Finite Group Databasebeta

← C13×#36698 #15723037

Subgroups — C13×#36698 #15723037

Order 3328.

1484 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2844C211yesmaximal, characteristic, complemented
2C13×#2838C214yesmaximal, complemented
3C13×#2836C214yesmaximal, complemented
4C13×#2833C212yesmaximal, complemented
5C13×#2830C212yesmaximal
6C13×#2822C211yesmaximal, characteristic, complemented
7C13×#2820C212yesmaximal
8C13×#2401C214yesmaximal, complemented
9C13×#2399C212yesmaximal, complemented
10C13×#2396C214yesmaximal, complemented
11C13×#2395C212yesmaximal
12C4×C13×#125C212yesmaximal, complemented
13C4×C13×#124C211yesmaximal, characteristic
14C2×C13×#125C2212yes—
15C2×C13×#124C2211yescharacteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2212yes—
18C2×C4×D4×C13C2211yescharacteristic
19C2×C13×#117C2212yes—
20C13×#401C2214yes—
21C13×#400C2214yes—
22C13×#400C2214yes—
23C13×#400C2214yes—
24C13×#400C2212yes—
25C13×#400C2214yes—
26C13×#399C2214yes—
27C13×#399C2212yes—
28C13×#398C2212yes—
29C13×#398C2212yes—
30C13×#398C2214yes—
31C13×#398C2214yes—
32C13×#398C2212yes—
33C13×#398C2214yes—
34C13×#397C2214yes—
35C13×#397C2214yes—
36C13×#397C2214yes—
37C13×#397C2212yes—
38C13×#397C2214yes—
39C13×#396C2214yes—
40C13×#396C2214yes—
41C13×#396C2214yes—
42C13×#395C2214yes—
43C13×#395C2212yes—
44C13×#395C2212yes—
45C13×#395C2214yes—
46C13×#394C2214yes—
47C13×#393C2214yes—
48C13×#391C2211yescharacteristic
49C13×#390C2211yescharacteristic
50C13×#389C2212yes—
51C13×#389C2212yes—
52C13×#388C2214yes—
53C13×#387C2214yes—
54C13×#387C2214yes—
55C13×#382C2211yescharacteristic
56C13×#382C2212yes—
57C4×C13×C4⋊C4C2214yes—
58C4×C13×C4⋊C4C2212yes—
59C4×C13×C4⋊C4C2214yes—
60C4×C13×C4⋊C4C2212yes—
61C4×C13×C4⋊C4C2214yes—
62C4×C13×C22⋊C4C2214yes—
63C4×C13×C22⋊C4C2214yes—
64C4×C13×C22⋊C4C2212yes—
65C13×#376C2212yes—
66C43×C13C2211yescharacteristic
67C22×Q8×C13C2311yescharacteristic
68C22×Q8×C13C2312yes—
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13C2312yes—
71C13×#125—28no—
72C13×#124—24no—
73C4×Q8×C13—44no—
74C4×Q8×C13—42no—
75C4×D4×C13—42no—
76C13×#117—44no—
77C2×C13×C4⋊C4C2314yes—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2312yes—
80C2×C13×C4⋊C4C2312yes—
81C2×C13×C4⋊C4C2312yes—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C4⋊C4C2314yes—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C4⋊C4C2314yes—
86C2×C13×C4⋊C4C2314yes—
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2312yes—
90C2×C13×C4⋊C4C2312yes—
91C2×C13×C4⋊C4C2314yes—
92C2×C13×C4⋊C4C2312yes—
93C2×C13×C4⋊C4C2312yes—
94C2×C13×C22⋊C4C2314yes—
95C2×C13×C22⋊C4C2314yes—
96C2×C13×C22⋊C4C2314yes—
97C2×C13×C22⋊C4C2314yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2312yes—
100C2×C13×C22⋊C4C2314yes—
101C2×C42×C13C2312yes—
102C2×C42×C13C2314yes—
103C2×C42×C13C2312yes—
104C2×C42×C13C2314yes—
