Finite Group Databasebeta

← C13×#33571 #15719910

Subgroups — C13×#33571 #15719910

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3550C211yesmaximal, characteristic, complemented
2C13×#3022C212yesmaximal, complemented
3C13×#3018C211yesmaximal, characteristic
4C13×#2205C214yesmaximal, complemented
5C13×#2203C214yesmaximal, complemented
6C13×#2135C212yesmaximal, complemented
7C13×#2132C211yesmaximal, characteristic, complemented
8C13×#585C2211yescharacteristic
9C13×#575—21no—
10C2×C13×#137—22no—
11C13×#563—21no—
12C13×#563C2212yescomplemented
13C13×#559—21no—
14Q82×C13C2212yescomplemented
15C13×#556—22no—
16D4×Q8×C13—22no—
17C13×#542—24no—
18C13×#536—21no—
19C13×#536C2212yes—
20C13×#533—21no—
21C13×#532C2211yescharacteristic
22C13×#456C2212yes—
23C13×#456C2218yes—
24C13×#455—21no—
25C13×#455—24no—
26C13×#454C2212yes—
27C13×#453—21no—
28C13×#421—22no—
29C2×C13×#104—21no—
30C13×#413C2211yescharacteristic
31C13×#413C2212yes—
32C13×#356C2212yescomplemented
33C13×#356C2218yescomplemented
34C13×#355C2212yescomplemented
35C13×2−1+4—41no—
36C13×2−1+4C2312yes—
37C13×H(5,𝔽2)—21no—
38C13×H(5,𝔽2)—22no—
39C13×H(5,𝔽2)—41no—
40C2×C13×#41—21no—
41C2×C13×#41—22no—
42C2×C13×#41—42no—
43C2×C13×#41D411yescharacteristic
44C2×C13×#41C2311yescharacteristic
45C22×Q8×C13—21no—
46C22×Q8×C13D412yes—
47C13×#137—28no—
48C13×#137—22no—
49C13×#137—41no—
50C13×#137—44no—
51C13×AGL(1,ℤ/8)—22no—
52C13×AGL(1,ℤ/8)—41no—
53C13×#135—42no—
54C2×C13×Q16—42no—
55C2×C13×SD16—42no—
56C2×C13×M16—21no—
57C2×C13×M16—22no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8—24no—
62C13×C4⋊Q8C2311yescharacteristic
63C13×C4⋊Q8C2314yes—
64C13×#127D411yescharacteristic
65C13×#126—24no—
66C13×#126—24no—
67C13×#125—22no—
68C13×#124—22no—
69C13×#124—24no—
70C13×#124D411yescharacteristic
71C13×#124D414yes—
72C13×#124C2311yescharacteristic
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—24no—
80C13×C22⋊Q8—24no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×#121—22no—
84C4×Q8×C13—22no—
85C4×Q8×C13—22no—
86C4×Q8×C13—24no—
87C4×D4×C13—24no—
88C4×D4×C13—22no—
89C13×#117—22no—
90C13×#117—21no—
91C13×#117D412yes—
92C2×C42×C13D411yescharacteristic
93C13×#104—22no—
94C13×#104—22no—
95C13×#104—28no—
96C13×#101C2314yes—
97C13×#101C2312yes—
98C13×#100—21no—
99C13×#100—22no—
100#33571C1311yesmaximal, characteristic, direct product factor, Sylow
101C13×#41—22no—
102C13×#41—24no—
103C13×#41—22no—
104C13×#41—24no—
105C13×#41—41no—
106C13×#41—41no—
107C13×#41—42no—
108C13×#41—41no—
109C13×#41—41no—
110C13×#41—41no—
111C13×#41—42no—
112C13×#41—42no—
113C13×#41—44no—
114C13×#41—41no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—21no—
120C2×Q8×C13—42no—
121C2×Q8×C13—42no—
122C2×Q8×C13—42no—
123C2×Q8×C13—81no—
124C2×Q8×C13—81no—
125C2×Q8×C13C2×D414yes—
126C2×Q8×C13C2×D411yescharacteristic
127C2×Q8×C13C2411yescharacteristic
128C2×D4×C13—22no—
129C2×D4×C13—21no—
130C2×D4×C13—22no—
131C2×D4×C13—21no—
132C2×D4×C13—42no—
133C2×D4×C13—44no—
134C2×D4×C13—41no—
135C2×D4×C13—42no—
136C2×D4×C13C2×D411yescharacteristic
137C2×D4×C13C2×D412yes—
138C2×D4×C13C2×D411yescharacteristic
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—41no—
144C22×C4×C13—42no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D412yes—
147C13×Q16—48no—
148C13×Q16—42no—
149C13×SD16—48no—
150C13×SD16—42no—
151C13×SD16—42no—
152C13×D8—42no—
153C13×M16—22no—
154C13×M16—24no—
