Finite Group Databasebeta

← C13×#29404 #15715743

Subgroups — C13×#29404 #15715743

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2330C211yesmaximal, characteristic, complemented
2C13×#2319C211yesmaximal, characteristic
3C13×#2083C211yesmaximal, characteristic, complemented
4C13×#2071C211yesmaximal, characteristic
5C13×#2059C211yesmaximal, characteristic, complemented
6C13×#2025C211yesmaximal, characteristic
7C13×#1926C211yesmaximal, characteristic
8C13×#1925C211yesmaximal, characteristic
9C13×#1921C211yesmaximal, characteristic, complemented
10C13×#1921C211yesmaximal, characteristic, complemented
11C13×#1920C211yesmaximal, characteristic, complemented
12C13×#1918C211yesmaximal, characteristic, complemented
13C13×#1862C211yesmaximal, characteristic
14C13×#1862C211yesmaximal, characteristic
15C13×#1840C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#107C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#390C2211yescharacteristic
28C13×#389—21no—
29C13×#389—21no—
30C13×#389C2211yescharacteristic
31C13×#389C2211yescharacteristic
32C13×#389C2211yescharacteristic
33C13×#389C2211yescharacteristic
34C13×#388—21no—
35C13×#388—21no—
36C13×#387—21no—
37C13×#387—21no—
38C13×#384C2211yescharacteristic
39C13×#381—21no—
40C13×#380—21no—
41C4×C13×C4⋊C4C2211yescharacteristic
42C4×C13×C4⋊C4C2211yescharacteristic
43C4×C13×C4⋊C4C2211yescharacteristic
44C13×#376C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55C13×#336C2211yescharacteristic
56C13×#336C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×#125—22no—
66C13×#125—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C42×C13—21no—
90C2×C42×C13—21no—
91C2×C42×C13—21no—
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C13×#107—22no—
96C13×#107—22no—
97C13×#107—22no—
98C13×#106—22no—
99C13×#102—22no—
100C13×#102—22no—
101C13×#102—22no—
102C13×#102—22no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#29404C1311yesmaximal, characteristic, direct product factor, Sylow
115C24×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13#4112yes—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—24no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—81no—
131C22×C4×C13—81no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C2×C8×C13—21no—
140C2×C8×C13—21no—
141C2×C8×C13—21no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4—81no—
167C13×C4⋊C4—81no—
168C13×C4⋊C4—81no—
169C13×C4⋊C4—81no—
170C13×C4⋊C4#4112yes—
171C13×C4⋊C4#4112yes—
172C13×C4⋊C4#4112yes—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—81no—
175C13×C22⋊C4—81no—
176C13×C22⋊C4—81no—
177C13×C22⋊C4—81no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—81no—
185C42×C13—81no—
186C42×C13—81no—
187#2330C2×C1311yescharacteristic, complemented
188#2319C2×C1311yescharacteristic
189#2083C2×C1311yescharacteristic, complemented
190#2071C2×C1311yescharacteristic
191#2059C2×C1311yescharacteristic, complemented
192#2025C2×C1311yescharacteristic
193#1926C2×C1311yescharacteristic
194#1925C2×C1311yescharacteristic
195#1921C2×C1311yescharacteristic, complemented
196#1921C2×C1311yescharacteristic, complemented
197#1920C2×C1311yescharacteristic, complemented
198#1918C2×C1311yescharacteristic, complemented
199#1862C2×C1311yescharacteristic
200#1862C2×C1311yescharacteristic
201#1840C2×C1311yescharacteristic, complemented
202C23×C13—22no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13C22×D411yescharacteristic
210D4×C13—22no—
211D4×C13—22no—
212D4×C13—41no—
213D4×C13—41no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—84no—
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C132−1+411yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C2×#125C22×C1311yescharacteristic
265C2×C4×D4C22×C1311yescharacteristic
266C2×#107C22×C1311yescharacteristic
267C2×#107C22×C1311yescharacteristic
268C2×#107C22×C1311yescharacteristic
269C2×#106C22×C1311yescharacteristic
270C2×#102C22×C1311yescharacteristic
271C2×#102C22×C1311yescharacteristic
272C2×#102C22×C1311yescharacteristic
273C2×#102C22×C1311yescharacteristic
274#390C22×C1311yescharacteristic
275#390C22×C1311yescharacteristic
276#389—21no—
277#389—21no—
278#389C22×C1311yescharacteristic
279#389C22×C1311yescharacteristic
280#389C22×C1311yescharacteristic
281#389C22×C1311yescharacteristic
282#388—21no—
283#388—21no—
284#387—21no—
285#387—21no—
286#384C22×C1311yescharacteristic
287#381—21no—
288#380—21no—
289C4×C4⋊C4C22×C1311yescharacteristic
290C4×C4⋊C4C22×C1311yescharacteristic
291C4×C4⋊C4C22×C1311yescharacteristic
292#376C22×C1311yescharacteristic
293#340C22×C1311yescharacteristic
294#340C22×C1311yescharacteristic
295#340C22×C1311yescharacteristic
296#340C22×C1311yescharacteristic
297#340C22×C1311yescharacteristic
298#340C22×C1311yescharacteristic
