Finite Group Databasebeta

← C2×C13×#1867 #15707226

Subgroups — C2×C13×#1867 #15707226

Order 3328.

1994 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#518C211yesmaximal, characteristic
2C22×C13×#99C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#385C212yesmaximal, complemented
5C13×#1867C218yesmaximal, direct product factor
6C2×C13×#342C212yesmaximal, complemented
7C23×D4×C13C2211yescharacteristic
8C24×C4×C13C2211yescharacteristic
9C13×#518—22no—
10C13×#518—24no—
11C13×#518C2214yes—
12C2×C4×D4×C13—22no—
13C2×C4×D4×C13—22no—
14C2×C13×#117—21no—
15C22×C13×C4⋊C4—22no—
16C22×C13×C22⋊C4—21no—
17C22×C13×C22⋊C4—21no—
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2212yes—
21C2×C13×#99C418yescomplemented
22C2×C13×#99C2214yes—
23C13×#386—22no—
24C13×#386C2214yes—
25C13×#385—24no—
26C13×#385C2218yescomplemented
27C2×C13×#95—22no—
28C2×C13×#95—21no—
29C13×#342C2218yescomplemented
30C25×C13D411yescharacteristic
31C25×C13C2311yescharacteristic
32C22×D4×C13—22no—
33C22×D4×C13—22no—
34C22×D4×C13—24no—
35C22×D4×C13C2×C414yes—
36C22×D4×C13D412yes—
37C22×D4×C13Q814yes—
38C22×D4×C13C2312yes—
39C23×C4×C13—21no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—21no—
43C23×C4×C13—21no—
44C23×C4×C13—22no—
45C23×C4×C13—21no—
46C23×C4×C13—21no—
47C23×C4×C13—44no—
48C23×C4×C13D411yescharacteristic
49C23×C4×C13D412yes—
50C23×C4×C13D412yes—
51C23×C4×C13C2312yes—
52C4×D4×C13—28no—
53C4×D4×C13—28no—
54C4×D4×C13—28no—
55C4×D4×C13—28no—
56C13×#117—24no—
57C13×#117—24no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—28no—
61C2×C13×C4⋊C4—48no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—44no—
75C2×C13×C22⋊C4C2×C418yescomplemented
76C2×C13×C22⋊C4D414yes—
77C2×C13×C22⋊C4C2312yes—
78C2×C13×C22⋊C4C2314yes—
79C2×C13×C22⋊C4C2314yes—
80C2×C42×C13—22no—
81C13×#99C2×C4116yescomplemented
82C13×#95—28no—
83C13×#95—24no—
84C2×#1867C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—22no—
88C24×C13—42no—
89C24×C13—42no—
90C24×C13—42no—
91C24×C13—42no—
92C24×C13C4⋊C414yescomplemented
93C24×C13C22×C412yes—
94C24×C13C2×D411yescharacteristic
95C24×C13C2×D412yes—
96C24×C13C2×D412yes—
97C24×C13C2×D411yescharacteristic
98C24×C13C2×D412yes—
99C24×C13C2×Q812yes—
100C24×C13#4114yes—
101C24×C13C2411yescharacteristic
102C2×D4×C13—28no—
103C2×D4×C13—28no—
104C2×D4×C13—24no—
105C2×D4×C13—28no—
106C2×D4×C13—28no—
107C2×D4×C13—24no—
108C2×D4×C13—24no—
109C2×D4×C13—24no—
110C2×D4×C13C4⋊C418yescomplemented
111C2×D4×C13C22×C414yes—
112C2×D4×C13C2×Q814yes—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—24no—
117C22×C4×C13—28no—
118C22×C4×C13—28no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—24no—
123C22×C4×C13—24no—
124C22×C4×C13—24no—
125C22×C4×C13—24no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—44no—
130C22×C4×C13—44no—
131C22×C4×C13—48no—
132C22×C4×C13—44no—
133C22×C4×C13—44no—
134C22×C4×C13—44no—
135C22×C4×C13—42no—
136C22×C4×C13—41no—
137C22×C4×C13—42no—
138C22×C4×C13—41no—
139C22×C4×C13—44no—
