Finite Group Databasebeta

← C13×#24353 #15710692

Subgroups — C13×#24353 #15710692

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic
2C13×#2627C212yesmaximal, complemented
3C13×#2322C211yesmaximal, characteristic
4C13×#2062C212yesmaximal, complemented
5C13×#2030C212yesmaximal, complemented
6C13×#1996C212yesmaximal, complemented
7C13×#1890C212yesmaximal
8C13×#1867C212yesmaximal
9C13×#1799C211yesmaximal, characteristic
10C13×#554—24no—
11C13×#554—22no—
12D4×Q8×C13—22no—
13C13×#544—21no—
14C13×#543—21no—
15C13×#543C2212yes—
16C13×#533—21no—
17C2×C13×#123C2211yescharacteristic
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8C2212yes—
20C13×#518C2212yes—
21C2×C4×D4×C13C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C2×C13×#99C2212yes—
24C13×#400—22no—
25C13×#398—24no—
26C13×#395—22no—
27C13×#389—21no—
28C13×#388—21no—
29C13×#387—21no—
30C13×#386C2211yescharacteristic
31C13×#385—21no—
32C13×#385C2211yescharacteristic
33C13×#385C2214yes—
34C13×#381C2211yescharacteristic
35C13×#381C2214yes—
36C13×#380C2212yes—
37C4×C13×C22⋊C4C2211yescharacteristic
38C13×#342C2214yes—
39C13×#342C2214yes—
40C13×#342C2212yes—
41C22×Q8×C13—21no—
42C22×Q8×C13D412yes—
43C22×D4×C13C2311yescharacteristic
44C23×C4×C13D411yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—24no—
51C13×#125—22no—
52C13×#125—24no—
53C13×#123—22no—
54C13×#123Q814yescomplemented
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—24no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—24no—
66C13×C22⋊Q8—24no—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—24no—
72C4×D4×C13—24no—
73C13×#117—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—24no—
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C4⋊C4D414yes—
86C2×C13×C4⋊C4D412yes—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C13×C22⋊C4C2311yescharacteristic
92C2×C13×C22⋊C4C2314yes—
93C2×C13×C22⋊C4C2311yescharacteristic
94C2×C13×C22⋊C4C2314yes—
95C2×C13×C22⋊C4C2311yescharacteristic
96C2×C42×C13—21no—
97C2×C42×C13D411yescharacteristic
98C13×#99—24no—
99C13×#95—21no—
100C13×#95—22no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—24no—
104C13×#95—24no—
105C13×#95—21no—
106C13×#95—24no—
107C13×#95—21no—
108#24353C1311yesmaximal, characteristic, direct product factor, Sylow
109C24×C13C2×D411yescharacteristic
110C24×C13C2411yescharacteristic
111C2×Q8×C13—22no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13—22no—
115C2×Q8×C13—82no—
116C2×Q8×C13—82no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13C2×Q812yes—
120C2×D4×C13#4112yes—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—24no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—81no—
135C22×C4×C13—81no—
136C22×C4×C13—81no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D414yes—
140C22×C4×C13C2×D414yes—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×Q812yescomplemented
147C13×C4⋊C4—22no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—82no—
163C13×C4⋊C4—81no—
164C13×C4⋊C4—84no—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—21no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—81no—
176C13×C22⋊C4C2×Q812yescomplemented
177C42×C13—24no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—81no—
181#3501C2×C1311yescharacteristic
182#2627C2×C1312yescomplemented
183#2322C2×C1311yescharacteristic
184#2062C2×C1312yescomplemented
185#2030C2×C1312yescomplemented
186#1996C2×C1312yescomplemented
187#1890C2×C1312yes—
188#1867C2×C1312yes—
189#1799C2×C1311yescharacteristic
190C23×C13—21no—
191C23×C13—21no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13C22⋊Q812yes—
197C23×C13C22×D411yescharacteristic
198C23×C13C22×D412yes—
199C23×C13C22×Q811yescharacteristic
200C23×C13C2×#4111yescharacteristic
201C23×C132−1+412yes—
202Q8×C13—44no—
203Q8×C13—82no—
204Q8×C13—82no—
205Q8×C13—82no—
206D4×C13—24no—
207D4×C13—24no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—24no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—44no—
229C2×C4×C13—44no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—44no—
234C2×C4×C13—44no—
235C2×C4×C13—41no—
236C2×C4×C13—44no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—44no—
241C2×C4×C13—81no—
242C2×C4×C13—82no—
243C2×C4×C13—82no—
244C2×C4×C13#12011yescharacteristic
245C2×C4×C13#12011yescharacteristic
246C2×C4×C13#12012yes—
247C2×C4×C13C22⋊Q812yes—
248#554—24no—
249#554—22no—
250D4×Q8—22no—
251#544—21no—
252#543—21no—
253#543C22×C1312yes—
254#533—21no—
255C2×#123C22×C1311yescharacteristic
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8C22×C1312yes—
258#518C22×C1312yes—
259C2×C4×D4C22×C1311yescharacteristic
260C22×C4⋊C4C22×C1311yescharacteristic
261C2×#99C22×C1312yes—
262#400—22no—
263#398—24no—
264#395—22no—
265#389—21no—
266#388—21no—
267#387—21no—
268#386C22×C1311yescharacteristic
269#385—21no—
270#385C22×C1311yescharacteristic
