Finite Group Databasebeta

← C13×#10992 #15697331

Subgroups — C13×#10992 #15697331

Order 3328.

1658 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic
2C22×C13×#99C211yesmaximal, characteristic
3C13×#2308C211yesmaximal, characteristic
4C2×C13×#381C212yesmaximal, complemented
5C2×C13×#342C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C24×C4×C13C2211yescharacteristic
8C2×C13×#123—22no—
9C2×C13×#123—24no—
10C2×C13×#123—24no—
11C2×C13×#123C414yescomplemented
12C22×C13×C4⋊C4—21no—
13C22×C13×C22⋊C4—21no—
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2211yescharacteristic
17C2×C13×#99—22no—
18C2×C13×#99—24no—
19C13×#386—24no—
20C13×#381—24no—
21C13×#381—21no—
22C13×#381—24no—
23C13×#379—21no—
24C2×C13×#95—24no—
25C13×#342—24no—
26C25×C13D411yescharacteristic
27C25×C13C2311yescharacteristic
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13—22no—
31C22×D4×C13—22no—
32C22×D4×C13—22no—
33C22×D4×C13—22no—
34C22×D4×C13C2×C412yes—
35C22×D4×C13D412yes—
36C23×C4×C13—22no—
37C23×C4×C13—21no—
38C23×C4×C13—21no—
39C23×C4×C13—21no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13C2×C412yes—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D414yes—
48C23×C4×C13D414yes—
49C13×#123—216no—
50C13×#123—28no—
51C13×#123—28no—
52C2×C13×C4⋊C4—28no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C22⋊C4—28no—
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—24no—
70C2×C13×C22⋊C4C2×C412yes—
71C2×C13×C22⋊C4D414yes—
72C2×C13×C22⋊C4D414yes—
73C13×#99—28no—
74C13×#95—216no—
75C13×#95—24no—
76#10992C1311yesmaximal, characteristic, direct product factor, Sylow
77C24×C13—22no—
78C24×C13—21no—
79C24×C13—22no—
80C24×C13—21no—
81C24×C13—44no—
82C24×C13—44no—
83C24×C13C22⋊C412yes—
84C24×C13C22×C411yescharacteristic
85C24×C13C2×D411yescharacteristic
86C24×C13C2×D412yes—
87C24×C13C2×D411yescharacteristic
88C24×C13C2×D412yes—
89C24×C13C2×D412yes—
90C24×C13C2×D412yes—
91C24×C13#4112yes—
92C24×C13#4112yes—
93C2×D4×C13—22no—
94C2×D4×C13—22no—
95C2×D4×C13—24no—
96C2×D4×C13—24no—
97C2×D4×C13—22no—
98C2×D4×C13—24no—
99C2×D4×C13—24no—
100C2×D4×C13—22no—
101C2×D4×C13—42no—
102C2×D4×C13—42no—
103C2×D4×C13—42no—
104C2×D4×C13—42no—
105C2×D4×C13—42no—
106C2×D4×C13—42no—
107C2×D4×C13—42no—
108C2×D4×C13—42no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—24no—
113C22×C4×C13—24no—
114C22×C4×C13—24no—
115C22×C4×C13—24no—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13—24no—
119C22×C4×C13—21no—
120C22×C4×C13—24no—
121C22×C4×C13—24no—
122C22×C4×C13—22no—
123C22×C4×C13—24no—
124C22×C4×C13—21no—
125C22×C4×C13—24no—
126C22×C4×C13—24no—
127C22×C4×C13—24no—
128C22×C4×C13—24no—
129C22×C4×C13—44no—
130C22×C4×C13—41no—
131C22×C4×C13—41no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—41no—
137C22×C4×C13—41no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13—48no—
141C22×C4×C13—48no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13C22⋊C412yes—
145C22×C4×C13C22⋊C414yescomplemented
146C13×C4⋊C4—216no—
147C13×C22⋊C4—216no—
148C13×C22⋊C4—22no—
149C13×C22⋊C4—24no—
150C13×C22⋊C4—24no—
151C13×C22⋊C4—24no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—42no—
154C13×C22⋊C4—42no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4—42no—
157C13×C22⋊C4—42no—
158C13×C22⋊C4—84no—
159C13×C22⋊C4C22⋊C414yescomplemented
160C22×#123C2×C1311yescharacteristic
161C22×#99C2×C1311yescharacteristic