140C22×C4×C13—44no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—82no—
145C22×C4×C13—82no—
146C22×C4×C13C4⋊C414yescomplemented
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2×D414yes—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—416no—
153C13×C22⋊C4—28no—
154C13×C22⋊C4—28no—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—24no—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—48no—
162C13×C22⋊C4—42no—
163C13×C22⋊C4C22×C418yescomplemented
164C42×C13—28no—
165C2×#518C2×C1311yescharacteristic
166C22×#99C2×C1311yescharacteristic
167C2×#386C2×C1311yescharacteristic
168C2×#385C2×C1312yescomplemented
169#1867C2×C1318yesdirect product factor
170C2×#342C2×C1312yescomplemented
171C23×C13—24no—
172C23×C13—22no—
173C23×C13—24no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—24no—
177C23×C13—22no—
178C23×C13—24no—
179C23×C13—42no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—44no—
183C23×C13—42no—
184C23×C13—41no—
185C23×C13—44no—
186C23×C13—48no—
187C23×C13—41no—
188C23×C13—42no—
189C23×C13—48no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—84no—
194C23×C13—81no—
195C23×C13—81no—
196C23×C13C2×C4⋊C412yes—
197C23×C13C2×C4⋊C412yes—
198C23×C13C2×C4⋊C414yescomplemented
199C23×C13C4×D414yes—
200C23×C13C4×D414yes—
201C23×C13#12011yescharacteristic
202C23×C13#12012yes—
203C23×C13#12011yescharacteristic
204C23×C13C22⋊Q814yes—
205C23×C13C22⋊Q814yes—
206C23×C13#12312yes—
207C23×C13#12312yes—
208C23×C13C23×C411yescharacteristic
209C23×C13C22×D411yescharacteristic
210C23×C13C22×D412yes—
211C23×C13C22×Q811yescharacteristic
212C23×C13C2×#4112yes—
213D4×C13—28no—
214D4×C13—28no—
215D4×C13—216no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—28no—
222C2×C4×C13—28no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—44no—
226C2×C4×C13—416no—
227C2×C4×C13—44no—
228C2×C4×C13—44no—
229C2×C4×C13—42no—
230C2×C4×C13—48no—
231C2×C4×C13—44no—
232C2×C4×C13—42no—
233C2×C4×C13—44no—
234C2×C4×C13—44no—
235C2×C4×C13—44no—
236C2×C4×C13—44no—
237C2×C4×C13—44no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—82no—
242C2×C4×C13—82no—
243C2×C4×C13—84no—
244C2×C4×C13—84no—
245C2×C4×C13—84no—
246C2×C4×C13C2×C4⋊C414yescomplemented
247C23×D4C22×C1311yescharacteristic
248C24×C4C22×C1311yescharacteristic
249#518—22no—
250#518—24no—
251#518C22×C1314yes—
252C2×C4×D4—22no—
253C2×C4×D4—22no—
254C2×#117—21no—
255C22×C4⋊C4—22no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C22⋊C4C22×C1311yescharacteristic
259C22×C22⋊C4C22×C1312yes—
260C22×C22⋊C4C22×C1312yes—
261C2×#99C4×C1318yescomplemented
262C2×#99C22×C1314yes—
263#386—22no—
264#386C22×C1314yes—
265#385—24no—
266#385C22×C1318yescomplemented
267C2×#95—22no—
268C2×#95—21no—
269#342C22×C1318yescomplemented
270C22×C13—28no—
271C22×C13—24no—
272C22×C13—24no—
273C22×C13—28no—
274C22×C13—22no—
275C22×C13—21no—
276C22×C13—22no—
277C22×C13—21no—
278C22×C13—22no—
279C22×C13—21no—
280C22×C13—22no—
281C22×C13—21no—
282C22×C13—24no—
283C22×C13—42no—
284C22×C13—44no—
