Finite Group Databasebeta

← C13×#19029 #15705368

Subgroups — C13×#19029 #15705368

Order 3328.

824 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic
3C2×C13×#501C211yesmaximal, characteristic, complemented
4C13×#3139C211yesmaximal, characteristic, complemented
5C13×#1664C214yesmaximal, complemented
6C13×#1663C214yesmaximal, complemented
7C13×#1531C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic
10C13×#564C2212yes—
11C13×#563C2212yes—
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×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#501—22no—
27C13×#501C2214yes—
28C13×#501C2212yes—
29C13×#491C2214yes—
30C13×#489C2212yes—
31C13×#487—21no—
32C13×#487—21no—
33C13×#483—21no—
34C13×#480—21no—
35C13×#477—21no—
36C13×#476—21no—
37C13×#432C2211yescharacteristic
38C2×C13×#107—21no—
39C2×C13×#106—21no—
40C13×#419—22no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yes—
44C13×#330C2214yes—
45C13×#330C2214yes—
46C13×#329C2212yes—
47C22×Q8×C13—21no—
48C2×C13×M16—21no—
49C22×C8×C13—21no—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8—21no—
52C13×C4⋊Q8—22no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8D411yescharacteristic
57C13×C4⋊Q8D411yescharacteristic
58C13×C4⋊Q8C2312yes—
59C13×#126—22no—
60C13×#126—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—21no—
64C13×#125—22no—
65C13×#125—22no—
66C13×#125—21no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#125—22no—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—21no—
74C13×#125—21no—
75C13×#125D412yes—
76C13×#125C2312yes—
77C13×#125C2312yes—
78C13×#125C2311yescharacteristic
79C13×#124C2311yescharacteristic
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—21no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8D411yescharacteristic
92C13×#121D411yescharacteristic
93C4×Q8×C13—21no—
94C4×Q8×C13—22no—
95C4×Q8×C13—21no—
96C4×Q8×C13—21no—
97C4×Q8×C13—21no—
98C4×Q8×C13D411yescharacteristic
99C4×D4×C13—22no—
100C4×D4×C13—21no—
101C4×D4×C13D411yescharacteristic
102C13×#117—22no—
103C13×#117—21no—
104C13×#117—22no—
105C13×#117—21no—
106C13×#117D412yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C42×C13C2311yescharacteristic
115C13×#107—24no—
116C13×#107—22no—
117C13×#106—24no—
118C13×#106—22no—
119C13×C4⋊C8—21no—
120C13×#103—22no—
121C13×#103—24no—
122C13×#103—24no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19029C1311yesmaximal, characteristic, direct product factor, Sylow
131C2×Q8×C13—22no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—22no—
135C2×Q8×C13—44no—
136C2×Q8×C13—41no—
137C2×Q8×C13C2×D411yescharacteristic
138C2×D4×C13—21no—
139C2×D4×C13C2×D411yescharacteristic
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—41no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C13×M16—42no—
149C2×C8×C13—24no—
150C2×C8×C13—22no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—41no—
178C13×C4⋊C4—41no—
179C13×C4⋊C4C2×D412yes—
180C13×C4⋊C4C2×D412yes—
181C13×C4⋊C4C2×D412yes—
182C13×C4⋊C4C2×D411yescharacteristic
183C13×C4⋊C4C2×D412yes—
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C42×C13—22no—
195C42×C13—22no—
196C42×C13—22no—
197C42×C13—22no—
198C42×C13—21no—
199C42×C13C2×D411yescharacteristic
200C42×C13C2×D411yescharacteristic
201C42×C13C2×D411yescharacteristic
202C42×C13C2411yescharacteristic
203#3563C2×C1311yescharacteristic
204#3238C2×C1311yescharacteristic
205C2×#501C2×C1311yescharacteristic, complemented
206#3139C2×C1311yescharacteristic, complemented
207#1664C2×C1314yescomplemented
208#1663C2×C1314yescomplemented
209#1531C2×C1311yescharacteristic, complemented
210#1528C2×C1311yescharacteristic, complemented
211#1524C2×C1311yescharacteristic
212C23×C13—21no—
213C23×C13#12011yescharacteristic
214Q8×C13—41no—
215Q8×C13—44no—
216Q8×C13—42no—
217Q8×C13—81no—
218Q8×C13—82no—
219Q8×C13—82no—
220D4×C13—41no—
221D4×C13—42no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—81no—
236C2×C4×C13—82no—
237C2×C4×C13—82no—
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#12011yescharacteristic
240C2×C4×C13#12011yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C8×C13—24no—
245C8×C13—42no—
246C8×C13—42no—
247#564C22×C1312yes—
248#563C22×C1312yes—
249#557—21no—
250#554—21no—
251#552—21no—
252#552—22no—
253#552—21no—
254#544—21no—
255#544—21no—
256#541—21no—
257#541—22no—
258#539—21no—
259#533C22×C1311yescharacteristic
260C2×C4⋊Q8C22×C1311yescharacteristic
261#529C22×C1311yescharacteristic
262C2×#125C22×C1311yescharacteristic
263#501—22no—
264#501C22×C1314yes—
265#501C22×C1312yes—
266#491C22×C1314yes—
267#489C22×C1312yes—
268#487—21no—
269#487—21no—