162#2308C2×C1311yescharacteristic
163C2×#381C2×C1312yescomplemented
164C2×#342C2×C1312yescomplemented
165C23×C13—28no—
166C23×C13—24no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—44no—
173C23×C13—44no—
174C23×C13—44no—
175C23×C13—44no—
176C23×C13—44no—
177C23×C13—44no—
178C23×C13—48no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—44no—
182C23×C13—82no—
183C23×C13—84no—
184C23×C13C2×C22⋊C411yescharacteristic
185C23×C13C2×C22⋊C411yescharacteristic
186C23×C13C2×C22⋊C411yescharacteristic
187C23×C13C4×D412yes—
188C23×C13C4×D412yes—
189C23×C13#12012yes—
190C23×C13#12012yes—
191C23×C13#12012yes—
192C23×C13#12011yescharacteristic
193C23×C13#12011yescharacteristic
194C23×C13#12112yes—
195C23×C13#12112yes—
196C23×C13#12112yes—
197C23×C13#12112yes—
198C23×C13#12112yes—
199C23×C13#12112yes—
200C23×C13#12311yescharacteristic
201C23×C13#12312yes—
202C23×C13#12311yescharacteristic
203C23×C13#12412yes—
204C23×C13#12712yes—
205D4×C13—44no—
206D4×C13—44no—
207D4×C13—44no—
208D4×C13—44no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—22no—
212C2×C4×C13—28no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—44no—
216C2×C4×C13—48no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—44no—
220C2×C4×C13—44no—
221C2×C4×C13—44no—
222C2×C4×C13—42no—
223C2×C4×C13—44no—
224C2×C4×C13—44no—
225C2×C4×C13—42no—
226C2×C4×C13—48no—
227C2×C4×C13—48no—
228C2×C4×C13—44no—
229C2×C4×C13—44no—
230C2×C4×C13—48no—
231C2×C4×C13—84no—
232C2×C4×C13—84no—
233C2×C4×C13—84no—
234C23×D4C22×C1311yescharacteristic
235C24×C4C22×C1311yescharacteristic
236C2×#123—22no—
237C2×#123—24no—
238C2×#123—24no—
239C2×#123C4×C1314yescomplemented
240C22×C4⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C22⋊C4C22×C1312yes—
243C22×C22⋊C4C22×C1312yes—
244C22×C22⋊C4C22×C1311yescharacteristic
245C2×#99—22no—
246C2×#99—24no—
247#386—24no—
248#381—21no—
249#381—24no—
250#381—24no—
251#379—21no—
252C2×#95—24no—
253#342—24no—
254C22×C13—22no—
255C22×C13—24no—
256C22×C13—22no—
257C22×C13—24no—
258C22×C13—24no—
259C22×C13—24no—
260C22×C13—24no—
261C22×C13—24no—
262C22×C13—24no—
263C22×C13—24no—
264C22×C13—41no—
265C22×C13—41no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—41no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—42no—
273C22×C13—42no—
274C22×C13—44no—
275C22×C13—44no—
276C22×C13—42no—
277C22×C13—82no—
278C22×C13—84no—
279C22×C13—84no—
280C22×C13#37911yescharacteristic
281C22×C13#38612yes—
282C22×C13#38611yescharacteristic
283C22×C13#38611yescharacteristic
284C22×C13#39012yes—
285C22×C13#39212yes—
286C22×C13#39212yes—
287C22×C13#39412yes—
288C22×C13#39412yes—
289C22×C13#45814yes—
290C4×C13—44no—
291C4×C13—44no—
292C4×C13—42no—
293C4×C13—84no—
294C4×C13—84no—
295C25D4×C1311yescharacteristic
296C25C23×C1311yescharacteristic
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4C2×C4×C1312yes—
304C22×D4D4×C1312yes—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4C2×C4×C1312yes—
315C23×C4D4×C1311yescharacteristic
316C23×C4D4×C1314yes—
317C23×C4D4×C1314yes—
318#123—216no—
319#123—28no—
320#123—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4C2×C4×C1312yes—
340C2×C22⋊C4D4×C1314yes—
341C2×C22⋊C4D4×C1314yes—
342#99—28no—
343#95—216no—
344#95—24no—
345C2×C13—21no—
346C2×C13—22no—
347C2×C13—21no—
348C2×C13—22no—
349C2×C13—22no—
350C2×C13—22no—
351C2×C13—22no—
352C2×C13—82no—
353C2×C13#143811yescharacteristic