105C2×C42×C13C2311yescharacteristic
106C2×C42×C13C2311yescharacteristic
107C2×C42×C13C2312yes—
108C2×C42×C13C2311yescharacteristic
109C13×#95C2314yes—
110C13×#95C2314yes—
111C13×#95C2314yes—
112C13×#95C2314yes—
113C13×#95C2312yes—
114C13×#95C2312yes—
115C13×#95C2314yes—
116C13×#95C2314yes—
117C13×#95C2314yes—
118C13×#95C2314yes—
119C13×#95C2314yes—
120C13×#95C2314yes—
121C13×#95C2314yes—
122C13×#95C2314yes—
123C13×#95C2314yes—
124C13×#95C2312yes—
125C13×#95C2312yes—
126#36698C1311yesmaximal, characteristic, direct product factor, Sylow
127C24×C13C2412yes—
128C2×Q8×C13—22no—
129C2×Q8×C13—41no—
130C2×Q8×C13—42no—
131C2×Q8×C13—41no—
132C2×Q8×C13—44no—
133C2×D4×C13—22no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C22×C4×C13—24no—
137C22×C4×C13—28no—
138C22×C4×C13C2412yes—
139C22×C4×C13C2412yes—
140C22×C4×C13C2414yes—
141C22×C4×C13C2414yes—
142C22×C4×C13C2412yes—
143C22×C4×C13C2414yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2411yescharacteristic
146C22×C4×C13C2414yes—
147C22×C4×C13C2412yes—
148C22×C4×C13C2411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C13×C4⋊C4—28no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—28no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4—44no—
157C13×C4⋊C4—44no—
158C13×C4⋊C4—44no—
159C13×C4⋊C4—44no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—44no—
167C13×C22⋊C4—28no—
168C13×C22⋊C4—44no—
169C13×C22⋊C4—44no—
170C13×C22⋊C4—44no—
171C13×C22⋊C4—44no—
172C13×C22⋊C4—44no—
173C13×C22⋊C4—42no—
174C42×C13—28no—
175C42×C13—22no—
176C42×C13—24no—
177C42×C13—24no—
178C42×C13—28no—
179C42×C13—42no—
180C42×C13—41no—
181C42×C13#4114yes—
182#2844C2×C1311yescharacteristic, complemented
183#2838C2×C1314yescomplemented
184#2836C2×C1314yescomplemented
185#2833C2×C1312yescomplemented
186#2830C2×C1312yes—
187#2822C2×C1311yescharacteristic, complemented
188#2820C2×C1312yes—
189#2401C2×C1314yescomplemented
190#2399C2×C1312yescomplemented
191#2396C2×C1314yescomplemented
192#2395C2×C1312yes—
193C4×#125C2×C1312yescomplemented
194C4×#124C2×C1311yescharacteristic
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—22no—
200C23×C13C2511yescharacteristic
201Q8×C13—44no—
202Q8×C13—48no—
203D4×C13—44no—
204C2×C4×C13—21no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—21no—
208C2×C4×C13—22no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—21no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—24no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—48no—
233C2×C4×C13C2×#4114yes—
234C2×C4×C13C2×#4112yes—
235C2×C4×C13H(5,𝔽2)12yes—
236C2×C4×C132−1+414yes—
237C2×#125C22×C1312yes—
238C2×#124C22×C1311yescharacteristic
239C2×C4×Q8C22×C1312yes—
240C2×C4×Q8C22×C1311yescharacteristic
241C2×C4×D4C22×C1311yescharacteristic
242C2×#117C22×C1312yes—
243#401C22×C1314yes—
244#400C22×C1314yes—
245#400C22×C1314yes—
246#400C22×C1314yes—
247#400C22×C1312yes—
