Finite Group Databasebeta

← C13×#34522 #15720861

Subgroups — C13×#34522 #15720861

Order 3328.

2216 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#562C211yesmaximal, characteristic
2C13×#2382C211yesmaximal, characteristic, complemented
3C13×#2379C212yesmaximal, complemented
4C13×#2368C214yesmaximal, complemented
5C13×#2363C214yesmaximal, complemented
6C13×#2359C214yesmaximal, complemented
7C13×#2335C214yesmaximal, complemented
8C13×#2325C214yesmaximal, complemented
9C13×#2323C214yesmaximal, complemented
10C4×C13×#125C211yesmaximal, characteristic, complemented
11C4×C13×#124C212yesmaximal, complemented
12C13×#562C4116yescomplemented
13C2×C13×#125C2211yescharacteristic
14C2×C13×#124C2212yes—
15C2×C13×#123C2214yes—
16C2×C13×C22⋊Q8C2214yes—
17C2×C13×#121C2214yes—
18C2×C4×Q8×C13C2212yes—
19C2×C4×D4×C13C2212yes—
20C2×C4×D4×C13C2214yes—
21C2×C13×#117C2214yes—
22C13×#391C2212yes—
23C13×#391C2214yes—
24C13×#390C2212yes—
25C13×#390C2214yes—
26C13×#389C2212yes—
27C13×#389C2214yes—
28C13×#389C2214yes—
29C13×#388C2214yes—
30C13×#388C2214yes—
31C13×#388C2214yes—
32C13×#388C2214yes—
33C13×#388C2214yes—
34C13×#388C2214yes—
35C13×#387C2214yes—
36C13×#387C2214yes—
37C13×#387C2214yes—
38C13×#387C2214yes—
39C13×#387C2214yes—
40C13×#386C2214yes—
41C13×#386C2214yes—
42C13×#386C2214yes—
43C13×#385C2214yes—
44C13×#385C2214yes—
45C13×#385C2214yes—
46C13×#382C2212yes—
47C13×#382C2211yescharacteristic
48C13×#380C2214yes—
49C4×C13×C4⋊C4C2212yes—
50C4×C13×C4⋊C4C2214yes—
51C4×C13×C4⋊C4C2214yes—
52C4×C13×C22⋊C4C2214yes—
53C4×C13×C22⋊C4C2214yes—
54C4×C13×C22⋊C4C2214yes—
55C4×C13×C22⋊C4C2214yes—
56C2×C13×#95C2214yes—
57C43×C13C2211yescharacteristic
58C22×Q8×C13C2312yes—
59C22×D4×C13C2314yes—
60C22×D4×C13C2312yes—
61C23×C4×C13C2314yes—
62C23×C4×C13C2314yes—
63C23×C4×C13C2314yes—
64C13×#125C2×C418yescomplemented
65C13×#124C2×C4116yescomplemented
66C13×#123C2×C4132yescomplemented
67C13×C22⋊Q8C2×C4132yescomplemented
68C13×#121C2×C4132yescomplemented
69C4×Q8×C13—44no—
70C4×D4×C13—44no—
71C4×D4×C13—48no—
72C13×#117—48no—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C4⋊C4C2312yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C4⋊C4C2312yes—
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C22⋊C4C2314yes—
84C2×C13×C22⋊C4C2314yes—
85C2×C13×C22⋊C4C2314yes—
86C2×C13×C22⋊C4C2314yes—
87C2×C13×C22⋊C4C2314yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C13×C22⋊C4C2314yes—
91C2×C13×C22⋊C4C2314yes—
92C2×C42×C13C2314yes—
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2312yes—
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2314yes—
97C2×C42×C13C2312yes—
98C2×C42×C13C2314yes—
99C2×C42×C13C2314yes—
100C2×C42×C13C2311yescharacteristic
101C13×#95C2314yes—
102C13×#95C2314yes—
103C13×#95C2314yes—
104C13×#95C2314yes—
105C13×#95C2314yes—
106C13×#95C2314yes—
107C13×#95C2314yes—
108C13×#95C2314yes—
109C13×#95C2314yes—
110C13×#95C2314yes—
