Finite Group Databasebeta

← C13×#19028 #15705367

Subgroups — C13×#19028 #15705367

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic
3C13×#3138C211yesmaximal, characteristic, complemented
4C2×C13×#490C211yesmaximal, characteristic, complemented
5C13×#1658C214yesmaximal, complemented
6C13×#1657C214yesmaximal, complemented
7C13×#1531C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C13×#564C2212yescomplemented
11C13×#563C2212yescomplemented
12C13×#557—21no—
13C13×#554—21no—
14C13×#552—21no—
15C13×#552—22no—
16C13×#552—21no—
17C13×#544—21no—
18C13×#544—21no—
19C13×#541—21no—
20C13×#541—22no—
21C13×#539—21no—
22C13×#533C2211yescharacteristic
23C2×C13×#127C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#496C2212yes—
27C13×#490—22no—
28C13×#490C2214yes—
29C13×#490C2214yes—
30C13×#490C2212yes—
31C13×#486—21no—
32C13×#486—21no—
33C13×#460—21no—
34C13×#459—21no—
35C13×#450—21no—
36C13×#447—21no—
37C13×#432C2211yescharacteristic
38C13×#418—22no—
39C2×C13×#102—21no—
40C2×C13×#102—21no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yescomplemented
44C13×#330C2214yescomplemented
45C13×#330C2214yescomplemented
46C13×#329C2212yescomplemented
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13—21no—
50C2×C13×SD16—22no—
51C2×C13×D8—22no—
52C2×C13×M16—21no—
53C22×C8×C13—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8D411yescharacteristic
58C13×C4⋊Q8D411yescharacteristic
59C13×#127—21no—
60C13×#127—21no—
61C13×#127—21no—
62C13×#127C2312yes—
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—22no—
67C13×#126—21no—
68C13×#125—22no—
69C13×#125—22no—
70C13×#125—21no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125—21no—
78C13×#125—21no—
79C13×#125D412yes—
80C13×#125C2312yes—
81C13×#125C2311yescharacteristic
82C13×#125C2312yes—
83C13×#124C2311yescharacteristic
84C13×#123—22no—
85C13×#123—22no—
86C13×#123—21no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8D411yescharacteristic
96C13×#121D411yescharacteristic
97C4×Q8×C13—21no—
98C4×Q8×C13—22no—
99C4×Q8×C13—21no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×Q8×C13D411yescharacteristic
103C4×D4×C13—22no—
104C4×D4×C13—21no—
105C4×D4×C13D411yescharacteristic
106C13×#117—22no—
107C13×#117—21no—
108C13×#117—22no—
109C13×#117—21no—
110C13×#117D412yes—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4D411yescharacteristic
116C2×C42×C13C2311yescharacteristic
117C13×C4⋊C8—21no—
118C13×#102—24no—
119C13×#102—24no—
120C13×#102—24no—
121C13×#102—24no—
122C13×#102—22no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19028C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—41no—
132C2×Q8×C13—22no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13C2×D411yescharacteristic
136C2×D4×C13—21no—
137C2×D4×C13—22no—
138C2×D4×C13—22no—
139C2×D4×C13—22no—
140C2×D4×C13—44no—
141C2×D4×C13—44no—
142C2×D4×C13—41no—
143C2×D4×C13—41no—
144C2×D4×C13—41no—
145C2×D4×C13—82no—
146C2×D4×C13C2×D411yescharacteristic
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C13×SD16—82no—
155C13×D8—82no—
156C13×M16—42no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C2×C8×C13—42no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4C2×D412yes—
184C13×C4⋊C4C2×D412yes—
185C13×C4⋊C4C2×D412yes—
186C13×C4⋊C4C2×D412yes—
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C4⋊C4C2×D411yescharacteristic
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C42×C13—22no—
199C42×C13—22no—