248#400C22×C1314yes—
249#399C22×C1314yes—
250#399C22×C1312yes—
251#398C22×C1312yes—
252#398C22×C1312yes—
253#398C22×C1314yes—
254#398C22×C1314yes—
255#398C22×C1312yes—
256#398C22×C1314yes—
257#397C22×C1314yes—
258#397C22×C1314yes—
259#397C22×C1314yes—
260#397C22×C1312yes—
261#397C22×C1314yes—
262#396C22×C1314yes—
263#396C22×C1314yes—
264#396C22×C1314yes—
265#395C22×C1314yes—
266#395C22×C1312yes—
267#395C22×C1312yes—
268#395C22×C1314yes—
269#394C22×C1314yes—
270#393C22×C1314yes—
271#391C22×C1311yescharacteristic
272#390C22×C1311yescharacteristic
273#389C22×C1312yes—
274#389C22×C1312yes—
275#388C22×C1314yes—
276#387C22×C1314yes—
277#387C22×C1314yes—
278#382C22×C1312yes—
279#382C22×C1311yescharacteristic
280C4×C4⋊C4C22×C1314yes—
281C4×C4⋊C4C22×C1312yes—
282C4×C4⋊C4C22×C1314yes—
283C4×C4⋊C4C22×C1312yes—
284C4×C4⋊C4C22×C1314yes—
285C4×C22⋊C4C22×C1314yes—
286C4×C22⋊C4C22×C1312yes—
287C4×C22⋊C4C22×C1314yes—
288#376C22×C1312yes—
289C43C22×C1311yescharacteristic
290C22×C13—42no—
291C22×C13—44no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13—44no—
295C22×C13C22×#4111yescharacteristic
296C22×C13C2×H(5,𝔽2)11yescharacteristic
297C22×C13C2×2−1+412yes—
298C22×C13#58511yescharacteristic
299C22×C13#58512yes—
300C4×C13—22no—
301C4×C13—24no—
302C4×C13—44no—
303C4×C13—42no—
304C4×C13—44no—
305C4×C13—42no—
306C4×C13—41no—
307C4×C13—44no—
308C4×C13—42no—
309C4×C13—42no—
310C4×C13—44no—
311C4×C13#56314yes—
312C22×Q8C23×C1311yescharacteristic
313C22×Q8C23×C1312yes—
314C22×D4C23×C1311yescharacteristic
315C23×C4C23×C1312yes—
316#125—28no—
317#124—24no—
318C4×Q8—44no—
319C4×Q8—42no—
320C4×D4—42no—
321#117—44no—
322C2×C4⋊C4C23×C1314yes—
323C2×C4⋊C4C23×C1314yes—
324C2×C4⋊C4C23×C1312yes—
325C2×C4⋊C4C23×C1312yes—
326C2×C4⋊C4C23×C1312yes—
327C2×C4⋊C4C23×C1312yes—
328C2×C4⋊C4C23×C1311yescharacteristic
329C2×C4⋊C4C23×C1311yescharacteristic
330C2×C4⋊C4C23×C1312yes—
331C2×C4⋊C4C23×C1314yes—
332C2×C4⋊C4C23×C1312yes—
333C2×C4⋊C4C23×C1312yes—
334C2×C4⋊C4C23×C1312yes—
335C2×C4⋊C4C23×C1314yes—
336C2×C4⋊C4C23×C1314yes—
337C2×C4⋊C4C23×C1314yes—
338C2×C4⋊C4C23×C1314yes—
339C2×C22⋊C4C23×C1314yes—
340C2×C22⋊C4C23×C1314yes—
341C2×C22⋊C4C23×C1312yes—
342C2×C22⋊C4C23×C1314yes—
343C2×C22⋊C4C23×C1314yes—
344C2×C22⋊C4C23×C1314yes—
345C2×C22⋊C4C23×C1314yes—
346C2×C42C23×C1314yes—
347C2×C42C23×C1311yescharacteristic
348C2×C42C23×C1312yes—
349C2×C42C23×C1312yes—
350C2×C42C23×C1314yes—
351C2×C42C23×C1311yescharacteristic
352C2×C42C23×C1312yes—
353C2×C42C23×C1311yescharacteristic
354#95C23×C1314yes—
355#95C23×C1312yes—
356#95C23×C1312yes—
357#95C23×C1314yes—
358#95C23×C1314yes—
359#95C23×C1314yes—
360#95C23×C1314yes—
361#95C23×C1312yes—
362#95C23×C1312yes—
363#95C23×C1314yes—
364#95C23×C1314yes—
365#95C23×C1314yes—
366#95C23×C1314yes—
367#95C23×C1314yes—
368#95C23×C1314yes—
369#95C23×C1314yes—
370#95C23×C1314yes—
371C2×C13—82no—