271#385C22×C1314yes—
272#381C22×C1311yescharacteristic
273#381C22×C1314yes—
274#380C22×C1312yes—
275C4×C22⋊C4C22×C1311yescharacteristic
276#342C22×C1312yes—
277#342C22×C1314yes—
278#342C22×C1314yes—
279C22×C13—22no—
280C22×C13—21no—
281C22×C13—22no—
282C22×C13—21no—
283C22×C13—22no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13—42no—
287C22×C13—42no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13—81no—
291C22×C13C2×#12011yescharacteristic
292C22×C13C2×C22⋊Q811yescharacteristic
293C22×C13#53611yescharacteristic
294C22×C13#54812yes—
295C22×C13D4×Q812yes—
296C4×C13—22no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—22no—
300C4×C13—42no—
301C4×C13—42no—
302C4×C13—41no—
303C4×C13—44no—
304C4×C13—44no—
305C4×C13—41no—
306C4×C13—84no—
307C4×C13—81no—
308C4×C13—81no—
309C22×Q8—21no—
310C22×Q8D4×C1312yes—
311C22×D4C23×C1311yescharacteristic
312C23×C4D4×C1311yescharacteristic
313C23×C4C23×C1311yescharacteristic
314C23×C4C23×C1311yescharacteristic
315C23×C4C23×C1311yescharacteristic
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—24no—
319#125—22no—
320#125—24no—
321#123—22no—
322#123Q8×C1314yescomplemented
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—24no—
340C4×D4—24no—
341#117—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4D4×C1311yescharacteristic
353C2×C4⋊C4D4×C1314yes—
354C2×C4⋊C4D4×C1312yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4D4×C1311yescharacteristic
359C2×C22⋊C4C23×C1311yescharacteristic
360C2×C22⋊C4C23×C1314yes—
361C2×C22⋊C4C23×C1311yescharacteristic
362C2×C22⋊C4C23×C1314yes—
363C2×C22⋊C4C23×C1311yescharacteristic
364C2×C42—21no—
365C2×C42D4×C1311yescharacteristic
366#99—24no—
367#95—21no—
368#95—22no—
369#95—21no—
370#95—21no—
371#95—24no—
372#95—24no—
373#95—21no—
374#95—24no—
375#95—21no—
376C2×C13—21no—
377C2×C13—22no—
378C2×C13—21no—
379C2×C13—22no—
380C2×C13—42no—
381C2×C13#240911yescharacteristic
382C2×C13#302611yescharacteristic
383C2×C13#302811yescharacteristic
384C24C2×D4×C1311yescharacteristic
385C24C24×C1311yescharacteristic
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—82no—
391C2×Q8—82no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4C2×Q8×C1312yes—
395C2×D4C13×#4112yes—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—81no—
410C22×C4—81no—
411C22×C4—81no—
412C22×C4C2×D4×C1311yescharacteristic
413C22×C4C2×D4×C1311yescharacteristic
414C22×C4C2×D4×C1314yes—
415C22×C4C2×D4×C1314yes—
416C22×C4C2×D4×C1311yescharacteristic
417C22×C4C2×D4×C1311yescharacteristic
418C22×C4C2×D4×C1312yes—
419C22×C4C2×D4×C1311yescharacteristic
420C22×C4C2×D4×C1312yes—
421C22×C4C2×Q8×C1312yescomplemented
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C4⋊C4—81no—
439C4⋊C4—84no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—24no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—24no—
450C22⋊C4—81no—
451C22⋊C4C2×Q8×C1312yescomplemented
452C42—24no—
453C42—21no—
454C42—21no—
455C42—81no—
456C13#2435311yescharacteristic, direct product factor, Sylow
457C23—21no—
458C23—21no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23C13×C22⋊Q812yes—
464C23C22×D4×C1311yescharacteristic
465C23C22×D4×C1312yes—
466C23C22×Q8×C1311yescharacteristic
467C23C2×C13×#4111yescharacteristic
468C23C13×2−1+412yes—
469Q8—44no—
470Q8—82no—
471Q8—82no—
472Q8—82no—
473D4—24no—
474D4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—44no—
508C2×C4—81no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4C13×#12011yescharacteristic
512C2×C4C13×#12011yescharacteristic
513C2×C4C13×#12012yes—
514C2×C4C13×C22⋊Q812yes—
515C22—22no—
516C22—21no—
517C22—22no—
518C22—21no—
519C22—22no—
520C22—41no—
521C22—41no—
522C22—42no—
523C22—42no—
524C22—41no—
525C22—41no—
526C22—81no—
527C22C2×C13×#12011yescharacteristic
528C22C2×C13×C22⋊Q811yescharacteristic
529C22C13×#53611yescharacteristic
530C22C13×#54812yes—
531C22D4×Q8×C1312yes—
532C4—21no—
533C4—21no—
534C4—22no—
535C4—22no—
536C4—42no—
537C4—41no—
538C4—44no—
539C4—44no—
540C4—41no—
541C4—42no—
542C4—84no—
543C4—81no—
544C4—81no—
545C2—21no—
546C2—22no—
547C2—21no—
548C2—22no—
549C2—42no—
550C2C13×#240911yescharacteristic
551C2C13×#302611yescharacteristic
552C2C13×#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×#2627C2semidirect
4. C13×#2062C2semidirect
5. C13×#2030C2semidirect
6. C13×#1996C2semidirect
54. C13×#123Q8semidirect
108. #24353C13direct (N × H)
146. C22×C4×C13C2×Q8semidirect
176. C13×C22⋊C4C2×Q8semidirect
182. #2627C2×C13semidirect
184. #2062C2×C13semidirect
185. #2030C2×C13semidirect
186. #1996C2×C13semidirect
322. #123Q8×C13semidirect
421. C22×C4C2×Q8×C13semidirect
451. C22⋊C4C2×Q8×C13semidirect
456. C13#24353direct (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×#26272
C13×#23222
C13×#20622
C13×#20302
C13×#19962
C13×#18902
C13×#18672
C13×#17992
#2435313