111C13×#95C2314yes—
112#34522C1311yesmaximal, characteristic, direct product factor, Sylow
113C24×C13C2414yes—
114C2×Q8×C13—42no—
115C2×Q8×C13—42no—
116C2×Q8×C13C22×C418yes—
117C2×D4×C13—42no—
118C2×D4×C13—44no—
119C2×D4×C13—44no—
120C2×D4×C13—42no—
121C2×D4×C13C22×C4116yes—
122C2×D4×C13C22×C418yes—
123C22×C4×C13—28no—
124C22×C4×C13—44no—
125C22×C4×C13—44no—
126C22×C4×C13—44no—
127C22×C4×C13—44no—
128C22×C4×C13—44no—
129C22×C4×C13—44no—
130C22×C4×C13—44no—
131C22×C4×C13C22×C4116yes—
132C22×C4×C13C2414yes—
133C22×C4×C13C2414yes—
134C22×C4×C13C2411yescharacteristic
135C22×C4×C13C2414yes—
136C22×C4×C13C2411yescharacteristic
137C22×C4×C13C2412yes—
138C22×C4×C13C2414yes—
139C22×C4×C13C2414yes—
140C22×C4×C13C2412yes—
141C22×C4×C13C2411yescharacteristic
142C13×C4⋊C4—28no—
143C13×C4⋊C4—42no—
144C13×C4⋊C4—44no—
145C13×C4⋊C4—44no—
146C13×C4⋊C4—42no—
147C13×C4⋊C4—44no—
148C13×C4⋊C4—42no—
149C13×C4⋊C4C22×C4116yes—
150C13×C4⋊C4C22×C4116yes—
151C13×C4⋊C4C22×C418yes—
152C13×C22⋊C4—28no—
153C13×C22⋊C4—28no—
154C13×C22⋊C4—44no—
155C13×C22⋊C4—44no—
156C13×C22⋊C4—44no—
157C13×C22⋊C4—44no—
158C13×C22⋊C4C22×C4116yes—
159C13×C22⋊C4C22×C4116yes—
160C13×C22⋊C4C22×C4116yes—
161C42×C13—28no—
162C42×C13—24no—
163C42×C13—22no—
164C42×C13—42no—
165C42×C13—44no—
166C42×C13—41no—
167C42×C13—44no—
168C42×C13—44no—
169C42×C13C22×C414yes—
170C2×#562C2×C1311yescharacteristic
171#2382C2×C1311yescharacteristic, complemented
172#2379C2×C1312yescomplemented
173#2368C2×C1314yescomplemented
174#2363C2×C1314yescomplemented
175#2359C2×C1314yescomplemented
176#2335C2×C1314yescomplemented
177#2325C2×C1314yescomplemented
178#2323C2×C1314yescomplemented
179C4×#125C2×C1311yescharacteristic, complemented
180C4×#124C2×C1312yescomplemented
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13C23×C418yes—
188C23×C13C2511yescharacteristic
189Q8×C13—48no—
190D4×C13—416no—
191D4×C13—48no—
192C2×C4×C13—24no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—21no—
196C2×C4×C13—22no—
197C2×C4×C13—21no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—24no—
201C2×C4×C13—22no—
202C2×C4×C13—24no—
203C2×C4×C13—22no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—21no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—416no—
215C2×C4×C13—88no—
216C2×C4×C13—88no—
217C2×C4×C13C23×C412yes—
218C2×C4×C13C23×C414yes—
219C2×C4×C13C23×C418yes—
220C2×C4×C13C23×C418yes—
221C2×C4×C13H(5,𝔽2)14yes—
222C2×C4×C132−1+412yes—
223#562C4×C13116yescomplemented
224C2×#125C22×C1311yescharacteristic
225C2×#124C22×C1312yes—
226C2×#123C22×C1314yes—
227C2×C22⋊Q8C22×C1314yes—
228C2×#121C22×C1314yes—
229C2×C4×Q8C22×C1312yes—
230C2×C4×D4C22×C1312yes—
231C2×C4×D4C22×C1314yes—
232C2×#117C22×C1314yes—
233#391C22×C1314yes—
234#391C22×C1312yes—
235#390C22×C1314yes—
236#390C22×C1312yes—
237#389C22×C1312yes—
238#389C22×C1314yes—
239#389C22×C1314yes—
240#388C22×C1314yes—
241#388C22×C1314yes—
242#388C22×C1314yes—