155C13×M16—41no—
156C13×M16—42no—
157C2×C8×C13—42no—
158C2×C8×C13—41no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—24no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—24no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—22no—
175C42×C13—24no—
176C42×C13—22no—
177C42×C13—21no—
178C42×C13C2×D411yescharacteristic
179C42×C13C2×D411yescharacteristic
180C42×C13C2×D414yes—
181#3550C2×C1311yescharacteristic, complemented
182#3022C2×C1312yescomplemented
183#3018C2×C1311yescharacteristic
184#2205C2×C1314yescomplemented
185#2203C2×C1314yescomplemented
186#2135C2×C1312yescomplemented
187#2132C2×C1311yescharacteristic, complemented
188C23×C13—21no—
189C23×C13—42no—
190C23×C13—41no—
191C23×C13#12012yes—
192C23×C13#12011yescharacteristic
193Q8×C13—22no—
194Q8×C13—24no—
195Q8×C13—41no—
196Q8×C13—44no—
197Q8×C13—44no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13—42no—
201Q8×C13—42no—
202Q8×C13—82no—
203D4×C13—22no—
204D4×C13—24no—
205D4×C13—41no—
206D4×C13—42no—
207D4×C13—44no—
208D4×C13—41no—
209D4×C13—44no—
210D4×C13—42no—
211D4×C13—42no—
212D4×C13—41no—
213D4×C13—81no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
219C2×C4×C13—24no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—24no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—44no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—82no—
232C2×C4×C13—82no—
233C2×C4×C13#12011yescharacteristic
234C2×C4×C13C22×D412yes—
235C2×C4×C13C22×D411yescharacteristic
236C8×C13—42no—
237C8×C13—44no—
238#585C22×C1311yescharacteristic
239#575—21no—
240C2×#137—22no—
241#563—21no—
242#563C22×C1312yescomplemented
243#559—21no—
244Q82C22×C1312yescomplemented
245#556—22no—
246D4×Q8—22no—
247#542—24no—
248#536—21no—
249#536C22×C1312yes—
250#533—21no—
251#532C22×C1311yescharacteristic
252#456C22×C1318yes—
253#456C22×C1312yes—
254#455—21no—
255#455—24no—
256#454C22×C1312yes—
257#453—21no—
258#421—22no—
259C2×#104—21no—
260#413C22×C1312yes—
261#413C22×C1311yescharacteristic
262#356C22×C1312yescomplemented
263#356C22×C1318yescomplemented
264#355C22×C1312yescomplemented
265C22×C13—22no—
266C22×C13—21no—
267C22×C13—41no—
268C22×C13—42no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—162no—
273C22×C13—161no—
274C22×C13C2×#12011yescharacteristic
275C4×C13—22no—
276C4×C13—21no—
277C4×C13—22no—
278C4×C13—41no—
279C4×C13—44no—
280C4×C13—41no—
281C4×C13—44no—
282C4×C13—42no—
283C4×C13B(4,𝔽2)11yescharacteristic
284C4×C13B(4,𝔽2)11yescharacteristic
2852−1+4—41no—
2862−1+4C23×C1312yes—
287H(5,𝔽2)—21no—
288H(5,𝔽2)—22no—
289H(5,𝔽2)—41no—
290C2×#41—22no—
291C2×#41—21no—
292C2×#41—42no—
293C2×#41D4×C1311yescharacteristic
294C2×#41C23×C1311yescharacteristic
295C22×Q8—21no—
296C22×Q8D4×C1312yes—
297#137—28no—
298#137—22no—
299#137—41no—
300#137—44no—
301AGL(1,ℤ/8)—22no—
302AGL(1,ℤ/8)—41no—
303#135—42no—
304C2×Q16—42no—
305C2×SD16—42no—
306C2×M16—22no—
307C2×M16—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—22no—
311C4⋊Q8—24no—
312C4⋊Q8C23×C1311yescharacteristic
313C4⋊Q8C23×C1314yes—
314#127D4×C1311yescharacteristic
315#126—24no—
316#126—24no—
317#125—22no—
318#124—22no—
319#124—24no—
320#124D4×C1311yescharacteristic
321#124D4×C1314yes—
322#124C23×C1311yescharacteristic
323#123—22no—
324#123—22no—
325#123—22no—
326#123—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333#121—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—24no—