200C42×C13—22no—
201C42×C13—22no—
202C42×C13—21no—
203C42×C13C2×D411yescharacteristic
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2411yescharacteristic
207#3563C2×C1311yescharacteristic, complemented
208#3217C2×C1311yescharacteristic
209#3138C2×C1311yescharacteristic, complemented
210C2×#490C2×C1311yescharacteristic, complemented
211#1658C2×C1314yescomplemented
212#1657C2×C1314yescomplemented
213#1531C2×C1311yescharacteristic, complemented
214#1528C2×C1311yescharacteristic, complemented
215#1524C2×C1311yescharacteristic, complemented
216C23×C13—21no—
217C23×C13—42no—
218C23×C13—82no—
219C23×C13—82no—
220C23×C13—82no—
221C23×C13#12011yescharacteristic
222Q8×C13—41no—
223Q8×C13—42no—
224Q8×C13—81no—
225Q8×C13—82no—
226D4×C13—41no—
227D4×C13—42no—
228D4×C13—42no—
229D4×C13—44no—
230D4×C13—44no—
231D4×C13—42no—
232D4×C13—82no—
233D4×C13—82no—
234D4×C13—82no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—41no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—81no—
248C2×C4×C13—82no—
249C2×C4×C13#12011yescharacteristic
250C2×C4×C13#12011yescharacteristic
251C2×C4×C13#12011yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C8×C13—42no—
256C8×C13—42no—
257C8×C13—42no—
258#564C22×C1312yescomplemented
259#563C22×C1312yescomplemented
260#557—21no—
261#554—21no—
262#552—21no—
263#552—22no—
264#552—21no—
265#544—21no—
266#544—21no—
267#541—21no—
268#541—22no—
269#539—21no—
270#533C22×C1311yescharacteristic
271C2×#127C22×C1311yescharacteristic
272#529C22×C1311yescharacteristic
273C2×#125C22×C1311yescharacteristic
274#496C22×C1312yes—
275#490—22no—
276#490C22×C1314yes—
277#490C22×C1314yes—
278#490C22×C1312yes—
279#486—21no—
280#486—21no—
281#460—21no—
282#459—21no—
283#450—21no—
284#447—21no—
285#432C22×C1311yescharacteristic
286#418—22no—
287C2×#102—21no—
288C2×#102—21no—
289C4×M16C22×C1311yescharacteristic
290C2×#97C22×C1311yescharacteristic
291#330C22×C1314yescomplemented
292#330C22×C1314yescomplemented
293#330C22×C1312yescomplemented
294#329C22×C1312yescomplemented
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—82no—
301C22×C13—82no—
302C22×C13—82no—
303C22×C13—164no—
304C22×C13#45412yes—
305C22×C13C2×#12011yescharacteristic
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—42no—
312C4×C13—41no—
313C4×C13—41no—
314C4×C13—42no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—41no—
318C4×C13#45412yes—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C2×SD16—22no—
323C2×D8—22no—
324C2×M16—21no—
325C22×C8—21no—
326C4⋊Q8—22no—
327C4⋊Q8—21no—
328C4⋊Q8—22no—
329C4⋊Q8D4×C1311yescharacteristic
330C4⋊Q8D4×C1311yescharacteristic
331#127—21no—
332#127—21no—
333#127—21no—
334#127C23×C1312yes—
335#126—22no—
336#126—22no—
337#126—22no—
338#126—22no—
339#126—21no—
340#125—22no—
341#125—22no—
342#125—21no—
343#125—22no—
344#125—22no—
345#125—22no—
346#125—22no—
347#125—22no—
348#125—22no—
349#125—21no—
350#125—21no—
351#125D4×C1312yes—
352#125C23×C1312yes—
353#125C23×C1311yescharacteristic
354#125C23×C1312yes—
355#124C23×C1311yescharacteristic
356#123—22no—
357#123—22no—
358#123—21no—
359C22⋊Q8—22no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8D4×C1311yescharacteristic
368#121D4×C1311yescharacteristic
369C4×Q8—21no—
370C4×Q8—22no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8D4×C1311yescharacteristic
375C4×D4—22no—
376C4×D4—21no—
377C4×D4D4×C1311yescharacteristic
378#117—22no—
379#117—21no—
380#117—22no—