243#388C22×C1314yes—
244#388C22×C1314yes—
245#388C22×C1314yes—
246#387C22×C1314yes—
247#387C22×C1314yes—
248#387C22×C1314yes—
249#387C22×C1314yes—
250#387C22×C1314yes—
251#386C22×C1314yes—
252#386C22×C1314yes—
253#386C22×C1314yes—
254#385C22×C1314yes—
255#385C22×C1314yes—
256#385C22×C1314yes—
257#382C22×C1311yescharacteristic
258#382C22×C1312yes—
259#380C22×C1314yes—
260C4×C4⋊C4C22×C1312yes—
261C4×C4⋊C4C22×C1314yes—
262C4×C4⋊C4C22×C1314yes—
263C4×C22⋊C4C22×C1314yes—
264C4×C22⋊C4C22×C1314yes—
265C4×C22⋊C4C22×C1314yes—
266C4×C22⋊C4C22×C1314yes—
267C2×#95C22×C1314yes—
268C43C22×C1311yescharacteristic
269C22×C13—28no—
270C22×C13—28no—
271C22×C13—28no—
272C22×C13—44no—
273C22×C13—44no—
274C22×C13—44no—
275C22×C13—44no—
276C22×C13C24×C411yescharacteristic
277C22×C13C2×H(5,𝔽2)12yes—
278C22×C13C2×2−1+411yescharacteristic
279C22×C13#58512yes—
280C22×C13#58511yescharacteristic
281C4×C13—28no—
282C4×C13—28no—
283C4×C13—24no—
284C4×C13—22no—
285C4×C13—24no—
286C4×C13—22no—
287C4×C13—44no—
288C4×C13—44no—
289C4×C13—41no—
290C4×C13—44no—
291C22×Q8C23×C1312yes—
292C22×D4C23×C1314yes—
293C22×D4C23×C1312yes—
294C23×C4C23×C1314yes—
295C23×C4C23×C1314yes—
296C23×C4C23×C1314yes—
297#125C2×C4×C1318yescomplemented
298#124C2×C4×C13116yescomplemented
299#123C2×C4×C13132yescomplemented
300C22⋊Q8C2×C4×C13132yescomplemented
301#121C2×C4×C13132yescomplemented
302C4×Q8—44no—
303C4×D4—44no—
304C4×D4—48no—
305#117—48no—
306C2×C4⋊C4C23×C1314yes—
307C2×C4⋊C4C23×C1314yes—
308C2×C4⋊C4C23×C1312yes—
309C2×C4⋊C4C23×C1314yes—
310C2×C4⋊C4C23×C1312yes—
311C2×C4⋊C4C23×C1314yes—
312C2×C4⋊C4C23×C1312yes—
313C2×C4⋊C4C23×C1314yes—
314C2×C4⋊C4C23×C1314yes—
315C2×C4⋊C4C23×C1312yes—
316C2×C22⋊C4C23×C1314yes—
317C2×C22⋊C4C23×C1314yes—
318C2×C22⋊C4C23×C1314yes—
319C2×C22⋊C4C23×C1314yes—
320C2×C22⋊C4C23×C1314yes—
321C2×C22⋊C4C23×C1314yes—
322C2×C22⋊C4C23×C1314yes—
323C2×C22⋊C4C23×C1314yes—
324C2×C22⋊C4C23×C1314yes—
325C2×C42C23×C1314yes—
326C2×C42C23×C1312yes—
327C2×C42C23×C1311yescharacteristic
328C2×C42C23×C1314yes—
329C2×C42C23×C1314yes—
330C2×C42C23×C1311yescharacteristic
331C2×C42C23×C1312yes—
332C2×C42C23×C1314yes—
333C2×C42C23×C1311yescharacteristic
334#95C23×C1314yes—
335#95C23×C1314yes—
336#95C23×C1314yes—
337#95C23×C1314yes—
338#95C23×C1314yes—
339#95C23×C1314yes—
340#95C23×C1314yes—
341#95C23×C1314yes—
342#95C23×C1314yes—
343#95C23×C1314yes—
344#95C23×C1314yes—
345C2×C13—48no—
346C2×C13C4×H(5,𝔽2)12yes—
347C2×C13C4×2−1+411yescharacteristic
348C2×C13#354512yes—
349C2×C13#354811yescharacteristic
350C2×C13#355311yescharacteristic
351C24C24×C1314yes—
352C2×Q8—42no—
353C2×Q8—42no—
354C2×Q8C22×C4×C1318yes—
355C2×D4—42no—
356C2×D4—44no—
357C2×D4—44no—
358C2×D4—42no—
359C2×D4C22×C4×C13116yes—
360C2×D4C22×C4×C1318yes—
361C22×C4—28no—
362C22×C4—44no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4—44no—
367C22×C4—44no—
368C22×C4—44no—
369C22×C4C22×C4×C13116yes—
370C22×C4C24×C1314yes—