337C4×D4—24no—
338C4×D4—22no—
339#117—22no—
340#117—21no—
341#117D4×C1312yes—
342C2×C42D4×C1311yescharacteristic
343#104—22no—
344#104—22no—
345#104—28no—
346#101C23×C1314yes—
347#101C23×C1312yes—
348#100—21no—
349#100—22no—
350C2×C13—21no—
351C2×C13—42no—
352C2×C13—41no—
353C2×C13—81no—
354C2×C13—82no—
355C2×C13C2×B(4,𝔽2)11yescharacteristic
356#41—22no—
357#41—24no—
358#41—22no—
359#41—24no—
360#41—41no—
361#41—41no—
362#41—42no—
363#41—41no—
364#41—41no—
365#41—41no—
366#41—42no—
367#41—42no—
368#41—44no—
369#41—41no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—21no—
375C2×Q8—42no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—81no—
379C2×Q8—81no—
380C2×Q8C2×D4×C1314yes—
381C2×Q8C2×D4×C1311yescharacteristic
382C2×Q8C24×C1311yescharacteristic
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—42no—
388C2×D4—44no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4C2×D4×C1311yescharacteristic
392C2×D4C2×D4×C1312yes—
393C2×D4C2×D4×C1311yescharacteristic
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—42no—
400C22×C4C2×D4×C1311yescharacteristic
401C22×C4C2×D4×C1312yes—
402Q16—48no—
403Q16—42no—
404SD16—48no—
405SD16—42no—
406SD16—42no—
407D8—42no—
408M16—22no—
409M16—24no—
410M16—41no—
411M16—42no—
412C2×C8—42no—
413C2×C8—41no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C42—24no—
431C42—22no—
432C42—21no—
433C42C2×D4×C1311yescharacteristic
434C42C2×D4×C1311yescharacteristic
435C42C2×D4×C1314yes—
436C13#3357111yescharacteristic, direct product factor, Sylow
437C23—21no—
438C23—42no—
439C23—41no—
440C23C13×#12012yes—
441C23C13×#12011yescharacteristic
442Q8—22no—
443Q8—24no—
444Q8—41no—
445Q8—44no—
446Q8—41no—
447Q8—44no—
448Q8—41no—
449Q8—42no—
450Q8—42no—
451Q8—82no—
452D4—22no—
453D4—24no—
454D4—41no—
455D4—42no—
456D4—41no—
457D4—44no—
458D4—44no—
459D4—42no—
460D4—42no—
461D4—41no—
462D4—81no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4C13×#12011yescharacteristic
483C2×C4C22×D4×C1312yes—
484C2×C4C22×D4×C1311yescharacteristic
485C8—42no—
486C8—44no—
487C22—22no—
488C22—21no—
489C22—41no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—41no—
494C22—162no—
495C22—161no—
496C22C2×C13×#12011yescharacteristic
497C4—22no—
498C4—21no—
499C4—22no—
500C4—41no—
501C4—44no—
502C4—41no—
503C4—44no—
504C4—42no—
505C4C13×B(4,𝔽2)11yescharacteristic
506C4C13×B(4,𝔽2)11yescharacteristic
507C2—21no—
508C2—42no—
509C2—41no—
510C2—81no—
511C2—82no—
512C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C13C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C13
prime radicalC13×#3018C2
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3550C2semidirect
2. C13×#3022C2semidirect
4. C13×#2205C2semidirect
5. C13×#2203C2semidirect
6. C13×#2135C2semidirect
7. C13×#2132C2semidirect
12. C13×#563C22semidirect
14. Q82×C13C22semidirect
32. C13×#356C22semidirect
33. C13×#356C22semidirect
34. C13×#355C22semidirect
100. #33571C13direct (N × H)
181. #3550C2×C13semidirect
182. #3022C2×C13semidirect
184. #2205C2×C13semidirect
185. #2203C2×C13semidirect
186. #2135C2×C13semidirect
187. #2132C2×C13semidirect
242. #563C22×C13semidirect
244. Q82C22×C13semidirect
262. #356C22×C13semidirect
263. #356C22×C13semidirect
264. #355C22×C13semidirect
436. C13#33571direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35502
C13×#30222
C13×#30182
C13×#22052
C13×#22032
C13×#21352
C13×#21322
#3357113