285C22×C13—44no—
286C22×C13—42no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13—42no—
290C22×C13—44no—
291C22×C13—48no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13—82no—
295C22×C13—84no—
296C22×C13#38512yes—
297C22×C13#38514yes—
298C22×C13#38512yes—
299C22×C13B(4,𝔽2)12yes—
300C22×C13#45812yes—
301C22×C13C22×C4⋊C411yescharacteristic
302C22×C13C2×C4×D412yes—
303C22×C13C2×#12011yescharacteristic
304C22×C13C2×C22⋊Q812yes—
305C22×C13C2×#12311yescharacteristic
306C4×C13—24no—
307C4×C13—48no—
308C4×C13—44no—
309C4×C13—44no—
310C4×C13—44no—
311C4×C13—82no—
312C25D4×C1311yescharacteristic
313C25C23×C1311yescharacteristic
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—24no—
317C22×D4C2×C4×C1314yes—
318C22×D4D4×C1312yes—
319C22×D4Q8×C1314yes—
320C22×D4C23×C1312yes—
321C23×C4—21no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—22no—
328C23×C4—21no—
329C23×C4—44no—
330C23×C4D4×C1311yescharacteristic
331C23×C4D4×C1312yes—
332C23×C4D4×C1312yes—
333C23×C4C23×C1312yes—
334C4×D4—28no—
335C4×D4—28no—
336C4×D4—28no—
337C4×D4—28no—
338#117—24no—
339#117—24no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—48no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C1318yescomplemented
358C2×C22⋊C4D4×C1314yes—
359C2×C22⋊C4C23×C1312yes—
360C2×C22⋊C4C23×C1314yes—
361C2×C22⋊C4C23×C1314yes—
362C2×C42—22no—
363#99C2×C4×C13116yescomplemented
364#95—28no—
365#95—24no—
366C2×C13—22no—
367C2×C13—21no—
368C2×C13—21no—
369C2×C13—22no—
370C2×C13—22no—
371C2×C13—24no—
372C2×C13—44no—
373C2×C13#186714yesdirect product factor
374C2×C13C2×#38511yescharacteristic
375C2×C13C2×B(4,𝔽2)11yescharacteristic
376C2×C13C2×#45811yescharacteristic
377C24—21no—
378C24—21no—
379C24—22no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24C13×C4⋊C414yescomplemented
385C24C22×C4×C1312yes—
386C24C2×D4×C1311yescharacteristic
387C24C2×D4×C1312yes—
388C24C2×D4×C1312yes—
389C24C2×D4×C1311yescharacteristic
390C24C2×D4×C1312yes—
391C24C2×Q8×C1312yes—
392C24C13×#4114yes—
393C24C24×C1311yescharacteristic
394C2×D4—28no—
395C2×D4—28no—
396C2×D4—24no—
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4C13×C4⋊C418yescomplemented
403C2×D4C22×C4×C1314yes—
404C2×D4C2×Q8×C1314yes—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—48no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—42no—
427C22×C4—44no—
428C22×C4—41no—
429C22×C4—42no—
430C22×C4—41no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—82no—
437C22×C4—82no—
438C22×C4C13×C4⋊C414yescomplemented
439C22×C4C2×D4×C1312yes—
440C22×C4C2×D4×C1314yes—
441C22×C4C2×D4×C1314yes—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—416no—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—48no—
454C22⋊C4—42no—
455C22⋊C4C22×C4×C1318yescomplemented
456C42—28no—
457C13C2×#186711yescharacteristic, direct product factor, Sylow
458C23—24no—
459C23—22no—
460C23—24no—
461C23—22no—
462C23—24no—
463C23—22no—
464C23—24no—
465C23—22no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—44no—