371C22×C4C24×C1314yes—
372C22×C4C24×C1311yescharacteristic
373C22×C4C24×C1314yes—
374C22×C4C24×C1311yescharacteristic
375C22×C4C24×C1312yes—
376C22×C4C24×C1314yes—
377C22×C4C24×C1314yes—
378C22×C4C24×C1312yes—
379C22×C4C24×C1311yescharacteristic
380C4⋊C4—28no—
381C4⋊C4—44no—
382C4⋊C4—42no—
383C4⋊C4—44no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—44no—
387C4⋊C4C22×C4×C13116yes—
388C4⋊C4C22×C4×C13116yes—
389C4⋊C4C22×C4×C1318yes—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C22⋊C4C22×C4×C13116yes—
397C22⋊C4C22×C4×C13116yes—
398C22⋊C4C22×C4×C13116yes—
399C42—28no—
400C42—24no—
401C42—22no—
402C42—44no—
403C42—44no—
404C42—42no—
405C42—44no—
406C42—41no—
407C42C22×C4×C1314yes—
408C13#3452211yescharacteristic, direct product factor, Sylow
409C23—24no—
410C23—24no—
411C23—24no—
412C23—24no—
413C23—24no—
414C23—24no—
415C23C23×C4×C1318yes—
416C23C25×C1311yescharacteristic
417Q8—48no—
418D4—416no—
419D4—48no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—416no—
443C2×C4—88no—
444C2×C4—88no—
445C2×C4C23×C4×C1312yes—
446C2×C4C23×C4×C1314yes—
447C2×C4C23×C4×C1318yes—
448C2×C4C23×C4×C1318yes—
449C2×C4C13×H(5,𝔽2)14yes—
450C2×C4C13×2−1+412yes—
451C22—28no—
452C22—28no—
453C22—28no—
454C22—44no—
455C22—44no—
456C22—44no—
457C22—44no—
458C22C24×C4×C1311yescharacteristic
459C22C2×C13×H(5,𝔽2)12yes—
460C22C2×C13×2−1+411yescharacteristic
461C22C13×#58511yescharacteristic
462C22C13×#58512yes—
463C4—24no—
464C4—22no—
465C4—28no—
466C4—28no—
467C4—24no—
468C4—22no—
469C4—44no—
470C4—44no—
471C4—41no—
472C4—44no—
473C2—48no—
474C2C4×C13×H(5,𝔽2)12yes—
475C2C4×C13×2−1+411yescharacteristic
476C2C13×#354512yes—
477C2C13×#354811yescharacteristic
478C2C13×#355311yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#562C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2382C2semidirect
3. C13×#2379C2semidirect
4. C13×#2368C2semidirect
5. C13×#2363C2semidirect
6. C13×#2359C2semidirect
7. C13×#2335C2semidirect
8. C13×#2325C2semidirect
9. C13×#2323C2semidirect
10. C4×C13×#125C2semidirect
11. C4×C13×#124C2semidirect
12. C13×#562C4semidirect
64. C13×#125C2×C4semidirect
65. C13×#124C2×C4semidirect
66. C13×#123C2×C4semidirect
67. C13×C22⋊Q8C2×C4semidirect
68. C13×#121C2×C4semidirect
112. #34522C13direct (N × H)
171. #2382C2×C13semidirect
172. #2379C2×C13semidirect
173. #2368C2×C13semidirect
174. #2363C2×C13semidirect
175. #2359C2×C13semidirect
176. #2335C2×C13semidirect
177. #2325C2×C13semidirect
178. #2323C2×C13semidirect
179. C4×#125C2×C13semidirect
180. C4×#124C2×C13semidirect
223. #562C4×C13semidirect
297. #125C2×C4×C13semidirect
298. #124C2×C4×C13semidirect
299. #123C2×C4×C13semidirect
300. C22⋊Q8C2×C4×C13semidirect
301. #121C2×C4×C13semidirect
408. C13#34522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5622
C13×#23822
C13×#23792
C13×#23682
C13×#23632
C13×#23592
C13×#23352
C13×#23252
C13×#23232
C4×C13×#1252
C4×C13×#1242
#3452213