Finite Group Databasebeta

← C13×#15174 #15701513

Subgroups — C13×#15174 #15701513

Order 3328.

1418 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#398C211yesmaximal, characteristic, complemented
2C2×C13×#397C211yesmaximal, characteristic
3C2×C13×#388C211yesmaximal, characteristic
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5C13×#1443C212yesmaximal, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1439C211yesmaximal, characteristic
8C13×#1439C212yesmaximal
9C13×#1437C212yesmaximal
10C13×#1436C212yesmaximal, complemented
11C13×#1434C211yesmaximal, characteristic, complemented
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2212yes—
21C22×C42×C13C2211yescharacteristic
22C22×C42×C13C2212yes—
23C13×#398—24no—
24C13×#397—24no—
25C13×#388—24no—
26C4×C13×C4⋊C4—24no—
27C2×C13×#95C2212yes—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2212yes—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C25×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—42no—
60C2×C13×C4⋊C4D414yes—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—42no—
74C2×C13×C22⋊C4—42no—
75C2×C42×C13—24no—
76C2×C42×C13—24no—
77C2×C42×C13—42no—
78C2×C42×C13—42no—
79C2×C42×C13D414yes—
80C13×#95—24no—
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—24no—
84C13×#95—22no—
85C13×#95—22no—
86C13×#95—24no—
87C13×#95—24no—
88C13×#95—24no—
89C13×#95—24no—
90C13×#95—24no—
91C13×#95—42no—
92#15174C1311yesmaximal, characteristic, direct product factor, Sylow
93C24×C13—21no—
94C24×C13—21no—
95C24×C13—21no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—21no—
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13#4112yes—
104C24×C13C2411yescharacteristic
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D414yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13#4114yes—
161C22×C4×C13#4114yes—
162C22×C4×C13#4112yes—
163C22×C4×C13#4112yes—
164C22×C4×C13#4114yes—
165C13×C4⋊C4—28no—
166C13×C4⋊C4—28no—
167C13×C4⋊C4—48no—
168C13×C4⋊C4—44no—
169C13×C22⋊C4—28no—
170C13×C22⋊C4—48no—
171C13×C22⋊C4—48no—
172C13×C22⋊C4—44no—
173C13×C22⋊C4—44no—
174C42×C13—28no—
175C42×C13—48no—
176C2×#398C2×C1311yescharacteristic, complemented
177C2×#397C2×C1311yescharacteristic
178C2×#388C2×C1311yescharacteristic
179C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
180#1443C2×C1312yescomplemented
181#1441C2×C1311yescharacteristic, complemented
182#1439C2×C1311yescharacteristic
183#1439C2×C1312yes—
184#1437C2×C1312yes—
185#1436C2×C1312yescomplemented
186#1434C2×C1311yescharacteristic, complemented
187C23×C13—22no—
188C23×C13—24no—
189C23×C13—22no—
190C23×C13—24no—
191C23×C13—22no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—41no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—41no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13C22×D411yescharacteristic
211C23×C13C22×D411yescharacteristic
212C23×C13C2×#4111yescharacteristic
213C23×C13C2×#4112yes—
214C23×C13C2×#4111yescharacteristic
215C23×C13C2×#4111yescharacteristic
216C23×C13C2×#4112yes—
217C23×C13C2×#4112yes—
218C23×C13H(5,𝔽2)11yescharacteristic
219C23×C13H(5,𝔽2)11yescharacteristic
220C23×C132−1+412yes—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—22no—
244C2×C4×C13—41no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—41no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—41no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—41no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—41no—
270C2×C4×C13—42no—
271C2×C4×C13—41no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13#12114yes—
280C2×C4×C13#12314yes—
281C22×C4⋊C4C22×C1311yescharacteristic
282C22×C4⋊C4C22×C1311yescharacteristic
283C22×C4⋊C4C22×C1312yes—
284C22×C4⋊C4C22×C1311yescharacteristic
285C22×C22⋊C4C22×C1311yescharacteristic
286C22×C22⋊C4C22×C1311yescharacteristic
287C22×C22⋊C4C22×C1311yescharacteristic
288C22×C22⋊C4C22×C1312yes—
289C22×C22⋊C4C22×C1312yes—
290C22×C42C22×C1311yescharacteristic
291C22×C42C22×C1312yes—
292#398—24no—
293#397—24no—
294#388—24no—
295C4×C4⋊C4—24no—
296C2×#95C22×C1311yescharacteristic
297C2×#95C22×C1312yes—
298C2×#95C22×C1311yescharacteristic
299C2×#95C22×C1312yes—
300C2×#95C22×C1312yes—
301C2×#95C22×C1312yes—
302C2×#95C22×C1311yescharacteristic
303C2×#95C22×C1312yes—
304C2×#95C22×C1312yes—
305C2×#95C22×C1312yes—
306C2×#95C22×C1311yescharacteristic
307C2×#95C22×C1312yes—
308C22×C13—44no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—44no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13C2×#12111yescharacteristic
320C22×C13C2×#12311yescharacteristic
321C22×C13#52511yescharacteristic
322C22×C13#52511yescharacteristic