354C2×C13#189012yes—
355C2×C13#202214yes—
356C24—22no—
357C24—21no—
358C24—22no—
359C24—21no—
360C24—44no—
361C24—44no—
362C24C13×C22⋊C412yes—
363C24C22×C4×C1311yescharacteristic
364C24C2×D4×C1311yescharacteristic
365C24C2×D4×C1312yes—
366C24C2×D4×C1311yescharacteristic
367C24C2×D4×C1312yes—
368C24C2×D4×C1312yes—
369C24C2×D4×C1312yes—
370C24C13×#4112yes—
371C24C13×#4112yes—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—24no—
378C2×D4—24no—
379C2×D4—22no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—44no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4C13×C22⋊C412yes—
424C22×C4C13×C22⋊C414yescomplemented
425C4⋊C4—216no—
426C22⋊C4—216no—
427C22⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—42no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—84no—
438C22⋊C4C13×C22⋊C414yescomplemented
439C13#1099211yescharacteristic, direct product factor, Sylow
440C23—28no—
441C23—24no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—42no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23—48no—
454C23—42no—
455C23—42no—
456C23—44no—
457C23—82no—
458C23—84no—
459C23C2×C13×C22⋊C411yescharacteristic
460C23C2×C13×C22⋊C411yescharacteristic
461C23C2×C13×C22⋊C411yescharacteristic
462C23C4×D4×C1312yes—
463C23C4×D4×C1312yes—
464C23C13×#12012yes—
465C23C13×#12012yes—
466C23C13×#12012yes—
467C23C13×#12011yescharacteristic
468C23C13×#12011yescharacteristic
469C23C13×#12112yes—
470C23C13×#12112yes—
471C23C13×#12112yes—
472C23C13×#12112yes—
473C23C13×#12112yes—
474C23C13×#12112yes—
475C23C13×#12311yescharacteristic
476C23C13×#12312yes—
477C23C13×#12311yescharacteristic
478C23C13×#12412yes—
479C23C13×#12712yes—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—44no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—28no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—48no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—48no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—48no—
506C2×C4—84no—
507C2×C4—84no—
508C2×C4—84no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—24no—
514C22—24no—
515C22—22no—
516C22—24no—
517C22—22no—
518C22—24no—
519C22—41no—
520C22—41no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—44no—
531C22—42no—
532C22—82no—
533C22—84no—
534C22—84no—
535C22C13×#37911yescharacteristic
536C22C13×#38612yes—
537C22C13×#38611yescharacteristic
538C22C13×#38611yescharacteristic
539C22C13×#39012yes—
540C22C13×#39212yes—
541C22C13×#39212yes—
542C22C13×#39412yes—
543C22C13×#39412yes—
544C22C13×#45814yes—
545C4—44no—
546C4—44no—
547C4—42no—
548C4—84no—
549C4—84no—
550C2—21no—
551C2—22no—
552C2—21no—
553C2—22no—
554C2—22no—
555C2—22no—
556C2—22no—
557C2—82no—
558C2C13×#143811yescharacteristic
559C2C13×#189012yes—
560C2C13×#202214yes—
subgroupG/H
center, socleC23×C13#120
commutatorC24C22×C4×C13
Frattini, cosocleC25C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ 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×#381C2semidirect
5. C2×C13×#342C2semidirect
11. C2×C13×#123C4semidirect
76. #10992C13direct (N × H)
145. C22×C4×C13C22⋊C4semidirect
159. C13×C22⋊C4C22⋊C4semidirect
163. C2×#381C2×C13semidirect
164. C2×#342C2×C13semidirect
239. C2×#123C4×C13semidirect
424. C22×C4C13×C22⋊C4semidirect
438. C22⋊C4C13×C22⋊C4semidirect
439. C13#10992direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C22×C13×#992
C13×#23082
C2×C13×#3812
C2×C13×#3422
#1099213