372C2×C13#346011yescharacteristic
373C2×C13#346112yes—
374C2×C13C2×#56311yescharacteristic
375C2×C13#352911yescharacteristic
376C2×C13#353112yes—
377C24C24×C1312yes—
378C2×Q8—22no—
379C2×Q8—41no—
380C2×Q8—42no—
381C2×Q8—41no—
382C2×Q8—44no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—41no—
386C22×C4—24no—
387C22×C4—28no—
388C22×C4C24×C1312yes—
389C22×C4C24×C1312yes—
390C22×C4C24×C1314yes—
391C22×C4C24×C1314yes—
392C22×C4C24×C1312yes—
393C22×C4C24×C1314yes—
394C22×C4C24×C1312yes—
395C22×C4C24×C1311yescharacteristic
396C22×C4C24×C1314yes—
397C22×C4C24×C1312yes—
398C22×C4C24×C1311yescharacteristic
399C22×C4C24×C1311yescharacteristic
400C4⋊C4—28no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—28no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—44no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—44no—
414C4⋊C4—44no—
415C4⋊C4—44no—
416C4⋊C4—44no—
417C22⋊C4—28no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C22⋊C4—44no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C42—28no—
425C42—22no—
426C42—24no—
427C42—24no—
428C42—28no—
429C42—42no—
430C42—41no—
431C42C13×#4114yes—
432C13#3669811yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—22no—
435C23—24no—
436C23—24no—
437C23—22no—
438C23C25×C1311yescharacteristic
439Q8—44no—
440Q8—48no—
441D4—44no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—48no—
471C2×C4C2×C13×#4114yes—
472C2×C4C2×C13×#4112yes—
473C2×C4C13×H(5,𝔽2)12yes—
474C2×C4C13×2−1+414yes—
475C22—42no—
476C22—42no—
477C22—44no—
478C22—42no—
479C22—44no—
480C22C22×C13×#4111yescharacteristic
481C22C2×C13×H(5,𝔽2)11yescharacteristic
482C22C2×C13×2−1+412yes—
483C22C13×#58512yes—
484C22C13×#58511yescharacteristic
485C4—22no—
486C4—24no—
487C4—42no—
488C4—41no—
489C4—44no—
490C4—42no—
491C4—42no—
492C4—44no—
493C4—44no—
494C4—42no—
495C4—44no—
496C4C13×#56314yes—
497C2—82no—
498C2C13×#346011yescharacteristic
499C2C13×#346112yes—
500C2C2×C13×#56311yescharacteristic
501C2C13×#352911yescharacteristic
502C2C13×#353112yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC22×D4×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2844C2semidirect
2. C13×#2838C2semidirect
3. C13×#2836C2semidirect
4. C13×#2833C2semidirect
6. C13×#2822C2semidirect
8. C13×#2401C2semidirect
9. C13×#2399C2semidirect
10. C13×#2396C2semidirect
12. C4×C13×#125C2semidirect
126. #36698C13direct (N × H)
182. #2844C2×C13semidirect
183. #2838C2×C13semidirect
184. #2836C2×C13semidirect
185. #2833C2×C13semidirect
187. #2822C2×C13semidirect
189. #2401C2×C13semidirect
190. #2399C2×C13semidirect
191. #2396C2×C13semidirect
193. C4×#125C2×C13semidirect
432. C13#36698direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28442
C13×#28382
C13×#28362
C13×#28332
C13×#28302
C13×#28222
C13×#28202
C13×#24012
C13×#23992
C13×#23962
C13×#23952
C4×C13×#1252
C4×C13×#1242
#3669813