323C22×C13#52912yes—
324C22×C13#52912yes—
325C22×C13#52912yes—
326C22×C13#53212yes—
327C22×C13#53211yescharacteristic
328C22×C13#53511yescharacteristic
329C22×C13#53611yescharacteristic
330C22×C13#53912yes—
331C22×C13#53912yes—
332C22×C13#54611yescharacteristic
333C22×C13#54611yescharacteristic
334C22×C13#54812yes—
335C22×C13#55112yes—
336C22×C13#55212yes—
337C22×C13#55311yescharacteristic
338C22×C13#55311yescharacteristic
339C22×C13#55312yes—
340C22×C13#55612yes—
341C22×C13#55612yes—
342C4×C13—24no—
343C4×C13—24no—
344C4×C13—44no—
345C4×C13—44no—
346C4×C13—42no—
347C4×C13—44no—
348C4×C13—42no—
349C4×C13—81no—
350C4×C13—81no—
351C4×C13—82no—
352C25C23×C1311yescharacteristic
353C23×C4C23×C1311yescharacteristic
354C23×C4C23×C1311yescharacteristic
355C23×C4C23×C1312yes—
356C23×C4C23×C1312yes—
357C23×C4C23×C1311yescharacteristic
358C23×C4C23×C1311yescharacteristic
359C23×C4C23×C1312yes—
360C23×C4C23×C1312yes—
361C23×C4C23×C1311yescharacteristic
362C23×C4C23×C1311yescharacteristic
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4D4×C1314yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42D4×C1314yes—
393#95—24no—
394#95—22no—
395#95—22no—
396#95—24no—
397#95—22no—
398#95—22no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—42no—
405C2×C13—82no—
406C2×C13#239511yescharacteristic
407C2×C13#253511yescharacteristic
408C2×C13#254511yescharacteristic
409C2×C13#255812yes—
410C2×C13#256012yes—
411C2×C13#257712yes—
412C2×C13#259412yes—
413C2×C13#259911yescharacteristic
414C2×C13#260311yescharacteristic
415C2×C13#262311yescharacteristic
416C2×C13#285411yescharacteristic
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24C13×#4112yes—
428C24C24×C1311yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4C2×D4×C1312yes—
480C22×C4C2×D4×C1314yes—
481C22×C4C2×D4×C1312yes—
482C22×C4C2×D4×C1312yes—
483C22×C4C2×D4×C1312yes—
484C22×C4C13×#4114yes—
485C22×C4C13×#4114yes—
486C22×C4C13×#4112yes—
487C22×C4C13×#4112yes—
488C22×C4C13×#4114yes—
489C4⋊C4—28no—
490C4⋊C4—28no—
491C4⋊C4—48no—
492C4⋊C4—44no—
493C22⋊C4—28no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C22⋊C4—44no—
497C22⋊C4—44no—
498C42—28no—
499C42—48no—
500C13#1517411yescharacteristic, direct product factor, Sylow
501C23—22no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—42no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C22×D4×C1311yescharacteristic
525C23C22×D4×C1311yescharacteristic
526C23C2×C13×#4111yescharacteristic
527C23C2×C13×#4112yes—
528C23C2×C13×#4111yescharacteristic
529C23C2×C13×#4111yescharacteristic
530C23C2×C13×#4112yes—
531C23C2×C13×#4112yes—
532C23C13×H(5,𝔽2)11yescharacteristic
533C23C13×H(5,𝔽2)11yescharacteristic
534C23C13×2−1+412yes—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4C13×#12114yes—
594C2×C4C13×#12314yes—
595C22—42no—
596C22—44no—
597C22—44no—
598C22—42no—
599C22—42no—
600C22—81no—
601C22—82no—
602C22—82no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C2×C13×#12111yescharacteristic
607C22C2×C13×#12311yescharacteristic
608C22C13×#52511yescharacteristic
609C22C13×#52511yescharacteristic
610C22C13×#52912yes—
611C22C13×#52912yes—
612C22C13×#52912yes—
613C22C13×#53211yescharacteristic
614C22C13×#53212yes—
615C22C13×#53511yescharacteristic
616C22C13×#53611yescharacteristic
617C22C13×#53912yes—
618C22C13×#53912yes—
619C22C13×#54611yescharacteristic
620C22C13×#54611yescharacteristic
621C22C13×#54812yes—
622C22C13×#55112yes—
623C22C13×#55212yes—
624C22C13×#55311yescharacteristic
625C22C13×#55311yescharacteristic
626C22C13×#55312yes—
627C22C13×#55612yes—
628C22C13×#55612yes—
629C4—24no—
630C4—24no—
631C4—44no—
632C4—42no—
633C4—44no—
634C4—44no—
635C4—42no—
636C4—81no—
637C4—82no—
638C4—81no—
639C2—82no—
640C2C13×#239511yescharacteristic
641C2C13×#253511yescharacteristic
642C2C13×#254511yescharacteristic
643C2C13×#255812yes—
644C2C13×#256012yes—
645C2C13×#257712yes—
646C2C13×#259412yes—
647C2C13×#259911yescharacteristic
648C2C13×#260311yescharacteristic
649C2C13×#262311yescharacteristic
650C2C13×#285411yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#398C2semidirect
4. C2×C4×C13×C4⋊C4C2semidirect
5. C13×#1443C2semidirect
6. C13×#1441C2semidirect
10. C13×#1436C2semidirect
11. C13×#1434C2semidirect
92. #15174C13direct (N × H)
176. C2×#398C2×C13semidirect
179. C2×C4×C4⋊C4C2×C13semidirect
180. #1443C2×C13semidirect
181. #1441C2×C13semidirect
185. #1436C2×C13semidirect
186. #1434C2×C13semidirect
500. C13#15174direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3982
C2×C13×#3972
C2×C13×#3882
C2×C4×C13×C4⋊C42
C13×#14432
C13×#14412
C13×#14392
C13×#14372
C13×#14362
C13×#14342
#1517413