Finite Group Databasebeta

← C13×#23905 #15710244

Subgroups — C13×#23905 #15710244

Order 3328.

1744 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3485C211yesmaximal, characteristic
2C2×C13×#536C211yesmaximal, characteristic, complemented
3C2×C13×#458C212yesmaximal, complemented
4C13×#2614C212yesmaximal, complemented
5C13×#2022C214yesmaximal, complemented
6C13×#1899C212yesmaximal, complemented
7C13×#1890C212yesmaximal, complemented
8C13×#1782C211yesmaximal, characteristic, complemented
9C2×C13×H(5,𝔽2)C2211yescharacteristic
10C22×C13×#41C2211yescharacteristic
11C23×Q8×C13C2211yescharacteristic, complemented
12C13×#547—24no—
13C13×#546—24no—
14C13×#536—21no—
15C13×#536—28no—
16C13×#534—21no—
17C13×#534C2212yes—
18C2×C13×C4⋊Q8—21no—
19C2×C13×#124—21no—
20C13×#525—21no—
21C2×C13×#123—21no—
22C2×C13×#123C2214yes—
23C2×C13×#123C2212yes—
24C2×C13×#123C2212yes—
25C2×C13×#123C2212yescomplemented
26C2×C13×C22⋊Q8—21no—
27C2×C13×C22⋊Q8—21no—
28C13×#518C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic, complemented
30C13×#458—28no—
31C2×C13×#99C2214yes—
32C2×C13×#99C2212yes—
33C2×C13×#99C2212yescomplemented
34C13×#395—24no—
35C13×#393—24no—
36C13×#381C2214yescomplemented
37C13×#381C2212yescomplemented
38C13×#342C2214yescomplemented
39C13×H(5,𝔽2)—24no—
40C13×H(5,𝔽2)—42no—
41C2×C13×#41—24no—
42C2×C13×#41—21no—
43C2×C13×#41—24no—
44C2×C13×#41—22no—
45C2×C13×#41—42no—
46C22×Q8×C13—21no—
47C22×Q8×C13—21no—
48C22×Q8×C13—24no—
49C22×Q8×C13—24no—
50C22×Q8×C13—42no—
51C22×Q8×C13D411yescharacteristic
52C22×D4×C13—21no—
53C22×D4×C13—22no—
54C22×D4×C13D411yescharacteristic
55C22×D4×C13C2312yes—
56C22×D4×C13C2311yescharacteristic
57C22×D4×C13C2311yescharacteristic
58C23×C4×C13D411yescharacteristic
59C23×C4×C13D411yescharacteristic
60C23×C4×C13C2312yes—
61C23×C4×C13C2311yescharacteristic
62C13×C4⋊Q8—28no—
63C13×C4⋊Q8—22no—
64C13×#124—28no—
65C13×#124—22no—
66C13×#123—24no—
67C13×#123—22no—
68C13×#123—24no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—24no—
73C13×#123—24no—
74C13×#123—22no—
75C13×#123—24no—
76C13×#123—28no—
77C13×#123—44no—
78C13×#123D418yescomplemented
79C13×C22⋊Q8—28no—
80C13×C22⋊Q8—28no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—24no—
83C13×#121—22no—
84C13×#121—24no—
85C13×#121—24no—
86C13×#120—22no—
87C13×#120—22no—
88C13×#120—22no—
89C4×D4×C13—24no—
90C4×D4×C13—24no—
91C13×#117—21no—
92C13×#117—24no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—24no—
98C2×C13×C4⋊C4D414yes—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4D414yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C13×C22⋊C4C2312yes—
107C2×C13×C22⋊C4C2312yes—
108C2×C42×C13—21no—
109C13×#99—24no—
110C13×#99—28no—
111C13×#99—42no—
112C13×#95—28no—
113C13×#95—24no—
114#23905C1311yesmaximal, characteristic, direct product factor, Sylow
115C24×C13—21no—
116C24×C13C2×D412yes—
117C24×C13C2×D411yescharacteristic
118C24×C13C2×D411yescharacteristic
119C24×C13C2411yescharacteristic
120C13×#41—416no—
121C13×#41—48no—
122C13×#41—42no—
123C13×#41—42no—
124C2×Q8×C13—24no—
125C2×Q8×C13—21no—
126C2×Q8×C13—24no—
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—41no—
130C2×Q8×C13—416no—
131C2×Q8×C13—42no—
132C2×Q8×C13—42no—
133C2×Q8×C13—42no—
134C2×Q8×C13—42no—
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—22no—
138C2×D4×C13—21no—
139C2×D4×C13—22no—
140C2×D4×C13—24no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—24no—
147C2×D4×C13—24no—
148C2×D4×C13—22no—
149C2×D4×C13—41no—
150C2×D4×C13—48no—
151C2×D4×C13—42no—
152C2×D4×C13—42no—
153C2×D4×C13C2×D414yes—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—24no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—24no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—24no—
169C22×C4×C13—41no—
170C22×C4×C13—41no—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D414yes—
174C22×C4×C13C2×D414yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D414yes—
