Finite Group Databasebeta

← C13×#19022 #15705361

Subgroups — C13×#19022 #15705361

Order 3328.

892 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C2×C13×#501C211yesmaximal, characteristic, complemented
4C13×#3141C211yesmaximal, characteristic, complemented
5C13×#1664C214yesmaximal, complemented
6C13×#1661C214yesmaximal, complemented
7C13×#1530C211yesmaximal, characteristic, complemented
8C13×#1528C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C13×#563C2212yes—
11C13×#562C2212yes—
12C13×#554—21no—
13C13×#553—21no—
14C13×#553—21no—
15C13×#547—22no—
16C13×#547—21no—
17C13×#544—21no—
18C13×#540—21no—
19C13×#539—22no—
20C13×#539—21no—
21C13×#537—21no—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#501—22no—
27C13×#501C2214yes—
28C13×#497C2212yes—
29C13×#491C2212yes—
30C13×#489C2214yes—
31C13×#487—21no—
32C13×#486—21no—
33C13×#462—21no—
34C13×#461—21no—
35C13×#451—21no—
36C13×#448—21no—
37C13×#432C2211yescharacteristic
38C2×C13×#107—21no—
39C2×C13×#106—21no—
40C13×#417—22no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yes—
44C13×#330C2214yes—
45C13×#329C2212yes—
46C13×#329C2214yes—
47C2×C13×#41—22no—
48C2×C13×#41D412yes—
49C22×Q8×C13—21no—
50C2×C13×Q16—22no—
51C2×C13×SD16—22no—
52C2×C13×M16—21no—
53C22×C8×C13—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8D411yescharacteristic
60C13×C4⋊Q8C2312yes—
61C13×#127D411yescharacteristic
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—21no—
65C13×#125—22no—
66C13×#125—21no—
67C13×#125—21no—
68C13×#125—21no—
69C13×#125D412yes—
70C13×#125C2311yescharacteristic
71C13×#125C2312yes—
72C13×#124C2312yes—
73C13×#124C2311yescharacteristic
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—21no—
79C13×#123—22no—
80C13×#123—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8D411yescharacteristic
88C13×#121—22no—
89C13×#121—22no—
90C13×#121—21no—
91C13×#121—21no—
92C13×#121—22no—
93C13×#121—22no—
94C13×#121—21no—
95C13×#121—21no—
96C13×#121D411yescharacteristic
97C4×Q8×C13D411yescharacteristic
98C4×D4×C13—22no—
99C4×D4×C13—22no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—21no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13D411yescharacteristic
106C13×#117—21no—
107C13×#117—21no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
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×#107—24no—
118C13×#106—24no—
119C13×C4⋊C8—21no—
120C13×#103—24no—
121C13×#103—22no—
122C13×#103—22no—
123C13×#102—24no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19022C1311yesmaximal, characteristic, direct product factor, Sylow
131C13×#41—44no—
132C13×#41—84no—
133C2×Q8×C13—22no—
134C2×Q8×C13—22no—
135C2×Q8×C13—41no—
136C2×Q8×C13—82no—
137C2×Q8×C13C2×D412yes—
138C2×Q8×C13C2×D411yescharacteristic
139C2×D4×C13—22no—
140C2×D4×C13—21no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13C2×D412yes—
146C2×D4×C13C2×D411yescharacteristic
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—41no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C13×Q16—82no—
159C13×SD16—82no—
160C13×M16—42no—
161C2×C8×C13—24no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—22no—
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⋊C4—41no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4C2×D411yescharacteristic
186C13×C4⋊C4C2×D411yescharacteristic
187C13×C4⋊C4C2×D412yes—
188C13×C4⋊C4C2×D412yes—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—21no—
201C42×C13—22no—
202C42×C13—21no—
203C42×C13C2×D411yescharacteristic
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2411yescharacteristic
207#3559C2×C1311yescharacteristic
208#3218C2×C1311yescharacteristic, complemented
209C2×#501C2×C1311yescharacteristic, complemented
210#3141C2×C1311yescharacteristic, complemented
211#1664C2×C1314yescomplemented
212#1661C2×C1314yescomplemented
213#1530C2×C1311yescharacteristic, complemented
214#1528C2×C1311yescharacteristic, complemented
215#1524C2×C1311yescharacteristic, complemented
216C23×C13—22no—
217C23×C13—21no—
218C23×C13#12011yescharacteristic
219Q8×C13—41no—
220Q8×C13—42no—
221Q8×C13—42no—
222Q8×C13—42no—
223Q8×C13—82no—
224Q8×C13—82no—
225D4×C13—41no—
226D4×C13—42no—
227D4×C13—44no—
228D4×C13—42no—
229D4×C13—42no—
230D4×C13—81no—
231D4×C13—82no—
232D4×C13—82no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—82no—
246C2×C4×C13—81no—
247C2×C4×C13—82no—
248C2×C4×C13—82no—
249C2×C4×C13—82no—
250C2×C4×C13—82no—
251C2×C4×C13#12011yescharacteristic
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C8×C13—24no—
258C8×C13—42no—
259C8×C13—42no—
260#563C22×C1312yes—
261#562C22×C1312yes—
262#554—21no—
263#553—21no—
264#553—21no—
265#547—22no—
266#547—21no—
267#544—21no—
268#540—21no—
269#539—22no—
270#539—21no—
271#537—21no—
272#532C22×C1311yescharacteristic
273C2×C4⋊Q8C22×C1311yescharacteristic
274#529C22×C1311yescharacteristic
275C2×#125C22×C1311yescharacteristic