470C23—42no—
471C23—41no—
472C23—44no—
473C23—48no—
474C23—41no—
475C23—42no—
476C23—48no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—81no—
481C23—81no—
482C23—84no—
483C23C2×C13×C4⋊C412yes—
484C23C2×C13×C4⋊C412yes—
485C23C2×C13×C4⋊C414yescomplemented
486C23C4×D4×C1314yes—
487C23C4×D4×C1314yes—
488C23C13×#12011yescharacteristic
489C23C13×#12012yes—
490C23C13×#12011yescharacteristic
491C23C13×C22⋊Q814yes—
492C23C13×C22⋊Q814yes—
493C23C13×#12312yes—
494C23C13×#12312yes—
495C23C23×C4×C1311yescharacteristic
496C23C22×D4×C1311yescharacteristic
497C23C22×D4×C1312yes—
498C23C22×Q8×C1311yescharacteristic
499C23C2×C13×#4112yes—
500D4—216no—
501D4—28no—
502D4—28no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—28no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—48no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—416no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4—84no—
533C2×C4C2×C13×C4⋊C414yescomplemented
534C22—22no—
535C22—21no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—22no—
541C22—21no—
542C22—28no—
543C22—24no—
544C22—24no—
545C22—28no—
546C22—24no—
547C22—42no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—41no—
552C22—41no—
553C22—42no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—48no—
558C22—82no—
559C22—84no—
560C22C13×#38512yes—
561C22C13×#38514yes—
562C22C13×#38512yes—
563C22C13×B(4,𝔽2)12yes—
564C22C13×#45812yes—
565C22C22×C13×C4⋊C411yescharacteristic
566C22C2×C4×D4×C1312yes—
567C22C2×C13×#12011yescharacteristic
568C22C2×C13×C22⋊Q812yes—
569C22C2×C13×#12311yescharacteristic
570C4—24no—
571C4—48no—
572C4—44no—
573C4—44no—
574C4—44no—
575C4—82no—
576C2—22no—
577C2—21no—
578C2—21no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—44no—
583C2C13×#186714yesdirect product factor
584C2C2×C13×#38511yescharacteristic
585C2C2×C13×B(4,𝔽2)11yescharacteristic
586C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C13×#385C2semidirect
5. C13×#1867C2direct (N × H)
6. C2×C13×#342C2semidirect
21. C2×C13×#99C4semidirect
26. C13×#385C22semidirect
29. C13×#342C22semidirect
75. C2×C13×C22⋊C4C2×C4semidirect
81. C13×#99C2×C4semidirect
84. C2×#1867C13direct (N × H)
92. C24×C13C4⋊C4semidirect
110. C2×D4×C13C4⋊C4semidirect
146. C22×C4×C13C4⋊C4semidirect
163. C13×C22⋊C4C22×C4semidirect
168. C2×#385C2×C13semidirect
169. #1867C2×C13direct (N × H)
170. C2×#342C2×C13semidirect
198. C23×C13C2×C4⋊C4semidirect
246. C2×C4×C13C2×C4⋊C4semidirect
261. C2×#99C4×C13semidirect
266. #385C22×C13semidirect
269. #342C22×C13semidirect
357. C2×C22⋊C4C2×C4×C13semidirect
363. #99C2×C4×C13semidirect
373. C2×C13#1867direct (N × H)
384. C24C13×C4⋊C4semidirect
402. C2×D4C13×C4⋊C4semidirect
438. C22×C4C13×C4⋊C4semidirect
455. C22⋊C4C22×C4×C13semidirect
457. C13C2×#1867direct (N × H)
485. C23C2×C13×C4⋊C4semidirect
533. C2×C4C2×C13×C4⋊C4semidirect
583. C2C13×#1867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5182
C22×C13×#992
C2×C13×#3862
C2×C13×#3852
C13×#18672
C2×C13×#3422
C2×#186713