Finite Group Databasebeta

← C13×#25948 #15712287

Subgroups — C13×#25948 #15712287

Order 3328.

1082 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic
2C13×#2503C212yesmaximal, complemented
3C13×#2486C211yesmaximal, characteristic
4C13×#2030C214yesmaximal, complemented
5C13×#1996C212yesmaximal, complemented
6C13×#1890C214yesmaximal
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×#123C2212yes—
16C2×C13×C22⋊Q8—21no—
17C2×C13×C22⋊Q8C2212yes—
18C13×#518C2212yes—
19C2×C4×D4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C2×C13×#99C2212yes—
22C13×#400—24no—
23C13×#398—21no—
24C13×#397—21no—
25C13×#391—22no—
26C13×#389—21no—
27C13×#382—22no—
28C13×#381C2218yes—
29C13×#381C2212yes—
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×#123—28no—
47C13×C22⋊Q8—22no—
48C13×C22⋊Q8—22no—
49C13×C22⋊Q8—24no—
50C13×C22⋊Q8—24no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—24no—
59C4×Q8×C13—22no—
60C4×Q8×C13—22no—
61C4×D4×C13—22no—
62C4×D4×C13—22no—
63C4×D4×C13—24no—
64C4×D4×C13—24no—
65C13×#117—22no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4D412yes—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D414yes—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4C2314yes—
81C2×C13×C22⋊C4C2312yes—
82C2×C13×C22⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4C2314yes—
84C2×C42×C13—22no—
85C2×C42×C13D411yescharacteristic
86C13×#99—24no—
87C13×#95—22no—
88C13×#95—22no—
89C13×#95—21no—
90C13×#95—28no—
91C13×#95—22no—
92C13×#95—28no—
93#25948C1311yesmaximal, characteristic, direct product factor, Sylow
94C24×C13C2×D411yescharacteristic
95C24×C13C2411yescharacteristic
96C2×Q8×C13—22no—
97C2×Q8×C13—22no—
98C2×Q8×C13—22no—
99C2×Q8×C13—22no—
100C2×Q8×C13—44no—
101C2×Q8×C13—82no—
102C2×D4×C13—22no—
103C2×D4×C13—22no—
104C2×D4×C13#4114yes—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—24no—
110C22×C4×C13—24no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—24no—
114C22×C4×C13—24no—
115C22×C4×C13—42no—
116C22×C4×C13—42no—
117C22×C4×C13C2×D412yes—
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×D414yes—
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D412yes—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—24no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—22no—
136C13×C4⋊C4—24no—
137C13×C4⋊C4—42no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—42no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4—44no—
142C13×C22⋊C4—24no—
143C13×C22⋊C4—24no—
144C13×C22⋊C4—22no—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—22no—
147C13×C22⋊C4—24no—
148C13×C22⋊C4—24no—
149C13×C22⋊C4—24no—
150C13×C22⋊C4—44no—
151C42×C13—24no—
152C42×C13—21no—
153C42×C13—21no—
154C42×C13—44no—
155#3501C2×C1311yescharacteristic
156#2503C2×C1312yescomplemented
157#2486C2×C1311yescharacteristic
158#2030C2×C1314yescomplemented
159#1996C2×C1312yescomplemented
160#1890C2×C1314yes—
161C4×#99C2×C1311yescharacteristic
162C23×C13—21no—
163C23×C13—21no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13#12412yes—
169C23×C13C22×D411yescharacteristic
170C23×C13C22×D412yes—
171C23×C13C2×#4112yes—
172C23×C132−1+412yes—
173Q8×C13—44no—
174Q8×C13—82no—
175Q8×C13—82no—
176Q8×C13—82no—
177D4×C13—28no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—24no—
181C2×C4×C13—22no—
182C2×C4×C13—21no—
183C2×C4×C13—24no—
184C2×C4×C13—24no—
185C2×C4×C13—21no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—44no—
191C2×C4×C13—41no—
192C2×C4×C13—44no—
193C2×C4×C13—44no—
194C2×C4×C13—42no—
195C2×C4×C13—44no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—44no—
202C2×C4×C13—48no—
203C2×C4×C13—81no—
204C2×C4×C13—82no—
205C2×C4×C13—82no—
206C2×C4×C13#12011yescharacteristic
207C2×C4×C13#12012yes—
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12412yes—
210#554—22no—
211#554—24no—
212D4×Q8—22no—
213#544—21no—
214#543—21no—
215#543C22×C1312yes—
216#533—21no—
217C2×#123C22×C1312yes—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C22×C1312yes—
220#518C22×C1312yes—
221C2×C4×D4C22×C1311yescharacteristic
222C22×C4⋊C4C22×C1311yescharacteristic
223C2×#99C22×C1312yes—
224#400—24no—
225#398—21no—