270#483—21no—
271#480—21no—
272#477—21no—
273#476—21no—
274#432C22×C1311yescharacteristic
275C2×#107—21no—
276C2×#106—21no—
277#419—22no—
278C4×M16C22×C1311yescharacteristic
279C2×#97C22×C1311yescharacteristic
280#330C22×C1312yes—
281#330C22×C1314yes—
282#330C22×C1314yes—
283#329C22×C1312yes—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—41no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13#45412yes—
290C22×C13C2×#12011yescharacteristic
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—42no—
297C4×C13—41no—
298C4×C13—41no—
299C4×C13—42no—
300C4×C13—42no—
301C4×C13—42no—
302C4×C13—41no—
303C4×C13—82no—
304C4×C13#45612yes—
305C22×Q8—21no—
306C2×M16—21no—
307C22×C8—21no—
308C4⋊Q8—22no—
309C4⋊Q8—21no—
310C4⋊Q8—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8D4×C1311yescharacteristic
315C4⋊Q8D4×C1311yescharacteristic
316C4⋊Q8C23×C1312yes—
317#126—22no—
318#126—22no—
319#126—22no—
320#126—22no—
321#126—21no—
322#125—22no—
323#125—22no—
324#125—21no—
325#125—22no—
326#125—22no—
327#125—22no—
328#125—22no—
329#125—22no—
330#125—22no—
331#125—21no—
332#125—21no—
333#125D4×C1312yes—
334#125C23×C1312yes—
335#125C23×C1311yescharacteristic
336#125C23×C1312yes—
337#124C23×C1311yescharacteristic
338#123—22no—
339#123—22no—
340#123—21no—
341C22⋊Q8—22no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8D4×C1311yescharacteristic
350#121D4×C1311yescharacteristic
351C4×Q8—21no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8D4×C1311yescharacteristic
357C4×D4—22no—
358C4×D4—21no—
359C4×D4D4×C1311yescharacteristic
360#117—22no—
361#117—21no—
362#117—22no—
363#117—21no—
364#117D4×C1312yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4D4×C1311yescharacteristic
371C2×C4⋊C4D4×C1311yescharacteristic
372C2×C42C23×C1311yescharacteristic
373#107—24no—
374#107—22no—
375#106—24no—
376#106—22no—
377C4⋊C8—21no—
378#103—22no—
379#103—24no—
380#103—24no—
381#102—22no—
382C22⋊C8—21no—
383#97—21no—
384#97C23×C1312yes—
385#97C23×C1312yes—
386#97C23×C1312yes—
387C4×C8—21no—
388C2×C13—22no—
389C2×C13—81no—
390C2×C13C2×#45411yescharacteristic
391C2×C13C2×#45611yescharacteristic
392C2×C13#302211yescharacteristic
393C2×Q8—22no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—44no—
398C2×Q8—41no—
399C2×Q8C2×D4×C1311yescharacteristic
400C2×D4—21no—
401C2×D4C2×D4×C1311yescharacteristic
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—41no—
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C2×D4×C1311yescharacteristic
409C22×C4C2×D4×C1311yescharacteristic
410M16—42no—
411C2×C8—24no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4C2×D4×C1312yes—
442C4⋊C4C2×D4×C1312yes—
443C4⋊C4C2×D4×C1312yes—
444C4⋊C4C2×D4×C1311yescharacteristic
445C4⋊C4C2×D4×C1312yes—
446C4⋊C4C2×D4×C1311yescharacteristic
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—21no—
451C22⋊C4—22no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42C2×D4×C1311yescharacteristic
462C42C2×D4×C1311yescharacteristic
463C42C2×D4×C1311yescharacteristic
464C42C24×C1311yescharacteristic
465C13#1902911yescharacteristic, direct product factor, Sylow
466C23—21no—
467C23C13×#12011yescharacteristic
468Q8—41no—
469Q8—44no—
470Q8—42no—
471Q8—81no—
472Q8—82no—
473Q8—82no—
474D4—41no—
475D4—42no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—81no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4C13×#12011yescharacteristic
493C2×C4C13×#12011yescharacteristic
494C2×C4C13×#12011yescharacteristic
495C2×C4C22×D4×C1311yescharacteristic
496C2×C4C22×D4×C1311yescharacteristic
497C2×C4C22×D4×C1311yescharacteristic
498C8—24no—
499C8—42no—
500C8—42no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22C13×#45412yes—
507C22C2×C13×#12011yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—42no—
514C4—41no—
515C4—41no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4C13×#45612yes—
522C2—22no—
523C2—81no—
524C2C2×C13×#45411yescharacteristic
525C2C2×C13×#45611yescharacteristic
526C2C13×#302211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#121D4
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
3. C2×C13×#501C2semidirect
4. C13×#3139C2semidirect
5. C13×#1664C2semidirect
6. C13×#1663C2semidirect
7. C13×#1531C2semidirect
8. C13×#1528C2semidirect
130. #19029C13direct (N × H)
205. C2×#501C2×C13semidirect
206. #3139C2×C13semidirect
207. #1664C2×C13semidirect
208. #1663C2×C13semidirect
209. #1531C2×C13semidirect
210. #1528C2×C13semidirect
465. C13#19029direct (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×#32382
C2×C13×#5012
C13×#31392
C13×#16642
C13×#16632
C13×#15312
C13×#15282
C13×#15242
#1902913