381#117—21no—
382#117D4×C1312yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C1311yescharacteristic
387C2×C4⋊C4D4×C1311yescharacteristic
388C2×C42C23×C1311yescharacteristic
389C4⋊C8—21no—
390#102—24no—
391#102—24no—
392#102—24no—
393#102—24no—
394#102—22no—
395#102—22no—
396C22⋊C8—21no—
397#97—21no—
398#97C23×C1312yes—
399#97C23×C1312yes—
400#97C23×C1312yes—
401C4×C8—21no—
402C2×C13—22no—
403C2×C13—81no—
404C2×C13—162no—
405C2×C13C2×#45411yescharacteristic
406C2×C13C2×#45411yescharacteristic
407C2×C13#302111yescharacteristic
408C24—41no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8C2×D4×C1311yescharacteristic
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—82no—
423C2×D4C2×D4×C1311yescharacteristic
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4C2×D4×C1311yescharacteristic
429C22×C4C2×D4×C1311yescharacteristic
430C22×C4C2×D4×C1311yescharacteristic
431SD16—82no—
432D8—82no—
433M16—42no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—42no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4C2×D4×C1312yes—
461C4⋊C4C2×D4×C1312yes—
462C4⋊C4C2×D4×C1312yes—
463C4⋊C4C2×D4×C1312yes—
464C4⋊C4C2×D4×C1311yescharacteristic
465C4⋊C4C2×D4×C1311yescharacteristic
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42C2×D4×C1311yescharacteristic
481C42C2×D4×C1311yescharacteristic
482C42C2×D4×C1311yescharacteristic
483C42C24×C1311yescharacteristic
484C13#1902811yescharacteristic, direct product factor, Sylow
485C23—21no—
486C23—42no—
487C23—82no—
488C23—82no—
489C23—82no—
490C23C13×#12011yescharacteristic
491Q8—41no—
492Q8—42no—
493Q8—81no—
494Q8—82no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—44no—
500D4—42no—
501D4—82no—
502D4—82no—
503D4—82no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4C13×#12011yescharacteristic
519C2×C4C13×#12011yescharacteristic
520C2×C4C13×#12011yescharacteristic
521C2×C4C22×D4×C1311yescharacteristic
522C2×C4C22×D4×C1311yescharacteristic
523C2×C4C22×D4×C1311yescharacteristic
524C8—42no—
525C8—42no—
526C8—42no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—164no—
536C22C13×#45412yes—
537C22C2×C13×#12011yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—42no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—41no—
550C4C13×#45412yes—
551C2—22no—
552C2—81no—
553C2—162no—
554C2C2×C13×#45411yescharacteristic
555C2C2×C13×#45411yescharacteristic
556C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3217C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3563C2semidirect
3. C13×#3138C2semidirect
4. C2×C13×#490C2semidirect
5. C13×#1658C2semidirect
6. C13×#1657C2semidirect
7. C13×#1531C2semidirect
8. C13×#1528C2semidirect
9. C13×#1524C2semidirect
10. C13×#564C22semidirect
11. C13×#563C22semidirect
43. C13×#330C22semidirect
44. C13×#330C22semidirect
45. C13×#330C22semidirect
46. C13×#329C22semidirect
130. #19028C13direct (N × H)
207. #3563C2×C13semidirect
209. #3138C2×C13semidirect
210. C2×#490C2×C13semidirect
211. #1658C2×C13semidirect
212. #1657C2×C13semidirect
213. #1531C2×C13semidirect
214. #1528C2×C13semidirect
215. #1524C2×C13semidirect
258. #564C22×C13semidirect
259. #563C22×C13semidirect
291. #330C22×C13semidirect
292. #330C22×C13semidirect
293. #330C22×C13semidirect
294. #329C22×C13semidirect
484. C13#19028direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#32172
C13×#31382
C2×C13×#4902
C13×#16582
C13×#16572
C13×#15312
C13×#15282
C13×#15242
#1902813