226#397—21no—
227#391—22no—
228#389—21no—
229#382—22no—
230#381C22×C1318yes—
231#381C22×C1312yes—
232#380—21no—
233#380C22×C1311yescharacteristic
234C4×C22⋊C4C22×C1312yes—
235#342C22×C1318yes—
236#342C22×C1312yes—
237C22×C13—22no—
238C22×C13—21no—
239C22×C13—22no—
240C22×C13—21no—
241C22×C13—22no—
242C22×C13—42no—
243C22×C13—42no—
244C22×C13—42no—
245C22×C13—41no—
246C22×C13—41no—
247C22×C13—81no—
248C22×C13C2×#12011yescharacteristic
249C22×C13C2×#12411yescharacteristic
250C22×C13#53611yescharacteristic
251C22×C13#54814yes—
252C4×C13—22no—
253C4×C13—21no—
254C4×C13—22no—
255C4×C13—41no—
256C4×C13—44no—
257C4×C13—44no—
258C4×C13—41no—
259C4×C13—82no—
260C4×C13—84no—
261C4×C13—82no—
262C4×C13#45812yes—
263C22×Q8—21no—
264C22×Q8D4×C1312yes—
265C22×D4C23×C1311yescharacteristic
266C23×C4D4×C1311yescharacteristic
267C23×C4C23×C1312yes—
268C23×C4C23×C1311yescharacteristic
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—24no—
272#125—22no—
273#125—24no—
274#123—28no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287C4×Q8—22no—
288C4×Q8—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—24no—
292C4×D4—24no—
293#117—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4D4×C1311yescharacteristic
303C2×C4⋊C4D4×C1312yes—
304C2×C4⋊C4D4×C1314yes—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4D4×C1311yescharacteristic
308C2×C22⋊C4C23×C1312yes—
309C2×C22⋊C4C23×C1314yes—
310C2×C22⋊C4C23×C1311yescharacteristic
311C2×C22⋊C4C23×C1314yes—
312C2×C42—22no—
313C2×C42D4×C1311yescharacteristic
314#99—24no—
315#95—22no—
316#95—22no—
317#95—21no—
318#95—28no—
319#95—22no—
320#95—28no—
321C2×C13—21no—
322C2×C13—24no—
323C2×C13—21no—
324C2×C13—42no—
325C2×C13#243611yescharacteristic
326C2×C13C2×#45811yescharacteristic
327C2×C13#302811yescharacteristic
328C24C2×D4×C1311yescharacteristic
329C24C24×C1311yescharacteristic
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—44no—
335C2×Q8—82no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4C13×#4114yes—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4C2×D4×C1312yes—
352C22×C4C2×D4×C1311yescharacteristic
353C22×C4C2×D4×C1311yescharacteristic
354C22×C4C2×D4×C1311yescharacteristic
355C22×C4C2×D4×C1314yes—
356C22×C4C2×D4×C1314yes—
357C22×C4C2×D4×C1311yescharacteristic
358C22×C4C2×D4×C1311yescharacteristic
359C22×C4C2×D4×C1312yes—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—42no—
374C4⋊C4—41no—
375C4⋊C4—44no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—22no—
379C22⋊C4—24no—
380C22⋊C4—22no—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—44no—
385C42—24no—
386C42—21no—
387C42—21no—
388C42—44no—
389C13#2594811yescharacteristic, direct product factor, Sylow
390C23—21no—
391C23—21no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23C13×#12412yes—
397C23C22×D4×C1311yescharacteristic
398C23C22×D4×C1312yes—
399C23C2×C13×#4112yes—
400C23C13×2−1+412yes—
401Q8—44no—
402Q8—82no—
403Q8—82no—
404Q8—82no—
405D4—28no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—48no—
431C2×C4—81no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4C13×#12011yescharacteristic
435C2×C4C13×#12012yes—
436C2×C4C13×#12011yescharacteristic
437C2×C4C13×#12412yes—
438C22—22no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—22no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22C2×C13×#12011yescharacteristic
450C22C2×C13×#12411yescharacteristic
451C22C13×#53611yescharacteristic
452C22C13×#54814yes—
453C4—21no—
454C4—22no—
455C4—22no—
456C4—41no—
457C4—44no—
458C4—44no—
459C4—41no—
460C4—82no—
461C4—84no—
462C4—82no—
463C4C13×#45812yes—
464C2—21no—
465C2—24no—
466C2—21no—
467C2—42no—
468C2C13×#243611yescharacteristic
469C2C2×C13×#45811yescharacteristic
470C2C13×#302811yescharacteristic
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×#2503C2semidirect
4. C13×#2030C2semidirect
5. C13×#1996C2semidirect
93. #25948C13direct (N × H)
156. #2503C2×C13semidirect
158. #2030C2×C13semidirect
159. #1996C2×C13semidirect
389. C13#25948direct (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×#25032
C13×#24862
C13×#20302
C13×#19962
C13×#18902
C4×C13×#992
#2594813