL(1,ℤ/8)12yes—
234C2×C4×C13C22×D412yes—
235C8×C13—44no—
236#544C22×C1311yescharacteristic
237#542—22no—
238#541—22no—
239#539—21no—
240#539C22×C1312yes—
241#537C22×C1311yescharacteristic
242#536—21no—
243#533—22no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8C22×C1311yescharacteristic
246#529—22no—
247#529—21no—
248#529C22×C1312yes—
249C4×#41—21no—
250C2×C4×Q8C22×C1311yescharacteristic
251#501—22no—
252#489—22no—
253#483C22×C1314yes—
254#480C22×C1314yes—
255#477—22no—
256#476—22no—
257#432C22×C1312yes—
258#398C22×C1312yes—
259#398C22×C1312yes—
260#391—21no—
261#389—21no—
262#389—21no—
263C4×C4⋊C4C22×C1311yescharacteristic
264#328C22×C1314yes—
265#327C22×C1314yes—
266#324C22×C1312yes—
267#324C22×C1312yes—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—42no—
271C22×C13—42no—
272C22×C13—42no—
273C22×C13C2×#12011yescharacteristic
274C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C13#57511yescharacteristic
276C4×C13—22no—
277C4×C13—22no—
278C4×C13—21no—
279C4×C13—22no—
280C4×C13—44no—
281C4×C13—41no—
282C4×C13—42no—
283C4×C13—42no—
284C4×C13—41no—
285C4×C13—41no—
286C4×C13—42no—
287C4×C13—82no—
288C4×C13#45612yes—
289C2×#41—21no—
290C22×Q8—21no—
291C22×Q8D4×C1311yescharacteristic
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C4⋊Q8—44no—
297#126—22no—
298#126—22no—
299#126—22no—
300#126—22no—
301#125—21no—
302#125—22no—
303#125—22no—
304#125—22no—
305#125D4×C1312yes—
306#124—22no—
307#124—21no—
308#124D4×C1312yes—
309#123—22no—
310#123—22no—
311#123—22no—
312#123—22no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—21no—
318C22⋊Q8—22no—
319C22⋊Q8C23×C1312yes—
320#121—22no—
321#121—21no—
322#121C23×C1312yes—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8D4×C1312yes—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4D4×C1312yes—
335#117—22no—
336#117—22no—
337#117—21no—
338#117—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4D4×C1311yescharacteristic
344C2×C4⋊C4C23×C1312yes—
345C2×C4⋊C4C23×C1311yescharacteristic
346C2×C4⋊C4C23×C1311yescharacteristic
347C2×C42—22no—
348C2×C42—21no—
349C2×C42D4×C1311yescharacteristic
350C2×C42D4×C1311yescharacteristic
351C2×C42C23×C1311yescharacteristic
352#107—24no—
353#106—24no—
354C4⋊C8—22no—
355#103—24no—
356#102—24no—
357C22⋊C8C23×C1314yes—
358#97—22no—
359#95—22no—
360#95—22no—
361#95C23×C1312yes—
362C2×C13—21no—
363C2×C13—21no—
364C2×C13—82no—
365C2×C13#300611yescharacteristic
366C2×C13C2×#45611yescharacteristic
367C2×C13#302811yescharacteristic
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—41no—
375C2×Q8—42no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8C2×D4×C1312yes—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4C2×D4×C1312yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4C2×D4×C1311yescharacteristic
389C22×C4C2×D4×C1311yescharacteristic
390C22×C4C2×D4×C1311yescharacteristic
391C22×C4C2×D4×C1311yescharacteristic
392C22×C4C2×D4×C1311yescharacteristic
393C22×C4C2×D4×C1311yescharacteristic
394C22×C4C24×C1311yescharacteristic
395C2×C8—24no—
396C4⋊C4—24no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—24no—
413C4⋊C4—44no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—44no—
417C4⋊C4C2×D4×C1312yes—
418C4⋊C4C2×D4×C1312yes—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C42—22no—
429C42—22no—
430C42—21no—
431C42—22no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42—42no—
436C42C2×D4×C1312yes—
437C42C2×D4×C1312yes—
438C13#1834411yescharacteristic, direct product factor, Sylow
439C23—22no—
440C23C22×D4×C1311yescharacteristic
441Q8—44no—
442Q8—42no—
443Q8—42no—
444Q8—84no—
445Q8—81no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—81no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4C13×#12011yescharacteristic
477C2×C4C13×#12012yes—
478C2×C4C13×#12011yescharacteristic
479C2×C4C13×AGL(1,ℤ/8)12yes—
480C2×C4C22×D4×C1312yes—
481C8—44no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22C2×C13×#12011yescharacteristic
488C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
489C22C13×#57511yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—22no—
494C4—44no—
495C4—41no—
496C4—42no—
497C4—42no—
498C4—41no—
499C4—41no—
500C4—42no—
501C4—82no—
502C4C13×#45612yes—
503C2—21no—
504C2—21no—
505C2—82no—
506C2C13×#300611yescharacteristic
507C2C2×C13×#45611yescharacteristic
508C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#537C22
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×#2546C2semidirect
4. C13×#1611C2semidirect
6. C13×#1609C2semidirect
7. C13×#1509C2semidirect
8. C13×#1467C2semidirect
114. #18344C13direct (N × H)
186. #3238C2×C13semidirect
187. #2546C2×C13semidirect
188. #1611C2×C13semidirect
190. #1609C2×C13semidirect
191. #1509C2×C13semidirect
192. #1467C2×C13semidirect
438. C13#18344direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34612
C13×#32382
C13×#25462
C13×#16112
C13×#16102
C13×#16092
C13×#15092
C13×#14672
#1834413