179C13×C4⋊C4—24no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—28no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—28no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—48no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—24no—
189C13×C22⋊C4—28no—
190C13×C22⋊C4—24no—
191C13×C22⋊C4—28no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—24no—
196C13×C22⋊C4—24no—
197C13×C22⋊C4—24no—
198C13×C22⋊C4—24no—
199C13×C22⋊C4—48no—
200C13×C22⋊C4C2×D414yes—
201C42×C13—24no—
202C42×C13—22no—
203#3485C2×C1311yescharacteristic
204C2×#536C2×C1311yescharacteristic, complemented
205C2×#458C2×C1312yescomplemented
206#2614C2×C1312yescomplemented
207#2022C2×C1314yescomplemented
208#1899C2×C1312yescomplemented
209#1890C2×C1312yescomplemented
210#1782C2×C1311yescharacteristic, complemented
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—22no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—24no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—44no—
223C23×C13—82no—
224C23×C13#12012yes—
225C23×C13C22×D411yescharacteristic
226C23×C13C22×D412yes—
227C23×C13C22×D412yes—
228C23×C13H(5,𝔽2)12yes—
229Q8×C13—44no—
230Q8×C13—48no—
231Q8×C13—48no—
232Q8×C13—42no—
233D4×C13—28no—
234D4×C13—44no—
235D4×C13—42no—
236D4×C13—44no—
237D4×C13—42no—
238D4×C13—42no—
239D4×C13—44no—
240D4×C13—44no—
241D4×C13—84no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—28no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—21no—
252C2×C4×C13—24no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—28no—
257C2×C4×C13—24no—
258C2×C4×C13—44no—
259C2×C4×C13—44no—
260C2×C4×C13—44no—
261C2×C4×C13—44no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—44no—
266C2×C4×C13—44no—
267C2×C4×C13—48no—
268C2×C4×C13—44no—
269C2×C4×C13—82no—
270C2×C4×C13#12012yes—
271C2×C4×C13#12012yes—
272C2×C4×C13#12012yes—
273C2×H(5,𝔽2)C22×C1311yescharacteristic
274C22×#41C22×C1311yescharacteristic
275C23×Q8C22×C1311yescharacteristic, complemented
276#547—24no—
277#546—24no—
278#536—21no—
279#536—28no—
280#534—21no—
281#534C22×C1312yes—
282C2×C4⋊Q8—21no—
283C2×#124—21no—
284#525—21no—
285C2×#123—21no—
286C2×#123C22×C1314yes—
287C2×#123C22×C1312yes—
288C2×#123C22×C1312yes—
289C2×#123C22×C1312yescomplemented
290C2×C22⋊Q8—21no—
291C2×C22⋊Q8—21no—
292#518C22×C1311yescharacteristic
293C2×#117C22×C1311yescharacteristic, complemented
294#458—28no—
295C2×#99C22×C1312yes—
296C2×#99C22×C1314yes—
297C2×#99C22×C1312yescomplemented
298#395—24no—
299#393—24no—
300#381C22×C1314yescomplemented
301#381C22×C1312yescomplemented
302#342C22×C1314yescomplemented
303C22×C13—24no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—41no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—44no—
315C22×C13—81no—
316C22×C13—84no—
317C22×C13—81no—
318C22×C13—162no—
319C22×C13C2×#12011yescharacteristic
320C22×C13C2×#12011yescharacteristic
321C22×C13#53411yescharacteristic
322C22×C13D4214yes—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—44no—
327C4×C13—42no—
328C4×C13—41no—
329C4×C13—44no—
330C4×C13—44no—
331C4×C13—84no—
332H(5,𝔽2)—24no—
333H(5,𝔽2)—42no—
334C2×#41—24no—
335C2×#41—21no—
336C2×#41—24no—
337C2×#41—22no—
338C2×#41—42no—
339C22×Q8—21no—
340C22×Q8—21no—
341C22×Q8—24no—
342C22×Q8—24no—
343C22×Q8—42no—
344C22×Q8D4×C1311yescharacteristic
345C22×D4—21no—
346C22×D4—22no—
347C22×D4D4×C1311yescharacteristic
348C22×D4C23×C1312yes—
349C22×D4C23×C1311yescharacteristic
350C22×D4C23×C1311yescharacteristic
351C23×C4D4×C1311yescharacteristic
352C23×C4D4×C1311yescharacteristic
353C23×C4C23×C1312yes—
354C23×C4C23×C1311yescharacteristic
355C4⋊Q8—28no—
356C4⋊Q8—22no—
357#124—28no—
358#124—22no—
359#123—24no—
360#123—22no—
361#123—24no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—24no—
366#123—24no—
367#123—22no—
368#123—24no—
369#123—28no—
370#123—44no—
371#123D4×C1318yescomplemented
372C22⋊Q8—28no—
373C22⋊Q8—28no—
374C22⋊Q8—22no—
375C22⋊Q8—24no—
376#121—22no—
377#121—24no—
378#121—24no—
379#120—22no—
380#120—22no—
381#120—22no—
382C4×D4—24no—
383C4×D4—24no—
384#117—21no—