299#340C22×C1311yescharacteristic
300#340C22×C1311yescharacteristic
301#336C22×C1311yescharacteristic
302#336C22×C1311yescharacteristic
303#336C22×C1311yescharacteristic
304#336C22×C1311yescharacteristic
305#336C22×C1311yescharacteristic
306#336C22×C1311yescharacteristic
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13#52511yescharacteristic
315C22×C13#52511yescharacteristic
316C22×C13#53611yescharacteristic
317C22×C13#57611yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C22×C13#57811yescharacteristic
321C4×C13—41no—
322C4×C13—42no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—42no—
326C4×C13—41no—
327C4×C13—42no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13#55211yescharacteristic
335C4×C13#55211yescharacteristic
336C4×C13#55611yescharacteristic
337C4×C13#55611yescharacteristic
338C22×D4C23×C1311yescharacteristic
339C23×C4—21no—
340C22×C8C23×C1311yescharacteristic
341C22×C8C23×C1311yescharacteristic
342C22×C8C23×C1311yescharacteristic
343C22×C8C23×C1311yescharacteristic
344#125—22no—
345#125—22no—
346C4×D4—22no—
347C4×D4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C23×C1311yescharacteristic
357C2×C4⋊C4C23×C1311yescharacteristic
358C2×C4⋊C4C23×C1311yescharacteristic
359C2×C4⋊C4C23×C1311yescharacteristic
360C2×C4⋊C4C23×C1311yescharacteristic
361C2×C4⋊C4C23×C1311yescharacteristic
362C2×C4⋊C4C23×C1311yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42C23×C1311yescharacteristic
372C2×C42C23×C1311yescharacteristic
373C2×C42C23×C1311yescharacteristic
374#107—22no—
375#107—22no—
376#107—22no—
377#106—22no—
378#102—22no—
379#102—22no—
380#102—22no—
381#102—22no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95D4×C1311yescharacteristic
390#95D4×C1311yescharacteristic
391#95D4×C1311yescharacteristic
392#95D4×C1311yescharacteristic
393C2×C13—82no—
394C2×C13#259911yescharacteristic
395C2×C13#311911yescharacteristic
396C2×C13#312011yescharacteristic
397C2×C13#312211yescharacteristic
398C2×C13#312411yescharacteristic
399C2×C13#324111yescharacteristic
400C2×C13#324311yescharacteristic
401C24—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4C13×#4112yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—81no—
417C22×C4—81no—
418C22×C4C2×D4×C1311yescharacteristic
419C22×C4C2×D4×C1311yescharacteristic
420C22×C4C2×D4×C1311yescharacteristic
421C22×C4C2×D4×C1311yescharacteristic
422C22×C4C2×D4×C1311yescharacteristic
423C22×C4C2×D4×C1311yescharacteristic
424C22×C4C24×C1311yescharacteristic
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—81no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4C13×#4112yes—
457C4⋊C4C13×#4112yes—
458C4⋊C4C13×#4112yes—
459C22⋊C4—24no—
460C22⋊C4—81no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—81no—
471C42—81no—
472C42—81no—
473C13#2940411yescharacteristic, direct product factor, Sylow
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×D4×C1311yescharacteristic
482D4—22no—
483D4—22no—
484D4—41no—
485D4—41no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4C2×C13×#4111yescharacteristic
527C2×C4C2×C13×#4111yescharacteristic
528C2×C4C2×C13×#4111yescharacteristic
529C2×C4C2×C13×#4111yescharacteristic
530C2×C4C13×2−1+411yescharacteristic
531C2×C4C13×2−1+411yescharacteristic
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C13×#52511yescharacteristic
544C22C13×#52511yescharacteristic
545C22C13×#53611yescharacteristic
546C22C13×#57611yescharacteristic
547C22C13×#57611yescharacteristic
548C22C13×#57711yescharacteristic
549C22C13×#57811yescharacteristic
550C4—41no—
551C4—42no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C13×#55211yescharacteristic
564C4C13×#55211yescharacteristic
565C4C13×#55611yescharacteristic
566C4C13×#55611yescharacteristic
567C2—82no—
568C2C13×#259911yescharacteristic
569C2C13×#311911yescharacteristic
570C2C13×#312011yescharacteristic
571C2C13×#312211yescharacteristic
572C2C13×#312411yescharacteristic
573C2C13×#324111yescharacteristic
574C2C13×#324311yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C13×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2330C2semidirect
3. C13×#2083C2semidirect
5. C13×#2059C2semidirect
9. C13×#1921C2semidirect
10. C13×#1921C2semidirect
11. C13×#1920C2semidirect
12. C13×#1918C2semidirect
15. C13×#1840C2semidirect
114. #29404C13direct (N × H)
187. #2330C2×C13semidirect
189. #2083C2×C13semidirect
191. #2059C2×C13semidirect
195. #1921C2×C13semidirect
196. #1921C2×C13semidirect
197. #1920C2×C13semidirect
198. #1918C2×C13semidirect
201. #1840C2×C13semidirect
473. C13#29404direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23302
C13×#23192
C13×#20832
C13×#20712
C13×#20592
C13×#20252
C13×#19262
C13×#19252
C13×#19212
C13×#19202
C13×#19182
C13×#18622
C13×#18402
#2940413