276#501—22no—
277#501C22×C1314yes—
278#497C22×C1312yes—
279#491C22×C1312yes—
280#489C22×C1314yes—
281#487—21no—
282#486—21no—
283#462—21no—
284#461—21no—
285#451—21no—
286#448—21no—
287#432C22×C1311yescharacteristic
288C2×#107—21no—
289C2×#106—21no—
290#417—22no—
291C4×M16C22×C1311yescharacteristic
292C2×#97C22×C1311yescharacteristic
293#330C22×C1314yes—
294#330C22×C1312yes—
295#329C22×C1312yes—
296#329C22×C1314yes—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—42no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—41no—
305C22×C13#45512yes—
306C22×C13C2×#12011yescharacteristic
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—42no—
313C4×C13—42no—
314C4×C13—41no—
315C4×C13—41no—
316C4×C13—42no—
317C4×C13—41no—
318C4×C13—82no—
319C4×C13#45612yes—
320C2×#41—22no—
321C2×#41D4×C1312yes—
322C22×Q8—21no—
323C2×Q16—22no—
324C2×SD16—22no—
325C2×M16—21no—
326C22×C8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—22no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8D4×C1311yescharacteristic
333C4⋊Q8C23×C1312yes—
334#127D4×C1311yescharacteristic
335#126—22no—
336#126—22no—
337#126—21no—
338#125—22no—
339#125—21no—
340#125—21no—
341#125—21no—
342#125D4×C1312yes—
343#125C23×C1312yes—
344#125C23×C1311yescharacteristic
345#124C23×C1311yescharacteristic
346#124C23×C1312yes—
347#123—22no—
348#123—22no—
349#123—22no—
350#123—22no—
351#123—21no—
352#123—22no—
353#123—22no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8D4×C1311yescharacteristic
361#121—22no—
362#121—22no—
363#121—21no—
364#121—21no—
365#121—22no—
366#121—22no—
367#121—21no—
368#121—21no—
369#121D4×C1311yescharacteristic
370C4×Q8D4×C1311yescharacteristic
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4D4×C1311yescharacteristic
379#117—21no—
380#117—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4D4×C1311yescharacteristic
388C2×C4⋊C4D4×C1311yescharacteristic
389C2×C42C23×C1311yescharacteristic
390#107—24no—
391#106—24no—
392C4⋊C8—21no—
393#103—24no—
394#103—22no—
395#103—22no—
396#102—24no—
397C22⋊C8—21no—
398#97—21no—
399#97C23×C1312yes—
400#97C23×C1312yes—
401#97C23×C1312yes—
402C4×C8—21no—
403C2×C13—22no—
404C2×C13—82no—
405C2×C13—81no—
406C2×C13C2×#45511yescharacteristic
407C2×C13C2×#45611yescharacteristic
408C2×C13#302111yescharacteristic
409#41—44no—
410#41—84no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—41no—
414C2×Q8—82no—
415C2×Q8C2×D4×C1312yes—
416C2×Q8C2×D4×C1311yescharacteristic
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4C2×D4×C1312yes—
424C2×D4C2×D4×C1311yescharacteristic
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4C2×D4×C1311yescharacteristic
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436Q16—82no—
437SD16—82no—
438M16—42no—
439C2×C8—24no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C1311yescharacteristic
464C4⋊C4C2×D4×C1311yescharacteristic
465C4⋊C4C2×D4×C1312yes—
466C4⋊C4C2×D4×C1312yes—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C42—22no—
480C42—21no—
481C42C2×D4×C1311yescharacteristic
482C42C2×D4×C1311yescharacteristic
483C42C2×D4×C1311yescharacteristic
484C42C24×C1311yescharacteristic
485C13#1902211yescharacteristic, direct product factor, Sylow
486C23—22no—
487C23—21no—
488C23C13×#12011yescharacteristic
489Q8—41no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493Q8—82no—
494Q8—82no—
495D4—41no—
496D4—42no—
497D4—44no—
498D4—42no—
499D4—42no—
500D4—81no—
501D4—82no—
502D4—82no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4C13×#12011yescharacteristic
522C2×C4C13×#12011yescharacteristic
523C2×C4C13×#12011yescharacteristic
524C2×C4C22×D4×C1311yescharacteristic
525C2×C4C22×D4×C1311yescharacteristic
526C2×C4C22×D4×C1311yescharacteristic
527C8—24no—
528C8—42no—
529C8—42no—
530C22—21no—
531C22—21no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22C13×#45512yes—
539C22C2×C13×#12011yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—42no—
546C4—42no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—82no—
552C4C13×#45612yes—
553C2—22no—
554C2—82no—
555C2—81no—
556C2C2×C13×#45511yescharacteristic
557C2C2×C13×#45611yescharacteristic
558C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3559C2
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
2. C13×#3218C2semidirect
3. C2×C13×#501C2semidirect
4. C13×#3141C2semidirect
5. C13×#1664C2semidirect
6. C13×#1661C2semidirect
7. C13×#1530C2semidirect
8. C13×#1528C2semidirect
9. C13×#1524C2semidirect
130. #19022C13direct (N × H)
208. #3218C2×C13semidirect
209. C2×#501C2×C13semidirect
210. #3141C2×C13semidirect
211. #1664C2×C13semidirect
212. #1661C2×C13semidirect
213. #1530C2×C13semidirect
214. #1528C2×C13semidirect
215. #1524C2×C13semidirect
485. C13#19022direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32182
C2×C13×#5012
C13×#31412
C13×#16642
C13×#16612
C13×#15302
C13×#15282
C13×#15242
#1902213