Finite Group Databasebeta

← C13×#25853 #15712192

Subgroups — C13×#25853 #15712192

Order 3328.

1094 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic
2C13×#2502C212yesmaximal, complemented
3C13×#2487C211yesmaximal, characteristic
4C13×#2062C214yesmaximal, complemented
5C13×#1996C212yesmaximal, complemented
6C13×#1867C214yesmaximal
7C4×C13×#99C211yesmaximal, characteristic
8C13×#554—22no—
9C13×#554—24no—
10D4×Q8×C13—22no—
11C13×#544—21no—
12C13×#543—21no—
13C13×#543C2212yes—
14C13×#533—21no—
15C2×C13×C22⋊Q8—21no—
16C2×C13×C22⋊Q8C2212yes—
17C13×#518C2212yes—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×C13×#99C2212yes—
21C13×#400—21no—
22C13×#399—21no—
23C13×#398—24no—
24C13×#391—22no—
25C13×#389—21no—
26C13×#386C2212yes—
27C13×#385C2218yes—
28C13×#385C2212yes—
29C13×#384—22no—
30C13×#380—21no—
31C13×#380C2211yescharacteristic
32C4×C13×C22⋊C4C2212yes—
33C13×#342C2218yes—
34C13×#342C2212yes—
35C22×Q8×C13—21no—
36C22×Q8×C13D412yes—
37C22×D4×C13C2311yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—24no—
44C13×#125—22no—
45C13×#125—24no—
46C13×C22⋊Q8—22no—
47C13×C22⋊Q8—22no—
48C13×C22⋊Q8—24no—
49C13×C22⋊Q8—24no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—24no—
57C13×C22⋊Q8—24no—
58C4×Q8×C13—22no—
59C4×Q8×C13—22no—
60C4×D4×C13—22no—
61C4×D4×C13—22no—
62C4×D4×C13—24no—
63C4×D4×C13—24no—
64C13×#117—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—28no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4D412yes—
75C2×C13×C4⋊C4D414yes—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4C2312yes—
81C2×C13×C22⋊C4C2311yescharacteristic
82C2×C13×C22⋊C4C2314yes—
83C2×C13×C22⋊C4C2314yes—
84C2×C42×C13—22no—
85C2×C42×C13D411yescharacteristic
86C13×#99Q818yescomplemented
87C13×#95—22no—
88C13×#95—22no—
89C13×#95—21no—
90C13×#95—28no—
91C13×#95—22no—
92#25853C1311yesmaximal, characteristic, direct product factor, Sylow
93C24×C13C2×D411yescharacteristic
94C24×C13C2411yescharacteristic
95C2×Q8×C13—22no—
96C2×Q8×C13—22no—
97C2×Q8×C13—22no—
98C2×Q8×C13—22no—
99C2×Q8×C13—44no—
100C2×Q8×C13—82no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13C2×Q814yes—
104C22×C4×C13—24no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—24no—
112C22×C4×C13—42no—
113C22×C4×C13—42no—
114C22×C4×C13—82no—
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D414yes—
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D412yes—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—24no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—24no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4—42no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—42no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—88no—
140C13×C4⋊C4—82no—
141C13×C22⋊C4—24no—
142C13×C22⋊C4—24no—
143C13×C22⋊C4—22no—
144C13×C22⋊C4—24no—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—22no—
147C13×C22⋊C4—24no—
148C13×C22⋊C4—82no—
149C13×C22⋊C4C2×Q818yescomplemented
150C42×C13—24no—
151C42×C13—21no—
152C42×C13—21no—
153C42×C13—44no—
154#3501C2×C1311yescharacteristic
155#2502C2×C1312yescomplemented
156#2487C2×C1311yescharacteristic
157#2062C2×C1314yescomplemented
158#1996C2×C1312yescomplemented
159#1867C2×C1314yes—
160C4×#99C2×C1311yescharacteristic
161C23×C13—21no—
162C23×C13—21no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13C4⋊Q812yes—
168C23×C13C22×D411yescharacteristic
169C23×C13C22×D412yes—
170C23×C13C22×Q812yes—
171C23×C132−1+412yes—
172Q8×C13—44no—
173Q8×C13—82no—
174Q8×C13—82no—
175Q8×C13—82no—
176D4×C13—28no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—24no—
180C2×C4×C13—22no—
181C2×C4×C13—21no—
182C2×C4×C13—24no—
183C2×C4×C13—24no—
184C2×C4×C13—21no—
185C2×C4×C13—28no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—44no—
189C2×C4×C13—44no—
190C2×C4×C13—42no—
191C2×C4×C13—44no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—44no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—48no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—81no—
203C2×C4×C13—82no—
204C2×C4×C13—82no—
205C2×C4×C13#12011yescharacteristic
206C2×C4×C13#12012yes—
207C2×C4×C13#12011yescharacteristic
208C2×C4×C13C4⋊Q812yes—
209#554—22no—
210#554—24no—
211D4×Q8—22no—
212#544—21no—
213#543—21no—
214#543C22×C1312yes—
215#533—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C22×C1312yes—
218#518C22×C1312yes—
219C2×C4×D4C22×C1311yescharacteristic
220C22×C4⋊C4C22×C1311yescharacteristic
221C2×#99C22×C1312yes—
222#400—21no—
223#399—21no—
224#398—24no—
225#391—22no—
226#389—21no—