385#117—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4D4×C1314yes—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4D4×C1314yes—
398C2×C22⋊C4C23×C1314yes—
399C2×C22⋊C4C23×C1312yes—
400C2×C22⋊C4C23×C1312yes—
401C2×C42—21no—
402#99—24no—
403#99—28no—
404#99—42no—
405#95—28no—
406#95—24no—
407C2×C13—21no—
408C2×C13—24no—
409C2×C13—21no—
410C2×C13—42no—
411C2×C13—81no—
412C2×C13—82no—
413C2×C13#240311yescharacteristic
414C2×C13#302812yes—
415C24—21no—
416C24C2×D4×C1312yes—
417C24C2×D4×C1311yescharacteristic
418C24C2×D4×C1311yescharacteristic
419C24C24×C1311yescharacteristic
420#41—416no—
421#41—48no—
422#41—42no—
423#41—42no—
424C2×Q8—24no—
425C2×Q8—21no—
426C2×Q8—24no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—416no—
431C2×Q8—42no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—22no—
449C2×D4—41no—
450C2×D4—48no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4C2×D4×C1314yes—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4C2×D4×C1312yes—
472C22×C4C2×D4×C1311yescharacteristic
473C22×C4C2×D4×C1314yes—
474C22×C4C2×D4×C1314yes—
475C22×C4C2×D4×C1311yescharacteristic
476C22×C4C2×D4×C1311yescharacteristic
477C22×C4C2×D4×C1311yescharacteristic
478C22×C4C2×D4×C1314yes—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—28no—
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—28no—
485C4⋊C4—24no—
486C4⋊C4—48no—
487C22⋊C4—22no—
488C22⋊C4—24no—
489C22⋊C4—28no—
490C22⋊C4—24no—
491C22⋊C4—28no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—48no—
500C22⋊C4C2×D4×C1314yes—
501C42—24no—
502C42—22no—
503C13#2390511yescharacteristic, direct product factor, Sylow
504C23—21no—
505C23—21no—
506C23—21no—
507C23—22no—
508C23—21no—
509C23—21no—
510C23—24no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—82no—
517C23C13×#12012yes—
518C23C22×D4×C1311yescharacteristic
519C23C22×D4×C1312yes—
520C23C22×D4×C1312yes—
521C23C13×H(5,𝔽2)12yes—
522Q8—44no—
523Q8—48no—
524Q8—48no—
525Q8—42no—
526D4—28no—
527D4—44no—
528D4—42no—
529D4—44no—
530D4—42no—
531D4—42no—
532D4—44no—
533D4—44no—
534D4—84no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—28no—
550C2×C4—24no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—48no—
561C2×C4—44no—
562C2×C4—82no—
563C2×C4C13×#12012yes—
564C2×C4C13×#12012yes—
565C2×C4C13×#12012yes—
566C22—24no—
567C22—22no—
568C22—22no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—44no—
576C22—41no—
577C22—42no—
578C22—81no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22C2×C13×#12011yescharacteristic
583C22C2×C13×#12011yescharacteristic
584C22C13×#53411yescharacteristic
585C22D42×C1314yes—
586C4—22no—
587C4—22no—
588C4—22no—
589C4—44no—
590C4—44no—
591C4—42no—
592C4—41no—
593C4—44no—
594C4—84no—
595C2—21no—
596C2—24no—
597C2—21no—
598C2—42no—
599C2—81no—
600C2—82no—
601C2C13×#240311yescharacteristic
602C2C13×#302812yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3485C2
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. C2×C13×#536C2semidirect
3. C2×C13×#458C2semidirect
4. C13×#2614C2semidirect
5. C13×#2022C2semidirect
6. C13×#1899C2semidirect
7. C13×#1890C2semidirect
8. C13×#1782C2semidirect
11. C23×Q8×C13C22semidirect
25. C2×C13×#123C22semidirect
29. C2×C13×#117C22semidirect
33. C2×C13×#99C22semidirect
36. C13×#381C22semidirect
37. C13×#381C22semidirect
38. C13×#342C22semidirect
78. C13×#123D4semidirect
114. #23905C13direct (N × H)
204. C2×#536C2×C13semidirect
205. C2×#458C2×C13semidirect
206. #2614C2×C13semidirect
207. #2022C2×C13semidirect
208. #1899C2×C13semidirect
209. #1890C2×C13semidirect
210. #1782C2×C13semidirect
275. C23×Q8C22×C13semidirect
289. C2×#123C22×C13semidirect
293. C2×#117C22×C13semidirect
297. C2×#99C22×C13semidirect
300. #381C22×C13semidirect
301. #381C22×C13semidirect
302. #342C22×C13semidirect
371. #123D4×C13semidirect
503. C13#23905direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34852
C2×C13×#5362
C2×C13×#4582
C13×#26142
C13×#20222
C13×#18992
C13×#18902
C13×#17822
#2390513