227#386C22×C1312yes—
228#385C22×C1312yes—
229#385C22×C1318yes—
230#384—22no—
231#380—21no—
232#380C22×C1311yescharacteristic
233C4×C22⋊C4C22×C1312yes—
234#342C22×C1312yes—
235#342C22×C1318yes—
236C22×C13—22no—
237C22×C13—21no—
238C22×C13—22no—
239C22×C13—21no—
240C22×C13—22no—
241C22×C13—42no—
242C22×C13—42no—
243C22×C13—42no—
244C22×C13—41no—
245C22×C13—41no—
246C22×C13—81no—
247C22×C13C2×#12011yescharacteristic
248C22×C13C2×C4⋊Q811yescharacteristic
249C22×C13#53611yescharacteristic
250C22×C13D4×Q814yes—
251C4×C13—22no—
252C4×C13—21no—
253C4×C13—22no—
254C4×C13—48no—
255C4×C13—41no—
256C4×C13—44no—
257C4×C13—44no—
258C4×C13—41no—
259C4×C13—82no—
260C4×C13—82no—
261C4×C13#45812yes—
262C22×Q8—21no—
263C22×Q8D4×C1312yes—
264C22×D4C23×C1311yescharacteristic
265C23×C4D4×C1311yescharacteristic
266C23×C4C23×C1312yes—
267C23×C4C23×C1311yescharacteristic
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—24no—
271#125—22no—
272#125—24no—
273C22⋊Q8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—24no—
276C22⋊Q8—24no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—24no—
284C22⋊Q8—24no—
285C4×Q8—22no—
286C4×Q8—22no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—24no—
290C4×D4—24no—
291#117—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4D4×C1311yescharacteristic
302C2×C4⋊C4D4×C1312yes—
303C2×C4⋊C4D4×C1314yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4D4×C1311yescharacteristic
307C2×C22⋊C4C23×C1312yes—
308C2×C22⋊C4C23×C1311yescharacteristic
309C2×C22⋊C4C23×C1314yes—
310C2×C22⋊C4C23×C1314yes—
311C2×C42—22no—
312C2×C42D4×C1311yescharacteristic
313#99Q8×C1318yescomplemented
314#95—22no—
315#95—22no—
316#95—21no—
317#95—28no—
318#95—22no—
319C2×C13—24no—
320C2×C13—21no—
321C2×C13—21no—
322C2×C13—42no—
323C2×C13#243411yescharacteristic
324C2×C13C2×#45811yescharacteristic
325C2×C13#302711yescharacteristic
326C24C2×D4×C1311yescharacteristic
327C24C24×C1311yescharacteristic
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×Q8—82no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4C2×Q8×C1314yes—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—82no—
348C22×C4C2×D4×C1312yes—
349C22×C4C2×D4×C1311yescharacteristic
350C22×C4C2×D4×C1311yescharacteristic
351C22×C4C2×D4×C1314yes—
352C22×C4C2×D4×C1311yescharacteristic
353C22×C4C2×D4×C1311yescharacteristic
354C22×C4C2×D4×C1314yes—
355C22×C4C2×D4×C1311yescharacteristic
356C22×C4C2×D4×C1312yes—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4—42no—
369C4⋊C4—41no—
370C4⋊C4—42no—
371C4⋊C4—41no—
372C4⋊C4—88no—
373C4⋊C4—82no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—22no—
377C22⋊C4—24no—
378C22⋊C4—24no—
379C22⋊C4—22no—
380C22⋊C4—24no—
381C22⋊C4—82no—
382C22⋊C4C2×Q8×C1318yescomplemented
383C42—24no—
384C42—21no—
385C42—21no—
386C42—44no—
387C13#2585311yescharacteristic, direct product factor, Sylow
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23C13×C4⋊Q812yes—
395C23C22×D4×C1311yescharacteristic
396C23C22×D4×C1312yes—
397C23C22×Q8×C1312yes—
398C23C13×2−1+412yes—
399Q8—44no—
400Q8—82no—
401Q8—82no—
402Q8—82no—
403D4—28no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—21no—
412C2×C4—28no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—48no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4C13×#12011yescharacteristic
433C2×C4C13×#12012yes—
434C2×C4C13×#12011yescharacteristic
435C2×C4C13×C4⋊Q812yes—
436C22—22no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—22no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—41no—
445C22—41no—
446C22—81no—
447C22C2×C13×#12011yescharacteristic
448C22C2×C13×C4⋊Q811yescharacteristic
449C22C13×#53611yescharacteristic
450C22D4×Q8×C1314yes—
451C4—21no—
452C4—22no—
453C4—22no—
454C4—48no—
455C4—41no—
456C4—44no—
457C4—44no—
458C4—41no—
459C4—82no—
460C4—82no—
461C4C13×#45812yes—
462C2—24no—
463C2—21no—
464C2—21no—
465C2—42no—
466C2C13×#243411yescharacteristic
467C2C2×C13×#45811yescharacteristic
468C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC22×D4×C13C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2502C2semidirect
4. C13×#2062C2semidirect
5. C13×#1996C2semidirect
86. C13×#99Q8semidirect
92. #25853C13direct (N × H)
149. C13×C22⋊C4C2×Q8semidirect
155. #2502C2×C13semidirect
157. #2062C2×C13semidirect
158. #1996C2×C13semidirect
313. #99Q8×C13semidirect
382. C22⋊C4C2×Q8×C13semidirect
387. C13#25853direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35012
C13×#25022
C13×#24872
C13×#20622
C13×#19962
C13×#18672
C4×C13×#992
#2585313